The Cultural Context of Medieval Learning

S Y N T H E S E L I B R A R Y

MONOGRAPHS ON EPISTEMOLOGY,

LOGIC, METHODOLOGY, PH ILOSOPHY OF SCIENCE,

SOCIOLOGY OF SCIENCE A ND OF KNOWLEDGE,

AND ON THE MATHEMATICAL METHODS OF

SOCIAL A ND BEHAVIORAL SCIENCES

Managing Editor:

J a a k k o H i n t i k k a , Academy o f Finland and Stanford University

Editors:

R o b e r t S. C o h e n , Boston University

D o n a l d D a v i d s o n , Rockefeller University and Princeton University

G a b r i ë l N u c h e l m a n s , University o f Leydèn

W e s l e y C. S a l m o n , University o f Arizona

V O L U M E 76

B O S T O N S T U D IE S IN T H E P H IL O S O P H Y O F S C IE N C E

EDITED BY ROBERT S. COHEN A N D MARX W. WAR TOFSKY

V O L U M E X X V I

THE CULTURAL CONTEXT OF MEDIEVAL LEARNING

P R O C E E D IN G S O F T H E F IR S T IN T E R N A T IO N A L C O L L O Q U IU M

O N P H IL O S O P H Y , S C IE N C E , A N D T H E O L O G Y IN

T H E M ID D L E A G E S - S E P T E M B E R 1973

Edited with an Introduction by

J O H N E M E R Y M U R D O C H and E D IT H D U D L E Y S Y L L A

D. R E ID E L P U B L IS H IN G C O M P A N Y

D O R D R EC H T -H O L LA N D / BOSTON-U.S.A.

International Colloquium of Philosophy, Science, andTheology in the Middle Ages, 1st, North Andover, Mass. 1973.The cultural context of medieval learning.

(Boston studies in the philosophy of science ; v. 26) (Synthese Library)

Includes bibliographical references and index.1. Philosophy, Medieval—Congresses. 2. Science,

Medieval—Congresses. I. Murdoch, John Emery, 1927- ed. II. Sylla, Edith Dudley, ed. HI. Title. IV. Series. Q174.B67 vol. 26 [B721] 501s [189] 75-2497ISBN 90-277-0560-7 ISBN 90-277-0587-9 pbk.

Library of Congress Cataloging in Publication Data

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All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht, Holland

No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher

Printed in The Netherlands by D. Reidel, Dordrecht

P R E F A C E

The comparative historical sociology o f science - for lack o f an adequate and more economical name - is as many-sided as it is many-syllabled. The present volume exhibits the confluence not only o f historical and sociological contexts o f science, but also o f the concrete philosophit^l, theological, political, and legal contents which investigation o f a particular comparative case study requires. The choice o f the particular period, its rationale, and the fruitfulness o f the results, is well described in the Introduction by the editors. Professors Murdoch and Sylla. A ll scholars will understand our admiration for the skill, intelligence, and care with which John Murdoch and Edith Sylla have brought the prepared materials and the reported discussions into this beautifully integrated and lucidly articulated book. It was John Murdoch who took on the demanding task o f organizing the intellectual spectrum o f interests and competences that resulted in as original and rich an exploration as the conference afforded and this book presents. This volume shows again how wide a perimeter o f conceptual issues the history and philosophy o f science can generate, when they are conceived in the fuller contexts o f their origin, development, and social milieu. Appreciating as we do the editors’ note o f caution about the treatment o f social, political, and economic factors in the analysis o f medieval thought and culture, it also becomes clear to us that a rigorous and careful investigation o f the relations between material culture and both conceptual activities and institutional forces is desired in order to enlarge and deepen these studies. Need we add that we hope to see other periods treated with equal care and penetration? We also expect that philosophers o f modern science will find here insights into their own conceptual problems, as well as some historical roots of these problems.

Center fo r the Philosophy and History o f Science, Boston University August 1974.

ROBERT s. COHEN

MARX W. WAR TOFSKY

T A B L E O F C O N T E N T S

PREFACE V

C O L L O Q U IU M P A R T I C I P A N T S IX

AU D IT O R S X

JOHN E. MU RD O CH a n d EDITH D U D L E Y S Y L L A / In tro d u c t io n 1

P A R T I. IS L A M

r o s h d i r a s h e d / Recommencements de l’algèbre aux X le et X llesiècles 33Discussion 57

NAB IL SHEHABY / The Influence o f Stoic Logic on Al-Jassas’sLegal Theory 61Discussion 80

JOSEF V A N ESS / The Beginnings o f Islamic Theology 87Discussion 104

MUHSIN MAHDi / Science, Philosophy, and Religion in Alfarabi’sEnumeration o f the Sciences 113Comments 146

P A R T II. T H E T W E L F T H A N D T H IR T E E N T H C E N T U R IE S

IN T H E L A T IN W E ST

RICHARD MCKEON / The Organization o f Sciences and the

Relations o f Cultures in the Twelfth and Thirteenth Centuries 151 Discussion 184

T U L L i o GREGORY / La nouvelle idée de nature et de savoir scientifique au X lle siècle 193 Discussion 212

VIII TABLE OF CONTENTS

BRIAN STOCK / Experience, Praxis, Work, and Planning in Bernard o f Clairvaux: Observations on the Sermones in Cantica 219Discussion 262

P A R T III. T H E F O U R T E E N T H , F IF T E E N T H , A N D S IX T E E N T H

C E N T U R IE S IN T H E L A T IN W EST

JOHNE. M U R D O C H / From Social into Intellectual Factors: An Aspect o f the Unitary Character o f Late Medieval Learning Discussion

EDITH DU DLEY s y l l a / Autonomous and Handmaiden Science: St. Thomas Aquinas and William o f Ockham on the Physics o f the Eucharist Discussion

HEiKO A. OBERMAN / Reformation and Revolution: Copernicus’s Discovery in an Era o f Change Discussion

G U Y B E A U jo u A N / Réflexions sur les rapports entre théorie et pratique au moyen âge Discussion

CHARLES B. SCHMITT / Philosophy and Science in Sixteenth-Century Universities : Some Preliminary Comments Discussion

271339

349391

397429

437477

485531

INDEX 539

C O L L O Q U IU M P A R T IC IP A N T S

Marie-Thérèse d’Alverny, Centre National de la Recherche Scientifique, Paris, and Centre d’Études supérieures de Civihsation mediévale de Poitiers.

Guy Beaujouan, École Pratique des Hautes Études, Paris.Richard Frank, Department o f Semitic and Egyptian Languages and

Literature, The Catholic University o f America, Washington, D.C.Jean Gagné, Institut d’Études Médiévales, Université de Montréal.Tullio Gregory, Istituto di Filosofia délia Università di Roma.Muhsin Mahdi, Department o f Near Eastern Languages and Civilization,

Harvard University, Cambridge, Massachusetts.Richard McKeon, Department o f Philosophy, University o f Chicago.John E. Murdoch, Department o f History o f Science, Harvard Univer

sity, Cambridge, Massachusetts.Heiko A. Oberman, Institut für Spàtmittelalter und Reformation, Univer-

sitat Tübingen.Roshdi Rashed, Centre National de la Recherche Scientifique, Paris.Abdelhamid I. Sabra, Department o f History o f Science and Department

o f Near Eastern Languages and CiviHzation, Harvard University, Cambridge, Massachusetts.

Charles B. Schmitt, The Warburg Institute, University o f London.Nabil Shehaby, The Institute o f Islamic Studies, McGill University,

Montréal.Brian Stock, The Pontifical Institute o f Mediaeval Studies, Toronto, and

Centre for Medieval Studies, University o f Toronto.Edith Dudley Sylla, Department o f History, North Carolina State Uni

versity at Raleigh.Josef van Ess, Orientalisches Seminar der Universitat Tübingen.

A U D IT O R S

Caroline Bynum, The Divinity School, Harvard University, Cambridge, Massachusetts.

Joan Cadden, Department o f History o f Science, Harvard University, Cambridge, Massachusetts.

Jean Christensen, Department o f History o f Science, Harvard University, Cambridge, Massachusetts.

Myron Gilmore, Department o f History, Harvard University, Cambridge, Massachusetts.

William Graham, Department o f Near Eastern Languages and Civilization, Harvard University, Cambridge, Massachusetts.

Jocelyn Hillgarth, Department o f History, Boston College.Stephen Victor, Division o f Natural Sciences, Monteith College, Wayne

State University, Detroit, Michigan.

JOHN E. MUR DOCH A ND EDITH D U D L E Y SYLLA

IN T R O D U C T IO N

Conferences and colloquia are held and their results often published, but very rarely is any account provided o f why and how they came to be. Such an account would naturally not be as significant as the “ proceedings” or “ acts” themselves. In this instance, however, something beyond the simple recording o f the date and circumstances o f the birth o f a colloquium, some glimpse o f the deliberations that occurred in its period o f gestation, may help explain the purpose o f the event and the character or nature o f the eventual offspring.

The history o f the present Colloquium should begin with its conception, an outgrowth o f an earlier meeting at Cumberland Lodge in Windsor Park, England, in the summer o f 1971 devoted to the historical sociology o f science in the large. Partly as a result o f the problems found to be inherent in a meeting whose scope was so all-encompassing, it was then decided that a more modest gathering, not in terms o f the number o f participants, but in terms o f the historical period covered, would form an appropriate and more effective sequel. The period tentatively chosen was the Middle Ages. Would not the concentration afforded by an intellectual and social history limited to medieval science prove valuable in yielding a special case o f the kind o f historical inquiry in mind?

The question was thus put and arrangements to derive its answer were set in motion. Planning o f the meeting was assisted by the extraordinary generosity o f the Study Group on the Unity o f Knowledge, an organization funded by the Ford Foundation under a grant to the University o f California, Davis. In addition to consultations involving both American and European medievalists in Boston, London, and Paris, the Vth International Congress o f Medieval Philosophy held at Madrid, Cordoba, and Granada in September 1972 presented an especially opportune occasion for a planning discussion involving a good number o f interested scholars and prospective participants.

J. E. Murdoch and E. D. Sylla (eds.), The Cultural Context o f Medieval Learning, 1-30. All Rights Reserved.

Quite early in these discussions and consultations it was unanimously agreed that the forthcoming Colloquium should address itself to much more within medieval thought than the history o f science. The addition o f philosophy and theology was viewed as indispensable; the history o f medieval law was also considered as a valuable potential supplement, although efforts to secure its representation were eventually unsuccessful. With this broader segment o f medieval thought in view, the decision was made - to quote the initial terms in which the Colloquium goals were envisaged - to focus upon three areas: (a) the interdisciplinary relations o f philosophy, science, and theology in the Middle Ages and, where pertinent, the relations these disciplines had to other areas o f intellectual endeavor; (b) the institutional and social factors that may have affected the origin, growth, and maintenance o f philosophy, science, and theology as viable disciplines; and (c) cross-cultural factors that may be elicited as operative between Islam and the Latin West, and secondly, between each o f these and the Greek learning that was absorbed in the formation o f their philosophical, scientific, and theological doctrines and traditions.

The Colloquium itself flourished under the four-fold sponsorship o f the Department o f the History o f Science, the Center for Middle Eastern Studies, and the Committee on Medieval Studies, all o f Harvard University, and the Center for the History and Philosophy o f Science o f Boston University. Through the efforts o f the last-named sponsor, the meetings were held at Osgood Hill, the Boston University Conference Center located on a one hundred and fifty-three acre estate in North Andover, Massachusetts. There, the Victorian mansion that forms the nucleus o f the estate provided room and board for all participants and presented a comfortable parlour in which to hold our discussions in an informal and productive way.

II

2 J. MUR DOCH A N D E. SYLLA

The central purpose o f the Colloquium was intended, and turned out, to be discussion and mutual interchange. The invited papers, therefore, were circulated to all participants in advance, both to those who were contributing papers in their own right and to the invited “ commentators at large” : Marie-Thérèse d’Alverny, Richard Frank, Jean Gagné, and Abdelhamid Sabra. This allowed us to dispense with all but a brief introductory résumé

IN T RO DUC T IO N

by each author. Selected participants were designated as “ pre-assigned commentators” for each paper, but since the whole purpose o f these “ prepared” comments was that they serve as informal catalysts setting the discussion in motion and not that they provide central or definitive analyses and criticisms o f a given paper, the contributions o f these initial commentators have not been formally distinguished from other comments in the discussions published in the present volume. Muhsin Mahdi’s paper was circulated in advance together with the other papers, but events prevented him from attending the Colloquium itself. Inasmuch as it was decided not to discuss his paper in his absence it is accompanied in what follows simply by short written comments and his reply.

Four o f the five days o f the Colloquium were spent in discussing the invited contributions and the issues they raised, the participants being joined on these occasions by a few additional scholars from the Boston area who also had the opportunity to read the papers in advance and thus contribute to the discussion if they so wished. The Colloquium opened with a single day devoted to Islamic topics, was followed by a second day devoted to the twelfth and the thirteenth centuries in the Latin West, and concluded with two days treating the later Middle Ages.

The discussions were extensive and open, unencumbered by any fear o f being too critical, yet always relaxed and good-humored even when reaching the level o f rather heated debate. We regret that it was not possible to reproduce them in anything near their entirety, but selectivity was the necessary course. Although note should be made o f the fact that those parts o f the discussions that are included have had to be condensed considerably, the principle we adopted was that o f deleting certain “ debates” in toto so that those that we have preserved would not suffer from an underrepresentation o f their substance. This seemed far preferable to the alternative course o f having a little, but inadequate, bit o f every point and issue raised.

In reducing the whole to something roughly less than one-quarter o f its original size, we have tried to retain something o f the live “ give and take” o f the actual proceedings. We have also given some priority to the inclusion o f those segments o f the discussions that seemed to deal with points or themes o f more general interest, especially when such points addressed themselves to problems or ideas that appeared in the discussion o f more than one paper. Some preference was also given to those aspects o f the

J. MURDOCH A N D E. SYLLA

discussions that directed themselves toward the stated goals o f the Colloquium.

The extent to which these initial goals were realized can only be measured by comparing them with the papers and discussions contained in the present volume. Perhaps it will be useful here, however, to set forth briefly the content o f the papers not in themselves but as related to the overall goals the Colloquium was planned to serve. This will, o f course, yield an interpreted view o f the contributions, but one, we trust, that is not at odds with the thrust o f each paper considered apart from the Colloquium and its goals and discussions.

The first, interdisciplinary theme o f the Colloquium was particularly emphasized in relation to the later Middle Ages, but it was also apparent in the other sessions. Thus, at the very beginning o f the Islamic section, Roshdi Rashed’s paper on the development o f algebra in the eleventh and twelfth centuries addressed itself to the problem o f the interrelations o f arithmetic and algebra during this period. Similarly, in discussing the application o f Stoic logic within the field o f Islamic law, Nabil Shehaby considered how logical material might be treated differently within a legal work than within a purely logical context. Interdisciplinary relations also came out strongly in the discussion o f Josef Van Ess’s paper on the origins o f theology in Islam in the first century A.H. when a question was raised as to how one ought to define Islamic theology or kalâm: proposed definitions in terms o f subject matter, methodology, or attitude all seemed to have their difficulties. Touching upon the relations between disciplines in yet another way, Muhsin Mahdi’s paper on Alfarabi’s Enumeration o f the Sciences emphasized that the coexistence in Islam of political science with jurisprudence and theology made the strict division o f sciences into practical and theoretical practically untenable.

In the twelfth and thirteenth century section, Tullio Gregory’s paper on the new idea o f nature and scientific knowledge in the twelfth century demonstrated that this new conception o f nature cut across disciplinary lines, influencing theological as well as scientific and philosophical work. Although Richard McKeon’s paper did not specifically treat interdisciplinary factors, their presence was continually felt in his description and analysis o f the organization o f the sciences in Greek, Hebrew, Latin, and Islamic culture.

In the session on the late Middle Ages, John Murdoch’s paper on the

IN T RO DUC T IO N

unity o f late medieval learning confronted most directly the general question o f the medieval relations o f philosophy, science, and theology, maintaining that philosophy and the greater part o f science formed a single discipline within the later medieval period and that there was also a weaker unity between philosophy-science and theology. Edith Sylla’s paper on autonomous and handmaiden science compared the relations o f science and theology in the thirteenth century as represented by St. Thomas Aquinas and in the fourteenth century as represented by William of Ockham through an examination o f the two authors’ respective treatments o f the physics o f the Eucharist. She concluded that whereas Aquinas modified his physics in the service o f theology, Ockham maintained the autonomy o f physics even when this meant that physics was less able to meet the needs o f religious explanation.

Heiko Oberman’s paper setting Copernicus within the larger context o f the era o f reformation and revolution proposed a new view o f the first encounter between the Protestant Reformation and Copernicanism, and indicated a common background to these two sixteenth century reform movements in nominalism and in the medieval campaign contra vanam curiositatem. He showed how the same basic rejection o f metaphysics could have very different effects within theology and within science, in theology leading to a reliance on revelation and faith, while in science leading to an emphasis on experience.

Guy Beaujouan’s paper on the relations o f theory and practice in the Middle Ages was directly and indissolubly related to both the interdisciplinary and the institutional and social themes o f the Colloquium. Addressing himself to the problem o f uncovering evidence o f the medieval relations between theoretical knowledge and techniques used in everyday life, Beaujouan argued that to examine the relation o f science and savoir faire from a medieval point o f view it is necessary not only to think o f Renaissance architects and engineers, but also to examine such areas as music, number symbolism, alchemy, maps, the illustration o f scientific manuscripts, and astronomical instruments. Discussing particular examples taken from the areas o f architecture and building vis-à-xis practical geometry, and navigation vis-à-vis astronomical instruments, Beaujouan brought into sharper focus the many problems faced by the historian who has aspirations o f studying the medieval relations o f theory and practice. On the side o f practice there were, one must assume, in

J. MUR DOCH A N D E. SYLLA

numerable oral traditions and trade secrets, not to mention artifacts, o f which there remain no trace, and on the side o f theory the works that do remain seem to be at variance with the presumed practice. Yet he showed how with ingenuity one can elude at least some o f these problems and find evidence where hitherto none seemed to exist. Beaujouan was joined by Gregory, McKeon, and others in the discussions in emphasizing that the utilization o f accepted twentieth century notions o f science to identify the proper theoretical sciences o f the Middle Ages can only distort the understanding o f the historical situation. Rashed insisted, however, that the more exact sciences develop differently from more diffuse intellectual enterprises.

The difficulties facing the medieval historian came into view also when the problem o f the role o f institutional and social factors was discussed and suggestions were put forth as to how one might ameliorate these difficulties, even strike new ground, through the consideration o f problems and sources that have heretofore remained untreated. Rashed argued, for example, that, although the present status o f the history o f Arabic mathematics necessarily makes any evaluation o f the impact o f social factors upon its evolution at best conjectural, it would appear that eleventh and twelfth century Islamic algebra as a mature scientific discipline developed in a totally internal fashion, social factors impinging upon it only through the intermediary o f other disciplines, notably observational astronomy and arithmetic, the last named discipline itself unified - and here social influence would enter if the conjecture is correct - due to the computational needs o f the rising class o f commercial scribes. Again on the social factors theme. Van Ess’s paper drew attention to the possible impact o f the religious exigencies o f Islamic society upon the origins o f kalam and upon the role its practitioners had to play within this society. Yet another aspect o f the importance o f religious factors was indicated by Mahdi when he drew attention to Alfarabi’s simple juxtaposition o f political science with the traditional sciences o f jurisprudence and theology. In not troubling to explain just how these disciplines are connected, Alfarabi was most likely merely reflecting the situation in which a member o f the religious community found himself. The juxtaposition o f these sciences is, then, an historical accident mirroring social fact, and not at all a theoretical necessity, since philosophy and political science can and do exist in cultures that lack a revealed religion, jurisprudence, or theology and vice versa.

IN T R O DUC T IO N

In the twelfth and thirteenth century section, an extensive and straightforward claim for the importance o f social factors was made by Brian Stock. His contribution analyzing the Sermones in cantica o f Bernard o f Clairvaux stressed the pivotal position played by Bernard’s attitudes toward work and action as furnishing evidence o f a bridge between economic and social changes on the one hand and intellectual and cultural changes on the other; in particular - revitalizing in a way, and applying to medieval society, the insight o f Max Weber’s “ work ethic” - he sketched a possible connection between the rise o f rational decision procedures rooted in material culture and the development o f a “ scientific rationality.” Gregory’s paper showed how the new conception o f nature appearing in the twelfth century was reflected also in positive evaluations o f technology and o f civil life.

In the late Middle Ages section, Murdoch dealt with the question o f just what one can and cannot accomplish through attention to social factors. The institution o f the medieval university, he argued, was o f unquestionable and crucial importance in the overall establishment and support o f the unity o f late medieval learning. Faculty o f Arts materials and methods acting upon and influencing the concerns o f the Faculties o f Theology and even, though to a lesser extent, vice versa. Yet the factor o f university context as usually considered falls short o f being able to explain, he maintained, the particular intellectual developments that characterized this unity. Further appeal to the intellectual history o f the universities in terms o f the works produced under their aegis and not to statutes, acta, and other university documents as such was held forth as being likely to provide the most fruitful avenue for future investigations. In a similar vein, Sylla’s paper urged that the institutional factors most frequently considered by historians do not furnish a sufficient explanation o f the development o f the autonomy o f the sciences in later medieval thought, since Aquinas and Ockham both worked within the institutional context o f the medieval university, each spending an important part o f his time at the University o f Paris. Attention must be paid also to such factors as concepts o f intellectual integrity, proper scientific procedure, and so forth.

Charles Schmitt’s paper on philosophy and science in sixteenth century universities was squarely directed to the issue o f social and institutional factors. Collecting and synthesizing evidence about philosophy and science

within universities in this later period, he examined the effects o f humanism, the Reformation, and scientific change on the teaching o f philosophy, while at the same time emphasizing the hurdles to be overcome by any historian who attempts to study European universities over a period o f a century or two and the consequent need to approach such a task in terms o f the diverse factors dominant in different universities at different periods o f time. A more complete and complex picture o f institutional differences within medieval universities should eventually allow the consideration o f institutional factors to make a greater contribution to the understanding o f late medieval and Renaissance intellectual development.

Concerning the third, cross-cultural theme o f the Colloquium, in the Islamic section, Shehaby’s paper presented a detailed argument for the influence o f one particular aspect o f Greek thought, that o f Stoic logic, upon a specific work in Islamic jurisprudence. The ensuing discussion concerned itself largely with the critical examination o f the specific claim made by Shehaby o f the impact o f one culture upon another, and in passing also raised the question o f just which criteria in general need be satisfied in order to establish with reasonable clarity the influence or traces o f a “ foreign” doctrine or idea within a work or document belonging to a different culture. Shehaby’s problem was particularly interesting because the influence he was trying to trace was both interdisciplinary and intercultural. Although less central to the major burden o f his paper. Van Ess’s investigation o f the origin o f kalâm also broached the problem o f the influence o f the Greek upon the Arabic, in this instance in terms o f the religious policy o f the Byzantine Empire having a possible effect upon the role o f the theologian in Islamic society.

In the twelfth and thirteenth century section, McKeon’s paper confronted the methodological problems o f studying the interaction o f cultures in the specific case o f the impact o f Islamic culture on the Latin West. While arguing that the Latin West’s interpretation o f Arabic culture was no more objective or reliable than any other interpretation, he maintained that the effects o f Arabic culture on Latin culture could be viewed concretely in terms o f the changes that occurred in the Latin encyclopedia or organization o f the sciences as the result o f the contact o f the two cultures. The translation o f Arabic and Greek scientific works into Latin led to a shift o f emphasis in the West from words to things, and to the opening up o f new sciences in the thirteenth century and after

o J. MURDOC H A N D E. SYLLA IN T RO DUC T IO N

wards. Gregory’s paper indicated how the twelfth century translations from the Arabic impressed Latin scholars with the relative poverty o f their own previous scientific work. The contact with Islam, he argued, helped to break down traditional symbolic modes o f thought and to produce a new view o f nature. In addition to Platonism, Arabic astrology was an important factor in this transformation, nature itself being sometimes identified with planetary influences.

Although as the papers themselves stand there may have been less emphasis upon cross-cultural factors than upon the other two themes o f the Colloquium, the discussions were richer in this regard. It was not possible to publish all o f these discussions and, consequently, much that did transpire is not reflected in the present volume, but often an issue or point raised during the discussion o f the Islamic contributions resurfaced during the “ Latin phases” o f the debate and thus brought to the fore a logical comparison, i f not the actual historical contact, o f the two cul

tures.The final afternoon session was devoted to an evaluation o f the pre

vious days’ deliberations, to an assessment o f what lacunae there may have been in the enterprise begun at the Colloquium, and to a discussion o f what questions and topics might be most deserving o f treatment at some future point, be it in research or within the context o f a similar colloquium.

There was need, it was felt, for a certain amount o f conceptual and geographical broadening in any such future deliberations. Law and especially medicine clearly require to be taken more into account. So also astrology, alchemy, and other “ occult sciences,” the more so as the way in which they seem to bear on other factors within medieval society differs appreciably from what obtains in the cases o f philosophy and theology. It would also be desirable to move the geographical center o f gravity slightly more to the south, to consider in particular the intellectual trends in sway at Italian and Iberian universities.

One o f the primary elements that emerged from the Colloquium was the repeated observation that intellectual and social factors were inevitably and inextricably connected. As a case history that might prove to be especially profitable in revealing the nature o f this connection, an appreciable amount o f discussion was devoted to the problem o f the translation and transmission o f knowledge. Much effort has thus far been expended

10 J. M URDOCH A N D E. SYLLA

by historians in sorting out just which translations of Greek and Arabic materials may have been made, and by whom and when, and even what character these translations themselves had. But little has been done with the purposes and motives for making the translations, or with the complicated question o f when, why, and how a given translation came to be used. A book translated was not a book read nor, a fortiori, a book understood. These problems, however, are just those that involve the interplay o f social circumstances, be these circumstances those concerned with the question o f why there was a demand for translating a given philosophical, scientific, or theological work in the first place, or those having to do with didactic or teaching requirements relevant to its eventual use.

The concentration upon the relations between disciplines that was everywhere evident during the Colloquium drew attention to the added work needed in the discrimination and characterization o f the disciplines themselves. To what extent, for example, are method, attitude, and approach, and not merely content, factors that are discipline-bound? Or in what way might they be helpful in distinguishing divisions or sects within a discipline? What relations ought the historian to establish between empiricism and rationalism, or other epistemological or logical factors, in elucidating the nature, for example, o f theology in Islam or the Latin West?

The same kind o f problem occupies a rather unique position in the history o f science. How should science be related to other areas o f intellectual endeavor and how should it be distinguished from them? Perhaps it makes little sense to distinguish it sharply from other areas o f thought and it is far better to put our heads to sorting out the great variety o f things that can be called “ science” in a given period. But what difference does the “ given period” make? How varied will our judgment be o f the continuum that may exist between science, philosophy, and theology as we move, not just from the Middle Ages to other historical periods, but even simply within the medieval period itself?

Lastly, there is little doubt o f the fact that one o f the most reliable indicators o f just which problems and ideas will prove fruitful subjects for future examination is the frequency with which particular issues continually reappeared throughout the general discussions. Many o f the points o f recurrent interest will be apparent from reading the discussions pub

INTRO DUCTIO N 11

lished below. Among them is the problem of correlating theory with practice, ideas with actions. Is this a correlation - no matter how difiicult it may be for the historian to establish - that pertains rather more exclusively to the histories o f science, theology, and law, and not especially to the core discipline o f philosophy in the Middle Ages? Alternatively, what new kinds o f inquiries should be undertaken in order to delineate the different modes o f applying mathematics and logic within all areas o f medieval thought and is the particular mode o f application in any way affected or directed by the area in question? Finally, a problem that has been endemic to the history o f science constantly appeared as a significant issue when discussing philosophy and theology as well: What, briefly put, is the importance o f observation, experience, and experiment? In particular, is the occurrence o f such notions in what has traditionally been the raw material o f the history o f science in any way influenced by the formulation and exercise o f the same or related notions in other segments o f intellectual endeavor? This kind o f problem too, old as it is, seems likely to provide profitable food for thought.

I l l

As is obvious from this brief account, the participants addressed themselves to the initial goals o f the Colloquium in many and diverse ways. To attempt to calculate the overall significance o f a meeting whose papers and discussions are so varied would be a precarious undertaking at best: each participant in or reader o f the proceedings will have his perspective. Perhaps, however, it is permissible at this point for the editors o f the proceedings to set forth their own views o f the results o f the Colloquium, especially as we see these results bearing upon its original goals and upon the alternatives historians might in the future adopt in their treatment o f the whole area o f medieval learning.

These views are our own, moreover, not merely insofar as they give our interpretation o f the possible significance o f the Colloquium, but also because they present a fair number o f our own ideas and conclusions concerning the historiography o f medieval science and learning. For some time we had already given appreciable thought to just which elements this historiography should contain and to what approach it should take in order to provide the most adequate portrayal o f the status

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and development o f learning in the Middle Ages. Our conclusions - some o f them admittedly, still in preliminary form - have undoubtedly contributed much to the perspective from which we have viewed the results o f the Colloquium. Yet the fact that many o f these results, we believe, in turn served to underscore and supplement our ideas and conclusions renders what follows a not inappropriate manner in which to present our assessment o f the Colloquium itself.

O f its three original themes, the second, concerned with “ the institutional and social factors that may have influenced the origin, growth, and maintenance o f philosophy, science, and theology as viable disciplines,” appears prima facie to be the one most directly relevant to the Colloquium’s circumstantial origin in the historical sociology o f science. But the very fact that even this second theme refers to “ philosophy, science, and theology” rather than to science alone indicates that even before the Colloquium took place there was at least a subliminal awareness on the part o f its planners that for the historical sociology - or more appropriately, the social history - o f medieval science at any rate, the so-called interdisciplinary factors that lay at the center o f the first theme are equally relevant. In fact, as the Colloquium assumed shape, it became apparent that the two initial aims o f the Colloquium were more two sides o f a single coin than their separate statement might lead one to believe. The interconnections o f medieval disciplines could not be understood without understanding the development and maintaining o f these disciplines as social enterprises and vice versa. In every case it appeared necessary to look not only at single isolated scholars or their works, but at intellectual communities and at the cultural context in which they worked. Given this, there seemed to be hopes for a more accurate historical perspective, at least i f the cultural context is understood in sufficient depth and detail.

Some notion o f just what profit might be reaped from this due attention to context can be had by sifting out the views expressed during the Colloquium with respect to the problem o f what continuities and discontinuities, what similarities and dissimilarities, historians ought to elicit from the material before them. One might expect that in such a Colloquium as this continuity or similarity would be the keynote: the Middle Ages might seem “ all o f a piece,” so that it would not be difficult to make generalizations covering the whole o f medieval philosophy, science, or

INTRODUCTION 13

theology. And indeed historical surveys spanning long periods o f time often do treat the Middle Ages as a single indivisible unit. The first impact o f the papers presented at the Colloquium must be, however, a recognition o f the tremendous diversity within the Middle Ages from century to century, from culture to culture, and within a given century and culture from discipline to discipline or school to school. A close familiarity with twelfth century Latin theology, to cite an obvious example, does not at all guarantee easy access to eleventh century Arabic mathematics. Somewhat less obviously, neither does a detailed knowledge o f twelfth century theology in the West promise an understanding o f theological endeavor in the fourteenth. Historians o f medieval philosophy, science, and theology in a meeting similar to the present one are not at all condemned to hear repetitions o f the same, age-old topics.

Nevertheless, once one has pushed beyond the initial realization o f how much one has yet to learn, a second impact o f a group o f papers like that before us may tend in the opposite direction. One begins to sense continuities over time, to perceive similarities, for example, between concepts developed in Islam and, apparently quite independently, in the Latin West. And one begins to wonder whether there might not be unknown connections between diverse periods or cultures that would account for these similarities. A feeling o f confidence is engendered suggesting that knowledge within one’s own special field may provide insight into problems encountered by historians with other specialities. When one’s primary territory is the Middle Ages, this confidence may even assume the form of feeUng that medieval concerns were very much like some modern concerns. Moving a step further, these initial glimpses o f apparent similarities may be reinforced by the creation o f a suitable glossary establishing links between the terms in which a problem is discussed in one language, period, or culture, and the terms in which it is discussed in another period. Indeed, since in order to understand an unfamiliar period it is often necessary to translate the contentions o f its sources into more familiar terms, this reinforcing o f similarities is quite likely. Yet this necessity “ to translate in order to understand” bears a directional asymmetry. That is, when the translation in question is that o f an earlier source into terms o f later material, the potential danger o f distortion is considerable. Viewing a substantial segment o f the history o f medieval science as not much more than the history o f Galilean ideas copied in advance is a case

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in point. On the other hand, when earlier terms or ideas seem to be required in order to comprehend a later source, the danger o f misinterpretation, although surely still present, appears less. The necessity o f translation may then be an accurate reflection o f the fact that the later source actually utilized or was influenced by earlier material. Even so, further confirmation and testing o f the similarity thus established is always in order.

Setting aside, however, further distinctions as to the various types o f similarities or continuities over time that are characteristic o f this “ second impact” o f the papers and discussions, one arrives at yet a third manner in which they impinge upon one’s historical sense. It is an impact that, on balance, seems to have been the predominant one animating the whole Colloquium. It finds its primary locus in the realization that the initial similarities that came to the fore in “ stage two” do not in fact extend very far. History does not often repeat itself in very great detail. Thus, although there may in fact exist many partial similarities, in most cases there is a decided disequilibrium in favor o f dissimilarities. And after all, diiference in time or in cultural context almost guarantees that there will also be differences at the level o f connotations and ramifications.

It is here that the extreme importance o f considering and understanding cultural context comes to the fore. Not only does a diversity o f cultural context - and it must be kept in mind that a sufficient difference in time within a single “ culture” will frequently carry with it a different cultural context - provide a warrant for the presumption o f differences, but an adequate grasp o f such context will afford one a way to determine precisely what these differences are. I f one turns away from similarities over time and focuses instead upon similarities over diverse areas o f thought within a given cultural context, then the conceptions, methods, and doctrines operative within that context are all but bound to receive sharper definition and be more completely understood. Readdressing, then, the question o f the relations o f such conceptions to temporally and culturally distinct ones that are reputed to “ resemble” them, a more adequate assessment o f the measure o f this resemblance can be made. In particular, a more precise account can be made o f the extent o f whatever differences they may have, not only in nature and meaning, but also in the motives behind their formulation and the purposes they were ultimately seen to serve.

I NTRO DUCTIO N 15

This investigation o f “ similarities over diverse areas o f thought” is, of course, a direct appeal for that consideration o f interdisciplinary factors that functioned as one o f the principal themes o f the present Colloquium. Perhaps such a consideration is not in itself sufficient for an exhaustive delineation o f the cultural contexts to which historians o f medieval thought must address themselves, but it surely appears to be a necessary ingredient.

In the foregoing, the “ three stages o f impact” o f the Colloquium have been stated rather abstractly without benefit o f the examples the papers and discussions themselves will provide. Apart from the Colloquium itself, however, these stages reflect in miniature, as it were, episodes that the historiography o f medieval learning has gone through. The history of medieval philosophy has, for example, moved through a pattern that has seen a shift from concern with dissimilarities and discontinuity with modern philosophy to emphasis upon similarities and then back again, but the historiography o f medieval science presents an even clearer case in point. Thus, the earliest histories o f science, like that o f WiUiam Whewell, took the radical diversity o f medieval and modern science for granted, i f indeed the differences that existed between the vocabularies and methods o f argument o f medieval and Newtonian science were not considered to be so great as to militate against taking anything medieval to be “ science” at all. The second stage was entered under the tutelage of Pierre Duhem when greater familiarity with the relevant medieval sources enabled historians to glimpse any number o f apparent similarities between medieval and modern science despite their overall divergence. Since Duhem, historians have tended to stress the similarities and possible historical connections between medieval and modern, without ascribing, to be sure, to the rather exaggerated claims he made for the medieval invention o f the very fundamentals o f the Scientific Revolution to be wrought by the likes o f Galileo and Descartes. More and more, however, following and extending the path marked out by Anneliese Maier, historians o f medieval science are entering the third stage o f impact in which both similarities and differences are given their proper due and in which a picture o f medieval science in its own right emerges, a picture not continuously colored by over-attention to the differences or similarities between the medieval and the modem. Maier began to place medieval science into its proper philosophical context. Both as a result o f the Col


loquium and more generally as a result o f our own thinking, we conclude that we are now at a point at which medieval science must be put more completely into its philosophical context and into its theological context as well. Only then will medieval science be presented in a properly understood, properly interpreted, way.

Success in such a venture demands much more than the constant dipping into theological and ostensibly philosophical sources for the raw material with which to build the history o f medieval science, something that Duhem himself had already done with considerable expertise. It also demands that this “ raw material” be properly related to the philosophical and theological context from which it has been drawn, a desiderandum that might be most effectively obtained, the present Colloquium suggests, by the kind o f collaborative enterprise it represents.

In general, then, the results o f a colloquium such as this recommend the third stage or position as that which is historically most sound and profitable, a stage that goes beyond the initial “ culture shock” to see similarities, but one that also gives more weight to differences and to the care that must be taken to come to a true recognition o f these differences. It is not, however, a recommendation that can be pursued without problems. Simultaneously desirable and difficult, “ third stage” analysis forces the historian to recognize similarities and differences at the same time and to try to understand them in as exhaustive a fashion as possible.

On a concrete level the problem o f recognizing diversity in similarity appeared in a variety o f forms again and again during the Colloquium. One o f the most common was the problem o f translation. What entitles one to assume that the substitution o f one word or concept for another is justified? Is it enough, for example, that two terms are somewhere defined similarly in each o f two languages or must one in addition show that they occur within larger contexts that are also demonstrably similar? Is it sufficient to pay attention to the context o f but a single work or must one consider other contemporaneous works as well? I f one looks at contemporaneous works, will it do to look merely at works by the same author in the same field or must one take into account all the works in any field that an author may have written or even all contemporaneous works whatsoever? The fact that, for instance, the medieval Latin and Arabic words for experiment, experience, trial, or comparison appear in every corner o f learning - in theology as well as in science and philosophy - seems to in-

IN T R O DUC T IO N 17

dicate the dangers o f hmiting one’s sources too narrowly, or inversely the benefits to be gained by exchanges o f information between historians o f the same period but o f different specialties.

Another concrete form in which the problem o f thoroughly understanding and balancing similarities and differences appeared was that, one might say, o f “ proper perspective.” Can one write, for instance, the history o f earlier mathematics or the history o f earlier science as a history o f only the recognizably scientific? Many would advocate, and indeed have taken, this approach, tied as it is to the belief common among many historians o f science in the essential immutability o f science itself. Or does such an approach invariably, even inevitably, distort the picture? Is it not better to ignore what came later and to try to think as a medieval? This naturally has the advantage o f remaining truer to the medieval context, but does it by the same token lead one to concentrate on things within the medieval context that are so different from modern ideas that they therefore are o f little interest to most historians o f science working in other periods? Similarly, can one write the history o f medieval theology without taking a particular religious stance? In order to have a result with some historical value, must one not at least assume the ultimate importance o f the theological issues discussed? But perhaps in such matters the history o f science is not at one with the history o f philosophy or theology. It might be argued, for instance, that a more modern perspective, more determinant presuppositions, follow from the fact that science is cumulative or progress-determinable in ways in which philosophy is not. But then, having said that, what is to be made o f the fact that so much o f medieval science is inextricably bound up with the likes o f “ non-cumulative” philosophy? What happens to arguments for the virtue o f a modern perspective then?

In the final analysis, although some participants favored a rigorously medieval perspective and others favored a more retrospective approach, it was at least clear that quite different perspectives can each have some validity and hence that, no matter how well documented, one cannot take a history written from one perspective and use it as established fact to rule out the possibility o f divergent histories. Nevertheless, returning again to the interdisciplinary emphasis within the Colloquium, it seems fair to claim that no perspective should be adopted for writing the medieval history o f one discipline that would totally disregard input and results

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derived from the histories o f other disciplines. To be sure, the historian o f science, the historian o f philosophy, and the historian o f theology can take the same set o f medieval documents and use them to write very different histories. But, at their most successful, these different histories should not be written in complete independence from one another. They can, and should, be o f value to each other without being homogenized into a single overall picture. The history o f theology in the fourteenth century in the Latin West should not be written, for instance, without due attention paid to many o f the central conceptions and methods that were operative in logic and science during the same period. Or, to return again to the example o f Galileo, even when one’s perspective is the “ vertical” one whose major concern is to show just what impact medieval notions may have had upon his thought, a strong case can be made for the collaborative, interdisciplinary analysis o f the development o f these notions within their proper medieval context and within the late fifteenth and the sixteenth century as well. For only then, the argument reads, will the historian know precisely what it was that may have had an impact upon GaUleo. And is such a determination not a prerequisite stage to elucidating exactly how he may have interpreted, altered, and added to these notions in the formulation o f his own views?

Thus, the histories o f philosophy, theology, and science jointly can better indicate what new sorts o f data in general can, and should, be looked at. What is more, broader, interdisciplinary perspectives, and the consequent use o f such new sorts o f data (or more intensive use o f the old kinds o f data) can enable the historian to avoid unhistorical excerpting o f the intellectual record, excessive modernization o f such excerpts through translations that ignore context, and the creation o f pseudo-causal chains based on conceptual similarity where evidence o f any historical connection is lacking. Cooperation between historians o f theology, philosophy, and science can also assist in removing one o f the main difficulties o f medievalists in these fields, namely that the modern divisions and distinctions between the fields themselves often do not fit well with the medieval data, so that, for instance, it is far from simple to construct sensible distinctions between what should count as philosophy, science, or theology in the Middle Ages itself.

The implicit recommendation o f the Colloquium was, then, that the future histories o f medieval science, philosophy, and theology would do

IN T RO DUC T IO N 19

well to imitate the collaborative, interdisciplinary structure o f the Colloquium itself. Perhaps not the least o f the reasons why such a recommendation should be heeded is that the present day community o f historians being urged to indulge in such collaboration parallels rather neatly the medieval intellectual community o f scholars that produced the very material demanding historical treatment. In whatever sense philosophers, scientists, theologians, and lawyers were then one, so should those who today address themselves to the history o f what these medievals accomplished act as one. Indeed, we feel that the importance o f collaborative, interdisciplinary history is so central that each historian should go beyond the stage o f taking into account and absorbing the accomplishments o f his fellow historians working in “ sister disciplines” and proceed to engage in doing some history in these fields himself. To appeal once again to the analogy between the concert o f disciplines at the present Colloquium and in the Middle Ages itself, this radical degree o f collaboration is needed because the very structure o f medieval learning requires it.

Thus far we have drawn out but one side o f what we see as the results o f the Colloquium, a side concerned primarily with the similarities and differences across diverse periods and cultures, and with the benefits to be derived when historians whose bailiwicks are neighbors but not identical come to grips with such similarities and differences. Another major implication that can be drawn from the Colloquium results, we believe, from the efforts made by the participants, and from the difficulties they confessed in making such efforts, in addressing themselves to the second theme o f the meeting: the “ social factors that may have affected the origin, growth, and maintenance o f philosophy, science, and theology as viable disciplines.” There was something o f a unanimous admission o f the fact that, whatever arguments and problems there may be for later periods concerning the validity or necessity o f the usual social explanations o f intellectual development, they are multiplied for the medieval period. This is true, it was felt, first o f all because the intellectual history that might or might not be explained by social factors has yet to be delineated in adequate detail and secondly because the sorts o f data usually used to build up a description o f the social factors themselves are often simply not available for the medieval period. Material concerned with the university milieu and the studia o f the various religious orders might appear to form a notable exception, but even there a need was felt for much further work

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before the precise nature and impact o f the relevant social factors could be realized.

The Colloquium participants agreed, moreover, that little gain was to be derived from the repeated application o f standard theories o f social influence on intellectual developments without having data in hand to support or challenge these theories. The data very likely will be, it was suspected, incommensurable with such theories or sociologies o f knowledge. Theories o f social influence that may work (let us assume) for modern science or learning, howsoever accurate and productive they may be when applied to the modern period, may not work at all for things medieval.

This general uneasiness concerning the macro-sociology o f intellectual phenomena in the Middle Ages should not be construed, however, to imply a wholesale disapproval o f the social history o f medieval learning. To the contrary, it is only to draw attention to the kind o f work that has to be done if such history is to be informative and elfective. Thus, there appeared agreement to the effect that a history which simply juxtaposes- and many “ sociologies” o f medieval learning seem to do just that - social factors o f the most non-intellectual sort with theoretical developments cannot be expected to explain anything. As at least a partial remedy, one suggestion was that it is necessary to find intermediaries that connect external factors with specific aspects o f the theoretical development in question (arithmetic functioning as an intermediary, for instance, between commercial needs and Arabic algebra). To generalize the argument, unless one establishes in some detail the existence and nature o f such intermediaries, the amount o f illumination afforded the history o f medieval learning by pointing to the importance of, for example, universities, particular bureaucratic classes, or specific aspects o f material culture will be, if not minimal, at least not what it can be. However, even when such intermediaries have been determined and set forth with appropriate emphasis, we believe that one should also recognize that, although one may thereby be successful to some extent in detecting the mutual influences o f social and intellectual factors, there will not be some single “ grand scheme” concerning intermediaries by which such influences are governed, but instead a variety o f different means all o f which depend upon specific, local cultural factors. One is again necessarily drawn back to the crucial importance o f considering cultural context in detail.


On the other hand, such reservations, at times outright skepticism, with respect to the potential value o f a social history o f medieval learning - and one should note that they occurred more frequently in the discussions than we have been able to indicate by those portions here published - can be mitigated, we believe, by a further consideration. And here we speak less as interpreters o f things expressed during the Colloquium and more as exponents o f our own views o f what should count in the Middle Ages and in other segments o f intellectual history as a social factor in the first place.

Among historians, the term ‘social’ appears traditionally to be taken as opposed to ‘intellectual’, a dichotomy that was accordingly almost always in mind when the problem o f “ social factors” entered into the discussions during the Colloquium. Interpreted in this sense, social elements are non-intellectual factors that are in one way or another effective within the intellectual realm. Political and economic influences, social or tribal divisions, technological or craft traditions, would here be the kind o f thing that would qualify as “ social.” Occasionally something intellectual is allowed to qualify as social, but then this is almost always intellectual material that is not “ directly relevant” to the science, or discipline, in question, or even to the metascience or metadiscipline involved. Various doctrines or dogmas within religion would be typical examples.

It was this traditional sense o f ‘social’ that was involved, we feel, when Colloquium participants rightly counseled that patience was in order when it comes to writing the social history o f medieval learning. In particular, it was claimed that it is far too early to formulate anything like definitive answers concerning the influence upon medieval intellectual history o f such social factors as the economy o f feudalism, the divisions o f medieval society into social classes, or the attitudes o f these social classes toward learning. And the same caveat should be observed when it conies to assessing the formative role within medieval learning o f presumably more directly relevant traditional social factors such as the institutional framework o f the university, membership in a specific religious order, the impact o f changing techniques o f communication, and so forth. One must expect to do a substantial amount o f work and to exercise great ingenuity in thinking o f new ways to obtain information about such social influences.

But before this future stage can be realized, there is another aspect o f

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the social history o f medieval learning to be examined. This aspect stands every chance in our eyes o f being more important and more instructive than what might follow. It has to do with another way in which one can count social factors. In this second sense ‘social’ is opposed, not to ‘intellectual’ , but rather to ‘individual’. One o f the consequents o f viewing social factors in this fashion is that the historian focuses upon intellectual communities and not upon isolated philosophers, scientists, or theologians, and does so even when there is no available evidence that these communities were also “ social” ones in the more traditional (i.e., social vj. intellectual) sense. How the historian might come to grips with a relevant intellectual community under such circumstances needs a word or two o f explanation. But as a prerequisite, something should also be said first o f what might be seen as constituting such intellectual communities, and, secondly, o f just how central a position they should occupy in the labors o f the historian o f medieval learning.

As one would expect, the make-up o f the intellectual communities we have in mind follows no hard and fast rule. Basically, one has to do with groups o f scholars who can be connected by some definite resemblance o f intellectual factors present in their writings. These intellectual factors may be specific ideas, doctrines, or beliefs, or on a less immediately evident plane, particular methods, attitudes, or approaches. The resemblance presumably derives from the scholars’ being directly familiar with one another’s works, a familiarity arising, perhaps, from attending lectures, reading each other’s writings, or even from some other form o f more personal contact. On the other hand, the resemblance o f intellectual factors is often present when there is no evidence, perhaps even counter evidence, o f such familiarity. We may never be able to estabhsh, for example, that one scholar heard or read another, or that they both studied at the same university or at one time or another belonged to some single social community (in the traditional sense o f ‘social’); yet we may, with caution, judge them to belong to the same intellectual community on the grounds o f the sorts o f resemblance o f intellectual factors o f which we have been speaking.

In thus speaking o f medieval intellectual communities where there is little extant evidence o f actual social contact there is an inherent danger o f falling prey to the temptation o f imagining such intellectual communities almost at will. One might find evidence to construct a veritable


hierarchy o f intellectual communities. Only some o f these, however, are likely to provide informative and fruitful input for the social history o f medieval learning. Surely a substantial amount o f further research will be required to furnish a comprehensive understanding o f the nature and eflfects o f medieval intellectual communities: the problem is that any number o f intellectual communities might be discriminated on the basis o f common factors deriving almost automatically from the utilization o f the scholastic method, from the Aristotelian base o f the material taught and consumed in the Faculties o f Arts, or from the central role played by Lombard’s Sentences in theological education and debate. It is not seldom that factors such as these give a fair measure o f continuity to medieval intellectual endeavors when one can show on other grounds that the results, and even the intents, o f these endeavors are quite opposed to one another. What is more, although such factors might furnish reason for speaking o f an intellectual community in a rather loose sense - o f all natural philosophers as Aristotelians, for example - they are not likely to afford evidence o f those intellectual communities that had an impact upon intellectual change. If, however, one can discriminate intellectual communities whose members are either consciously or unconsciously pursuing similar intellectual goals, one would seem to be closer to the mark. As historians, on occasion we might be able to encapsulate this similarity by applying such labels as “ Scotist” or “ Thomist” or the like. But in most instances the relevant similarity o f intellectual goals will not likely prove to be so easily describable; it will, we believe, have to be excavated from the much more uncharted terrain o f a similar way o f doing philosophy, science, or theology.

What sources and what evidence it may prove profitable to tap for such future excavations will be discussed below. But before suggestions in this wise are broached, something should be said o f how central a role intellectual communities should play in the writing o f the history o f medieval learning. To be sure, it should not be taken as so central as to legislate out o f existence any treatment o f individual thinkers. One would, and should, still have articles and books on, for instance, aspects o f Ockham’s theology or on Richard Swineshead’s Liber calculationum’, they would not have to be replaced by corresponding monographs dealing with the early fourteenth century English Franciscans or the “ Merton School.” An “ isolated” logical analysis of, say, Ockham’s theory o f supposition or a math

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ematical analysis o f one o f the tracts o f the Liber calculationum would still be useful, and perhaps even necessary, for the historian to have. One cannot, however, stop there. A truly adequate historical treatment o f Ockham or Swineshead requires, we believe, that they be considered, not in isolation, but as very much part o f the intellectual context to which they belonged. This includes first, as we have indicated above concerning the interdisciplinary theme o f the Colloquium, that the contemporary developments in various other academic disciplines be taken into account, but also second that the ties o f scholars to each other be reckoned with.

Indeed, few medieval scholars worked in anything like total isolation. Most medieval learning was rather an activity that was developed and carried on at a university, within a religious community, or, less frequently, at a royal court. Groups o f people came together at such institutions, wandered from one to the other, learned from each other, read or heard about each other’s work directly or through intermediaries, and often became adherents o f or opponents to this or that doctrine or idea as a result. O f course, these intellectual communities or groups o f scholars did not carry out their work as groups; almost no medieval Sentence Commentary or Questions on Aristotle was a “ joint project” in today’s sense o f the term. Yet it is most important never to lose sight o f the fact that medieval scholars did interact with each other in a multitude o f ways. I f this is so, does it not follow that the historian cannot hope to elicit the full and proper meaning and importance o f even those particular fragments o f Ockham and Swineshead that we have used as examples without giving due consideration to the intellectual communities to which these authors belong and in which they produced their works? One would think so.

Now a social history that operates with intellectual communities o f this sort seems a far more fertile field for the medieval historian than a social history taken in the more traditional sense. The kind o f evidence needed for the latter is frequently either not forthcoming or only to be had after a long period o f further research, but even if it were more plentiful, we believe that the social history based on intellectual communities as we have described them will in the final analysis prove to be the more informative and productive. The relevant social factors in the sense o f ‘social’ vs. ‘individual’ are not only more available, but are also more immediately related to intellectual activity, and provide the material for formulating a


dimension o f the history o f medieval learning as a social enterprise that will not likely be obtainable by other means. In particular, their more intimate connection with the very substance o f intellectual endeavor makes them much more effective in contributing to the explanation o f some o f the more specific aspects o f intellectual change than social factors o f the more traditional kind. They stand a good chance, that is, o f telling us things about the meaning o f particular intellectual moves, about how they may have come to be and why they were taken, and not merely about the general framework or milieu in which such moves

transpired.The question remains, o f course, just what kind o f evidence there is

that will allow one to establish the existence o f relatively well defined intellectual communities if social factors o f the more traditional sort are, or at least can be, excluded from consideration.

The point o f departure must be, we believe, the writings themselves o f any number o f scholars flourishing in this or that period in the Middle Ages. Our research to date leads us to believe that if, and when, these writings clearly exhibit common methods or languages o f analysis, common canons o f evidence and certitude, o f what constitutes an acceptable “ fact” or doctrine, common views concerning intellectual integrity, and so forth, then it is likely that the authors o f these writings constituted, in effect, an intellectual community, a community that is likely to serve the historian as an effective guide in exploring that hitherto largely unchar- tered terrain we have mentioned above o f the similar way in which philosophy, science, and theology was done. A community that is so defined or determined stands a better chance, we feel, o f revealing more about the “ shape” o f medieval learning and about the major changes that occurred within it, than would a community based merely on adherence to common ideas or doctrines. What is more, similarity in content among works, in the employment even o f all but identical arguments, appears to be not nearly so adequate evidence o f the existence o f a cohesive intellectual community as are the more structural, common features just mentioned, since such similarities are frequently found among authors and writings that we know on other grounds to belong to distinctly opposing camps.

Several other points might be noted. To begin with, there is little evidence that the members o f an intellectual community need be working, or even have worked, in the same discipline or that they need be tied, for

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example, to a single university or other institutional milieu. In point o f fact, were one to restrict one’s investigations merely to scholars working in natural philosophy or to individuals teaching or studying at Paris, it seems highly likely that one could easily demonstrate that the resulting intellectual community was “ incomplete,” that is, that one could establish that scholars in other disciplines or at other universities indulged in intellectual activities that reveal them to be, on grounds o f the very same criteria, just as much, perhaps even more, part o f the intellectual community in question. Secondly, the criteria we have by example suggested as determinative o f a given intellectual community have by design not taken into account more traditional social factors. Indeed, in many instances it will undoubtedly prove to be the case that such factors can never be taken into account, the only available evidence that such and such a scholar belonged to this or that intellectual community being solely and always o f the kind we have mentioned. Yet there will surely be many other instances in which “ social” evidence o f a more traditional sort is forthcoming (for example, all the members o f an intellectual community being Franciscans, being English, being arts students at Padua at such and such a time, etc.). In these cases, this supplementary evidence will obviously function as confirmation o f the intellectual community, giving it, one might say, an added “ social base” in the more traditional sense. When such “ other evidence” is not present, establishment o f an intellectual community on the basis o f criteria similar to those cited above will naturally tell the historian to be “ on the lookout” for such evidence.

Those who are familiar with work in the history o f medieval philosophy and theology over the past several decades will recognize that the kind o f social, intellectual community history o f which we have been speaking bears points o f resemblance with recent attempts to set up criteria to determine who might properly be called “ nominalists,” “ terminists,” or even “ modernists” in the later Middle Ages. Such attempts appear to have met with partial success at best, and have utilized criteria that are more restrictive, and at times less well defined and tested, than those we have suggested above. In many instances the criteria have been constructed largely from the works o f a single author or from a relatively narrow selection o f works within a single discipline and hence qualify less as evidence for the existence o f intellectual communities than the types o f evidence that we have in mind.


The kinds o f initial sources that we feel the historian should turn to in attempting to formulate this intellectual community based social history o f medieval learning reflect what was, on a broader scale, one o f the most interesting results o f the Colloquium. This was the recognition o f the ways in which the medieval historian, faced with an almost critical lack o f the ordinary kinds o f social data, can find out about certain social factors (for the most part those based on the opposition social vs. individual, we would suggest) simply on the basis o f the scientific, philosophical, or theological works themselves. More accurately, appeal should be made not merely to the works (that much will provide an excellent beginning), but to the manuscripts o f the works, that is, to the additional information that the various copies o f a single work can provide. It has already been indicated that an intellectual community whose existence has initially been established on the basis o f evidence appearing within the written works themselves should, whenever possible, have its existence confirmed by supporting social evidence o f a more traditional sort. Yet, beyond this more familiar evidence provided by the likes o f biographical and institutional factors, the codicological information that can be gleaned from an examination o f a number o f manuscript copies o f a single work furnishes evidence o f an important and unique sort for the medieval historian o f intellectual communities.

Thus, although information pertinent to the existence and scope o f an intellectual community is often to be had from the citations (and from the manner o f citation) in a given work itself, the marginal expansion o f these citations in various copies o f the work may well add to this information, and even, by identifying the citation beyond a mere quidam, change its significance in a most important way. Yet over and above citations, the varied manuscripts o f a given work often yield “ intellectual community” evidence by the way in which the codices were put together (which works are to be found with which), by the manner o f their annotation, and so forth. Given such information, one can often infer a good deal about who knew whom, who read or studied whom, and what influences there may have been between cultures or disciplines. Since not a few o f these codices were student “ notebooks,” or at least manuscripts that were extensively utilized by students, the codicological information they contain may well tell us things about magister-discipulus relations that we can learn in no other way. And knowing o f such relations is certainly crucial to building


up a history based on intellectual communities. Finally, these annotated copies o f works at times provide another input that is at one level o f remove from that furnished by the v ork itself. They may tell us, that is, not simply that there was such an intellectual community, but that certain scholars were aware o f it as an intellectual community, aware that it existed and aware that they belonged to it or were partaking o f it.

As we trust is everywhere implicit in what we have said, the consideration o f intellectual communities by the medievalist is but a specific response to the necessity o f taking into account the full relevance o f cultural context. As such, intellectual communities should be investigated from an interdisciplinary point o f view. As an example o f the advantages o f such a point o f view, it seems relevant to note that any study o f medieval intellectual communities is sure to benefit substantially i f it can appeal repeatedly to the history o f theology. For we have immeasurably more material dealing with the theological community than we do for those communities tied to the Faculties o f Arts. But the evidence is not only more plentiful; it is in a variety o f ways more informative in kind. In particular, the criteria we have listed above as likely to afford evidence for the existence o f intellectual communities are frequently more evidently displayed in theological works than in those concerned with artes material. In any event, it seems likely that the examination o f theological works, central as they were within medieval learning, will give rise to questions to be asked about all intellectual communities that would not otherwise be noted were one limited to philosophical and scientific works alone.

Admittedly, something o f a re-education will be necessary for the historian to equip himself to ply his trade in a field outside his original specialty. But this can be much facilitated by cooperation. The potential benefits are well worth the effort. To be sure, the study o f medieval learning, especially when viewed as a social enterprise, would also be wise to avail itself o f the assistance to be derived from medieval social and economic history in general. But, as in the present Colloquium, collaborative activity on behalf o f historians o f philosophy, science, and theology is not just a beginning. It is the required nucleus for the whole.

IV

The assistance and counsel we have received in the planning and holding


o f the present Colloquium, and in preparing the publication o f the contributions and discussions that formed its substance, have been both constant and considerable. The sponsorship o f Harvard and Boston Universities has naturally been a sine qua non for the very occurrence o f the Colloquium. But personal indebtedness has been no less important.

To Robert S. Cohen and Marx Wartofsky we owe numerous thanks for their efforts in arranging and finding a locale for the Colloquium and, especially, for their help in seeing its proceedings into print as a volume o f the Boston Studies in the Philosophy o f Science. The whole staff o f the Osgood Hill Conference Center o f Boston University, and particularly Betsy McCoy Faught, who took leave o f her duties with the Center for the History and Philosophy o f Science to join us in North Andover, did far more than we imagined needed to be done, or even could be done, to make the meeting a comfortable and enjoyable one and to bring all to

pass smoothly.The first step in moving the Colloquium’s discussions towards print we

owe to John Novak, who brought the required technology into our midst and saw to its proper operation, and especially to Jean Christensen, who patiently tended the equipment to assure that all parts o f our Anglo- French mélange received appropriate electronic preservation. Exceeding his role as participant, Jean Gagné has been o f more help than we can ever acknowledge in getting the French interventions from the state o f magnetic impulses into written form, revising them, and advising us in innumerable extremely helpful ways with respect not merely to la partie française, but to the Colloquium’s publication as a whole. Abdelhamid Sabra rendered us similar indispensable assistance in the transcription o f Arabic and the resolution o f other problems concerning the papers and discussions constituting the Islamic section o f that published here,

George Molland brought the critical eye o f a fellow historian o f medieval science to bear upon the present introduction, and Barbara Rosen- krantz did the same from the quite different vantage point o f a scholar in American social history and history o f science. Their advice has proved exceedingly valuable and welcome. Those parts o f it we have found space and energy enough to follow have unquestionably made this introductory section a better product. The faults and ambiguities we have not managed to remedy are, o f course, our own.

No stage o f the Colloquium would have proceeded beyond ground level


without the constant assistance o f Ruth Bartholomew. Our gratitude is without measure: from the inception o f the very idea o f the Colloquium, through the substantial volume o f correspondence involved in its planning, through the innumerable versions and revisions o f the discussions, to the final draft o f this very introduction, her help has been absolutely essential.

Finally, the most profound acknowledgment must go to the participants and auditors themselves. Without their contributions, their unbridled efforts, interest, and enthusiasm, the Colloquium would have come nowhere near being the success we believe it was.

P A R T I

ISLAM

Harvard University

North Carolina State University at Raleigh

ROSHDIRASHED

R E C O M M E N C E M E N T S DE L ’ A L G È B R E

A U X X le E T X l l e S IÈ C LE S

Parfois encore l’histoire de l’algèbre classique est relatée comme la succession de trois événements séparés: la constitution de la théorie des équations quadratiques, la résolution plus ou moins générale de l’équation cubique, l’introduction et le développement du symbolisme algébrique. Au premier événement on associe souvent le nom d’al-Khwarizmi, au second on rattache toujours ceux des mathématiciens de l’école italienne, et en particulier de Tartaglia et de Cardan, au troisième enfin sont liés les noms de Viète et de Descartes.

Au X IXe siècle déjà, les travaux de Woepcke sur al-Karajï et al-Khay- yâmî, et plus récemment ceux de P. Luckey sur al-Kâshï, ont montré que le précédent schéma est incomplet, voire inexact. Le premier, avec sa traduction de l’algèbre d’al-Khayyâmï révélait notamment que c’est bien avant le XVIe siècle que la théorie des équations cubiques accomplissait un réel progrès. Tous deux, par leurs travaux sur al-Karajï et al-Kâshï, laissaient même entrevoir que l’histoire de l’algèbre ne peut être retracée indépendamment de celles du calcul algébrique abstrait.

Mais en dépit de ces études, certains historiens continuent à concevoir l’histoire de l’algèbre classique selon le même schéma. Il reste que cette situation n’engage pas la seule responsabilité des historiens : elle est due, en partie au moins, au fait que les algèbres d’al-Karajï, d’al-Khayyâmï, et surtout d’al-Kàshï pouvaient paraître elles-mêmes peu intégrables dans de véritables traditions mathématiques. L ’information incomplète et partielle sur les mathématiques arabes présentaient jusqu’à une date récente, et d’une certaine manière présente encore ces travaux comme des oeuvres individuelles, faute de connaître les traditions dans lesquelles elles s’insèrent. Dans ces conditions, l’on comprend la tentation toute naturelle pour l’historien de poser la question controversée des origines, laquelle se transforme aussi rapidement en question de l’originalité.

Dans cet exposé, nous voulons revenir, brièvement, à ces traditions mathématiques elles-mêmes, pour soutenir que l’algèbre classique fut renouvelée dès la fin du Xe siècle, que ce renouvellement ne se présenta

Murdoch and E. D. Sylla (eds.), The Cultural Context of Medieval Learning, 33-60. 11 Rights Reserved.

34 R. RASHED

pas seulement comme une réactivation de l’algèbre reçue, mais comme un véritable recommencement, ou des recommencements à proprement parler.

On peut en effet reconnaître deux traditions mathématiques auxquelles l ’algèbre est liée. La première est celle de l’arithmétique - “ art scientifique” disaient les mathématiciens et bibliographes arabes - théorie des nombres et art du calcul - ou logistique - l’une et l’autre fortement liées. Ce développement fut l’oeuvre des arithméticiens arabes eux-mêmes, il eut également pour cause la traduction des Livres Arithmétiques de Diophante. Pour renouveler cette discipline, al-Karajï et ses successeurs mettront à profit à la fois le développement et leur connaissance de l’algèbre telle qu’elle fut pratiquée depuis al-Khwarizmi. La deuxième tradition est associée aux travaux de certains géomètres: surtout ceux que préoccupèrent les déterminations infinitésimales et de ceux qui cherchaient à faire progresser l’algèbre par la géométrie. Représentant cette tradition, al-Khayyâmï et Sharaf al-Dïn al-Tùsï ont été amenés, comme on le verra, à l’étude algébrique des courbes; ils ont posé les fondements de la géométrie algébrique.

Pour justifier ces prétentions, cet exposé rapide ne se propose d’autre tâche que de répondre aux questions suivantes: Quels sont ces commencements? Quels furent leurs moyens et leurs raisons probables?

Si l’on veut caractériser brièvement la tâche des algébristes, au moins de ceux de la première tradition, on peut dire qu’ils eurent pour projet l’arith- métisation de l’algèbre, telle qu’elle avait déjà été constituée par al-Khwa- rizmi, puis développée par ses successeurs comme Abu Kâmil (850-930). Il s’agit en fait, délibérément, comme l’écrira plus tard al-Samaw*al “ d’opérer sur les inconnues au moyen de tous les instruments arithmétiques, comme l’arithméticien opère sur les connues” . La tâche est claire et l’algèbre acquiert la signification qui est désormais la sienne: il s’agit, d’une part d’appliquer de manière systématique les opérations de l’arithmétique élémentaire aux expressions algébriques - les inconnues algébriques- et, d’autre part, de considérer les expressions algébriques indépendamment de ce qu’elles peuvent représenter, pour pouvoir leur appliquer ces opérations générales qui sont appliquées aux nombres.

RECOMMENCEMENTS DE L ’ ALGÈBRE 35

Déjà manifeste dans l ’oeuvre d’al-Karaji (mort au début du X le siècle), poursuivie et perfectionnée par ses successeurs, la réalisation de ce projet a amené, comme on peut le constater un siècle plus tard avec al-Samaw’al (mort en 1175), l’extension du calcul algébrique abstrait et l’organisation de l’exposé algébrique autour de l’application successive des différentes opérations de l’arithmétique. Il suffit pour s’en convaincre de parcourir al-Fakhrl d’al-Karajî, ou al-Bâhir d’al-Samaw^al. Ces traités d’algèbre ont eu pour principal résultat de donner une meilleure connaissance de la structure algébrique des nombres réels. Mais comme ce résultat et d’autres de moindre importance obtenus par ces algébristes ont souvent été attribués à des mathématiciens tardifs comme Chuquet, S t i f e l , e t comme ces résultats expriment précisément un changement de la rationalité algébrique, qu’il nous soit permis de reprendre ici ce que nous avons exposé ailleurs pour décrire rapidement la démarche de nos auteurs et démontrer les affirmations que nous venons d’avancer.

Dans al-Fakhrl, al-Karajï commence par étudier les différentes “ puissances de l’inconnue” . Après avoir énoncé de manière verbale, c’est-à-dire non symbolique, que x”* = :x^~^x pour m = 1, 2 , 9 , il note qu’ “ il en est ainsi à l’infini” et que “ lorsqu’on multiplie l’une quelconque de ces puissances par un certain nombre de racines, le produit est l’ordre de la puissance suivante” . On peut donc dire qu’al-Karajï définit x'*=x'*~^x pour tout entier positif n.

Al-Karajï essaie ensuite d’étendre la notion de puissance algébrique d’une quantité, puissance définie en quelque sorte par récurrence, à son inverse, et donne quelques résultats importants tels que: (1/x")-(1/a:'") = _ l/^«+m Cette généralisation sera précisée et achevée par ses successeurs qui, grâce à la définition de la puissance nulle x° = l pour x^O , ont pu finalement énoncer une règle équivalente à: x":>^ = x ” ' "* pour tout m, n s i .

C’est seulement par suite de la généralisation du concept de puissance algébrique que l’on s’efforcera d’appliquer les opérations de l’arithmétique aux expressions algébriques. Cette application aura pour conséquence immédiate l’un des premiers exposés d’algèbre des “ polynômes” .

En effet, dans son al-Fakhri, al-Karajï ne se contente pas d’étudier l’addition, la soustraction, la multiplication, la division, l’extraction de la racine des monômes, mais aussi celles des polynômes. Toutefois s’ il énonce bien dans le cas des polynômes des règles générales pour +/ —, x , il

36 R. RASHED

n’en va pas de même pour la division et l’extraction de la racine. En fait il ne considère que la division d’un polynôme par un monôme; et s’il extrait la racine carrée, il se borne à celle d’un polynôme à coefficients rationnels positifs.

On peut d’ailleurs comprendre les difficultés d’al-Karajï à partir de sa conception même du statut des nombres négatifs. Bien qu’il eût écrit dans al-Fakhrî “ qu’il faut compter les quantités négatives comme des termes” , il semble que la tradition ait condamné cette reconnaissance des nombres négatifs à rester timide. S’il acceptait en effet sans réserve de soustraire un nombre positif d’un autre, il n’admit pas directement que jc — ( —j ) = = x + y. On comprend dans ces conditions la difficulté de donner des règles générales pour la division et l ’extraction de la racine carrée des polynômes à coefficients rationnels. Au X lle siècle cependant les successeurs d’al-Karajï énonceront les règles des signes en toute généralité:

(1)(2)(3)(4)(5)(6) (7)

■^<0, >><0< 0, < 0, |x| ^ 0< 0, j ^ 0, |x| ^ |>'| => X - j ^ 0

x ^ 0 = > 0 —x < 0 = > 0 —

ou comme l’écrit al-Samaw’al, “ le produit d’un nombre négatif - al-nàqi^ - par un nombre positif - al-zâHd - est négatif, et par un nombre négatif est positif. Si nous soustrayons un nombre négatif d’un nombre négatif supérieur, le reste est leur différence négative. Celle-ci reste positive si nous soustrayons un nombre négatif d’un autre négatif inférieur. Si d’un nombre positif nous soustrayons un nombre négatif, le reste est leur somme positive. Si d’une puissance vide {martaba khâliya) nous soustrayons un nombre positif, le reste est le même négatif, et si d’une puissance vide nous soustrayons un nombre négatif, le reste est le même nombre positif” .

Munis de ces règles, les successeurs d’al-Karajï pouvaient achéver la tâche et proposer une théorie de la divisibilité des polynômes et de l’extraction de la racine carrée d’un polynôme à coefficients rationnels. La méthode proposée par al-Samaw’al n’est autre que l’extension de l’algo-


rithme d’Euclide pour la division des entiers aux expressions de forme

/ = Zk= —m

m, « e Z +

D ’une manière précise, il ne s’agit pas absolument de la division ordinaire dans l’anneau des polynômes X [x], K étant un corps; mais dans un anneau A [x ]= [Q {x ) + Q {llx )]. Al-Samaw’al ne s’intéresse pas d’ailleurs explicitement au degré du reste. Cependant, les résultats de la division sont exacts, puisque diviser

n'/ par ^ n 'eZ+

k = — m'

revient en fait à diviser x Y par x “g, a = sup (m, m '); on est alors amené à un problème de division dans ^ [x ].

Faut-il encore noter qu’on continuera à diviser la division dans l’anneau A [x ] au moins jusqu’au XVIIe siècle? Parfois d’ailleurs, au lieu de ces éléments de l’anneau A [x], al-Samaw’al considère des polynômes au sens strict: c’est alors qu’il définit la méthode de la division avec reste. Dans tous les cas - ce qui confirme en plus une conception suffisamment élaborée de sa démarche - il représente, dans des tableaux, chacun des éléments de la division - les éléments de l’anneau A [x] ou K [x ] - par la suite de ses coefficients positifs et négatifs.

La théorie de la division permet en outre d’étudier un autre chapitre non moins important de cette algèbre: l’approximation des fractions entières par les éléments de A [x]. On a par exemple:

/ (x ) + 30x 10 _ 5 20 10 _ 40 _ 20 80

6x + 12 3 X 3x^+

3x' 3x

40Z ï

où al-Samaw’al obtient une sorte de développement limité de <p(x) = — / {x )lg (x ). Cette approximation est valable seulement pour x suffisamment grand, ce que l’auteur ne précise pas.

Comme on a pu ainsi étendre la division ordinaire aux polynômes, nos algébristes suivent une démarche analogue pour l’extraction de la racine carrée d’un polynôme. Al-Karajï avait déjà proposé deux méthodes pour l’extraction de la racine carrée d’un polynôme à coefficients dans Q +,toutes deux fondées sur le développement ( x + jH -----h = x^ + (2x-'ry)y-\----- f-(2x + 2> H----- \-w) w. La méthode d’al-Karaji se trouve déjà

38 R. RASHED

généralisée dans al-Bâhir où l’on procède à l’extraction de la racine carrée d’un polynôme à coefficients dans Q, ou plus précisément l’extraction de la racine d’un élément carré de l’anneau A [;\;]. Ainsi pour extraire la racine carrée de:

B = 25x® - 30x" + 9x^ - 40x^ + 84x - 116x + 64

48 100 96 64------- 1--- 2------ 3 + ~4X X X X

au moyen de la méthode des tableaux, il écrit:

B = 25x^ + (lOx^ - 3x^) ( - 3x^) + (lOx" - 6x^ - 4) ( - 4)

+ lOx^ - 6x^ - 8 +

2 _ 4 + _ _X

4 )= 5x - 3x

d’où la racine. Al-Samaw’al présente cet exemple comme l’illustration d’une méthode générale (tariq' âmm).

A la suite de l’extension du calcul algébrique aux expressions rationnelles, al-Karajî et ses successeurs poursuivent la réalisation du même projet et veulent montrer, comme il l’écrit, “ comment opérer au moyen de la multiphcation, la division, l’addition, la soustraction et l’extraction des racines” sur les quantités irrationnelles algébriques. Al-Samaw*al pose la question presque dans les mêmes termes: “ comment utiliser les instruments arithmétiques dans les quantités irrationnelles (al-maqâdîr al-?umm)T

Outre les résultats proprement mathématiques que l’on obtient par cette extension, l’on s’engage dans une étude particulièrement importante pour l’histoire des mathématiques : il s’agit pour ainsi dire de l’interprétation algébrique de la théorie contenue dans le livre X des Eléments, considéré jusque là par les mathématiciens de la tradition de Pappus, même de l ’importance d’Ibn al-Haytham, comme un livre de géométrie. Avec nos algébristes, ces concepts se rapportent désormais aux grandeurs en général, numériques et géométriques, et la théorie prend sa place, par l’intermédiaire de l’algèbre dans le domaine de la théorie des nombres.

RECOMMENCEMENTS DE L ’ALGÈBRE 39

Sans se poser fort heureusement la question de l’existence du corps des nombres réels, al-Karajï et ses successeurs partent des définitions du livre X pour se placer immédiatement à un plan général. Pour se donner les conditions au moyen desquelles il peut reconnaître que les expressions obtenues par combinaison de plusieurs radicaux sont irrationnelles, al- Karajï procède comme Euclide, à cette différence près cependant qu’il étend les concepts du livre X à toute quantité algébrique.

Dans al-Badi\ il écrit:

“les monômes sont infinis : le premier est rationnel absolument comme cinq, le deuxième est le rationnel en puissance, comme racine de dix, le troisième est défini par rapport à son cube, comme le côté de vingt, le quatrième est la médiale définie par rapport à son carré-carré comme la racine de la racine de dix, le cinquième est le côté du quadrato-cube, ensuite le côté du cubo-cube et ainsi se divise à l’infini” .

De la même manière que les monômes, les binômes se divisent à l’infini. A la suite de cette explication, les mathématiciens donnent des règles générales pour les différentes opérations, en particulier:

( 1/m + yl/m ^ [yKxlyf^"' ± If]^/'"

et reprennent comme al-Samaw*al un bon nombre des problèmes du livre X pour donner des solutions algébriques équivalentes à celles d’Eu- clide, ou d’autres solutions nouvelles.

C ’est donc avec cette tradition que se constitue l’algèbre des polynômes et que l ’on parvient à une meilleure connaissance de la structure algébrique des nombres réels; notons en outre un nouveau retour à la théorie des nombres, lequel fournit à la discipline de ces algébristes les instruments qui lui manquaient. Ce retour est orienté: la préférence est désormais accordée aux démonstrations algébriques; c’est précisément à cette occasion que l ’on voit apparaître une forme de démonstration par induction mathématique finie.

Dans un chapitre à'al-Fakhrî intitulé; “ Chapitres et théorèmes utiles à la résolution des problèmes au moyen de l’algèbre” , de même que dans un texte de l’auteur qui fut conservé par son successeur al-Samaw’al, al-Karajî reprend quelques-uns des problèmes de la théorie des nombres, tel celui de la somme de n premiers entiers naturels, de leurs carrés et de leurs cubes; de la formule du binôme,... Si certains de ces théorèmes restent chez al-Karajî sans démonstration véritable, s’ils se présentent

40 R. RASHED

encore sans démonstration dans les livres des arithméticiens comme al- Baghdâdï (mort en 1037) par exemple - dans al-Takmila - au X lle siècle, en revanche, ils sont prouvés algébriquement. Il s’agit entre bien d’autres des propriétés suivantes:

2 » ( « + 1) (2n + 1)

fc=l

n / n \2

k = l \ k = l /(2)

toutes deux prouvées, comme nous l’avons montré ailleurs, par une forme gauche de l’induction complète appelée “ régression” .

(3) (a + i ) " = i k = l

(4) (aby = a et b commutant et ne N

toutes deux prouvées par une forme d’induction complète pratiquée encore d’une certaine manière, au XVIIe siècle.

Mais al-Karajî et ses successeurs n’ont pas produit seulement dans les chapitres d’algèbre que l’on vient de voir; leur oeuvre s’étend à bien d’autres domaines: la théorie des équations bicarrées, l’analyse indéterminée, les systèmes d’équations linéaires. En ce dernier chapitre par exemple, al-Samaw’al résout un système de 210 équations à 10 inconnues.

A part l’ensemble de ces résultats et des nouvelles méthodes liées à l’arithmétisation de l’algèbre, relevons l’apparition d’une certaine réflexion sur les mathématiques, une philosophie non du philosophe mais du mathématicien. Même si cette réflexion ou philosophie est thématique et non systématique, même si, comparée aux systèmes métaphysiques célèbres du moyen âge, elle peut paraître d’architecture sommaire et d’argumentation faible, elle eut au moins l’avantage d’être provoquée par la pratique du mathématicien à l’oeuvre. C ’est peut-être pour cette raison qu’elle n’est pas mentionnée dans l’histoire de la pensée médiévale, absorbée par la philosophie traditionnelle, le “ kalàm” , et la réaction traditionaliste à ces tendances représentées par Ibn Taymiyya ou Ibn Hazm. Quoi qu’il en soit, même si cette pensée emprunte ses thèmes à Pappus ou éventuellement à Proclus, l’intervention de la nouvelle algèbre est manifeste; elle donne aux thèmes des contenus différents.


A partir de l’algèbre en effet, on engage la réflexion sur le statut de cette discipline, ses rapports avec la géométrie, sa méthode, la classification des problèmes et des propositions. Rappelons à ce propos qu’al-Samaw*al, après avoir explicitement identifié algèbre et analyse, devait ainsi modifier la position de ce thème qui resta essentiel pendant de longs siècles de philosophie mathématique: l’analyse et la synthèse; il renvoie d’ailleurs à un ouvrage entièrement consacré à ce problème qui n’a malheureusement pas été retrouvé. Chacun sait l’importance de cette identification au XVIIe siècle. Plus encore, dans le langage de la logique de son époque mais recouvrant un contenu différent, le même al-Samaw*al donne une classification des propositions mathématiques aussi importante que difficile à interpréter. C ’est ainsi qu’il classe les propositions en:

I. Nécessaires;II. Possibles;

III. Impossibles.

I. Les propositions nécessaires: a: Première sous-classe:a-1: “ les propositions” ou “ les problèmes dont le recherché se trouve

dans tous les nombres” , autrement dit les identités: exemple: si z = x + y alors z jx + zjy= (z lx) • (z/y).

a-2: “ dont le recherché se trouve en une infinité de nombres” , autrement dit proposition qui a une infinité de solutions sans être une identité:exemple x+ lO = a ^

x - lO = b ^a-3 : “ dont les solutions sont nombreuses mais [en nombre] fini” beau

coup de problèmes indéterminés servent d’exemples. a-4: “ qui a une seule solution” : exemple xa = u , xb = u=^u=alb^. b : Deuxième sous-classe : l ’auteur classe une deuxième fois les proposi

tions “ nécessaires” selon le nombre des conditions qu’elles doivent vérifier, c’est-à-dire une ou plusieurs conditions.

b-1: une seule condition: exemple, soient a et b, deux nombres donnés, déterminer xety\x^ -\-y^=a,xy=b\comme condition nécessaire on trouve

b-2: plusieurs conditions, exemple: un système d’équations de n équations à m inconnues,

42 R. RASHED

II. Les propositions possibles:II s’agit de propositions dont on ne sait démontrer ni la vérité ni la fausseté ou, comme l’écrit al-Samaw*al: “ En toute proposition que considère l’algébriste ou le géomètre, il obtiendra inévitablement une démonstration de son existence (l ’existence de ses solutions) et il l’appellera alors nécessaire, ou de son (leur) impossibilité, il l ’appellera alors impossible, ou encore il ne trouvera de démonstration ni de son (leur) existence, ni de sa (leur) négation ou impossibilité ; il n’en sait rien donc et l’appellera alors possible, puisqu’il n’aura pu démontrer ni son (leur) existence, ni sa (leur) négation. Car ceci (si l’on démontre l’existence et la non-existence) renverrait alors à la négation de ce qui est et à l ’impossibilité du nécessaire, ce qui est absurde.” L ’auteur ne donne malheureusement, l’on comprendra pourquoi, aucun exemple. Il rappelle seulement qu’il ne faut pas confondre problèmes possibles et problèmes indéterminés: ces derniers, en elfet sont nécessaires.

III. Les propositions impossibles:Il s’agit de propositions qui “ si l ’on supposait l’existence (de ses solutions), cette existence conduirait à une absurdité” .

Le moins que l’on puisse dire est que cette réflexion sur la pratique mathématique, notamment de la nouvelle algèbre, a conduit le mathématicien à infléchir les notions aristotéliciennes de nécessaire, possible et impossible vers celles de calculabilité et indécidabilité sémantique. Elles sont en outre mises en rapport avec la notion de résolubilité d’une équation et plus généralement de calculabilité.

Lorsque al-Samaw*al parle d’une proposition nécessaire A, il veut dire prouver A ou non A, tandis que par proposition possible A, il entend que A est indécidable ou que l’on n’a guère de méthode soit pour prouver A, soit pour réfuter A.

On voit donc comment la nouvelle pratique du mathématicien a provoqué une réflexion de philosophie mathématique. L ’historien de la philosophie médiévale arabe aurait tort, croyons-nous, de l’ignorer.

II

L ’on vient de voir que le projet des algébristes arithméticiens se présente directement sous le signe de l’extension; celle du domaine d’ap-


plication des opérations arithmétiques. Les résultats obtenus par ces mathématiciens ne sont pas importants seulement par eux-mêmes, mais également parce qu’ils ont rendu possible un autre commencement de l ’algèbre. Celui-ci n’est plus lié à l’arithmétique mais se rattache à la géométrie. Il se présente de prime abord beaucoup moins sous le signe de l’extension que sous celui de la systématicité : il s’agit d’organiser l’étude des équations cubiques et d’en élaborer la théorie. Pour comprendre la portée de cette tâche, il nous faut revenir à l’histoire de la théorie des équations cubiques, et tout d’abord à l’exposé qu’en a donné al-Khay- yâmî lui-même (1048-1123).

Dans son algèbre, al-Khayyâmï écrit:

Il se rencontre dans cette science (l’algèbre) des problèmes dépendant de certaines espèces très difficiles de théorèmes préliminaires, dans la solution desquels ont échoué la plupart de ceux qui s’en sont occupés. Quant aux Anciens, il ne nous est pas parvenu d’eux d’ouvrage qui en traite; peut-être, après avoir cherché les solutions et après les avoir étudiées, n’en auraient-ils pas pénétré les difficultés. Ou peut-être leurs recherches n’en exigeaient pas l’examen; ou enfin leurs ouvrages à ce sujet, s’il y en a, n’ont pas été traduits dans notre langue. Quant aux modernes, c’est al-Mâhâni qui, parmi eux, conçut l’idée de résoudre algébriquement le théorème auxiliaire employé par Archimède dans la quatrième proposition du second livre de son traité de la sphère et du cylindre; or, il fut conduit à une équation renfermant des cubes, des carrés et des nombres qu’il ne réussit pas à résoudre après en avoir fait l’objet d’une longue méditation. On déclara donc que cette solution était impossible, jusqu’à ce qu’apparut Ja‘far al-Khâzin qui résolut l’équation à l’aide des sections coniques.

Al-Khayyâmi poursuit:

Après lui (al-Khâzin) tous les géomètres auraient besoin d’un certain nombre des espèces des susdits théorèmes et l’un en résolut une, l’autre une autre. Mais aucun d’e i « n’a rien émis sur l’énumération de ces espèces, ni sur l’exposition de cas de chaque espèce, ni sur leurs démonstrations, si ce n’est relativement à deux espèces, que je ne manquerai pas de faire remarquer. Moi, au contraire, je n’ai jamais cessé de désirer vivement faire connaître avec exactitude toutes ces espèces, ainsi que de distinguer parmi les cas de chaque espèce les possibles d’avec les impossibles, en me fondant sur des démonstrations.

Dans ce texte important pour l’histoire de l’algèbre, al-Khayyâmï aflirme donc que:

(1) Rien n’est parvenu des Grecs concernant la théorie des équations cubiques. Si Archimède a posé un problème géométrique en mesure d’être ramené à une équation cubique, ni lui ni ses commentateurs n’ont toutefois pu formuler algébriquement ce problème. C ’est à al-Mâhâni qu’est revenue cette tâche et à al-Khazîn qu’ il faut attribuer la solution.

44 R. RASHED

Mais ni l’un, ni l’autre, ni leurs prédécesseurs, ni leurs contemporains, n’ont essayé d’élaborer une véritable théorie des équations cubiques.

(2) L ’on doit distinguer non seulement entre un problème géométrique pouvant être ramené à une équation cubique et sa traduction algébrique, mais encore entre la résolution de l’un ou l’autre de ces problèmes et l ’élaboration d’une théorie des équations cubiques.

Le problème du statut de cette théorie se précise: l’appréciation de sa propre oeuvre par al-Khayyânü correspond-elle à l’histoire effective, au moins telle que nous la connaissons?

Chacun sait que les mathématiciens grecs avaient rencontré les problèmes de duplication du cube, trisection de l’angle, tous deux problèmes du Sème degré. Plus encore, les mathématiciens arabes ont connu et largement discuté la proposition auxiliaire utilisée par Archimède, mais dont la démonstration manque au Traité sur la sphère et le cylindre. On sait également qu’elle peut être ramenée à une équation cubique de la forme

— ex+a^b=0 qui fut résolue par Eutocius et à nouveau par des mathématiciens arabes comme Ibn al-Haytham. Cette solution eut pour moyen l’intersection de la parabole x^=ay et de l ’hyperbole y {c—x)=ab. A aucun moment cependant les mathématiciens, avant al-Mâhânï, n’avaient songé à ramener ce problème ou un autre, tel la duplication du cube {x ^ = l), à leurs expressions algébriques.

Il est significatif que la tendance à traduire algébriquement les problèmes du 3ème degré se renforce au Xe siècle pour deux raisons, au moins: le progrès manifeste de la théorie des équations du second degré et les besoins de l’astronomie. Le progrès de la dite théorie a donné aux al- gébristes le modèle des solutions algébriques - par radicaux - auquel ils veulent se conformer pour les équations de degré supérieur et surtout de l’équation cubique. L ’astronomie a posé, directement, des problèmes multiples du 3ème degré. Al-Màhânî (mort en 874-884?) fut lui-même astronome. Mais c’est surtout al-Bïrûnï (973-1048) qui pour déterminer les cordes de certains angles afin de construire la table des sinus, formula explicitement les deux équations cubiques:

— 3;c — 1 = 0 où ;c est la corde d’un angle de 80°— 3jc + 1 = 0 où jc est la corde d’un angle de 20°

Ces deux équations ont été résolues par tâtonnements.


Or ces traductions algébriques de problèmes du 3ème degré par al- Mâhâni, al-Bîrüni et d’autres mathématiciens contemporains de ce dernier, comme Abu’l-Jùd ibn al-Layth, ont posé un problème jusque-là impensé: peut-on ramener ces problèmes à des équations cubiques? peut- on par ailleurs classer l’ensemble des problèmes du 3ème degré, sinon pour tenter une solution aussi élégante - par radicaux - que celle de l’équation du second degré, au moins pour donner des solutions systématiques? Ces deux questions ne pouvaient être pensées sans le développement de la théorie des équations bicarrées et du calcul algébrique abstrait, c’est-à- dire sans le premier renouvellement de l’algèbre avec al-Karajï. Pas plus les mathématiciens grecs que les mathématiciens arabes n’avaient, avant ce renouvellement, posé la question. Le problème et la démarche d’al- Khayyâmï pour lui fournir une solution va constituer un autre commencement de l’algèbre.

Avant d’entreprendre leur solution, al-Khayyâmï commence donc par donner une classification des équations de degré inférieur ou égal à 3, On a parfois assimilé cette étude à une théorie géométrique des équations cubiques. Si toutefois par théorie géométrique l’on entend l’utilisation de figures géométriques pour déterminer les racines réelles positives de ces équations, cette assimilation est sans doute abusive. Car la figure géométrique ne joue qu’un rôle auxiliaire dans l’algèbre d’al-Khayyâmï, et surtout dans celle de son successeur Sharaf al-Dïn al-Tùsî (mort en 1213 environ); et loin de s’astreindre à ces figures, les mathématiciens pensent fonction et étudient au moyen de leurs équations : les courbes. En effet si les solutions de ces équations sont obtenues au moyen de l’intersection de deux coniques, il reste que, dans chaque cas, cette intersection est démontrée algébriquement, c’est-à-dire au moyen des équations des courbes. Ainsi dans l’oeuvre d’al-Khayyâmî et surtout dans celle d’al-Tùsï, et sans entrer dans le détail de leur démonstration, on trouve parmi bien d’autres les exemples suivants :

- La méthode poursuivie pour résoudre x^ + ax=b revient à résoudre simultanément les deux équations :

/1 b

2 a(équation du cercle)

x^ = y ja y (équation de la parabole)

46 R. RASHED

OÙ ^a\ le double du paramètre de la parabole: b = ad, d: diamètre du cercle.

- ce qui donne l’équation; A:(x^+ûrjc—è)=0 . En éliminant la solution triviale on obtient bien l’équation cherchée.

- La méthode poursuivie pour résoudre x^=ax-{-b revient à résoudre simultanément les deux équations :

— y/a y équation de la parabole

y équation de l’hyperbole équilatère

où y/a\ le double du paramètre de la parabole, bja diamètre transversal de l’hyperbole.D ’où x{x^ — ax—b)=Q. Si l ’on élimine la solution triviale, on obtient notre équation.

On peut encore multiplier les exemples, pour montrer qu’une histoire encore à faire de la géométrie algébrique ne peut se faire sans l’examen de l’apport de ce courant algébrique à cette discipline.

Aussi importantes que cette étude sont la saisie et l’expression par al-Tüsï de l’importance du discriminant dans la discussion des équations cubiques. Ainsi pour considérer l’existence des racines positives de l’équation x^ + a = bx {a, b'^0), il constate d’abord que toute solution (positive) de cette équation doit être plus petite ou égale à b ' ; car si Xq est une racine, on obtient:

x l + a = bxQ d’où Xq ^ bxQd’où Xq < ô

d’autre part cette racine doit vérifier l’égalité bx—x^ = a.Al-Tüsî cherche la valeur pour laquelle y = b x —x^ atteint son maxi

mum, et trouve en annulant la dérivée première : x = {bl3y^^. Ce maximum est donc:

b{bl3y/^ - {blZfi^ = 2{b l3fi^ .

Il existe donc une racine positive si et seulement si


Le rôle du discriminant D = b^ l2 7 -a j4 est ainsi établi et algébriquement élaboré pour l’étude de l’équation cubique.

Déjà localisé, le rôle du discriminant n’est cependant pas généralisé : le discriminant n’intervient pas encore dans les solutions canoniques, c’est- à-dire par radicaux. C’est pour remédier à cette difficulté que les mêmes mathématiciens ont développé une méthode de résolution des équations numériques à laquelle se rattache pour l ’essentiel la méthode dite “ de Viète” , comme je l’ai montré ailleurs.

On savait en effet qu’al-Khayyâmï avait trouvé une telle méthode pour résoudre les équations x" = q. On savait aussi qu’avant al-Khayyâmî, al- Birüni s’était occupé du même problème. Mais du traité d’al-Bïrünï il ne reste que le titre, tandis que de celui d’al-Khayyâmî on n’a qu’un résumé récapitulatif, qui permettra de comprendre que cette méthode avait pour base le développement de (a+b-\— k)", neN. Grâce au Traité des équations d’al-Tûsi, on connaît maintenant non seulement l’existence d’une telle méthode pour des équations de type x" = , mais pour le cas général. Cette méthode apphquée par al-Tùsï à toutes les équations traitées, peut être décrite rapidement de la manière suivante:

x ” + ûi c" H----- h a „ -ix = N

et posons / (:ic)= jc"+ ûtix"“ H----- H _ ix.La fonction est plusieurs fois dérivable. On peut reconnaître à quel in

tervalle appartient la racine, soit xe [10^ lO'’" ], x est donc de formep l(y + p i 10 “ H----- hp, et tel que r = [mjn] où m est l’ordre décimal deN, [m/n] est la partie entière de mjn.

- On détermine =polO*^ ou bien par division ou bien par la recherche du plus grand entier de n® puissance contenu dans N.

- On pose Nx = N — f (^ i)

et x = x ^ + x 2 , N i = g {x 2) où g est un polynôme en X2 dedegré « — 1.

On obtient comme valeur approchée de X2 , x^ définie par:

i V i = n x ’[ ~ ^ x 2 + a i { n — 1 ) x \ ~ ^ x 2 H------- \ - 2 a „ ^ 2 X i ^ 2 ++ a„_iX2

On reconnaît ici la dérivée de / au point x^

(1)

48 R. RASHED

et

X2 =f ' M

On opère ensuite par itérations successives.Supposons déterminées

x = + ^2 + ” * 4 - X f c _ i k = 2,...,n

Une valeur approchée de est donnée par la formule:

Nu (2)où

Nk = N - f {x^ + x '2

= ^ l + ^ 2 + - ^ k - l

Ainsi une valeur approchée de x sera:

Xi + ^2 H----- 'r x'„ où les X- sont donnés par (2).

Or si al-Tûsï n’applique cette méthode qu’à l’objet auquel il consacre son Traité, les équations de degré inférieur ou égal à 3, tout indique cependant qu’il l ’avait conçue d’une manière générale. D ’ailleurs le résumé récapitulatif d’al-Khayyâmî exposait déjà le problème en toute généralité.

Méthode de résolution des équations numériques, études des courbes au moyen des équations, localisation du rôle du discriminant dans la solution des équations cubiques, sont les chapitres de l’algèbre renouvelée. La distance parcourue depuis l’oeuvre d’al-Khwarizmi ne se mesure donc pas seulement par rapport à la seule extension de la discipline mais aussi par le changement de sens de la connaissance algébrique. Si en effet l’algèbre s’affirme comme la science des équations algébriques, celles-ci ne sont pas seulement liées à des nombres et à des segments, elles se rapportent également à des courbes dans le plan, l’algèbre intègre alors des techniques présentes dans la tradition qui a participé activement à son renouvellement: celle des infinitésimalistes. On peut citer parmi ces techniques l’usage des transformations affines par un infinitésimaliste comme Ibrâhîm ibn Sinân.


C’est ainsi qu’al-Jusï, au moyen d’une transformation affine x ^ x + a ou x -^ a —x, réduit les équations à résoudre à d’autres équations dont il connaît la solution.

Pour résoudre ces équations, al-Tüsï étudie le maximum des expressions algébriques. Il prend d’une manière systématique, sans toutefois la nommer, la dérivée première de ces expressions qu’il annule, et démontre que la racine de l’équation obtenue, substituée dans l’expression algébrique, donne le maximum.

Une fois qu’il a trouvé l’une des racines d’une équation cubique, il lui arrive, pour déterminer l’autre racine, d’étudier une équation du second degré qui n’est autre que le quotient de la division de l ’équation cubique par (x — r ), où r est la racine trouvée. En d’autres termes, il sait que le polynôme ax^-\-bx^+ cx + d est divisible par { x - r ) , si r est une racine de l’équation ax^+bx+cx-V d=0 .

Enfin après avoir étudié l’équation, il essaie de déterminer une borne supérieure et une borne inférieure de ses racines réelles.

Si nous avons tenu à rappeler ces résultats, ce n’est pas seulement pour présenter des faits historiques encore inconnus, mais surtout pour montrer le niveau théorique et technique de cette algèbre et la complexité des problèmes historiques qu’elle pose dès que l’on cesse de recenser les résultats pour en comprendre l’histoire. C ’est ainsi que l’on voit apparaître avec ces algébristes l’emploi de la dérivée au cours de la discussion des équations algébriques et au cours de la résolution des équations numériques. Chacun sait cependant que, lié à la recherche des maxima, l’usage de la “ dérivée première” n’était pas nouveau. Cependant, suscité par tel exemple ou tel autre, il restait occasionnel, et ce n’est qu’avec ces algébristes et surtout avec al-Tüsï que la notion de dérivée deviendra partie intégrante de la résolution des équations algébriques et numériques. La généraUsation de cet usage sera en fait obtenue à la suite de celle de la théorie des équations que l’on essayait alors d’élaborer, d’une part, et par les recherches des mathématiciens dont l’activité s’exerçait en d’autres domaines, d’autre part.

En effet, les travaux de Banü Mùsâ, d’Ibn Qurra, de son petit-fils Ibrâhîm ibn Sinân, d’al-Qühï, d’Ibn al-Haytham et de tant d’autres non algébristes sur les déterminations infinitésimales ont indirectement préparé les tentatives de nos algébristes. Par leur refus d’interpréter géométriquement les opérations algébriques, déjà manifeste chez Banù Mûsâ et réaf

50 R. RASHED

firmé par leurs successeurs, par la découverte de nouvelles lois arithmétiques nécessaires au calcul des surfaces et des volumes, ils ont donné à ces algébristes des techniques éprouvées pour la recherche des maxima. Mais la simple énumération et la classification des problèmes du 3ème degré, nécessaires pour élaborer la théorie des équations avec laquelle l’algèbre se confondait déjà, la recherche d’une méthode pour résoudre des équations cubiques ont étendu le domaine d’application des techniques des infinitésimalistes et notamment de la recherche de la dérivée première. Présente grâce aux infinitésimalistes, étendue par les algébristes, la notion de “ dérivée” fut condamnée à la discrétion par suite de la faiblesse du symbolisme algébrique. C’est ce qui explique, selon nous, son usage systématique, bien qu’elle demeure sans nom ni titre.

III

Il y a un demi-siècle à peine, P. Tannery écrivait que l’algèbre arabe “ ne s’élève d’ailleurs nullement au dessus du niveau atteint par Diophante” . On peut sans doute s’étonner de lire une telle appréciation, qu’elle pût encore se faire, surtout après les travaux de Woepcke. Mais en deçà de tout étonnement, on peut voir dans cette appréciation beaucoup plus l’idéologie de l’historien que les conclusions de son propre travail historique. D ’ailleurs si dans le cas de P. Tannery cette idéologie est apparente, elle est souvent moins manifeste chez d’autres historiens comme Zeuthen et plus récemment Bourbaki.

Si j ’ai tenu à rappeler l’afiîrmation de Tannery, c’est beaucoup moins pour redresser un tort fait à l’histoire de l’algèbre que pour montrer une difficulté majeure de l’étude sociologique de la science dans son histoire. Pour un P. Tannery, par exemple, cette étude ne pouvait être que la réponse à la question: quelles sont les conditions culturelles à la suite desquelles l’algèbre est restée sans progrès aucun, dans l’état où elle a pu se présenter chez les Anciens? Et faute de s’interroger sur les conditions de la production algébrique, l’on se préoccupe de son absence; or le résumé que nous venons d’en faire montre bien que l’on est nécessairement amené à se demander pourquoi et comment l’algèbre s’est renouvelée, non seulement par rapport aux Anciens - à supposer d’ailleurs qu’ils aient eu une algèbre - mais également par rapport aux premiers algébristes arabes : al-Khwarizmi et Abù Kâmil.


Déterminée par l’idéologie de l’historien, la manière de poser la question ne peut donc entraîner que des réponses contradictoires. Manifeste au niveau de la question, cette idéologie se retrouve dans la formulation de la réponse. Supposons pour un moment que la deuxième question soit globalement la bonne, rien n’interdit de chercher la réponse dans des directions différentes. C ’est ainsi que, partis du développement incomparable de l’algèbre par rapport aux mathématiques hellènes et médiévales latines, M. Arnaldez et le regretté L. Massignon ont pensé que l’arabe comme langue sémitique “ a eu pour résultat d’infléchir les connaissances qu’elle exprimait dans le sens d’une pensée analytique, atomistique, occasionnaliste et apophtegmatique” . Une étude récente sur “ l’involution sémantique de concept” expose comment les langues sémitiques tendent à la formation abrégée et abstraite, “ algébrisante” , par contraste avec la “ géométrisation aryenne” . Selon ces auteurs la structure linguistique est donc responsable du développement “ d’une science des constructions algébriques” . Il est donc clair que même si c’est la bonne question qui est posée, rien ne défend la réponse contre une autre idéologie, qui remonte dans le précédent exemple à Ernest Renan.

S’interroger sur les raisons historiques de la production algébrique doit donc passer d’abord par le rejet de l’idéologie à plus d’un niveau : celui de la question et celui des éléments de la réponse. Mais une condition nécessaire et manifestement non suffisante de neutralité idéologique serait de connaître d’abord l’état de la discipline examinée. Pour l’historien des sciences arabes cette connaissance reste fragmentaire et imparfaite. Cette simple constatation montre que nous sommes encore loin du but de ce colloque et qu’il est prématuré de poser à l’heure actuelle la question des conditions sociales de la production scientifique.

Deux autres éléments nous confirment dans notre attitude, il faut bien l’avouer, négative. En effet, pour l’algèbre examinée ici, un problème algébrique ne peut être posé que de manière intrinsèque, et l’autonomie de l’algèbre est déjà recherchée et confirmée au plan de la production des théorèmes et de l’invention des propositions. La part des philosophies, des idéologies, est reléguée à une seconde et lointaine instance. Cette clôture épistémologique caractérise toute discipline formée et la question des conditions de la production doit, avant d’être proposée, à la fois se médiatiser et se fragmenter. Sa médiatisation exige que l’on passe par toutes les disciplines - ici arithmétique, trigonométrie, astronomie d’observa-

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tion... - auxquelles la discipline est liée; sa fragmentation requiert que l’on connaisse les poids respectifs des facteurs culturels qui peuvent d’une manière ou d’une autre influencer la production scientifique. A défaut de pouvoir détailler, on tombe forcément dans l’une ou l’autre de ces deux illusions: transcendantale ou empirique. La première fait prendre les moyens de poser le problème pour le problème lui-même, et ainsi les éléments d’une doctrine durkheimienne, weberienne ou même marxiste pour l’explication elle-même. On a le plus souvent des considérations générales qui ne cernent pas les faits que l’on est censé expliquer. L ’illusion empirique laisse croire que l’énumération des éléments culturels est une réponse suffisante. Ces deux illusions toutefois dominent encore les explications du phénomène de la production scientifique.

Elles ne peuvent d’ailleurs que se renforcer dans le cas qui nous intéresse ici, à cause de la rareté même des études scientifiques sur l’empire musulman et surtout sur son, ou ses systèmes économiques.

Mais est-on fondé de se réfugier en cette position négative, s’interdisant tout examen du problème proposé à ce colloque? Une attitude rigoriste ferait pencher vers cette abstention, sans doute à juste titre, mais en laissant la place aux considérations les plus vagues. Je pense qu’il importe ici de prendre ses risques en exploitant la seule possibilité qui reste: formuler des conjectures plausibles mais qui ne prétendent nullement remplacer une véritable réponse, indiquer une ou plusieurs hypothèses de recherche. II faut donc s’engager à médiatiser la question des déterminations sociales de la nouvelle algèbre, et au lieu de la prendre pour poiht de départ, revenir aux disciplines qui ont le plus activement participé à son avènement.

Entre toutes, deux disciplines ont contribué à la constitution de la nouvelle algèbre: l’arithmétique et les différentes branches de l’astronomie d’observation. La première est intervenue dans la transformation de l’ancienne algèbre, nous l’avons vu, par la transposition de ses opérations à l’algèbre, une fois ces opérations dégagées et systématisées, et également par la généralisation au niveau des expressions algébriques de certaines de ses techniques telles que l’algorithme d’EucUde pour la division et l ’extraction de la racine carrée. L ’astronomie, pour ses propres besoins, a contraint l’algébriste à reprendre le problème des équations numériques et surtout étudier les courbes au moyen des équations.

La question des déterminations sociales de la nouvelle algèbre se


précise et se pose de prime abord en liaison avec les différentes branches de l’astronomie et de l’arithmétique. Seul l’exemple de l’arithmétique nous préoccupe ici.

Si l’on revient à l’oeuvre des arithméticiens qui ont précédé l’avènement de cette algèbre, algébristes eux-mêmes dans la plupart des cas, on constate souvent une double préoccupation: développer leur discipline, lui fournir “ un domaine d’exercice” . Par “ domaine d’exercice” nous entendons un terrain d’exemples, sans liaison nécessaire, où l’application de l’instrument mathématique est suscitée pour rationaliser une pratique empirique, donc résoudre théoriquement des problèmes pratiques. On peut alors mesurer la portée de l’instrument mathématique, indépendamment de l’importance de l’exemple choisi ou de l’efficacité de la solution obtenue.

Développement théorique et application de l’arithmétique pour rationaliser une pratique empirique, telles sont les deux tâches souvent assignées par les mathématiciens à leurs traités d’arithmétique. Elles permettent d’identifier quelques orientations de la recherche.

La composition et l’étendue de l’empire ‘abbasside ont mis en présence et confronté plusieurs arithmétiques. Deux d’entre elles, digitale et indienne, ont posé aux mathématiciens des problèmes à la fois théoriques et pratiques. SoUicités en particulier par l’administration de l’État, les mathématiciens ont essayé de développer chacune d’elles à l’aide d’autres connaissances mathématiques, justifier les règles de chacune, les comparer plus ou moins implicitement, les composer pour parvenir à en fonder et faciliter l’usage, donner une sorte de vade-mecum du fonctionnaire. Parfois, d’ailleurs, un même mathématicien composait un traité pour chaque arithmétique: al-Karajï, par exemple.

Que les traités d’arithmétique aient été suscités, au moins en partie, par les besoins de l’administration, le fait est attesté par les auteurs eux- mêmes.

Dans son traité: Des besoins en science arithmétique des ^'kuttàb'* ( écrivains, secrétaires, fonctionnaires des bureaux de l ’administration) , “ ummâV* (préfets, percepteurs des impôts) et autres” , al-Bûzjanï présente ainsi son livre comme “ un livre comprenant l’ensemble de ce dont ont besoin l’accompli et le débutant, le subordonné et le chef en arithmétique, art du fonctionnaire Qiinà at al-kitâba), pratique de l’impôt foncier et toutes les sortes de pratiques en cours dans les dlwâns, proportion, multiplication,

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division, mensuration, taxe foncière, partage, change et autres pratiques utilisées par les différentes catégories des hommes pour traiter entre eux de leurs affaires et dont ils ont besoin dans leurs moyens de vivre” .

La même préoccupation se manifeste dans le traité d’al-Karajï: al- Kàfi.

On la retrouve mais simplement indiqué dans les traités d’arithmétique indienne. C’est ainsi qu’Ibn Labbân (1000 environ) écrit en conclusion de son ouvrage: “ Ces fondements sont suffisants pour l’ensemble du calcul astronomique et des pratiques en cours entre les hommes” . Son élève al-Nasawi (1030 environ) qui avait commencé par composer un traité d’arithmétique en persan pour l’administration de Rayy, en donna par la suite une version arabe, “ de manière à ce que les hommes en fassent usage dans les différentes affaires en cours entre eux et les astronomes dans leur art” .

On pourrait multiplier les exemples empruntés aux mathématiciens de cette génération, c’est-à-dire dès la fin du IXe siècle. C’est en effet la période de l’empire ‘abbaside où l ’on assiste:

(1) à la consolidation et au développement des institutions administratives au niveau de l’empire,

(2) à la multiplication des images réduites de ces institutions au niveau des provinces, par suite de l’affaiblissement du pouvoir des Khalifs,

(3) à l’apparition d’une couche sociale, celle des “ kuttâb” ou fonctionnaires, liée à la multiplication des administrations {dlwàns) et de leurs images réduites.

L ’existence autonome de cette couche sociale, son poids sociologique, étonnaient déjà les historiens de l’époque: Al-Tabarï, al-Sûlï, al-Mas'üdï, et surtout al-Jahshayârï, dans son livre Al-Wyzara wa’l kuttâb, en ont donné une description détaillée. On sait d’ailleurs que l’arabisation des dlwàns avait commencé relativement tôt, entre 700 et 705 selon les provinces, comme le rappellent al-Jahshayârï et al-Kindï, l ’historien.

A la fin de l’empire ‘ummayade, un de ces fonctionnaires, Hârùn ibn ‘Abd al-Hamïd, traçait déjà le type idéal de ses collègues. D ’après un texte conservé par al-Jahshayàrî et rapporté par Ibn Khaldûn, on sait qu’il s’agit d’un lettré connaissant son arithmétique. Outre des qualités morales et sociales, il doit posséder des connaissances en arabe, histoire, arithmétique et sciences religieuses, selon les besoins de son travail. C’est en ce sens que A. Metz écrit que le fonctionnaire “ est le représentant de la cul


ture littéraire et qu’il ne traitait des sciences religieuses que selon les besoins de son travail et de sa culture” . Il ajoute: “ Cette couche de fonctionnaires est ce qui distingue le plus l’État musulman de l’Europe au début du moyen âge” .

En sorte que c’est l’existence de cette couche sociale qui a incité, pour la formation de ses membres, à la rédaction de traités, non seulement en arithmétique, mais également en géographie économique, comme le célèbre livre de Qudâma ibn Ja'far sur l’impôt foncier, de lexiques de la langue philosophique, économique, scientifique de l’époque, comme celui d’al-Khwarizmi: Mafâtîh al-^ulûm. Or pour caractériser cette couche, l’on ne peut mieux dire que C. Cahen, quand il écrit: “ Une bureaucratie, c’est-à-dire régime dominé par une armée de scribes spécialisés devenus une sorte de caste qui dure quand califs et vizirs passent; paperasserie, c’est-à-dire régime dans lequel est couché par écrit en détail tout ce qui peut l’être selon des règles techniques ou stylistiques qui, connues d’eux seuls, leur assurent le monopole des métiers” . Dîwàns financiers, Dlwàns de l’armée, Dlwàns des postes (des renseignements généraux), Dlwàns des correspondances (chancellerie), et un bon nombre d’autres Dlwàns avaient tous en commun un besoin de compatibilité financière et étaient demandeurs de traités d’arithmétique sûrs et maniables pour leurs pratiques.

Or, ce que l’on a convenu d’appeler “ domaine d’exercice” de l’arithmétique est constitué précisément par ces problèmes posés aux fonctionnaires des Dlwàns, C ’est ainsi que les chapitres 4 et 5 d’Abu’l Wafâ* sont consacrés aux problèmes financiers comme tels, tandis que le chapitre 6 concerne les questions de gestion des biens, paiement aux soldats de leurs salaires, gages et soldes, les licences de passage à accorder ou à refuser aux navires de commerce voyageant sur les fleuves et aux marchands circulant sur les routes, les envois de correspondances et courriers, et toutes autres affaires administrées par les Dlwàns.

On comprend dès l’abord, par la confrontation des deux arithmétiques, que facilité et rapidité du maniement sont devenues des critères de préférence. C’est en effet pour marquer l’importance de l’arithmétique indienne qu’al-Uqlîdisï avançait ces valeurs pratiques et écrivait:

La plupart des arithméticiens sont obligés de s’en servir dans leur pratique: pour ce qu’elle comprend de facilité et de rapidité, le peu à retenir, la brièveté du temps mis à répondre, le peu de réflexion sur ce qu’elle concerne qu’ils trouvent nécessairement entre leurs mains... Nous disons donc qu’elle est une science et une pratique, qui exigent un instrument, de même qu’en exigent un l’écrivain, le fabriquant, le chevalier dans leur

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pratique; car s’il manque au fabriquant, ou s’il lui est difficile de trouver ce par quoi il exerce sa pratique, il ne pourra parvenir à ce dont il a besoin dans cette pratique; pour saisir ceci, il n’est guère de difficulté, d’impossibilité ou de préparation”.

Il semble donc que ce soit pour répondre à deux nouveaux besoins et conformément à ces nouvelles normes que le mathématicien est revenu à l’arithmétique, digitale ou indienne, dont il entreprend de justifier les règles et d’organiser l’exposé. Ce retour, la confrontation au moins implicite des arithmétiques, a fait apparaître beaucoup plus clairement qu’auparavant la généralité et la nature abstraite du concept d’opération. Vues de cette manière, et en quelque sorte systématisées, les opérations sont dès lors des moyens d’organiser l’exposé arithmétique. La présence de plusieurs arithmétiques a eu pour conséquence, en effet, de relativiser les systèmes de numération pour montrer que l’essentiel est dans le choix de la base et dans les opérations à appliquer. Al-Uqlidisï, déjà, n’hésitait pas à déclarer: “ Il est possible de remplacer ces neuf chiffres (hurüf) par d’autres chiffres, soit par des chiffres Abjad, soit par des chiffres romains, soit par des chiffres arabes” , idée devenue commune à tel point qu’al- Khwarizmi al-kâtib peut écrire dans l’ouvrage cité: “ L ’on écrira à l’aide de ces chiffres (Abjad), comme les arithméticiens indiens, ce qui consiste à écrire au moyen de neuf chiffres, allant de V^alif au tà\ et ce signe sera posé dans les cases vides, à la place du zéro dans le calcul indien” .

Autrement dit, une fois le choix de la base effectué, on peut substituer aux chiffres de l’arithmétique indienne n’importe quel système de signes. Mais dans ces conditions, les opérations n’épousent plus l’écriture particulière du système de numération. C ’est d’une manière suffisamment générale qu’al-Karaji distingue deux classes de données: les quantités rationnelles et irrationnelles, et les opérations de multiplication, division, élévation des puissances, addition et soustraction.

Mais ce sont précisément ces opérations qui ont permis d’organiser l’exposé de manière systématique au début de l’arithmétique indienne, et si elles jouent ce rôle dans l’arithmétique digitale, c’est de manière aussi systématique, mais moins complète. C ’est ainsi que l’exposé d’al-Uqlïdisî, Ibn-Labbân, al-Nasawï s’agence par les opérations +/ —, x/-^ et par l’extraction de la racine, tandis que dans l’arithmétique digitale, on a essentiellement x/-i-, et parfois seulement l’extraction de la racine, la loi de composition + / — étant supposée connue.

Conçues de manière plus générale et plus abstraite que dans le passé,


axe d’organisation des traités, les opérations sont rendues disponibles à d’autres applications, et c’est comme telles qu’elles se présentaient à qui se proposaient d’étendre le calcul algébrique. Celui-ci pouvait également généraliser en algèbre les résultats obtenus par l’application de ces opérations en arithmétique: C ’est à al-Karajî et à ses successeurs, al-Shahrazùrï et al-Samaw’al, que revint cette tâche.

Centre National de la Recherche Scientifique. Paris

D I S C U S S I O N

R. RASHED : L ’un des thèmes de ce Colloque est le problème du rapport entre science et société dans l’histoire de la pensée scientifique. Comme ce qui m’intéresse c’est l’algèbre,il me faut d’abord décrire le plus exactement possible l’état de cette discipline: les questions que l’on va poser sur le rapport entre science-société sont déterminées elles- mêmes par la connaissance que l’historien a de l’état de cette science. Cette difficulté est encore plus grande quand il s’agit de mathématiques en général et d’algèbre en particulier. Je voudrais dire que l’algèbre est un terrain à la fois privilégié et contraignant. Privilégié dans la mesure où, si rapports il y a entre science et société, ils peuvent être déterminés par ce que j ’appelle une clôture épistémologique dans la production mathématique. Par “clôture épistémologique”, je voudrais dire simplement qu’à partir d’un certain seuil, à partir d’un certain stade de développement de la science, un théorème de l’algèbre est produit, et seulement produit, par une série d’autres théorèmes qui existaient auparavant; il n’y a pas de raisons extérieures. Cette clôture permet de rendre plus évident ce rapport science-société, de le rendre plus apparent que dans d’autres disciplines ne possédant pas la même maîtrise conceptuelle. Mais cette clôture épistémologique est justement assez contraignante dans la mesure où, s’il y a des rapports entre science et société, ou algèbre et société, il faudrait multiplier les disciplines intermédiaires pour voir à quel niveau et comment se situent ces rapports. Je vais montrer que l’on ne peut absolument pas examiner le rapport entre algèbre et société (ou conditions sociales) sans passer au moins par l’arithmétique et par l’astronomie, c’est-à- dire sans dénombrer les différentes branches de l’arithmétique et celles de l’astronomie.

J. g a g n e : Tu as affirmé tout à l’heure que la clôture épistémologique rendait le rapport que tu étudies apparent. C’est ça que je voudrais éclairer. Tu as dit: il rend le rapport plus apparent. Je me demande si au contraire il ne le rend pas moins apparent.

R. RASHED : Je préfère utiliser les mots “privilégié et contraignant” . Si par exemple l’algèbre s’est développée à partir de la résolution de questions pratiques, à ce niveau élémentaire on peut immédiatement voir l’intervention de ces raisons pratiques et de problèmes pratiques. Si, par exemple, l’algèbre s’est développée pour la détermination ou le partage d’un héritage, ceci s’intégre dans un système économique que l’on peut déterminer. On peut voir le rapport d’une manière directe. La partage de l’héritage peut utiliser de l’algèbre, mais l’algèbre dans son développement - et c’est ce que j ’essaye de démontrer - n’a absolument pas besoin du partage de l’héritage, ce qui revient à dire qu’il n’y a pas production de théorèmes, inventés pour des raisons extrinsèques.

s. VICTOR : Dès que l’algèbre se fait science, ça continue comme science indépendante ;

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là je suis complètement d’accord. Quand on invoque ces raisons pour dire qu’il n’y a jamais eu de rapport entre la répartition des héritages et le commencement de l’algèbre, je ne suis pas d’accord, parce qu’un rapport a bien existé aux débuts de l’algèbre.

R. RASHED : Ceci est peut-être vrai pour l’algèbre à ses premiers commencements avec al-Khwarizmi, Abû Kâmil... etc., mais ne l’est plus aux Xle et Xlle siècles.

G. beaujouan : Il y a un problème du décollage et, une fois qu’une science a décollé, alors elle continue à vivre sur sa logique interne avec une beaucoup moins grande sensibilité aux stimulants externes de ses débuts.

R. RASHED : Je n’ai pas dit qu’il y a une clôture épistémologique chez al-Khwarizmi ou chez Abù Kâmil. Je parle des Xle et Xlle siècles.

j. MURDOCH: But you have excluded only one kind of social relation, if you want to call it that. That is, you have excluded the influence of something exterior or social on the invention, discovery, or production of a given theorem. But this ignores, it seems to me, a much more frequent kind of thing and that is, once a theorem is discovered, once it is established, what are the social factors acting upon its utilization, its application?

R. hashed: D ’accord pour le problème des applications. Mais si l’on revient à la constitution même de l’algèbre on peut voir comment les éléments sociaux vont intervenir, c’est-à-dire non pas en algèbre en tant qu’algèbre, mais au moyen de l’arithmétique, au moyen de l’astronomie, au moyen d’autres disciplines, qui ne sont pas l’algèbre.

j. mxjrdoch: But will we get a “third man” argument here? You say that for the application of algebra to external things you have to proceed by the intermediary of arithmetic. Well, let’s take arithmetic. For the application of arithmetic - forget algebra for the moment - do you need another intermediary to apply arithmetic, and if so, why, and if not, why not?

r . RASHED : Ça dépend de l’état de l’arithmétique. C ’est pour cela que j ’ai dit qu’il fallait savoir de quelle arithmétique il s’agit. Pour le moment, j ’essaye simplement de montrer la difficulté concernant l’algèbre: Qu’appelle-t-on donc condition privilégiée et contraignante en ces disciplines qui permettent de poser le problème des rapports entre science et société? “Privilégié” dans la mesure où s’il y a un rapport, il sera plus déterminé, plus apparent que par exemple le rapport entre science et société pour la métaphysique, ou pour la physique du moyen âge, où un ensemble d’idéologies peuvent intervenir. Tel n’est pas le cas pour l’algèbre; nous avons une discipline qui est déjà neutre par rapport à ces idéologies. Donc on peut étudier directement les rapports entre science et société. Mais, d’autre part, nous sommes liés par le niveau même de cette discipline; par le fait même qu’elle est déjà scientifique, nous avons un peu les mains liées pour considérer l’intervention des éléments sociaux dans sa formation.

J. MURDOCH: Yet you would claim that our hands are less tied when it comes to the consideration of the impact of social factors upon arithmetic.

E. sylla : Isn’t it just an historical fact that when you look in algebraic works you don’t see social connections, but when you look in arithmetic works you do, they tell you about applications?

R. RASHED : That is an historical fact, but there is something more than this fact. You have at least three systems of arithmetic - Indian, digital, and sexagesimal - and the question arises why, at a certain moment, they tried to unify arithmetic. What does it mean, unify arithmetic? And how do they do it? And what are the constraints moving them to do it? The conjecture that I have made in answer to these questions is very simple: that it is the existence of a new social class, the class of scribes as a social organization. They ask for this unified kind of arithmetic; they need this kind of unification for calculations. The development of arithmetic was produced by this kind of


social need as can be proved by the books written by mathematicians like Abû-1-Wafâ’, al-Karaji, al-Shahrazüri, al-Samaw’al, etc., especially for this new class, and by the kind of problems dealt with in these books.

A. sabra: But you have to show this in a much more concrete way. That is to say, you have to show what kind of problems these people, these scribes, were working on and how and why they required this kind of unified arithmetic. Furthermore, I wonder whether in the social factors that have been proposed we have been able to go beyond considerations that are at best vague.

J. MURDOCH: Yes, but Roshdi has made it less vague in the sense that he has said that a socially catalyzed cause has conditioned developments in arithmetic which were in turn only a necessary condition for the development of algebra and that the development of algebra came out of this existing necessary condition in a totally internal way.

A. sabra : Yes, all right, but what we have been discussing is algebra, not arithmetic. And what has come out of the discussion of algebra, and out of what Roshdi himself is saying, is that in the period he has been working on the development of algebra is an internal one. That makes sense. But one wonders about what happened in the period between al-Khwarizmi and Abû Kâmil. You don’t talk about that. One doesn’t know much about it and this makes treating it a bit difficult.

r . RASHED : Yes, it is difficult just as all questions about origins are difficult. You cannot answer them. I even consider it mistaken to ask them now. One gets at best anecdotal history.

A. sabra : I don’t think that looking for origins necessarily leads to a history which is just discoveries and anecdotes. In fact, I don’t see how an historian of mathematics can get away from this question of origins. I don’t think you can ignore it. After all, it gives you a research program. One might see, for example, a certain similarity between a theorem that is found in one of those authors like al-Kâshï and something in China. Now of course it would be wrong to go on just from there and say: “See, similar, therefore, this comes from that.” No, this is not very interesting. But if this leads you to ask whether it is possible that such a transmission could have taken place, then it becomes fruitful. What you will then do with it as an historian is still a problem; I am not saying that history ends there.

r . RASHED : II faudrait tout de même prévenir le risque de voir la question des origines, si elle peut être résolue, se transformer en une question d’originalité.

G. beaujouan : Si c’est l’originalité, on retombe dans la problématique des précurseurs.

A. sabra : That is why I was trying to protect myself by saying that what you do with the question of origins afterward is something else. That is to say, the cluster of questions that are somehow involved in this concept of originality, which is not a clear concept, still remain. Take the work of someone like Kennedy. He is interested in the questions of transmission. Yet Kennedy somewhere says in one of his articles that once you have a theorem, you are faced with something that has an intrinsic value. I was very much moved by that statement because it is true. The important thing for the historian is the intrinsic value that somehow resides in a new theorem, a new discovery. But I don’t think that this releases the historian from further research. Because by bringing in questions of origins, the problem of originality and of intrinsic value becomes more complicated. It also becomes more interesting and historically richer. Once you throw this away, it seems to me that eventually you will end up by doing, not history, but something like the philosophy of science. Thus, for the time being, I am saying that the questions of origins and originality still remain.

60 R. RASHED

R. RASHED : Mais le problème des origines comprend au moins deux questions: une question d’attitude d’abord, c’est-à-dire poser le problème des origines sans le transformer en une question d’originalité; mais aussi cette autre question qui consiste à ne pas confondre la genèse historique et la structure logique de la théorie que l’on est en train d’étudier. Ces deux questions sont souvent confondues. Et c’est ça qui permet de trouver de l’algèbre chez Euclide, de la théorie de l’information chez Aristote et ainsi de suite. C’est donc une question de décision et de stratégie. Mais ceci dépend également de l’histoire des sciences dont il s’agit et quelle est notre connaissance de cette histoire. Par exemple, dans l’histoire des sciences arabes, on ne sait même pas qui a inventé quoi. Quand Luckey et beaucoup d’autres à sa suite parlaient, par exemple, de Kâshî, ils ne savaient pas que al-Samaw’al et al-Tûsi ont déjà une bonne partie des découvertes attribuées à Kâshi. Luckey et ses successeurs intéressés par la question des origines sont allés chercher celles-ci en Chine. Faute non seulement logique mais aussi historique. C’est à quoi mene la question des origines, au moins au stade actuel.

A. sabra ; What you are doing now is working in the research program of the historian filling in the gaps.

R. RASHED : J’ai dit simplement quelles sont les conditions nécessaires à un travail utile sur les origines. Ces conditions peuvent engager à refuser les solutions faciles de continuité. Faut-il rappeler que la continuité historique n’est pas nécessairement une continuité logique. Restituer historiquement une oeuvre c’est d’abord l’analyser, en saisir sa structure logique. Par exemple, étudier le texte de Karaji, comme algébriste, sans comprendre quelle est la contribution essentielle apportée par Karaji, engager aussitôt un travail sur les origines, comme c’est souvent le cas, c’est perdre l’essentiel, perdre l’apport de Karaji. Chercher les origines de son algèbre, c’est remonter nécessairement à al-Khwarizmi, Abû-Kâmil. Supposons même que l’on connaisse tous les prédécesseurs de Karaji, on ne comprendra plus, si l’on s’arrête là, l’essentiel de sa tâche, c’est-à-dire un nouveau départ de l’algèbre grâce à ce que j ’ai appelé arithméti- sation de celle-ci. Peut-être parvient-on à bien chercher les origines quand l’on sépare genèse historique et structure logique, mais alors la question des origines sera complètement transformée.

A. sabra ; What you are saying is really not against this program; you are just saying that if you have to do it you should, of course, do it well.

j. MURDOCH: One might say that your unhappiness with the history of mathematics has to do with the way it is usually done. That is, if one asks what the entities are between which we are trying to fill the gaps, in most histories of mathematics - Cantor, Tropfke, for example - what they’re doing is concentrating on results or on theorems or on particular kinds of examples. This is what is traced. It is extremely difficult to find someone tracing within algebra, let us say, the use of false position; not just where it occurs, but why. Or who used the theory of proportion? Where? Why? That is, tracing methods, conceptions, apart from results. Now that kind of thing, it seems to me, is incredibly more productive.

NAB IL SH E H AB Y

T H E I N F L U E N C E O F S T O IC L O G I C O N

A L - J A S S À S ’ S L E G A L T H E O R Y

In the Usülal-Fiqh o f Abù Bakr al-Râzï al-Jassâ§ (b. 305/917-d. 370/981), not yet published,^ there is a section devoted to what is called “ the indicant o f a discourse” and to “ that which is particularly mentioned.” Al-Jassas has this to say about them:

Every discourse (khifâb) that comes from God, exalted be He, and the prophet, upon him be peace, cannot be devoid of significance (fffida ). The meaning {m a'm ) of some (such discourse) is sometimes grasped with the intellect {ma'qûlan) through the utterance ilafy). Others signify {yufid) a judgement (fiukm) and a meaning whose explanation (bayàn) may come in a second (significant discourse). Of the discourse whose meaning is grasped with the intellect through the utterance some signify by way of indication (min jihat al-dalala) a meaning for which the utterance is not put (laysa mawdü^an lahu), as when God, exalted be He, says; “And don’t say uf (an expression of anger and displeasure) to them (your parents)” (Q, 17, 23). This signifies two meanings. One is the forbiddance of this ejaculation iqawt) itself. Also it signifies by way of indication the forbiddance of what is above that - shouting at, beating, and killing them (I, 39v).

Al-Jassas then gives a few more examples all from the Qur’an. One such example is the verse in which God addresses the prophet saying: “ I f thou asketh pardon for them seventy times, God will not pardon them” (Q. 9, 80). “ What is intended (al-murad)” al-Jassas says, “ is not this number itself but that, no matter how many times the prophet asks for it, it will not come” (I, 39v). Al-Jassas adds:

There is plenty of this kind (of discourse) in the Qur’an, the smart (traditions), and people’s habits of speaking. This is (what is called) the indicant of a discourse whose indication of what it indicates should be attentively considered (wa hâdhà huwa dalil al-khifab al-ladhi yajibu iUibaru dalâlatihi "alà mà dalla ^alayhi) (I, 39v).

Immediately after that al-Jassâs turns to the second issue: what is particularly mentioned {al-makhsüs bi’l-dhikr). He dismisses as wrong the claim that

anything (Jcullu shay') which has two descriptions (waffayn) one of which is particularly mentioned in that part of the judgement to which it is related, indicates that the other (description) is to be judged the opposite way (bi-khilafihi) (I, 39v-40r).

J. E. Murdoch and E. D. Sylla (eds.). The Cultural Context o f Medieval Learning. 61-85.AH Ifiohtv

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He also dismisses the claim that

whatever has several descriptions, some of which are particularly mentioned, indicates that the rest are to be judged the opposite way (I, 40r).

He says that there is no evidence either in language or in the shar ‘ for such claims. The hanafï viewpoint on this he says is

that that particularly mentioned... does not indicate that the others (that are not particularly mentioned) should be given the opposite judgment (I, 40r).

This is true, he continues,

whether we have two descriptions one of which is particularly mentioned or many descriptions some of which are particularly mentioned (I, 40r).

He then adds that this is what Abû’ l-Hasan al-Karkhï (b. 260/873- -d. 340/952) used to say in claiming that it is the viewpoint o f the Hanafis. Al-Karkhi said that Abû Yûsuf al-Qâdî (d. 182/798) gave the following example in support o f this view. In the Qur’an God says to the prophet: “ We have made lawful for thee ... the daughters o f thy uncles paternal and aunts maternal, thy uncles maternal and aunts maternal who immigrated with thee” (Q. 33, 50). This does not indicate, Abù Yüsuf says, that the daughters o f the uncles and aunts mentioned who did not immigrate with him are unlawful. Al-Jassas then relates that he does not know the view o f the early Hanafis on this; but that he heard many hanafï masters (shuyükh) expressing the view that i f the particularization in question is given in the form o f a number, as when the prophet says “ There are five (types of) women whom a mahram (i.e. a person in a degree o f consanguinity precluding marriage) can kill...,” the judgement involving the others should be the opposite o f the judgement concerning those who are particularly mentioned. On the other hand, when the particularization does not take a numerical form, these Hanafis adopt al- Karkhi’s view mentioned above. Al-Jassas himself supports al-Karkhi on this issue and says:

It is not possible for something (sh a f) to be an indicant... if it does not necessitate in any way (what we regard as) that which is indicated by it (I, 40r).

He then asks the reader to look at some examples in the Qur’an where a description is particularized such as when God says: “ Don’t kill your children for fear o f poverty” (Q. 17,31). “ This does not indicate,” he says,

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“ that one is allowed to kill his own children in cases other than hunger”

(I, 39v-40v).Taken in themselves and in isolation from any exterior evidence these

extracts can be said to state the following:(1) Every discourse in the Qur’an or the sunna is significant.(2) In some o f these significant discourses the intellect can grasp the

meaning through the utterance.(3) In others the meaning is explained by another significant discourse.(4) In the type o f discourse whose meaning can be grasped through the

utterance there is a sub-class in which the utterance signifies by indication a second meaning: that which is indicated. This new meaning is not what the utterance originally gives. When the utterance signifies by indication a second meaning or “ that which is indicated,” it is called “ the indicant

o f discourse.”(5) The following views are wrong and therefore unacceptable:

(a) I f we have a thing that has two descriptions, and only one o f them is mentioned (“ particularized” or “ particularly mentioned” ) in a certain judgement, then the other description should be judged the opposite way. I f one o f them is said to be A, then the other

should be not-A.(b) I f we have a thing that has several descriptions, some o f which were mentioned in a certain judgement, then the rest should be

judged the opposite way.(c) Only when one o f the two descriptions is particularized in a numerical form, i.e., given in the form o f a number, can we say that the other description is to be judged the opposite way. This is the view o f some o f the late hanafi masters (al-Jassas’s contempo

raries).These views are wrong because we cannot regard an utterance as an

indicant unless it necessitates that which we regard as indicated by it, and this is not the case in any o f the above views.

Our next step will be to try to elucidate further and explain al-Jassas’s laconic statements by resorting not only to other places in his text but also and primarily to the views o f the Stoics on logic. We do not yet have independent evidence that al-Jassas, or any o f the early Muslim jurists for that matter, was familiar with the works o f the Stoics in any form. Yet the similarity in terminology and views cannot escape one’s notice. What fol

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lows would thus be a study not only o f the transference o f one culture to another but also o f the influence o f one discipline upon another.

The background and content o f al-Jassas’s opening sentences are fairly well explained in Diogenes Laertius’s Lives o f Eminent Philosophers (VII, 57). Diogenes presents us with the following Stoic distinctions:

There is a difference between <pcovf| (“utterance”) and X,é iç (“speech”); because, while (pcovfi may include mere noise, is always articulate. Xéîç again differs from X,ôyoç..., because the latter always signifies (the word used here is oîinavxiKôç) something, whereas Xéîç as for example pXixupi may be unintelligible, which A,ôyoç never is.^

A second report we would like to cite here is that o f Sextus Empiricus; Against the Logicians, II, 11-12:

The Stoics say that three things are linked together, that which is signified (armaivôêvov) that which signifies (arâivov) and the object (xuyKdvov); of these that which signifies is the <pcûvf| as, for example, ‘Dion’, that which is signified is the thing itself, which is revealed by it and which we apprehend (àvxiA,anPàvco) as subsisting with our thought but the barbarians do not understand, although they hear the cpcavfi, while the object is that which exists outside, as for example Dion himself. Of these two are corporeal, that is the (pcovfi and the object, while one is incorporeal, that is, the thing which is signified, i.e., the X,8kx6v, which is true or false.^

What we are told in the first passage is that a person can make sounds using the letters o f the alphabet without this utterance o f letters (léîç) signifying anything. When an articulated utterance does signify something it is called Xôyoç. Admittedly, one can read /chitdA as either Xôyoç or Xéîç. There are two reasons for taking -ôyoç as the equivalent o f khitdb, however. One is the strong evidence we have in support o f taking qawl as the equivalent o f X,8 iç. This will come out in the discussion o f bayan (“ explanation” ) below. The second reason is also drawn from the same context. In his discussion o f bayan, al-Jassas gives as an example o f an explanation by means o f qawl (X,éÇiç) “ all the initiated duties whose meanings are conceived through ?ahir ( ‘the appearance’ or ‘literal meaning o f’) al- khitdb” (I, 65r). But what does a khitàb signify? A ma^nâ, meaning, we are told, that we grasp with the intellect either in the same discourse through the utterance or in some other discourse. With obvious differences - but still fairly clearly - some o f these views come out in the passage we have quoted above from Sextus. What the passage tells us in part is this : that which signifies, armaivov, is the (p©vf|, an utterance or sound; and the thing signified, armaiv6|ievov, is the Xektôv, that which is meant or,

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simply, meaning. The third element mentioned is the existing object, TuyKàvov. The first noticeable difference between Sextus’s account and the statement o f al-Jassas is the absence o f Arabic words for armaîvov and CTtmaivojievov (see below). Another omission in al-Jassas’s passage is the reference to the existing object. In other places in his book (particularly where he treats general and particular names) al-Jassa§ does talk about the existing object, and the words he uses for it are (“ thing, substance” ) or ayn makh$û§a ( “ particular thing” or “ substance” ), e.g., I, Ir, Iv, 3v, l lv , 34v, 35r and shakhs (“ individual” ) or shakh§ makhsüs (“ particular individual” ), e.g., I, Ir, 11 v. In the above passage al-Jassas talks o f the process o f grasping a meaning with the intellect through the utterance. Though àvxi>-a|xpàv0 (which corresponds well with ya^^qil) does exist in Sextus’s text, Sextus says nothing o f grasping the ^.ektov through the (pcovfj. The relevance o f this point will be appreciated if seen in the fight o f what al-Jassas says next, namely that a khifab may signify a meaning and a judgement that is explained in another khifàb. Both processes, the apprehension o f the meaning through the utterance and explanation, can be better understood if we examine another cryptic passage in al-Jassas’s book. In the new passage (I, 65r-66r) al-Jassas relates

that

an early scholar {ahl al-Hlm) said that an explanation (bayan) occurs (yaqa') through five things; speech (bi'l-qawl), writing (bi'l-khaft), gesticulation (bi'1-ishàra), the knuckles (bVl-uqod) - by which he means the knuckles when used for counting i'uqad al-bisâby - and the indicative signal (al-m?ba'^ al-dâlla).^

Al-Jassâs then goes on to say that the early scholar® talked about all this thusly: An explanation by speech is Hke all the initiated (mubtada*a) duties whose meanings are apprehended by the intellect (al-ma^qülatu ma'^ànlhà) through the appearance or literal form o f a discourse. Both God and the prophet initiate judgements and duties by speech. Such self- explanatory judgements {ahkàm) are called explanations. Both also explain through speech some other statement or judgement made before either by specifying the meaning o f a statement containing general terms, and this is called takh$l$\ or by abrogating a previously-made statement (naskh), i.e., explaining that the duty ordered before is, henceforth, not be followed. Again God and the prophet may explain using writing. This happens in case they initiate a judgement or rufing or when they abrogate or specify the meaning o f a statement made before. The example he gives

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o f such writing in the case o f God is what is written in the Preserved Tablet {al-lawh al-mahfüz). For this is God’s written bayàn, he says. In the case o f the prophet the letters he wrote to his companions are bayàn. Gesticulation, however, is a means only the prophet can use in explaining something (e.g., when he explained that by ‘month’ he meant thirty days, he spread his ten fingers and moved his arms three times). After this al- Jassas adds that the prophet can also explain certain things by performing or doing them {bVl-fiH) in front o f others, such as his performing the prayer which incidentally the Qur’an does not explain. Last o f all is the explanation which we reach through al-nusba al-dalla. There are two types o f explanations we reach through this means, al-Jassas explains. One is rational proofs (al-dalaîl al-âqliyya) hke those used to prove that God is One and Just and all other attributes. These are not liable to change and thus have a better degree o f confirmation {âkad) than the second, namely, verbal indicants {dalâîl al-lafz) which are used in legal theory. Verbal indicants are employed by jurists when they exercise their own judgement (ijtihàd) in order to explain divine law (al-shariâ). A lthough we say that a bayàn may be reached by verbal indicants, it should be clear that they only lead to ghàlib al-zann, “ most-likely opinion.”

We are told that the first means o f explanation is qawl. The question that comes to the mind is whether in the case o f God this qawl could mean the articulated sound. The question is all the more relevant because al- Jassas belonged to the muHazila school o f theology, and the MuHazila are known for their rejection o f any anthropomorphic interpretation o f God’s attributes. However, with regard to the divine Xoyoq (kalàm), it is definitely clear that they thought o f it as at least created. Al-Ash‘ari (b. 260/873-d. 324/935) tells us that the famous Mu‘tazili Ibrahim ibn Sayyar al-Nazzam (d. 221/835 or 231/845) thought o f divine kalàm as a body that is an audible sound caused and created by God.^® I f we take the passage as a whole we cannot escape the conclusion that what is meant here is the material qawl, >-8 iç. The same can be said o f the second means o f explanation: writing. In the case o f the prophet it is obvious that khatt is meant in the sense o f material writing. But does this apply also to God? What we know o f the Mu*tazila allows for a material interpretation o f writing as used here. For the MuHazila did keep the traditionalist view that the Qur’an is inscribed in the Preserved Tablet, which al-Jassas gives as an example o f divine writing. But whether the Mu‘tazila see the tablet

STOIC LOGIC A ND AL-JASSÀS 67

mentioned as a material entity on which God literally inscribed the words o f the Qur’an is not certain. M y own impression is that a material interpretation o f qawl and khatt when ascribed to God did not seem to the Mu‘tazila a breach o f their well-known anti-anthropomorphic interpretation o f the divine attributes. It is the material qawl and khatt, I think, that al-Jassa§ is thinking o f here whether we speak o f the prophet’s qawl and khatt or God’s. This is also true o f gesticulation though in this case anthropomorphism would be unavoidable if God is said to explain by gesticulation. Al-Jassas was aware o f this for he regards an explanation by gesticulation as exclusively the prophet’s job.^^ Again in the case o f the knuckles used in counting, it is obvious that such a means o f explanation cannot be but material. Unfortunately al-Jassas says nothing on this method o f counting and its role in Islamic law and among Mushm jurists.

What o f al-nusba al-dàllal For a partial explanation o f it we will resort to Sextus, Against the Logicians, II, 141-158. Sextus speaks o f a distinction between pre-evident and non-evident things. The first are immediately and o f themselves presented to the senses and the intellect, while the second are things that are not apprehensible o f themselves, the latter in turn being divided into absolutely non-evident and naturally non-evident. Absolutely non-evident are said “ to be those things whose nature it is never to be presented to human apprehension, as is the fact that the stars are even in number or odd.” The naturally non-evident “ are the things which are everlastingly hidden away and are not capable o f presenting themselves clearly to our perception ... such as the existence ... o f an infinite void outside the universe.” Then Sextus says that some, but not all, o f these classes o f things require a signal (we follow R. G. Bury’s translation with slight modification) :

For obviously neither the absolutely non-evident nor the manifest things admit of a signal. But things naturally non-evident, and things temporarily so, have need of thiskind of observation effected by signal __ Signal also has revealed itself as two-fold -the ‘commemorative’, which appears to be chiefly of use in the case of things temporarily non-evident, and the ‘indicative’ (èvÔEiKxiKÔç), which is deemed proper for adoption in the case of things naturally non-evident - thus the commemorative signal, when observed in conjunction with the thing signified in a clear perception brings us... to a recollection of the things observed along with it and now no longer clearly perceived - as in the case of smoke and fire... but the indicative is of a different kind — The soul, for instance, is one of the things naturally non-evident for such is its nature that it never presents itself to our clear perception, and being such, it is announced ‘indicatively’ by the bodily motions... . *

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There are, thus, two types o f signals. One leads us to connect two things that were previously seen together, like smoke and fire; and the other helps us to infer new information about things that are never present to our perception such as the soul whose existence is deduced from the bodily motions. It is the second signal which is called indicative. Al-Jassas does not exactly say that. Among explanations that use indicative signals, he only distinguishes between rational proofs used by theologians and verbal indicants that are employed by jurists when they exercise their own judgement. It is plausible to assume that by rational proofs he meant logical proofs. This is probably his (or his source’s) interpretation o f the ‘indicative signal’ occurring in Sextus. In the case of ijtihâd (“ exercising one’s own judgement” ), the method that al-Jassas could have had in mind for inferring new rulings is qiyâs, “ analogy” (see below). What we are not told is what al-nu$ba al-dalla is and what exactly is its role in the method o f analogy used by jurists. Is the signal he has in mind material, as we are inclined to think? This is an important question because Sextus {Against the Logicians, II, 177) says that Epicurus and the leaders o f his school have stated that the signal is sensible, while the Stoics say it is intelligible. I f I am correct in my interpretation o f al-Jassas’s words, the contrast he makes between rational proofs and verbal indicants may be one between, on the one hand, inferences in which Stoic logic is used and, on the other, those logical deductions made by the philosophers. Odd as it may sound, this understanding o f the matter could be supported by (a) the Stoics’ well- known literal approach to logic and (b) the means through which Stoic material came to Islam, namely, Graeco-Roman rhetoric.i® In any case what concerns us here is the meaning o f nu$ba as used by jurists and the conjectured parallelism between it and ariixeiov. For this we will examine other Arabic texts.

In the chapter on bayân in al-Risala o f al-Shafi'i (b. 150/767-d. 204/820) we read:

There are things that God explained (abanahu) to his creatures by a definite discourse (nof?) (in the Qur’an).... A second category consists of (those duties) the obligation of which He established in His Book, but the modes of which He made clear by the tongue of His prophet.... A third category, consists of that which the Apostle of God established by example or exhortation, but in regard to which there is no precisely defined rule from God (in the Qur’an).... A fourth category consists of what God commanded His creatures to seek through ijtihâd.... Thus (God), glorified be His praise, indicated to (men) {dallahum) - should they be at a distance from the sacred mosque - the correct

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(way of) ijtihâd with regard to those (things) that He prescribed to them, by using the intellects (a l-uqûl) that He implanted (rakkaba) in them and that discriminate between things and their opposites and the signs Calâmât) that (He) erected {nasaba) for them when the sacred mosque, towards which He commanded them to turn their faces, is out of sight. For God said.... “And by signs iâlâmât) and by the stars they are guided” (Q, 16, 16).i«

Afterwards al-Shàfi‘ï explains that the last kind o f bayân is qiyàs. There are obvious similarities between al-Shâfi‘î and al-Jassas. Both talk about self-explanatory statements made by God and the prophet, and both refer to the process o f explanation by means o f analogy. The only difference is in terminology. While al-Jassas speaks o f inferences by analogy in which al-nusba al-dalla is used, in explaining the same method al-Shâfi‘ï tells o f the * alâma that God erected {nasaba) to his creatures like the stars. ®

Another text we would Uke to examine is that of Abù*al-Husayn al-Basrï (d. 436/1044), al-Mu'-tamad. Al-Basri divided the methods (turuq) o f Islamic law {fiqh) in two: dalâla and amâra (“ sign” ).!^ In the first, valid reasoning (al-na?ar al-sahih) leads to knowledge {Him) and in the second it leads to most-likely opinion {ghalib al-zann).^^ In another place he says 21 that jurists call the amàrât (“ signs” ) used in Islamic law, as in the case o f analogy, adilla (pi. o f dalil). It is clear from this that what al- Jassas calls nusba dalla, as used in legal theory, is the same as al-Basrï’s amâra and what, according to al-Basrî, jurists call dalil.

The third text we want to cite is that o f Abù Bakr al-Bâqillânï (d. 403/1013), al-Tamhid. Al-Bâqillânî elaborates on the meaning o f dalil and says that “ it is the guide {murshid) to knowing what is absent from the senses and what is not known necessarily. It is all those signs that can be erected {mâ yun§abu min al-amàrât) and all those gesticulations that can be supplied {mâyûradu min al-imâ* wa al-ishârât) that will lead to knowing what cannot be known through necessity or through the senses.” He also says that it is for this reason that the erected signs {al-*âlâmât al- man^ûba) and the guiding stars {al-nujûm al-hâdiya) are called indicants, adilla. He then repeats that saying that “ an indicant is the means {asbab) that leads to knowing what is not known by necessity or the senses such as al-amârât, al-âlâmât and al-ahLwàl^ through which we acquire deduced knowledge {al-mustanbafât).” ^ He finally says that this indicant is al-hujja, “ the argument.” Here we are presented with a group o f terms all o f which mean a sign or signal that leads to a type o f knowledge that we cannot get either through the senses or by necessary or logical proofs.

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Curiously, nu§ba is not among them, though the verb nasaba is coupled with ^alàma as in al-Shafi‘i ’s and al-Bâqiilânï’s texts, or with amàra as in

al-Basri.Among Muslim philosophers who sometimes treat such problems in

their logical works, Ibn Sïnâ (b. 370/980-d. 428/1037) puts the matter

briefly in his al-Shifa* :

Some people, who are called the ones who infer what is absent (from the senses) from what is present, seek all syllogisms from the sign {wa inna qawman min al-ladhina yusammawna bi 'l-mustadillina min al-shahid "ala al-ghffib yaflubHna al-qiyâsât kullahâ min al-alâma).^^

He also criticizes the use o f the word dalil in cases such as the inference o f fire from smoke.^s This is the same as the example given by Sextus for the commemorative signal. It is very likely that Ibn Sïnâ’s criticism is here

levelled against the jurists.Taken together, these texts, distributed over a period o f almost three

centuries, give strong support to our interpretation o f msba being the same as the Stoic signal. In the last text some support can also be found for seeing the nusba used by jurists as being identical with the commemo

rative signal.To sum up: there are two kinds o f explanations according to al-Jassas

(and al-Shâfi‘î). One is non-inferential such as when God and the prophet initiate self-explanatory judgements in a definite discourse; and this can take place either in speech, writing, or, in the case o f the prophet alone, gesticulation. The second is brought forward by drawing inferences when, for example, signals are used. This drawing o f inferences is called ijtihâd, and the method used is presumably qiyâs, “ analogy.” This, again, comes very close to what Sextus says in his critical report:

In general, also, everything conceived is conceived in two main ways, either by way of clear impression or by way of transference from things clear, and this way is threefold - by similarity, or by composition, or by analogy

Then he says:

For things conceived by analogy have something in common with the things wherefrom they are conceived, as for instance from the common size of men we conceived by way of increase the Cyclops and by way of decrease the pygmy.^s

What led us to bayàn, the reader recollects, is what we read in the opening passage quoted from al-Jassâs’s book. He there said that some discourses

STOIC LOGIC A N D AL-JASSÀS 71

signify a meaning that is grasped with the intellect through the utterance while others signify a meaning that is explained in another discourse. The wording o f al-Jassâs’s statement may suggest that we can speak o f an explanation only when the meaning o f an utterance A is found in B. As became clear above, this is not so; and al-Jassas, to be fair, did not say that that is the only kind o f explanation there is. What we learned from his account o f bayàn is that apart from the self-explanatory statements given by God and the prophet, there are also others that are meant to specify or qualify a previous statement made by either God or the prophet or to limit its application to a certain period o f time. A ll such statements are explanations. But what about the process o f apprehending the meaning o f a statement through the utterance? Is it necessarily non-inferential? The answer is “ no.” This we get from the sentence following that passage quoted at the outset. What it amounts to is this: in the case o f the discourses in which the meaning is not to be sought in another discourse, one sometimes infers by indication a meaning and a judicial ruling other than what the utterance o f the discourse signifies. For example, in the imperative “ Don’t say uf to your parents” the utterance signifies an order not to utter that particular word. But the same imperative indicates another one, e.g., not to shout at your parents. It is this second imperative which al- Jassas calls madlûl (“ that which is indicated” ). As before the trouble here is with the words madlûl and dalil (“ indicant” ). For, as became clear in the discussion o f bayàn, these words are connected with a process o f inference in which some signal is used. Though the information given on al-nusba is very scanty, we can still, I think, give a description o f the process involved in the above example using al-nu^ba. For one can treat the original meaning signified by the imperative as a signal, nusba, to the other meaning or meanings (don’t shout at, don’t k ill... etc.) that are given the label madlUl. O f course we still have other problems left. One is why he called the utterance dalil and not the signal itself? Presumably because in the first place the meaning that became a signal was known through and is associated with the utterance; and since the utterance is something material, something we can point to for example, his preference was for it in naming the dalil. Another problem for which we have no answer is the absence o f equivalent Greek words for dalil and madlûl. What we have is the pair referred to before: aTmaivov-armaivo^evov {significans-significatum). Did Muslim jurists, or whoever introduced the Arabic words.

72 N. SHEHABY

coin dalîl and madlül using aT||xaîvov and armaivôjxevov as models? Or did they see or interpret the Greek words as conveying the stronger meaning that the Arabic words give?

We now move to the final point. It concerns particularization, takhsi . The question o f particularization is an offshoot o f the division legal theorists made between general (^àmm) and particular {khàss) words. To al- Jassas, when a word names an individual, e.g. Muhanmiad (the prophet that is), or a definite situation or incident, such as a particular war between the prophet and the infidels, it is called a particular. A general word, on the other hand, is what one would call a class name, for example, ‘father’ , ‘adulterer’ , ‘man’ . The use o f particular words in a legal text guarantees, with some exceptions (I, 56v-57r), that the statement (khabar) or imperative (amr)^^ in which it occurs is a definite discourse (nass). That is, a discourse that is to be accepted independently o f any other discourse in the established legal texts and that we know for certain is neither qualified nor abrogated anywhere in the mentioned texts. But the existence of a general term(s) in a sentence is more often than not a mark that the sentence in question is an indefinite discourse (mujmal) (I, lr-3r and 53v-61r). For in a large number o f cases such general terms are particularized in some other passage either in the same text or in another accepted text. However, when al-Jassas came to discuss the role o f general terms in legal decisions, his position was not clear. The point is worth elaborating, not only because o f its relevance to the discussion o f general terms in legal texts, but also because it shows the influence o f the jurist’s theological commitments on the formation o f his legal theory.

According to al-Jassas the role o f general terms in legal decisions was a controversial issue among Muslim jurists (I, 6vff). One (unnamed) group thought that a sentence in which a general term occurs should be suspended (waqf), i.e., should not be used as a basis for any legal decision unless we become certain that it is not particularized anywhere in our texts. Another group thought that it should be suspended only if it is a statement {khabar) and not if it is an imperative (amr). For a statement in their view is less important in legal matters than an imperative. The first simply states something and in most cases does not require anything from us, while an imperative is an order that strongly suggests obedience. Yet a third group thought that a sentence containing general terms should be treated as though it had already been particularized, and that we should continue


to treat it that way until we become certain one way or another. Al-Jassas then adds that some people claim that Abù Hanïfa (the founder o f the hanafi school o f law to which al-Jassas belongs) was among the first group, i.e., “ an advocate o f the doctrine o f waqf.'’ For those who make such a claim say that this was Abù Hanïfa’s view regarding sinners: that one should suspend judgement on whether they will be tortured in hell or not, for God, according to him, may forgive them. (Al-Jassas refers to this theological doctrine, usually called irja*, as waqf, except once where he quoted someone else on irjâ\ “ postponement.” ) Al-Jassas says that Abù Hanifa’s theological position is not dictated by his stand regarding general terms. It is rather the result o f what God says in many places in the Qur’an that He forgives all. But when al-Jassas comes to explain his own view on the same issue, he makes conflicting statements. He first flatly rejects what he again terms as the doctrine o f waqf with regard to sentences containing general terms. But later he says that a jurist who is capable o f exercising his own judgement (mujtahid) should suspend judgment whenever he is faced with sentences like these. But the layman i^amml) must take them as they are if he happened to come across one (I, lOv). Al-Jassas in my opinion seems to be in favor o f waqf in legal matters. But since this doctrine is somehow linked with the theological doctrine o f irjà', a doctrine which as a Mu‘tazilï he rejects, he, in the context in which that hnk is discussed, denied any connection with it.

The whole discussion o f ^àmm and khàss points in one direction: that while the existence o f a term referring to a particular thing or situation in a sentence is more often than not a reliable way o f telling that the sentence in question is definite (i.e., cannot be qualified), this is not so with sentences containing general terms. For example, God says in the Qur’an that all Muslims should take part in a religious war (jihàd). But this is not definite since it is in fact qualified in the sunna stating that such participation is not a duty. Where do we look for such a qualification? The stock- in-trade answer is: the Qur’an and the established sunna (“ tradition” ). Al-Jassâ§, however, mentions another source: the intellect (al-^aql). He makes it expUcitly clear that the intellect can be used to qualify sentences in the Qur’an. God, for instance, says “ O people fear your God” {passim), but the intellect dictates that neither children nor the insane can be included under ‘people’ here. The question, o f course, is how does one exercise such a faculty? The answer is by using the method o f analogy.

74 N. SHEHABY

qiyâs. Briefly put, if we have, say, two cases ;c and y, and if the ruling regarding x is already established and not so with y, then we can say that y is governed by the same ruling that governs ;c once we find a cause {Hlla) that a: and y share. For example, the Qur’an forbids Muslims to drink khamr. Now if a Muslim is given some liquid other than khamr and he wants to know if he is allowed to drink it, then he looks for the Hlla ( “ cause,” “ reason” ) for forbidding khamr. The cause, as jurists claim, is its strong effect on one’s mind. Thus, i f the liquid at hand also has that effect, it is to be regarded as forbidden. Applied to sentences involving particularization, one can say that a sentence y can be particularized in the same manner as x, i f jc and y share the same Hlla. It is this Hlla that allows us to make inferences such as the above. What Hlla is and how it is related to the signal discussed above is a subject I intend to take up in a future paper.30

But even with the little information given here about Hlla, we are at least able to point to some factor that allows us to infer a particularization that does not exist in the accepted texts. This is relevant because o f the criticism al-Jassas made against other jurists when discussing particularization. One o f the criticized views was that if we have a thing with two descriptions one o f which is particularized in a judgement, the other must be judged the opposite way. Al-Jassas’s answer, which also applies to the other two views listed before, is that there is nothing in the original judgement which indicates that the other description should be judged the opposite way, i.e., the proposed ruling cannot be inferred from the original one. For such an inference to take place, it is necessary to have a Hlla or signal, and that is not available in the situations mentioned in these views.

Stoic fragments on this issue are not as clear and articulate as one would wish. According to Diogenes Laertius,^! Diogenes o f Babylon defined a common name, Ttpoatiyopia (which Mates translates “ class name” ), as signifying a common quality, Koivf) tüoiôttiç, e.g., man, horse; whereas a proper name, ovo|ia, expresses a quality peculiar to an individual, tôia 7C01ÔTT1Ç, e.g., Diogenes, Socrates. It seems from this that the division o f names into common and proper is based on another division, made within the Stoic category “ quality,” between common quality and particular quahty. We also find a reference in Philo 2 to what the Stoics called individually qualified entities (îôicoç tüoioç). He reports that

STOIC LOG IC A ND AL-JASSÂS 75

Chrysippus regarded Theon, who has only one foot, as an individually qualified entity. I f Dion, who has all his members, loses one foot, Theon will suffer destruction. Because, to Chrysippus, two individually qualified entities cannot exist in the same substrate (uTcoKeiixevov).®^

My aim in writing this paper was to clarify some o f the most obscure, and at the same time crucial, passages in al-Jassas’s Usül al-Fiqh. These passages reveal part o f the logical apparatus that Muslim legal theorists used in building up their systems. In many instances this apparatus reflects a striking resemblance to Stoic views on logic, even though there is no proof that Stoic writings were available to MusHms. Some o f this logic was also employed by the mutakallimm (theologians) ; and it is for this reason that the above reflections may prove to have a wider significance by helping to decipher certain methods used in kalam. What I would like to add here is that the Stoic material in al-Jassas’s book does not come from the Aristotelian commentators. As I have shown in my recent The Propositional Logic o f Avicenna, the Stoic material in Avicenna’s treatment o f conditional propositions and syllogisms in contrast bears the stamp o f the Peripatetic philosophers.

M cGill University

Glossary

‘âmm. opp. khâ?^. General, TipoaTiYopia (?). A class name like ‘man’, ‘adulterer’.Terms such as these are more often than not qualified or particularized, takhfi?. For this reason discourses in which such terms occur are in many cases and in the opinion of most jurists to be suspended, wagf. That is, the legal ruling which they reveal will not be followed until we become certain that it is not qualified anywhere else in legal texts. See pp. 69-70 and al- Jaççâç’s U$ûl, I, lr-3r and 53v-61r. Cf. Diogenes, Lives, VII, 58 and Sextus, Ag. the Log., II, 133,

amr. Imperative, n pôaxaKXiKÔv. According to some Muslim jurists an imperative, unlike a statement, khabar, q.v., strongly suggests obedience and therefore is more important in legal matters than a statement. Al-Jaççâç, U?ûl, I, 6v-7r and Hr. For the distinction cf. Sextus, Ag. the Log., II, 71.

*ayn. Existing object or thing, xuYKdvov. Sometimes al-Jaççâç speaks of 'aynmakh^ü?a, “particular object or thing” (U?ül, I, Ir-lv , 3v, llv , 34v, 35r). Used interchangeably with shakh?, “ individual” or shakhs makhsü?, “particular individual” (I, Ir, llv ). Another word that also refers to objects is shay\ “ thing,” (I, 39v-40r) though it may have a wider sense. See Sextus, Ag the Log., II, 11-12.

baym. Explanation. It is said of (1) a definite discourse, no??, q.v., initiated by God in the Qur’an or the prophet in the sunna. (2) A discourse in which

God or the prophet particularizes, takhfi?, or abrogates, naskh, another judgement, hukm, q.v., in the Qur’an or suma. (3) A discourse inferred from another made in the Qur’an or the sunna by using analogy, qiyâs. This method is carried out with the help of signals, nu?ba, q.v. Al-Ja§§âç, Ufül, I, 39v, 65r-66r. Al-Shâfi‘i, Risâla (ed. cit., note 16), pp. 21-25 in particular. Cf. Sextus, Ag. the Prof., Ill, 40, 49.

dalil. (1) Indicant. Correlative with madlül, “that which is indicated.” By anindicant is meant verbal evidence in the established legal texts that leads to a new ruling. Cf. nusba. See al-Jasçâs, U^ül particularly I, 39v and 65r. In al-Bâqillâni, al~Tamhid (ed. cit., note 23), pp. 13-14, dalil is equated with the signal that leads us to know things that are neither present to the senses or capable of being known necessarily. Dalil and madlül were probably translations of arinaivov and arinaivonevov and were given this new meaning by jurists or their sources. See Sextus, Ag. the Log.,II, 11-12.(2) dalil may also mean logical proof as in al-Jasçâ§, Usül, e.g., I, 65r where he speaks of al-dalffil al-âqliyya, “rational proofs.” The word is used in this sense in al-Ba?ri, al-MuUamad (ed. cit., note 19), vol. 1, pp. 9-10. AI-Baçri’s statement resembles what we find in Sextus, Ag. the Log., I, 25. The Greek word used there corresponding with dalil is àjiôSsiîç.

hukm. Judgement, àîœna. A general term that refers to legal rulings in the Qur’an or the sunna or those rulings inferred from these sources by accepted methods.

khabar. Statement, à7tô(pavaiç. It is used of statements made by God or the prophet. Regarded by some jurists as less suggestive of obedience than an imperative, amr, q.v. Al-Ja§çâç, C/sm/, 16v-7r and Hr. For the distinction between statements and imperatives see Sextus, Ag. the Log., II, 71.

khas?. opp. *amm. Particular, ovona(?). A word that refers to an individual object such as the prophet Muhammad. Save in a few cases, when such terms occur in a discourse we can regard that discourse as definite, na$$, q.v. Al-Jaççàç, U§ül, I, lr-3r and 53v-61r. For the cases where a particular can be qualified see I, 56v-57r. Cf. Diogenes, Lives, VII, 58 and Sextus, Ag. the Log., II, 133.

khifab. A discourse, X,ôyoç, made by God or the prophet that is always significant. Cf. qawl and lafz. See Diogenes, Lives, VII, 57 and Sextus, Ag. the Log., II, 275-76. See al-Jaççâç, U?ül, I, 39v and 65r.

lafz. Utterance, (pcovfi which may include mere noise. Cf. qawl and khifab. Seeal-Ja§?a§,C/sw/, I, 39v. Also Diogenes, Lives, VII, 57 and Sextus, Ag. the Log., II, 275-76.

madlûL That which is indicated. See dalil.makh^fif That which is particularly mentioned or individually qualified, 15((dç bVl-dhikr. Ttoioç (?). The wording of a legal ruling in the Qur’an or sunna may have

several references. When one of these references is declared in the Qur’an or surma to be the one meant by the ruling, it is said to be particularly mentioned. See al-Ja?çâç, Usûl, I, 39v-40r. Cf. Philo, On the Eternity o f the World, 48-49 and Plutarch, De communibus notitiis, 1077 CD.

ma'nâ. Meaning, X,8ktôv. It has that meaning at least in the context of al-Jaççà§’s discussion of God’s or the prophet’s qawl, q.v., and khifab, q.v. (U$ül,I, 39v). See Sextus, Ag. the Log., II, 11-12, 70 and 80.

76 N. SHEHABY STOIC LOGIC AND AL-JA§SAS 77

mujmal

na??.

rmsba.

qawl

shakhf.shay*.ya'qil.

opp. na??, q.v., and mufassar. Indefinite discourse, i.e., one that may be qualified or abrogated, naskh, in the established legal texts such as the discourse containing general terms, ‘â/wm, q.v., or whose meaning is liable to different interpretations. Al-Jaççâç, U?ül. I, lr-3r and 53v-61r. opp. mujmal. Definite discourse. A discourse in the Qur’an or the sunna whose meaning is not liable to any interpretation other than what its literal wording reveals and which can neither be particularized or abrogated, naskh, such as the text that orders the punishment of deliberate killing. See al-Jaççâç, Usül, I, Ir-lv .Signal, arineîov. Al-Ja§sâs (U?ül, I, 65r) speaks of two uses of al-nusba al-dâlla (“ indicative signal”). One he labels rational proof and the other is employed by jurists when they exercise their own judgement, ijtihâd, and involves verbal indicants (see dalil). The example for the first is the theological proofs that God is One and Just... etc. The other is the inferences in which analogy, qiyâs, is used (see p. 63), Cf. Sextus, Ag. the Log., II, 141-158. In al-Risâla (ed. cit., note 16), pp. 24 and 38-39, al-Shafi‘i speaks of the process of analogy, qiyâs, in which we, for example, infer the position of the sacred mosque in Mecca using the stars that God erected as signs to His creatures (al-alâmàt al-latina§aba lahum). Here the verb nasaba is coupled with the word 'alama (“sign”). Al-Baçrî in al-MuUamad also uses the verb na$aba coupled with amâra (sign) ; see, e.g., al-Mu'tamad (ed. cit., note 19), vol. 2, pp. 803-804. He also (vol. 1, pp. 10-11) distinguishes between this sign (amâra) which leads to most- likely opinion and a proof (dalil, q.v.) which leads to knowledge. Also al-Bâqillâni, al-Tamhid (ed. cit., note 23), pp. 13-14, says that what is not present to the senses and what cannot be known necessarily is known through what is erected (yun?ab) of signs, amâra, 'alâma... etc. Al-Jaççâ$ also uses the words amâra, ‘alâma, and sima interchangeably to mean “sign” in the above sense (II, 45v and 46v). The word al-nu?ba was also used to translate the Aristotelian category xô KeîaOai. It was also used in astrology to translate Gejia or ôiâGena. See note 7.Speech, X,é iç, which is always articulate but not necessarily significant. Cf. khifâb and laf?. See al-Ja§?à§, C/sm/, I, 39v and 65r. See Diogenes, Lives, VII, 57 and Sextus, Ag. the Log., II, 275-76.Individual, See ' ayn.Thing. See âyn.Grasp with the intellect, dvTiXanPctvco. Al-Jaççâ§, Ufül, I, 39v. Cf. Sextus Ag. the Log., II, 11-12.

N O T E S

In preparing this paper I relied on two separate MSS for the two volume work of al- Jaâ$, both of them in Dâr al-Kutub, Cairo. Volume I (MS no. 191) consists of 150 folios. Volume II (MS no. 26) of 165 folios. The references below are to the relevant folios of Volume I.* Diogenes Laertius, Lives o f Eminent Philosophers, tr. R. D. Hicks (London and Cambridge, Massachusetts, 1965), vol. 2, p. 167. Hicks’s translation has been modified slightly. Œ Sextus Empiricus, Against the Logicians, II, 275-76, tr. R.G. Bury, Loeb Classical Library (London and Cambridge, Massachusetts, 1967).

78 N. SHEHABY

3 William and Martha Kneale, The Development o f Logic, first ed. (Oxford, 1962), p. 140. A few changes have been made in Martha Kneale’s translation. Cf. Against the Logicians, II, 70, 80 and 264.4 Al-Shâfi‘i in al-Risâla, ed. A. M. Shakir (Cairo, 1940), pp. 23-24 uses the word ayn in the same sense.5 In the immediately succeeding passage al-Jaç?âç uses the word shay' which may have a wider meaning including material, mental, and perhaps imaginary entities.« Hisàb al-aqdox al-uqad (dactylonomy) is the art of expressing numbers by the positions of the fingers. See The Encyclopaedia o f Islam, new edition, ed. B. Lewis et a lii (Leiden and London, 1971), Vol. 3, under hisab al-aqd.’ In Ibn Man?ür (d. 711/1311), Lisàn al-'Arab (Beirut, 1955), vol. 1, al-nasb = wa4' al-shay' wa rafîhi (“putting something and raising it”) ; al-na?iba = kullu mâ nu§iba fa- juHla âlaman (“anything which is erected and made as a sign or a signpost”); al-yan- sûb = ‘alamun yunsabu f i al-falât (“a sign or a signpost erected in the waterless desert or the open space” ); al-nasb and al-nusub = al-âlam al-mansub... al-sanam (“ the erected sign or signpost or the idol”); al-nusba=âl-sàriya (“the mast”). R. Dozy, Supplément aux Dictionnaires Arabes, 3rd ed. (Leiden «& Paris, 1967) vol. 2, has an entry for nasba = “érection, élévation.” His source for this is Hélot, Dictionnaire de Poche fr . -ar. et ar.-fr., 4e tirage, Alger. Dozy in the same entry gives a second meaning for the word as used in astrology “ thème céleste, e.g. nasb al-talV = dresser I’horoscope.” Dozy does not say why he wants to read na§ba here. Cf. C. A. Nallino, ‘Del Vocabolo Arabo NIÇBA (Con SAD)', Rivista degli Studi Orientali, vol. 8 (1919-20), p. 643, who reads ni?ba and says that the word as used in astrology is a translation of the Greek Gé ia or 0m08|ia. Dozy gives the version nisba as meaning “construction, disposition,” Neither of these derivations {nasba, nisba) is cited by Lisàn a l-Arab or al-Fayrûzabâdi (b. 729/1329-d. 817/1414), al-Qâmüs al-Muhif (Cairo, n.d.). However, Butrus al-Bustani in Muhit al-Muhit (Beirut, 1870), vol. 2, gives the derivation nisba and quotes for this al-Uariri (b. 446/1054-d. 515/1121 or 516/1122), Maqâmât (see De Sacy, Les Séances de Hariri, reprinted in Amsterdam in 1968 from the Paris ed. of 1853, vol. 2, pp. 560-561) which says fa-inkharafna ila shaykhin rakini al-nisba — “So we hastened (or sped) to a Shaykh stoutly erect” (tr. F. Steingass, The Assemblies o f a l-ÿariri [London, 1898], Vol. 2, p. 124). De Sacy in his commentary on this says; al-ni?bafiUa min al- intisdb. Al-Harir! is C. A. Nallino’s sole support for reading nisba in his article {pp. cit., pp. 637-646) tracing the meaning of the word in the fields of rhetoric {balâghd), philosophy, and astrology. He is followed in this reading by G. E. von Grunebaum in his article on bayân in The Encyclopaedia o f Islam, new edition, vol. 1. Cf. Bibliotheca Geographorum Arabicorum IV : Indices, Glossarium et Addenda et Emendanda Ad Part, no /-///, M. J. De Goeje [1st éd., 1879], 2d. ed. (Leiden, 1967), p. 864, who also reads niÿba while at the same time mentioning nasba quoting Dozy for this vocalization. Nallino (p. 642) quotes M. Horten, Die spekulative und positive Theologie des Islam nach Razi (Leipzig, 1912), p. 355, who also reads ni?ba, for the use of the word in translating the Aristotelian category xô Ksïa0ai. It seems that both De Goeje and Horten relied on al-Uariri in this reading, for the texts they quote are given without the short vowels.® Cf. Abu ‘Uthmân ‘Amr ibn Bahr al-Jahi? (b. 160/776-d. 255/868), al-Bayan wa’l- Tabyin, 2d. ed., ed. H. Sandubi (Cairo, 1932), vol. 1, p. 78, where in a chapter entitled al-bayàn, he says that the “ indicants {dalâlât) to meanings are five things: utterance (al-laf?), gesticulation {al-ishara), knuckles {al-uqad) writing {al-khaff) and the state (al-hâl) which is called nusba.” Cf. his al-Hayawân (Cairo, A. H. 1323), vol. 1, p. 23.

STOIC LOGIC A N D AL-JASSÂS 79

9 The MS reads fa-yaqùlu âlâ hâdhà which shows that the explanation given of the above five meanings of bayân is the early scholar’s. If so, then he could not be al-Jahi? who says nothing of this sort. It is possible, however, that the scribe supplied the dots for the first word to make it fa-yaqûlu; for in the absence of dots it could be read (“we then say”), meaning that what follows is al-Jaççâç’s own exposition.

Maqàlât al-Islàmiyyin, 2d éd., ed. H. Ritter (Wiesbaden, 1963), pp. 191 and 587-88. Cf. Diogenes Laertius, VII, 44, 55-70.

12 I follow B. Mates, Stoic Logic (Berkeley and Los Angeles, 1961), p. 13 and his glossary p. 135 in translating aTl^leîov by “ signal” .13 Sextus, Against the Logicians, II, 149-155.14 See Galeni Institutio Logica, ed. Carl Kalbfieisch (Leipzig, 1896), III, 5 and J. S. KieflFer, Galen’s Institutio Logica, English Translation, Introduction and Commentary (Baltimore, 1964), pp. 76 and 130-33. See also my The Propositional Logic o f Avicenna (Dordrecht-Boston, 1973), pp. 8 and 14.1® See Joseph Schacht, The Origins o f Muhammadan Jurisprudence (Oxford, 1967), pp. 99-100.1* Al-Risâla, ed. A. M. Shakir (Cairo, 1940), pp. 21-25. See the English tr. Islamic Jurisprudence: ShâfiTs Risâla, translated with an Introduction. Notes and Appendices by Majid Khadduri (Baltimore, 1961), pp. 67-70. The quotations from al-Risâla here are from this translation with some changes.1’ Al-Risâla, pp. 38-39; Eng. tr. pp. 77-78.18 Cf. Aristotle's Prior and Posterior Analytics, A Revised Text with Introduction and Commentary by W. D. Ross (Oxford, 1949), 70a3-b38 and 75a33 where the occurrences of crmeîov are translated by Tadhâri (ca. 790-ca. 850) by 'alâma-, see A. Badawi, Manfiq Arisfû (Cairo, 1948), vol. 1. Abû Bishr Mattâ (ca. 870-ca. 940) in his translation of the Posterior Analytics gives âlâma as a translation of crilieîov which occurs only once 99a3; see Badawi, op. cit. (Cairo, 1949), vol. 2.19 Al-Baçri, al-MuUamad, ed. M. Hamidullah et alii (Damascus, 1964-65), 2 vols. Al-Baçri also talks of the signs erected by God naâba al-amârât, vol. 2, pp. 803-4, 709 and 712. Cf. Sextus, Ag. the Log., 1,25 “whereas the non-evident things are discovered by means of signs and proofs” (ànôôeiîç, R. G. Bury’s translation).2» Op. cit., vol. 1, pp. 9-10.21 Op. cit., vol 2, p. 690.22 Al-Jâhi?, as said in note 8 above, identifies hâl with nusba. It is interesting to note that the word al-hâl was also used to translate the Aristotelian category xô tïoiôv; see Ishaq ibn Wahb (10th cent. A.D.), al-Burhân f i Wujüh al-Bayân, ed. A. Matlub et al. (Baghdad, 1967), p. 83. It is also worth noticing that Ibn Wahb treats analogy under what he calls al-bayân bi'1-iUibâr and says that it is the means for knowing the things which cannot be known either through the senses or necessarily (ibid., p. 73).2» Al-Bâqillâni, al-^Tamhid, ed. R. J. McCarthy (Beirut, 1957), pp. 13-14.^ Ibn Sina, al-Shifff: al-Qiyas, ed. S. Zayed (Cairo, 1964), p. 575.2® Ibn Sina, op. cit., p. 573.2* Al-J^çâç also uses the words 'alâma, amâra and sima to mean “sign” (II, 45v, 46v). As said in note 7 above nusba was used to translate the Aristotelian category xô KeïaOai, As far as we can see the earliest such use, quoted by Nallino, op. cit. (note 7), p. 641, is that of Ishaq ibn unayn (d. 298/910 or 299/911). See also Rasffil al-Kindi al-Falsafiyya, ed. M. A. Abu Rida (Cairo, 1950), vol. 1, p. 366, which is not quoted by Nallino. The editor of al-Kindî’s text reads al-nasba.

80 N. SHEHABY

27 Against the Professors, tr. R, G. Bury, Loeb Classical Library (London and Cambridge, Masschusetts, 1961), III, 40.28 Op. cit.. Ill, 49.29 For a distinction between a statement and an imperative see Sextus, Ag. the Log.,II, 71.3° Cf. Ibn Sina, op. cit. (note 24), p. 576, who claims that the jurists call al-âlama (“sign”), 'illa. Also al-Ba§ri, op. cit. (note 19), where he sometimes speaks of amâra (“sign”) as being the same as Hlla (vol. 2, pp. 804,825, 831 and 833) and sometimes says that amâra indicates the Hlla (vol. 2. pp. 802-804 and 826).31 Lives, VII, 58; see also Sextus, Against the Logicians, II, 133.®2 On the Eternity o f the World, 48-9, in Philo, English tr. F. H. Colson, Loeb Classical Library (London and Cambridge, Massachusetts, 1941) vol. 9. See J. M. Rist, Stoic Philosophy, (Cambridge, England, 1969), pp. 160-64.33 Cf. Plutarch, De communibus notitiis'. Moralia, vol. vi, fasc. 2, Rencensuit et emendavit Max Pohlenz (Leipzig, 1959), 1077CD.

D I S C U S S I O N

A. sabra: What you have been doing in arguing for the influence of Stoic logic in your paper is comparing things that overlap, but do not coincide completely with one another. But to establish that something is really identifiable as Stoic, it is not enough to show that there is overlap. And when I read your text, what I feel is that, to be sure, the parallelism between what you have here and certain discussions in Stoic logic is apparent; but what is also apparent and what impresses me perhaps even more, is the fact that the Arabic text functions independently of any reference to the Stoics. That is to say, if you read it as Arabic, it makes sense - maybe not one hundred per cent - but to a very, very large extent it is self-sufficient. One can make a distinction between this kind of text and an early philosophical text, for example. An early philosophical text, like one by al-Kindi, is obviously full of things which could only have existed in Arabic as a result of translation, but I don’t have the same feeling when I read a text, even an early text, in jurisprudence or in kalam. And this makes me feel a bit cautious about crossing the border and bringing in the Stoics; for the context seems to suggest that the Arabic words in such texts have a life of their own and are not to be explained by bringing in foreign elements. If one is to argue for the presence of Stoic elements, then there must be a resemblance between your text and its Stoic antecedent that is based on the consideration of what we might call “proper parts.” To be a proper part in two systems of thought that are being compared, a concept must function in a significantly similar manner in the two systems. It is, for example, futile to be told that in certain contexts the Arabic ma'nâ corresponds to the Greek lekton, if the two words function differently in the two conceptual systems in which they occur. Thus I think that if you construct a large number of proper parts to which you find correspondences, then one can make a case for your thesis. But with this condition, that you compare proper parts in the sense that I have specified.

N. SHEHABY : But One must realize that books entitled Ufûl al-fiqh are different from works on philosophy. In the former one has, if you wish, applied logic, you are introducing an apparatus which you intend to apply to a certain different field such as law.So what happens when you open book on Usûl al-fiqh is that you find certain preliminary problems - what are the sources of the law?, how do you explain legal texts? - and


as you read you find yourself suddenly faced with a passage which is fu ll of, I would say, operational definitions, logical concepts, and terminology loaded with meanings. Out of nowhere! And then all of that is used or applied to those cases that we are supposed to be discussing, such as legal points or legal questions. Of course, if you read the whole book, it isn’t Sextus Empiricus; you don’t read it that way because it isn’t an exposition of Stoic philosophy. No, it is a book on legal theory in a special sense of the word. But when you come to a section entitled dalil al-khifab or al-makh^ü$ b i'l- dhikr, then you find that the Arabic is no longer really Arabic. You find yourself with sentences loaded with definitions and meanings which are used all through that section, or succeeding sections, but applied to a topic which is completely Islamic: About hojj (“pilgrimage”), about prayer, about this sort of thing. Of course, this is Islamic; the Stoics didn’t discuss such things.

R. frank: But for the terminology that you have in your text, I think you want to go back to the grammarians; it is all there from Sibawayh on, which takes you back a long way.

N. SHEHABY : Well, these people were in close contact, but you can’t say who influenced whom.

A. SABRA : You are saying that by referring these problematic features to grammar and so on, you still need an explanation. But the question is, do you need an explanation from something outside this Islamic context? This is really the question.

N. SHEHABY: Definitely, otherwise you wouldn’t understand a word; you wouldn’t proceed at all.

j. VAN ESS : The paper treats a difficult matter. This is to a great extent due to the lack of texts: Logic was used, but not explained. It is therefore legitimate to approach the problem from new sources, in this case from usül al fiqh. But one thing should always be kept in mind: usül al-fiqh is not logic, but hermeneutics; its aim is to build up canonical law on the basis of the Scripture; it always has do with exegesis. It is not reflection about the laws of thinking, but about the treatment of a text. Comparing it with Stoic logic means to compare hermeneutics with epistemology. This has, I think, some consequences for this paper.

Let me proceed from the passage you quote where bayân, “explanation,” is said to be realized in five different ways. We are dealing here with a structure of six terms: one genus (bayân) and five species. There is no Stoic parallel for the structure as a whole nor even for the genus itself, but you suggest a Stoic origin for two of the five species: qawl = Xéîç and nu?ba dalla = atijaeiov èvSeiKxiKÔv.

Now Xéîç, according to the passage from Sextus Empiricus you quote, not only comprises words, but also unintelligible combinations of sounds like pXizvpi. Qawl on the contrary is a subdivision of bayân, i.e., is supposed to “explain” something; it is always meaningful and intelligible. Here we are confronted with the difference of intention that I pointed out in the beginning: the Stoics aimed at a theory of language and of knowledge; this is why they start with (pravfi ( = “noise,” but also “vowel”), and then proceed to Xéîç i.e., something that is composed of these noises, but does not necessarily have a meaning, and Xôyoç, i.e., something meaningful. The u^ül al-fiqh, on the contrary, as a science of hermeneutics is from the beginning only concerned with meaningful speech. If it is therefore necessary to equate qawl with a Stoic term, I would always propose Xôyoç and not X,é iç.

Now in your opinion Xôyoç already has an equivalent, namely, khifâb. This would leave me with the problem why two words have to be equated with the same Stoic term. Of course, the problem only exists if I accept the hypothesis that we meet Stoic influence

82 N. SHEHABY

in this passage, which - to make this clear right from the beginning - I do not believe to be the case. But even then the question remains why there are two words, qawl and khifab, used for nearly the same thing. I think it is because they are used in a different context. Qawl is the normal expression, the word one would expect everywhere. Khifab, however, is typical for usùlal-fiqh: it does not mean any meaningful utterance irrespective of its intention, but “allocution, address,” i.e., an intentional utterance directed to somebody and therefore apt for exegesis: the Qur’an as revelation or a tradition ihadlth) of the Prophet as relevant to his community. Khifab is qawl seen under a particular aspect, an aspect that is tied so specifically to the situation of revelation-based religion that I would be surprised to find an exact Stoic pendant for it.

Concerning the nu?ba al-dàlla we have to proceed from the entire spectrum of the term which you try to reconstruct. The question is whether the equation nusba = CTT1HSÎOV stands at the beginning from which all other examples for the usage of the word and its derivatives in similar contexts may be deduced, or whether this equation is the fortuitous result of an autonomous development of the root. After all, the verb nasaba does not imply the meaning “sign,” but has to be accompanied by a word of this sense (amâra, ^alàma, dalîl), and it is one of these words (dalil) which you yourself afterward equate with ariiaaîvov, a term which is not very much different from armeîov in Stoic logic. This needs further investigation.

N. SHEHABY : It is not, I think, quite exact to say that u?ül al-fiqh is not logic but hermeneutics. The apparatus used, for example, by al-Jaçsâs and al-Ghazâli is partly logic and partly hermeneutics. It should also be clear that the Stoics were concerned with language and grammar. In their logical studies, they made use of semantics as well as the theory of deduction. Echoes of both of these exist in works of u?ül al-fiqh.

Though I have not yet been able to prove it, the word bayàn seems to me to be another Arabic word for Xôyoç, and I don’t find it strange that more than one Arabic word was used to convey the meanings of A,ôyoç. X,é iç is the vehicle through which meanings are given. This, I think, is what Sextus wanted to say. Thus, there is nothing odd in saying that an explanation can be given through X,é iç. It is true that in isolation the passage dealing with al-nu?ba does not reveal much. But my interpretation is nevertheless strongly supported by the constant use which you point out of the verb na?aba with words such as ^alâma or amâra (“sign”) by al-Shâfi‘i and other legal theorists as well as theologians. I have examined this problem in more detail in an article “7//a and Qiyas in Early Islamic Legal Theory” which will appear in the Journal o f the American Oriental Society.

R. f r a n k : The paper seems to betray an unfamiliarity with the Arabic terminology involved. There is nothing at all “ laconic” about what al-Jaç§âç says in the texts you cite. All he says in your first citation, for example, is that the intended sense of some statements may be grasped immediately through the explicit terms and words Qafy) while others may require a further context of interpretation and that in some instances the sense that a statement is meant to convey through a particular phrase or expression may not be restricted simply to that which it has if taken narrowly in its most common and primary lexical meaning (mâ wudi'a lahu). Lafz is not (pcovf) but, here as in all similar contexts, means the (Arabic) words of the expression or statement as opposed to the “meaning” (al-ma'nà or al-murad): what one is talking about or referring to (al-madlül *alayhi, if you wish); nor is al-dalil to be understood as always restricted to a reference to “a second meaning.” One seems here to be fishing for parallels - rajman bi'l-ghayb, as it were - without close attention to usage and context.

In al-Jassa$’s source, al-Jahi? is treating al-bayan, viz., how one may communicate


something clearly to another (al-bayan is not so much “explanation” as conveying clearly what you want to say in the first pla:e). In the passage cited he distinguishes five forms o i bayàn, two that are linguistic, viz., talking and writing, and three that are non-verbal. The last of these, al-nu?ba, is that one produces through some object or set of objects a situation reflecting on which the intended observer will understand the meaning or message that is meant to be conveyed. In al-Jâhi?’s context this is the furthest removed from vocal speech and the one that most plainly requires reflective inquiry {nazar) on the part of the observer (though it need not be the least clear: bayyin). The expression na?b al-adilla, as Professor Van Ess has noted, is also common in the kalâm and elsewhere. In the kalam, however the dalâ'il or 'adilla man?uba (as also the 'amàràt), in contrast to the context of al-Jahi?, may include things such as one’s intuition of moral imperatives or may be verbal and so include, e.g., the text and content of the Qur’an.

Your parallels with the Stoa appear to be only half parallels that reflect no systematic coincidence of conception but only a partial overlap of the subject matter under consideration, viz., the uses of language. It is to be remarked that the sciences of exegesis, law, and theology are, in Islam, closely allied to and significantly dependent upon the linguistic sciences, grammar, and lexicography. The terminology with which you are here concerned was elaborated largely in conjunction with the linguistic sciences and one should note that it is these, the earliest disciplines to achieve their full development in Islam, that seem to have been elaborated almost entirely without influence from non- Muslim sources.

N. SHEHABY: I entirely agree with Professor Frank that law, theology, grammar, etc. are allied sciences. I myself tried to show this in the case of theology and legal theory. Jurists, theologians, grammarians, etc. all lived in the same intellectual milieu and in several cases collaborated with each other closely. But it is also important to say that this milieu was largely and primarily indebted to Greek thought. It is this more fundamental source which interested me particularly as I began to explore the field of legal theory. The passages quoted from al-Ja§çâç’s book contain some of the basic terms used by all Muslim jurists constantly and in diflferent contexts. My aim here was to clarify as much as I can their meaning in order to be able to explain their usages in more complex contexts. Though these passages do help in a way, they are unfortunately less detailed and articulate than I wished. I am afraid it is Professor Frank’s unfamiliarity with legal terminology which makes him tend towards a simplistic approach in understanding terms such as nu$ba. The term dalil, innocent as it may look in the context discussed in my paper, is the key for understanding the position of Dàwüd ibn Khalaf al-?àhiri, the head of the ahiri (literalist) school of law, regarding analogy and textual interpretation. Al-Jaççâç has some interesting things to say about Dâwûd and his use of dalil which cannot be understood without reference to the passage I quoted. I have dealt with this in the same paper I have just mentioned in replying to Professor Van Ess.

j. VAN ess: I would like to make a small personal remark: I find myself in a very funny situation because I myself believe in the Stoic influence on the logic of kalâm', I tried to prove this in an article. So from that general point of view I am completely in line with Nabil, whereas I do not believe in his example. So if, by chance, the atmosphere of the discussion would have turned out to be that of beliefs in Stoic influence, then I would have tried to bring up other examples, very tentative examples.

A. sabra : As far as such statements of belief are concerned, I think that it is not unlikely that there was some influence in one sense or another. I never wanted to say

84 N. SHEHABY

that there was no such thing. My objection is, rather to the method of establishing such influence, not just to these specific examples, but to the method as such.

N. SHEHABY : Let me comment on this. As I told you, I am not a reductionist. I am not trying to say that every bit of the work of al-Jaçsâç can be found to come from some particular text that we have from the Stoics or anything like that. All I am saying is that there is a huge edifice here and that part of the apparatus in it does come from Stoic sources, and without understanding that part, I can’t really deal with the rest.

R. mckeon: I think that you have been looking to the wrong criterion by which to determine what the Stoic logic is and whether it was an influence in the case at hand. It is not necessary for the jurist to quote Stoic logic or to refer to it to establish an influence. Take the following example. You begin an interpretation of a text by saying: There is the symbol, there is the (pcovfi ; it is written or spoken, and it is a material thing; moreover, it denotes something, and that is a material thing too. Now, it is possible for a grammarian to deal with the semantics of this notation; consequently, up to that point, the grammarian would be suflicient. However, if you then argue about the significance, the meaning and the denotation, you employ a A,ôyoç which is immaterial; this is the XeKxôv, And so on. Now an Arabic jurist, if he wanted to appeal to logic, could have gone to several other logics beside the Stoic. If he had gone to Aristotle’s logic, he would not have dealt with symbols, signs, cpcovfi, cttih8îov, but he would have begun with homonyms, synonyms, and paronyms. These are words which already have their meaning and denotata established and therefore you would not find this separation between the sign and what it symbolized. Alternatively, if he had gone to atomistic logic - let us say Epicurus rather than Democritus - he would have thrown away all of the verbal significances entirely and he would have had a logic which was a canonic, and therefore he would not get into this problem of signs and signified. He might also have gone to the sophistic logic, and then he would talk about antilogisms, and once more the sign would not appear because for any proposition there is more than one interpretation. It seems to me, therefore, it is not a question of whether you can understand the text without reading in some logic or other. If you are understanding the text by picking out the words and what they are designating in an argument, then you are being Stoic.

R. f r a n k : Well, I would agree perfectly with this. I suspect that there are a lot of Stoic elements.

r . mckeon: No, I don’t mean elements, I mean a structure of argumentation. Therefore, I think, without knowing much Arabic I could fix up that vocabulary at the end of the paper. The only thing that is wrong with that vocabulary is that it operates as if it were a lexicon in which univocal terms are being translated. Make it sufficiently broad, and you will find the same ambiguities in Greek and in Arabic.

A. sabra : But, even if that were so, that would mean that theoretically it is possible to substitute the one for the other. But why do so?

R. m ckeon: Let me answer. I give a course at Chicago in jurisprudence. It is offered in the Philosophy Department and in the Law School. And the whole point of the course is to break the dogmatism by which lawyers know exactly what law is. Consequently, I introduce what amounts to four different logics for the law. I take particular cases andI interpret the argument according to one logic, and another logic, and then another logic. It seems to me that this is the method that was used in the paper. That is to say, you begin with a discussion of jurisprudence, jurisprudence deals with the law of God and with the customary law; they are both divine and, therefore, both authoritative. But having established them as fully authoritative, you are still stuck with what they


mean. This is the structure of inquiry I found in the paper. That is, it would seem to me in general that one of the problems in jurisprudence would be to take a law, well established, solid and divine, and give it meaning.

j. MURDOCH: I don’t really wish to speak to that. But just let me ask you a question about the kind of test that you mentioned earlier for the occurrence of Stoic logic first here and then there. My knowledge of Stoic logic is not that great, but is it not correct that one of the central notions is that the X,eKxà were involved in the problem of what a proposition stands for? Now, we know that in the Latin West - in the twelfth century on the one hand in Abelard and, on the other hand, in the fourteenth century in a number of people - this same concern comes up. But we are also reasonably certain that the Latins didn’t get it from the Stoics. Consequently, you don’t want to say that this is the influence of Stoic logic, any more than you want to maintain that the existence of Stoic propositional logic and medieval Latin propositional logic necessarily means the influence of one upon the other, although that there is a doctrinal, a formal, similarity, there is no question. So, could it not simply be the case that there is a formal similarity in al-Ja§sa§ with some Stoic doctrine or other, but that he somehow invented his view independently. But perhaps finding a whole pattern of argumentation, a collection of resemblances, in both, moves more in Nabil’s direction.

R. mckeon: N o, you see, there is a structure which can be described in considerable detail, and I think that the paper assembles all of the elements of it. In the setting up of the logic, you can take as your basic element the single word. The single word is usually meaningless; it is an X. You can, however, put an X in a proposition, a proposition in an argument, and an argument in a system based on principles. Now in the course of his discussion, the author of the paper separated the semantic question of the meaning of the word, or jurists who said that the meaning of a single word would be enough, from those who had set up a proposition which would be a judgment. You also have logics which depend on the semantic development of an argument. And finally there are systematic logics. Now the peculiarity - and I give the name Stoic to it for this reason - is that the Stoic logic is a propositional logic; it is not a logic of concepts, it is not a logic of inferences, it is not a logic of systems. Since it is a propositional logic, the determination of the meaning of the proposition requires something peculiar; therefore, the A,ektôv comes in. And if you have in the Arabic jurisprudence the emergence of the proposition in a central place - which would be very good for the law - and also have a need for the interpretation of it which removes it from the mere designation of particular cases, then those two characteristics would be enough for me to say that it is Stoic logic. As I say, propositional logics were fairly late. I don’t think that any of the great dialecticians or logicians of Hellenic times had propositional logics. The Stoics developed a propositional logic in the Hellenistic period. Consequently, this is one of the hallmarks. As a result of it, a curious kind of materialism is connected with it, the materialism of the (pcovfi and the materialism of the things signified. By my distant view, the mutakallimün were materialists in precisely this sense and therefore would fit in the materialistic logical structure quite naturally. Consequently, if jurists were coming along they would be materialists as no Christian jurist would be. This would be the rough answer concerning the grounds by which I would name this, with our author. Stoic. Am I wrong in this interpretation?

n . SHEHABY : No, Certainly not. I would certainly agree with you.

JOSEF V A N ESS

T H E B E G I N N I N G S O F I S L A M I C T H E O L O G Y

Theology is not as central a phenomenon for Islam as it is for Christianity. The educational system o f the Islamic Middle Ages concentrated on law and hadith, the tradition o f the Prophet; madrasas and mosques offered chairs in jurisprudence, but not in theology. Even the famous Nizamiyya, the >va^/-endowed “ university” founded by the wazïr Nizâmalmulk some decades before the first crusade, although for a long time credited in European research with a shift towards the opposite, a “ victory” o f Ash*arite theology, did not in fact contribute much to change the situation.i And when Islam today tries to adjust to the demands o f the modern world it does so not so much through experimenting with new theological and philosophical notions, but through providing fresh interpretations for the old juridical problems o f a religion-oriented society. Nevertheless, Western orientalists usually keep to their own value systems, and understand Muslim “ Geistesgeschichte” mainly as a history o f theology and philosophy, not as a history o f law.

But if we do not want to change our idiosyncrasies we must at least provide a justification, and this justification may be found in the fact that in the earliest centuries o f Islam when intellectual life was not yet fully institutionalized, theology seems indeed to have captured minds. Theologians about whose juridical preoccupations we hear very little, played an important role at the court o f the first Abbasids in the newly founded capital o f Baghdad. Only later, especially after the mihna, the “ inquisition” initiated by the government in the first half o f the third century H., when jurisprudence turned out to be the “ safer” science in so far as there a difference o f opinion did not necessarily involve proscription and persecution, did it start outshining the fascination o f theology, which in its turn was increasingly regarded as a dangerous game o f autocratic intellectuals.

Thus having discovered that what European Islamic studies have accomplished until now was not so meaningless after all, we may venture to vindicate a second bias o f Western scholarship which seems to be hidden

J. E. Murdoch and E. D. Sylla (eds.). The Cultural Context of Medieval Learning, 87-111. All Rights Reserved.

J. V A N ESS

in the formulation o f our topic: the belief that the beginnings are always more interesting and more important than the end, the Pre-Socratics more fascinating than Plotinus, Giotto more stimulating than Titian, young scholars more “ promising” than older ones. Now, the beginnings at least tell us how something came into existence, and sometimes even why it did so. In history nothing is necessary in itself; it is only by hindsight that we sometimes get the impression that something could not have happened otherwise. Although there nearly always was theology in Islam we cannot say that Islam could not have done without theology. Judaism, which is the religion most comparable to Islam in many respects, never developed theology to such an extent, and when it did so (I am thinking o f Sa'adya, for instance) it was only undergoing the influence o f Islam. And we have just noticed that even in Islam itself there was, later on, an increasing number o f people who might have wished that their religion had done without theology.

So why do we have theology in Islam, and how did it start? In general one tries to find an answer by referring to the Mu'tazilites, “ premiers penseurs de l’Islam,” as A. N. Nader called them.^ This would bring us into the second century H.: Wasil ibn ‘Atâ* died in 131, ‘Amr ibn ‘Ubayd about 144; Dirâr ibn *Amr, the first personality o f the “ school” about whose theological conceptions we have solid and rather sufficient information, died about 200. Dirâr was already a systematician, but Wasil probably was not. We would know more about the latter’s original intentions if we had better knowledge o f the purpose o f his famous du'^at mentioned in a poem by Safwan al-Ansârî.^ Were they missionaries, sent out in order to convert all the non-Muslims who still lived everywhere in the Muslim oekumene, in the towns, but even more in the rural districts? Wasil himself was engaged in apologetics; later generations still remembered having seen his “ Thousand questions against the Manicheans.” Theology, then, would have started as an apologetic struggle against the “ unbelievers.”

However, we need not enter into further speculations about these activities, because Wasil and the Mu'tazila are apparently not the key to our question. There was Muslim theology before the Mu‘tazilites, in the first century H.; it is rather improbable that all these “ sectarian” movements characteristic for intellectual life in the time o f the early Umayyads- the Kharijites, the Qadarites, the Murji*ites - only indulged in politics

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without developing any theological “ superstructure.” We can even prove the contrary: about 75 H. the caliph ‘Abdalmalik started a correspondence with the Ibadites at Basra that is still preserved in a late Khârijite source.® And about the same time, at least not after 80 H., his Iraqian governor al-Hajjaj, at his instigation, wrote a letter to Hasan al-Basrï asking him to expound the principles and proofs o f Qadarite doctrine. The Risala that Hasan al-Basri wrote in response is still preserved. Since Ritter’s edition o f the text in 1933, no one has seriously questioned its authenticity, and taking all the arguments together I think it is really impossible to do so.’

But two difficulties still remain to be solved. In spite o f the documents we have cited, the textual basis is still very meager, and the stylistic form typical for Mu'tazilite theology, the dialectical structure o f answer and response, the so-called kalam, is not yet to be found in the two testimonies mentioned. Characteristically enough, it is with the term ‘kalam’ that the Arabs once and for all circumscribed the nature o f theology; theology in the realm o f Islam is not named after its contents as in Latin or Greek, as “ knowledge about God,” but after its style o f argumentation: one “ talks” (kallama) with the opponent by asking questions and reducing his position to meaningless alternatives.® This does not mean that there was no other way o f expressing oneself, but it certainly hints at a marked prevalence o f this specific styhstic device; it is here that the polemical intention o f early Mu'tazilite theology found its adequate form. In the first century H., however, the situation seems to have been different: the letter o f the Ibadites and that o f Hasan al-Basri are theology in so far as they treat theological problems, but they are not kalam.

Should we infer from this that there was no kaldm at all at that time? This might be too hasty a conclusion, merely built upon an argumentum e silentio. We must not forget that the intentions o f the two texts we mentioned do not favor the usage o f ‘kalam’ : neither Hasan al-Basri nor the Ibadites were asked to enter into an imaginary dialogue with their opponents as this is usually presupposed in later kalam texts, but simply to expound their ideas, and this is what they do. And besides that, if we really search for material that hints in the opposite direction we might come up with at least a few relevant passages. Muhammad al-Baqir, the fifth Imam o f the Shi*ites, who died in 177/735, is presented as using a kalam argument in a report preserved by Kulini in his Kàfi.^ ‘Umar II

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who reigned from 99 until 101 is said to have emphasized his ability in kalàm, especially with respect to his discussions with the Shi*ites.i® And a certain Suhar al-‘Abdï who had closer contact with Ahnaf ibn Qays and Mu*awiya (reigned 41/661-60/680) and who is even supposed to have lived “ back” in the time o f the Prophet, is quoted by the late Khàrijite author al-Shammâkhï as having given the following advice concerning the Qadarites: “ Talk with them about (divine) knowledge {kallim ûhum f V I- Him). I f they admit it, they contradict (their doctrine) ; i f they deny it they fall into unbelief.” 12 Suhar al-*Abdi was the teacher o f the famous Ibadite scholar Abû ‘Ubayda Muslim ibn Abï Karima al-Tamimi (first half o f the second century H.) ; we may suppose that he held a moderate predestinarian outlook similar to that o f the Ibadites. In its contents, then, the passage just translated corresponds more or less to what we would expect from a man like Suhar. In its wording and in its structure, however, it holds some surprises. I f it is authentic, it would prove that not only the verb kallama - and perhaps also the noun kalàm - was already used for this kind o f theological discussion, but that even one o f the most frequent stylistic features o f later dialectics, proceeding by alternatives and the “ if- if not” disjunction, was not unknown to scholars o f the first century.

But are these texts really authentic? Let us take the warning o f the Mu^tazilite al-Nazzam seriously: the mere accumulation o f lies does not amount to truth. '* Or, slightly adapted to our situation, the mere accumulation o f uncertainties does not establish historical facts. Doubt may be expressed about the reliability o f all these quotations. The Shi*ite Imams, and especially Ja‘far al-Sadiq together with his father Muhammad al- Bâqir, are widely suspected o f merely serving as mouth-pieces o f later ideas and forms o f expression. *Umar IPs picture in history is distorted by the attempt o f later historiographers to portray him as the great reformer o f the Umayyad dynasty or even as the Mahdi o f the “ year o f the donkey” (100 H.).is And the source that gives us the report about Suhar al-‘Abdi is, as we said, rather late (Shammâkhï died in 928/1522); Ibn Sa‘d only mentions him with a few words.i® The thesis we want to defend - that Muslim civilization did not slowly develop the art o f theology and especially o f kalàm, but rather grew up with it - sounds too radical to be established by these isolated items. We are too accustomed to the idea that the Arabs “ o f the desert,” masters o f poetry and language

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but uncultivated in all occupations o f an urban society, including theology, started their culture as it were from a vacuum and only gradually severed their inherited predilections. We adhere too stubbornly to the conviction that literature in Umayyad times was mainly transmitted orally so that it is hard for us to accept readily the possibility o f immediate theological production. We need more source material.

This material exists. And although it too can be questioned, it makes the basis o f our argumentation broader and somewhat more reliable. The Zaydï Imam al-Hàdï ila’l-haqq Yahyâ ibn al-Husayn (died 298/911), founder o f the Zaidite community in the Yaman and grandson o f the famous Qasim ibn Ibrahim (died 246/860) who initiated the turn o f the Zaydiyya towards the doctrine o f free will, counted among his many writings a refutation o f a treatise against the Qadariyya that he attributes to Hasan ibn Muhammad ibn al-Hanafiyya, grandson o f ‘A li and brother o f the well-known Abù Hàshim, who tried to take over the heritage o f Mukhtar and who is said to have finally transmitted it to the ‘Abbasids. '^ The book o f al-Hadi ila’l-haqq is preserved in several manuscripts, and with it a considerable number o f extensive fragments o f the text against which it polemicizes.18 This text brings us again into the first century H. ; Hasan ibn Muhammad ibn al-Hanafiyya died between 99/718 and 101/720, i f not earlier. And here we meet again, together with much discussion about the interpretation o f relevant Qur*anic passages, the same disjunc- tional structure we found in the advice o f Suhar al-‘Abdi. Now, however, it is not isolated and sporadic, but used prolifically as the main stylistic device in a rather schematic way. Let me give you one or two examples ;

Tell us [Hasan ibn Muhammad ibn al-IJanafiyya addresses his Qadarite opponents], whether God (only) wanted the Good with them (i.e., with mankind) and then later established it (i.e.. Hell) for them, or whether He wanted the Evil with them (right from the beginning)! - If they say: “He wanted the Good with them,” they should be answered: “How is that, as He created it (Hell) knowing that they would not have any profit from it and that it would only do harm to them?” If they, however, assume that He created it for them in order to do harm to them, their doctrine is refuted.^®

The argumentation perhaps needs some comment. I f Hell was created right from the beginning, the author wants to say, then God must have preordained Evil; otherwise this act would have been meaningless. The proof is rather defective. Two possible objections are at least passed over in silence. The Qadarites could have answered that God does not preordain Evil, but simply foreknows it, and that foreknowledge does not

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mean predestination; or they could have claimed that Hell does not yet exist, but will be created after the Last Judgment when it turns out to be necessary. Both solutions have been proposed, the first one already by Hasan al-Basri in his Risâla to the caliph ‘Abdalmalik,2i and the second by Dirar ibn ‘Amr, the MuHazilite mutakallim o f the second century .22 The fact that they are not alluded to in our text seems to show that the author did not know them, because his treatise could only serve as instruction for predestinarians on how to deal with Qadarite arguments if he really mentioned in it all the possible subterfuges to be expected from them. That this was indeed his intention may be illustrated by a second paragraph:

Could they ignore something that God made them know, or could they not do so? - If they then say; “No,” their doctrine is refuted. If, however, they say: “Yes,” then go on and ask: “Could they ignore God himself, i.e., ignore that He is the creator of everything and the molder of everything?” If they then say: “ (No), yet this is inborn ifitra) and nobody is rewarded for it, all mankind knows that He is God,” then you should answer; “Could they then ignore that God created day and night. Heaven and Earth, this world and the world to come, and mankind and all creatures just how and in whatever way he wanted?” If they then say; “Yes,” they lie and all people are witness that they lie. If, however, they say: “No,” they join you (and give up their opinion).^»

Here the same scheme is applied over several steps, obviously in order to incorporate all counterarguments known at the moment the book was written. The level o f the argumentation seems to fit the situation o f the late first century; Ghaylan al-Dimashqi who was executed under the caliph al-Hisham (105/724-125/743) uses the term fitra for rather elaborate speculations, and we have enough testimony to be sure that the beginnings o f this concept go back to the first century, to the Qur’an and the famous hadlth al-fitra transmitted under the name o f Abù Hurayra.^^

The argument brought forth by Hasan ibn Muhammad ibn al-Hanafiyya sounds rather inconclusive: no Qadarite denied that something that is known to someone can no longer be ignored; but they did hold that there are, besides the fitra, many knowable things that one could not know a priori, but which one may come to know by one’s own intellectual endeavor. The author is not very well acquainted with the speculative pos- sibiUties o f the Qadarite position. He wants to write a manual on how to deal best with the “ heresy” o f free will, but the ideas he refers to and the ideas he brings up himself are strangely immature. This primitiveness is characteristic for nearly all the fragments preserved, and it is best ex

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plained by the assumption that they really date from a time when theology was still primitive. There is no internal evidence in the forty excerpts made by al-Hâdï ila’l-haqq that would point to the inauthenticity o f the

text.But it is difiicult to overcome skepticism. May we really dare assume

that such a book was written at so early a time that the fabrication o f paper was not yet known in the Arab countries and when papyrus or parchment were rather expensive? Was the Qadariyya really worth such an effort and such costs in those days when in other fields the literary activity was still rather limited? And besides that, wherever Hasan ibn Muhammad ibn al-Hanafiyya is mentioned in the biographical dictionaries his anti-Qadarite bias which we have just taken for granted is passed over in silence. We hear that he was interested in theological questions, but his outlook seems to have been diiFerent. He is considered to have been the first Murji’ ite; hardly any source forgets to mention, or even to quote, his K. al-Irja\ the first text connected with this movement.^s But this negative evidence also possesses a positive side. I f there really was a K. al-Irjà^ by Hasan ibn Muhammad ibn al-Hanafiyya we need no longer reflect about the possibility o f theological production under the early Umayyads, and we are hence more prepared to believe that the same author wrote a second book on theological problems. Being a MurjiMte does not exclude one’s being a predestinarian; on the contrary, both positions seem to have been frequently combined. 6

Extensive quotations from the K. al-Irja ' are given by Dhahabï (died 748/1348 or 753/1352-3) in his Ta^rîkh al-Islàm '^ and by Ibn Hajar (died 852/1449) in his Tahdhîb al-Tahdhîb.^^ The text was thus known until the ninth/fifteenth century, although not separately but through the medium o f earlier secondary sources. W. Madelung has recently treated these fragments and strongly argued for their authenticity.But in the meantime we have been able to broaden our base. We now possess the source used by Ibn Hajar, the K. al-Iman by Ibn Abi ‘Umar al-‘Adanî (died 243/858),3o and there we get the complete text o f the K. al-Irjà^ on approximately three folios. But the treatise does not help us in our search for examples o f kalam; it is written in the form o f a letter addressed to the Shi‘ites in Iraq, and therefore, like Hasan al-Basri’s risâla to ‘Abdalmalik, does not offer any opportunity for the occurrence o f the stylistic features mentioned above. But it gives us rich information about the political

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Standpoint o f its author and thereby enables us to form a better judgment o f his theological decisions. Let me also therefore quote a short passage from it:

If someone wants to ask us about our position and our opinion, we are people whose master is God, whose religion is Islam, whose guide is the Qur’an, and whose prophet is Muhammad.... Among the chiefs of our community (cûimmatîm) we approve of Abû Bakr and ‘Umar, we approve their being obeyed, and we condemn their being opposed. We are enemies of their enemies. (But) we reserve our judgment {nurji) about those among them (i.e., the chiefs of the community) who first participated in the schism (of the community: ahl al-furqa al-uwal). We make every effort to remain loyal to Abù Bakr and ‘Umar, because the community did not engage in fighting or dissension with respect to them nor did they doubt about anything concerning them. “Reservation” is only due concerning those who are blamed by the people, whereas we were not present (in order to build up a judgment of our own)....

Among those whom we treat as our enemies are those wishful Saba’ites {al-SabaHyya al-mutamanniya) who came forward with the Qur’an (i.e., used it as a pretext) and openly slandered the Umayyads... in reproaching for their sin those who had committed it while committing it themselves (afterward) when they had an opportunity; in seeing the temptation of (sin) without knowing the way out of it. They took members of a noble Arab family (ahla bay tin min a l-Arab) as their imam and made them responsible for their religious view^^ by declaring their solidarity with what they loved and their antipathy to what they hated: violators of the Qur’an and followers of the soothsayers (kuhhan). They hope for a “reversal” that will take place in a resurrection before the “Hour” ; they distort the Book of God and practice bribery in their jurisdiction....

There is another feature by which these Saba’ites whom we have witnessed show their enmity. They say: “We are guided (by God) to a (special) revelation from which (all other) people went astray, and to secret knowledge.” They claim that the Prophet concealed nine-tenths of the Qur’an. But if the Prophet really had concealed something of what was revealed by God he would have concealed the affair of the wife of (his adopted son) Zayd... .3»

Hasan ibn Muhammad ibn al-Hanafiyya dictated this letter to his client ‘Abdalwahid ibn Ayman who lived in Mecca and with whom he seems to have been on friendly terms, and he asked him to recite it publicly everywhere but we also hear that he himself fought for his conviction in the circle o f the Kûfian genealogist Abu’l-Saq‘ab Jakhdab ibn Jar‘ab.35 There seems to be hardly any doubt that the text was directed mainly against extremist Shi'ite factions in Kufa. The Saba*iyya whom he attacks were adherents o f Mukhtar who, after the failure o f the revolt (in 67/687), nourished chiliastic hopes and perhaps justified them by referring to secret parts o f the Qur*an that they claimed to have been suppressed or not received by the rest o f the community. It had been Mukhtar who, by


killing those responsible for the murder o f Husayn, had “ reproached those who had done it for their sin, but then had done it himself,” and it was he who had “ taken a member o f a noble Arab family (or: a member o f the ahl al-bayt) as his Imàm"’ Hasan ibn Muhammad ibn al-Hanafiyya implicitly declares Mukhtar’s allegiance to his father to be nothing more than intrusion and imposture. He himself, although an ‘Alid and, at that time, one o f the heads o f the clan, steers a surprisingly moderate course. He does not identify himself with any propaganda against the Umayyads and he accepts Abü Bakr and ‘Umar as righteous caliphs. Only in the case o f “ those who first participated in the schism o f the community” does he practice abstention and refrain from any judgment, i.e., upon ‘Uthman

and *Ali,This sounds rather surprising, but to a certain extent it ceases to be so

if we no longer look at it with the categories o f later centuries, when the gulf between Sunnites and Shi‘ites had become unbridgeable. Hasan ibn Muhammad ibn al-Hanafiyya is an ‘Alid, but not necessarily a Shi‘ite; there were many *Alids, even among the grandsons o f ‘Ali, who never thought o f any opposition against the Umayyad regime and rather preferred to live quietly off their pensions. And the acknowledgement o f Abù Bakr and ‘Umar is taken over by Zayd ibn ‘A li (died 122/740) who still must have known our author, a remote uncle o f his. Our sources stress the fact that he lost his Kûfian adherents for just this reason. The zrya* in the attitude towards ‘Uthman and ‘A li is approved and further developed by the first Mu'tazilites,®® whereas the later Murji’a starts to understand the term in a different way. ' A ll this together with the special flavor o f the letter, its “ atmospheric precision,” seems to point to the conclusion that the document is authentic. I agree with Madelung that with this declaration Hasan ibn Muhammad ibn al-Hanafiyya “ made his peace with the Umayyad regime.”

But i f this really is the case, we must ask a further question. Why did Hasan feel induced to betray the cause o f Mukhtar and to make such an open avowal o f his anti-extremist and antirevolutionary attitude? We may assume that some sort o f political pressure or at least persuasion stood behind it. Hasan’s half-brother Abù Hâshim obviously maintained close contact with those followers o f Mukhtar who were later called Kaysaniyya, but at that time SabaMyya.^» And when Mukhtar’s situation in Iraq had become desperate, Hasan himself had still tried to join him, but only

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arrived at Kùfa after his death. After a vain attempt to create a nucleus o f resistance at Nisibis he was arrested by troups o f ‘Abdallah ibn al-Zubayr and thrown into prison.ô The K. al-Irja* seems to have been written, as W. Madelung has suggested with convincing arguments, shortly after 73/692 when ‘Abdalmalik finally had succeeded in defeating Ibn al-Zubayr and tried to lump together his empire, which was torn asunder and exhausted by the centrifugal tendencies o f the past, by means o f a cautious pohcy o f religious harmony.4i In the year 73 H. Hasan’s father Muhammad ibn al-Hanafiyya acknowledged the political facts and paid allegiance to the caliph, and his son seems to have shared his realistic attitude.

Something else may have come in. It is not impossible that ‘Abdalmalik could have profited from the chronic financial weakness o f the ‘Alids. Hasan ibn ‘A li had, as is well known, been bought by Mu*awiya, and Husayn is reported to have asked Marwan for 4000 dinars.^s Zaynal‘abidin accepted money from Mukhtar, and he was happy when ‘Abdalmalik allowed him to keep it. ® jq game way, Muhammad ibn al-Hanafiyya visited ‘Abdalmalik in Damascus to confess to him that he was highly indebted. The caliph then assumed all his obligations. Only with those o f Muhammad ibn al-Hanafiyya’s mawàli did he show some reserve.^^ This proves that the head o f the ‘Alid family had not only spoken for himself, but also for all those who felt beholden to him and for whom he regarded himself responsible. The chiefs o f the Banû Hàshim found themselves in the same role as the chieftains o f pre-Islamic tribes; their code d’honneur sometimes demanded from them more generosity than they could afford. But if they accepted the money they needed from those who had always been rich and who grew even richer now by having access to the governorships and other attractive posts, from the Banù Quraysh, they had to pay a price. Muhammad ibn al-Hanafiyya had accomplished the bay' a and, acceding to mild pressure from the side o f the caliph during his later visit in Damascus, had given away the sword o f the Prophet which at that time still was in the possession o f his f a m i l y . jt is not improbable that his son Hasan wrote his AT. al-Irja* as a token o f suggested gratitude.

It seems significant that what appears to be the only Qur*anic exegesis transmitted from Hasan ibn Muhammad ibn al-Hanafiyya in Tabari’s commentary similarly centers around a financial problem and offers a rather pragmatic solution. Hasan comments upon Sûra 8/41 where the


distribution o f booty is regulated. According to the text, the one-fifth o f the booty that is not given to the warriors is kept in reserve for six different recipients, among them God, the Prophet, and the “ relatives” {dhu'l- qurba, singular understood in a general sense). Now God, obviously, was always treated rather stingily; he only got a small sum destined for the maintenance o f the Ka‘ba. But with the next two recipients one soon encountered difficulties, with the Prophet because he had died, and with the “ relatives” because one had to define who was meant by them. Opinions sprang up Hke mushrooms, most o f them, o f course, only reflecting personal interests. The ‘Alid Zaynarâbidïn, contemporary o f Hasan, tried to identify the “ relatives” with the Banü Hâshim. Other traditions show, however, that the government did not take this exegesis seriously. For them the “ relatives” were the Banû Quraysh as a whole, and Qatâda (died 117/735 or 118/736) formulated it even more generally: dhul-qurbd are all those in power after the Prophet. Hasan ibn Muhammad ibn al- Hanafiyya now held the view that the share o f the Prophet should go to his relatives, i.e., mainly to the Banû Hàshim, the share o f the dhu’l-qurba, however, to the relatives o f the caliph.ê He knew that the problem had already been controversial in the time o f Abû Bakr and ‘Umar ; and with his solution he tried to estimate realistically the chances o f his family to obtain at least some o f the money administered by the Umayyads. It does not seem impossible that this fatwd was transmitted by Tabari and his sources because for some time it really represented the practice o f distribution applied by ‘Abdalmalik.

I f this long detour has succeeded in bringing some evidence for the authenticity o f the K. al-Irjà\ then we may also have gained something for Hasan’s Radd âlà'1-Qadariyya. ‘Abdalmalik supported predestinarian ideas. He wanted his subjects to believe that the power, the “ kingship” (mulk) given to him and to his family was a possession {mulk) granted by God and inalienable according to His divine will. The caliphate is, in the words o f the poet Farazdaq, right guidance (huda). He who rebels against it goes astray {dalala).^’ On the other hand, revolutionary activities could always be justified with Qadarite ideology. This becomes obvious towards the end o f the Umayyad epoch, in the time o f Yazid III^® and perhaps o f Hisham, but it is already alluded to in the proclamation made by ‘Amr ibn Sa‘id al-Ashdaq in Damascus when he planned his insurrection against ‘Abdalmalik in 69/689. ® Here, too, Hasan ibn Muhammad ibn

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al-Hanafiyya thus corresponded to the caliph’s intentions and perhaps to his expectations; fortunately we possess at least one testimony from a rather independent source that confirms that he indeed detested the Qadarites.50 But in contrast to the K. al-Irja\ the text o f his refutation o f the Qadariyya was ignored by the later biographical and bibliographical tradition. This probably happened because it was soon taken over by Zaydites who agreed with Hasan’s lenient attitude towards the first two caliphs and who preserved his predestinarian outlook at least for some generations. When, towards the middle o f the third century, the Zaydite community changed its opinion, the text that until then had been respected had to be refuted. This is why it reached us together with the corrections o f al-Hâdî ila’l-haqq.

This conclusion has many consequences. The questions we asked in the beginning and which seemed to augment our skepticism must now be answered in the afiirmative. There was a written hterature in the first century o f Islam, and there did exist at that time a certain familiarity with the technique o f kalam, although it was still handled with a somewhat helpless rigidity. Even the term ‘kalam’ seems at least “ on the way” ; Hasan ibn Muhammad ibn al-Hanafiyya once uses ‘takallama’ as Suhar al-‘Abdï did o f ‘kallama’ , both o f them presupposing a technical meaning for the root.

The first consequence is the easiest to accept. There were other books written under the early Umayyads. In an article on this topic, R. Blachère pointed to the works o f ‘Abïd ibn Sharya and Wahb ibn Munabbih.^i We mentioned the Risala o f Hasan al-Basrï and the correspondence between ‘Abdalmalik and the Ibadites. We might add the historical work o f Salim ibn Hutay*a (?) - frequently quoted by the Khârijite author al- Barrâdï in his Jawàhir al-muntaqât - or the recently discovered letters o f the Ibadite Jabir ibn Zayd al-Azdï (died 93/711).S2 We must, o f course, always keep in mind the danger o f spuriousness; quite a lot o f “ testimonies” o f the first century are simply the result o f antedating. But this does not mean that everything was forged or that nobody wrote anything. Arab culture did not start from a vacuum; life went on as it had been before, and Syria or Egypt had always been civilized countries. Papyrus and parchment were perhaps expensive, but Greek or Syriac literature had not suffered much from this fact. It only meant that the poor could not express themselves in a written form, but they would not have done this


anyway. The state always needed documents and written records. M. Brav- mann has adduced some material testifying that in Medina ‘Uthman had something like state archives.53 Seen under this aspect, the fact that Hasan ibn Muhammad ibn al-Hanafiyya apparently wrote his books in Medina ceases to be so astonishing. Medina was not “ the desert” ; until the end o f the time o f ‘Abdallah ibn al-Zubayr the town had been the center o f the Islamic empire. Papyrus and parchment were nothing new in this corner o f the world, and Hasan was rich enough to pay for them - if he did not get them free from the chancery o f the caliph.

May we assume that the same chancery also provided for some theological assistance? This might help us to explain the unexpectedly early usage o f kalam style. For it is this detail that remains striking; here the historical threshold has been shifted back nearly one century. But do we really need such an assumption? Dialectical style, proceeding by question and response, the fictitious dialogue, had always been famiUar to Christian theology; it was in the time o f the Umayyads that John o f Damascus wrote his AidA-e^iç XpicTTiavoO Kai SapaKrjVoO.^^ And Hasan not only lived in Medina; he also frequented the Iraq where Christian theology had been flourishing for centuries. In his youth he had been in Nisibis^s which through its famous Nestorian academy for a long time had attracted the most brilliant minds.®® We do not plead for Christian “ influence.” We simply mean that people went on doing what they had always done before, and that if they themselves had not done it before, they at least found ample opportunity to become acquainted with it in their rapidly widening world. There was something like a common stock o f ideas, but there does not seem to have been any “ influence” in the sense that the Muslims were awakened to a certain problem by Christian counterarguments and that they consciously rectified their position in order to avoid being molested again. Christian polemics as represented by John o f Damascus did not influence the Qadarite movement or bring it into existence as C. H. Becker believed; both are simply two facets o f a theological discussion that affected the Christian and Muslim milieu alike. O f course, the Christians knew what the problems were longer than the MusUms, because Christianity existed before Islam. When the Qadar- ites said that God cannot be held responsible for the fornication practiced by man, they simply repeated what the Nestorian Bâbai had said when he polemicized against the determinism o f Henânâ, the head o f the

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school o f Nisibis (died 610).5S But they were not led to repeat it by Christian influence. They simply profited from a common treasury o f arguments.

It is even less likely that they were influenced by John o f Damascus himself. Although he, like his father Sergius and his grandfather, cooperated with the Muslims and for some time at least lived at their court,®® the feeling o f superiority held by his Muslim masters certainly prevented him from gaining too much - or any - influence in theological affairs. We hear nothing about discussions between Christians and MusUms at the court o f Mu‘awiya, ‘Abdalmalik, or Walïd, as the ‘Abbasid caliph al- Mansûr used to arrange between Muslims and Zoroastrians. John wrote his AidXs^iç only after he had retired from the Umayyad court to the monastery o f St. Sabas. And the argument he uses concerning the problem o f God’s responsibility for man’s fornication is rather complicated and unique. It is not found in this specific form in any Muslim source.

The Muslims were still living among a Christian majority, but in spite o f this the religious contacts seem to have been weak. One needed the Christians and one sometimes held them in high esteem as the example o f Akhtal shows. But one did not ask them for their advice in theological questions. There were enough neophytes who could solve these problems by the experience they brought into the new religion. The Christians did the administration and collected the taxes. They even were allowed to build churches - in contrast to the famous decree wrongly ascribed to ‘Umar I. But from the beginning one seems to have felt an antipathy to teaching them the Qur’an.® We may perhaps compare the situation to what can be experienced even nowadays in a “ levantine” city like Beirut. Different communities live together, they deal with each other, they do business with each other, they do the administration and - today - even politics together, but they never talk to each other about their religion and consequently they are to an astonishing degree ignorant o f what their neighbors believe. In spite o f all loyalty, there is also distance and an unmistakable amount o f mutual contempt. Had there been religious contacts, there would have been controversy ; but there is not one text pointing in this direction. Cl. Cahen has stressed the fact that Christian testimonies about Islam o f the first century H., rare as they are, completely lack aggressiveness.®^ They do not yet contain the usual polemical clichés known from later sources. Christians seem to have regarded Islam as a


new sect in the long series o f heresies they were accustomed to. This turned out to be an error, but an understandable one for a period when Islam was not yet defined in its “ dogmatic” structure. And the Muslims, just because o f this undefined status o f their reUgion, were not yet able to start an attack themselves. Moreover they felt superior anyway.

Theology in Islam did not start as polemics against unbelievers. Even the kalâm style was not developed or taken over in order to refute non- Muslims, especially the Manicheans, as one tended to believe when one saw the origin o f kalàm in the missionary activities o f the MuHazila. Theology started as an inner-Islamic discussion when, mainly through political development, the self-confident naiveté o f the early days was gradually eroded. The initiative for lifting these discussions to a literary level seems to have been taken by the caliph ‘Abdalmalik. He was interested in a dialogue in order to cool down existing tensions or in order to propagate his own theologico-political views, and he had the personnel and the financial resources to start such an enterprise. With this attitude, as with many other things, he followed the heritage that he found in the country in which he decided to choose his capital: the tradition o f the Byzantine emperors whose impact had molded the Syrian milieu for cen

turies.

UniversMt TübingenN O T E S

This has been elucidated especially by George Makdisi; cf. his articles ‘Muslim institutions of learning in eleventh-century Baghdad’, Bulletin o f the School o f Oriental and African Studies, 24 (1961), 1-56; ‘Law and Traditionalism in the Institutions of Learning of Medieval Islam’ in Theology and Law in Islam, ed. G. E. von Grunebaum (Wiesbaden, 1971), p. 75-88; and ‘The Madrasa as a Charitable Trust and the University as a Corporation in the Middle Ages’ in Actes Congrès International d ’Arabisants et d ’Islamisants, Bruxelles 1970 (Brussels, 1971: Correspondance d’Orient nr. 11), pp. 329-337 (especially p. 333).2 Albert N. Nader, Le Système philosophique des MuUazila {Premiers penseurs de l ’Islam), (Beirut, 1956).® Cf. J. van Ess, ‘Pirâr b. ‘Amr und die Cahmiya’, Der Islam 43 (1967), 241-279 and44 (1968) 1-70; Louis Gardet, Études de philosophie et de mystique comparées (Paris, 1972) 102 flF. A fragment of one of his works may have been preserved or at least reflected in a passage in Ibn Hisham’s K. al-Tîjàn (cf. my forthcoming article in: Festschrift A. Abel, p. 108flF.).* Cf. Jâhi?, al-Bayân wa’l-tabyin, ed. ‘Abdassalâm Muhammad Hârûn, (Cairo, 1380/ 1960), 125,6; Ibn al-Murtadâ, Tobaqât al-MuUazila, ed. S. Diwald-Wilzer (Wiesbaden- Beirut, 1961), 32, 4 ff.

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5 a . Ibn al.Murta4a (note 4) 35,1 ff.« Cf. E. Sachau, ‘Religiose Anschauungen der Ibâ^itischen Muhammedaner’, Mitteilun- gen des Seminars f i ir Orientalische Sprachen, II. Abt. 2 (1899), 52 flF.: R. Rubinacci,11 califfo ‘Abd al-Malik b. Marwan e gli Ibâçliti’, Annali delVlstituto Universitario Orientale di Napoli n.s. 5 (1952), 99-121 ; J. Schacht, ‘Sur l’expression “Sunna du Prophète” Mélanges d’Orientalisme offerts à Henri Massé (Teheran, 1963), pp. 361 -365. 7 Cf. H. Ritter, ‘Studien zur islamischen Frômmigkeit I: Hasan al-Baçrî’, Der Islam 21 (1933) 1-83; J. Obermann, ‘Political theology in early Islam: al-Hasan al-Basri’s treatise on qadar’. Journal o f the American Oriental Society 55 (1935), 138-162; M. Schwarz, ‘The Letter of al-lJasan al-Ba§ri’, Oriens 20 (1967) 15-30; J. van Ess, Anfange muslimischer Theologic (Beirut, 1975).® Cf. J. van Ess, Die Erkenntnislehre des "Adudaddin al-Ici (Wiesbaden, 1966), 56 fF. ; id., ‘The Logical Structure of Islamic Theology’, in Logic in Classical Islamic Culture, ed. G. E. von Grunebaum (Wiesbaden, 1970), p. 23 f.9 a . Kulini, Kàft, (Teheran, 1338-9) VIII 318, 6 flF.

Cf. Abü Zakariyyâ’ Yazid al-Azdi, Ta'rikh al-Maw?il, ed. IJabiba (Cairo, 1387/1967), 5, 5f.

Because the divine foreknowledge is supposed to preordain the actions of man.12 Cf. Ahmad ibn Sa‘id al-Shammâkhî, K. as-Siyar (Lith., Cairo, n.d.), 81, 2 f.; biographical material concerning §uhâr al-*Abdi cf. my Anfange muslimischer Theologie (note 7).13 Cf. Encyclopaedia o f Islam, 2nd ed.. Ill 649 f. (Art. ‘Ibâdiyya’).1 Cf. J. van Ess, Das Kitab an-Nakt des Na??àm und seine Rezeption im Kitâb al-Futyà des Gàhiz {Abhandlungen der Akademie der Wissenschaften Gottingen, Phil.-Hist. lü., 3. Folge, Nr. 79: Gottingen, 1972), pp. 114 ff.1® For the “year of the donkey” cf. T. Nagel, Untersuchungen zur Entstehung des abbasidischen Kalifates (Bonn, 1972), p. 55.; the concept is derived from Sura 2/259. 1® Ibn Sa‘d, fabaqdt (ed. Sachau) VII, 61f.1’ For Abü Hâshim cf. Encyclopaedia o f Islam, 2nd ed., s.n.; for his “testament” cf. T. Nagel, op. cit., (note 15), p. 45 ff.18 Cf. F. Sezgin, Geschichte des arabischen Schrifttums (Leiden, 1967 ff.) vol. 1, p. 595; my edition of the text in Anfange muslimischer Theologie (note 7).2" Fragment nr. 5 of my edition; cf. Anfange muslimischer Theologie (note 7).21 Cf. Der Islam 21 (1933), 77, 4 ff. and M. Schwarz in Oriens 20 (1967), 29 f.22 Cf. ‘Abdalqâhir al-Baghdâdi, U?ûl al-din (Istanbul, 1346/1928), p. 237,-4 f.; Der Islam 43 (1967), 279 and my article in Festschrift A. Abel, p. 124ff.23 Fragment nr. 6 of my edition; cf. Anfange muslimischer Theologie (note 7).24 For the development of the /ra-concept and the history of the hadlth al-fifra cf. my Zwischen fladit und Theologie (Berlin, 1974), p. lOlff.25 Cf., e.g., Ibn Sa‘d, Jabaqat, V 241,19 (the report can be traced to Ayyüb al-Sakh- tiyâni according to Ibn Kathir) and below notes 27 and 28.26 The so-called “Qadarite Murji’ites” like Ghaylân al-Dimashqi are only a seeming exception. They owe their classification among the Murji’ites only to the endeavor of Mu'tazilite heresiographers to distinguish their own school from these “forerunners” (cf. W. Madelung, Der Imam al-Qàsim ibn Ibrahim und die Glaubenslehre der Zaiditen (Berlin, 1965), p. 239).27 Ed. IJusamaddin al-Qudsi (Cairo, 1947 ff.) Ill 359, 1 ff.28 Haydarabad, 1325 ff., II 321, 5 ff.29 In his Qâsim ibn Ibrahim (note 26), p. 228 f.


3® Cf. Sezgin, op. cit., (note 18), vol. 1, p. 111.81 Literally: “suspended their religion around their neck” (galladühum dinahum).32 Dawla. Incidentally this is the earliest passage where the word is used in this sense.33 Cf. my edition and commentary of the text in Arabica 21 (1974), 20 ff. especially section 5 ff; for Muhammad’s affair with the wife of his adopted son cf. Sura 33/37 and W. M. Watt, Muhammad at Medina (Oxford, 1956) 329 ff.34 Cf. Ibn yajar, Tahdhib al-Tahdhib II 321, 4 f.35 Cf. Ibn ‘Asâkir, Ta'rikh Dimashq, Tahdhib by ‘Abdalqadir Badrân (Damascus, 1329/ 1911 flf.), IV 246, -7 ff.3® Cf. my article in Arabica 21 (1974), 52.37 Cf. Madelung, Qâsim ibn Ibrahim (note 26), p. 231 flf,38 Cf. Madelung, op. cit., (note 26), p. 229.39 Cf. my article in Arabica 21 (1974), 34. Abü Hâshim is said to have collected hadith in support of the “Saba’iyya” (cf. his biography in the Ta^rlkh Dimashq by Ibn ‘Asâkir, MS Damad Ibrahim Pa§a 877, fol. 17b-19b).4® Cf. Dhahabi, Ta'rlkh al-Islam III 359, 12 f. and Mas'ûdï, Murüj al-dhahab, ed. C. Barbier de Meynard et Pavet de Courteille (Paris, 1861 flf.), V 176 f.41 Cf. Madelung, Qâsim ibn Ibrahim (note 26) p. 229.42 Cf. Ibn Sa‘d, Jabaqât V 159, 5 flf.43 Cf. Ibn Sa‘d, Jabaqât V 158, 1 flf.44 Cf. Ibn Sa‘d, Tabaqât V 82, 24 flf.45 Cf. Ibn Sa'd, Tabaqât V 83, 15 flf.4® Cf. Tabarî, Tafsir, ed. Mahmüd Muhammad Shâkir and Ahmad Muhammad Shâkir (Cairo, ca. 1960 flf.) XIII 548 flf., especially 550 f., nr. 16102 f.47 Cf. W . M. Watt, ‘God’s Caliph, Qur’ânic Interpretations and Umayyad claims’, Iran and Islam, Minorsky Memorial Volume (Edinburgh, 1971) 565-574, especially p. 568 flf.; my Zwischen Hadit und Theologie (note 4).48 Cf. J. van Ess, ‘Les Qadarites et la Gailânïya de Yazid III’, Studia Islamica 31 (1970), 269-286.49 Cf. Tabari, Ta'rikh II 784.5® Cf. Ibn Batta, Ibâna, ed. H. Laoust {La profession de fo i d'Ibn Batfa; Damascus, 1958) 32, 4 f. "51 R. Blachère, ‘Regards sur la littérature narrative en arabe au I®> siècle de l’Hégire (V IP s. J.C.)” , Semitica 6 (1956), 75-86. For Wahb ibn Munabbih cf. also R. G. Khou- ry, Wahb b. Munabbih, 1-2 (Wiesbaden, 1972).52 Cf. R. Rubinacci in Annali dell’Is tit uto Universitario Orientale di Napoli 4 (1952), 104 flf. and Ennami in Journal o f Semitic Studies 15 (1970), 65.53 Cf. his article in Arabica 15 (1968), 87-89. [= T h e Spiritual Background o f Early Islam (Leiden, 1972), 311 flf.].54 The authenticity of the dialogue presents some diflficulties; the condition of its text is rather bad, and one version is attributed to John’s pupil Theodorus Abü Qurra. Nevertheless one usually counts it among John’s works (cf., e.g., H.-G. Beck, Kirche und theologische Literatur im byzantinischen Reich (Munich, 1953), 478, and D. J. Sahas, John o f Damascus on Islam (Leiden, 1972), p. 99 flf. where it is argued that Theodorus may have written down the treatise and transmitted it). One should avoid drawing conclusions from it that go too far concerning the degree of the development of contemporary Muslim theology. The Christian author may have ascribed arguments to his fictitious Muslim opponent which take on dialectical value only in the context of his own argumentation, or they may have been added later on, perhaps by Theodorus

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(cf., e.g., Sahas 114 f. where a connection with the discussion concerning the created- ness of the Qur’an is supposed which did not yet exist at that time). For an example of “kalam” structure comparable to that in âsan ibn Muhammad b. al-ânafiyya’s treatise, cf. Sahas ISl.88 Cf. above p. 96.5® Cf. A. Voobus, History o f the School o f Nisibis (Louvain, 1965).8’ I owe this expression to a discussion with Professor A. Udovitch at Princeton.58 Cf. Voobus, School o f Nisibis (note 56), p. 260.89 His grandfather Mançûr b. Sarjûn had kept a high oflSce under Mu'awiya. His father, obviously the famous Sarjün of the Arab sources, seems to have had great influence on ‘Abdalmalik; he was perhaps responsible for the whole tax administration of Syria and Egypt. John himself left the court and retired to the monastery of St. Sabas near Jerusalem; the reasons and the date of this decision are not quite clear (perhaps after Hishâm’s accession to the throne and because of the deteriorating conditions of the Christian subjects under Muslim rule). In Byzantium his family and he himself were regarded as “Quislings.” As the last publication on the subject (which frequently only repeats the results reached by Lammens and Nasrallah or P. Khoury), cf. D. J. Sahas, John o f Damascus on Islam (note 54), especially p. 26 fif. and 44 f. «0 Cf. Sahas (note 54), p. 145.

For the history of this specific problem cf. my Zwischen Ifadit und Theologie (Berlin, 1974), p. 95 ff.

Cf. A. S. Tritton, The Caliphs and their Non-Muslim Subjects^ 2nd ed., (London, 1970), pp. 6, 18 f., 43, 167. Also A.-T. Khoury, Les théologiens byzantins et l'Islam (Louvain, 1969), p. 30 If.

Cf. his article in Revue de l ’histoire des Religions 166 (1964), 51-58.This brings up the question whether ‘Abdalmalik’s initiative had any consequences

for the importance of the mutakallimm for Muslim society in the following centuries and how the position of a theologian was ranked in the social hierarchy of that time. There is no doubt that the mutakallimün possessed great influence at the court of the early Abbasids, until the milpm when the jurists started to take over; Sh. Pines has reminded us of some material which points in this direction (cf. his article in Israel Oriental Studies 1 (1971), 229ff.). I am, however, not quite convinced that Pines’s further thesis that the mutakallimün “were a fundamental political and social institution of Islam” and “ indispensable” for its intellectual life already in Umayyad times {ib. 228 and 232) can, for the moment, be sufiiciently documented by the sources we have. Fârâbî (who is extensively quoted by Pines, p. 225 ff".) is no real substitute: when he stresses the apologetic outlook of kalam, he does not think of its importance for society and especially not of a definite function of the mutakallimün at a certain given time, but uses the language of an Aristotelian for whom all thinkers who do not stick to the syllogistic method are “dialecticians.”

D I S C U S S I O N

J. VAN ESs; I would like to rearrange the material of my paper in order to make it more apt for discussion and also in order to bring it a little bit closer to the topic of our Colloquium. What I wanted to prove was that Islamic theology already existed in the first century Hijra. However, this statement is imprecise in three respects. (1) Because the first century Hijra is, of course, an arbitrary interval; I should have said, rather.


that Islamic theology, in my opinion, started about the year 70 Hijra, in the second half of the reign of the Caliph ‘Abdalmalik. (2) Secondly, the term theology itself is not altogether precise. In the present context, I do not mean by theology religious movements or religious parties. These religious partisan movements existed earlier (for instance, the Kharijites) and their existence implies the existence of religious discussions, but discussions that were rather more concerned with political issues. In my paper I limited theology to kalam. The two terms are not identical; there are other kinds of theology, other theological procedures, which one would not immediately call kalam. However, the theology in question in my paper is always that of kalam.

A. sabra: So it follows immediately from what you say that to talk about the beginning or origin of Islamic theology is not at all the same as talking about the beginning or origin of kalam.

J. van ess: I am inquiring into the beginnings of the term ^kalam' and of kalam procedure. Theology, for instance, also occurs in the treatise, or rather the epistle, writtoi by âsan al-Baçri to the Caliph ‘Abdalmalik concerning the question of the free will ; but this is not kalâm. He simply expounds his opinions in answer to the Caliph. It is an exposition of a doctrine, but not kalâm in the proper sense. Kalâm is something else. Kalâm in Arabic is not defined by reference to its contents as, theo-logia, something about God, a logos about God, but it is defined in terms of its stylistic form, the dialectical method of argumentation. If you effect a “ kalâm” you have effected a speech. You proceed, for instance, by a dilemma. You say: We have one statement; if this statement is true, then there follows either A or B; now I can prove that A is wrong, and I can also prove that B is wrong; therefore it follows that the statement itself is also wrong. This is a kalâm.

A. sabra : Is this a definition of kalâmlJ. VAN ess: This is a kalâm, the procedure used in kalâm which is called kalâm. So

kalâm, therefore, in my opinion, here means a procedure. This is what is usually meant if you have a theological text and the word ^kalâm' appears in the title. In such a case, you have discussion about a topic that usually occurs according to a certain structure, by question and response, for instance. It is often something like an imaginary trial: One knows that a given individual has such and such an opinion; then somebody else asks this person: do you believe that?, he has to answer. This question and response scheme is frequently built up into the form of dilemmas. Now, I wanted to find out at what time this peculiar structure of thinking occurs for the first time. This is what I wanted to do, to ask about "'kalâm" in this restricted sense. And the result, for me at least, was that one does find this peculiar structure of thinking in the first century Hijra.

Finally, my initial statement is imprecise in a third sense (3) because I am only interested in theology or in kalâm in a written form. I wanted to prove in my paper that kalâm existed in a written form since the year, say, 70 Hijra. Now let me try to enumerate the problems and the consequences involved in all of this.

First, the results for the history of Arabic literature and the history of Arabic civili- ^tion. The most important problem here is that of early literacy. What I am maintaining nieans that there were written texts not from the beginning, but from a very early date in the Hijra era. This has to be opposed to the popular dogmas of the importance of the oral tradition in Islam and of the amazing memory of the Arabs. It has been claimed, for example, that there was only, or mostly, an oral tradition in the first century Hijra. I think that this idea is a bit romantic. Against it, early literacy is proved by the existence of early texts. If you recall my paper, you will notice that I wanted to prove that two texts, two theological texts, date from the first century Hijra, both written

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by the same author, a man named Çasan ibn Muhammad ibn al-^anafiyya who was a grandson of the fourth Caliph ‘Ali, and who died about the year 100. Moreover, there are yet other texts. This, then, is the result for the history of literature: A certain proof of early literacy.

Secondly, the consequences for the history of theology, sub-divided into two questions: (1) that of the origins of Islamic theology, and (2) that of the role of the theologian in society. First, then, the question of the origins of Islamic theology, and now not only of “ kalam structure,” but of theological endeavors on the whole. It seems, at least in the two texts that I found, that theology emerged or came about through the instigation of the Caliph; the Caliph may have initiated religious policy in the style of a Basileus. That is, the Caliph may have acted because of political reasons - this is what I wanted to prove, at least to make probable, in my paper. It seems that he tried to appease the revolutionary elements; at first the extreme Shi'ites, and then the upholders of free will whom he tried to refute as well as appease. Perhaps (I don’t dare say obviously) he did the latter because free will meant responsibility, and responsibility meant control by others, even control of the Caliph. We can show by the texts, for example, that the Qadarites upheld the opinion that the Caliph must be deposed if he commits grave sins, while, on the other hand, predestination can be used in order to show that the political power is simply a token of divine guidance.

Secondly, there is the problem of the role of the mutakallimün, of the theologians, in society. It is an interesting point but a very difficult one; with it we perhaps come closest to one of the topics of our Colloquium. If we can prove that from the very beginning theology was connected with politics and that the Caliph tried to support theology as polemical, to use theology against his political opponents in the style of the Byzantine Basileus, then we can assume that this situation went on in the next decades and perhaps also during the next two centuries. You know that Heraclius, the last Basileus before the Muslim invasion, brought forth monotheletism in an attempt to make theological policy in his own realm; and you also know that only the Maronites remained of this attempt because the Muslims then inundated the Byzantine empire. Now the question is whether the mutakallimün were connected with the empire and with the Caliphate as well. I am not yet finished with this problem and can only refer to some possible relevant evidence. The mutakallimün had to convert people. I am not sure whether they really accompanied the armies - as Pines tried to show in his last article - but I would point to the fact that the mutakallimün were invited to the court under the Abbasids and were used as ambassadors to unbelievers.

R. hashed: Because they were mutakallimünlj. VAN ESs: That is the problem. I cannot prove that it is so and I am really hesitant

about it. We only have stories in the biographies of the mutakallimün where the Mu‘tazilites are praised for the fact that one of them was sent by Hârün al-Rashid to India in order to discuss theology with the so-called Sumaniyya. Of course, this is a legend and one is a little bit uncomfortable with it. We need much more material and it is very difficult to enter into such, should I say, sociological questions. As a matter of fact, they are historical ones, but our texts are not written expressly to answer such questions; they are not interested in them as such; for them all that is involved went without saying. So we have to build up our conclusions from marginal remarks and this is always a rather difficult business. Still, operating under such limitations, I think that in these early times the mutakallimün - let us say even the whole religious class - were not yet an independent block. On the contrary, the state tried to establish theological policy by means of the mutakallimün. Recall, for example, the famous mihna, the in-


quisition, the persecution of the naive believing people of Bagdhad, under M a’mun. Here, it seems to have happened that, at one and the same time, we have to do with, on the one hand, a religious critique of the state or of the political power, and, on the other hand, with a critique oîkalàm, of theology. I think that this is rather significant. For only at that time, it seems to me, did the community and the class of religious people, theologians and jurists, start to regard themselves as independent of the religious authority of the Caliphs. This would mean that the conmion dogma proffered in all of the general surveys of Islam - that there is no difference between state and church in Islamic culture - is only true for perhaps the first two, two and a half, centuries. Not afterward, because then you have the jurists on one side and the Caliphs on the other.

A. sabra : I would like to ask you whether, on the basis of your theory or hypothesis on the origin of kalam, you would venture to speculate about the nature of kalâm or its characteristics in general? That is, would you as a result of your view necessarily take this form, this style, to be the characteristic that distinguishes kalâm from other disciplines, or would you take something else as the key characteristic?

J. VAN ESs: This is a problem. Kalâm is not always the same; we have I don’t know how many centuries of kalâm. Some years ago I thought that kalâm was essentially dialectical and polemical; the mutakallimün were always on the attack, they were destructive, negative, they did not build up. Now, I have changed my opinion. But I am not a systematician, I am still an historian with respect to the problem. I think I now know what caused my mistake in holding this earlier opinion. Two things. First, I was misled by Maimonides and al-Fârâbi, by all of those Aristotelians who saw kalâm as dialectic; of course, this fitted into their scheme. This is one thing. The second is the fact that at the beginning kalâm is for the most part polemical; but this has something to do with the situation. The Muslims were a minority. They were living in the towns, and even in the towns there were many Christians, Jews, Manicheans, and so forth so that they had to convert people, they had to polemicize against them, they had to convince them.

A. sabra : When I became involved in kalâm, I noticed that all of the authorities who propagated the view that kalâm is polemical were enemies of kalâm. For example, Ibn Khaldün; he did not like kalâm and had no use for it, and it is not at all clear whether he knew much about it. As a matter of fact, it would seem that he hadn’t seen all those books that he talks about in the Muqaddimah. And the case is similar with men like Maimonides and al-Fârâbi.

R. fr an k : ‘Abd al-Jabbàr makes a distinction at one point: There is a question raised and he says that we can take that question either bi al-fariq al-Hlmi or bi al-tariq al-Jadali, that is, either in a way that would involve the science that we are dealing with or in a dialectical way. Then he immediately says that we could use the dialectical way to show that the question at hand really isn’t pertinent to the thesis under discussion and thus be rid of it. But, on the other hand, he proceeds to deal with the question because he says that the question is important, and so we should use the fariq 'ilmi, the scientific method, if you wish, in treating the question. In a sense, therefore, he is making a distinction between what is surely a dialectical argument, what happens when you » e opposing an opponent, and what happens when you pose a question as a

/ question within your own framework.A. sabra : Yüsuf! My question is still not answered. Kalâm is not polemics, although

it may have started as polemics. It is not theology, because theology is only part of it. It is not this dialectical structure, because the dialectical structure is only a form and these people were not arguing for the sake of arguing. So what is it?

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j. VAN ess: I think that our problem is that you are always arguing in an “ontological” way, and I am always arguing in a “nominalistic” way. You want to know something about what kalâm is. I only wanted to explain where the word ‘kalâm' comes from.

A. sabra: Yes, but as someone who has spent some time studying kalàm, what are your feelings about it? At one time you had the view that it is polemics, and now you have given that up. Why?

J. VAN Ess: It depends upon the situation. I cannot say that kalâm is this or that; kalâm is seven centuries and even more of texts. And &rst you would have to read these texts.

R. fr a n k : I think that, after Abû Hâshim, you have to call it theology.A. sabra : Why do you have to call it theology? If you were to translate ‘theology’

into Arabic literally and then apply this word to what a mutakallim does in the section of his work that deals with “physics,” he would not accept it. He would tell you that ‘theology’ denotes the section that comes at the end when one talks about God. So why should we call it theology if they didn’t?

But let me try another approach by asking the following question: If you were to ask a representative Christian theologian whether he had any source for his knowledge or belief in the existence of God other than a piece of reasoning which is based on something common to all humans - that is to say, either on experience or on the principles of pure reason - what would his answer be?

R. mckeon: They would have divided into two sorts. And this is true all the way back to St. Augustine. There were those who said that theology is an architectonic science and, therefore, all sciences would get their first principles from theology. And Augustine would talk about the signs, the images, and the vestiges, of God. Then there were others who said, no, there are two kinds of science; there are the theological sciences and there are the human sciences, and theology does not furnish the first principles of human sciences.

A. sabra: Well, the reason I am asking this question is because for me a mutakallim is a man who would answer, “No.” That is to say, a mutakallim is a mutakallim if and only if, apart from a process of reasoning based on principles that are common to all human beings, he has no access whatsoever to knowledge of the existence of God. And these principles may be either empirical or non-empirical; they use the word (farwrf, “necessary,” and the necessary includes both, it includes something like the law of identity, a logically necessary proposition, and it would also include that which is given in experience.

J. VAN ESs: That is true, at least for the Mu'tazilites. A Mu‘tazilite mutakallim would never rely on Scripture because he would say that Scripture is only true if there is a God who revealed this Scripture. Therefore, we have first to prove the existence of God. But if we could prove the existence of God by Scripture, we would have a vicious circle. In order to avoid the vicious circle we must prove the existence of God by rational means, and we are convinced right from the beginning that our results agree perfectly with Scripture.

R. m ckeon: But this is true of the Christian too. The Christian would not take Scripture, but would say that we must prove the existence of God and that we can do it in one of two ways.

A. sabra: But are they rational? And if these ways are rational, are there besides these rational ways, ways that are not rational?

R. mckeon: There are the a priori proofs and the a posteriori proofs. Both of them are rational, but those who hold to the a priori proofs say that the a posteriori are not


rational, and those who hold to the a posteriori proofs hold that the a priori are not rational.

E. s y lla : Isn’t there also revelation?a . sabra: Yes, that’s what I wanted. A mutakallim would not base his beliefs on

revelation. Yet what 1 am saying is that if you define a mutakallim with reference to his position vis-à-vis knowledge, then I can explain why the kalâm people were very often in opposition to not only philosophers, who would be committed to another theory of knowledge as can very easily be shown, but would also be in opposition to the jurists whose position on knowledge also differs from theirs, and even in opposition to the mystics for similar reasons. That is to say, I can see the situation more clearly,I can understand why certain things happened in the history of kalâm vdth the help of this definition.

r . rashed : Someone like Ibn Taymiyya, is he a mutakallim or not? The problems treated by Ibn Taymiyya are in most cases problems of the mutakallimün. Yet Ibn Taymiyya is one who thinks that the existence of God is fifra (“native to the mind”).

A. sabra : Right, right. That is in agreement with my definition or criterion; that is why I don’t consider him a mutakallim. And that is why I would also not consider Ghazali a mutakallim, although he wrote on kalam. Why? If you read Ghazâli on kalâm, what he says is that there are certain intelligent people whose heart is in the ri^ t place so to speak, but who have certain doubts about God because of their intellectual bent or, maybe because they have also been exposed to philosophy or something like that. Thus, they are troubled. For such people, kalâm would be a good thing because, he hopes, through a study of kalâm they are going to get rid of these troubles. If you are not in that situation, then leave kalâm alone. It’s not for you. From which I would deduce, again, that Ghazâli is not a mutakallim. Why? Because a mutakallim is a man who starts from a fundamental distinction between belief and knowledge', he says that true belief may be something that you start with, perhaps because of your education, upbringing, or whatever, but that is not enough. In order to be a mutakallim, you have to reach knowledge. And to reach knowledge you have to transform your belief into knowledge. Be careful. You don’t transform belief into knowledge by producing arguments for this belief. You are in fact involved in substituting something else for your belief because you are going to engage in a process of reasoning which has nothing to do - save perhaps by accident - with that belief. Once you reach that something else, that stage, then what you have is no longer belief, but knowledge.

T. GREGORY: Je crois qu’on doit réfléchir sur la définition proposée par M. Sabra. D a bien raison de dire qu’il n’y a pas un kalâm qu’on puisse définir en dehors de l’oeuvre des mutakallimün. Par ailleurs il ne faut pas utiliser le mot “ théologie” et parler de théologie musulmane; il faut dire kalâm, qui est une chose tout à fait différente et particulière à la civilisation de l’Islam. Ainsi, je suis toujours heurté par mes collègues historiens de la philosophie du moyen âge qui utilisent le mot “théologie” pour définir la position de S. Augustin. Pour S. Augustin, le mot “théologie” n’a que le sens de Varron: mythologie; aussi on doit être très prudent en parlant de la théologie de S. Augustin ou de la théologie de S. Anselme, ne serait-ce que parce que ils n’avaient pas le mot. De même, il faut dire pour la civilisation de l’Islam: “kalâm”, pas “ théologie” .

Si nous acceptons complètement la définition de M. Sabra, on doit même dire qu’il y a les kalâm - au pluriel - des mutakallimün', on ne peut pas individualiser quelque- chose de méta-historique. Dans l’historiographie occidentale, par exemple, il y a longtemps une historiographie thomiste qui définissait la théologie des théologiens du

110 J. VAN ESS

moyen âge selon ses rapports avec la théologie de Thomas d’Aquin. Ici, nous avons une réalité plus historique; et il y a les kalâm, qui sont les fruits de la spéculation des mutakallimün.

M. Sabra a posé la question: quel est le rapport entre la croyance, la foi et l’intellect? C’est toujours un équilibre instable, et chaque mutakallîm a résolu le problème pour lui-même. Il n’y a pas une orthodoxie dans l’Islam comme dans la réligion chrétienne. C’est plus facile d’y tenir des positions différentes. On ne peut que dire: les kalâm, ce sont l’oeuvre des mutakallimün. On doit d’ailleurs toujours tenter de faire sortir la définition d’une certaine discipline de l’oeuvre de ceux qui l’ont pratiquée.

A. sabra: In fact, the theory of knowledge that I outlined is not only the Mu'tazilite theory, it is also the theory of the leading Ash'arites. So it is not restricted to one school, but to these two largest schools.

N. shehaby: Sabra, it seems to me that we can use neither the word ‘theology’ nor the word ‘kalâm’. For you want to restrict kalâm to a particular genre of writing. You take certain characteristics that you find in certain writings that you don’t find in others such as those of Ghazâli or Ibn Taymiyya, and you say “ I call that, or that part of the corpus, kalâm."

A. sabra: I am trying to identify the discipline and a group of people at the same time. These people existed as groups, the kalâm people, the fuqahâ' (the jurists), the philosophers (Jalâsifa) and so on; they existed as groups that had certain commitments, they subscribed to certain things that were in conflict with one another, and I feel that I have to understand this situation as well as the doctrine. It seems to me that the two go together. For it seems that, save for some residual puzzles or problems here and there, if you take knowledge as a criterion, I can distinguish between all of these groups.

R. rashed: Excuse me. M. Van Ess, I have a question now: Do you agree with this definition of kalâml

j. VAN ESs: I am not quite sure. Yours is the systematical approach; therefore, you are concerned with defining things. Mine was the historical approach, I only wanted to know where it is that the word ‘kalâm’ is used for the first time.

A. sabra: Perhaps so, but I take it that producing a definition or criterion is part of the attempt to understand the situation historically. Yes, it is systematic in a way, butI am interested in historical explanation, I want to understand the historical situation. And I believe the definition helps.

R. rashed: I should like to follow this whole debate about defining kalâm with another question and ask you if it is possible to give a social explanation, or any kind of explanation, of the beginnings of kalâml

J. VAN ess: I cannot go beyond what I have already said. The only thing that I thought I could render probable was that the earliest examples of theology we have seem to owe their existence to the political intentions of the Caliph. But this, of course, is not a sociological explanation. I am unable to say anything about the social background of kalâm, and of the mutakallimün, at that time. I would, perhaps, be able to find some examples for the social background in ‘Abbàsid times where we have more texts. But even then, when you read the text, you feel a certain amount of desperation.

R. rashed: I am more convinced now than ever that it is impossible to examine a question of origins.

J. VAN ESs: Perhaps you expect too much of an Islamicist. Islamic studies are one century behind Latin medieval studies; there are only a few Arabicists. Islamic studies means everything about Islam, not simply Islamic theology, but also philosophy, literature, law, even music and whatever else you may wish. It is impossible to give ready


results about all of this. We are at the very beginning of things, as perhaps the classical philologists were in the sixteenth and seventeenth centuries; we are acting like the humanists. So to ask social questions may be good, but at present you will get either no answer or only vague answers.

J. MURDOCH: But I thought that I heard you say that part of the origin or the development of what the mutakallimün were doing had to do with the necessity of conversion within the villages.

J. VAN ess: Perhaps. This was a mere suggestion. I have but two or three texts - that’s all.

J. MURDOCH: But you are in better shape than the classicists. There, for the question, especially the social question, of the origins of natural philosophy in the sixth centuryB.C., there are almost no texts at all.

J. VAN ESS: Well, we have about two million Arabic or Persian manuscripts in the world. There are more than 500,000 in Istanbul alone. Only a small percentage of the texts - perhaps six or seven per cent - are known and printed. Of the rest, you may know a few titles if you are patient enough to go through the catalogues. But many of the titles of the works are not even known, not to speak of the contents. Therefore, Arabic studies are simple and difiicult at the same time. They are difficult because Arabic is a diflBcult language; one has to learn it. They are simple, because once you know Arabic, you need only go to Istanbul, take any manuscript, try to read it, write an article on it with the title: “We read for you....” And that’s it.

R. rashed : Things are better for you than they are for us in the history of Islamic science.

S C IE N C E , P H IL O S O P H Y , A N D R E L IG IO N IN

A L F A R A B I ’ S E N U M E R A T IO N O F T H E S C IE N C E S *

I. PR EL IM INARY REMARKS

One o f the striking features o f classical Islamic philosophy is the prominence o f political philosophy and the incorporation o f jurisprudence and theology into philosophy by subordinating them to political philosophy. During the ten centuries that separated Cicero from Alfarabi, one cannot point to a single great philosopher for whom the problem o f philosophy was inseparable from the problem o f political philosophy or in whose writings political philosophy occupies a massive, central, or decisive position. Political philosophy may not be totally absent from pagan and Christian Platonism in the Hellenistic period, but it is marginal and subterranean, or else overwhelmed by metaphysics, theology, and mysticism.i

O f Alfarabi’s political works, the fifth chapter o f the Enumeration o f the Sciences, entitled “ On Political Science, the Science o f Jurisprudence, and the Science o f Theology” (“ De scientia ciuili...., et de scientia iudicandi, et de scientia eloquendi” or “ De scientia ciuili et scientia legis et scientia elocutionis” ), is perhaps the earliest and best known statement on political science in the Middle Ages. It was available in Arabic as well as in Hebrew and Latin translations. And it was known through summaries, paraphrases, and quotations in all these languages. It was intended as an introductory statement and forms part o f a book intended for the beginner, a contribution to general education, as it were. It is a good text with which to begin.

Since Alfarabi wrote a few other introductory statements o f this sort, it is worthwhile to look first at his Introduction where he states what he intends to do in this book in particular. Alfarabi’s intention is to enumerate the “ generally known” (mashhüra) sciences and make known their content, parts, and the content o f each part (43.4-6). The book is divided into five chapters, covering (1) the science o f language, (2) the science o f logic, (3) the sciences o f mathematics, (4) natural science and divine

^ Cultural Context o f Medieval Learning, 113-147.

MUHSIN MAHDI

114 M. MAHDI

science (metaphysics), and (5) political science, the science o f jurisprudence, and the science o f theology. The uses to which one can put the content o f the book are also five in number. First, the student who wants to learn and inquire into any one o f these sciences will know to what he should turn and into what he should inquire, and also the benefit o f learning or inquiring into that science. Second, one can use the book to compare the sciences as to their excellence, utility, precision, and so on. Third, it can be used to test the claim o f an ignorant man who pretends to know a science by asking him to enumerate its parts and give its content. Fourth, it can be used to test someone who knows a certain science so as to find out how much o f it he knows. Finally, the book can be used by someone who is after a quick education, and likes to learn the outline o f every science, imitate the men o f science, and be thought to belong to them. The five uses are thus intended for different kinds o f readers. The first two are for the student who wants to learn. He will make use o f it to know, first, what he is about to engage in. But the book is also meant to be useful to the student who wants, not just to “ learn” a science, but to “ inquire into” it, compare it with other sciences, and learn the relative excellence, utility, precision, and so on, o f all the sciences. This seems to be the highest positive use o f the book. So far as the genuine student o f science is concerned, this book is a beginning and an end : he begins with it before he goes on to study the individual sciences, and he comes back to it after having studied them to learn what he should “ inquire into” and about their relative rank and excellence. The next two uses are meant for testing others, both those who merely claim to know and those whose knowledge is incomplete. Alfarabi does not state the qualities o f the man who will do the testing. The assumption is that it will be someone who himself is ignorant o f these sciences, but likes to test others, and will therefore read this book for that purpose. The last use, too, is somewhat problematic. Merely to learn the outline o f every science and to appear to be learned do not seem particularly worthy objectives. A ll one can say is that, at this initial stage, it is difficult to distinguish between the genuine and spurious student or between the potential philosopher and the potential sophist.

Alfarabi’s enumeration o f the sciences is not conventional or haphazard. The book consists o f five chapters and has five uses (43-44). Attention is drawn to the third or central chapter on the sciences o f mathematics, whose seven divisions are enumerated in the Introduction (43.7-9 ; cf. 75.3).

ALFAR A B I ’ S ‘ ENUMERATION OF THE SCIENCES’ 115

The fourth chapter includes, not one, but two sciences (natural science and divine science [metaphysics]). And the fifth chapter includes three sciences (political science, the science o f jurisprudence, and the science o f theology), which are simply listed without indicating what they have in common.

When we turn from the Introduction to the divisions and subdivisions o f the book’s five chapters, we find the following arrangement. (1) The science o f language is divided into seven “ major” parts; the seventh, the science o f the rules that govern poems, is subdivided into three parts. (2) The science o f logic is divided into eight parts, the first three o f which deal with the rules o f syllogism in general and its parts, and the rest deal with the rules o f the five modes o f reasoning proper. (3) The science o f mathematics, like the science o f language, is divided into seven “ major” parts, o f which the second, the science o f geometry, is subdivided into two parts and the fifth, the theoretical science o f music, is subdivided into five “ major” parts. (4) Natural science, like the science o f logic, is divided into eight parts, but these are eight “ major” parts; and divine science is divided into three parts. (5) Political science, the science o f jurisprudence, and the science o f theology, finally, are each divided into two parts. So, the five chapters cover a total o f eight sciences, divided into thirty-nine parts, o f which twenty-two are “ major” and seventeen are not “ major.” Three o f the thirty-nine parts (the seventh, the seventeenth, and the twentieth, all o f which are “ major” parts) are subdivided into a total o f ten parts, o f which five are “ major” and five are not “ major.” In the center o f both the thirty-nine and the forty-nine parts stands the theoretical science o f music, the fifth part o f the book’s third or central chapter; and, like the book as a whole, it is divided into five major parts. Finally, three o f the eight sciences (natural science, divine science, and political science, which have a total o f thirteen parts) are set apart from the other five (and their twenty-six parts or, with their subdivisions, thirty-six parts) by emphasizing the substantive “ science” rather than its subject matter, with the consequence that one cannot easily separate the “ science” from its subject matter - one cannot, for instance, say “ natural” instead o f “ natural science” as one can say “ language” instead o f the “ science o f language.” Even without going into fancy numerological notions, the numerology o f the Enumeration o f the Sciences calls attention to a number o f peculiarities for which there are no ready or conventional answers.

116 M. MAHDI ALFA R AB I ’ S ‘ ENUMERATION OF THE SCIENCES’ 117

Why is the science o f mathematics so central? Why are the science o f the rules that govern poems, the science o f geometry, and the theoretical science o f music emphasized by giving them subdivisions? Why is divine science (metaphysics) combined with natural science in the same chapter? And why is political science combined with the science o f jurisprudence and the science o f theology?

One way to see how Alfarabi puts his building blocks together is to compare their arrangement with other generally known arrangements o f the sciences. These are basically two. The first is the Aristotelian classification o f the philosophic sciences into theoretical sciences (mathematics, physics, and metaphysics) and practical sciences (ethics, politics, and economics). The second is a more comprehensive classification o f all the sciences, both philosophic and non-philosophic, which existed in the Islamic community. The principle o f this latter classification is not the distinction between theoretical and practical philosophy or science, but rather the distinction between philosophy (or science as defined by philosophy) and other disciplines that are not philosophic or scientific in the sense that they owe their principles, methods, and conclusions (but especially their principles or premises), to unaided human reason. Depending on how one looked at the source o f the principles or premises o f these sciences, they were called Arabic, traditional, legal, or Islamic sciences. They included two main branches : the sciences o f language - that is, the Arabic language - which were considered instrumental or propaedeutic, and the religious sciences - that is, the Islamic religious sciences - which included the Koranic sciences and the sciences o f the Tradition o f the Prophet (these being the primary sources o f religious doctrine and practice), and such ancillary sciences as jurisprudence and theology. A ll these sciences were also considered indigenous because their subject matter was originally given or articulated by the convention o f a particular nation or by revelation, and distinguished from the foreign sciences or the sciences o f the ancients, whose subject matter is given or articulated by nature or human reason. Broadly speaking, the difference between the traditional or religious and the rational or philosophic sciences was understood in the following way. To find out whether a linguistic expression or religious belief is correct, one must go back to linguistic usage or the revealed texts, which are the final authority in such matters; while to know whether a mathematical or natural law is correct, one observes and thinks, and this

is the final authority. Now, compared with these two classifications, Alfarabi’s classification is “ unprecedented” and follows a “ method which had not been followed by anyone else.” 2 it ignores the principle underlying the classification o f the philosophic sciences into practical and theoretical as well as the principle underlying the classification o f all the sciences into rational or philosophic and traditional or religious. His “ generally known” sciences encompass more than the philosophic sciences. They include the sciences o f language, and the science o f jurisprudence and the science o f theology, which no one before had classified as philosophic sciences. These traditional or religious sciences are integrated into the philosophic sciences. Yet their integration is not effected on the basis o f the principle underlying either o f the two generally known classifications.

II. SCIENCE, ART, A ND PHILOSOPHY

Looking again at the five chapters that make up the Enumeration o f the Sciences one notices that in a number o f places Alfarabi departs from the program announced in the Introduction. Indeed, almost one-third o f the book consists o f digressions in which Alfarabi discusses subjects that fall outside the enumeration o f the generally known sciences and their parts and sub-parts and content. As I see it, there are seven such digressions.(1) The first occurs at the beginning o f the first chapter where Alfarabi defines “ rules” {qawânîn) and their relation to “ arts” (^anaH^) and “ instrument” (aid) (45.6^6.8). The second, third, and fourth occur in the second chapter, whose arrangement is curious in that only a small part o f it (70.6-72.10) enumerates the parts o f the science o f logic. It begins with(2) a lengthy “ report” on the utility o f logic, its subject matter, and the meaning o f the title “ logic” (54.16-63.13). This is followed by (3) an exposition o f the classes o f syllogism, syllogistic arts, syllogistic statements, and the major and minor parts o f syllogistic statements (63.14-70.5). And, after the enumeration o f the parts o f logic, the chapter concludes with (4) a defense o f the primacy o f the “ fourth part” in relation to the other seven parts o f logic (72.11-74.13). In the enumeration o f the eight parts o f logic, this fourth part was said to contain “ the rules o f the affairs that make up philosophy and everything by which its [philosophy’s] activities become more complete, excellent, and perfect” (71.3^). (5) The fifth occurs in the third chapter, after enumerating arithmetic and geo

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metry; it comments on the principles and methods o f these two sciences and on Euclid’s exclusive use o f synthesis in the Elements (79.5-12). (6) The sixth occurs at the beginning o f the fourth chapter and consists o f an extended discussion o f natural and artificial bodies (91.7-95.11). (7) The last occurs at the end o f the fifth chapter and details the ways in which theologians defend their religions (108.10-113.7). I will try to show that the general purpose o f these digressions is to clarify the relation between “ science,” “ art,” and “ philosophy,” and contribute to an understanding o f their ranks o f order (cf. 44.2-4 with 113.8).

In the expression “ the science o f language” the term “ science” is initially used in a broad sense: it includes the ability to memorize and recite and, in general, all powers and occupations that are useful or necessary conditions for possessing knowledge or perfecting it, but are not themselves knowledge. Next, it is restricted to knowledge as distinguished from these ancillary conditions. For instance, the “ science” o f simple expressions (lexicography) may require one to memorize the simple expressions in a particular language, but in a more strict sense the lexicographer’s science is knowledge o f the meaning or signification o f each o f these expressions (45.3-4). Further, only two parts o f the science o f language (the science o f simple expressions and the science o f compound expressions) consist o f knowledge o f the significations o f expressions. The other five parts are sciences in a still more restricted sense in that they deal with the “ rules” that govern these expressions. While originally and according to the ancients a rule meant any instrument or practical device used to protect the practitioner o f an art against error (e.g., the plumb line), to encompass everything in his art so that nothing escapes him (e.g., arithmetical tables), or to facilitate an overview o f the content o f his art (e.g., the outline o f a long book), Alfarabi uses the term in a more general way. A rule is a “ universal, that is, comprehensive statement” that embraces many individual things belonging to an “ art,” It is only when a number o f such rules are formed and brought together in the mind according to a definite order that an art with a particular subject matter is formed ; it is only through these rules and their proper ordering that an art stakes out a field o f its own and excludes what belongs to other arts, discovers its own errors, and facilitates its own learning and preservation. This is true o f “ all the arts, whether practical or theoretical” (45.15). To return to the parts o f the science o f language, the first two parts (the science o f simple


expressions and the science o f compound expressions) can be said to consist o f direct knowledge o f their subject matter, which is made up o f many individual things (words, speeches, poems). This is not true o f the last five, i.e., the science o f the rules o f simple expressions (phonetics and morphology), the science o f the rules o f compound expressions (prefixes and suffixes, and syntax), the science o f the rules o f correct writing, the science o f the rules o f correct reading, and the science o f the rules o f poetry (metrics, verse-endings, proper usage). Unlike the first two, these last five parts do not consist o f direct knowledge o f individual expressions, but o f knowledge o f the general rules that govern these expressions, arranged in an orderly manner so as to encompass the behavior o f certain parts or aspects or groups o f expressions under certain conditions, e.g., when spoken, written, used in poems, and so on. Occasionally, Alfarabi calls what appears to be one or another o f the last five parts (e.g., writing and grammar) an “ art,” as when he Hsts “ writing” along with “ medicine, husbandry, and carpentry” (45.14-15) or when, in Chapter II, he compares the “ art o f logic” with the “ art o f grammar.” But in such cases “ art” does not necessarily mean the same thing as “ science,” for one may have the “ science o f the rules o f correct writing” without being able to write correctly, let alone elegantly or artistically. Alfarabi argues that the “ science o f the rules” is useful and even indispensable for the correct practice o f the art, but not sufficient for practicing it well. In any case, Alfarabi persists in calling each one o f the last five parts o f the science o f language the “ science o f the rules o f” whatever these rules govern ; he does not identify any o f them as “ art,” nor does he explain how it may serve or is related to a corresponding art. Finally, and unlike the direct knowledge o f the expressions o f a particular language which makes up the first two parts o f the science o f language, the sciences o f the rules o f these expressions afford Alfarabi the opportunity to compare various languages and indicate the common subject matter o f many o f these rules, even though the names given to linguistic phenomena and to linguistic habits may be different in different languages. Still, the science o f language in all its parts deals with a particular language, its expressions, and their rules. Even where it deals with rules that are analogues in or common to a number o f or all languages, it is concerned with these rules in so far as and in the manner they apply to a particular language. The treatment o f what is common to the languages o f all nations belongs to logic.

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In the chapter “ On the Science o f Logic” Alfarabi speaks o f “ logic,” the “ rules o f logic,” the “ science o f logic,” the “ science o f the rules o f logic,” and the “ art o f logic.” Unlike the seven parts o f the science o f language, however, none o f the eight parts o f logic is called a “ science.” Strictly speaking, none o f them is called an “ art” either. Each part is said to be made up o f “ rules” or “ statements,” which means that the distinction between the two kinds o f science that obtained in Chapter I is no longer relevant; all o f logic is o f the “ science o f the rules o f” type and no part o f it deals with individual things. Logic deals with the rules o f intelligibles. These rules, like the rules o f grammar and prosody, and such instruments as balances, rulers, and the pairs o f dividers, are meant to test the intelligibles in which one is subject to error, i.e., the ones apprehended by reflection and inference and reasoning iqiyâs). It is argued that logic is necessary for whoever does not wish to base his convictions on mere opinion, but on knowledge and insight. As to the argument that logic is not necessary, or that experience in dialectical arguments and discussions, experience in mathematics (geometry and arithmetic), or a perfect innate disposition, may be enough to insure correctness in any o f the sciences- this argument is said to deserve the same answer as the argument that experience or a perfect innate disposition are substitutes for the rules o f grammar as means for testing correct language. Unlike grammar, which tests the correctness o f expressions in a particular language, logic tests the correctness o f expressions in so far as they designate the intelligibles in any language ; it gives rules regarding such expressions in so far as they are common to all languages. Further, it gives rules for the correctness o f the intelligibles themselves as they are in the mind, as inner speech. In doing these two things, logic aims at the correct development o f the innate power that distinguishes man as man, so that this power may perform its activity (inner thought and the expression o f thought) in the most correct manner possible. This power can be described as the ability to make a statement (an inner speech or an external expression) with which one corrects or verifies an opinion, which the ancients (Aristotle) call qiyàs: reasoning or syllogism. When properly selected and compounded and arranged, the intelligibles and the rules that govern them form the subject matter o f the science or art o f logic.

In Chapter I Alfarabi referred in passing to the distinction between practical and theoretical arts. In the sense that they do something or per


form an activity, all arts are o f course practical. In Chapter II, when speaking o f the innate power o f reason or speech, Alfarabi says “ it is the power by which man acquires the intelligibles, the sciences, and the arts, by which deliberation takes place, and by which he distinguishes noble from base actions.” Here, the “ arts” are grouped together with the “ sciences” and the acquired intelligibles, and separated from the deliberative and moral- that is, the two practical - faculties. Since the aim o f logic is the correct development o f this innate power or reason or speech as a whole, the “ art” o f logic would appear to be the overarching art, the so-called art o f arts. But as we turn to consider the eight parts o f logic, we learn that none o f them is an “ art.” Each is made up o f a set o f rules employed in what are called the “ syllogistic arts.” On first view, one may get the impression that these arts are “ logical arts,” and that the first three parts o f logic (dealing with the rules o f single intelligibles, o f propositions, and o f syllogisms common to the five syllogistic arts) contain rules that are employed by the “ arts” o f logic, which are presumably the last five parts o f logic; demonstration, dialectic, sophistry, rhetoric, and poetics. But this impression is false. Each o f the last five parts o f logic, too, is said to consist o f rules, but now they are said to be rules by which one examines or tests a special kind o f statements, the ones that belong to the “ arts” o f demonstration, dialectic, sophistry, rhetoric, and poetics, respectively. One must, then, distinguish between, e.g., the rules by which one examines dialectical statements and the dialectical statements themselves or the “ affairs that make up the art o f dialectic and by which its activities become more perfect, excellent, and effective” (71.6-8). Alfarabi does not say that there are five logical arts; what he says is that there are five “ syllogistic arts” ; and, when he expounds the character o f each o f these arts in the third digression, he is not speaking about the (logical) rules by which one examines what makes up each o f these syllogistic arts, but about the syllogistic arts themselves. The distinction between syllogistic and non- syllogistic arts is not based on whether an art does or does not employ reasoning or syllogism, but on the character o f the ultimate activity o f the art (the activity that proceeds from it after it is perfected). Only demonstration, dialectic, sophistry, rhetoric, and poetics are arts whose ultimate activity consists in the employment o f reasoning or syllogism in speech or argument. Other arts, e.g., medicine, employ reasoning and syllogism too, but this is not their ultimate activity; when the art

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o f medicine is perfected and moves on to perform its ultimate activity, it heals the sick. In turn, this does not mean that the arts whose ultimate activity is to employ reasoning or syllogism may not lead to practical activities of abstention from practical activities. Indeed, they all do. However, as syllogistic arts, they produce this practical activity by means o f the kind o f reasoning or syllogism they employ rather than by doing or making anything else. Two o f these arts, rhetoric and poetics, are arts in this sense as well as crafts {sinà'^a as well as san a), that is, arts o f making various classes o f speeches and poems (71.13-12, 72.5-6). Finally, Alfarabi says that each one o f the eight parts o f logic is to be found “ in a book” and proceeds to give an account o f what is “ in” each o f these eight books (the traditional six books o f the Organon and the Rhetoric and the Poetics). This account makes it clear that while each one o f these eight books includes the rules o f the respective part o f logic, it may include other things as well, e.g., in the case o f the Rhetoric and the Poetics, an account o f the arts o f rhetoric and poetics, an account o f the craft o f making rhetorical speeches and poems, and so forth. Then, all the content o f these eight books is identified as the subject o f the “ art” or “ science” o f logic, resulting in the kind o f ambiguity that has bedeviled historians o f logic. To resume, each one o f the eight parts o f the “ science” or “ art” o f logic contains certain rules (i.e., universal statements) governing the parts o f the syllogism (1-2), or by which one tests the syllogisms common to the five syllogistic arts (3), or by which one tests only the particular kind o f syllogism employed by the art o f demonstration (4), dialectic (5), sophistry (6), rhetoric (7), or poetics (8). They are, strictly speaking, instruments o f the five arts o f reasoning. Historians o f logic need not therefore be puzzled about Alfarabi’s incorporation o f the “ practical arts” o f rhetoric and poetics into the Organon. The arts o f rhetoric and poetry are no more logical arts or parts o f logic than the arts o f sophistry, dialectic, or demonstration. Whether and to what extent any o f these arts is “ practical” or “ theoretical” is an independent question which the traditional arrangement o f the Organon (as can be seen from the ambiguous status o f the arts o f sophistry and dialectic) did not answer either.

Chapter I I culminates in a digression in praise o f the fourth part o f logic as the part that is “ most emphatically prior in dignity and superiority” and as being the “ primary intention” o f logic, while the other parts are either preparatory or introductory to it (parts 1-3), or else aides

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and as it were instruments that are more or less useful for the fourth part or whose exposition is meant to alert the one who seeks the “ certain truth” against the danger o f falling, unawares, into the use o f one o f the four methods (parts 5-8). The exposition o f the latter (parts 5-8) for their own sake and for the service they render the practitioners o f the art corresponding to each, is only a “ secondary intention” o f logic. According to its primary intention, logic as a whole is said to provide the “ certain methods,” to aim at the “ certain science,” and to help one guard against the use o f methods that lead to mere opinion or an image o f the truth. Now, the fourth part o f logic corresponds to the first syllogistic art, the art o f demonstration or the art that employs demonstrative statements which produce the “ certain science.” Alfarabi’s account o f this part is as follows. “ In the fourth [part o f logic, or the book that contains it] are (a) the rules by which one examines demonstrative (burhàniyya) statements and (b) the rules o f the affairs that make up philosophy and everything by which its [philosophy’s] activities become more complete, excellent, and perfect” (71.3-4). Our first impulse is to identify “ demonstrative statements” or the art o f demonstration with “ philosophy,” especially in view o f the fact that in at least two other (logical) works Alfarabi appears to use the expressions “ art o f demonstration” and “ art o f philosophy” interchangeably {Introductory ‘Risalah’ on Logic, 211, Expressions, 107-108), and o f the fact that he “ translates” the titles Prior Analytics and Posterior Analytics as “ Syllogism” and “ Demonstration” respectively (71.1-2,71.5). Further, in these other two works “ philosophy” or the “ art o f philosophy” is said to contain certain “ parts” or “ arts” or “ sciences,” which are four in number (the science o f mathematics, natural science, divine science, and political science; this last called also “ political philosophy” and “ practical philosophy” ), which seems to explain the arrangement or the remaining chapters o f the Enumeration o f the Sciences. The primary intention o f logic is to provide rules for the art o f demonstration or philosophy, which consists o f four parts or arts or sciences, and these will be treated, in the order just enumerated, in Chapters III-V . But we must also consider the following difficulties. This view leads us to expect a “ demonstrative” political or practical science. Alfarabi’s account o f the fourth part o f logic is explicit about the fact that it contains two sets o f rules; and the rules by which one examines demonstrative statements are clearly separated from the “ rules o f the affairs that make up philosophy.” (We may believe that

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these “ affairs” include demonstrative statements, but we have no reason to assert that that is all they include. In any case, Aristotle’s Posterior Analytics will not support such an assertion.) Finally, the two other works to which we have just referred do not give an account o f the parts o f philosophy, but merely mention them. It is therefore useful to see whether the suggestion o f a thoroughly demonstrative philosophy is born out by Alfarabi’s account o f the sciences in the remaining parts o f the Enumeration o f the Sciences.

Like the seven “ major” parts o f the science o f language, each o f the seven “ major” parts o f the science or sciences o f mathematics (cf.75.2-3 with 43.7) is called a “ science.” In the case o f four o f them, Alfarabi explains “ what is [generally] understood by this name,” and it turns out that in every case the name is ambiguous. In the case o f arithmetic (1) and geometry (2), the name “ science” covers two “ sciences,” one “ practical” and the other “ theoretical.” Only theoretical arithmetic and theoretical geometry, which investigate their respective subject matter as such, absolutely, or without qualification, are “ to be included among the sciences.” Practical arithmetic and practical geometry, though generally called “ sciences,” are not in fact sciences. They investigate their subject matter as applied to bodies “ in which the multitude deals in market transactions and political transactions” and bodies that are the materials o f various artisans (carpenters, blacksmiths, builders, and farmers), i.e., in each case the material o f a special “ practical art.” In the case o f the science o f the stars (4), the name “ science” covers two things, which are not distinguished by Alfarabi as practical science and theoretical science. They are (a) judgments o f the stars (astrology), which is merely a power or vocation that enables man to fortell the future, and mathematical astronomy, which is “ the one to be counted among the sciences and included in mathematics.” In the case o f the science o f music (5), finally, the name “ science” covers two sciences, one “ practical” and the other “ theoretical.” But practical music is not called an art; the theoretical, on the other hand, is called an “ art,” but it is not said to be “ the one to be included (or counted) among the sciences.” Theoretical music covers the principles and causes o f notes and melodies, their composition, adaptation to musical instruments, the manner o f their production, etc., up to, but not including, their actual production in natural or artificial instruments, which is the work o f the practical musician. (The uncertainty regarding the place

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o f theoretical and practical music among the arts and sciences invites comparison with political science and political activity.) The names o f the remaining three parts o f mathematics do not seem to present serious problems. The science o f aspects (optics [3]) is a special field o f (theoretical) geometry and is called an “ art.” And the science o f weights (6) deals with the principles governing two kinds o f instruments (balances and lifts); while the science o f (mechanical) devices (7) deals with the applicability o f mathematical knowledge to natural bodies, the production o f instruments, and in general the “ principles o f practical, political arts.” To summarize. There appear to be two purely theoretical mathematical sciences, theoretical arithmetic and theoretical geometry. Optics and mathematical astronomy seem to be more specialized mathematical sciences or arts. And weights and mechanical devices merely apply some o f the things discovered in other mathematical sciences or arts and serve specialized practical, political arts. Theoretical and practical music form a parallel structure that descends from theoretical knowledge (knowledge o f notes and melodies as intelligibles) to the actual production o f melodies. The generally understood name “ science” covers all o f these things; it covers theoretical sciences that are sciences in the genuine sense, theoretical sciences that are also arts (but not practical arts), and practical sciences that give the principles o f the particular practical, political arts. This should make it clear already that the science or sciences o f mathematics cannot be a single, thoroughly demonstrative, art. Demonstration in the highest sense - that is, giving the causes and explaining the “ why”- is mentioned twice only, in connection with geometry and optics, which is a special field o f geometry (78.8, 80.11). (When “ demonstration” is mentioned again in connection with mechanical devices [88.12-13, 89.3], it refers to things whose “ existence” only is demonstrated in mathematics.) Otherwise, mathematics for the most part “ inquires,” “ investigates,” etc., but does not demonstrate, which means that there are inquiries or investigations that are theoretical and lead to “ certain science,” but are not demonstrative. After enumerating theoretical arithmetic and theoretical geometry, Alfarabi interrupts his enumeration to remind the reader that geometry consists o f foundations and principles, which are limited, and other things derived from these, which are unlimited. Then he adds: “ There are two methods o f inquiring into it [geometry], the method o f analysis (tahlti) and the method o f synthesis (tarktb). The ancient prac

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titioners o f this science used to combine in their books both methods, except Euclid who organized the content o f his book [the Elements] according to the method o f synthesis alone” (79.9-12), (In the Harmonization, 8.20ff., the “ affair” o f division [qisma] and synthesis [tarkîb\ with respect to giving a complete account o f definitions is compared to climbing and descending from the same ladder and the two are said to be quite different.) Here, then, we have one o f the important “ affairs that make up philosophy” - the method, indeed, that leads to the discovery o f the principles o f theoretical science in general - that is not covered by demonstration. In the Enumeration of the Sciences Alfarabi confines himself to hinting at the importance o f this method and at his view that theoretical science and philosophy includes more than demonstrative statements. The view o f theoretical science or philosophy that restricts it to demonstrative statements is, in a sense, a generally known view o f science, too. Since the Enumeration o f the Sciences enumerates the generally known sciences, the structure o f each o f its chapters imitates Euclid’s Elements, starting, as it were, from the top o f the ladder and descending to the ground, to the principles o f the practical, political arts employed by the multitude in the marketplace and the city.

III. N A T U R A L , DIVINE, A N D PO L IT IC AL SCIENCE

The sixth and seventh digressions introduce the fourth chapter and conclude the fifth, setting the two chapters and the five sciences they include apart from the rest o f the book. The exposition o f natural science has the following features in common with the exposition o f the science o f logic. Both are preceded by relatively long introductions. Both are divided into eight parts. None o f the parts has subdivisions and none is called a science or an art. Logic was seen as the counterpart o f grammar; natural science is seen as the counterpart o f the practical arts. The subject matter o f natural science is natural bodies presented as the counterparts o f the artificial bodies produced by art and the human will, to which frequent references were made in the practical sciences o f mathematics, especially the science o f devices (mechanics), which immediately preceded the fourth chapter. Nevertheless, the digression on natural and artificial bodies, which is almost as long as the enumeration o f the parts o f natural science and divine science taken together, does not assume the sciences o f mathe

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matics in the way that logic assumed the sciences o f language. Instead, the reader is invited to consider artificial bodies, the products o f the practical arts, as analogues o f natural bodies. Such things as “ body” (e.g., a garment) and “ attributes constituted by the body” (its smoothness), the “ agent” that brings it about (the weaver), “ purpose” and “ end” (warmth), “ form” (interweave o f warp and woof) and “ matter” (the yarn), are said to be more apparent in artificial bodies. Most o f them can be observed directly by sense-perception, and the rest (e.g., the intoxicating power o f wine and the healing power o f medicines) can be seen indirectly through observing the activities o f artificial bodies. Because the principles o f artificial bodies and o f their attributes are better known to the “ multitude” {jumhUr) than the principles o f their natural counterparts, the multitude give the names o f the principles better known to them to the natural principles and treat the two sets o f principles as though they were the same. “ It is customary in the arts,” on the other hand, “ to transfer to the things contained in them the names that the multitude apply to the likenesses o f those things” (95.6-8). The principles o f natural bodies are less apparent than the principles o f artificial bodies, most o f their forms and matters cannot be observed by sense-perception, and “ for us, their existence can only be verified by reasoning and certain demonstrations” (94.1-2). Yet Alfarabi gives no reasoning or demonstration to prove the existence o f any o f the principles o f natural bodies, let alone the cause of their existence. The eight “ major” parts o f natural science (which are arranged in a descending order, from the principles common to all natural bodies to stones, plants, and animals) “ inquire” and “ investigate” ; they do not “ explain,” “ make evident” or “ demonstrate” anything at all. Natural science is an exclusively “ inquisitive” science. And its inquiries appear to be confined to the principles o f bodies as such, rather than their ultimate causes or their practical uses. Nothing is said about God or the unmoved mover, intellect, or even the soul, although soul and intellect at least must be inquired into in the parts that deal with plants (7) and animals (8). Unlike the mathematical sciences, which have so-called “ practical sciences” or practical arts as their counterparts, and some o f which study the principles o f the practical, political arts, there is no such thing as a “ practical” science or art that corresponds to any o f the parts o f natural science, and none o f these parts is said to have anything to do with any practical, political art, not even where we might expect a certain relation, such as between the study o f minerals (6)

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and the art o f mining, the study o f plants (7) and the art o f agriculture, or the study o f animals (8) and the art o f medicine. There is no such thing as a practical or applied natural science or art. Indeed, Alfarabi goes so far as to avoid the terms “ practical” and “ theoretical” altogether in connection with natural science and its parts.

A ll this is true o f natural science. But it is not true o f the fourth chapter as a whole; for we must still consider divine science and its three parts. Now, divine science (like political science, the science o f jurisprudence, and the science o f theology) lacks the kind o f introduction that connects it with what has preceded and the concluding remark that indicates the fact that the enumeration has been completed. The result is that the part dealing with this science (like those dealing with the three sciences that make up the fifth chapter) becomes purely enumerative, free o f any connective tissue that may explain possible ranks o f order or the direction governing the enumeration. This is all the more strange in view o f the fact that the connection between natural science and divine science is a commonplace in traditional introductions to divine science. Its absence indicates one o f two things. Divine science may be simply a continuation o f natural inquiry under a different name. But this would imply that “ beings as beings” into which divine science inquires are nothing more than natural bodies and their principles. Or, there is no special connection between the two sciences, which is what Alfarabi’s exposition seems to point to, but which makes one even more baffled as to why the two sciences are treated together in one chapter, and without any explanation.

Divine science is divided into three parts. The first investigates beings as beings and their attributes. Nothing further is said about this part. The second investigates “ the principles [or premises] o f the demonstrations in the particular theoretical sciences,” verifies and makes known their substances and special attributes, and enumerates and criticizes the corrupt opinions held about them by the “ ancients.” A “ particular” theoretical science is defined as a science which inquires into a “ special” kind o f being. The principle o f the independence o f the particular theoretical sciences is, then, the “ particularization” o f beings into kinds or genera. Three such sciences are listed: the science o f logic, the sciences o f mathematics, and natural science. Logic, which was never called a theoretical science in Chapter II, is now explicitly counted as one o f the three particular theoretical sciences ; it is assumed that the “ intelligibles” with which logic deals


are a special “ kind o f being,” different from mathematical and natural beings. This means that, except for Chapter I (which dealt with the science o f language), the book has been enumerating nothing but “ theoretical” sciences so far: three “ particular” theoretical sciences (logic, mathematics, and natural science), which study the intelligibles or intelligible beings, mathematical beings, and natural beings, respectively. And now we have a divine science, which is not itself called a theoretical science, yet its second (or central) part investigates the principles o f the three particular theoretical sciences. It would seem that we have covered all the theoretical sciences. I f their subject matter is being as being, the principles o f particular kinds o f being, and the particular kinds o f being themselves, we have accounted for all o f it.

The third part o f divine science investigates “ the beings that are neither bodies nor in bodies.” This last (or eleventh) part o f the fourth chapter does eleven things, which are ordered as follows. In the first five it demonstrates the existence o f these beings that are not bodies or in bodies (the so-called intelligences), explains that they are many, demonstrates that their number is finite, demonstrates that they form a hierarchical order and demonstrates that this order terminates in a being that is simply perfect, one, first, and prior, and explains that it bestows being and so on on every other being - all this without the benefit o f revelation. Then in the sixth (or central) paragraph, the third part o f divine science explains that the supreme being described so far is that which one ought to “ believe” God - that is, presumably, the God o f revelation - to be (100.13-14). The last five paragraphs enumerate, make known, and explain God’s attributes, the generation o f beings through or by God, their order, the goodness o f God’s activities, and finally refute all the false views about God’s activities that impute imperfection to him and the beings created by him: “ it refutes them all by demonstrations that provide certain science, such that it will be impossible for man to have any misgiving or entertain a doubt about it and impossible for him to abandon it at all” (101.8-10). Unlike the ten preceding parts o f the fourth chapter, none o f which demonstrated anything at all (the “ investigation” o f principles o f demonstrations in the tenth part [the second part o f divine science] was o f course not itself demonstrative), the eleventh begins and ends with demonstrations; it is the most demonstrative o f all the sciences; indeed, it contains more demonstrations than all the sciences in the book. We have, it would

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appear, finally found a science, or one part o f a science, which, i f not thoroughly demonstrative, is at least largely demonstrative.

But against this, we must weigh the evidence o f Alfarabi’s more philosophic works (the commentary on Aristotle’s Metaphysics known as the Book o f Letters, the short work On the Purposes of Aristotle’s Metaphysics, and the Philosophy o f Aristotle), where he argues directly or indirectly against the inclusion o f what corresponds to this third part o f divine science in metaphysics or against the view that it has an important or central place in metaphysics. (Since he also says that it is elaborated by Aristotle in book Lambda o f the Metaphysics, he indicates, in effect, that book Lambda is an exoteric work and does not represent Aristotle’s doctrine o f being.) The only way to explain this discrepancy is to take seriously Alfarabi’s statement in the Introduction o f the Enumeration of the Sciences that his purpose is to enumerate the “ generally known” sciences and their parts - that is, generally known to the multitude who understand the principles o f natural bodies in terms o f the principles o f artificial bodies and apply the same names to both. However this may be, Alfarabi’s enumeration o f the theoretical sciences (logic, mathematics, and natural science) culminates in a divine science, which in turn culminates in an account o f the universe that is orderly, hierarchical, and free o f injustice, imperfection, conflict, disharmony, or evil o f any kind. This account o f God and the universe is made into a part o f divine science, placed in the same chapter as natural science, and followed immediately by political science, jurisprudence, and theology, which are placed in the next chapter. This arrangement is quite different from the arrangement that emerges from Alfarabi’s more extensive accounts o f divine science and political science in which what is here called the third part o f divine science is joined to political science. The Virtuous City and the Political Regime, which are clearly political works, begin abruptly with an account o f God and the universe (in exactly the same fashion as in the third part o f divine science in this book) and proceed without interruption to give an account o f man and o f what is produced by human will and art : human associations, the principles and forms o f political life, and the particular, political arts. The fusion o f divine science and political science can be interpreted in two ways. In Alfarabi’s political works, it must be interpreted as a “ political” theology and cosmology. In Avicenna, on the other hand, politics becomes an appendage o f divine science. The Enumeration o f the

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Sciences separates divine science from political science, and yet enumerates them in the same order in which they appear in Alfarabi’s political works. Even more important, perhaps, is the distinction between divine science and so-called revealed theology, which belongs to a separate chapter with political science and jurisprudence. Divine science is separated from theology by political science and jurisprudence, which means that, in order properly to arrive at so-called revealed theology, one must first go through political science and jurisprudence.

IV. POL IT ICAL SCIENCE 1 A N D 2

Alfarabi’s political science (which he also calls political philosophy) is the political science o f the ancients, ofFla.to’s Republic and Aristotle's Politics. It speaks o f rulership and kingship, cities and nations, and science and philosophy, but says nothing about prophecy or divine lawgivers, religion, or theology. His jurisprudence and theology, on the other hand, are decidedly “ modern.” The very teTms{fiqh and kalâm) employed to designate these two sciences are specifically Islamic. They are sciences that follow in the footsteps o f prophecy, the divine lawgiver, and divine revelation. They have to do with the opinions and actions o f a religious community. They contain no reference to philosophy or kingship or the city. A deliberate effort is made to create two different and contrasting atmospheres : ancient and modern, a pre-religious or non-religious political science, and religious sciences that assume revelations, divine laws, and a number o f religious communities. The account o f political science avoids the name o f God altogether. The account o f jurisprudence and theology is saturated with such expressions as God, divine things, divine revelation, divine intellects, divine mysteries, and miracles. There is one apparent exception to all o f this. When investigating human activities and their ends, political science “ explains that some o f them [the ends] are true happiness, while others are presumed to be happiness although they are not. That which is true happiness cannot possibly be o f this life, but o f another life after [or beyond] this, which is the life to come [or the other life] ; while that which is presumed to be happiness consists o f such things as wealth, honor, and pleasures, when these are made the only ends in this life” (102.9-13). This statement recalls the religious view o f happiness as the happiness o f the next life, o f paradise or the beatific vision, which is said to be true

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happiness, as against the happiness o f this life, which is said to be presumed and not genuine happiness. Yet it also recalls the philosophic view that man should not confine his ends in this life to such things as wealth, honor, and pleasures, but seek a higher end, such as virtue or knowledge: he should lead “ another” life in “ this” life. Alfarabi appears to be using the Aristotelian and Platonic distinction between presumed and true happiness to interpret the religious distinction between this life and the other life. (Cf. Religion, 52.18, 55.7-8, where the goods [and the happiness] o f this world are said to be the things which are called good by the multitude - that is, they are vulgar goods.)

The central theme o f political science is what Alfarabi calls “ virtuous rulership” or the “ virtuous royal craft” - that is, the art o f the ruler who establishes, rules, and preserves the virtuous city or nation and whose end is true happiness, which is attained by good, noble, and virtuous deeds. It is distinguished from ignorant rulerships, which establish ignorant cities and nations whose ends (such as wealth and honor) are only presumed to be happiness. To the question “ What constitutes the virtuous royal craft?” Alfarabi gives two answers, which occur in two slightly different accounts o f political science.

1. In the first account (102.4-104.15), political science performs seven functions, which cover the subject matters o f what Aristotle calls ethics and politics, without explicitly distinguishing between ethics and politics. In the first four, political science investigates actions, ways o f life, and moral habits, without reference to the city or the nation. In the fifth, it explains that these cannot exist in man except when “ distributed in cities and nations according to a certain order and are practiced in common” (102.16-103.1). This leads to what political science does next, which is to explain the necessity o f rulership, that one becomes a ruler by virtue o f a craft and a positive disposition, that this is called “ royal craft,” “ kingship,” or whatever one chooses to call it (103.5-6), and the divisions o f rulership. The seventh and last step is to explain what constitutes the “ virtuous royal craft.” The virtuous royal craft is said to be composed o f two powers or faculties, (1) the faculty for general rules, and (2) the kind o f competence or expertise (hunka) acquired through long experience, observation, and practice in particular situations - actions, men, and cities. This is explained by the analogy o f the art o f medicine: the physician becomes a


“ perfect” practitioner by knowing the general rules he learns from medical books and, in addition, a power acquired from long experience, observation, and practice. Thus the subject matters o f the virtuous royal craft and o f political science are not coextensive. Political science gives two things, (a) the general rules and (b) the general patterns o f their determination or application in particular cases and times. Like medical books and medical science, political science provides only the first power or faculty required by the virtuous royal craft. It leaves the actual determination or application to another faculty, which cannot be acquired through science. Furthermore, according to this first account, political science and political rulership (including the “ virtuous royal craft” ) are self-sufficient and concerned exclusively with practical or political matters. They are not in any way dependent on, or in need of, the theoretical sciences. The horizon o f the “ virtuous royal craft” is defined by political science or the general rules o f political life as such. It is true that the royal craft requires “ another faculty, other than this science” (104.13), but this is a faculty that can be acquired through “ long practice in political deeds” (104.1-2), that is, dealing with the particular cases encompassed by the general rules given by poHtical science. In this respect, this political science corresponds to the last five parts o f the science o f language and the last five parts o f the science o f logic. It provides the rules necessary for the correct practice o f the art o f politics.

2. The occasion for giving a second account o f political science is the division o f this science into two parts (104,16flf.). (A quick look at the way A lfarabi presents the other sciences in this book is sufficient to show that it was by no means necessary for him to repeat a full-fledged account o f political science just because he needed to indicate its divisions. He could have started his account o f political science, as he frequently does in the case o f other sciences, by saying, “ this science consists o f two parts,” and then presented the content o f the science under the two headings; or else he could have finished his account with a short indication o f the way in which it divides itself.) According to the second account o f political science, the two parts o f this science perform four and fourteen functions respectively. The four steps in the first part correspond to the first four steps o f the first account; they are summarized and re-ordered, and the new order, broadly speaking, recalls Aristotle’s Ethics, even though the distinction

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between ethics and politics is again absent. The second part elaborates and adds substantially to the last three steps o f the first account. (It is stated at this point that the matters discussed here are to be found in Aristotle’s Politics, but that “ this [second division o f political science] is [to be found] also in Plato’s Republic and in books by Plato and others” [105.5-6]. Almost the entire section which follows next corresponds to parts o f Alfarabi’s Philosophy o f Plato.) There are a number o f new elements in this second account which are specifically Platonic. The most important o f these is the explanation o f the things that go into making up the “ virtuous royal art.” These are no longer the two faculties given in the first account - that is, the faculty for general rules (given by political science) and the competence acquired through long practice in political deeds. Instead, their exact number is now left open; only some o f them are mentioned; and the implication is that other things may be added. “ They include,” he says, “ the theoretical and practical sciences” (106.1), to which the faculty acquired through experience should be joined. The experiential faculty is the same in both accounts. But for the general rules provided by political science alone in the first account, Alfarabi now substitutes “ the theoretical and practical sciences” (both in the plural), and possibly other things as well. The establishment and preservation o f the “ virtuous city” are made contingent on a man who possesses this “ virtuous royal craft” and on the uninterrupted succession o f such princes or kings. This political science also explains the proper selection, upbringing, and education o f future kings, so that they come to possess this kind o f “ royal craft” and become “ fully” or “ completely” accomplished kings. Unlike these true kings, those whose rulership is ignorant should not be called kings at all; they do not need “ either theoretical or practical philosophy,” but can run their cities or nations by the experiential faculty alone, provided they are clever or perceptive and good imitators o f earlier igno

rant kings.In contrast to this second account, the first account o f political science

was much more sober and “ practical.” It gave a classification o f regimes and rulerships, confined the task o f political science to the formulation o f general rules o f political life and general patterns o f their application, confined the powers or faculties o f the “ virtuous royal craft” to knowledge o f these general rules and to what can be learned from experience, and did not even raise the question o f the non-virtuous royal crafts or how they


operate. On the crucial question as to what kind o f knowledge and competence the virtuous ruler needs in order to establish and rule a virtuous city, the answer was clear: political experience and political science are enough. While political experience is, o f course, one o f the requirements in the second account also, it is now mentioned as a matter o f course, does not occupy as important a place as it did in the first account, and is debunked at the end as the hallmark o f ignorant rulers. This is especially significant if we remember that in a parallel work {Religion, 58.15- 59.1) Alfarabi says o f this experiential faculty that it is the faculty which “ the ancients [i.e., Aristotle] call ‘prudence.’ ” As to the higher faculty for the general rules given by political science, neither this faculty, nor political science, are mentioned as such. They are included in something much larger, which comprehends the theoretical and practical sciences, or theoretical and practical philosophy, as well as perhaps some other, unspecified things; and the place o f political science (or o f the faculty for the general rules o f political life), which was clear and circumscribed in the first account, is not specified in this larger whole. The first account o f poUtical science or political philosophy is not criticized directly. It is silently replaced by an account o f political science whose central theme- the things which constitute the royal virtuous craft, and the selection and training o f the kings who will be able to establish and preserve the virtuous city - cannot be provided by political science as such. And because the “ regime” in this second account is constituted by the operation o f the virtuous royal craft (103.6), political science cannot (either by itself or in cooperation with political experience) establish or preserve the virtuous city.

It is time to ask why nowhere in this book is political science or political philosophy called either a practical or a theoretical science. Since Alfarabi knows o f this distinction and makes use o f it in the second account in connection with the virtuous royal craft, we can surely ask whether his political science is a practical or a theoretical science. So far, we have encountered the distinction between theoretical and practical arts, which was not elaborated, and theoretical and practical sciences, where the theoretical were included among the sciences proper, while the practical were excluded from the sciences proper and said to be practical arts or to study the principles o f the practical, political arts. Then we have been presented with his accounts o f political “ science” or political “ philosophy,” which

136 M. MAHDI

is not one o f the practical or political “ arts” mentioned previously. Finally, we are told that its central or highest theme is a “ positive disposition” or “ craft” whose activity consists in the production and preservation o f the regime, the political regime, which in turn establishes and preserves all the particular actions and positive dispositions and crafts in the city. This seems to be the supreme or ruling science or art, which includes and transcends all the arts and sciences practiced in the virtuous city. In the first account o f political science, on the other hand, where the royal art is said to be made up o f two elements, the general rules o f political life provided by political science and the experience acquired in political life itself, we have a political science that does not deal with any o f the theoretical sciences mentioned so far, nor is any o f the themes treated by it constituted by these theoretical sciences. We can, therefore, safely call this first political science a practical science or art, in the sense that it deals exclusively with things done and made by man, his activities and ways o f life whose principles are human will and choice; and call the royal craft the supreme practical craft or art, since it estabUshes and preserves the regime which makes possible what the citizens do and make. This would be practical science or art or philosophy as against theoretical science or art or philosophy (logic, mathematics, natural science, and divine science). The difficulty we encountered in the account o f true happiness (which was said to be possible in “ another” life, meaning a life beyond or higher than the life dedicated to such things as wealth, honor, and pleasures, to vulgar goods or ends) can be resolved by identifying the “ other” life with the virtuous life (the life dedicated to virtue for its own sake) and by calling the “ other” city the “ virtuous” city, its rulership the “ virtuous” rulership, and the craft which establishes and preserves it the “ virtuous” royal craft. For all intents and purposes, this first account o f political science must identify the good, the noble, and the virtuous with the moral virtues, which fall within the class o f things whose principle is human will and choice, and which are isolated from theoretical science. The “ virtue” or the “ art” o f the “ virtuous royal craft” in the second account o f political science, in contrast, is not exclusively a practical virtue or a practical art, for it is constituted by (1) the theoretical and practical sciences and (2) political experience. We saw that political experience is the same in both accounts. As for the “ general rules” o f political life given by political science in the first account, Alfarabi now substitutes the “ theo


retical and practical sciences” or theoretical and practical philosophy: the theoretical sciences - that is, logic, mathematics, natural science, and divine science; and the practical sciences, perhaps the parts o f the first account o f political science and the arts subordinate to it. This interpretation is confirmed by the parallel passage in the Book o f Religion (60.6-7), where the full or complete operation o f this virtuous royal craft requires “ knowledge o f the general rules o f this art [politics], which is to be coupled with theoretical philosophy, and to which prudence is to be joined.” (Theoretical sciences = theoretical philosophy; practical sciences= the general rules o f this art [given by political science]; the experiential faculty = prudence.)

It is plain that a political science whose central theme is the virtuous city established and preserved by this royal craft and the education o f kings who are “ completely” kings, is not strictly a practical science or strictly a theoretical science. It is not any o f the theoretical or practical arts or sciences enumerated so far. This political science must cover and order all o f them, not as enumerated in this book, but as they must exist in the soul o f the king who is completely king - that is, in their proper “ ranks o f order.” It is thus a political science or philosophy which includes, transcends, and rules all the “ theoretical and practical sciences” or “ theoretical and practical philosophy” (expressions that occur only in this account o f political science and nowhere else in the book). In this sense, the upward movement from the science o f language to the science o f logic, the science o f mathematics, and to natural science and divine science, has not as yet lost its momentum. The first account o f political science as a mere practical science was only an interlude that made possible the account o f a political science that in a way includes more and is therefore more comprehensive than all the theoretical and practical sciences enumerated so far.

V. JURISPRUDENCE A N D THEOLOGY

Jurisprudence and theology are each called a “ science” and an “ art.” But the name “ science” occurs only in the titles o f the two sections and in the remark concluding the first. The brief exposition o f the two disciplines concerns the “ art o f jurisprudence” and the “ art o f theology” exclusively. Unlike any o f the theoretical and many o f the practical sciences or arts

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mentioned so far, the arts o f jurisprudence and theology, about which Alfarabi speaks here, exist and are practiced in certain nations only and at a certain stage in their development. There ought to have existed a lawgiver who had legislated a divine law {sharl'^d) or a religion {milla) for a particular nation (the city, in the singular, now disappears from view, cf. 107.13). Religion consists o f two broad classes o f things, which are defined and determined by the lawgiver; opinions and actions. Opinions are legislated about such things as God, his attributes, the universe, and so forth; and actions are legislated about such things as prayers and civic transactions. So long as the lawgiver is on the scene, he will be the one who defines and determines what ought to be believed or done, and supports or defends these beliefs and actions by persuading his followers and others to accept them. After the lawgiver or the founder o f the religion leaves the scene, there will remain opinions and actions which he did not have time, or did not consider important enough, to attend to himself, and new issues and situations arise which will require new determinations as to what one should believe or do. Also, the opinions and actions which the lawgiver had determined will require support and defense against new objectors and new objections. It is at this point that Alfarabi’s exposition begins. The art o f jurisprudence is the “ positive disposition” {malaka) that enables man to make the new determinations, and the art o f theology is the “ positive disposition” that enables man to defend the religion. Since the things that need to be determined or defended in the religion are either opinions or actions, jurisprudence and theology each has two parts, dealing with opinions and actions respectively. Jurisprudence proceeds as follows. It learns the “ purpose” o f the lawgiver from the religion he had legislated for that particular nation and the things which the lawgiver had already determined in his religion. On the basis o f these two things, it “ discovers” or “ infers” what determinations are to be made about things o f which the lawgiver had not spoken explicitly or things that did not exist in his time. Theology, on the other hand, does not make new determinations. It takes what the lawgiver had determined, defends them, and refutes what disagrees with them. Alfarabi’s account o f theology is followed by an extensive exposition o f the opinions o f various theological schools as to what methods and opinions should be employed in supporting one’s religion, all o f which belong to the rules o f the syllogistic arts enumerated in the science o f logic. (He does not explain the methods

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employed by the art o f jurisprudence, but there are indications that jurisprudence applies some o f the same rules o f logic.) This is the last o f the seven digressions to which I have sought to draw attention througliout this paper. It is also the most dramatic part o f a somewhat undramatic book, highUghting the proclivity o f the defenders o f religions for shining armor and sharp weapons. Its main effect, however, is to draw attention away from the question o f the relation between jurisprudence and theology, and political science.

One notices, first, that like the science o f language - and unlike logic, mathematics, natural and divine science, and political science - jurisprudence and theology are not single universal sciences. There are as many arts o f jurisprudence and as many arts o f theology as there are religions or divine laws. (The terms “ nation” and “ nations,” whose frequent use was a hallmark o f the first chapter on the science o f language, are replaced here by the terms “ religion” and “ religions.” ) Alfarabi states what all these arts do, their end, and the methods they employ to achieve their end. Only in this formal sense does he speak o f the science or art o f jurisprudence or theology. To know what each does in particular, one must learn the particular opinions and actions legislated by a particular lawgiver and the purpose o f his religion, and then see how the jurists o f this religion employ the methods described by Alfarabi in making new determinations or how the theologians o f this religion employ the methods he describes in defending the religion’s particular opinions and actions. On the surface at least, Alfarabi seems to be resigned to the multiplicity o f lawgivers and religions and juridical disciplines and theologies. Moreover, he abstains from praising or condemning any o f them as good or bad, virtuous, or vicious. Religion is defined in a perfectly neutral manner, and so are the religious sciences. Second, jurisprudence and theology are not substitutes for political science or alternative approaches to the study o f political life. They are not religious or sacred political sciences as against a “ secular” political science. They do not conduct any o f the investigations conducted in political science, give any o f the explanations given in it, or make any o f the distinctions made in it. Third, they are not parts o f political science. The two parts o f political science were stated and explained earlier. Neither jurisprudence nor theology corresponds, either wholly or in part, to either o f those parts. Fourth, and more gen- ®^ally, jurisprudence and theology do not investigate the truth or false

140 M. MAHDI ALFA R AB I ’ S ‘ ENUMERATION OF THE SCIENCES’ 141

hood o f the opinions given in any religion about God, his attributes, and the universe. This is the function o f the theoretical sciences enumerated earlier, especially the third part o f divine science. Nor do they investigate the nobility or baseness o f the actions demanded in any religion, distinguish the kind o f happiness achieved by performing these actions, or judge the purpose or end the lawgiver had in view in giving this religion. A ll this is the function o f poUtical science, which has been completed already.

Jurists and theologians perform certain defined practical tasks within an established religious community. Their success or failure is not contingent on their ability to conduct an independent inquiry or attain direct knowledge of things, either theoretical or practical. Their knowledge, in particular, is derivative. They learn what their lawgiver had in mind (his purpose) and his statements as transmitted through written or oral reports. For the rest, the power or faculty they employ in performing their task as jurists or theologians has to do with particular cases. Should this opinion be accepted or that action be performed? Or, how I can best support this opinion or defend this action, convince this man or this group o f men, or take care o f this objection or ward off that criticism? At best, the jurist makes use o f a limited kind o f experiential faculty or prudence which functions within a framework established by the lawgiver, and the theologian makes use o f certain dialectical and rhetorical arguments.

VI. THE L A W G IV E R , REL IGION , A N D PO LIT ICAL SCIENCE

The juxtaposition o f political science, and jurisprudence and theology, without an explicit transition from political science to the religious sciences and without stating explicitly the connection between them or their ranks o f order or how they form a single whole, mirrors the initial situation in which the student o f these sciences who is a member o f or lives in a religious community finds himself. On the one hand, he finds himself before a rational, philosophic science which claims to be the science o f practical life, to encompass the entire range o f the human ends in this and the other life, and to explain what man ought to do to achieve these ends. On the other hand, he is confronted with jurisprudence and theology, which claim that they are the sciences that determine what he must believe and do to achieve what appear to be the same ends. To understand why

Alfarabi is able to present these two claimants side by side without stating the relation between them, we must realize that the above situation is neither universal nor necessary. It does not represent the condition o f man as man. Philosophy and political science can exist and did exist in nations that did not possess revealed religions or jurisprudence or theology. And revealed religions existed and could continue to exist without philosophy or poUtical science. The coexistence o f these claimants can, therefore, be said to be an accident, a historical accident. Still, once they have come to coexist in the same community, the relation between them becomes a problem. Yet it is not an essential theoretical problem for political science in the sense that political science as political science must necessarily raise and answer the question o f revealed religion and jurisprudence and theology. It is, o f course, also not a problem which must or even can be discussed by jurisprudence or theology. But although historically and theoretically the relation between political science and the religious sciences is accidental, this does not mean it should not or could not be understood or clarified.

Since the claim o f jurisprudence and theology is practically more urgent, let us begin here. This claim is not based specifically on the methods o f these discipUnes but on the assumption that they follow in the footsteps o f a divine lawgiver, understand his purpose, and supplement his activities. They are admittedly subordinate arts, subordinate to the original, greater, and more comprehensive art o f the divine lawgiver. We must, then, go back or ascend to the divine lawgiver whom the jurists and theologians follow, and understand his art. To do so, we must follow in the footsteps o f the jurists and the theologians, and study all the things that the divine lawgiver declared or determined by speech or deed. This is the divine law or the religion he legislated. (The religious sciences necessary for a better comprehension o f the principal sources or roots o f the divine law, whether written or oral, are assumed by Alfarabi in this context.) And we must try to understand the divine lawgiver’s “ purpose” or “ intention” in legislating his religion in the nation for which he legislated it. As we look at these three things (the divine law, the purpose o f the lawgiver, and the nation for which he legislated this divine law), we perceive a possible link with some o f the things we learnt in political science. The divine lawgiver is a kind o f ruler or king, at least he performs some o f their functions. For instance, he defines and determines particular actions

142 M. MAHDI

which he asks a particular nation to perform in common so as to attain a certain end. He is not necessarily a theoretical man or a poUtical scientist, but a leader o f men. He decides what this particular group o f men must do or believe in, here and now, so as to achieve a designated end in this life and/or the next. Minimally, then, he is a ruler who possesses what Alfarabi called the experiential faculty (or prudence). But the fact that he possesses this faculty does not, by itself, prove that his purpose is to lead men to genuine happiness rather than some spurious kind o f happiness, or whether he does or does not possess what Alfarabi called the virtuous royal craft. The fact that divine lawgivers establish religions does not in itself prove that their religion is good or bad, true or false. The multiplicity o f religions that claim divine origin, their conflicting claims, and inter-religious theological controversies, point in the same direction.

The question, then, is whether one must be satisfied with learning the purpose o f the divine lawgiver and the divine lawgiver’s particular determinations, which is what jurists and theologians do; or whether one can go further and judge the character o f the divine lawgiver’s purpose. Jurisprudence and theology are constitutionally unfit either to raise or answer this question. PoUtical science, on the other hand, while it does not claim right here in this chapter that it can raise and answer this question with respect to divine laws and the communities based on them, does in fact claim that it can give an account o f all classes o f ends, actions, regimes, rulerships, and purposes, and distinguish between the true and the false, virtuous and nonvirtuous, among them - that it provides a standard and measure by which all past and present and future regimes and their founders can be investigated and judged. It is not, then, necessary to repeat this claim in connection with any particular kind o f polity.

The only difl&culty is this. Political science as presented in this book says nothing about lawgivers and laws, o f which divine lawgivers and divine laws are one species; or about the relation between the art or craft o f the lawgiver and the art or craft o f rulers who are not lawgivers; or about the relation between the regimes based on laws and the regimes not based on laws. This serious omission can be shown, however, to be intentional and deliberate. It has the practical consequence that the book avoids the necessity o f even enumerating certain delicate and controversial problems, which is perhaps not incompatible with the introductory character o f the book or with the fact that it did not promise to enumerate


all the sciences, but only the “ generally known” sciences (43.4). Unlike poUtical science, jurisprudence, and theology, the science or the division o f the science which is omitted here, and which we may call the philosophic and poUtical science o f divine laws and revealed religions, was surely not generally known to Alfarabi’s readers. It was in many ways a new science invented or estabUshed by Alfarabi himself.

VII. THE PHILOSOPHIC SCIENCE OF RE LIGION

The origins or the germs o f the new science, however, are contained in the “ ancient” science o f politics, especially in the second account o f poUtical science given by Alfarabi in this book. What distinguishes divine laws is the fact that they include both opinions about God, his attributes, and the universe, as weU as actions. What Alfarabi called the virtuous royal craft in the first account included, besides the experiential faculty, only the faculty for the general rules given by a poUtical science that had nothing to do with the theoretical sciences. This means that this ruling craft can establish and preserve a regime which contains only actions, not opinions. This limited kind o f poUtical science wiU not, obviously, be able to investigate divine laws. You recall, however, that in the second account, this same virtuous ruling craft was constituted, in addition to the experiential faculty, by the “ theoretical and practical sciences.” Unlike the former, this ruUng craft is prepared, therefore, to establish and preserve regimes which contain actions as well as the opinions contained in divine laws. That is, this ruler possesses the craft which includes both the theoretical sciences (including the third part o f divine science which deals with God and his attributes) and the practical sciences, and possesses the experiential faculty through which he can discover, or define and determine, the specific form in which both knowledge and action can be presented to a particular group o f men under given conditions. It is true that Alfarabi does not say aU this in so many words. But his silence here (106.1-4) is more telling than his explicit speech. He says that the experiental faculty must be joined to both the theoretical and practical sciences, and proceeds to say that the experiential faculty determines the particular “ actions, ways o f life, and positive dispositions.” Now “ positive dispositions” can, o f course, include knowledge and opinions. In fact it must, for otherwise it would be hard to understand why the experiential faculty should be

144 M. MAHDI

joined, not only to the practical sciences, but to the theoretical sciences as well.

But now comes the difïïculty. For Alfarabi also says that the regime founded by such a ruler cannot be preserved unless there is an uninterrupted line o f rulers who possess the very same qualifications as those o f the founder, which is why the question o f the education o f future rulers who are “ completely” kings becomes an important theme. This is so because a regime will inevitably degenerate in the absence o f such a ruler. Yet one o f the main reasons for laying down laws is that they be followed after the death o f the lawgiver, when the community is no longer ruled by a man who possesses his qualifications. And we know by now that the main reason for the existence o f jurisprudence and theology is to preserve the regime o f the divine lawgiver after his death, when the religious community no longer has a divine lawgiver at its head. During his lifetime, in fact, there was no law in the sense that jurists and theologians understand and practice it. What the divine lawgiver said or did was the living law, and he could change or abrogate it to meet new circumstances as they arose. No follower o f a divine law or a revealed religion would take exception to the proposition that the best time was the lifetime o f the divine “ lawgiver,” or that the best arrangement would be to have an uninterrupted line o f divine “ lawgivers.” There is, then, no disagreement regarding the desirability o f a state o f affairs in which men do not follow the law, even the divine law, o f a dead legislator, but are ruled continuously by Uving philosopher-kings or divine lawgivers. Nor, I believe, is there disagreement that this is a state o f affairs that is unlikely to obtain because such men are very rare; or that, in their absence, the best alternative is to follow their intention as embodied in what they said and did. So the question o f the laws or o f the regime ruled by laws remains an important theme o f political science. Alfarabi leads the reader to this theme in the Enumeration of the Sciences without discussing it explicitly.

What the Enumeration o f the Sciences does, however, is to pose the problem and express an intention. Political science now coexists with jurisprudence and theology: this is a massive historical fact which it cannot ignore. The first account o f political science, which is strictly practical, cannot coexist with jurisprudence and theology without being subordinated to or absorbed by them. Their subject matter is wider. It includes opinions about theoretical things and actions (e.g., prayers) which


are related to theoretical things. This practical political science on the other hand, deals with a special kind or one division o f actions. The only way this practical political science can preserve its independence and superior claim over its companions is to show that all these so-called theoretical opinions, and all these actions which are related to so-called theoretical opinions, are in fact practical. But then this practical political science will have to do two things. First, it has to prove this claim, which it cannot do if it remains a purely practical science. It must broaden its concern and somehow encompass all the theoretical sciences. It will need a theoretical dimension. Second, it must develop a new branch or part o f political science to deal with these theoretical opinions and with theoretically-oriented actions. This will be a “ practical” or political divine science or theology which keeps one eye on the theoretical sciences and another on human ends and actions. In this way, it will broaden its scope and deal with opinions as well as actions. This is now demanded by the facts o f political life. Alfarabi will do this in the Book o f Religion, which is the counterpart o f Chapter V o f the Enumeration o f the Sciences. What the Enumeration o f the Sciences has done is to show that the strict division o f sciences into practical and theoretical is no longer practically tenable. In the second account o f political science there are two kinds o f rulers: those who possess the “ theoretical practical sciences” (106.1) and those who “ do not need ... theoretical or practical philosophy” (106.16).

Harvard University

N O T E S

* Unless some other title is mentioned, all references in the text are to the pages and lines of Alfarabi’s Enumeration o f the Sciences (Ihsff a l-U lum ), ed. Osman Amine (2nd ed.; Cairo: Dâr al-Fikr al-‘Arabi, 1949). Two Latin versions of the work, one a translation, the other an adaptation, together with the Arabic text and a Spanish translation, can be consulted in Ângel Gonzalez Palencia, Al-Fàrâbî: Catàlogo de las ciendas (2nd ed. ; Madrid, 1953). The Latin translation (pp. 117-76), literal and generally accurate, is by Gerard of Cremona. The adaptation (pp. 83-115), first published by Camerarius, is ascribed on reasonable grounds to Gundissalinus (who made use of Alfarabi’s classification of the sciences in his own work, ‘De divisione scientiarum’) and was edited under his name by Manuel Alonso Alonso, S. J., Domingo Gundisalvo: De scientiis (Madrid, 1954). If we had more time at our disposal, we could have spoken profitably, perhaps, about

the so-called Hellenistic background of Alfarabi or the external history of the trans- minion of Greek learning through Syriac into Arabic, the early history of Islamic philosophy, Alfarabi’s account of his philosophic genealogy, and his critique of his

146 M. MAHDI

predecessors and contemporaries. One should also remember his impact on later Muslim, Jewish, and Christian philosophers, and especially the fact that, until the recovery of Aristotle’s Politics in the second half of the thirteenth century, he remained the political philosopher par excellence. But to speak about any of these topics intelligently and profitably presupposes an understanding of Alfarabi’s philosophy in general and the place he assigns to political philosophy in particular, and this in turn presupposes understanding his writings. This is where we must begin.2 Çâ ‘id al-Andalusi, Classes o f Nations {Jabaqat al-Umam), ed. Louis Cheikho (Beirut, 1912), p. 53.

C O M M E N T S

M.-Th. d’ALVERNY: Professor Mahdi’s appreciation of Farabi’s classification of the sciences is very interesting. I agree with him when he points out the importance of the digressions and developments that are the distinctive feature of this tract. Fârâbi has given a remarkable account of Arabic grammar in the long chapter dedicated to the science of language and he has given a prominent part to political philosophy, which M. Mahdi has stressed in particular. I would have emphasized as well that the chapters or “digressions” concerning engineering, optics and the science of weights are a mark of the development of Arabic science.

I should not say, however, that Farabi’s classification is “unprecedented.” When I read the Il^sff al-^ulüm, my own impression is that Fârâbi has very cleverly adapted and enlarged the current, so-called Alexandrian classification inherited by the Arabs from Ammonius and Olympiodorus (particularly the divisions of the Organon, including at the end rhetoric and poetics [cf. R. Walzer, Greek into Arabic, p. 133 f.]). He first added the “science of language” which had not been included in the Alexandrian schema nor previously in Aristotle due to the fact that it was a preliminary study and not a part of the encyclopedic system. Moreover, after ethics and politics, Fârâbi added the typical Islamic sciences, and kalam. Professor Mahdi tries to justify the separation between the “ theology” of the Metaphysics and “revealed theology,” namely, kalam. His analysis of Fârâbi’s motives for e x p o u n d in g a n d kalâm as an appendix to political science is very keen; revealed sciences rely on the “divine ruler.” We may add that it would be difiicult to join kalâm, based on Quranic revelation, with an abstract theology having a Neo-Platonic background.

It would be interesting to compare Fârâbi’s enumeration of the sciences with Avicenna’s. There are several, and there are important variations in each of them. In the last book of the Metaphysics of the Shifff, Avicenna gives an outline of revealed theology, law and ethics, including politics, in a demonstrative manner, all of the beliefs and customs of Islam deriving ultimately from the omnipotent will of God and His Providence. In the Ishârât, he includes sufism (mysticism) in his portrayal of the arts and sciences. Another, and rather different, enumeration is proposed in a Risala on the classification of the sciences (translated into Latin in the early sixteenth century by the physician Andrea Alpago). But Avicenna was apparently not interested in the theory of politics, perhaps because he had been obliged to practice politics, as I. Madkour once said.

We cannot share the opinion expressed by Professor Mahdi when he says (p. 146) that “ until the recovery of Aristotle’s Politics in the second half of the thirteenth century, he [Fârâbi] remained the political philosopher par excellence.” This is not true, I think, as far as the Christian philosophers are concerned. On this particular point.

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I do not think that either the translation of the Ihsff al-ulûm, or Gundissalinus’s adaptation of it met full understanding or appreciation.

M. m a h d i: Professor d’Alverny takes issue with §â‘id al-Andalusi (d. 1070) for considering Alfarabi’s classification of the sciences “unprecedented” (p. 117, n. 2) and gives her reasons as follows. There were, she suggests, the so-called Alexandrian classifications inherited by the Arabs, which Alfarabi very cleverly adapted and enlarged. He first “added” the sciences of language and then “added” theology and jurisprudence. All this is probably true. But I do not think that $â‘id al-Andalusi was taking issue with such a hypothesis or with the line of reasoning leading to it. Rather, he was thinkng of the two types of classification of the sciences mentioned in the paper, which were current in Arabic literature and with which he could compare directly the classification suggested by Alfarabi. It is in this context that I quoted him with approval. I must perhaps add that until one inquires more systematically and intelligently into the structure and intention of the so-called Alexandrian classifications of the sciences (e.g., into the reasons for and the meaning of the incorporation of rhetoric and poetics into the Organon in these classifications) it will not be easy to go very far in comparing them with this particular classification by Alfarabi.

Professor d’Alverny also takes issue with my remark in note 1, which states that “ until the recovery of Aristotle’s Politics in the second half of the thirteenth century, he [Alfarabi] remained the political philosopher par excellence.” I suspect that she understood this statement to mean that Alfarabi as a political philosopher was widely known or understood or admired by the Christian philosophers in the Latin West. This was obviously not the case. Whatever impact Alfarabi made on the Christian philosophers in the Latin West was surely not in the field of political philosophy as such. One must recall that, until the recovery of Aristotle’s Politics in the second half of the thirteenth century, there was no political philosophy and there were no political philosophers in medieval Western Christendom. This does not, of course, mean that there was no Christian political thought (e.g., among the legists and the publicists) during that period. For the history of the recovery of Aristotle’s Politics and especially for a critical list of the many commentaries on it, see Martin Grabmann, Die mittelalterlichen Kommentare zur Politik des Aristoteles (Munich, 1941).

G. beaujouan : Dans ce colloque, d’importantes choses ont été dites, notamment par les P' s. Murdoch et Sylla, pour éviter que ne se dressent ou se maintiennent des cloisonnements artificiels entre l’étude de la science médiévale et la compréhension de la théologie.

Un semblable effort reste à faire pour voir les connexions qui pouvaient exister entre les arts libéraux, la médicine et le droit, tels qu’ils étaient enseignés dans les universités du moyen âge et de la Renaissance (M. Schmitt a reconnu, ici même, cette lacune).

Cette liaison entre sciences et droit apparaît, du reste, beaucoup plus importante pour l’Islam que pour la Chrétienté. Je me suis déjà demandé, ailleurs, si en préconisant le recours routinier à des traités détaillés de jurisprudence, le malikisme n’avait pas freiné la spéculation rationnelle dans la science hispano-musulmane. Je me réjouis donc de ce que, dans le rapport du P Mahdi, l’accent soit mis sur la science politique et la jurisprudence.

Mais, dans VEnumération des sciences d’al-Fârâbï, je suis personnellement intrigué par le fait que, sous une même définition, la scientia de ingeniis Çilm al-biyal) englobe à la fois l’algèbre et diverses applications pratiques de la géométrie. Chez al-Fârâbi, cette association est-elle une “naiveté” ou, au contraire, l’écho d’une tradition déjà bien établie?

P A R T I I

THE TWELFTH AND THIRTEENTH CENTURIES IN THE LA T IN WEST

T H E O R G A N I Z A T I O N OF S C IE N C E S A N D T H E

R E L A T I O N S O F C U L T U R E S I N T H E

T W E L F T H A N D T H I R T E E N T H C E N T U R I E S

RICHARD MCKEON

The culture o f a people is discovered in its arts, its institutions, and its lore - in things made, things done, and things said. The culture o f a time is the culture o f peoples in contact and communication. Culture is a qualification o f peoples and an order o f “ learning,” and learning is both a process o f education and an organization o f sciences. Sciences are organized and developed in cultures, and cultures are known and characterized by sciences. The interactions and communications o f peoples are interpreted from the perspectives o f one or another o f the cultures in communication or from the perspectives o f an outside interpreter. The historian o f culture has interpreted the culture o f the Middle Ages variously from the time when Renaissance Humanists interpreted it into existence and gave it its name and its dogmatic, verbalistic characteristics, to present day scientific studies based on the invention o f a science o f culture and the rediscovery o f a culture for the Middle Ages in the nineteenth century. The historian o f science has interpreted medieval sciences from the time when early modern scientists interpreted them out o f existence as sciences, through the discovery o f items o f observation, method, or theory uncovered in medieval writings as modern science progressed to the present. The history o f cultures and o f periods and the history o f sciences and o f disciplines are written backwards from present conceptions o f culture and present interpretations o f science. The report from the perspective o f one o f the cultures in contact with other cultures is no more objective than the report o f later interpreters, but the interplay o f culture and science appears also in the effects o f the contact on the internal structure o f the cultures engaged. Latin reports o f Arabic culture in the twelfth century are neither objective nor reliable, but the effects o f Arabic science on Latin culture and on Latin science, philosophy, and religion provide mutual controls, and changes o f culture may be expressed concretely in terms o f changes in the organization o f the sciences. The perspectives o f cultures are grounded in the structure o f a system o f knowledge, and the facts alleged about influences and


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oppositions are given significance in the data relevant to operative arts o f inquiry.

The juxtaposition o f culture as structure o f values and culture as organization o f sciences in the twelfth and thirteenth centuries suggests a pattern for the investigation o f cultural and scientific communication and understanding. Viewed from the perspective o f the Latin West at the beginning o f the twelfth century, the contact o f cultures was the meeting o f two traditions, the tradition in which Latin Christian culture had been formed over a thousand years from elements borrowed from, or opposed to, the culture and erudition o f pagan antiquity adapted to the structure o f a theology based on the interpretation o f the Bible, and the tradition o f Islamic culture based on elements derived from the same ancient source adapted to a theological structure formed by interpretation o f the Koran and the Old and New Testaments. The contact o f Latin Christian culture with Arabic Muslim culture was mediated by scholars as well as by crusaders, traders, and statesmen. Translations o f works o f science, philosophy, and theology were stimulated by reports o f Arabic science, paraphrases, commentaries, and encyclopedic compendia which grew into a flood during the next two centuries. The “ arts” and “ values” o f Latin Christian culture had been adapted from Greek culture, yet, paradoxically, knowledge o f Greek sciences and o f the philosophy o f Aristotle was introduced into the West for the first time as a result o f contact with Islamic culture. The pattern that emerges from the contacts o f cultures at that time is a pattern o f four cultures structured on interpretations o f one, two, or three related sacred Books - the Old Testament, the New Testament, and the Koran - used to establish divergent systems o f arts, practices, and sciences developed from or constructed in reaction to a common source - Greek arts, sciences, and philosophies. The peoples o f the Books were also peoples o f encyclopedias, and the medieval cultural traditions o f Latin Christianity, Greek Christianity, Judaism, and Islam can be clarified and characterized by examination o f the world conceptions, consequential facts, and accepted methods ordered and set forth in the Latin, the Greek, the Hebrew, and the Arabic encyclopedias.

Medieval Latin encyclopedias were concrete and practical collections o f information about words and things. They were developed from Roman encyclopedias which had borrowed from the Greek the expression ‘enkuklios paideia’ and had given it a fixed meaning to apply to the cycle

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o f interrelated arts, which were also called human arts and liberal arts and which constituted elementary general education. Aristotle had used ‘paideia’ in the sense o f a “ general education” to form an ability to judge the presentation o f theses and arguments, but he reserved the “ organization o f knowledge” and the sciences for philosophy. Greek philosophies were encyclopedic in scope and method. Vitruvius and Quintilian used a circle o f arts and sciences as elementary prerequisites to professional studies like architecture and rhetoric, ordered by rules o f art, and Pliny the Elder used like interrelated arts and sciences as presuppositions to his Natural History. Varro enumerated nine such arts which became, with the elimination o f architecture and medicine, the seven medieval arts - the literary arts o f words o f the trivium, grammar, rhetoric, and dialectic, and the mathematical arts o f things o f the quadrivium, arithmetic, geometry, astronomy, and music. After Augustine had given Latin theology a framework which adapted Platonic structures to Christian doctrines and Boethius had adapted logical, dialectical, and rhetorical methods to that framework, the arts o f divine letters were related to the arts o f human letters. Book I o f Cassiodorus’s Institutiones treats divine letters. Book II the arts and disciplines o f liberal letters. Isidore o f Seville’s Origins or Etymologies treats the seven liberal arts in the first three o f twenty books before going on to the etymologies and natures o f other things, including an alphabetically ordered dictionary in Book X. Many o f Isidore’s other works were encyclopedic compendias: the De fide Catholica and the Sententiae o f theology, the De ordine creaturarum o f cosmography, the De natura rerum o f cosmography and meteorology, the Chronicon o f universal history. Hrabanus Maurus compiled a De universo or De rerum natura. The Venerable Bede wrote encyclopedias o f metrical art, rhetoric, and a De rerum natura.

Medieval Greek encyclopedias were learned and critical collections o f information about styles and contents o f literary works. Like the Latin encyclopedias, they developed in the Roman Empire from the second century, when Marcus Aurelius wrote his Meditations and Galen and Ptolemy wrote their encyclopedic scientific treatises in Greek, and laid the foundations o f a distinctive cultural tradition which continued after the separation o f the Eastern from the Western Empire. Literary humanistic centers flourished at the Imperial court. Philostratus reflects the cultural life patronized by Empress JuHa Domna in the second century in

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his Lives o f the Sophists. “ Hellenism” for Philostratus was purity and clarity o f prose style (as “ Latinity” was to be made a criterion o f stylistic excellence in the Renaissance), and his list o f sophists was a choice o f masters o f Greek literary style. Scientists, like Eudoxus, were included because o f the elegance o f their style. The ancient Sophists, Gorgias, Protagoras, Hippias, and Prodicus, have a place, although their interest in philosophy adulterated their sophistic accomplishments. The New Sophistic made its beginning about the time o f the beginning of the Christian era. One o f its effects was to concentrate attention and study on the Greek classics. Eunapius, who attached himself to the humanistic literary center o f Emperor Julian the Apostate in the fourth century, reflects the effort to return the Empire from Christian to pagan culture in his Lives o f the Philosophers and Sophists. He begins his “ lives o f the most celebrated philosophers and rhetoricians” with the Neoplatonists and closes it with accounts o f the iatrosophists who used sophistic arguments to cure psychological and physical ills. Eunapius’s teacher was a Christian sophist, and the study o f Greek language and Greek classics continued with the assistance o f Greek lexicons and encyclopedias. Photius in the ninth century compiled the Myriobiblion, a collection o f extracts from and abridgements o f 280 classical works, a Lexicon o f literary words and their usage, and the Amphilochia, a collection o f questions and answers in Scriptural interpretation. The Lexicon o f Suidas in the tenth century is a combination lexicon and encyclopedia, an epitome, according to its author, o f the sixth century lexicon o f Hesychius o f Miletus and a mine o f borrowings from a long line o f Greek encyclopedias. Latin encyclopedias were collections o f meanings o f words and differentiations o f things to which they are applied; Greek encyclopedias were collections o f usages o f words and o f excerpts or reviews o f outstanding instances o f their use. Psellos, in the eleventh century, organized his Didaskalia Pantodape or “ All-inclusive Instruction” by question and answer, beginning with God and creation, running through natural history and astronomy, and ending with various curious and practical questions.

Medieval Hebrew encyclopedias were circumstantial and dialectical collections o f information about laws and interpretations. They developed by use o f hermeneutic and analytic methods borrowed from Greek rhetoric and literary criticism applied to the Old Testament. The Greek translation o f the Septuagint made the Pentateuch available to Alexandrian Jews who


could not read Hebrew, and Philo Judaeus completed the process o f hel- lenization by elaborating and applying devices for its interpretation. The Talmud is an encyclopedia o f the oral laws in which the written law o f the Pentateuch was interpreted in application to varying circumstances and conditions and developed in logical consequences and relations. The oral tradition was put in written form and arrangement in the Mishnah to which commentaries were added in the Gemara. Two interpretative devices are employed: the dialectical formulation o f the law o f the Halacha (or way or path), and the narrative accounts o f the Hagada (or saying or tale). The evolution o f the meanings o f the term ‘Mishnah’ resembles those o f ‘paideia’ - from ‘repetition’ to ‘instruction’ to ‘ learning’ - erudition as method, as process, and as product. In the tenth century Saadia Gaon’s Opinions and Beliefs expanded the scope o f the encyclopedia to include consideration o f the relations o f philosophical doctrines to religious beliefs and reflected relations to the cultural traditions o f Islam. In the twelfth century Maimonides wrote a commentary on the Mishnah and the Mishneh Torah (“ Repetition o f the Law” ), a systematic exposition o f the law o f Moses as contained in the Pentateuch and as repeated in the vast Talmudic literature. He also wrote the Guide o f the Perplexed, for religious persons who, adhering to the Torah, have studied philosophy and are embarrassed by contradictions between the teachings o f philosophy and the literal sense o f the Torah, and a Short Treatise on the Art o f Logic to provide the art o f interpretation and o f thought.

Medieval Muslim encyclopedias were systematic and constructive collections o f information about principles and sciences. Like the Hebrew encyclopedias they had their origin in the Hellenism o f Alexandria, but they built on the scientific rather than the hermeneutic tradition. The Alexandrian scientific encyclopedia had been adapted to Christian theology by the Syrians when they translated Greek medical, astronomical, and philosophical works as well as the New Testament into Syriac. In the Syriac and Arabic traditions medicine occupied a central place among the sciences which were brought into relation with theology, and logic occupied a central place, as it did in Galen, in the study o f medicine. Alkindi, in the ninth century covered almost all the Greek sciences, and portions o f this work, including the Introduction to the Art o f Logical Demonstration and the De Intellectu, were translated into Latin. The “ Brethren o f Purity” constructed an encyclopedia to interpret and confirm religious

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revelation. Alfarabi wrote commentaries on various parts o f logic which included, in the Syriac and Arabic traditions, rhetoric and poetic as well as the Introduction o f Porphyry and therefore structured logic in the Neoplatonic interpretation which substituted dialectic for the scientific demonstration o f the Posterior Analytics', and his encyclopedic treatise on the classification and fundamental principles o f the sciences, the Enumeration o f the Sciences, has survived in two Latin translations. In the Muslim encyclopedias prior to the eleventh century, under the influence o f Greek commentators, the structure given to logic was sometimes Stoic or Epicurean rather than Neoplatonic, but since it was based on the first “ four books o f logic” - Porphyry’s Introduction, the Categories, the On Interpretation, and ih.Q Prior Analytics - it was never adapted to the Aristotelian structure o f the Posterior Analytics. Alfarabi expounded logic in commentaries following the traditional division into three kinds: Short Commentaries or Epitomes, Middle Commentaries or Paraphrases with supplementary explanations, and Great or Long Commentaries in which passages from the text o f Aristotle are quoted and discussed at length. The relation o f human sciences to theology in the encyclopedias took many forms and was the subject o f continuing controversy; there were defenders and opponents o f the kalam, the word, or the logos. It was sometimes held that revelation can be explained and established by human reason, sometimes that the truths o f faith exceed the power o f human expression and are distorted by human argument, sometimes that human sciences have their principles and flow from divine science, sometimes that human and divine sciences are distinct in principles and methods but are not mutually contradictory. Avicenna, in the eleventh century, constructed a vast medical encyclopedia in the Canon, which was translated into Latin in the twelfth century, and a philosophical encyclopedia in the A l Shifa or The Healing which was translated into Latin in part by Gundissalinus in the twelfth century and again, in fuller forms, in the fifteenth and sixteenth centuries - parts o f the logic and o f the physics (called in Latin Sufficientia because o f its arrangement by causes and principles), On the Heavens (which is probably inauthentic). On the Soul (frequently called, because o f its position in the work. The Sixth Book o f Natural Philosophy), On Animals, On Intelligences, On First Philosophy. The organization o f the sciences is based on the Aristotelian division o f the theoretical sciences adapted to Neoplatonic interpretations. In the twelfth century Averroes


composed an encyclopedic formulation o f medicine, the Kulligat translated the Colliget, or Generality, and a vast collection o f commentaries, long, medium and short, on the works o f Aristotle (in which the Politics is omitted and a commentary on the Republic o f Plato is put in its place), many o f which have survived only in Hebrew or Latin translation.

When Arabic medical works began to be translated into Latin in the tenth and eleventh centuries, the encyclopedic array o f sciences they contained was adapted to the Latin encyclopedia, which had been influenced by the Hebrew and Greek encyclopedias in the course o f its formation. The ambiguities and oppositions o f the four cultures can be formulated with greater accuracy in terms o f structural changes o f meanings and applications introduced by structures o f arts and sciences than by simple comparison and opposition o f crucial propositions and inferred intentions and principles. They ail treated o f words and things, but different methods were used for the definition o f words and the determination and classification o f kinds o f things. They all developed arts o f grammar, rhetoric, logic, and dialectic, but to suppose that the Latin trivium is assumed in the other three encyclopedias is to distort those arts as they were developed in the other encyclopedias and to obscure, in consequence, the efiect they had on the evolution o f the trivum. They all treated the mathematical and the physical sciences, but the quadrivium was a mode o f treating them which was characteristic o f the Latin encyclopedia as was the close relation o f mathematics and physics and even the reduction o f physics to mathematics. They all treated law and related the law o f Moses or o f Abraham to the laws o f the cosmos, o f natural things, o f virtuous action, and o f artistic creation, and there were controversies in the discussions o f all four encyclopedias concerning the relation o f divine, natural, and human laws. The influence o f the cultures on each other was therefore not the transfer en bloc o f definitions o f words, sciences o f things, methods o f discourse, thought, inquiry, proof, or scientific system, but rather the rearrangement o f schemata which they shared and the modification o f the data, methods, and truths organized in those schemata to new specification and evidence. The contact o f Latin with Muslim culture raised scientific questions and revived and altered questions which had become part o f the Latin tradition as a result o f contacts with the Greek and the Hebrew encyclopedias. From the vantage point o f the West, the contact may be examined in the modifications o f the structure o f the Latin

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encyclopedia and in the problems perceived and inquiries initiated as a consequence. The encyclopedia o f the liberal arts is enlarged, and the effect o f the alteration is to initiate new sciences and new arts distinct from those implicit or developed in the older encyclopedias in isolation or in communication with each other.

The Latin encyclopedia at the beginning o f the twelfth century took the form o f collections o f words or things, universal histories, and lives o f ecclesiastical writers. The encyclopedias o f words were organized according to the subject matters and methods o f the liberal arts; the encyclopedias o f things were organized according to cosmological classifications o f facts or hexamerous sequences o f creation. The translations from the Arabic began with medical works, moved through the related subject matters o f physica - astronomy, astrology, experimental science and magic - to handbooks on the organization o f the sciences or the division o f philosophy. The arts became the arts o f the physici, physicians or physicists, and the things became the subject matters o f the sciences, theoretic, practical, and productive. In the eleventh century Constantine the African translated Greek as well as Arabic medical works, including the Microtegni, the Megategni, and the Compendium of the Megategni o f Galen, the Book o f Divisions and the Book o f Experiments o f Rasis. The Pantegni is an adaptation o f the Royal Art o f Medicine o f A li ibn Abbas, which treats all phenomena o f nature in terms o f the contraries o f the elements. It is divided into two parts. Theory and Practice, theory being the perfect knowledge o f things seized by the intellect alone, practice the manifestation o f theory in things o f sense and in manual operations in accordance with theory. Bodies are formed from mixtures o f elements called complexions, which are instruments o f nature or o f the soul, or o f both. The De Imagine Mundi, probably by Honorius Inclusus about 1080, and the Liber Floridus o f Lambert o f Saint-Omer, about 1120, are in the older tradition o f Latin encyclopedias, compilations o f materials from Macrobius, Martianus Capella, Isidore, Bede, and Hrabanus Maurus. Later in the twelfth century the Philosophia Mundi o f William o f Conches, which has been attributed under various titles to Bede, William o f Hirschau, and Honorius o f Autun, shows the influence o f translation from the Arabic, particularly o f the Pantegni. Gundissalinus, in the second half o f the twelfth century, translated Avicenna’s De Anima, Metaphysics, and Posterior Analytics, Alfarabi’s De Intellectu and De Scientiis, Alkindi’s


De Intellectu, and Isaac Israeli’s Liber de Definitionibus. His treatise De Divisione Philosophiae which contains some o f his translations from Avicenna and Alfarabi, follows the lines o f Alfarabi’s organization o f the sciences: natural science, mathematics, divine science, grammar, poetic, rhetoric, logic, medicine, arithmetic, music, geometry, aspects (the Arabic science o f optics or perspectives), astrology, astronomy, the science o f weights, natural abilities or engines {de ingeniis, following the consequences o f complexions o f things and minds - engine and ingenuity - the purpose o f the science according to Gundissalinus is to teach ways o f thinking out and inventing means by which natural bodies may be adapted by artifice to uses rendered possible by the mathematical sciences), an abbreviation o f Avicenna’s analysis o f agreements and differences o f subjects, and finally a section on the parts o f practical philosophy. Adelhard o f Bath travelled in Italy, Greece, and possibly Asia Minor in search o f the new knowledge. He translated Euclid, wrote mathematical treatises, and a Quaestiones Naturales, and justified his wanderings in the De Eodem et Diverso by showing how the study o f the liberal arts in France is supplemented by study in Italy and completed by knowledge o f Greek sources. Thierry o f Chartres, in the manner o f the twelfth century, made a vast collection o f texts on the liberal arts in his Heptateuchon. The manuscript o f 595 pages contains portions o f forty-five works including Donatus and Priscian on grammar, Cicero, Severianus, and Martianus Cappella on rhetoric. Porphyry and Boethius, the Categories, On Interpretation, the first Book o f the Prior Analytics, selections from the Topics and the De Sophisticis Elenchis, but nothing o f the Posterior Analytics o f Aristotle, on logic, Boethius, Martianus Cappella, Isidore o f Seville, Frontinus, Columella, Gerbert, Gerland, Hyginus, Ptolemy and a short fragment on regular bodies ascribed to Adelhard o f Bath on the quadrivium. His On the Work o f the Six Days makes use o f the Timaeus for the interpretation o f Genesis. Two o f his pupils, Herman the Dalmatian and Robert o f Chester, dedicated their translation o f Ptolemy’s Planisphere to him as the anchor and sovereign o f the second philosophy, that is, the quadrivium.

Education in the Arabic tradition related medicine, law, and theology, and the mature career o f a scholar often included activities in all three. In the Latin tradition the hberal arts continued to constitute preliminary education, and after the foundation o f universities separate faculties o f

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medicine, law, and theology were established. The widely circulated encyclopedias o f the thirteenth century were assemblages o f facts, organized according to different plans. Alexander Neckham’s De Naturis defends natural science against the logical vagaries o f Paris and quotes Algazeli and Isaac Israeli. Thomas o f Cantimpré’s De Natura Rerum is an uncritical assemblage o f information about different kinds o f things - Books 1-3 on man, Books 4-9 on animals, Books 10-12 on plants. Book 13 on waters (rivers and fountains). Books 14-15 on stones and metals. Books 16-18 on astronomy, astrology, and meteorology. Book 19 on elements. Bartholomew o f Glanville addressed his encyclopedia On the Properties o f Things to plain people - simplices et rudes. He makes use o f Arabic works, undertakes to cover all things, lists authors cited, and organizes his chapters by propositions which state their positions in turn. Book 1 is on God, Book 2 on angels and demons. Book 3 on psychology. Books 4-5 on physiology. Book 6 on family life and domestic economy. Book 7 on medicine (largely derived from translations from the Arabic), Book 8 on cosmology and astrology. Book 9 on divisions o f time. Book 10 on form and matter and the elements, Book 11 on air and meteorology, Book 12 on flying creatures, Book 13 on water and fishes, dolphins, and whales. Book 14 on physical geography, Book 15 on pohtical geography (in 175 chapters). Book 16 on gems, minerals, and metals. Book 17 on trees and herbs. Book 18 on animals. Book 19 on color, odor, savor, food and drink, eggs, weights and measures, musical instruments. In the thirteenth century the Speculum Majus o f Vincent o f Beauvais made explicit in its four “ mirrors” four schemes o f organization used from antiquity to the medieval Latin encyclopedias - according to subject matter, according to sciences, according to practical problems, and according to chronology. The Speculum Naturalis is in 32 books and 3,718 chapters, in which the natures o f things are treated in the order o f their creation in the first 28 books, arranged in the sequence o f the six days o f creation; Book 29, “ On the Universe,” is concerned with the operations o f God since the creation; Book 30 with the nature o f things; Book 31 with the natural history o f man; and Book 32 with times and places. The Speculum Doctrinale presents human doctrines - grammatical, literary, and political as well as legal, mathematical, and physical - in 17 books; Book 1 contains an alphabetical dictionary o f about 2,300 words, and the remaining books run throught the sciences from the hberal arts to theology: Book 2 gram


mar; Book 3 logic, rhetoric, and poetry; Books 4-5 monastic sciences; Book 6 economics; Book 7 politics; Book 8 law; Books 9-10 crimes; Book 11 mechanical arts; Book 12 practical medicine; Books 13-14 theoretical medicine; Book 15 physics; Book 16 mathematics, including metaphysics; Book 17 theology. The Speculum Doctrinale contains no reference to the Arabic sciences o f optics or mechanics, but it does treat Arabic numbers. The Speculum Historiale is in 31 books and 3,792 chapters; it traces the history o f the world from creation to 1254, and it has 24 chapters on the deaths o f great men and the end o f the world. The Speculum Morale was added to Vincent’s three mirrors in the fourteenth century, about 1310-1325; it is in three books and 247 articles, arranged according to distinctions and divided into articles; it makes use o f the moral conceptions and differentiations o f Thomas Aquinas. Brunetto Latini’s French encyclopedia L i Livres dou Trésor, 1260-1267, is in three books: Book 1 on the origin o f the world and the history o f the Bible and of the foundations o f governments, astronomy, geography, and natural history; Book 2 on morality, reflecting Aristotle’s ethics and based on a collection o f extracts from moralists, entitled the Moralities o f the Philosophers', Book 3 on politics, beginning with a treatise on rhetoric based

on Cicero.The medieval Latin encyclopedias continued to be collections o f words

and things, o f verba and res, facta and acta, enlarged by contact with Arabic encyclopedias o f sciences, methods, and principles to include new words and new things. That enlargement included the ancient Greek sciences and the scientific works o f Aristotle, and it led therefore to a readjustment to the medieval Greek and Hebrew encyclopedias which had developed from the same ancient Greek sources. As the contact with Arabic encyclopedias had been adapted to the Latin liberal arts to reconstitute the quadrivium or second philosophy, so the readjustments to the Greek encyclopedia led to a reconstitution o f the methods and subject matter o f the trivium and the readjustments to the Hebrew encyclopedia gave new significances and application to hermeneutics as applied to human and divine letters and to the relations o f sciences to philosophy. John o f Salisbury’s Metalogicon reports the reconstitution o f the trivium on a basis adapted from the academic philosophy o f Cicero. Grammar is the foundation o f both philosophical inquiry and the practice o f virtue, for both are the product o f reading, doctrine, meditation, and application {Metalogicon

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i. 23). The study o f poetry and “ letters” also falls in the art o f grammar. John enumerates three possibihties - some assign poetry to grammar, some to rhetoric, and some to a special art, poetics - but John concludes that poetry must remain a part o f grammar or be dropped from the liberal arts {ibid. i. 17) and he describes in detail the use o f grammar in teaching Uterature employed by Bernard o f Chartres {ibid. i. 23). Peter Helias wrote a Latin grammar in hexameters, and the art o f poetry was expounded in Matthew o f Vendôme’s Ars Versifitoria in the twelfth century to be continued at the beginning o f the thirteenth century by the Poetria Nova o f Geoffrey o f Vinsaud, and the Laborinthus o f Evrard the German. The opposition o f a program o f grammar and letters and a program o f logic and the sciences became the battle o f the seven liberal arts in the thirteenth century between the universities o f Toulouse and Paris. With the victory o f logic, grammar was logicized and laid the foundations for the tradition o f speculative grammars or modes o f signifying. The battle, however, was between a grammar and a logic already rhetorized by Cicero and Quintihan. Aristotle’s Poetics was not translated into Latin until the end o f the thirteenth century, and it too was rhetorized in the Renaissance commentaries which adapted Horace’s Poetic Art to give poetic a rhetorical interpretation.

The Greek encyclopedia was literary and critical - analytical presentations o f the elements, style, and contents o f chosen great works; the Latin encyclopedia a collection and manual o f Uberal arts. The method o f the Greek encyclopedia derived from the demonstrative, epideictic rhetoric o f the Second Sophistic; that o f the Latin encyclopedia from the deliberative and judicial devices o f political and forensic rhetoric. The culture o f the Greek tradition was the culture o f the hterary and learned circles o f the Imperial court; the culture o f the Latin tradition was the culture o f episcopal and abbotal schools, o f Curias and councils. The struggle between programs o f grammatical studies o f literature and history and logical studies o f philosophy and science in the thirteenth century was a continuation o f cultural differences which were apparent in the contacts o f the two cultural traditions in the early centuries o f the Roman Empire. Greek Apologists, like Justin Martyr, Tatian, and Athenagoras, presented Christian doctrine in the context o f philosophic doctrines. Justin sought God through the philosophers - a Stoic, a Peripatetic, a Pythagorean (who urged the study o f geometry, astronomy, and music).


a Platonist, and an old man who converted him from the books o f the philosophers to Holy Scripture; and he was able to discover Christians prior to Christ. The Recognitions o f the pseudo-Clement o f Rome tells the story o f the family o f Clement, two parents and three sons who were separated and wandered through the world and through the doctrines o f philosophy, religion, and gnosticism until they were brought together and converted by Peter the Apostle and recognized themselves and the community and truths o f Christianity. Hippolytus o f Rome derives Christian heresies from Greek philosophical doctrines. Clement o f Alexandria’s sequence o f steps in Christian education - the Protrepticus, the Pedagogue, and the Strommata - makes use o f Greek philosophy and literature as a starting point for instruction concerning the teaching o f the Logos, and the Strommata is an encyclopedic carpetbag o f literary citation and information. Latin Apologists, like Tertullian (whose early writings were in Greek) and Arnobius, argue against the legaUty o f the persecution o f the Christians. The Greek community was held together by cultural bonds of literature and philosophy; the Latin community was a polity held together by institutions and laws. The Greek culture produced as a genre for its expression the Novel or Parable o f spiritual and intellectual wandering; the Latin culture found its genre in the Autobiography, as introduced by Augustine, o f the individual sinner seeking happiness or beatitude by intellectual discipline and moral enlightenment, and in the Hymn, which Ambrose used to preserve the Christian community from the threat o f transformation to Arianism. Justin encountered philosophical and religious cultures and communities o f peoples; Augustine moved from sin to cultivation o f himself, culture or Christian doctrina, and the cult o f God; Ambrose solidified the Christian ecclesia against imperial pressures to doctrinal variation. What were to become the Humanities in the Renaissance took their beginnings in two forms in the two traditions from the same distinctions; Themistius, writing in Greek in the fourth century A.D. and advocating a return from Christian to Greek culture, used the word ‘philanthropia’ to distinguish the hermeneutics o f human letters from that o f divine scripture, and so separated the humanities from theology; Aulus Gellius writing in Latin two centuries earlier argued that ‘humanitas’ is a translation o f ‘paideia’ and not o f ‘philanthropia’ for the study o f outstanding achievements, and so laid the bases for the liberal arts which were to be applied to the study o f divine as well as human

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letters. The Recognitions o f the pseudo-Clement survive in the Latin translation o f Rufinus, and Origen’s Principia was the subject o f attack and defense in the Latin tradition, highlighted in the quarrel o f Rufinus and Jerome.

The history o f the separation o f the two cultural traditions was traced as steps o f institutional growth in the Latin tradition and o f doctrinal evolution in the Greek tradition. The formation o f Latin Christianity was the construction o f a church and the institutional powers attributed to the pope, the curia, the bishops, and the councils for the interpretation o f doctrines and the judgment o f actions. The formation o f Greek Christianity was the formulation o f a theology and the derivation o f doctrines which followed as consequences and o f deviations which were shown to be erroneous and heretical. The early stages o f the cooperation and separation o f the two traditions were over issues and problems concerned with both - with structures o f power and action and with oppositions o f doctrine and their interpretation. The emperor Constantine summoned a “ general” council at Arles in 314 to deal with the problems o f the Donatist schism. After he had made himself sole emperor in 324, he summoned the first ecumenical council, the First Council o f Nicaea, in 325 to solve the conflict in the Eastern Church over Arianism. It established 20 canons and a synodical decree concerning the date o f Easter. The emperor exiled Arius from Egypt until he accepted the Creed o f Nicaea. The Eastern bishops expressed distrust o f the Council as a means o f resolving doctrinal disputes: Gregory o f Nazianzus wrote that he perferred to avoid all councils o f bishops, and the easterners refused to attend the Council o f Sardica in 343, which had been intended as an ecumenical council, when they learned that the westerners insisted on the attendance o f Athanasius. The council o f Chalcedon in 451 approved a series o f documents, including the Creed o f Nicaea and the Creed o f Constantinople, to establish a confession o f faith and confirmed a code o f canons which gave ecumenical authority to canons o f earUer local or provincial councils. The four general councils were canonized as the rule o f orthodoxy, and in the sixth century Gregory the Great wrote that he reverenced them as he reverenced the four Gospels.

From the viewpoint o f the Latin tradition, the process o f institutional change was marked by changes in the Empire and in the Church, and in particular by the separation o f the Eastern and Western Empires in 364,


and by the schism o f the Greek and Latin Churches, which began in the ninth century when the Eastern emperor made Photius patriarch over the objections o f the Romans. Photius was recognized as patriarch and was influential as compiler o f three characteristically Greek encyclopedias, the Myriobiblion, the Lexicon, and the Amphilochia. The first seven ecumenical councils from the First Council o f Nicaea in 325 to the Second Council o f Nicaea in 787 were recognized by both Churches. The Fourth Council o f Constantinople in 869-870, which confirmed the Roman sentence o f excommunication against Photius, was recognized as ecumenical by the Roman Church. A ll subsequent ecumenical councils from the eighth to the twenty-first, the Second Vatican Council in the twentieth century, were recognized by the Roman Church. Six o f these councils were held in the twelfth and thirteenth centuries, after a period o f more than 250 years between the eighth and ninth. They were councils o f reform, reaffirmation, and consolidation. The Fourth Lateran Council in 1215 condemned the errors o f the Albigenses and the Waldenses, and o f Joachim o f Fiore, and approved the teaching o f Peter Lombard on the Trinity. The Second Council o f Lyon in 1274 was summoned to end the Greek schism, to rescue the Holy Land, and institute a moral reform. Albertus Magnus and Bonaventura attended the Council, and Bonaven- tura died during its sessions.

The revival o f the study o f literature in the twelfth century did not lead to the transformation o f the Latin encyclopedia o f the liberal arts to the form o f the Greek encyclopedia o f literature and literary history and criticism. The Greek reader did not depend on translations o f the Greek classics, but he needed aids to understanding, appreciating, and using them. The Latin encyclopedia joined or opposed grammar and rhetoric in the interpretation o f poetry without setting up a separate science o f poetics to analyze and expound Virgil and to record figures and styles in Latin literature. There was an efflorescence o f poets who were frequently also philosophers - Bernard Sylvester, Alan o f Lille, Bernard o f Morlas, John o f SaUsbury, Hildebert o f Lavardin, and Peter Abailard - and the subjects o f their poems were frequently encyclopedic - cosmology, the nature and history o f things, morals. The structure o f the encyclopedia led to new developments in literature as well as in grammar and rhetoric and to new developments in canon law, theology, and philosophy as well as in dialectic and rhetoric.

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Saint Augustine laid down the structure o f the encyclopedia o f the liberal arts. His City o f God related the history o f terrestrial cities, and o f Rome in particular, to the City o f God and affirmed an affinity between Platonism and the Christian faith, relating the “ Platonic Sciences,” physics, logic, and ethics, to the three persons o f the Trinity; his De Trinitate explored the basic principles o f theology and their relations to philosophical problems; his De Doctrina Christiana applied the liberal arts to the interpretation o f the things and the words o f Scripture; and treatises on rhetoric and dialectic, attributed to him, were widely read. Boethius fitted his translations o f Aristotle’s Categories and On Interpretation and his commentaries on them to this Platonic frame with the help o f Porphyry’s Introduction to the Categories and his own logical treatises. The conflict o f canons led to the collection o f issues and the formulation o f methods o f resolving them from the ninth to the twelfth century by Hincmar, Gerbert, Berthold o f Constance, Ivo o f Chartres, and Alger o f Liège. Abailard’s Sic et Non is a collection o f seemingly contradictory texts from Scripture and the Church Fathers on 158 questions. Many o f the citations are the same as those in the collections o f Ivo o f Chartres, who had borrowed some o f them from earlier collections, and many reappear in the Sentences o f Peter Lombard and the Decretum o f Gratian, which was known as the “ Concordance o f Discordant Canons.” The twelfth century is an era o f Books o f Sentences. By virtue o f them it is easier to characterize the culture o f the twelfth century than any other period, for it is possible to make a list o f about 3,000 important texts with which all the learned men o f the period were likely to be familiar and to specify the methods by which they were interpreted and used. It is a culture distinct in content and orientation from the culture expressed and advanced by the books o f excerpts and paraphrases o f the Greek encyclopedia. The “ scholastic method” was formed by the conjunction o f the rhetoric o f resolving disputed questions and the dialectic o f constructing interdependent sequences and systems o f resolutions. The summas o f theology o f the thirteenth century are further systematizations o f the subject matter o f the Books o f Sentences o f the twelfth century - from God and Creation through man, his virtues and laws, to last things - treated step by step in questions to which possible answers are set in oppositions to be resolved by demonstrating one and refuting the other.

The earlier contacts o f the Latin with the Greek tradition, o f a culture


expressed in a methodological factual encyclopedia with a culture expressed in a literary doctrinal encyclopedia, were reechoed and expressed in the twelfth and thirteenth century in oppositions and adjustments o f grammar and rhetoric. The contacts o f the Latin with the Arabic tradition led to the readjustment and development o f logic in its relations to dialectic, rhetoric, and grammar under the influence o f the Arabic logic which had developed in relation to the sciences. Many o f the steps o f the two developments - the development o f the liberal arts relative to literature and their development relative to science - are the same in the two traditions because o f the operation o f ideas which entered into the origins o f both, independent o f but reinforced by intercultural influences. In both traditions the Aristotelian logic was adjusted to a Neoplatonic dialectic. The Arabic tradition had access to the Greek commentators, and therefore the adjustment was sometimes to the Stoic logistic or the Epicurean canonic, which Latin commentators o f the twelfth and thirteenth centuries learned about from Arabic commentaries and theories. In both traditions Porphyry’s Isagoge became part o f the canon o f Aristotelian logic. In the Neoplatonic dialectic categories were words, not terms as Aristotle presented them, that is, words with meanings and references; and they stood in need therefore o f an “ introduction” derived from the predicables which Aristotle treated as part o f dialectic in the Topics. The predicabilia provided theoretic bases for the predicamenta. Moreover, Aristotle distinguished four predicables - definition, genus, property, and accident. Porphyry broke “ definition” into its parts, and distinguished five “ words” - genus, species, differentia, property, and accident - and since the distinction o f genus and species, unlike the distinction o f genus and definition, introduces the elements o f a hierarchy, it planted the seeds o f “ Porphyry’s tree.” Such a hierarchy indicated the need o f a bottom as well as a top, and therefore Avicenna and Abailard introduced a sixth “ word,” independently, in the twelfth century - “ individual.”

Moreover, since logic was an art o f words, rhetoric and poetic became a part o f logic in the Syriac-Arabic tradition, and there were therefore eight books oflogic-thesix treatises o f the Organon, plus the Rhetoric and the P o e t i c s I n t r o d u c t i o n was added. In the thirteenth century, Thomas Aquinas too distinguished eight parts o f logic. The development o f logic in the two traditions was in part the gradual addition o f books o f logic, and in part the methodological changes in logic conse

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quent on their addition. In the ninth century, in the time o f Alfarabi, Arabic logic was based on the “ four books” o f logic, Porphyry’s Introduction and the first three treatises o f Aristotle’s Organon. In the twelfth century, in the time o f Abailard, Latin logic was based on the same four books - Boethius’s translations o f the Introduction, the Categories, and the On Interpretation, together with his commentaries on them, and his treatises on the syllogism, in the place o f the Prior Analytics. In both traditions the Neoplatonic framework o f predicables and topics provided dialectical devices to establish demonstrative syllogisms and principles, which made the Aristotelian devices o f the Posterior Analytics unnecessary. In that framework, the categories become “ principles” rather than terms, and in the twelfth century Gilbert de la Porrée wrote a Book o f Six Principles to fill the gap left by Aristotle’s failure to expound the last six categories as fully as the first four. Gilbert’s treatise was added to the canon o f the books o f Aristotelian logic, which came to be called the Old Logic, the Logica Vetus, after the New Logic, the Logica Nova, was constituted by the addition o f the new translations o f the last four treatises o f the Organon. Medieval manuscripts o f the Organon therefore contain eight treatises, the six parts o f the Organon and the treatises o f Porphyry and Gilbert. In 1255 the Six Principles was included among the books ofii- cially required in the Faculty o f Arts o f the University o f Paris, and commentaries on it were written by many philosophers, including Albertus Magnus, Robert Kilwardby, Antonius Andrea, Walter Burleigh, and Bongratia o f Acoli. Renaissance Humanists prepared new translations o f the Organon from the Greek to free it from the barbarisms o f medieval Latin, and to complete that process Hermolaus Barbarus translated the Six Principles into a more elegant humanistic Latin, which is the only form in which it was available until the original medieval text was published in the twentieth century. Albertus Magnus explains in his commentary why Gilbert called the ten first genera principles rather than categories: they are the first essences constituting in their essentiality and containing in the embrace o f their community all things which can be ordered according to the determination o f subject and predicate, and they are therefore ten principles o f things in which all resolution or analysis ends. Gilbert also wrote a commentary on the theological opuscula o f Boethius, in which the Neoplatonic framework o f this conception o f logic and o f the organization o f the sciences is more apparent. In “ the books o f


questions o f Boethius,” as Gilbert calls them in his prologue to the commentaries, God, interminable in magnitude, incomprehensible to contemplation, inexplicable in word, is rightly understood and laudably predicated. In the Commentary on How Substances in that they are, are Good, Gilbert explains that his procedure, and that o f Boethius, is like that followed in the mathematical disciplines o f arithmetic, geometry, music, astronomy, and many other disciplines, o f setting down at the beginning terms or rules. These common reasons, terms, rules, conceptions, prop- sitions, known naturally or through logic, are the indemonstrables, the propositions known through themselves - the rules o f grammar, the commonplaces o f rhetoric, the greatest propositions o f dialectic, the theorems o f geometry, the axioms o f music, the theorems o f measures, the axioms o f weights. The different faculties o f the mind are distinguished according to the genera o f things o f which they treat, and o f all the forms o f knowledge- natural, mathematical, theological, civil, rational - there is one, “ natural” or “ physical science,” which is more influential on human speech than the rest, and from it distinctions are transferred to the others in a proportional sense. In its narrow meaning, natural science is knowledge o f natural things, concrete and inabstract; in its broader meaning, the natural sciences are three, the strictly natural, the mathematical, and the theological. The mathematical sciences consider the inabstract forms o f natural things abstractly; they are named from mathesis or disciplina, the name applied to the seven liberal arts, and they separate inseparable things in order that their natures and properties may be perceived.

The coming o f the New Logic was not the substitution o f a complete logic for a partial logic. The Old Logic was a dialectical logic in which the discussion o f principles was based on Porphyry’s five words or predicables and on Boethius’s topics, which he derived from Cicero and Themistius ; the New Logic made available Aristotle’s Posterior Analytics and Topics, but principles were still sought dialectically in the Topics and not apo- deictically in Aristotle’s manner in the Posterior Analytics. In the thirteenth century the choice between these two conceptions o f principles led to the distinction between the Ancient Logic, Logica Antiqua, which reinstated the Posterior Analytics, and the Modern Logic, Logica Moderna, which found substitute sources o f principles in topics, sophisms, paradoxes, grammar, and mathematics.

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John o f Salisbury, whose Metalogicon is based on the New Logic, devotes six chapters to the Topics (Bk. Ill, 5-10) because “ the body o f the art” o f logic is Topics, Analytics, and Refutations, and Topics is the most important o f these for probable arguments. He merely touches on the Posterior Analytics briefly (Bk. IV, 6 and 8) because the art o f demonstration is employed by almost no one except mathematicians, and among mathematicians only by geometricians. Demonstrative logic is the logic o f judgment, topics the logic o f invention. Peter Abailard, who had been one o f John’s teachers and who professed to know only the books o f the Old Logic, although modern scholars have labored learnedly to show that he must have used the Prior Analytics and the Sophistical Refutations, undertook to write a systematic presentation o f the whole o f logic. Since the treatment was to be complete, he called three o f the five treatises o f his Dialectica by the names o f three o f the treatises o f the Organon which he had not read - the Prior Analytics, the Topics, and the Posterior Analytics - developing their meanings dialectically and giving them different subject matters than they had had for Aristotle. Scholars have been puzzled by these titles for more than a hundred years since Cousin first published parts o f the Dialectica, and the editor o f the excellent critical edition published 17 years ago dropped them because they are “ meaningless” and rearranged the contents o f the parts to fit the new titles he substituted for them. The puzzle is less inscrutable if Abailard’s treatment o f the contents o f the parts o f Aristotle which he did not know is compared with his treatment o f the Old Logic on which he wrote glosses which show a detailed knowledge - Porphyry’s Introduction, Aristotle’s Categories and On Interpretation, Boethius’s De Differentiis Topicis and De Divisionibus - and in which he sketches the dialectic o f his departure from Aristotle which he develops more fully in the Dialectica.

Treatise I is called the Book of Parts and is divided into three volumes o f which the first and the beginning o f the second is lacking in the one surviving manuscript. The epilogue o f Treatise I outlines the treatise: it is concerned with the parts o f speech {partes orationis) which he calls dictions {dictiones) in three steps, Antepredicamenta, Predicamenta, and Postpredicamenta. Abailard knew that these were the traditional three parts o f Aristotle’s Categories, yet it is clear that he treated the five words o f Porphyry’s Introduction in the missing first volume o f the First Treatise and not the antepredicamenta o f Aristotle, which he reserves for treatment


in Treatise II and Treatise V. In his commentary on Porphyry in the Logica Ingredientibus he demonstrates that the science o f the five words or predicables is necessary not only for the science o f the categories or predicaments but also for divisions, definitions, propositions, and argumentations. Moreover these sciences are reciprocally related since the nature and kinds o f words depend on their uses in statement and argument, and the nature and kinds o f arguments depend on the divisions and definitions o f words and statements. Cicero and Boethius, moreover, had set up “ a double division o f dialectic, which so include each other reciprocally that they comprise the whole o f dialectic” : the sciences o f discovery and judgment, and the sciences o f division, definition, and collection. Finally, Abailard puts words and things in a dialectical relation: they provide the difference between logic and physics, but both words and things are essential to both sciences. Things are considered in logic as a “ category,” like “ substance” or “ quantity,” is both a word and a thing- John o f Salisbury calls this the “ principle o f indifference” - and, in general, logic investigates the imposition o f words on things, while physics investigates whether the nature o f the thing conforms to the statement made about it.

The second volume o f the First Treatise is concerned with categories and treats the ten categories taken up in the central portion o f Aristotle’s Categories. Like Gilbert de la Porrée, Abailard fills in the six categories which are treated briefly by Aristotle. Gilbert considered categories principles, and therefore added a treatment o f six principles to the four expounded by Aristotle. For Abailard categories are not principles but significative words, and he therefore reorganizes the list o f the categories in order to treat first the two categories which are directly significative o f things, substance and quantity, which is “ inserted” in substance so that when we understand a substance we conceive its quantity, one or many. Thereafter, he goes on to the “ remaining categories,” which are adjacent to substance - time, place, and position briefly, relation in more detail, quality at length, and doing, undergoing, and having briefly.

The third volume o f the First Treatise lacks a title, but it begins by characterizing the preceding parts which had been devoted to determining (1) the significance o f names and (2) the natures o f the things designated by words used according to the ten categories. The next part (3) is to return to the significative word in order to determine how many “ modes o f sig

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nifying” there are. Names or nouns signify (1) in naming things by imposition and detennination, (2) in joining words in statement by generation or removal, afl&rmation and denial, (3) in framing demonstrations by adherence and concomitance, (4) in words significant naturally or by convention, in composite, indefinite, and definite dictions and in verbs. The First Treatise, thus, treats words in the three aspects in which they are “ parts o f speech” - as “ predicables” capable o f functioning in significant discourse, as predicaments signifiying meanings and designating things, and as “ modes o f signifying” operative in designation, statement, and demonstration. The five words o f Porphyry provide the ten categories o f Aristotle provide predicamenta, and the first four chapters o f the On Interpretation provide nouns and verbs, parts o f sentences or speeches, as postpredicamenta, in the discussion o f the parts o f speech in Treatise I, under the titles “ On the Five Words,” “ On Categories,” and “ On Interpretation.”

Treatise II is called “ On Categorical Propositions and Syllogisms or the Prior Analytics.” It opens with a statement o f purpose and method: now that individual significant words or dictions {singulae dictiones) have been treated, it is proper to go on to the composition o f statements or speeches {compositio orationum). The parts, significant words, are the matter; the perfection o f the whole is formed by conjoining them. Abailard does not propose to consider all kinds o f sentences but only true and false sentences, propositions, which are the sentences proper to dialectic. Simple or categorical propositions are prior in nature to, and form the matter of, hypothetical propositions which are constructed o f them, Aristotle has treated the forms and moods o f categorical syllogism briefly and obscurely. Boethius, making use o f hypothetical “ complexions” as developed by Theophrastus and Eudemus, had written on both. Abailard enumerates the seven works on “ Latin eloquence” that he had at his disposal in his work: Aristotle’s Categories and On Interpretation, Porphyry’s On the Five Words, and Boethius’s Divisions, Topics, Categorical Syllogism and Hypothetical Syllogisms. The Dialectica will set forth a summa o f the art they exposit, beginning with speech {oratio) and going on to propositions and syllogisms o f which speech is the genus. Treatise II is therefore in three parts - on sentences, propositions, and syllogisms - which are again reciprocally related to each other. Its organization follows that o f Boethius’s On the Categorical Syllogism, which is divided


into two books one on the categorical proposition and its parts, based on Aristotle’s On Interpretation, the second on the categorical syllogism, based on Aristotle’s Prior Analytics.

Part I o f Treatise II lacks a title, but it begins with the definition o f a sentence or speech {oratio), treats proposition as a kind o f speech, and examines the parts and kinds o f propositions. A sentence is vocal sound (voa:) which is significant by convention and is composed o f significant parts, and the definition o f the sentence can therefore be derived from the definition o f parts in Treatise I. However, the “ parts o f speech,” pars orationis, are predicates, nouns and verbs, while the “ terms o f a sentence,” terminus orationis, are parts o f a significant whole, subjects and predicates, and the transition between the first two treatises is the final chapter o f Treatise I, after the extended treatment o f nouns, on the verb. Among the kinds o f sentences - enumerations, interrogations, deprecations, imperatives, and desideratives - propositions have the distinctive mark o f being true or false in signification. They depend therefore on distinguishing ideas o f understanding {intellectus) and existence o f things {existentia rei) in the designations o f the words and in the “ consequences” signified in words and designated in things. Part 2 distinguishes the kinds o f simple categorical propositions by differences o f predicates and subjects: (1) afl&rmative and negative propositions by differences o f predicates, (2) universal, particular, indefinite, and singular propositions by diff'erences o f subjects, (3) one proposition and multiple propositions by the multiplication o f terms by differences o f meanings which make different nouns o f the same term, and (4) past, present, and future propositions by differences o f time in the verb.

Simple affirmative and negative propositions may be related as contraries or contradictories by the opposition o f two simple categorical sentences or in a single complex hypothetical sentence, and it is at this point that Abailard introduces the diversities o f meanings which Aristotle treated partly in the antepredicamenta o f the Categories and partly in the De Sophisticis Elenchis: equivocation, univocation, diverse parts, times, relata, and modes. Simple categorical propositions are related by opposition relative to meanings and by subsumption relative to things. Modal propositions are modes or modifications o f simple propositions. The modification may be adverbial (by an adverb which modifies the predicate) or casual (by changing the case o f a predicate, making it the subject

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o f an adjective signifying a mode). “ Socrates possibiliter est episcopus” is an adverbial modal proposition. “ Socrates possibile est esse episcopus” is a casual modal proposition, since “ is possible” is predicated o f the predicate “ to be a bishop.” Modal propositions are related by opposition and equipollence.

Part 3 turns from simple categorical propositions to complex categorical propositions. The analysis in Part 2 has been o f propositions in the present tense. Consideration o f time, the fourth kind o f simple categorical proposition, introduces the problem o f future contingents - it is certain that a future event will occur or not occur, but not determinately that it will or will not. The consequences in statement are distinct from the consequences in occurrence, and questions o f meaning and reference change with the change o f time. Freedom o f the will, fate, and divine providence are involved in this problem, as is the philosophic difference between Peripatetics and Stoics who respectively deny and affirm necessity in nature. In dialectic it is a problem o f consequences, requiring rules concerning antecedents and consequents. The distinction between propositions which are one and propositions which are multiple, or between composite and simple propositions, which appUes to hypothetical as well as categorical sentences provides the transition to the treatment o f the categorical syllogism, which is a speech ipratio) in which from something posited something else follows o f necessity. The problems o f time were problems o f imposition relating future propositions to events which become determinate in the present; they are formulated in terms o f antecedents and consequents in judgments and events. The problems o f the syllogism are problems o f subsumption relating universal and particular, affirmative and negative; they are consequences formulated in the rules o f mediate inference, as the consequences o f simple and modal propositions were formulated in the rules o f immediate inference.

Treatise II I is called “ The Topics.” Its organization is set forth in the opening section : hypothetical syllogisms will be examined in terms o f the hypothetical propositions o f which they are composed, as categorical syllogisms were analyzed. But since the meaning o f a hypothetical proposition depends on conditions from which consequences follow, places must be examined as seats o f inference and evidences o f truth before hypothetical propositions and syllogisms are examined in the next book, the Posterior Analytics. The Topics, therefore, has the same relation to


the Posterior Analytics as the Parts o f Speech has to Prior Analytics - uninfluenced by the relations which the corresponding parts o f Aristotle’s Organon may be thought to have had to each other. Consequently, although the manuscript does not indicate a division into parts (the Cousin edition follows the manuscript, the deRijk edition marks off two parts), three steps can be distinguished in the argument, comparable to the three parts o f Treatise I. In the Parts o f Speech the sequence was from dictions through significant dictions to modes o f signifying - all o f which are individual words considered as predicables, as predicaments, and as nouns and verbs. In the Topics the sequence is from places o f inference to consequences o f inference to principles o f inference - all o f which are places. It is a sequence from underlying evidence through consequential use o f evidence to antecedent statement o f principles o f evidence. In the first step, a place or locus is defined as a force o f inference {yis inferentiae) or, more strictly, a seat o f argument {argumenti sedes). Inference is the derivation o f consequences from places, and syllogistic inference is one kind o f consequence. In the second step, places are divided into maxims (maxima propositio) and differences o f maxims. A maxim establishes many consequences by a common mode o f proof, as “ what is predicated o f the species is predicated o f the genus.” The “ differences o f maxims” and “ topical differences” arise from the difiFerent meanings assigned to terms and connectives, such as the basic division derived from the different senses o f the adverb “ whence” in inferences: it may be used in a material causal mode, in an illative mode, or in a local mode. In the course o f examining and enumerating maxims or maximal propositions, Abailard introduces the distinction o f opposites, relatives, simultaneities, priorities, contraries, privations and habits, affirmation and negation which Aristotle treated as postpredicaments in the Categories. The third step is the examination o f differences o f places - inherent, extrinsic, and medium- as they are exhibited in two divisions o f places, by Themistius and Cicero, which are different in their bases but can be reduced one to the other. Themistius seeks the differences o f places in differences o f things signified, and his division contains a discussion o f differences o f motions which contributed to the language o f differentiation in the history o f physics. Cicero seeks the difference o f places in differences o f modes o f formulation, and his division contains a discussion o f wholes and parts, likenesses and differences, antecedents and consequences, which provided language

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o f differentiation in the history o f rhetoric, law, and philosophy. The combination o f the two constitutes the dialectic o f places.

Treatise IV is called “ The Posterior Analytics.” It is based on “ The Topics,” as “ The Prior Analytics” is based on “ The Parts o f Speech.” Moreover, as “ The Prior Analytics” follows a sequence from sentence through categorical proposition to categorical syllogism, all o f which are sentences (that is, simple vocal forms) and all categorical complexions (that is, combinations o f categorial words), so “ The Posterior Analytics” follows a sequence from hypothesis through hypothetical proposition to hypothetical syllogism, all o f which are hypotheses (that is, conditional combinations o f simple sentences) and topical consequences (that is, inferences derived from places). In the first step, a hypothesis is defined as a proposition accepted “ by consent” in a discussion or “ by condition” in a proposition. The discussion o f hypothetical propositions is limited to the second, internal conditions. A hypothetical proposition has three parts - antecedent, consequent, and condition - and its meaning is in the statement o f the condition, as in “ I f he is a man, he is an animal,” not in the statement o f a substantive truth. The condition may be a conjunction or a disjunction. A hypothetical proposition is composed o f propositions as a categorical proposition is composed o f terms, and the consequence o f a categorical syllogism may therefore be stated in a hypothetical proposition. In the second step, hypothetical propositions are divided into kinds - natural and temporal, simple and composite. The third step is the analysis and classification o f hypothetical syllogisms.

Treatise V is “ On Divisions and Definitions.” The method o f the entire Dialectica has been by definition and division - o f words, o f sentences, o f arguments, and o f hypotheses. The dialectical summation and characterization o f the method is in the division and definition o f division and definition, which are defined as speeches or sentences, orationes, and are divided into kinds by determinations o f meanings and modes o f signifying. Aristotle had argued that Plato’s method o f division was no proof, and he sought principles o f demonstration in causes rather than definitions. But the tradition o f the Aristotelian logic which Abailard received from Boethius had been so thoroughly Platonized that demonstration had become division and definition. Boethius had adduced the authority o f Andronicus o f Rhodes, Plotinus, and Porphyry to prove that knowledge o f the science o f dividing had always been held in high honor in the “ peri


patetic disciplines,” and in like fashion he constructed the “ peripatetic tradition” concerning definition from Cicero’s analysis o f definitions in the Topica. The joining o f the two yields a rhetorico-dialectical logic which is a science as well as an art, a part as well as an instrument o f philosophy, whose subject matter is ratio and oratio (two related or identical translations o f the Greek logos), and in which proof is by division (even first principles can be proved, since they too can be divided) and the beginning, end, and process o f proof is by definition (all words, statements, and arguments, and argumentations are definitions). Abailard’s contribution to logic or dialectic was to make these identities and differences explicit and to work out the structure o f their reciprocal interrelations, marking them off emphatically by giving each part in the sequential analysis and by naming it after a part in Aristotle’s Organon, topping off the summation with a comprehensive analysis o f division and definition which owes a great deal, indirectly, to Plotinus’s commentary on Plato’s Sophist and to Cicero’s adaptation o f the commonplaces to rhetorical determination and definition. His systematization o f logic was not widely influential because his students and contemporaries knew from their study o f the New Logic that he was wrong about Aristotle, and his modern editors and interpreters adumbrate the errors o f his textually ungrounded innovations and praise him for anticipating some points o f modern logic.

The history o f the development o f logic in the Latin West is structured by these shifting alterations. The verbal arts were three, but the third art o f the trivium was sometimes called logic, sometimes dialectic. The two words were sometimes used as synonyms, but their use sometimes signified an antagonistic opposition between Platonizing and Aristotelianizing traditions. Aristotle used dialectike and logike as general terms. When he distinguished the general art o f logic from the general arts o f dialectic and rhetoric, he often used the title o f the two central treatises o f the Organon and called it analytic. Alexander o f Aphrodisias applies, and he may have been the first to do so, the term “ logic” to the whole o f the art o f the Organon in his commentaries on Aristotle. Cicero divides the systematic analysis of discourse {ratio disserendi) into two parts, an art o f invention or topics and an art o f judgment or dialectic. Boethius begins his De Differentiis Topicis with the statement, “ Every systematic analysis o f discourse {ratio disserendi), which the ancient peripatetics called logic, is divided into two parts, one o f invention the other o f judgment. The Greeks called

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the part which purges and instructs judgment ‘analytic,’ which we can name ‘resolutory.’ The part which aids and supplies the faculty o f invention is called ‘topic’ by the Greeks and ‘ local’ by us.” In the eleventh century Garland the Computist begins Book IV o f his Dialectica, De Topicis Differentiis, with the statement that all logic, that is, the science o f words or disputations (sermocinabilis vel disputabilis scientia) is divided into invention and judgment, and he calls the first ‘places,’ and the second ‘syllogisms.’ Peter Abailard in the twelfth century called dialectic an art o f words and divided it, on the authority o f Cicero, into the sciences o f invention and judgment.

When the “ New Logic” made the last four books o f the Organon available, a choice was possible concerning methods o f establishing the principles o f logic and organizing the structure o f logic in accordance with them. Those who based their method on the Posterior Analytics came to be known as adherents to the Ancient Logic, the Logica Antiqua, and those who blazed new paths follow the Modern Logic, the Logica Moderna. William of Ockham provides a vantage point from which to survey the development o f the Ancient and the Modern Logics in the thirteenth century. He wrote two systematic treatises on logic, one based on the old logic. Expositio Aurea et admodum Utilis super Artem Veterem, the other covering the new logic, Summa Totius Logicae, and his logical analyses are punctuated with attacks on the modern logic. He used the ancient logic on the old and the new. Logic is not a science but an art concerned with fabrications, with significative signs. According to these criteria, the commentaries o f Albertus Magnus, Aquinas, and Duns Scotus adhered to the ancient logic, but not those o f the pseudo-Scotus which have attracted the interest o f logicians today. Paradoxically there could be no “ ancient logic” until the text o f the Posterior Analytics was made available in the “ new logic,” and the protagonists o f the ancient logic could then expound it, as Ockham did, in application to either the old or the new logic. It is as difiScult to determine what logic was taught in the arts courses o f universities in the thirteenth century as it is in the twentieth century, since all the books o f the “ old” and the “ new” logic are named among the requirements by the middle o f the century and slowly thereafter the works o f the “ modern” terministic logicians were added. Paradoxically “ modern” logic is contained in the “ old” logic, that is, it goes back at least to the transformation o f the “ logic” o f the Organon by


analyses o f meaning in terms o f things, words, or ideas in the Stoic logic, the Ciceronian rhetoric, the Neoplatonic dialectic, and the wedding o f the three in the dialectical rhetoric o f Boethius, but with the appearance o f the new logic “ modern” logicians had a choice among conceptions o f principles and among methods o f deriving them from commonplaces, for they could go to Aristotle’s Topics and De Sophisticis Elenchis rather than to Cicero’s or Boethius’s Topics and with the translation o f Aristotle’s Rhetoric, they could learn to differentiate rhetorical from dialectical places. Petrus Hispanus called the modern art ‘dialectic’ in his Summulae Logicae ; William o f Sherwood called it ‘logic’ in his Introductiones in Logicam, but he held that logic is concerned with dialectical reasoning. Both Peter and William base logic or dialectic on the “ properties o f terms,” but, paradoxically, the analysis o f truth does not turn on categorematic terms, which signify things and their properties, but on syncategorematic terms, like ‘air, ‘ i f ’, ‘both’, ‘neither’ , which are “ consignificative.” Or if the moderns chose to turn to grammar rather than to dialectic, rhetoric, or sophistic, the “ speculative grammars” presented them with “ modes o f signifying” correlated with “ modes o f understanding” and “ modes o f being,” and proceed, paradoxically, from the relations o f words to the meanings and references o f categorematic words.

The emergence o f the modern logic is marked by a contact o f the Latin and the Greek traditions. A treatise entitled Synopsis o f Aristotle’s Science of Logic has been attributed to Michael Psellos, who wrote commentaries on Porphyry, and on Aristotle’s Categories and On Interpretation in Greek in the eleventh century, and the terministic logics would in that case have been derived by translation from a Greek source. It is now thought that the Synopsis is a translation from Latin into Greek by Georgios Scholarios in the fifteenth century and that the Greeks learned about modern logic from the Latins.

Contacts between the Hebrew and the Greek and Latin encyclopedias had occurred early in the two traditions. Philo’s hermeneutic method o f interpreting Scripture had been adapted to the Greek tradition by Basil and to the Latin tradition by Ambrose, through whose influence it played a crucial role in the conversion o f Augustine. In the twelfth century Maimonides used the interpretation o f homonyms as the central device in his Guide fo r the Perplexed, and made the transition from words to reality by setting down twenty-five propositions about motion from Aristotle’s

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Physics as the bases for an a posteriori demonstration o f the existence o f God. Earlier he had written a treatise which was called in the Arabic original Short Treatise on the Art o f Logic, and in the Hebrew translation O f Logical Terminology.

The old logic was a stage in the evolution o f Hebrew as well as Latin and Arabic logic. The first five o f the fourteen chapters o f the Logical Terminology treat the proposition by explaining the terms used in its analysis. The chapters usually end with enumeration o f terms interpreted in the chapter, as, in Chapter 1 four terms are interpreted - subject, predicate, proposition, and sentence. Chapters 6 to 8 treat the syllogism, the moods o f the syllogism, and the kinds o f syllogisms or demonstrations : four kinds o f assertion which require no proof - sense data, axioms, widespread opinions, and traditional assertions - and five kinds o f syllogisms and their arts - demonstrative, dialectical, rhetorical, sophistical, and poetic - are expounded in the interpretation o f seventeen terms. Chapters 9 to 13 are concerned with terms important in science and demonstration. Chapter 9 sets forth the causes o f natural and artificial things in the interpretation o f ten terms. Chapter 10 treats logical terms - the predi- ables o f Porphyry, which Maimonides calls “ the five general notions enumerated by the ancients,” and the categories or predicamenta o f Aristotle- in the interpretation o f seventeen terms. What is interpreted as logical terms, however, are the predicables; the categories are treated as kinds o f predicables, genera, and only the first o f them, substance, is submitted to interpretation.

The relation o f logic, thus Platonized, to the books o f the Organon o f Aristotle is explained by Maimonides in this tenth chapter on logical terms. “ These ten highest genera constitute what is called ‘the ten categories.’ The exposition o f the particularities o f these categories and o f examples o f their middle genera and their species does not enter into the framework o f the present work. A ll that constitutes the matter o f the first book o f the Logic [of Aristotle]. The second book is devoted to the study o f composite rational notions [in judgments]; that is the book On Interpretation. The third is the book o f the Syllogism [Prior Analytics]. We have already said enough concerning the moods and figures o f the syllogism. These three books contain in germ the matter o f the five following books [o f the Organon]. The first o f these five books, that is to say, the fourth o f the collection o f books, is the book o f Demonstration [Posterior Analytics];


the fifth is the book o f Dialectic [Topics] ; the sixth is the book o f Rhetoric', the seventh is the book o f Sophistic; the eighth is the book o f Poetic.” Maimonides’s Organon had the eight books customary in the Arabic tradition; and the five predicables had become six for Maimonides as for Avicenna and Abailard, by the addition o f ‘individual’ to Porphyry’s five.

Chapters 11 and 12 treat the postpredicamenta o f Aristotle’s Categories: Chapter 11 adding essential-accidental, and actual-potential to Aristotle’s four kinds o f opposites - treated in sixteen terms; Chapter 12 treating the kinds o f priority and posteriority in nine terms. Chapter 13 returns to the antepredicamenta, that is to the opening chapters o f Aristotle’s Organon, in which he distinguishes homonyms, synonyms, and paronyms - equivocal, univocal, and derivative terms - and adds to them the ‘distinct term’ o f grammar, and divides homonyms into six kinds - (1) homonyms properly so-called, (2) appellatives, (3) amphibologies, (4) homonyms by generalization and by specification, (5) metaphorics, and (6) homonyms by extension - interpreted in eighteen terms. The final chapter, Chapter 14, is a classification o f the sciences, beginning with the interpretation o f ‘logic’ . The term logic is derived from logos “ which is commonly considered by the ancient sages o f civilized peoples as a homonym with three acceptations” : (1) the faculty o f reason, (2) rational ideas or the internal language o f the mind, and (3) verbal expression o f thought or external language. Aristotle’s art o f logic has a double function : to provide rules applicable to the internal and the external language. ‘Art’ according to the ancients, is also a homonym signifying theoretical and practical arts. ‘Philosophy’ is a homonym signifying the art o f demonstration and the sciences in general, which in turn designate theoretical and practical, that is, human and poHtical philosophy. The theoretic sciences are divided into mathematics, physics, and theology. Logic is not a science but an instrument o f all the sciences. The practical sciences are divided into (1) individual morality, (2) domestic morality, (3) politics o f the city, and (4) national or international pohtics. The organization o f the sciences is stated in the interpretation o f twenty-four terms. One hundred seventy- five terms are interpreted in the fourteen chapters o f the Terminology. They are terms which apply in the art o f logic, but they are also used in physics, theology, and political science.

Alfarabi’s Short Commentary on Aristotle’s Prior Analytics uses differ

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ent devices on the old logic from those o f Maimonides. Maimonides states his purpose to explain the technical terms used in logic; his treatise centers on homonyms and ends with the analysis o f homonyms. Alfarabi states his purpose to show what syllogism and inference are, and his treatise ends with the statement o f methods o f establishing propositions to serve as principles in syllogistic reasoning. Like Maimonides, Alfarabi starts with statements, divides them into parts, subjects and predicates, differentiates them into kinds, affirmative and negative, categorical and conditional, universal and particular, and sets forth the oppositions o f categorical statements, but his differentiations depend on things signified rather than on the relations o f meanings o f words. The second step o f the analysis is likewise similar. Like Maimonides, as preparation for the treatment o f the syllogism, he enumerates four kinds o f statements which may serve as premisses - received statements (Maimonides’s widespread opinion), well-known statements (Maimonides’s traditional assertions), sensory statements (Maimonides’s sense-data), intellectual statements (Maimonides’s axioms). Both analyze the fourteen valid moods o f the categorical syllogism and then analyze the kinds o f conditional syllogism. From that point they diverge. Maimonides derives from the four kinds o f propositions which require no proof the differentiation o f demonstrative, dialectical, rhetorical, sophistical, and poetic syllogisms, and settles down to the analysis o f terms. Alfarabi moves from the ostensive analysis o f the arguments o f categorical and conditional syllogisms by way o f the method o f reductio ad impossibile, compound syllogisms, and induction to the differentiation o f four principles o f establishing premisses. Abailard, Maimonides, and Alfarabi illustrate three ways in which principles are treated in the “ old” logic. Two are “ modern” ways, one is “ ancient.” It is the old logic because its subject matter is limited to terms, propositions, and syllogisms. Abailard’s method is modern because principles are found, throughout the work, by the dialectical devices o f division and definition. Maimonides’s method is modem because principles are found, throughout the work, in the shifting meanings o f words. Alfarabi’s method is ancient because principles are found beyond the compositions o f terms, propositions, and syllogisms by induction and transfer.

The Latin Christian culture o f the twelfth century was a culture o f Sentences and o f methods for the concordance o f their discordances. The


translation o f works o f science and philosophy which resulted from the contact with Arabic culture made the culture o f the thirteenth century in the West a culture o f disputed questions and quodlibetal questions - questions to which new answers could be established and questions about anything whatever. The Latin Christian encyclopedia was an encyclopedia o f the liberal arts - the disciplines o f words o f the trivium and o f things o f the quadrivium. The Arabic encyclopedia was an encyclopedia o f sciences and principles - the knowledge o f things and o f the laws and principles in which the nature and operation o f things and o f men are expressed. In the Latin tradition the sciences and the organizations o f the sciences were methodologically adapted traditional structures - theoretic, practical, and poetic relative to subject matters; physics, logic, and ethics relative to the transcendental sources o f their principles; philosophy, poetry and history relative to the methods o f the arts. The translation o f Arabic and Greek sciences shifted the emphasis from the signifying words to the signified things, and opened up a plurality o f sciences with different possible meanings and subject matters and a plurality o f methods with different possible consequences and applications. They developed in adversary oppositions and in dialectical assimilations during the thirteenth century and laid the foundations for the beginnings o f science and the rebirth o f letters in the readjustment o f theology to the sciences and o f hermeneutics to literary criticism. Thomas Aquinas adapted from Maimonides the concept o f creatio ab aeterno and a posteriori proof o f the existence o f God, and distinguished natural theology from revealed theology by the difference o f principles established inductively from principles received by revelation. He wrote commentaries on only two parts o f Aristotle’s Organon, the On Interpretation and the Posterior Analytics. Bonaventura derived the principles o f science dialectically from the truths o f wisdom; he wrote a treatise on The Reduction of the Arts to Theology. Roger Bacon sought truth in experience and in “ experimental science” and found the principles o f new scientific discoveries in the interpretation o f Scripture; he wrote commentaries on Aristotle, a Summa Grammatica, a Summulae Dialecticae, and a Communia Mathematica. The Latin Aver- roists were condemned for holding a doctrine o f two truths and bringing philosophy into conflict with theology, and in so doing casting doubt on the two ways o f logic and the unified intellect o f dialectic.

The consideration o f cultures in terms o f the structure or encyclopedia

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o f organizations o f sciences suggests answers to two puzzling questions about the contacts o f cultures in the twelfth and thirteenth centuries: Why did the other Western traditions based on Greek culture learn about Greek science only from the Arabic tradition? and Why did the introduction o f that knowledge into the Latin Christian tradition prepare the foundations for modern science? The Latin Christian encyclopedia was an organization o f arts and disciplines, which had tended to lay emphasis on the formulation o f those disciplines, the arts o f words and in particular the arts o f logic and rhetoric, the arts o f statement and proof, and o f invention and judgment. The structure o f the arts o f things was implicit, however, in the arts o f words, and the introduction o f sciences o f things and methods o f inquiry into the nature and operations o f things made explicit the interrelations o f that methodological structure. The multiplicity o f logics made it possible to seek the principles o f motion and the laws o f motion not only by induction from observed motions, but by the commonplaces o f dialectic concerning motion, from the paradoxes o f motion considered as a sophism, from the specificities and perspectives o f motion suggested by rhetorical invention, from the numbers and proportions o f calculation. Moreover, as the quadrivium became the subject o f attention as second philosophy the double character o f the quadrivium, as a homonym, as arts o f mathematics and arts o f things, laid the foundations for the two roads to the universal mathematics o f Descartes and the universal mechanics o f Newton. In a culture o f disciplines contact with facts and sciences yields, when the tradition o f disciplines is strong, new disciplines and new facts uncovered by the disciplines o f new sciences.

The University o f Chicago

D I S C U S S I O N

R. MCKEON : What I propose to do is to explain what I was trying to do in the paper. I don’t explain it in the paper. My enterprise was part of the John Murdoch enterprise. For a long time I have watched him look for unities, primary, secondary, and universal languages. And I have occasionally tried to tell him that he needed another dimension: in addition to the universal languages, the universal languages were structured. For example, although it is the case that one begins in the fourteenth century to talk about the intension and remission of forms, it is a beginning in which physical and metaphysical meanings are attached to terms which have a long pre-history going back to rhetorical amplification and diminution. Late medieval usage, as a result, discloses a


variety of intensions and remissions of forms. Therefore, if we can get these universal languages structured and still keep them empty, then we have a means by which to look for the origins of sciences without having a classified catalogue of sciences in the beginning.

I came to this through a problem presented by a later stage in the history of science.I was working on the seventeenth century, and, like all good students, I knew what the Euclidean method was. It was the method of postulates and the deductive system. And then I read Fermat, Pascal, Descartes, Spinoza, Huygens, Tschirnhaus, and they all said that the Euclidean method was heuristic; it was not deductive.

It seems to me that the problem that I was set in this conference is very much like that, to see Arabic culture not as modem historians may describe it, but as the Latin West perceived it. I wanted to work with the culture of the twelfth and the thirteenth centuries in the West and to examine what came out of the contact with the Arabic culture.I wanted to ask two questions. One, why the Muslim tradition, which built on three sacred books and Greek culture, and the early Latin Christian tradition, which built on two sacred books and Greek culture, differed so radically that science emerged only through the Arabic tradition. And, two, having come into the Latin tradition, why was it that something explosive happened so that in the twelfth and thirteenth centuries you had the beginnings of the questions that led to modern science? I mean “why” here not in the sense of the question of origins, but rather what were the structural characteristics that come into the problem. I therefore tried to deal with the culture by taking the organization of the sciences dominant in a people at a time as an indication of what the culture was so that the organization of the sciences is the characteristic of the people and the contact of cultures is a contact of these organizations. The character of an organization of the sciences is not the organization of a library. The organization of the sciences is an organization of ideas. It is an organization of the expression of ideas. It is an organization of the nature of things. It is an organization of the arts that go on. The characteristics of a culture comprise all these dimensions.

Buried in the paper, I make two statements about the twelfth and thirteenth centuries and their characteristics. Three years ago I sent an edition of Abailard’s Sic et Non to the press. The Sic et Non led me to study its 158 questions. The entire body of the work is citations, and, therefore, in the preparation of the edition I had to go back to Ivo of Chartres and forward to Peter Lombard’s Sentences and Gratian’s Decretum. I had put the citations on three-by-five cards, and I came to the conclusion that if you wanted to know what the culture of the twelfth century was, you could list, let’s say, three thousand quotations that every intellectual would know. And you would have a method by which to deal with these quotations because each of the collections of canon law and the Sic et Non gives the method. If you have a pair of statements which seems to be contradictory on the same question, you consider who said it, to whom, under what circumstances, and for what purpose. The method is one of adjustment to circumstances. So the culture of the twelfth century, I say in the paper, is easier to describe than the culture of any other period that I know because you can tabulate it. By the thirteenth century this is totally changed. It is changed because three thousand quotations are no longer enough. The new translations bring in new data. The method is not a method of interpretation by consideration of circumstances. There is a multiplicity of methods. And, therefore, my argument is that there are elements in the structure of the Western Latin tradition that led to this thirteenth century result and these elements are what I call the encyclopedia.

The structure of the Latin encyclopedia was not Aristotelian. It was organized by

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dialectical principles derived from the Topics, not by apodeictical principles based on the Posterior Analytics. Topics are empty. They are places of discovery; they are also places of memory.

What I am saying about the Latin encyclopedia is essentially that it is an organization of arts which teach how to use empty places (Jopoi) for purposes of discovery and memory, both parts of rhetoric, form them into propositions {logoi) which can refer to things or conmiunicate or persuade, and modify them in thematic organizations in which narration in poetry and demonstration in geometry are modes (tropoi) of the same argumentative form. And then, finally, systematizations are formed when you take a position {theses) and organize the variety of propositions and the variety of interpretations.

What I wanted to do consequently was to look at the use of the topics to form propositions or logoi which can then be bent so that they move from one discipline to another in the modes, and which can then be organized. These distinctions provide four dimensions for the analysis of the variety of approaches to the organization of the sciences. In the thirteenth century, the new materials and methods were given a number of different structures. What Thomas Aquinas does with his revealed theology and his natural theology is, with respect to the sciences, quite different from what Bonaventura does, when he goes to theology to get the principles for all of the sciences. Roger Bacon talks about experimental science and gives instances of observation, but all of his first principles are found in the Bible, as in his theory of the rainbow.

It is these structures that I would want to look at in the thirteenth century. But observe what happens then. When you move from the thirteenth to the fourteenth century and the beginnings of new discussions, where do you go for principles? There were defenders of the method of the Posterior Analytics. There continued to be defenders of the dialectical method, and, as I quoted, there is a form of dialectical disputation concerning motion in which different opinions are balanced. Then the sophismata come in. De motu is, in the fourteenth century sense, a sophism, a series of sophisms. The sophism provides as a principle the paradox. Therefore one of the innovations is that in a good respectable science from the fourteenth century on, instead of seeking a principle which is clear and certain and intuitively verifiable, a good science can be respectable only if it gets a principle which is a paradox. And this is still going on in science. Physics can afford paradoxes. The less exact sciences can’t.

And, therefore, and here I will end, the answer to the questions that I posed in the beginning is that the Latin tradition in the twelfth century - it had really begun in the eleventh century, it had come out of medicine, the translations of Constantine the African - moved without any contradiction into cosmology, into physics, into Gun- dissalinus’s organization of the sciences, then into Aristotle. The transition was one in which an encyclopedia which had been practicing the arts of discovery came into contact with an encyclopedia which presented systems of knowledge and principles. Therefore the principles and systems were subjected to a kind of transformation from dialectic to inquiry and led, in answer to the second question, to a reformulation of principles and a generation of new sciences.

j. g a g n e : N ous sommes devant un imposant concert à quatre voix; les traditions latine, hébraïque, grecque et arabique. C ’est un imposant concert où vous reconnaissez qu’il y a des lois de l’harmonie; et vous essayez d’énoncer les lois de l’harmonie. Mais j ’ai l’impression qu’en un sens le concert est tellement imposant, qu’il ressemble à ce concert de musica mundana où toutes les voix célestes sont engagées et produisent une mélodie inouïe. Aussi, il me semble que la meilleure façon d’amorcer la discussion c’est


de vous demander de préciser les sortes de notes que vous utilisez pour construire le concert.

J’aimerais attirer l’attention sur les charactéristiques structurales des traditions. Pourrions-nous nous attacher à considérer ensemble ces caractéristiques structurales? Par exemple, vous caractérisez la tradition latine du Xlle siècle à l’aide d’encyclopédies concrètes, pratiques, de mots et de choses. Est-ce que ce n’est pas insuffisant?

R. MCKEON : Non, c’est même trop. For a structure it is necessary (you use the analogy of music) merely to give the scale. A scale can be formed from two notes by adding a third, and in general by using a third relative to any pair. And consequently, the characteristics of the encyclopedias I am talking about can be given best by examining what is connected and the structure of connection. Although I began by contrasting the twelfth and thirteenth centuries, they have the same characteristic matter and structure as the encyclopedia which I began with in pagan Rome. The continuing characteristic is that it is concrete and therefore deals with a thing. And a thing can be either a word, a physical thing, an idea, or an art. This is the manner of continuity with difference of the encyclopedia from pagan Rome to the Renaissance. The Arabic encyclopedia was an encyclopedia of sciences and principles. What happened in the twelfth century was a structure of factual connection, which was common to the two encyclopedias, taking a different form, changing from a connection of liberal arts to a connection of sciences.

j. g a g n e ; Là vous entrez dans des lois de l’harmonie. Je pense qu’on devrait, avant d’étudier ces lois, continuer l’étude des charactéristiques structurales. Prenez la tradition arabique et la tradition grecque; qu’est-ce qui vous justifie de les opposer en termes d’une tradition littéraire et d’une tradition de principes et de sciences?

R. MCKEON ; Precisely because if you trace the Greek tradition through the Byzantine encyclopedias to the Middle Ages, they are encyclopedias like Photius and Suidas in which you get a great deal of literary information. Students of literary history can still go to them and get information. In the Arabic, on the other hand, what is central is the organization of the sciences and their characteristics. It is not the factual information of the Latin encyclopedias; it is rather the demonstrative organization of results of systematic inquiry.

Let me make a distinction. Discussions of intellectual history make use of two devices. One is to establish the accuracy of an interpretation; scholarly research makes use of such devices. The other is to examine the variety of interpretations that have been given to any document and any history; inquiry into structures makes use of such devices. There are as many interpretations of Aristotle’s Physics as there are interpretations of the nature of things. Part of my argument is that I am willing to take any one of them, but not indifferently. I am looking for the method by which, having made the choice and having recognized the multiplicity, one can go on to the consequences of that choice. In the case of Euclid, what are the consequences of making Euclid heuristic instead of deductive? I am not interested in proving that Euclid was heuristic, that Euclid was deductive. Since Euclid had two effects in the West, it would seem to me that the only reasonable thing to say is that Euclid is historically both. There are no facts except the known facts; there are no known facts except the expressed facts, and there are no expressed facts except the used facts. Therefore, I think that for our purpose it is better to look at the form rather than to examine further whether what I have done with the particular tradition is accurate or not.

J. Mu r d o c h ; But before we move there may I ask aren’t you looking at, for Latin encyclopedias, one kind of document, to wit, the Roman handbook tradition, Isidore, etc., and, when you come to Arabic culture, looking at another kind of document.

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basically, although you name others, al-Fârâbi, the Enumeration o f the Sciences, and ignoring, as you had to if you were going to deal with contact, other Arabic encyclopedias? I think that you could get words and things, you see, out of Qazwini who wasn’t translated.

R. MCKEON : If you want to ask what the Arabic encyclopedia is, you can’t do it by beginning with today’s conceptions. You can’t do it by asking a member of the culture. There are as many interpretations of the Arabic encyclopedia as there are perspectives into it. Therefore, in the opening paragraph of my paper, I say that there is no way of being objective, that anyone who pretends to be is talking nonsense. What I am looking for is the effect on an encyclopedia of study of the other encyclopedia. I then say that this is no more objective than anything else but it has the advantage of remaining within a single tradition. My essay is about the Western Latin tradition.

j. g a g n e ; Prenons-le sous un autre angle. Vous avez quand même voulu que ce concert soit joué sur un clavier latin; vous avez dit: regardons les traditions sous l’angle de l’encyclopédie latine. Et vous illustrez le développement, l’enrichissement des méthodes, l’enrichissement des sciences, quasiment à partir du seul exemple du trivium; c’est le trivium qui vous sert de modèle en quelque sorte pour montrer comment il y a eu enrichissement et développement, et pourquoi il y a eu développement.

R. MCKEON ; Ce n’est pas une induction que j ’ai faite ici. I am not trying to establish true propositions about the Western encyclopedia. What I am trying to do is to distinguish devices which will be discoverable in the contact of encyclopedias. The Arabic or the Hebrew encyclopedia differs from the Latin encyclopedia, even when they treat the same thing, because they don’t use these devices.

This is the reason why I go through the details of a laborious analysis of the Dialectica of Abailard. Aristotle distinguishes four predicables; definition, genus, property, and accident. Porphyry makes them five. The change looks very innocuous because, after all, a definition is made up of a genus and a differentia and a definition is of a species. Therefore there are five predicables: genus, species, differentia, property, and accident. But something very curious has happened. The second list produces a hierarchy, a hierarchy which we have called Porphyry’s tree. It is not a question of the operation of historical influence. The force of ideas operates : a tree needs a root. Avicenna added a sixth predicable - the individual - at the bottom of the tree. Abailard, who didn’t know about Avicenna (and Avicenna certainly didn’t know about Abailard) also adds a sixth predicable, and it’s the same one, the individual. Now the point that I am trying to make is that in order to study the relations of cultures it is important to see what the structure is that is common or unified that forces the man thinking about genera and species to see there is something missing, and therefore stick in individual. And what, in turn, separates the two so that similarly structured but differently conceived encyclopedias influence one another when they come into contact. And this is the reason why I interrupted. I could write a paper on the evolution of the trivium. In fact, I have done that elsewhere. What I tried to do here was to leave all of that out and to ask what are the typical methods? What are the typical data?

T. GREGORY: II faudrait souligner l’importance qu’a eue une autre tradition de la période hellénistique: l’interprétation de la nature donnée par le Physiologus, et l’importance qu’il a eu dans certaines encyclopédies latines. Alors ne faudrait-il pas aussi distinguer même les encyclopédies dans la tradition latine? Je trouve une différence profonde entre une encyclopédie du type de celles d’Isidorus ou de Hrabanus Maurus, symbolique et allégorique, et une encyclopédie du type de celles de Martianus Capella, pour la fin de l’antiquité, ou de Guillaume de Conches, d’Adélard de Bath et de Daniel


de Morley, où la structure de l’encyclopédie est très liée â l’observation concrète, et refuse les interprétations allégoriques et symboliques.

R. MCKEON: Mais je crois que vous avez tort. Il n’y a pas de telles différences entre ces encyclopédies. Ce sont la les manières d’interpréter des historiens du XIXe siècle;il faut relire ces textes au XXe siècle.

T. GREGORY: Si je considère le De universo de Hrabanus Maurus ou la lettre De naturis animalium de Pierre Damien, je trouve que la réalité physique est toujours mise en rapport avec des significations d’ordre moral et religieux.

R. MCKEON: Je ne trouve pas ça.M.-Th. d’ALVERNY: You have been mostly considering encyclopedias and general

knowledge, your harmony, in the tradition of logic. I was very interested by what you said of your preparation of the Sic et Non and of the three thousand quotations that the honest man in the twelfth century had to know to produce something like the Sic et Non, Gratian, and so on. It’s extremely interesting. But this means you are putting together two things which are not exactly the same; the intensive use of florilegia, about which nobody knows much but they are certainly extremely important for the history of culture in the High Middle Ages, and encyclopedias, which are a different thing. In the florilegia you have what you term to be the characteristic of the Greek encyclopedias, that is literary florilegia and the literary tradition where you have the florilegia of the auctores. So that is one thing: you should keep in mind that the florilegia are one tradition, and though the florilegia could be used in encyclopedias (and they were to quite an extent), ft’s a rather different tradition, and they don’t have exactly the same contents.

My second objection would be about your definitions of encyclopedias in the four different traditions. Two of the traditions have practically no impact on the Latin West, namely what you term the Hebrew encyclopedia (the only Hebrew encyclopedia which had some impact on the Latin West was Maimonides, but it was translated from a Hebrew adaptation of the original Arabic only in the thirteenth century) and the Greek encyclopedia (unfortunately Photius was never translated). So we are left with the Latin encyclopedia and the Arabic encyclopedia.

Let’s begin with the early tradition of the Latin encyclopedia. You have the Latin tradition of the artes liberales, and it came to be mixed, mostly in the time of Boethius and Cassiodorus, with the Alexandrian tradition of the classification of the sciences. It so happens that this Alexandrian traditional division of sciences is exactly the one that we find as the basis of the largest Arabic encyclopedias, Fârâbi and Avicenna, and at an earlier stage the Dchwân al-Çafâ’.

R. rashed : Je n’ai pas l’impression de très bien comprendre. Quand M. McKeon parle d’encyclopédie, il ne veut pas dire une classification des sciences, mais une sorte de conservatoire, presque idéalisé, de l’ensemble du savoir.

R. MCKEON : It’s the structures that I compared.M.-Th. d ’ALVERNY: I was speaking about the structure too. The structure does exist.R. MCKEON : In my paper I tried to show that there are five or six histories which

contradict each other. You have been reciting one of them. I accept that account and the aspects of encyclopedias that it brings to attention, but you should consider the aspects of encyclopedias on which the other histories are based, and the nature of the encyclopedia comes from the way in which one harmonizes and makes possible these very histories. This is why in the early discussion I said my method is not inductive. I have written inductive papers on the liberal arts. I have explained what books contained, but here I’m trying to build the structure of their inter-relations.

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G, beaujouan : Je reviens à une question élémentaire mais qu’a bien posée M. Gagné tout à l’heure; en lisant le texte de M. McKeon, je n’ai pas très bien compris pourquoi, dans l’appréhension de ses structures, il a choisi les encyclopédies au sens formel plutôt que n’importe quel corpus à large vulgarisation. J’ai l’impression qu’une partie des ambigüités de notre discussion tourne justement autour de ce problème.

R. rashed : Je voudrais alors poser deux questions: comment pouvez-vous dire, par exemple, je caractérise l’encyclopédie arabe, de telle et telle façon; comment avez-vous pu dégager ces éléments? Ma deuxième question: une fois cette opération faite, est-ce que, effectivement, cette encyclopédie peut caractériser une culture? Ne peut-on pas mieux caractériser, une culture par la différence, par l’écart - ce qui est beaucoup plus important, à mon sens - que par ce caractère commun?

R. MCKEON : First, with respect to the relation between history and structure. In the Western tradition histories have structures, and structures have histories. You begin with a history to structure what you take to be facts. Study of the facts suggests different ways in which they can be structured, and you can then go back and rewrite the history. It is not that history establishes facts. Immediate experience is confused; selection of elements provides focus and objects; structure orders discerned objects. Consequently, I have written two kinds of papers. I have written papers in which I try to explain what is the case, what the document says, and why it says what I interpret it to say. I have also written methodological papers in which I explain what it is that I have done and how I could have come out at another place and why I didn’t. The reason why this paper does not depend on the history is that it is meant to explain the histories. I begin with the structure and, therefore, I find a variety of histories.

The characteristics that I am using to mark off the differences of these encyclopedias are characteristics that are structural, not only the formal organizations of the sciences in the Arabic culture, but the structure of all attempts to organize a body of knowledge by principles. These I call encyclopedias. I am not trying to get a definition which will do justice for all varieties of encyclopedias, but I want to get a structure which will permit me to compare Arabic and Latin organizations of knowledge. Both deal with “sciences” and “facts.” But one is a structure of sciences; the other is a structure of facts. I don’t know a single systematic work in the Latin West (and I am using the word encyclopedia in a way that would bring in any organized work) which deals with principles and the structures of sciences. Latin encyclopedias present techniques, arts and facts by which to deal with concrete things. It’s important to separate the two structures because if a culture is based on arts by which to deal with concrete things, it may be interpreted, not as a simple-minded pragmatism, but as a comprehensive mode of thinking embracing the whole organization of knowledge.

Suppose one were interested in the treatment of the science of physics, in the Latin and in the Arabic encyclopedia. In the Latin encyclopedia inanimate and animate bodies are the subject matter of physics. Beginning with Pliny, running through Isidore of Seville, through Bartholomew the Englishman, to Vincent of Beauvais, there will be a large number of chapters : on man, animals, minerals, and so on. In the Latin encyclopedia it would be extremely difficult to tell when you were doing biology, when you were doing physics, when you were doing the arts, because facts from biology, physics, and the arts are in the same chapter. Now let me balance this structure with that of the Arabic encyclopedia. In the Arabic encyclopedia the sciences are enumerated and distinguished from each other or combined with each other. In the process of distinguishing them reasons are given for the distinction. The reasons provide the principles, of the sciences. They are not principles in any restricted Aristotelian sense, but they are


the means by which to put up a fence, a determination, an enclosure within which to locate not the facts that are ordered in the Latin encyclopedias, but the systematic demonstrations that organize the things within that enclosure. Consequently, the two encyclopedias cover the same subject matter by different structures of organization.

R. rashed : Supposons que l’encyclopédie arabe functionnât effectivement comme vous le dites. Quand vous parlez ainsi, vous avez en tête al-Fârâbi; vous prenez des éléments concrets et vous donnez à ces éléments concrets une forme universelle...

R. MCKEON : Non je ne crois pas.R. rashed : Il reste que vous présentez ces éléments comme des essences, ou presque.R. MCKEON: Non, aussi loin des essences que possible.r . rashed : Que sont-ils alors ces éléments, sont-ils des formes?R. MCKEON: Non, ce sont des lieux, des lieux places, topoi.R. rashed : Vous les présentez comme des schemata abstraits.R. MCKEON: Non, ils sont vides.R. rashed : V ous les dites vides, mais, à mon sens, ils sont surdéterminés historique

ment.R, MCKEON : Au contraire, l’histoire est déterminée par les places vides. Si on prend une

histoire, une proposition métaphysique, une proposition mathématique, un poème, un sophisme ce n’est pas une place vide, c’est une place pleine. Il faut faire un effort pour la vider, mais c’est possible. Quand le topos est vide, il ne peut pas être expliqué. Donnez-le un nom et vous avez déjà fait entrer des choses. The whole function of a place is to get it empty so that then you can put something in. But if you don’t get it completely empty, it’s notA place. Nevertheless, places are the sources of the discoveries of science. They are the source of the progress of our knowledge.

A. sabra : While you were giving this account I was listening to all the interesting things you were saying, but also to the questions that were asked. Many of them were on the concrete level. The reaction on your part has been that you did not want to engage in a discussion on this concrete level. Then another question began to be formulated in my mind - one that we all have to be clear about so that we don’t ask the kind of question that you think is not relevant to what you want to maintain: What would you consider to be the structure of evidence or an argument against your theory?

R. MCKEON: Evidence against my theory could mean evidence against the need to differentiate the form that the argument takes from the content. I don’t think there is any possible evidence of this kind: it cannot be demonstrated that discourse is possible without a difference of subject matter and form. But the project is refutable on a different level. It’s entirely possible that the scheme I have used, particularly the topos, logos, tropos, is not a pure form. It may be that it is impregnated with matter and, therefore, distorts what it structures. On this level I can think of things that are wrong with whatI have done, but it is a first approximation.

G. beaujouan : Mais, de toute manière, vous êtes obligé de procéder par induction à partir de ces encyclopédies pour prouver votre structure.

R. MCKEON: J’ai dit au commencement qu’il ne s’agissait pas du tout d’un essai d’induction; c’est un essai de méthode.

G. beaujouan : V ous ne pouvez pas prouver votre structure,R. MCKEON: D me suflSrait d’un autre rapport!G. beaujouan : Il y a quelque chose qui m’inquiétait un peu dans ce que j ’ai cru

entendre dans vos discours en anglais tout à l’heure: vous disiez qu’il y a des fois où vous faites des articles d’érudition comme ceux de Mlle d’Alvemy ou de M. Gregory,

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et il y a d’autres fois où vous faites de l’histoire structuraliste. Je ne vois pas pourquoi les deux choses doivent être séparées de façon manichéenne.

R. MCKEON : Nous sommes engagés dans des disciplines intellectuelles. Dans la même structure, on peut dégager un aspect ou un autre. J’ai écrit des articles, il y a vingt ans, que je croyais très bien documentés; j ’ avais examiné toutes les sources; j ’avais réfuté toutes les autres interprétations. Quand je les lis maintenant, je me dis: mais j ’étais un peu simple à ce moment là! J’ai maintenant une methode plus subtile qui peut indiquer des choses qui sont dans le texte, que je ne soupçonnais pas du tout, et qui sont maintenant beaucoup plus importantes. Maintenant, j ’essaye de faire l’histoire dans laquelle j ’explique aussi bien que possible les textes, les circonstances, les influences, et je mélange avec ça des examens méthodologiques dans lesquels il y a place pour ce que je faisais auparavant. Dans la première catégorie d’essais, quand je trouve une interprétation avec laquelle je ne suis pas d’accord, je la réfute. Quand je prends les mêmes exemples dans la seconde catégorie je dis: mais vous savez, il n’y a qu’une partie de vérité dans cette interprétation. Je crois que ces deux sortes d’essais ne sont pas en contradiction; l’une s’appluie sur l’autre, l’autre est le produit de la première. Pour la première fois, j ’ai essayé d’être complètement méthodologique, et je croyais que, dans la tradition de Murdoch, j ’aurais peut-être une chance!

j. MURDOCH: All right, let’s try. What you say is obviously not a creation ex nihilo, but ex aliquo, out of texts and circumstances. If we don’t want an absolute relativism in the sense that anything can be drawn from this aliquod or that one, can we not ask, given this source, given this text, whether your interpretation, what you see in it, is proper? Is it true? Let’s have alternative histories, but some of them should be refutable.

R. MCKEON : You are in process when you investigate, investigating not pre-existent facts or pre-existing conditions. For example, take al-Fârâbi and his classification of the sciences. If there are two interpreters, they will very frequently give you different organizations of the sciences, different statements of what the circumstances are, and from that point on there is an argument between them. Now if the discussion is of any interest, it will be because they don’t find the same thing on the same page. This is not a complete relativism. It is nailed down. And it is the condition of creative scholarship.

TULLIO GREGORY

L A N O U V E L L E I D É E DE N A T U R E ET DE S A V O I R

S C I E N T I F I Q U E A U X l l e S IÈ C L E

La lecture des traités De natura rerum du haut moyen âge fait clairement apparaître l’angle sous lequel ils offraient la contemplation du monde physique: comme la recherche, non de raisons ou de causes naturelles, mais de significations et d’enseignements religieux et moraux; ainsi le discours physique tournait immédiatement en discours édifiant, changeant la réalité en symboles et en allégories Selon une ancienne comparaison, la nature est un livre écrit par Dieu, qu’il convient de lire - comme l’Écri- ture - typice, allegorice, mystice-, le monde physique ne s’offre point à l’homme pour que celui-ci recherche les causes physiques des phénomènes - la seule cause directe étant en effet la volonté divine -, mais (ainsi que l’écrit Pierre Damien) ut altius considerantibus fiat spiritalis intel- ligentiae sacramentum: tous les êtres devenaient ici les symboles des vérités de la foi et des vertus chrétiennes {sacramentum salutaris allegoriae)^.

Le cosmos est ainsi transfiguré par une inépuisable mentalité symbolique dont les Bestiaires et les Lapidaires donnent assez bien l’idée: point de place pour la recherche des causes naturelles, puisque la nature des objets n’est pas dans leur consistance physique mais dans le fait qu’ils symbolisent une réalité différente, intelligible, qui est la seule vraie réalité.

Contrastant avec cette expérience, cette contemplation sacrée du cosmos, une nouvelle expérience, qui mûrit au cours du X lle siècle, prend un relief et une signification particuliers: elle propose une contemplation physique du monde s’efforçant de saisir la legitima causa et ratio^ de tout événement physique, en dehors des traditionnelles interprétations et transpositions allégoriques et symboliques; cette expérience dénote aussi la découverte d’une nouvelle dimension humaine dans un cosmos qui n’est plus un tissu de symboles mais une réalité substantielle où l’on peut lire autre chose que des messages spirituels, et qui permet à l’homme de mesurer ses nouvelles possibiUtés d’action.

Cette nouvelle attitude - qui est un élément tout autre que secondaire du grand mouvement de renaissance qui marque la vie européenne du X lle siècle - est abondamment prouvée par la multiplication des écrits

J. E, Murdoch and E. D. Sylîa (eds,), The Cultural Context of Medieval Learning, 193-218. AU Rights Reserved.

194 T. GREGORY

concernant des problèmes physiques, de philosophia mundi; les minces et élémentaires traités sur les arts du quadrivium contenus dans le De nuptiis de Marcianus Capella cèdent la place à toute une bibliothèque d’écrits scientifiques, les uns nouveaux, les autres traductions et remaniements d’oeuvres grecques et arabes. Ces dernières arrivaient alors en Europe par toutes les frontières, de l’Espagne, du sud de la France, du sud de l’Italie, et par les routes commerciales ouvertes vers les pays arabes et byzantins du bassin méditerranéen. La connaissance des nouvelles versions arabo- latines et gréco-latines est de la plus haute importance pour l’histoire de la culture européenne au X lle siècle: dans l’espace de quelques dizaines d’années, l’on redécouvrait en effet les oeuvres de Ptolémée et de Galien, d’Albumasar et d’Avicenne, d’Alfarabi et d’Alfarghani, des traités souvent anonymes ou pseudépigraphes d’astrologie, de magie, d’alchimie; enfin, vers la fin du siècle, commencèrent à circuler les oeuvres d’Aristote, ses livres de physique et de sciences naturelles.

Le X lle siècle eut immédiatement conscience de l’importance de l’acquisition de ces ouvrages scientifiques: en posant des problèmes d’ordre physique et en formulant une nouvelle conception de l’homme et du monde, ils bouleversaient certains points de vue intellectuels parmi les plus traditionnels; c’est ainsi que l’auteur (ou le traducteur?) anonyme du Liber Mamonis in astronomia put accuser les docteurs latins d’avoir entravé l’évolution culturelle de l’Europe (unde factum est ut que fere plenitudinem posset habere artium, nunc ceteris gentibus Europa videatur humilior) et put opposer à leur ignorance en matière d’astronomie l’enseignement lumineux de Ptolémée, in astronomia magnificus, et des Arabes: de même, un peu plus tard, Daniel de Morley opposera à la culture livresque et présomptueuse des maîtres parisiens la doctrine Arabum quae in quadruvio fere tota exis tit, qu’il était allé étudier à Tolède, où enseignaient les sapientiores mundi philosophi^. La recherche de nouvelles connaissances dans le sud de l’Europe, dans les régions limitrophes avec d’autres cultures, s’imposait comme une expérience exemplaire; quelques décades auparavant déjà, Adélard de Bath, pionnier de la nouvelle science et traducteur lui-même, avait souligné l’importance de la route du sud de l’Europe pour chercher de nouveaux enseignements philosophiques dans des traditions autres que la tradition latine: quod enim Gallica studia nesciunt, transalpina reserabunt; quod apud latinos non addisces, Graecia facunda docebit

LA NOUVELLE IDÉE DE NATURE AU X II SIÈCLE 195

L ’horizon culturel traditionnel est brisé; la lecture des nouveaux ouvrages dans leurs traductions gréco-latines et arabo-latines, en saturant de nouveaux intérêts et de raisons physiques la spéculation philosophique du siècle, permettait de sortir de la tradition des traités du haut moyen âge De natura rerum, de leur assiette imaginative et du transfert symbolique qui dissolvait le monde physique dans un système de symboles et d’enseignements divins; la nature se dégageait lentement, mais fermement, du domaine sacré, où l’avaient placée l ’enseignement chrétien primitif et la culture monastique, pour prendre corps et densité; n’étant plus conçue comme une simple voluntas Dei ou comme sacramentum salutaris allegoriae, mais comme vis genitiva, ignis artifex, causarum series, qualitas planetarum, regula mundi, elle devenait l’objet d’une ratio naturalis que la culture du haut moyen âge avait ignorée, et qui était destinée à conditionner tout discours philosophique ou théologique.

La vague et primitive cosmologie biblique, et les efforts concordistes de l’exégèse patristique et du haut moyen âge, sont abandonnés comme insuffisants et contra rationem ; de la Bible on souligne la finalité essentiellement morale et religieuse à laquelle la physique est étrangère: auctores veritatis philosophiam rerum tacuerunt, non quia contra fidem, sed quia ad aedificationem fidei, de qua laborant, non multum pertinebat ®.

Ainsi Guillaume de Conches, qui conduit dans ses oeuvres physiques- dans le Commentaire à Boèce, comme dans les gloses au Timée, dans le Philosophia mundi, comme dans le Dragmaticon - une polémique assidue contre une explication purement religieuse et théologique des événements naturels et contre une interprétation littérale de la Genèse, élabore une cosmologie où l’oeuvre directe de Dieu est limitée à la création des éléments et de l’âme humaine, tandis que la constitution toute entière de Vornatus, c’est-à-dire le KÔafioç est l’effet de causes secondes, et avant tout des astres : leur action est responsable de l’apparition de zones habitables sur la croûte terrestre et de l’origine de la vie; le règne végétal comme le règne animal et même la formation du corps humain d’Adam et d’Eve sont l’effet du mouvement des cieux :

Corporibus stellarum creatis, quia igneae sunt naturae, coeperunt movere se, et ex motu aera subditum calefacere: sed mediante aere aqua calefacta est. Ex aqua calefacta, diversa genera animalium creata sunt: quorum quae plus habuerunt superiorum elementorum, aves sunt. Unde aves modo sunt in aere, ex levitate superiorum, modo descendunt in terram, ex gravitate inferiorum. Alia vero quae plus aquae habuerunt, pisces sunt. In hoc solo elemento, nec in alio vivere possunt. Sic ergo pisces et aves facti

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sunt... Istis sic creatis ex aqua effectu superiorum, ubi tenuior fuit aqua ex calore et creatione praedictorum desiccata est et apparuerunt in ea quasi quaedam maculae, in quibus habitant homines, et alia animalia. Sed cum terra ex superposita aqua esset lutosa, ex calore bulliens, creavit ex se diversa genera animalium. ...Ex quadam parte vero in qua elementa aequaliter convenerunt, humanum corpus factum est. ...Et ex vicino limo, corpus mulieris esse creatum verisimile est, et ideo nec penitus idem quod homo est, nec penitus diversum ab homine, nec ita temperata ut homo, quia calidissima frigidior est frigidissimo viro; et hoc est quod divina pagina dicit: “Deum facisse mulierem ex latere Adae” . Non enim ad litteram credendum est, [ex]costasse [Deum] primum hominem’ .

Non enim ad litteram credendum est excostasse [Deum] primum hominem: c’était la liquidation du récit de la Genèse, la rupture, au nom de la ratio, d’une tradition exégétique suivie sans interruption depuis la plus haute antiquité chrétienne; Guillaume en est très conscient lorsqu’il engage une polémique contre les théologiens qui malunt nescire quam ab alio quaerere, et qui préfèrent avoir recours à des explications miraculeuses plutôt qu’à la recherche incessante de causes physiques :

...quoniam ipsi nesciunt vires naturae, ut ignorantiae suae omnes socios habeant, nolunt aliquem eas inquirere, sed ut rusticos nos credere, nec rationem quaerere, ut iam impleatur propheticum: ‘Erit sacerdos sicut populus’ [Is. XXIV, 2; Osée, IV, 9]. Nos autem dicimus, in omnibus rationem esse quaerendam®.

Cette ratio qui s’impose ici comme unique principe d’explication du processus de formation du monde est une ratio physique, c’est-à-dire liée à une conception de la nature comme causarum series, vis genitiva, comme objet d’une étude ayant pour but de saisir la legitima causa et ratio de chaque événement naturel, comme suggère le Timée. C ’est une ratio qui manifeste immédiatement sa force au moment même où elle impose une nouvelle direction à l’exégèse de VHexaëmeron: à l’intérieur d’une conception de la nature comme voluntas Dei tout est possible, et la lettre de la Bible peut être toujours acceptée au nom de l’insondable volonté de Dieu; là où la nature acquiert une consistance propre - et c’est là l’expérience qui mûrit dans le milieu de Chartres et plus largement au cours du X lle siècle -, lui correspond une ratio qui se pose, retrouvant les lois de la nature, en juge de Vauctoritas biblique, de la lettre de l’enseignement scriptural. Nous avons vu la position de Guillaume sur la création du premier couple humain, reportée dans le cadre des principes physiques, et le refus correspondant de la lettre de la Genèse pour ce qui concerne la formation du corps d’Adam et d’Eve; nous trouvons un autre exemple significatif de cette différente perspective dans la discussion d’un problème typique de la

LA NOUVELLE IDÉE DE NATURE AU XII SIÈCLE 197

tradition exégétique de VHexaëmeron, le problème de la présence des eaux au-dessus du ciel, dont parle la Bible et qui reflète une très ancienne cosmologie élémentaire. Dans la tradition exégétique patristique et médiévale, l’existence des eaux au-dessus du ciel était acceptée unanimement au nom de l’enseignement biblique, et quant on en cherchait une justification physique prévalait à la fin le recours à la volonté de Dieu: quaestio divina virtute solvitur quia ibi teneantur secundum Dei voluntatem, peut-on lire dans 1’oeuvre composite anonyme qui a pour titre De mundi constitutione^. L ’enseignement biblique est aussi constamment répété par les plus grands représentants de la culture du X lle siècle, comme par exemple Hugues de Saint-Victor et Abélard lui-même: dans la dialectique du Paraclet aussi, la nature se résout en effet dans la volonté de Dieu, si bien qu’il n’y a pas de sens, écrit-il, de se demander qua vi naturae les eaux tiennent au-dessus du firmament, car la seule volonté de Dieu est vis naturae

Or, ce discours, pour Guillaume de Conches, est justement le discours de quelqu’un qui ne connaît pas les vires naturae et n’ayant pas la possibilité de montrer la ratio des phénomènes naturels, recourt directement à la volonté de Dieu pour couvrir sa propre ignorance; qui, au contraire, se place du point de vue physique et du point de vue de la ratio qui lui correspond ne peut pas refuser la lettre de la Bible, car la présence des eaux au-dessus du firmament est contraire aux principes physiques, est contra rationem^^.

L ’exégèse doit donc elle aussi se plier aux exigences d‘une ratio, raison physique, qui porte à nier les enseignements bibUques fondés sur la lettre et sur une ancienne tradition herméneutique. Cette position porterait nécessairement à mettre en discussion la valeur des auctoritates de la tradition patristique dont était nourri le discours théologique. C ’est le problème que Guillaume de Conches affronte de nouveau dans le Dragmaticon et qu’il résout en reprenant la distinction, dont il avait déjà fait mention dans ses gloses à Boèce, entre les enseignements relatifs à la foi et les enseignements relatifs à la philosophie:

In eis quae ad fidem catholicam vel ad morum institutionem pertinent, non est fas Bedae vel alicui alii sanctorum patrum (citra Scripturae sacrae authoritatem) contradicere; in eis tamen quae ad philosophiam pertinent, si in aliquo errant, licet diversum aflSrmare. Etsi enim maiores nobis, homines tamen fuere^^

De même Adélard de Bath revendique la priorité de la ratio sur Vauctoritas (qui a son origine à partir de la ratio, comme avait déjà enseigné Jean

198 T. GREGORY

Scot Erigène), dénonçant la lettre comme meretrix, disponible à tous les usages, et indiquant la ratio comme iudex universalis:

Nisi enim ratio iudex universalis esse deberet, frustra singulis data esset. Sufficeret enim praeceptorum scriptori datam esse, uni dico vel pluribus; caeteri eorum institutis et auctoritatibus essent contenti. Amplius, ipsi, qui auctores vocantur, non aliunde primam fidem apud minores adepti sunt, nisi quia rationem secuti sunt, quam quicunque nesciunt vel negligunt, merito caeci habendi sunt. Neque tamen id ad vivum reseco, ut auctoritas me iudice spernenda sit. Id autem assero, quod prius ratio inquirenda sit; ea inventa, auctoritas, si adiacet, demum subdenda. Ipsa vero sola nec fidem philosopho facere potest, nec ad hoc adducenda est ®.

La découverte d’une nature comme causarum series - toute créature qu’elle est - détermine la naissance d’une conception de la ratio qui tend à éliminer le miraculeux, nécessaire à une conception plus ancienne de la nature comme voluntas Dei, et, tout en rendant possible la construction d’une philosophia mundi, détermine une nouvelle direction aussi bien dans l’exégèse que dans la réflexion théologique.

On ne s’étonnera pas que Guillaume de Saint-Thierry, illustre représentant de la culture monastique, attaque le maître de Chartres en soulignant les bases et l’agencement physiques de toute sa spéculation: homo physicus et philosophus physice de Deo philosophatur ', et en ce qui concerne la création d’Adam et d’Eve, philosophice seu magis physice describens, physico sensu interpretans, rejette la vérité de l’histoire en lui préférant sa doctrine physique {veritati historiae suum praefert inventum)^^.

Thierry de Chartres professe une exégèse analogue à celle de Guillaume de Conches; ainsi l ’école de Chartres - qui fera placer des ligures représentant les arts et les auteurs au portail royal de la cathédrale - nous apparaît tout de suite comme l’un des centres les plus importants de la nouvelle culture scientifique, nourrie de lectures “ physiques” d’origine grecque-arabe. Thierry lui-même offrira un commentaire de l’oeuvre des six jours secundum physicam qui excluait Vallegoricam et moralem lectionem'^ et où, toujours sous l’inspiration du Timée, la création s’effectuait grâce à l’interaction des éléments sous l ’action primaire et déterminante de Vignis et du mouvement céleste.

La présence constante du Timée de Platon se devine facilement derrière les cosmologies des maîtres de Chartres - mises sous une forme poétique par Bernard Silvestre, puis par Alain de Lille -, comme derrière toutes les cosmologies du X lle siècle en général.

Grande “ genèse” philosophique, le dialogue platonicien semblait se


prêter à une interprétation physique de la Genèse mosaïque, une fois identifié le démiurge avec le Dieu créateur et une fois résolu en termes physiques Vinvolucrum du mythe cosmogonique. C’est ainsi que les “ Dieux, fils de Dieux” du Timée deviennent les causes secondes qui ont pour mission de compléter l’oeuvre du créateur, et que Vanima mundi, principe et garantie de l ’ordre et du caractère organique du cosmos, deviendra bientôt V igneus vigor et la natura elle-même, après que l’on se fut efforcé, avec un succès incertain et discuté, de la situer dans la sphère divine comme troisième personne de la trinité ou divina dispositio.

Ce n’est donc pas un hasard si le renom du Timée est à son apogée au X lle siècle et donne naissance à la faveur dont jouit Platon comme maître de physique {...In causis rerum sentit Plato)'^^. Cette faveur ne déclinera que lorsque la conception péripatéticienne du monde, plus orgam'que, triomphera dans les écoles; c’est alors-depuis la seconde moitié duXIIIe siècle - qu’on reconnaîtra à Aristote le magistère de la science, rendant à Platon, selon une suggestion augustinienne, le magistère de la sagesse en tant que recherche et contemplation d’un monde intelligible; cette antithèse sera particulièrement chère aux platoniciens de la Renaissance,

Il faudra donc distinguer toujours, en parlant du platonisme du X lle siècle, d’une part l’influence plus générale du platonisme augustinien ou la présence d’un courant précis de néoplatonisme dionysien et érigénien (qui nous oriente vers la contemplation de mondes intelligibles hors de la réaUté physique, qui n’en est qu’une pâle image), et d’autre part un platonisme bien différent - lié à la lecture du Timée, de Chalcidius et de Macrobe - nettement orienté vers la contemplation du monde physique, après que l’opposition entre le sensible et l’intelligible eut été surmontée (tel était le sens du Timée), par l ’intermédiaire de l’oeuvre du démiurge et de l’âme du monde; ce sont là les deux “ platonismes” présents déjà dans la culture grecque après Aristote et qui sont à la base de la spiritualité hellénistique, surtout telle qu’elle se dégage des écrits hermétiques.

Sous l’influence du Timée, la pensée médiévale refaisait une expérience déjà réalisée par la culture hellénistique: le dialogue platonicien offrait une base pour concevoir le monde physique comme un tout vivant et organique {animal intelligens, unum et perfectum)^'^ où le rapport entre ses parties constituantes, le jeu des “ sympathies” et des “ antipathies” , et surtout le lien entre les cieux et les éléments inférieurs, permettaient d’élaborer un discours physique cohérent et concluant, sans extrapolations

200 T. GREGORY

allégoriques. Dans le cadre de cette cosmologie platonicienne, la physique stoïcienne vient prendre une nouvelle valeur avec sa doctrine de la nature comme ignis artifex, principe de mouvement et de vie des astres autant que du monde terrestre; natura est ignis artifex, ex quadam vi procedens in res sensibiles procreandas: physici namque dicunt omnia ex calore et humore procreari, énonce Hugues de Saint-Victor^®, en répétant une définition stoïcienne bien connue transmise par Cicéron, mais tout en visant aussi une position déjà affirmée parmi les physiciens contemporains; et, vers la fin du siècle, Alain de Lille, réunissant dans ses Distinctiones les différentes acceptions du terme “ nature” , rapportera auprès d’une définition de la nature aussi générale que potentia rebus naturalibus indita, ex similibus procreans similia une autre définition se rapportant plus directement à la science médicale : [Natura] dicitur naturalis calor, unde physicus dicit esse pugnam inter morbum et naturam, id est naturalem calorem^^.

La doctrine de Vignis artifex, virtus agitativa venant des cieux, et surtout du soleil, dont le rôle hégémonique parmi les planètes et dans la génération des choses est maintenant vigoureusement souligné {sol...mens mundi, rerum fomes sensificus, virtus siderum mundanusque oculus tam splendoris quam caloris immensitate perfunderat universa, écrit Bernard Silvestre 20), cette doctrine organisant par ailleurs Vordinata collectio creaturarum devient ainsi le motif central des nouvelles cosmologies du X lle siècle:

.. .ignis tantum agit, terra vero tantum patitur. Duo vero elementa, quae sunt in medio, et agunt et patiuntur... Ita igitur ignis est quasi artifex et efficiens causa; terra vero subiecta quasi materialis causa; duo vero elementa, quae sunt in medio, quasi instrumentum vel aliquid coadunativum quo actus supremi amministratur ad infima.

Ceci d’après Thierry 21 ; et Bernard Silvestre, transposant dans son poème philosophique l’expérience culturelle de Chartres enrichie d’influences hermétiques et arabes, célèbre l’union féconde de Vignis aethereus avec le sein de la terre 22.

Hermann de Carinthie, disciple de Thierry, en développant une cosmologie dans laquelle tout se résout par le lien réciproque des principes actifs et passifs {Mundi constitucio, universam generacionem fundanda, id primum debitum habebat, ut ex parte agente fieret, partequepaciente) et où le mouvement céleste préside à tout mouvement des éléments, voit dans le soleil princeps omnis geniturae, la source inépuisable de Vignis artifîcus qui, descendant des cieux dans les entrailles de la terre, y produit des êtres et


des phénomènes multiples. Dans son De essentiis, est déjà réalisée, d’une façon évidente, l’identification de l ’anima mundi du Timée avec la nature de la tradition stoïciennô23.

Encore une fois, Hugues de Saint-Victor témoigne d’une doctrine désormais répandue dans les milieux philosophiques contemporains lorsqu’il rapporte l’opinion des “ mathématiciens” , c’est-à-dire des astrologues et, d’une façon plus générale, des physiciens :

Hinc est quod mathematici mundum in duas partes diviserunt: in eam videlicet partem quae est a circulo lunae sursum, et in eam quae deorsum est. Et superlunarem mundum, eo quod ibi omnia primordiali lege consistant, naturam appellabant; sub- lunarem opus naturae, id est superioris, quia omnium genera animantium, quae in eo vitalis spiritus infusione vegetantur, a superioribus per invisibiles meatus infusum nutrimentum accipiunt, non solum ut nascendo crescant, sed etiam ut alendo subsistant^ .

La doctrine de Vignis artifex ou spiritus vitalis s’appuyait surtout sur la tradition stoïcienne, et n’était pas sans rapports avec la faveur dont jouissaient alors Cicéron et Sénèque, ainsi que Virgile, dont les vers du discours d’Anchise du Livre V I de VEnéide faisaient autorité auprès des auteurs du X lle siècle:

Principio caelum ac terras, camposque liquentis Lucentemque globum Lunae, Titania- que astra. Spiritus intus alit, totamque infusa per artus Mens agitat molem et magno se corpore miscet. Inde hominum pecudumque genus vitaeque volantum Et quae marmoreo fert monstra sub aequore pontus. Igneus est ollis vigor et caelestis origo Seminibus, quantum non noxia corpora tardant Terrenique hebetant artus moribundaque mem- bra25.

Vers célèbres dont les penseurs du X lle siècle saisiront vite le contenu philosophique, et qu’ils citeront avec des textes de Platon, de Cicéron, de Macrobe et de VAsclepius; le dernier écrit était déjà connu des Pères et à partir du X lle siècle (c’est le siècle auquel appartiennent les manuscrits les plus anciens) il jouit de la plus grande faveur; ici aussi la doctrine de Vignis se situait dans un contexte qui était la représentation exemplaire du syncrétisme de l’ère hellénistique, avec sa manière significative d’insister sur l’unité radicale du tout, thème sur lequel reviennent ponctuellement les cosmologies du X lle siècle:

Ignis solum quod sursum versus fertur, vivificum; quod deorsum, ei deserviens. At vero quicquid de alto descendit generans est; quod sursum versus emanat, nutriens. Terra sola in seipsa consistens omnium est receptrix omniumque generum, quae accepit, restitutrix. Hoc ergo totum, sicut meministi, quod est omnium vel omnia. Anima et mundus a natura comprehensa agitantur ita omnium multiformi imaginum qualitate variata, ut infinitae qualitatum ex intervallo species esse noscantur, adunatae tamen ad hoc, ut totum unum et ex uno omnia esse videantur®*.

202 T. GREGORY LA NOUVELLE IDÉE DE NATURE AU X II SIÈCLE 203

La doctrine du feu comme principe de vie, comme force naturelle originaire, se retrouvait aussi dans une tradition scientifique plus précise, la tradition médicale qui touchait à la doctrine des spiritus, au Ospixôv de la tradition hippocratique et à la ôiaTcXaaxiKfj ôuva)xiç de la doctrine galénique^^; c’est à cette tradition médicale que se rapporte le plus directement la définition d’Alain de Lille rappelée ci-dessus, et qui constitue la supposition préalable sur laquelle est bâtie la théorie médicale d’Ursus de Calabre, l’un des plus célèbres médecins de Salerne au X lle siècle:

Calor artifex est quidem omnium quae generantur, et ipse est causa generationis principalis; sicut generatio inter motus naturae est principalior, ita et calor, qui est in- ductivus generationis, inter activas qualitates principalior et fortior esse debet^».

L ’importance des écrits de la médecine grecque et arabe qui se propageaient alors en Europe - après les premières traductions de Constantin l’Africain au X le siècle, jusqu’à la version du Canon d’Avicenne en plein X lle siècle - n’est pas toujours pleinement évaluée, car les oeuvres de médecine (la tradition de cette science ne s’était jamais perdue au moyen âge, mais elle avait maintenant acquis une influence culturelle considérable) supposaient, et souvent développaient directement dans leur partie théorique, une conception générale du cosmos dont l’homme microcosme reflète la structure: de la doctrine de la composition élémentaire des corps, nécessaire pour une connaissance plus précise de leur complexio et de leur temperatura, à la doctrine des propriétés des différents êtres naturels pour en utiliser les capacités thérapeutiques, jusqu’à la science des rapports entre les cieux et le corps humain, fondamentale pour le diagnostic et le traitement des maladies.

Nulli dubium est - écrit Ursus de Calabre - superiora corpora, utpote quantitate maiora, puritate et loco digniora, virtute eflScatiora in inferioribus agere et secundum corporum complexionem variam, diversitate motus vel coniunctionis, inferiora corpora et magis similia vel mutationi habilia multiformiter permutare.

Et Daniel de Morley, rappelant un point classique de VIntroductorium de Albumasar, écrivait;

siderum virtus in medicina prepotens est... qui igitur astronomiam damnat, physicam necessario destruit. Non enim facile curat, qui causas rerum ignorat. Causam autem previderit astronomus, cui medendum sit et quare et quando, cum demum medicus utiliter accedit^*.

La médecine renvoyait donc à un discours cosmologique plus large et surtout se liait - selgn l’ancienne doctrine grecque de la |X8X,o0eaia - à la connaissance des mouvements et des influences célestes, suggestion à laquelle ne pourra pas échapper, dans ses visions mystiques, Herrade de Landesberg, qui tracera, dans un dessin fameux, les correspondances entre l’homme et les planètes.

Vultus huius seculi sunt subiecti vultibus celestibus^^, lit-on dans une maxime du Centiloquium (attribué à Ptolémée), texte fondamental pour l ’astrologie médiévale, traduit au X lle siècle par Jean de Séville et par Hugo Sanctallensis: c’est une oeuvre, annonçait Hugo Sanctallensis dans le prologue, de hüs que ad iudiciorum veritatem attinent, cum in illis totus astronomie consistat effectus secundum arahice secte verissimam inquisi- cionem et tam Grecorum quam Arabum, qui huius artis habiti sunt profe- xores famosissimi, auctoritatem .

Nous avons déjà rappelé quelques textes des cosmologies de Chartres, où le mouvement et l’ influence des cieux sont le fondement de toute l’oeuvre des causes secondes; et il est significatif que, dans des oeuvres dépendant plus directement de la science arabe, la natura elle-même s’identifie avec l ’action exercée par les planètes : elle est la qualitas planetarum dans le pseudo-hermétique De V I principiis à travers laquelle se réahse la divina dispositio, et les cieux constituent la natura elementans de Bernard Silvestre : est igitur elementans natura caelum stellaeque signifero pervagantes, quod elementa commoveant ad ingenitas actiones^^.

La fusion de la physique platonicienne avec les doctrines astrologiques arabes devient explicite chez Hermann de Carinthie, traducteur du Planisphère de Ptolémée (dédié à Thierry de Chartres comme à la “ réincarnation de Platon” ) et de Y Introductorium de Albumasar: dans son De essentiis, se dessine de plus en plus nettement sur un fonds platonicien la primauté des cieux, qui constituent la partie active du cosmos (la nature “ identique” de la cosmologie du Timéé) et exercent leur ducatus incontesté non seulement sur les éléments et sur le corps de l’homme mais sur tout le cours de l’histoire.

Peut-être que l’astrologie est justement l’expression la plus significative de la nouvelle conception de la nature dans laquelle la causalité directe sur tous les phénomènes du monde sublunaire est attribuée non plus à Dieu, mais aux cieux, qui, même s’ils sont considérés comme des instruments de Vopus creatoris, représentent cependant la tentative de définir un domaine

204 T. GREGORY

autonome de causalité naturelle: qui celum et terram, écrit Bernard Silvestre, creavit quibusdam creaturis super alias creaturas potestatem donant: ut septem planetis quibus totum mundum, cuncta eius elementa, in sua mutacione posse mutare disposuit 3.

De sorte que Hugo Sanctallensis pourra présenter la doctrine de la causalité et de l’influence des cieux comme reconnue par tous les philosophes :

Apud universos philosophie professores - écrit Hugo Sanctallensis - ratum arbitror et constans quicquid in hoc mundo conditum subsistendi vice sortitum est, haud dissimile exemplar in superiori circulo possidere^^.

Les cieux sont désormais considérés comme les véritables causes du mouvement et de la vie dans le cadre du monde physique:

Celum autem - peut-on lire dans la Philosophia de Daniel de Morley - quod sua natura movetur, movet predicta quatuor et permiscet et complexionatur ea, quia celum si non esset, procul dubio nec moverentur nec permiscerentur. Ex motu igitur eius figuratur substantia, que est sub circulo lune, multis figuris et permutatur de accidente ad accidens de forma ad formam, de figura ad figuram...»5

Ainsi les cieux deviennent les cronocratores, les dominateurs du temps et du cosmos : l’on pourra retrouver dans leurs fades les causes des événements physiques et y lire, préfigurée d’une façon emblématique, l’histoire du monde humain.

C ’est ainsi que Hermann de Carinthie pourra retrouver dans les cieux les étapes de l’histoire sacrée et profane, la succession des empires:

Hinc enim astrologi varios seculorum usus, hinc diversos humani generis status, hinc eciam diversa mundi imperia meciuntur. Sic enim regnum ludeorum sub Saturno describunt, Arabum dominiimi sub Venere et Marte, Romanum imperiimi sub Sole et love^®.

Et la sûreté des prédictions célestes, la précision de l’horoscope des religions comprenant l’annonce de l’incarnation du Christ, deviennent les arguments de la polémique contre la Hebraeorum caecitas:

...cum etiam in nature speculatione seculorumque serie vel barbare nacioni veritas Jhesu Christi prenotata fuerit^’ .

Ce sont là des thèmes que l’on retrouve dans toute la littérature scientifique de cette époque et qui marquent d’une façon très significative le naturalisme du X lle siècle. L ’auteur anonyme du De V I principiis - qui utilise largement les Matheseos libri de Firmicus Maternus - place dans la succession


des conjonctions célestes les principes et les lignes de l’évolution et de la civiUsation du genre.humain; dans cette perspective, son auteur finit par repousser toute référence spécifiquement chrétienne: la vie humaine, dans ses âges successifs, est soumise à l’influence des astres:

Principatus igitur planetarum naturam humanam ita moderatur et potestas eorum in humana vita sic ordinatur: principatus enim Lune incipit a nativitate pueri et disponit qualitatis aptitudinem secundum quantitatem annorum nutricionis, qui sunt iiii°= anni, deinde Mercurius, x,, inde Venus, viii,, deinde Sol novendecim, deinde Mars, xv., post lupiter. xii, Saturnus denique usque in finem vite.

Et si 1’homme pouvait vivre seulement sous le règne bénin de Jupiter, il en deviendrait immortel: Essent homines immortales si numquam in genituris hominum Jovis benignitas vinceretur La doctrine du péché et de la mort n’a point de place dans le monde de l’auteur anonyme ; dans d’autres textes, la doctrine de l’influence céleste sur l’histoire des hommes remplace le concept théologique de providence, dont elle pose à nouveau, sans les résoudre, tous les dilemmes.

Le fait de reconnaître la suprématie de la causalité céleste fondait la suprématie de l’astrologie dans le cadre d’une nouvelle conception du savoir où les sciences se subordonnaient entre elles en empruntant à l ’astrologie leurs principes premiers.

Qui ignorat celestium principia corporum et qualitates temporum constat eum ignorare naturas temporalium, écrit l’auteur de De V I principiis \ et Daniel de Morley:

llli vero qui syderis motibus vim et efiicatiam negant, adeo sunt impudentis amentie, ut antequam scientie disciplinam habeant, eius doctrine incipiant derogare. Unde quidam ex solo nomine astronomiam odio habent. Sed si attenderent quante dignitatis quanteque utilitatis foret, numquam nisi ex invidia ei derogarent. De dignitate eius invenitur, quod illius partes, secundum quod dixerunt sapientes primi, octo sunt; scientia de iudiciis, scientia de medicina, scientia de nigromantia secundum physicam, scientia de agricultura, scientia de prestigiis, scientia de alkimia, que est scientia de transformatione metallorum in alias species, scientia de ymaginibus... scientia de speculis et hec scientia largior est et lacior ceteris__ Utilitas vero astronomie non minimaperpendi debet. Astronomus namque, cum futuros rerum eventus prescierit, poterit eorum noxa repellere, vel evitare, ut sunt bellum publicum, generalis fames, universalis terre motus, exustiones, eluviones, communis hominum seu bestiarum pestilencia. Si vero ista penitus effugere nequeat, provisi tamen eventus, tolerantia multo levior est previdenti quam ignorantibus, quos improvisus atque repentinus percutit terror®®.

Daniel rassemble ainsi dans le cadre de l’astrologie toutes les disciplines qui, dans le De scientiis d’Alfarabi et le De divisione philosophiae de Gundisalvi, étaient classées dans la scientia naturalis', cette transposition

206 T. GREGORY

est significative, car elle rattachait à la contemplation du mouvement céleste et à la science des influences astrales tout un ensemble de sciences pratiques se rapportant à des tâches et à des buts humains. C’est là un élément de premier plan permettant d’apprécier la signification qu’avait pris le savoir astronomique: au moment où il semblait que l’astrologie dût enfermer l’homme dans les lois d’un destin déjà écrit et préfiguré dans les cieux, elle se trouvait à offrir une nouvelle possibilité d’action au moyen de la connaissance des rapports et des influences entre le ciel et la terre: la maxime du Centiloquium que nous avons soulignée, devient fondamentale pour comprendre la perspective du nouveau savoir: Vultus huius saeculi sunt subiecti vultibus celestibus, et ideo sapientes qui imagines faciebant stellarum introitum in celestes vultus inspiciebant, et tunc operabuntur quod debebant

La contemplation des figures célestes s’associe toujours, dans la science astrologique, à la recherche des moyens pour contrôler ces mêmes forces célestes dont le sage, l’astrologue a constaté l’influence; la doctrine des imagines, des electiones, des interrogationes, bref tout l’ensemble des techniques astrologiques représente l’expérience la plus considérable, ébauchée déjà au X lle siècle, d’un savoir qui s’efforce de sortir de son attitude purement contemplative et d’intervenir dans le jeu des forces qui gouvernent le cosmos; ainsi l ’homme, qui semblait enfermé dans le cercle des mouvements célestes, s’élève au-dessus d’eux et les domine au moyen de la raison : ratio imperat celo et avertunturftagitia, écrit Bernard Silvestre, reprenant une ancienne auctoritas d’Albumasar, dans la préface de VExperimentarius, manuel de géomancie qu’il se préparait à faire connaître à ses contemporains'*1.

L ’astrologie est ainsi liée à toutes les sciences qui, pendant des siècles, représenteront plus clairement la tentative de briser un monde solide et unitaire, hiérarchisé selon des formes et des essences immobiles, pour instaurer avec la nature un rapport nouveau, actif, susceptible de changer les espèces et les formes; la magie, l’alchimie, la géomancie, toutes ces branches du savoir - et les techniques qui leur étaient associées - promettaient un rapport nouveau avec la réalité physique, céleste et terrestre, que l’on sentait plus proche de l’homme et plus utile à sa vie.

Cet aspect de la science au X lle siècle semble répéter lui aussi une expérience déjà faite à l’ère hellénistique et dont témoigne amplement la littérature hermétique que l’on redécouvrait alors, directement ou par


l’intermédiaire de remaniements arabes; la figure d’Hermès connaît une nouvelle faveur: pater philosophorum, rex et philosophus et propheta qui in liberalibus et mechanicis artibus prevaluit et astronomiam prius elucidavit (ainsi que le célébraient la Tabula smaragdina et le De VIprincipiis, selon une doxologie précise), Hermès était le prototype du savant, mage, astrologue, prophète qui “ expérimente” et “ interroge” la réalité afin de la connaître et de la dominer; et, sur la base des enseignements du fabuleux Hermès, il semble possible de comprendre et de reproduire l’oeuvre de créateur par l’intermédiaire de pratiques de magie qui, à partir de la pierre philosophale - comme Dieu à partir du chaos -, permettent d’accomplir d’ “ admirables opérations” :

Sic mundus creatus est, hoc est, sicut mundus creatus est, ita et lapis noster factus est. Quia primitus totus mundus, et omne quod fuit in mundo, fuit una massa confusa, seu chaos confusum, ut superius dictum est, et postea per artificium summi creatoris, divisa est ista massa in quatuor elementa, mirabiliter separata et rectificata, propter quam separationem diversa fiunt. Ita possunt fieri diversa, aptatione nostri operis per separationem diversorum elementorum a diversis corporibus. Hinc erunt adoptationes mirabiles', id est, si separaveris elementa, fient mirabilia composita, apta nostro operi in nostri lapidis compositione. ...Sic habebis gloriam totius mundi, id est, hoc lapide sic composito, gloriam huius mundi possidebis. Ideo fugiet a te omnis obscuritas, id est omnis inopia et aegritudo.

Ainsi la Tabula smaragdina laisse entrevoir la possibilité d’un savoir opérant de façon créative dans un cosmos dont il faudrait savoir comprendre l’unité primordiale et radicale: quod est superius, est sicut quod est inferius ad perpetranda miracula rei unius

Et Daniel de Morley, confirmant la même doctrine: ideo sicut ab inexpugnabili sententia magni Hermetis habeo, audaciter cum illo unum tantum principium esse concedo

Comme on l’a très justement observé on ne saura séparer la célébration hermétique de la dignitas hominis, telle que la transmet une page célèbre de VAsclepius, de la science magique et astrologique recherchée et assurée par un grand nombre d’écrits de la littérature hermétique de l ’âge hellénistique ; de même, le sens des différentes cosmologies du X lle siècle serait difficilement compréhensible si l ’on ne soulignait pas la recherche de l’échelle humaine dans la nature, par l’intermédiaire des différents rapports, des multiples “ expériences” qui ont pour but de retrouver de nouveaux rapports avec elle.

L ’on peut dire que cette nouvelle idée de nature qui mûrit au X lle

208 T. GREGORY

siècle prend sa plus importante signification précisément dans les perspectives qu’elle ouvre au savoir scientifique à travers les suggestions de l ’astrologie, de la magie, de l’alchimie; mais pour comprendre le sens de cette expérience cruciale, ébauchée au X lle siècle, il est nécessaire de se libérer d’une conception étroite de l’histoire de la pensée scientifique qui réduit celle-ci à une liste des anticipations et des découvertes progressives des solutions que la science mathématique et expérimentale moderne considérera ensuite comme vraies.

Qui lira le prologue écrit par un anonyme traducteur sicilien de VAlma- geste de Ptolémée, avec l’assidue polémique contre ceux qui, ignorant la science des astres, la repoussent comme inutile et profane, peut saisir sur le v if la conscience d’une époque:

Sensisti vero et tu nonnullos hiis temporibus cause quam ignorant iudices audacissimos, qui, ne minus scientes videantur, quecunque nesciunt inutilia predicant aut profana... Rideant et insultent artium inimici, ignota iudicent, astrorum studium insaniam pre- dicent. Michi confiteor hec insania dulcis, michi dulce clamare cum Nasone:

Felices anime quibus hec agnoscere primum.Inque domos superas scandere cura fuit ®.

Du reste d’autres aspects de la culture du X lle siècle confirment le rapport nouveau qui s’instaure entre l’homme et la nature: on ne saurait négliger en elfet la nouvelle appréciation des arts mécaniques dans leur signification terrestre et mondaine, c’est-à-dire comme moyens utilisés par l’homme pour modifier et améliorer son miüeu naturel et sa propre condition humaine.

La page du Poîycraticus qui laisse comprendre le lien intime des arts mécaniques avec l’évolution de la société citadine et marchande, en rapport avec les nouvelles conditions de vie économique et civile, a la valeur d’un document plus encore, peut-être, que la célèbre page du Didascalicon d’Hugues de Saint-Victor, auquel fit écho, en la résumant, Richard de Saint-Victor.

En effet, par ces arts, rei publicae membra per terram gradiuntur, écrit Jean de Salisbury; il souligne efficacement à quel point le précepte cicéronien du lien nécessaire entre l ’étude de l ’éloquence et son utilisation civile doit être étendu à tous les arts, libéraux et mécaniques, ces derniers surtout ne progressant que grâce à la pratique: Adeo quidem ut si artem usumque dissocies, utilior sit usus expers artis quam ars quae sui usum non habet ... Progressus ab usu ab arte perfectio, si tamen iugi exercitatione fuerit solidata^^.


En fait, la conscience du lien entre l’art et son utilisation l’emporte sur la considération purement contemplative des arts, telle qu’elle subsistait chez d’autres contemporains: tel Adam de Balsam qui, lorsqu’il traite des ustensiles domestiques, oppose nettement la cognitio des techniques, qui appartient à la philosophia, à la possessio, qui lui est étrangère. Distinction affaiblie, mais encore présente, dans le Didascalicon d’Hugues de Saint- Victor, où tous les arts mécaniques, dans leur ratio, sont placés dans le cadre des discipHnes philosophiques; mais ici, dans le Didascalicon, on reconnaît toutefois la valeur irremplaçable des arts mécaniques pour permettre à l ’homme de surmonter les infirmitates dérivant du péché d’Adam47.

La libération des arts de leur état d’infériorité, correspond sans nul doute à l’évolution réelle des techniques au cours du X lle siècle, de celles qui se rapportaient à l’agriculture à celles qui avaient trait à la construction des grandes cathédrales, à celles enfin de la guerre, de la navigation, du commerce. Mais la compréhension de leur valeur, les premières tentatives pour voir leur signification et leur importance dans une société en plein progrès, leur englobement dans la considération - pour livresque qu’elle fût - des “ intellectuels” (du reste, on tend trop souvent à opposer l ’oeuvre des théoriciens à celle des techniciens : les écrits, par exemple, de médecine ainsi que les textes hermétiques, astrologiques, magiques, sont les premiers à nier cette opposition), ne peuvent être dissociés de l’attitude nouvelle et plus générale qui mûrissait peu à peu, dans les mêmes milieux, à l ’égard de la nature, avec l ’espoir confiant de connaître son dynamisme intime.

Les techniques, magiques ou mécaniques, trouvaient leur valeur et leur justification “ philosophique” du fait qu’elles étaient en relation avec une nature dotée d’un densité et d’une consistance propres.

Devant une nature sacramentum salutaris allegoriae, d’autres techniques entraient en action: c’était l ’exégèse allégorique, morale, anagogique, qui dissolvait la densité du symbole dans ses implications spirituelles: c’étaient là les techniques de Vhomo viator. Les autres - la navigatio, Varmatura, Varchitectura, le lanificium, la theatrica, etc. - étaient les techniques de Vhomo faber.

Ce n’est pas sans raison que la dignitas hominis, sur laquelle on insiste tellement au X lle siècle, sort du parallélisme traditionnel entre microcosme et macrocosme, pour souHgner les capacités de l’homme devant la nature.

210 T. GREGORY

sa capacité de connaître et d’agir pour devenir empereur et pontife de la nature même:

Viderit in lucem mersas caligine causas, ut natura nihil occuluisse queat... Omnia subi- ciat, terras regat, imperet orbi: Primatem rebus pontificiemque dedi'*®.

Bernard Silvestre résume ainsi la tâche de l’homme, à la ratio duquel VExperimentarius reconnaissait le pouvoir de dominer les cieux.

Il est difficile de sous-estimer la signification de ces pages et d’autres du même genre, surtout si on les rapproche des divers aspects de l’histoire culturelle et civile du X lle siècle, qui semblent graviter autour d’une nouvelle valorisation des réalités terrestres et profanes, autour d’une nature:

Cui velut mundi dominae, tributum singula solvunt

Au début du siècle, Adélard de Bath, dans la préface du traité sur l ’astrolabe, écrivait que si on ignore la structure du monde physique et sa ratio, on n’est pas digne d’y demeurer, et on devrait, si possible, en être chassé La culture du X lle siècle, dont Adélard avait été l’un des précurseurs, tira profit de cette leçon: l’homme, en cherchant la legitima causa et ratio des événements physiques et en construisant une philosophia mundi était devenu digne d’habiter ce monde et de le posséder.

Università di Roma

N O T E S

Pour un tableau général du problème, qu’il me soit permis de renvoyer à mon rapport au Ille Congrès International de philosophie médiévale (1964); L ’idea di natura nella filosofia medievale prima dell’ingresso délia fisica di Aristotele. I l secolo X II, publié dans les actes, La filosofia délia natura nel Medioevo, Milano, 1966, pp. 27-65.2 Pierre Damien, De bono religiosi statu et variarum animantium tropologia, dans Patrologia Latina 145, 779 et 771 ; cf. J. Leclerq, Saint Pierre Damien, ermite et homme d’Eglise, Rome, 1960, pp. 186 ss.3 Cette locution est dans la traduction chalcidienne du Timée (28A): omne autem quod gignitur ex causa aliqua necessario gignitur; nihil enim fit, cuius ortum non legitima causa et ratio praecedat {Timaeus a Calcidio translatus etc., éd. J. H. Waszink, Londinii et Leidae, 1962, p. 20, 20-22); le texte grec a seulement xcopiç aixiou. Liber Mamonis in astronomia, éd. C. H. Haskins, Studies in the History o f Mediaeval

Science, New York, 1960 (réimpr. de l’éd. de 1927), pp. 99-100; Daniel de Morley, Philosophia, éd. K. Sudhoff dans Archivfiir die Geschichte der Naturwissenschaften und der Technik 8 (1917), 1-40.


® Adélard de Bath, De eodem et diverso, éd. H. Willner dans Beitrage zur Geschichte der Philosophie des Mittelalters, 4, 1 Münster, 1903, p. 32.« Guillavmie de Conches, In Boethium, éd. P. Courcelle dans Archives d ’histoire doctrinale et littéraire du moyen âge 12 (1939), 5-140, 85.7 Guillaume de Conches, Philosophia I, 23 ; P .L . 172, 55-56 (cf. P.L . 90, 1137-38).8 Ibid., col. 56 (cf. P.L. 90, 1138).® De mundi constitutione, P .L . 90, 893.

Abélard, Expositio in Hexaemeron, P .L . 178, 746; Cf. T. Gregory, Considerazioni su “ratio”e "natura” in Abelardo dans Studi medievali 14, (1973), 287-300.

Guillaume de Conches, Philosophia H, 2-3; P.L. 172, 57-58; Dragmaticon, éd. Gratarol, Argentorati, 1567, p. 65ss.12 Guillaume de Conches, Dragmaticon, pp. 65-66.13 Adélard de Bath, Quaestiones naturales, éd. M. Müller, dans Beitrage 31,2, Münster, 1934, pp. 11-12.1 Guillaume de Saint-Thierry, De erroribus Guillelmi de Conchis, P .L . 180, 339-340. 1 Thierry de Chartres, De sex dierum operibus, éd. N . M. Hâring dans Commentaries on Boethius by Thierry o f Chartres and his School, Toronto, 1971, p. 555.1® Bernard Silvestre, De mundi universitate, éd. Barach-Wrobel, Innsbruck, 1876, p. 16. Sur la cosmologie de Bernard Silvestre, voir B. Stock, Myth arui Science in the Twelfth Century - A Study o f Bernard Silvester, Princeton, 1972.17 Platon, Timée, 30C, 33A.1® Hugues de Saint-Victor, Didascalicon I, 10, P.L . 176, 748; éd. Ch. B. Buttimer, Washington, 1939, p. 18.1® Alain de Lille, Distinctiones, P .L . 210, 871.

Bernard Silvestre, De mundi universitate, p. 44.21 Thierry de Chartres, De sex dierum operibus, p. 562.22 Bernard Silvestre, De mundi universitate, p. 29.23 Hermann de Carinthie, De essentiis, éd. M. Alonso, Comillas, 1946, pp. 48, 51-52, 89-92.2 Hugues de Saint-Victor, Didascalicon I, 7; P .L . 176, 746; éd. Ch. H. Buttimer, p. 14.25 Virgile, Enéide VI, 724-32.2® Asclepius, 2, éd. A. D. Nock & A. J. Festugière, Corpus Hermeticum, vol. 2 (Paris, 1945), p. 298.2’ Cf. Hippokrates, Ueber Entstehung und Aufbau des menschlichen Kôrpers [jrepi aapKÔv], von K. Deichgrâber, Leipzig-Berlin, 1935, pp. 2-6, 30ss. ; Galien, De nat.fac. I, 6; ‘Ali ibn al-‘Abbas, PantegnilV, 2 (éd. avec l’attribution à Constantin l’Africain, De communibus medico cognito necessariis locis, Basilae, 1539, p. 82).28 Libellus de effectibus qualitatum, éd. C. Matthaes {Der salernitaner Arzt Urso aus der 2. Halfte des 12. Jahrhunderts und seine beiden Schriften "De effectibus qualitatum” und “De effectibus medicinarum” , Boma-Leipzig, 1918), p. 17.29 Cf. R. Creutz, Die medizinisch-naturphilosophischen Aforismen und Kommentare des Magister Urso Salernitanus dans Quellen und Studien zur Geschichte der Naturwissenschaften und der Medizin 5, 1, Berlin, 1936, p. 63; Daniel de Morley, Philosophia, ed. cit., p. 32 (cf. Albumasar, Introductorium, Venetiis, 1506,1, 4).3“ Centiloquium Ptolomei, trad. Jean de Séville, Venetiis, 1519, fol. 97vb.31 Haskins, Studies, p. 69.32 Liber Hermetis Mercurii Triplicis de V I principiis, ed. Th. Silverstein dans Archives d’hist. doctr. et litt. du moyen âge 22 (1955), 248, 282; De mundi univ., pp. 30-31.

212 T. GREGORYî


33 Bernard Silvestre, Experimentarius, éd. M. Brini Savorelli dans Rivista critica di storia della filosofia, 14, (1959), 283-342, 312-313.

Haskins, Studies, p. 78.35 Daniel de Morley, Philosophia, p. 23.3® Hermann de Carinthie, De essentiis, p. 69, 72.37 Ibid., p. 29, avec la citation d’Albumasar, Introductorium VI, 2.38 Liber Her metis Mercurii Triplicis de V I principiis, p. 266,289 (cf. Firmicus Maternus, Matheseos libri VIII, Stutgardiae, 1968, pp. 56-57).39 Liber Her metis Mercurii Triplicis de V I principiis, p. 296; Daniel de Morley, P/w- losophia, p. 34; cf. Albumasar, Introductorium, I, 5.

Centiloquium Ptolomei, trad. Jean de Seville, Venetiis, 1519, p. 97vb.Bernard Silvestre, Experimentarius, p. 317.

42 J, Ruska, Tabula smaragdina. Ein Beitrag zur Geschichte der hermetischen Literatur, Heidelberg, 1926, p. 182, 185.43 Daniel de Morley, Philosophia, p. 14.44 Cf. E. Garin, Medioevo et Rinascimento, Bari, 1954, p. 154; aussi dans Giornale critico della filosofia italiana 29 (1950), 362-67.45 Haskins, pp. 192-93 (cf. Ovide, Fasti, I, 297-98).46 Jean de Salisbury, Policraticus, VI, 19; éd. Ch. Webb, Oxonii, 1909, vol. 2, pp. 57-58.4’ Cf. F. Alessio, La filosofia et le “artes mechanicae” nel secolo A7/dans Studi medievali 6 (1965), 71-161 ; voir aussi infra le rapport de G. Beaujouan.48 Bernard Silvestre, De mundi universitate, p. 56.49 Alain de Lille, De planctu naturae, P .L . 210, 447.5® Haskins, Studies, p. 29.

D I S C U S S I O N

R. mckeon; Mr. Gregory, I read your paper with great interest, and I agree with your general thesis that in the twelfth century there appeared a sense of nature that did not exist before. But having agreed, I find it difficult to express what it is that was new in that “ sense of nature.” I wonder whether you would tegin by saying more about the ratio physica and the causarum series which you find in the twelfth century and which you find lacking in the Physiologusl In other words, I would like to know what the new science looked like and what the old science looked like.

T. GREGORY: Le sens de la nouvelle conception du monde physique au Xlle siècle émerge justement en polémique avec la conception du haut moyen âge où la causalité divine joue un rôle prédominant et les phénomènes physiques sont considérés comme l’expression immédiate d’enseignements moraux et religieux: avec le Xlle siècle, s’affirme, au contraire, une conception selon laquelle on veut donner aux événements une explication “physique”, c’est-à-dire, selon un ordre de causalité naturelle, en ayant recours à un ensemble de causes secondes qui acquièrent, alors, une autonomie et deviennent le véritable objet de la philosophie. Dans la première conception - qui est une contemplation religieuse du cosmos - l’influence de S. Augustin est profonde par le fait qu’il réduit la nature à la voluntas Dei et par son attitude polémique envers la vana curiositas. Où la voluntas Dei est la cause directe des événements physiques, il n’y a pas de recherche des causarum series, parce qu’il n’y a pas alors de series causarum, mais la volonté de Dieu qui cause directement un phénomène physique. Selon un

exemple célèbre de S. Augustin, le miracle des noces de Cana est tout à fait naturel, tout conune le processus de maturation des vignobles et la production du vin, parce que Hans l’uji et dans l’autre cas c’est toujours la volonté de Dieu qui va produire directement des effets. C ’est une théorie, on peut dire, occasionnaliste avant la lettre. C’est une théorie aussi que S. Thomas reprochera aux Mutakallimün, qui disent que ce n’est pas Vignis qui va brûler mais Dieu en présence de Vignis', quand Dieu est la cause directe, il n’y a pas de recherche des causes naturelles.

Bien différente est la conception qui mûrit à Chartres et dans les milieux ouverts à l’influence de la science grecque et arabe: on voit naître une conception de la nature qui a consistance et autonomie propres. Par exemple, Guillaume de Conches, Thierry de Chartres et d’autres “physiciens” du Xlle siècle disent: voyez. Dieu a créé les éléments puis les éléments vont tourner et avec les mouvements des éléments vont se former les cieux; selon l’action des cieux la vie sur terre va se développer, et la vie ne dérive pas directement de Dieu mais des cieux, de Y ignis \ les corps des animaux sont aussi constitués par ce jeu des forces physiques, et le corps de l’homme l’est également par un certain jeu des forces physiques. Nous avons ici une causarum series, c’est-à-dire une succession de causes qui, à l’intérieur d’une conception de Dieu créateur, ont toujours une certaine autonomie, une certaine consistance. Et alors l’étude physique de cette causarum series prend une signification. C’est-à-dire qu’entre Dieu créateur et chaque événement physique il y a une series de causes.

Ce qui va diff'érencier à l’intérieur de la nouvelle mentalité scientifique du Xlle siècle cette nouvelle conception des causarum series de la conception de la nature qui remonte à l’âge hellénistique, à la littérature des mirabilia et du Physiologus, qui se développe au moyen âge dans la tradition allégorique et symbolique, c’est que dans la tradition al- légorique-symbolique chaque phénomène physique est étudié surtout pour sa signification d’ordre spirituel ou moral; alors on renvoie directement du phénomène non pas à la causarum series physique mais directement à des enseignements que les phénomènes peuvent donner. Par contre dans la mentalité qui se forme au Xlle siècle, on cherche à dégager cette causarum series du contexte symbolique; on met de côté le contexte symbolique et on cherche plutôt à pouvoir constituer une physique pour expliquer la connexion des causes. C’est la première fois qu’on va reconnaître aux causes physiques une consistance vraiment autonome, toujours à l’intérieur, évidemment, d’une idée de la nature comme créature. Le contraste entre ces deux conceptions opposées s’exprime d’une façon paradigmatique dans la polémique entre Guillaume de Saint-Thierry et Guillaume de Conches.

R. mckeon: The importance of discovering nature in the twelfth century is that it provides a beginning point from which later science would develop. You object quite rightly to a science that would make the world merely symbolic. But don’t you think that to find the beginning of science in magic, alchemy, and astrology is rather curious?

T. GREGORY: Je dirais d’abord que magie et astronomie ou astrologie sont des expressions de la nouvelle science du Xlle siècle; il faut se libérer des catégories du jugement qui sont nées en rapport avec une conception de la science différente et plus récente, Je rappellerai même que avant l’avènement de la science moderne on ne distinguait pas l’astrologie de l’astronomie. S’il faut à tout prix une différence - qu’il m’arrive rarement de trouver - on peut quelquefois isoler l’aspect mathématique de la science des astres, mais il faut dire que même après la traduction de VAlmageste de Ptolémée presque personne n’était capable de lire un texte mathématique du niveau du texte de Ptolémée. Aussi, je crois qu’il vaut mieux ne pas les distinguer; une astronomie mathématique surgira plus tard. On pourra dire plutôt que dans l’étude de l’astronomie-

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astrologie, certains développent plutôt les aspects mathématiques et d’autres insistent au contraire sur les influences des cieux, la science de iudiciis etc.

Au Xlle siècle l’astrologie est une des sciences physiques qu’il faut étudier comme science physique et non pas comme une chose basée sur des données imaginaires, car il s’agit bien d’une science positive pour les hommes du moyen âge. La théorie de l’influence des cieux disparaîtra seulement avec la naissance de la physique moderne, au XVIIe siècle. Je dis donc que l’astrologie, tout comme l’alchimie et la magie, sont des sciences physiques au sens plein du terme dans une période où elles étaient considérées comme sciences physiques. C ’est la science moderne, mécanique, mathématique, qui va repousser ces sciences comme des superstitions. Pendant le moyen âge et la Renaissance, elles sont pleinement sciences.

G. beaujouan : Le cas de l’astrologie et celui de la magie ne sont pas tout à fait semblables. Dans l’alchimie, il y a une part de mysticisme qui ne se trouve pas du tout dans cette espèce de rationalisme de code civil qui préside à l’astrologie.

T. GREGORY: Sans doute, mais la magie est très liée à l’astrologie, car on peut faire des opérations magiques dans la mesure où on connaît les rapports entre les natures, et le rapport entre les natures est déterminé par la connaissance de l’influence des astres. Aussi le magus doit-il connaître les influences des astres pour opérer d’une façon magique. Vous avez bien raison, l’astrologie-astronomie a un outillage que nous sommes tentés de qualifier du point de vue moderne - de plus scientifique, mais le magus est toujours un homme de science et il est reconnu comme tel par ses contemporains, surtout pour la magie naturelle; évidemment pas pour la magie noire.

G. beaujouan ; Croyez-vous qu’un astrologue du Xlle siècle se considérait comme un magusl Moi je crois que l’astrologue du Xlle siècle aurait été très surpris de se voir qualifier ainsi.

T. GREGORY: Non, je ne dis pas ça, mais je dis que le magus doit connaître l’astrologie; je dis que la magie est une science qui dépend de l’astrologie. Je ne dis pas que l’astrologue est aussi un magicien, mais que le magicien est toujours aussi astrologue, en ce sens que des notions d’astrologie sont toujours la base scientifique d’opérations magiques.

R. mckeon: I didn’t object to astrology as a basis of science. As a matter of fact, I would go further and accept magic as a basis for science. When Francis Bacon planned a new instauration of science its culmination was natural magic. But what I was looking for was the difl’erentiation, even in the twelfth century, between astrology as a superstition and as a science. It is this differentiation that I thought might be discerned by a sense of nature.

T. GREGORY: Je n’ai pas du tout nié ceci; j ’ai plutôt souligné le fait que l’astrologie dans plusieurs textes est indiquée comme le fondement de toutes les autres sciences physiques.

R. m ckeon: But not any kind of astrology. There were anti-astrologers and there were positive astrologers. There were those who made natural science on a foundation of principles and those who substituted astrology for scientia naturalis.

j. g a g n e : V ous avez assez facilement assimilé l’astronomie et l’astrologie à une science physique. Il me semble que c’est encore très rare au Xlle siècle. On assimile alors l’astronomie et l’astrologie principalement à la science mathématique. Et je voudrais en montrer un peu les conséquences: même si l’on dit que les corps célestes gouvernent le monde, on ne dit pas que la science des corps célestes gouverne la science du monde en aucune façon. Ce n’est que beaucoup plus tard que l’on bâtira ce genre de raisonnement, et il y a même des étapes intermédiaires avant qu’on y arrive. Vous avez


donné l’impression que le changement de mentalité implique que la science des corps célestes va gouverner la science du monde. Il me semble que c’est beaucoup plus tard.

T. GREGORY: La littérature astrologique est très riche au Xlle siècle et la thèse selon laquelle plusieurs “ sciences du monde” dépendent de l’astrologie est très répandue; j ’ai rappelé un texte significatif de Daniel de Morley, et d’autres auteurs aussi, de Hugo Sanctallensis à Ursus de Calabre, au De V Iprincipiis: ils insistent tous sur le fait que la connaissance des influences des cieux, et donc l’astrologie, est essentielle, soit pour la médecine, soit pour l’agriculture, soit pour d’autres sciences et techniques; on retrouve souvent ce que dit Albumasar, c’est-à-dire que la connaissance de l’astrologie permet des formes de contrôle et d’intervention sur les événements naturels. Du reste, ce sont ces nouveaux développements de l’astrologie qui peuvent faire comprendre certaines polémiques anti-astrologiques, destinées non pas à nier l’influence des cieux, mais seulement à nier la possibilité de tirer des prévisions sur l’avenir qui risquent ainsi de limiter la liberté humaine en la renfermant dans le cercle des influences célestes.

G. beaujouan : V ous parliez tout à l’heure de la difficulté de distinguer astronomie et astrologie. Il y a tout de même deux niveaux: c’est d’abord le vague contexte astrologique qui avait subsisté au haut moyen âge, et puis il y a le moment où on commence à réutiliser les tables astronomiques d’héritage arabe. Il se pose donc un problème de chronologie très important à l’intérieur même du Xlle siècle.

M.-Th. d’ALVERNY: D ’autant plus qu’im homme comme Guillaume de Conches était, je crois, tout à fait incapable de lire ces tables astronomiques. Je veux aussi dire que malgré tout la distinction astronomie-astrologie existe; et, ce qui est beaucoup plus important - et répond en partie à votre objection - : il y a cette distinction déjà marquée chez Isidore de Séville, qui est reprise dans le Didascalicon d’Hugues de Saint-Victor, entre l’astrologie naturelle et l’astrologie superstitieuse. De plus, le Didascalicon s’inspire de la distinction d’Isidore de Séville; il ajoute seulement quelques petites phrases sur les fonctions de l’astrologie naturelle, qui montrent que, même à une période contemporaine de Guillaume de Conches (vers 1130-1135), Hugues de Saint-Victor avait déjà entendu parler tout au moins des progrès de l’astrologie naturelle. L ’astrologie naturelle admet l’influence des astres, et sur toutes sortes de phénomènes, et beaucoup plus qu’on le croirait. En particulier, Hugues de Saint-Victor fait allusion à l’utilisation de l’astrologie pour la médecine. Il n’y a qu’une phrase, mais c’est tout de même suffisant pour se rendre compte que déjà de son temps les médecins sérieux commençaient à faire de l’astrologie et à observer les astres. Donc c’est un témoignage en faveur de la connaissance assez précoce déjà des textes d’astrologie. Ce que Jean de Salisbury attaque énergiquement, c’est l’astrologie superstitieuse, c’est-à-dire les judicia, la divination, et les jugements, etc. ; naturellement, c’est là qu’il entre en conflit avec des astrologues d’autre part très sérieux astronomes, parce que, comme mon Raymond de Marseille, ils soutiennent avec énergie que l’astrologie fait un tout et que les judicia font partie de l’astrologie. Les objections des théologiens viennent surtout du fait que les traités d’astrologie arabes qui sont traduits comprennent aussi l’astrologie judiciaire. Les amateurs, même des hommes scientifiques du type de Raymond de Marseille, qui sont des savants, des astronomes, qui s’occupent des tables astronomiques, etc., tiennent également à l’astrologie judiciaire.

B. sto ck : Vous avez montré qu’il y a une véritable science de la nature au Xlle siècle. Alors la question se pose: avait-on besoin d’Aristote pour cela?

T. GREGORY: Je crois que le moyen âge a obtenu à travers la connaissance d’Aristote im système vraiment plus scientifique de la nature. Un tel système n’était pas donné par la tradition platonicienne. La tradition platonicienne a commencé à réveiller des

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intérêts pour le monde physique et a de quelque façon préparé l’entrée d’Aristote; déjà vers la fin du Xlle siècle Aristote est introduit par des remaniements un peu platoniciens ; le premier Aristote physique et métaphysique qu’on va connaître de la fin du Xlle siècle est un Aristote influencé par la tradition d’Avicenne, etc. Je n’opposerai pas, comme on l’a fait, le platonisme humaniste du Xlle siècle à l’aristotélisme physique du XlIIe. Le platonisme du Xlle siècle introduit une conception du monde physique qui sera complétée par l’unique système de l’antiquité connu du moyen âge: le système d’Aristote. Ainsi voit-on dans la tradition franciscaine encore des éléments platoniciens, augustiniens; ainsi la théorie de la lumière, surtout, va se lier d’un côté avec les études d’optiques de la tradition arabe, et de l’autre avec les études aristotéliciennes.

R. rashed : Excusez-moi, je voudrais poser une question vraiment naïve: où se trouve le savoir scientifique dans tout cela?

T. GREGORY: Il y a une tentative de percevoir, d’expliquer la séquence ordonnée et autonome des causes. En ce qui concerne l’astrologie et la physique, en disant: lescieux exercent une certaine influence, une certaine causalité, et par cette influence et cette causalité il va se former la croûte terrestre, etc. ; c’est encore par les mouvements des cieux que se forment les animaux; nous voyons une tentative d’explication physique du cosmos.

R. rashed : Vous dites “explication physique”, mais le mot “physique”, ici, peut comporter plusieurs sens. Il aura un sens déterminé s’il y a vraiment des critères. Est-ce que ces critères existent? Ya-t-il des raisonnements, des démonstrations?

T. GREGORY: On ne doit pas poser le problème dans le sens de demander un ensemble de démonstrations comme l’exigerait un homme de science moderne: le concept de physique, d’expérience, de démonstration change au cours des siècles. L’influence des cieux, au Xlle siècle, comme il en était auparavant pour l’astrologie grecque et arabe et au cours de plusieurs siècles suivants, se présente comme une donnée de l’expérience et constitue le fondement de toute une conception du monde physique; cette conception est scientifique dans la mesure où elle veut donner une explication organique de certains phénomènes cohérente avec certains principes qui se placent dans ce que l’on conçoit comme ordre naturel, sans faire recours directement à la causalité divine.

A. sabra: T o answer the question about criteria: if you ask, not only in the twelfth century, but if you ask Ptolemy: “How do you, Ptolemy, know that these correspondences that you talk about in the Tetrabiblos exist, how do you know them to be true?” the answer is “My knowledge of these things is empirical. It is based on the experience of people over a long period of time.”

R. rashed: No, excuse me, we cannot say that it is empirical, because Mr. Gregory says also that there are all the symbolic interpretations. My difficulty now is how to join empirical criteria with symbolic interpretations. Which criteria are there now for knowledge?

G. beaujouan : L ’interprétation symbolique s’évanouit au moment où apparaît cette nouvelle forme. En d’autres termes, cette vision de la nature liée à l’astrologie est contraire à la conception symbolique.

R. rashed : Si l’astrologie intervient, elle intervient avec des symboles !M.-Th. d’ALVERNY: Si vous pensez à l’astrologie d’Abü Ma‘shar avec les images dans

le ciel, il est juste en effet de dire qu’il y a une nouvelle sorte de symboles qui s’élabore et qui aura un énorme succès artistique, mais là n’est pas l’aspect fondamental. De plus, au Xlle siècle, on a traduit Abü Ma'shar, et à partir du milieu du Xlle siècle, on commence à utiliser Abü Ma‘shar pour l’apologétique chrétienne, avec l’horoscope des religions et l’image de la Vierge et de l’enfant dans le ciel. Vous trouvez ça chez des


auteurs théologiques. Mais c’est autre chose, ce n’est pas la même chose que l’explication allégorique et morale qui, à la suite des pères de l’Eglise, était souvent ajoutée dans les traités De natura rerum.

R. rashed : Je comprends très bien qu’il y a un changement dans cette image du cosmos, peut-être un changement dans le mode de la connaissance, par l’intervention des séries de causes, mais ma question reste: si on veut parler d’un savoir quelconque, la première chose à donner, ce sont les critères de ce savoir. Bashy dit que les critères sont purement empiriques; est-ce qu’au Xlle siècle ces critères sont purement empiriques? Que veut dire empirique à l’époque? Est-ce qu’il y a d’autres critères?

T. GREGORY: Le concept d’empirie change d’un siècle à l’autre. Quand pour le problème des eaux super caelum les théologiens disent: c’est Dieu qui va mettre les eaux au-dessus du firmament, elles sont là parce que Dieu le veut; Guillaume de Conches, Thierry de Chartres disent: non, parce que les eaux sont plus lourdes que l’air et il n’est pas possible qu’il y ait des eaux au-dessus de l’air. En bien, il s’agit ici d’un discours scientifique, en tant que cohérent avec une certaine conception du rapport réciproque entre les éléments et en tant que refusant de faire recours à la volonté divine pour expliquer ce que la causalité naturelle ne peut admettre.

R, RASHED : Quelle théorie de la preuve a changé pour donner un autre savoir scientifique au X lle siècle?

T. GREGORY: En ce qui concerne le problème que j ’ai mentionné, ce qui change est le fait que la preuve se compose d’une théorie précise des qualités des éléments et de leurs rapports réciproques; il s’agit d’une ratio ou d’un argument physique qui s’oppose à la preuve d’ordre théologique religieux qui se résolvait à faire recours directement à la volonté de Dieu: la différence est évidente.

R. rashed : Donc le seul critère scientifique de la théorie, de la preuve, c’est le bon sens!

T. GREGORY: Ah, mais pour avoir une théorie de la preuve comme vous voulez, il faut attendre assez longtemps.

r . rashed : Non, elle a existé avant, pendant, et après. Si vous parlez d’une théorie scientifique, d’un savoir scientifique, il faudrait nous donner la doctrine de la preuve. Quand deux n’étaient pas d’accord, quels étaient les moyens à leur disposition pour trancher? Étaient-ce les moyens traditionnels? Les mathématiques intervenaient-elles ou pas? C ’est ça que je veux savoir surtout.

G. beaujouan : Vous posez le problème d’une manière qui n’est pas celle du Xlle siècle. Il faut distinguer deux choses différentes. Il y a d’abord une certaine philosophie de la nature pour laquelle sont imaginés des modèles plus ou moins satisfaisants. Bien. Ensuite, si vous prenez des cas particuliers comme diverses tables astronomiques, par exemple, alors là vous retombez dans une problématique de la science qui est la vôtre, mais c’est un problème complètement différent de celui posé par M. Gregory.

M.-Th. d ’ALVERNY: Puis-je maintenant dire quelque chose pour défendre un peu des gens que vous avez repoussés avec beaucoup de mépris, les prédécesseurs de la fin du Xe et du Xle siècle, parce que l’intérêt scientifique n’a pas surgi absolument comme par miracle du temps de Guillaume de Conches. Vous avez ces premières traductions ou adaptations d’astronomie et de mathématique, surtout d’astronomie; elles sont plutôt pratiques, ce sont des traités d’astrolabe. Cela commence à la fin du Xe siècle; et Ger- bert y a été pour quelque chose, puisque les premiers traités des usages de l’astrolabe, s’ils ne sont pas de lui, ont tout au moins été apportés par lui. D ’autre part, vous avez des traités d’astrologie qui sont non pas traduits directement mais adaptés de l’arabe et sont vraisemblablement de la fin du Xe siècle, tout au moins il y a un manuscrit de la

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fin du Xe, d’autres du Xle. Donc on s’y est intéressé, et il y a plusieurs textes de gens qui littéralement s’arrachent ou se prêtent des astrolabes. Donc là aussi vous avez un intérêt vraiment scientifique et un désir de recherche qui explique un petit peu la suite. Et il y a toute cette quantité de traductions médicales du grec et de l’arabe et l’introduction de la philosophie de Galien. Je crois qu’il est vrai de dire que cette nouvelle conception de la nature se révèle au Xlle siècle mais a été préparée par de la recherche scientifique beaucoup plus positive. Ce que l’on peut dire, c’est que c’est chez Guillaume de Conches qu’on voit intervenir ces recherches scientifiques dans des notions philosophiques. Mais la curiosité scientifique, la recherche des causes, ça existe déjà.

G. beaujouan : Dans les exemples que donne Mlle d’Alverny, la recherche est en réalité une recherche de textes, et pas une véritable recherche. Ces traités d’astrolabe sont finalement des traductions ou des adaptations. Dans le cas de Galien ce sont aussi des textes de Galien qu’on exhume. Dans le cas même de l’astrolabe, c’était un instrument d’une science dont on entrevoyait mal la finalité à ce moment-là.

M.-xh. d’ALVERNY: Oui, mais malgré tout ce sont des marques de curiosité et d’intérêt scientifique, c’est ça que je voulais dire. Bien sûr, c’est encore à l’état de première recherche. Ce sont des pionniers, mais ces pionniers existent et leur curiosité existe, et ils ont vraiment cherché quelque chose.

T. GREGORY: Je suis tout à fait d’accord. Et en ce qui concerne les médecins, j ’ai noté aussi dans mon rapport que la tradition médicale n’avait jamais disparue au cours du moyen âge et que surtout à la fin du Xle siècle elle s’enrichissait. Pour les autres considérations, je suis proche de M. Beaujouan, parce que pour l’espace d’un siècle, de la fin du Xe à la fin du Xle, vous pouvez citer seulement le fameux cas de Gerbert d’Auril- lac et des traités sur l’astrolabe. Il y avait une curiosité, mais il n’y avait pas une tentative de systématisation globale. Par contre, au Xlle siècle, nombreux sont ceux qui s’occupent de ces problèmes, une bibliothèque scientifique va se constituer. Et puis il y a une systématisation théorique du problème. La différence à souligner est justement ce qui sépare la curiosité de laquelle vous parlez et une bibliothèque qui va transformer la culture européenne.

BRIAN STOCK

E X P E R I E N C E , P R A X I S , W O R K , A N D P L A N N I N G

I N B E R N A R D O F C L A I R V A U X : O B S E R V A T I O N S

O N T H E S E R M O N E S I N C A N T I C A *

Inde est quod homines in praesenti a sese exsules per oblivionem, in alia per inanem sollicitudinem migrant saecula, non profutura, immo nec futura.

Hence it is that men, alienated from themselves in the present through oblivion, migrate through empty anxiety to other worlds which are not going to be of use to them, indeed, wh'ch are not even going to be.

De Consideratione 2.10

i n t r o d u c t i o n : MONASTICISM a n d ‘M O D E RNIZ A T IO N ’

In his controversial classic, The Protestant Ethic and the Spirit o f Capitalism, Max Weber made the following statement on the significance o f western monasticism for the rise o f rationally organized, scientific culture:

The significance in world history of the monastic plan of living (Lebensführung) in the West, in contrast with eastern monasticism,... is based on its general type {allgemeinen Typus). Beginning in principle with the Rule of St. Benedict, continuing with the Clu- niacs, again with the Cistercians and with decisive finality in the Jesuits, the [plan of living] had been emancipated from unsystematic withdrawal from the world and directionless self-torture. It had become a systematically improving method for a rational plan of living with the object of overcoming the status naturae, in order to free man from the power of irrational impulses and his dependency on the world and on nature, to subject him to the supremacy of a purposeful will, to place his actions under constant self-control through the consideration of their ethical consequences; and thus, objectively, to instruct the monk as a worker in the kingdom of God, and also subjectively through it to insure the salvation of his soul.^

In this statement, as in greater detail in Economy and Society,^ Weber suggested three ways in which western monasticism furthered the development o f the legal and organizational structures o f modern society. First it substituted ‘rationality’ for ‘irrationality’ in an attempt to overcome the limitations, as then conceived, o f the human condition. Then it gradually evolved a decision-making process which not only produced a ‘rational plan o f living’ , but also began to relate individual human action to wider ethical principles. Finally, it taught the monk, through discipline,

J. E. Murdoch and E. D. Sylla (eds.), The Cultural Context of Medieval Learning, 219-268. All Rights Reserved.

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obedience and the adoption o f a systematic ‘work ethic’ to postpone present consumption in anticipation o f future reward. In Weber’s view, monasticism thus played a vital role in institutionalizing what later writers called ‘economic rationality’ .

Weber’s observations on this subject formed part o f a general theory o f modernization in traditional societies, one which, with all its defects, “ has provided, probably more than any other specific thesis in the social sciences, a continuous focus o f scientific controversy .Ye t little o f the abundant scholarship devoted to the wider issues has concerned itself with authenticating or modifying Weber’s views on monasticism.^ One reason is that the theory o f economic development, o f which Weber’s views on monastic culture formed a part, has since his time largely been preoccupied with societies outside Europe. Still another reason derives from the manner in which the classical economic historians formulated the problem. Terms like ‘capitalism’ and ‘Protestant ethic’ created new problems in their wake. But a more serious defect arose from the narrowness o f the time dimension. In most studies the center o f gravity lay in the Reformation.® The search for the religious values that favoured or inhibited the emergence o f the modern economy focussed on the narrowly defined period in which capitalism, in an international sense, made its first appearance. The early literature falls into two stages, one in which the debate revolved around Calvinism and capitalism itself, another in which its main theme was Calvinism and Lutheranism.® This scholarly work did much to clarify the growth o f religious attitudes from the fifteenth to the seventeenth century, but it left the earlier period in a curious void. It also emphasized the discontinuities in an historical development which Weber had felt in its institutions to be continuous.

The early socioeconomic studies o f the question also contained another weakness. There was too much analysis, not enough concrete historical research. For example, in Weber and his contemporaries, medieval attitudes towards work, activism, and planning are inevitably derived from a single source, Aquinas. The great scholastic’s views are thrust onto the prescholastic period, o f which they are the logical consequence, and into a monastic milieu which was quite different from the later medieval university. Unwarranted assumptions are also made about Aquinas’s influence on later scholastic thought. Weber, for instance, asserts that all medieval Catholics held activity in this world to be morally neutral." He refers to

OBSERVATIONS ON BERNARD OF CLAIRVAU X 221

intentio in generalized Thomistic terms.® He assumes that medieval Christians expended labour not for accumulation and reinvestment, but ‘^naturali ratione^ for the preservation o f the individual and the whole” ® o f the community. Sombart’s treatment o f early medieval intellectual history is no better, and even Troeltsch, who is still cited as an authority, contents himself with repeating Weber’s insights while supporting them by documents written at least a century too late.^o Tawney, the most respected among the first generation o f Weber’s supporters, makes no important references to authors before the thirteenth century,^i nor does Weber’s most incisive early critic, H. M. R o b e r t s o n . ^ 2 classical economic historians opened a new area o f research but did not retrace its developmental stages in sufficient depth.

Nor, for their part, have professional medievalists, who, by and large, have written o f the period 1100-1350 in almost complete neglect o f the problem that Weber so brilliantly brought to the surface. Historians o f science, who perhaps had the most to gain from such an investigation, have been the most persistently internalist in perspective, For the social and intellectual changes o f the period confront them with an interesting paradox. On the one hand, they see the growth o f authoritarian attitudes which so seriously interfered with the emergence o f a free intellectual community in the Middle Ages ; on the other, the development o f a hitherto unprecedented set o f institutions, without whose establishment, Weber recognized, modern science and its unique social environment would not have been possible. Up to now they have kept these two aspects o f change in separate categories. Work in the field, by and large, has focussed on individual biography and intellectual achievement; it has not isolated the economic, social, and cultural variables through which traditional medieval civilization, hesitantly at first and always with great reluctance, began to adopt as its image o f betterment the values (and prejudices) later associated with scientific rationality. These changes may be thought o f as the external history o f medieval science, or, perhaps more accurately, as the prehistory o f modernization.

In the twelfth century no figure stands closer to the center o f this development than Bernard o f Clairvaux (1090-1153). Unquestionably the most influential author o f his age, he was also the protagonist in its most spectacular controversy, and scholarly opinion on the value o f his contribution has been sharply divided. Historians o f philosophy and theology

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have on the whole judged his achievement to be inimical to the growth o f rational science. He disliked scholasticism; he remained ignorant in large part o f the translators ; and he personally opposed three o f the century’s leading intellectuals, Gilbert Porreta, William o f Conches and Abelard. The character o f his style and thought would also seem to preclude any significant contribution to scientific culture. A monastic theologian, he devoted most o f his attention to the perfection o f the inner man, to the repatriation o f the human soul in God. The organization o f his writings is not logical or didactic; it is literary, affective, and symbolic. He seems at an early age to have acquired a strong dislike for the exercise o f logic without a practical function. Even historians o f theology have not known quite what to make o f Bernard. The early commentators saw him simply as a defender o f the faith; the later ones have tried unsuccessfully to assimilate him into the more structured patterns o f thirteenth-century thought. 14 Despite a renewal o f interest by specialists, he remains a figure known to all, respected by many and read by few. Yet, in the early history o f European modernization, practical religious thinkers like Bernard, whose influence was on action as well as thought at every stratum o f society, played a hitherto unrecognized role. Like their later counterparts, such as Calvin, they were confronted with widespread economic and social changes, and were forced to decide whether new values should supersede the old. The study o f the interaction o f their ideas with social history o f their times is only beginning.

This essay attempts to make a very limited contribution to this new area o f research. It provides no definitive solutions to the problems it it raises. Rather, it tries to re-open the subject, and to propose that the practical religious mind is a useful bridge between economic change and cultural values. Its specific topic is Bernard’s Sermons on the Song o f Songs, which, together with other sermons and De Consideratione, offer good examples o f his mature thinking between 1135 and 1153. The essay is not constructed around the classical themes o f medieval theology. It attempts to outline the way in which Bernard thinks, for he is above all a thinker o f relations rather than ideas. The most obvious weakness is the lack o f mention o f the economic and social changes taking place in his time, or even, within the essay itself, o f a philological analysis o f his central terms, along with an account o f their usage in other twelfth-century authors. Within these limitations, however, it does attempt to suggest categories

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for analyzing Bernard’s way o f thinking which emerge naturally out o f his thought itself. The first section discusses the notion o f experience, its relation to everyday reality as well as to higher, mystical forms o f knowledge. The second treats the connection between experience, as a normative activity, and learning and improvement; the third, the function o f knowledge as it relates to both thought and action. The fourth turns to the more general theme o f praxis, which, in Bernard’s terms, is conceived as a Pauline distinction between the internal and external man. The fifth section treats the active and contemplative life as aspects o f overall planning. The conclusion makes some suggestions for further research on the problem o f material success and spiritual progress among the

Cistercians.

I. THE V A LU E OF EXPERIENCE

The notion o f experience is central to Bernard’s whole endeavor.^^ In the Sermons on the Song o f Songs he returns again and again to the value o f experience, and some o f the simple phrases in which he uses the terms experiri, experimentum, or its derivatives provide useful points o f departure for his more complex ideas.

Sometimes he will employ experience as a commonplace, as in the

following examples:

Tale sane experimentum de Verbo habens...Soundly having such an experience o f the Word...

or:His praemissis ad cautelam... mexpertorum....^^Having prefaced these matters for the aid o f the inexperienced....

Soon however the careful reader begins to discern deeper meanings, as, for instance, when Bernard describes Christ’s reason for coming to earth,

...ut miserias hominum homo factus experimento sciret...,

...so that, having been made man, he might know the miseries o f men by experience...,

or, as in the following examples, in which Bernard describes his hermeneutic role as interpreter o f the Biblical text:

Quod tamen dixerim, non quasi expertus, sed quasi experiri cupiens;!®

Yet I should state this not as one experienced but as one desiring to experience;Loquor vobis experimentum meum quod expertus sum;^o I teli you my experience because I am experienced;Volo VOS experiri illud quod sanctus propheta consulit...I wish you to experience that which the holy prophet counsels... ;Porro in huiusmodi non capit intelligentia nisi quantum experientia attingit. 22

For in such a matter intelligence only grasps to the degree that experience attains;

or, again, when he imputes this type o f experience to the relationship between God and man, stating:

Tali namque experimento et tali ordine deus salubriter innotescit... ;23

For by such an experience and such an order God becomes known in a saving manner... ;

or, in a similar vein, when he speaks o f the converted Gentiles, who are

...illuminati spiritu sapientiae et suo experimento docti...

.. .illuminated by the spirit o f wisdom and taught by their own experience...;

or when he speaks o f the prophets o f the Old and New Testaments in a typological relationship to each other:

Tenebant nimirum proprio experimento huius sententiae veritatem...

Indeed, they were recalling the truth o f this proposition through their own experience....

Bernard even places a high value on experience when he is subordinating it to faith. On one occasion he speaks disparagingly o f "'experimentum fallax,'' but on most issues takes the opposite position, which he summarizes as follows:

Credant quod non experiuntur, ut fructum quandoque experientiae, fidei merito consequantur.2«

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-I

Let them place their trust in what they have not experienced, so that, by the merit o f faith, they may then also attain to the fruition o f experience.

It is perhaps unwise to separate Bernard’s notion o f experience from its wider contexts, to which we shall turn shortly. However, there are some general features which have already made their appearance. In an author often called a pure mystic, only a part o f experimentum or experientia is given over to metaphysical, non-empirical, or spiritual notions. Rather experience takes its point o f departure from an everyday, hard-headed, pragmatic approach to the meaning o f existence, and in particular to man’s reflection upon la vécue. Unless it were joined to something more intellectualized, it could not, in normal usage, be termed an ‘ idea’ . It is rather a co-ordinated set o f responses, partly sensorial and partly intellectual, to that aspect o f the present which either, through reflection, refers to the past, or through faith, to the future. It receives a good deal o f its meaning from the interpenetration o f historical events with lived experience. Its relation to the future may be described as a type o f psychological forecasting deeply involved, from man’s point o f view, in the practice o f charity, and from God’s, in the bestowal o f grace. It thus interrelates man and his maker through the medium of la vécue. It involves not only the intellectual faculties, but more often the whole world o f the senses, through which man experiences the flow o f life. Moreover, experience is not only a means by which the past and future can be related to the present ; it also provides a formula for uniting the general and the specific, the object and the subject, the text and its interpreter. Thus, the spiritual sense o f the text, which Bernard, in the Greek fashion, calls theoria or contemplatio, is not an abstract tool, an adjunct o f the scholastic method, a means o f wringing harmony from a welter o f discordant patristic opinions. The allegorical meaning o f the text is inseparable from the experience the text is presumably enhancing: as one understands it better, it informs and transforms one’s existence.

II. EXPERIENCE, LEARN ING, A N D IMPROVEMENT

All o f Bernard’s works o f practical theology may be described as attempts to structure raw experience according to external models o f conduct and

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rules for decision-making. The idea was aptly summed up in the title o f his little treatise De Praecepto et Dispensatione. In the first o f the Sermons on the Song o f Songs, he states that the Biblical text is not so much a cantica canticorum as a cantica graduum.^’ The sermons may be thought o f as a series o f steps or unrealized projects in moral reform. A little later in the same sermon he makes clearer the relationship between experience and learning:

But there is a canticle which with good reason surpasses all the others which we have mentioned by its own singular dignity and sweetness, as if all the others existed through it: and rightly I should call it the Song of Songs, since this one is the fruit of all the others. Only an anointing (unctio) teaches a canticle of this kind, only experience increases one’s knowledge. The experienced (experti) may recognize [it], the inexperienced (inexperti) may burn with desire, not so much for knowing (cognoscendi) as for experiencing (experiendi).

This passage makes essentially two statements. First, that initiation into the text is not only an intellectual process; it is also sensorial.2» The term unctio even suggests that one is besmearing oneself with ointment before a religious ceremony. Secondly, one’s knowledge is increased by experience, and this understanding too is not o f a purely intellectual kind; it is rather a product o f experience itself. Through these two paths one arrives at Bernard’s mysticism: immersion into the text is not cognitive but affective,

Sermons 4 and 5 present the first stages o f a doctrine o f spiritual progress intimately related to learning through experience. Sermon 4 begins with an allegorization o f the three kisses o f Song o f Songs 1:1 ; they become the three stages o f mystical and experiential progress. There are, he says, “ three states, or progressive states {affectus sive profectus) o f souls, made known adequately and manifested only to the experienced....’ ’ ^i In Sermon 5, something o f a parallel, he divides spirits into four basic types, brute, human, angelic and divine.^^ O f these, all need bodies except the last. The human spirit needs a body to ascend to the divine ; the angelic in order to bring about its own motion (since no motion, according to Bernard, is possible without a body). Thus the bodily parts o f both brutes and angels perform a certain utility.33

At this point the argument becomes more complex, leading to the first affirmation in the Sermons o f a philosophy o f action or o f work. Each o f the two abovementioned spirits, the brute and the angelic, acts in a different way. The irrationabilis spiritus, because it is merely corporeal, cannot

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raise itself up to the spiritual and intelligible. Yet it may help men who wish to do so. Bernard thus argues that all irrational spirits are instrumenta through which rational man may be aided in his search for spiritual

truth:

Yet in order to attain those ends, [the irrational spirit] is known by reason of its corporeal and temporal obedience to help those who are transferring all the benefit (usuni) of temporal things to the enjoyment (fructum) of eternal ones, ‘using this world’, so to speak, ‘as if not using it.’®

Bernard’s meaning here, as elsewhere, is inseparable from the rhetorical manner in which it is presented. It is also difficult to understand it in isolation from the Bibhcal text upon which it is an evident gloss. Here he is playing on ususfructus, which he separates into its two component terms in order to further the parallel statement o f 1 Corinthians 7:29-31, in which Paul describes the transitoriness o f all earthly things :

Hoc itaque dico, fratres: tempus breve est; reliquum est u t ... qui utuntur hoc mundo, tanquam non utantur, praeterit enim figura huius mundi.I teli you, brethren, the time is short. From now on, let those .. .who deal with the world do so as though they had no dealings with it. For the form o f this world will pass away.

In Bernard’s rephrasing o f the Pauline ""utentes hoc mundo tamquam non utentes,'" one has, in a nutshell, the theology o f work which is developed in various directions throughout the sermons. The problem is the fundamental ambivalence o f man before the material universe o f which he is, in part, a product, and which he in turn must appropriate to himself if he is to achieve his spiritual goals. The goals, o f course, are entirely spiritual. Therefore, although we must continually labor, our labor may be useless for attaining grace, which can only be bestowed from above. We must use this world, and those below us, the servi et pecora, must work for us, even though what we achieve may be without reward. We must fill up the time because the time is short.

In the next stage o f the argument Bernard makes these ideas clearer. The notion o f ‘using the world while not using it’ is systematically related to the first three levels o f spirits, the irrational, the rational and the angelic. In each case Bernard confirms that a material component is necessary for achieving the precondition o f spiritual progress, and it is through the

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desire for renewal, rather than the condition itself, that the brute and angelic spirits are related to man:

But it is clear that the spirit of man, which holds a place midway between the highest and the lowest, has a body to the extent of the necessity of both [the brute and angelic spirits], with the result that neither can [the irrational] advance without it, nor can [the angelic] give benefit to the other [i.e. the rational, man]... Therefore, since without the assistance of the body, the servile, bestial spirit would not suffice to absolve the debt of its condition, nor the celestial and spiritual to implement the ministry of piety, nor the rational soul to give counsel for the salvation of its neighbour or even for itself, it follows that every created spirit, whether that’t may help or whether that it may at once be helped and help, has, to that degree, need of corporeal assurance.®®

In the second part o f the sermon, Bernard returns to the same idea: without the corporis instrumentum no spiritual component can make man learn more or improve himself morally.^^ No angel, no soul, no man may act without a material agent. In fact, Bernard goes so far as to suggest that even the angels, acting upon each other, need matter. And if the angels cannot act upon man without the aid o f a body, it follows that man cannot raise himself towards the angels except through the same instrument. Thus the material components o f man and his world, in Bernard’s theology, are not merely the debased reminders o f original sin; they are quasi- technological instrumenta through the correct application o f which he may again raise himself up. Human labor and human tools are in part the preconditions for salvation.

Experience, then, in Bernard’s mind, is related to man’s spiritual progress, and man achieves amelioration, in part, through his activity in this world, using it, so to speak, and not using it. The object o f living is to arrive at this betterment, which is a precondition or preparation for grace. In order to realize these ends man must direct his activities towards certain long-range goals ; he must plan his existence so that it realizes the possibilities in his own renewal. Man cannot ever fully recreate the potentiality which was his in Eden, but he can, through order, discipline and obedience, through the reform o f his physical and spiritual life, imitate a more divine model. This model may be called the psychological ideal o f Cistercian monasticism. In Bernard’s eyes it is not a static but a dynamic conception, requiring ceaseless activity on the part o f the individual. It also requires that he devote himself to learning primarily through experience. This sort o f education, as much a discipline o f the spirit as o f the mind, implies a special relationship between action, experience, and the affective


capacity o f the mind. Experience informs action and action in turn instructs the mind. Thus there is a dialectical movement, discernible in Bernard’s style as well as in his thought, between experience and its referent, the subject and the object, man and the world. Bernard, as we shall see, often refers to these two in Pauline terms as aspects o f the ‘inner’ and ‘outer’ man. The ideal, for him, is a state in which, through experience, inner and outer, theory and practice become one. Moreover, consistent with his own theory, Bernard nowhere presents these ideas in an abstract or systematic fashion. Like the insights they provide, they arise from his own experience o f the Biblical texts on which he is commenting. 7

III. THE FUNCTIONS OF K N O W L E D G E

Speaking elsewhere o f this sort o f commentary, Bernard makes a typical statement:

Sed nec studium tam esse mihi ut exponam verba quam ut imbuam corda.®®But my desire is not so much to comment on words as to imbue hearts.

One might express this another way: his interest is not so much in the intellectual analysis o f meaning as in strengthening resolve for action. It follows that he has in mind two distinct types o f knowledge with two different functions: knowledge for its own sake, disinterested fact, and knowledge related to conduct, which enables one to pursue ideal goals. In contemporary terms we could say he is distinguishing between thought and action. Bernard derived this distinction principally from Paul, but in his imagination it became somewhat transformed. Paul had spoken at 1 Corinthians 8:1 o f the knowledge that puffs up {scientia inflat), but Bernard is more interested in the relative functional utility o f the two main types o f knowledge. For him, useful knowledge is the knowledge born o f experience; it is this which conduces towards the practice o f charity.

The distinction between Paul and Bernard perhaps deserves a little further amplification. In Sermon 29, Bernard, citing Paul, makes the following statement:

And see if Paul himself, who invites you to ‘better gifts’ [1 Cor 12:13], shall not insinuate charity among the others, whether he says that, with faith and hope [1 Cor


13:13] it is the better and supereminent knowledge {scientia) [or whether on the other hand he sends you the gift of grace.]®®

Unlilce Paul, Bernard is not merely contrasting the scientia which puffs up with that which leads to charity. He is attempting to place the contrast within a larger framework which includes experience. This relationship is made clear in Sermon 49, where he states:

Indeed, zeal without knowledge (scientia) is insupportable. Therefore, where striving (aemulatio) is most passionate, discretion, (discretio) the regulator (ordinatio) of charity, is most necessary. For zeal without knowledge is always found less efficacious and useful; what is more, it is even pernicious.'*®

Again, the knowledge o f which he speaks in this paragraph is derived from the mediating influence o f experience. For him, experience, knowledge and charity are intimately bound to each other. Experience is the mediator between theory and practice, while useful knowledge is that which conduces towards charity. Thus experience modifies the strictness o f the original Pauline and Augustinian dualism.

There are other aspects o f Bernard’s theory o f knowledge that merit special attention. However, central to the whole concern is a single theme: the nature o f human ignorance. Thinkers from Augustine to Bacon used this topos as a point o f departure for outlining the possibilities o f human progress in this world, and Bernard is no different. The clearest statement o f his ideas occurs in Sermon 36. He begins with a time-worn question: is all ignorance worthy o f being condemned? Here is his reply:

Indeed it seems to me that it is not, for all ignorance does not damn; rather, an innumerable number of things exist of which one may be ignorant without a diminished possibility of salvation. For example, if you do not know the mechanical arts, either that of the carpenter or the mason..., what impediment would there be to your spiritual health? Even without all those arts which are called liberal..., how many men have been saved, giving satisfaction in their ways of life and their works? How many does the apostle enumerate in the Letter to the Hebrews who are made blessed not in the knowledge (scientia) of letters but in a pure conscience (conscientia) and by a faith unfeigned [Hebr 11:1; Tim 1:5]. They all pleased God in their lives: not through the merits of knowledge but the merits of living.^i

It is important at this point to note what Bernard does not say. He is not condemning the study o f the mechanical arts or of literature. He is merely stating that they are not sufficient in themselves for guaranteeing salvation. Hence, in theory, a man may remain ignorant o f them and still be saved. He makes this point clear later in Sermon 36 :

Perhaps I appear to bruise knowledge, and, so to speak, to reprehend the learned and to prohibit the study of letters. Far from it. I am not ignorant of how much the students of letters have benefitted and still benefit the Church, whether in refuting its enemies or in giving instruction to the untaught. For I have read: ‘Because you have rejected knowledge, I for my part will reject you, lest you perform the ofiice of the priesthood for me’ [Os 4:6]. And I have read: ‘Those who would be learned shall shine forth like the splendor of the firmament, and those who teach many men justice as the stars in perpetual eternities’ [Dan 12:13]. But I also know where I have read, ‘knowledge puffs up’ [1 Cor 8:1], and again, ‘He who brings knowledge also brings suffering’ [lo 1:10]. You see that, when the one is inflating and the other deflating, there are different knowledges.^^

Nor is Bernard taking the position that the contemplative life is superior to the active. He is merely emphasizing a special kind o f activity directed towards the fulfilment o f spiritual goals. He makes this clear throughout the Sermons', a good example occurs when he allegorizes the lovers’ bed bestrewn with flowers in the Song o f Songs. The bed, he says, does not symbolize the passive life. Nor does it indicate that it suffices to complete an action only once. Rather it represents ceaseless activity:

But if, as I related in another sermon, a bed bestrewn with flowers is the conscience filled with good works, surely you will see, as the simile requires, that it by no means suffices to labour at what is good once or twice, unless you incessantly add new things to the old... Otherwise the flower of good works falls and withers, and in a short time the luster and strength are drained from it. ®

Perhaps only an author o f Bernard’s power could have wrung from so traditional a symbol o f passivity as thalamum a new expression for action. The conscience filled with good works is not a contemplative idea; it is an ongoing process requiring ceaseless vigilance. Thus, by implication, although the mechanical arts and liberal studies do not suffice for salvation, they may play an active role in the pursuit o f charity.

The important point o f departure in Sermon 36, then, is not the approval or disapproval o f secular studies. It is the fundamental contrast between scientia and conscientia, between knowledge for its own sake and knowledge for the collective spiritual goals o f man. In thus distinguishing between knowledge as it may be individually possessed and as it may be collectively shared, Bernard was o f course building on a distinction fundamental to the thought o f Paul, Augustine, and Benedict. But he gave it the characteristic stamp it was to bear throughout the thirteenth century in manuals for confessing and the cure o f souls. He therefore took the first positive steps after the classic age o f monasticism in the direction o f the social regulation

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o f human behaviour. In his thought these steps are still very largely theoretical: they are directed towards a limited monastic community, not the general public. But their importance in the methodological history o f the social sciences cannot be underestimated. For Bernard was suggesting that all forms o f detached knowledge, all scientiae, should be used primarily in the service o f individual or collective moral perfection. That is what he means by conscientia: collective knowledge and collective morality. This idea, and its implications, were to give rise in a much changed economic context to some o f the greatest tensions as well as achievements o f the thirteenth and fourteenth centuries.

It is o f special interest therefore, to complete the outline o f Sermon 36, and, in particular, to analyze the relation between thought and action. Bernard first suggests that, as man has little time on earth, he must decide on his priorities :

And [Paul] said; ‘Moreover, I say through that grace which is given to me to all who may be among you; do not be wise more than it is necessary to be wise, but be wise for seriousness [Rom 12:3]. He does not forbid them to be wise, but to be wise more than is necessary. And what is it ‘to be wise for seriousness?’ To observe most vigilantly what we know more completely or [to know it] before it may be necessary. For time is short [1 Cor 7:29]. Now while all knowledge, provided that it is supported by truth, is good in itself, nonetheless you, who hurry on account of the brevity of time ‘with fear and trembling’ [Phil 2:12] to work out your salvation of it [i.e. of knowledge], take care to know better and beforehand those things which you sense closer to salvation.'*^

Bernard here extends and modifies his notion that there are two different sorts o f knowledge. Again, he asserts that all knowledge, provided it is verified, is useful; but for man, who has but a short time on earth to prepare his salvation, some types o f knowledge take precedence over others. These are the types which he associates with the edification o f conscience. Important to note is that this type o f knowledge is directed towards the future, not the undefined future o f remote possibility, the future o f utopia and apocalypse, but rather the future determinable by man and understandable within his lifetime. It is a future related to his potential for reformed conduct. In other words, through his actions, through his reconstruction o f his own experience according to an external model, man, to the degree that he understands his situation, makes the moral universe in which he lives, and this psychological control helps him to determine his fate. Christian conscience is thus made a partial answer to the perennial problem o f uncertainty.


The next stage o f the argument consists o f two parts. The first develops the relationship between the type o f knowledge which is useful and the potential uses to which it may be put. The second, picking up an earlier theme, turns to the potentially retrograde effects o f knowledge for its own sake. Both parts are found in the following statement:

[Paul] says: ‘He who thinks he knows anything does not yet know the manner in which he ought to know’ [1 Cor 8:2]. You see that he does not approve of a man who knows many things if he should be ignorant of the manner of knowing (sciendi modum). You see, I repeat, how he establishes the fruit and utility (ususfructus) of knowledge in the manner of knowing. But what does he call the manner of knowing. What indeed, if not that you should know by what order, what zeal, and to what end it is necessary to know each thing. By what order, in order to know earlier what later leads to salvation; by what zeal, in order to know more ardently that which more vehemently leads to love; with what end, in order to know not for empty glory or curiosity or anything similar, but rather for your edification or that of your neighbour.

For there are some who wish to know much with this end, that they may know, and this is shameful curiosity. And there are those who wish to know in order that they themselves may be known, and this is shameful vanity... And likewise there are those who wish to know in order to sell their knowledge, for example, for money or for honors, and this is shameful profit (quaestus). But there are those who wish to know in order that they may be edified, and this is charity.^®

In addition to the distinction between types o f knowledge, Bernard introduces a difference between knowledge as a static and completed act, scientia, and knowledge as a process o f education or learning, sciendi modus. He also contrasts the positive role o f conscience in planning for the future with the disinterested market o f ideas. The ultimate purpose o f knowledge is to combat uncertainty and to prepare the way for salvation. Preparation, moreover, is not a state; it is a process. It cannot, o f course, insure salvation, but it can create its necessary condition, which is charity. The precondition for salvation thus rests on two collective ideas: conscience and charity. Conscience is the inner, psychological ordering; charity, the external. Together the two provide a framework in which the somewhat mystical Pauline notion o f love can be transmitted by ordinary human beings through their institutions and ideas. Bernard tries to bridge the gap between the individual and collective morality, between the responsibility o f each Christian for himself and wider obligations o f an all-embracing charity. Charity is a communal, family ideal, but one which issues from the individual conscience. Knowledge which promotes individualism but does not contribute to communal responsibilities is idle curiosity, vanity, or profiteering.

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The argument o f Sermon 36 has now been followed to the point at which Bernard has fully articulated his doctrine o f useful knowledge. It remains for him to indicate more clearly the relation between thought and action. This part o f his teaching, even more than what has preceded, is difficult to reduce to clearcut, factual statements, as it is deliberately presented in charged, symbolic language. To take a simple example, in linking the above argument with the next stage o f the discussion, Bernard states that thought and action should act like a good digestion. Knowledge is food, memory the stomach o f the soul. Food that is not digested does not promote health; similarly, knowledge, stored up in the memory, must be cooked over the fire o f charity - decocta igne caritatis - in order to issue in good works.^s From this, one concludes that thought, separated from action, is not useful.

One could not conclude however that the interplay between the two is dialectical. This is the burden o f the last part o f the sermon. The thought once again proceeds in two stages. First he establishes that knowledge must provide a dynamic model for conduct, a ratio for utihty and order:

Do you not perceive how truly the apostle sensed that ‘knowledge puffs up’ [1 Cor 8:1]? First I wish then that the soul know itself, since the rationale (ratio) of both utility and and order demands it: of order, to be sure, since our first object is what we ourselves are; but also of utility, since this kind of knowledge does not inflate but humbles, and is a certain preparation for edification.'*’

But how is the soul to know itself? In Sermon 36, Bernard gives a brief answer, one which must be amplified by his later teaching on reform. As long as I look inwardly upon myself, he says, my eyes are held in bitterness. This can only be overcome by holding out before myself a happy vision o f God {laeta visio Dei). The visio acts like an external model o f ideal charity, informing the actor’s experience o f introspection as he continually attempts to reform himself :

For by such an experience and such an order God becomes known in a saving manner... By this means the understanding of yourself will be a step towards an acquaintance (notitia) with God; and from this image, which is renewed (renovatur) in you, he will himself be seen. At the same time you yourself, beholding with evident trust the now revealed glory of the lord’s face, will be transformed into the same image, so to speak, from clarity to clarity by the spirit of the lord [2 Cor 3: IS].-*»

This is a remarkable passage, in which experience is related both to self- knowledge, or knowledge o f the subject, and understanding o f God, or knowledge o f the object. The latter acts as a model o f psychological


activity for the former. The model acts upon us as we, reflecting on ourselves, attempt to know our souls better; and thus it renews us through its image. By the activity o f our minds we in turn are transformed into the same image: as we come to know ourselves better, we also come to know God. What we know o f God, or that aspect o f him which is knowable, is only that which is related to man’s capacity to renew himself through reflective experience. In the interplay between the model held out before us and its internalization in our makeup, at the nexus o f the reflective experience which relates subject and object, is found the essence o f Bernard’s dialectic. By this means, man begins to depart from the regio dissimilitudinis, the country o f unlikeness, Bernard’s symbol o f man’s alienation from himself.^» Moreover, Bernard has not merely worked out a solution for internalizing a model o f ideal conduct. He has also made a new contribution to the classical problem o f image/likeness in the Fathers. He has restored the question to its primitive integrity, in which it comprises the central existential question facing a Christian. Although the matter must be put forward cautiously, has he not also used it as a bridge between the thought o f the Fathers and the first tentative stages o f social

planning?

So far in the discussion o f the uses o f knowledge, emphasis has been placed on its pragmatic function, its psychological utility. Yet there is another important side to the matter: the mystical. In his notions o f experience, charity and grace, Bernard often hovers between pragmatism and mysticism. For this reason his mysticism is seldom a state o f pure rapture ; nor is it a system. Rather it is designed to complement the pragmatic side o f experience. Like the pragmatic, it plays an important role in reforming man, and it does so in two ways. First it provides a mode for experiencing a foretaste o f grace while on earth. This is a very rare occurrence. It also touches upon the gradual process o f edification by which man improves himself. In this sense Bernard refers to the stages o f illuminatio.

The Sermones in Canrfca provide a number o f instances o f the illuminative side o f mystical experience. But the clearest statement o f Bernard’s meaning occurs in his third sermon for Christmas Eve. Its text is Exodus 16:6-7 :

Hodie scietis quia veniet Dominus, et mane videbitis gloriam eius.

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Today you shall know that the lord will come and in the morning you shall see his glory.

The exposition begins in the traditional manner o f discussing the sensus litteralis, then turns to the allegoricus. These words, Bernard says, refer to actual events, but they are also intended to signify later ones. More specifically, they recall a past event in such a way that it has present significance, thus interrelating the literal and the allegorical, history and experience. The two sets o f events are part o f a pattern o f préfiguration and fulfilment.50

The discussion o f this point then leads him to a second problem. He refers briefly to the future utopie state, and, finding himself uneasy with his own abstractness, returns to the present predicament o f man, which, owing to its brevity and lack o f illumination, is called the custodia in nocte.^^ This watch o f the night has httle value compared to the future regeneration o f man. Yet Bernard’s mind is so heavily oriented around the problem o f human reform in the present that he attempts to find some practical use for it. Some sort o f illumination must take place on earth, he argues, otherwise we should emerge into the final court o f judgment in total ignorance:

And even in this very time [i.e. the watch of the night], God exhibits reason for man, he bestows intelligence. For it is necessary that he should illumine man with the light of his knowledge as he leaves this world, lest, in departing extinguished from the home of the flesh and the shadow of death, he should not be able to be relighted in eternity.^z

In the next part o f the sermon, Bernard attacks the problem o f illumination and knowledge. The necessity o f illuminating man while he is on earth, he continues, is the reason why the son o f God showed himself amidst the gloom and darkness o f this world, in this place o f our banishment, hke a torch, a brilliant flame that pierces the darkness. Those who desire to be illumined may approach and be united with him in such a way that there is no longer any space between the two. For it is our sins that separate us from God, and as soon as these are removed, we come into contact with the true hght o f the universe, “ just as, when we want to light an extinguished taper, we touch it to another that is shining with flame.” But what is this illuminated knowledge, which, as the prophet Hosea says, shines before us like a star:


Quae est autem ista scientia? Profecto scire quia veniet dominus, etsi quando veniet scire non possumus. Hoc est illud totum quod postulatur a nobis.^^But what is this knowledge? To know certainly that the lord will come, even though we cannot know when he will come. This is all that is demanded o f us.

This type o f illumination is limited to the few, and it differs in emphasis from Augustinian doctrine, even though it uses the same symbols. Unlike Augustine, who said that man, though a fallen creature, could reclimb some o f the steps towards his lost divinity through the cultivation o f the liberal arts, Bernard suggests that man, as a creature alienated from true illumination, can be reanimated only through the type o f knowledge that influences character and behavior. Augustine emphasizes factual learning in the service o f Christianity; Bernard stresses the unity o f theory and practice in the formation o f conduct.

Acquiring this sort o f knowledge, then, is a process o f learning, partly factual, but mostly reflective and mystical. It proceeds in three stages, which Bernard calls poenitudo, correctio and sollicitudo.^^ The first step, penitence, requires a reversal o f one’s previous tastes: laughter is changed into tears, song into mourning, joy into grief, as one begins to dislike what pleased one before. The second step is improvement (correctio), which insures that the vices o f gluttony, pleasure, and pride are controlled. The first step is useless without the second. The purpose is not to pull the personality apart but to restructure it around new goals. But improvement will not continue to interrelate theory and practice unless the mind exercises an incessant influence over the body. Thus sollicitude or care, the third step, is necessary “ so that the human mind, in keeping constant watch over itself, may begin to walk with its own God and may anxiously scrutinize every part, lest she somehow ofiend the eyes o f so great a majesty.” 5« In psychological terms, the whole process may be summarized as follows. Man must restructure his personality, first by a reversal o f his previous, anarchic mores, second by imposing upon himself a new, externalized model for conduct, and thirdly, through praxis, by allowing consciousness to effect a re-examination o f all decisions governing action. Uniting his own symbolism to the Pauline idea o f renewal, Bernard says:


In poenitudine accenditur, in correctione ardet, in sollicitudine lucet, ut interius et exterius renovetur.In penitence [the mind] is kindled, in improvement it is set on fire, in sollicitude it radiates light, so that [man] is renewed within and without.

Illumination, then, is related to the knowledge that governs conduct. In the above statement, Bernard also suggests that the restructuring o f human conduct is brought about by a mystical union o f theory and practice. It is this point which he elaborates in the remainder o f the sermon. In the conscience o f a man seeking reform, he states, fear and joy wage a fierce battle. But this battle cannot be won. It is rather an unceasing struggle. At the center o f his humanist vision is not a cohesive but a conflict model o f human personality: “ Happy the conscience in which the conflict [of fear and joy] is being carried on incessantly, until that which is mortal is absorbed by life, until the fear in which in part it consists is emptied out and the joy which is its completion follows.” 8

Man then, while on earth, is engaged in a constant struggle, which will only be concluded at the end o f time, when the inherited state o f his nature, so to speak, shall wither away. Good and evil are not absolutes, abstractions detached from man, but rather essential aspects o f moral experience. Thus again practice informs theory. The pragmatic nature o f Bernard’s response is conveyed in a metaphor which follows. We are continually exposed, he says, to three principal evils: the world, the flesh and the devil, all o f which “ attempt to extinguish the light o f conscience.” 5» But man, who consists, in his bodily frame, o f a house built with hands, must work with his hands to protect himself. And with his hands alone he must erect the edifice o f conscience: “ Therefore the soul must be covered {tegenda) with both hands, that o f the heart and the body, lest perchance what has been lighted be extinguished.... And just as we do not easily forget that we are held in our own hands, so we should never forget the interests o f our souls, and their care should chiefly animate our hearts.” ®*

How is man, in practical terms, to do this? Bernard turns to this question in the last section o f the sermon. He recommends three methods for improvement: correctness o f work, purity o f intention and care for unity {rectitudo operis, puritas intentionis, custodia unitatis). The integration o f thought and action is evident from his opening words:

Cum ergo sic lumbi nostri praecincti fuerint, et lucernae ardentes, custodiendae sunt vigiliae noctis supra gregem cogitationem et actionum nostrarum.®^Since then our loins have been girded and our lamps lighted, the vigils o f the night must be kept over the flock o f our thoughts and actions.

The important point is that custody must be maintained at once over thought and action. Within this framework, the three prescriptions are then amplified. The first vigil, rectitudo operis, is outlined as in the Rule. The second relates the illuminating knowledge o f an external model to one’s internal conduct: “ The second, purity o f intention, takes as its purpose that the simple eye should make the whole body radiant: that, whatever you may do, you may do it according to God, so that grace may flow back to the place from which it pours forth.”

The third, the custody o f unity, relates the individual to the collective conscience. The communal ideal comes first. In the concluding words o f the sermon Bernard once again reiterates the central tenet in his whole theory o f knowledge : that man, by reforming his conduct, may restructure his personality, and, by setting up guidelines for decision making and planning, may combat the uncertainty o f his existence: “ In this way, then, on this day, the advent o f the only begotten kindles true knowledge in us, that knowledge, I say, which teaches that the lord will come - which is the enduring and stable foundation o f our conduct.” ®'

IV. p r a x i s : t h e i n t e r n a l a n d e x t e r n a l m a n

Attention has so far been concentrated on two questions, experience and knowledge. An analysis has been made o f the normative and mystical sides o f experience, and o f the cognitive and activist functions o f knowledge. It is now necessary to turn to the idea by which Bernard links the two, the internal and external nature o f man. Paul had written at 2 Corinthians 4:16:

... Licet is qui foris est, noster homo corrumpatur, tamen is qui intus est renovatur de die in diem.Although our humanity which is outside is in decay, yet that which is within is renewed from day to day.


The internality and externality o f man, also known as the image/likeness problem, had sustained much debate among earlier theologians, in particular Origen, Gregory o f Nyssa, and Eriugena. Using it as a point o f departure, monastic theology, for its part, had consistently developed the idea that the purpose o f living was the renewal o f the inner man.

Bernard, too, in taking up this well-known subject, assumes that man should dedicate his life to spiritual ends. However he differs from earlier thinkers in specifying how man should attain them. His thinking on the matter is not always consistent, and any attempt to reduce it to a few systematic propositions is bound to overlook essential details, especially o f language and phrasing. Nonetheless there is an overall shape to his thinking. Moreover, the subject is one to which, in diflFerent contexts, he returns again and again. For example, on one occasion, discussing the paradise o f the saints, he takes up the otherworldly asceticism o f earlier monastic writers Uke Peter Damian: “ Surely ... the saints, having spurned the superfluous ornament and worship o f their own exterior self, which is certainly corrupted, devote and occupy themselves with all diligence with the cultivation and embellishment o f the inner self, which is in the image o f God and which is renewed from day to day.” ®®

On another occasion he reworks the traditional imagery o f Paul’s interpretation o f original sin. Bernard believed, as did the Greeks, that in Eden sin had been added somewhat artificially and impermanently to man’s essential nature. At the end o f time, through the administration o f grace, it would presumably be removed. Bernard employs the metaphors o f ‘clothing’ and ‘covering’ from Colossians 3:10 {induentes novum, eum qui renovatur ... secundum imaginem ejus qui creavit), but also changes the idea slightly to suit his own idea o f alienation :

Non plane anima nativam se exuit formam sed superinduit peregrinam.®®For clearly the soul did not divest itself o f its form from birth but put on that o f a wanderer on top.

Bernard, in short, utilizes traditional expressions in attacking the problem, but goes considerably beyond them in proposing new solutions.

His most sustained series o f thoughts on the internal and external man occurs in the sermons which lead up to the twenty-third. Bernard prepares the way as early as Sermon 17, where, discussing allegory in a

manner later made famous by Dante, he states: “ We have transversed the shadows o f allegories {transivimus allegoriarum umbras)', it remains to inquire into moral meanings. Faith has been built up in order that life may be instructed. The intellect has been exercised in order that action may result.” ®

In Sermon 18, he turns to the relation between experience and work, and, in order to relate allegory to activity, he introduces the twin notions o f infusion and effusion. Thus the theme o f internality and externality makes an early appearance. In Sermon 20, the philosophy o f planned activity is related to love: one proceeds from amor carnalis to amor rationalis and then to amor spiritualis. Again, the steps begin on earth and lead upward. In Sermon 21 the major topic is sloth, and in Sermon 22 the four perfumes o f the bride are allegorized as various attractions to the spiritual life. Thus, when Bernard turns in Sermon 23 to the meaning o f the mystical garden, the reader (or listener) has had a long preparation for the idea that allegory is both a symbol o f alienation and a stimulus to action. In the garden Bernard has the perfect traditional image o f each: o f the state from which man fell and to which, through grace, he will return. It is therefore not surprising that he presents in this sermon one o f his most profound statements o f the manner in which man may actively renew his inner self.

In order to bring his thoughts together, Bernard utilizes as his text for the sermon not only Song o f Songs 1:3 ( ‘The king has brought me into his storerooms’), but the texts, in part, o f the sermons which precede. Thus, to the cellarium he unites the previously mentioned garden and bedchamber. What results is a trinity o f ideas for which he will find parallels throughout. The first occurs in the discussion o f the allegorical method itself. In the garden we discover “ the plain and simple history, in the storeroom the moral sense, and in the bedchamber the secret o f the theoretical contemplation.” ®® Let us begin with historia, the garden:

... The garden is history, and in a threefold sense. For it contains in itself the creation of heaven and earth, the reconciliation and the restoration: the creation, so to speak, as the sowing or planting of the garden and the reconciliation as the growing of what has been sown or planted. For in its own time, when the heavens were producing moisture and the clouds pouring down rain, the earth opened and budded a saviour. Through him is brought about the reconciliation of heaven and earth... But the future restoration is at the end of time. For there will be a new heaven and a new earth, and the good will be collected in the midst of the evil, as the fruit from the garden, in order to be placed again in the storerooms of God lApoc 21:1].®®

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I f this statement is original in its poetry or in stressing the utopie, there is nothing new in points o f doctrine. In fact, it underlines the literal and orthodox. It is, so to speak, the foundation upon which a rather unusual structure is to be erected. Bernard lays the first stages by stating, immediately afterwards, that he has other equally valid names for these three stages o f history. They are discipline, nature and grace. Thus the three stages o f Biblical history are redefined as three essential aspects o f man’s everyday existence. An attempt is made to effect a union between the unidirectional and irreversible movement o f history and the desirable direction o f man’s life in the here and now. This union allows him to interrelate allegory and alienation, to bring together the potential remoteness o f the text and man’s active aspirations on earth. One o f the most highly scrutinized o f Biblical ideas is thus imaginatively retransformed into the primitive meaning it had for the Greek Fathers: it is an inspiration to active reform.

The union o f the abstract and the concrete, as elsewhere, is brought about by referring both to experience. Yet here the idea is deepened. What are the moral conditions, he asks, for structuring experience? This is his answer:

... I should call the first discipline, the second nature, the last grace. In the first... you learn that you are inferior, in the second, equal, in the last, superior... Thus by the first you learn to be a disciple, by the second a comrade, by the third a master. For nature brought forth all men equal. But since, after the good of nature was corrupted by pride of morals, men were made impatient of equality - contending to be raised above each other... [and] provoking each other - first and foremost in the primary storeroom the irregularity of morals must be restrained by discipline. Then the stubborn will, worn away by the hard daily laws of our superiors, is humbled and healed, and retrieves through obedience the good of itself in nature which it had lost through pride. During this time it will have learned to keep itself quiet, insofar as it can, by natural affectivity alone, not by the fear of discipline; [and] along with all the other comrades of its own nature, that is, with all men, socially, [it will] pass over to the cell of nature.’®

This statement should not be separated from the monastic milieu for which it is intended. However, even in its proper context, it reveals a psychology o f learning which interrelates nature, experience, and the external constraints which can presumably shape both. The most important element is the stress on man’s capacity to reshape himself in the present. It is thus that the will, mollified by discipline, acquires the type o f obedience which it had in Eden. And Bernard makes it clear that in perfect obedience man has very nearly re-acquired this lost state while he is on


earth. The restoration through grace, which is the long-range goal, is not forgotten, but it recedes somewhat from the center o f the stage as attention is focussed on day-to-day behavior, on the continuity o f one’s experience. Reconciliatio, for all intents and purposes, is described as the product o f discipline and obedience, o f active labour in the present. Through these, man is directed from a state o f pure discipline, in which the will is perfected, to that o f nature, o f complete harmony o f thought and action. By means o f obedience and discipline, moreover, man appropriates, or rather re- appropriates, nature to himself. The nature that was once his is re-acquired in slow, painful steps. And by controlling nature, man thus controls the inner psychological world essential for renewal. In assimilating a nature that was once interior, but now, through alienation, is exterior, man too, inevitably, renews both sides o f his character at once. Bernard even implies that man, in regaining control over nature, also, to some degree, subdues the hostile world outside himself. It is almost as if the taming o f the countryside, in which the Cistercians were involved, acted as an unconscious motivation for his choice o f images for man’s renewal o f himself.

These are ideas which Bernard develops in the rest o f Sermon 23. Continuing the trinitarian symbolism, he turns next to the meaning o f the three cellars. The first two contain spices and unguents. Spices, like discipline, must be pounded out with mortar and pestle ; unguents, like obedient nature, flow freely. Nature herself is a ‘storehouse’ o f good discipline. The ideal o f nature, moreover, is not a fixed principle like natural law, but rather the normative function towards which man must continually strive.’ The third cellar, which presupposes the other two, is the winecellar. It represents the practice o f charity, through which, as a sort o f mystical inebriation, man obtains a foretaste o f grace in this world.'^^

The core o f the sermon occurs in the next section, in which Bernard presents his allegory o f paradise, the state o f perfect s e l f - k n o w l e d g e . jh e text is the king’s bedchamber from the Song o f Songs. Just as the bridegroom has many unguents, so the king has many bedchambers. As would be expected, Bernard gives examples o f three. Each is presented as a modified version o f the rhetorical topos o f the locus amoenus, the standard technique employed by medieval authors for illustrating various kinds o f ideal states. Here is the first o f the three:

There is a place in the home of the bridegroom, from which the governor of the universe himself decides on his laws and distributes his counsels, appointing laws for every


creature, their weight, measure and number. This place is high and secret, but not at all peaceful. For although, insofar as he is able, [God] disposes everything sweetly [Sap 8:1], he does nonetheless dispose. Nor does he permit a contemplative, who may by chance have reached this place, to remain inactive, but marvelously and delightfully he tires out the investigator and admirer and renders him untranquil.’^

The first locus, then, is the home o f law, o f disciphne. But it is also the residing place o f continual activity. Bernard, it should be recalled, has already suggested that there is a relation between the discipline that informs conduct and the model held out before it. Here he makes the relationship between the internal and external forces more explicit. The paradise o f disciphne is not a place where law rules as an absolute; it is rather one in which legal and normative action function together. Although God gives his orders in an unequivocal manner, the ideal that is held out to man is a process, a constant interplay o f action, discipline, and further action. Bernard has turned around a traditional motif and presented an unpeaceful paradise in which the only sin is not activity but its opposite.

The second locus amoenus, that o f judgment and fear, is outlined in similar terms. Through it, one proceeds once again from discipline to obedience. One also has a complete picture o f the two sides o f human reform in his mind: that o f activity seeking to conquer lack o f discipline and that o f an external model which is to be internalized by man. The real importance o f the second locus however arises from the discussion which follows it. Here he compares his first two paradises, giving his reasons why the first must lead to the second:

Do not yourself be disturbed then that I have given the beginning of wisdom to the second locus rather than the first. For in the one, as in a lecture-hall, we hear Sapientia as a mistress who teaches all things; in the other we are receiving. In the one we are instructed, but in the other we are influenced. Instruction renders us learned, our state of mind, wise. The sun does not light all that it warms. Similarly wisdom, which teaches many what is to be done, does not always quicken them for doing it. It is one thing to know of many riches but another to possess them; and it is not the report which makes a man rich but the possession. By the same reasoning, just as it is one thing to know God, it is another to fear him: and it is not recognition which makes a man wise but fear which affects him. You would not call a man wise whom knowledge puffs up [1 Cor 8:1]... God has a taste for the soul first when he influences it for fearing, not when he instructs it for knowing; and so well [it is written]: ‘The beginning of wisdom is the fear of the lord’ [Ps 110:10]... What then is the first locus! It only prepares for wisdom. There you are prepared so that here you may begin. Preparation is the understanding of things.’®

This passage brings together a number o f themes relating experience, knowledge and action. The first locus, that o f law, o f discipline, corre

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sponds in Bernard’s mind to knowing God; it is the place o f scientia, cognitio. It is a preparation for the second locus, in which one passes from understanding in a cognitive sense to activity, and, by implication, to a new level o f comprehension which blends theory and practice, thought and action. In Bernard’s terms one passes from instructio to affectio. Affectio is not a concept; it is a state o f mind. It is the disposition towards the good action. In the second locus, as in the first, there is ceaseless activity, but they are o f different kinds. In the first it is the activity o f learning facts; in the second, o f applying them. Overlooking both is the omnipotence o f the ultimate law-giver and decision-maker.

Two important implications arise from this sermon. The first, already emphasized, is that, in order for a man, in Bernard’s terms, to attain wisdom, he must effectively balance theory and practice. He must pass from discipline to obedience, and, in doing so, he arrives at a foretaste o f grace. Grace remains a future state, but it is one for which there is a manifestation on earth. This manifestation is mystical, not only in the sense o f coming from above, but also because it is an active reworking or synthesis o f the two previous states. Thus one passes from discipline to nature, which assimilates discipline into obedience, and from there to grace, which assimilates both. Grace, then, as man experiences it on earth, is both the application o f discipline and the appropriation o f nature. It is praxis, the identity o f subject and object. Bernard refers to this locus, as would be expected, in mystical language.

The second implication concerns his conception o f God. God is not defined, as in the School o f Chartres, naturalistically as the creative architect o f the physical universe, but rather psychologically as the arranger o f the ideal plan o f living. This is another way o f stating that God’s relationship to the world and to man is not in terms o f cause and effect but means and ends. Bernard says in a passage quoted above: ‘You fear the justice o f God, you fear his judgment.’ These are moral not causal injunctions, Hebraic or Pauline rather than Greek or naturalistic. Precedents for them may be found in earlier monastic writings, but Bernard takes the tradition further than previous writers, not only in the rigor and asceticism o f his formulations, but in making specific man’s psychological nature. What Bernard does, in fact, is to present a psychological approach to the relation between God and man. The mediator between the two is experience, through which man, by actively ordering his exist

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ence, appropriates nature to himself and leads himself to the ideal blending o f theory and practice which anticipates grace. Grace is not only a mystical ideal; its futurity is made present in man’s overall capacity for decision-making. Bernard summarizes his view o f reform in a few words in Sermon lA, where he relates the idea o f daily renovation to experience:

, .And from the examination and refutation o f my hidden aflfairs, I have marvelled at the profundity o f God’s wisdom; and, insofar as possible, from the perfecting o f my morals, I have experienced the goodness o f his meekness; and from the reformation and renovation o f the spirit o f my mind, that is, o f the interior man o f me, I have received in one way or another the loveliness o f his beauty.”

V. p l a n n i n g ; t h e a c t i v e a n d c o n t e m p l a t i v e l i f e

An outline has now been presented o f Bernard’s notions o f experience, useful knowledge, and reform. It has been clear throughout that such ideas gain their significance from certain assumptions about the active and contemplative life. The mystical and pragmatic sides o f experience, the cognitive and activist functions o f knowledge and the union o f theory and practice, o f the inner and outer man, all, to some degree, derive their meaning from Bernard’s conception o f the ideal plan o f living, which interrelates the traditional values o f the active or contemplative life. Monastic- ism, o f course, had never advocated a purely theoretical existence. Early writers had for the most part taken up positions midway between the two extremes. It is not clear how much Bernard actually took from previous authors on the subject. As elsewhere, he seems to build a few commonplaces, known to all, into a new and original synthesis.

Bernard is fond o f introducing the theme by contrasting the two classical terms otium and negotium. The following statement is typical:

‘Sapientiam scribae in otio’ [cf. EccU 38:25]. Ergo sapientiae otia negotia sunt; et quo otiosior sapientia, eo exercitior in genere suo.’ ^

The wise man speaks o f ‘the wisdom o f the scribe in leisure.’ Therefore the leisure o f wisdom is a time o f activity; and the more leisured wisdom, the more occupied with its kind.

o b s e r v a t i o n s o n BERNARD OF CLAIRVAUX 247

Two points are apparent from the beginning. First, the question o f activity and inactivity is related to the written word. The mediator between otium and negotium is the hermeneutic value o f the text. A written rather than oral model is thus proposed for conduct, one which, presumably, can be both standardized and easily communicated. Moreover, the choice is not between the active and contemplative life. It is rather that man, using the word as a model, must somehow make action inform contemplation. Thus, once again, he suggests a type o f praxis which interrelates allegory and experience. The second major point is that the active life recommended is o f a special kind. It is not the pursuit o f activity for its own sake, which would be meaningless. It is a sort o f planning, a continual redirecting o f the mind. Its order is psychological, not material. In Sermon 46, Bernard cites Paul’s well-known statement from 2 Thessalonians 3:10, { ‘Qui non laborare non manducet’), but he relates the idea to Christ’s exile from heaven and to man’s spiritual salvation.'^^ Statements therefore about human work and labor in Bernard should not be artificially separated from their contexts. Again, in Sermon 47, he idealizes this special type o f activity in a beautiful metaphor, stating that “ the bed bestrewn with flowers is the conscience filled with good works.” In sum, the idea o f actus is more complicated than it would first appear.

There are two general themes which run through Bernard’s writings on the active and contemplative Hfe. One is the notion o f affective thought, {affectus), that is, o f thought directed towards action, and its relation to charity. The other is a more theoretical statement o f the relation between consideratio and contemplatio. O f the two, the latter is by far the best known. Yet it depends for its meaning almost entirely on the former.

The difference between affective and effective charity is the subject o f Sermon 50. The question is whether charity is to be considered as a disposition o f the mind or as completed works. The text is Song o f Songs 2:4, '‘Ordinavit in me caritatem.’’ Bernard summarizes his position as follows:

Charity exists in activity {actu) and in a state of mind (affectu)... The former is commanded for merit; the latter is given in reward. And I do not deny that in the present life we can through divine grace make a beginning and even some progress; but clearly, we defend [the position] that happiness is a consummation o f thef^uture. But how could those things be commanded which could not in any way be implemented?... It has not escaped the legislator that the burden of the legislation exceeds the strength of men; but he judged it useful that they be reminded of their insufficiency by this very matter, in order that they might know soundly that they ought to strive towards this end of justice in proportion to their pdwers...

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Moreover, if we were indeed convinced that a law pertaining to a state of mind had been given, I should afBrm it. But the statement seems rather to pertain to the active (actuali). This appears in particular when the lord said: ‘Love your enemies’ [Lc 6:27], soon adding, on the subject of works, ‘Do good to them that hate you.’ Likewise in Scripture: ‘If your enemy is hungry, give him to eat; if he is thirsty, give him to drink’ IRom 12:20]. Here again you have what concerns action {de actu), not a state of mind (de affectu). Listen still again to the lord as he gives the command concerning the love of himself: ‘If you love me’, he says, ‘keep my commandments’ [lo 14:15]. Once again we are directed towards works... For, as regards labor, his instruction would have been useless, if, at the time, his love had been in a state of mind.®®

The difference between affective and effective charity is o f course more complex than is evident from this quotation. Yet, in general, the distinction is aptly summarized in the previously discussed opposition o f thought and action. In Bernard’s mind actus is related to affectus. It is clear, again, that grace is not bestowed on man on earth; but he can while in exile make some progress if he takes as his goal a reworking o f the spirit which is not a passive emotional state but an active striving after charity. Affective charity, moreover, moves upward from man toward God; effective, from man to man. And if the one implies the other, it is nonetheless true that affective charity has a higher value in his mind. In relating man and God, affective charity also holds an important position in Bernard’s overall approach to belief. Above it was pointed out that functional knowledge is in his mind a partial answer to the problem o f uncertainty. Affective charity illustrates how this works. Charity, through action, is ordered and directed towards the future; it becomes a type o f applied decision-making in the service o f higher ideals. Uncertainty cannot ever be fully resolved, for grace is not guaranteed. But man, by using various methods for gaining control over the day-to-day direction o f his life, makes his goals clearer and thereby less uncertain to himself. In his doctrine o f charity, Bernard is stating once again that thought, i.e. effective charity, comes first, but that action, affective charity, must follow.

Charity, then, is a sort o f practical or practicable philosophy, and it may be useful, before turning to more complex matters, to give a concrete example o f what Bernard has in mind. Fortunately he has provided one himself. In Sermon 26, deviating from the formal texts o f the Song o f Songs, he devotes a few lines to his brother Gerard, who had recently died. In Bernard’s eyes, his brother was an ideal-type o f the perfect monk. Here, in part, is what he says :

1 OBSERVATIONS ON BERNARD OF CLAIRVAUX 249

But why have I spoken of him acting externally, as if Gerard was ignorant of internal matters and lacking in spiritual gifts?... His comrades knew how much his habits and desires did not savor of the flesh but rather grew fervent with the spirit. Who was more rigid in keeping discipline than he, who stricter in castigating his body, more suspended in contemplation, more subtle in disputation?... He was not acquainted with literature, but he possessed the sense of one who discovers letters: and he had an illuminating spirit. He did not reveal himself to be small in the greatest tasks but rather greatest in the smallest. In the buildings, fields, gardens, water-works, indeed, in all the skills and jobs of the peasants - was there anything, I say, in this kind of activity which would have escaped Gerard’s ability? With ease he was the master of the stone-masons, carpenters, gardeners, shoemakers and weavers. And as he was, in the judgment of all, wiser than all, in his own eyes he was not wise.®^

The ideal monk, in Bernard’s view, is the wise p e a s a n t , the master o f all the practical arts, and, most o f all, the practical art o f reforming himself. Had the topos o f docta ignorantia ever reached so low in the social order in the previous history o f the classical tradition?

The most significant elaboration o f the theme o f the active and contemplative life does not occur in the sermons on the Song o f Songs, but in the short treatise Bernard wrote for the first Cistercian pope, Eugene III, entitled De Consideratione. Amid a great deal o f practical advice, Bernard summarizes his most important thoughts on the question in the dichotomy between consideratio and contemplatio. For Cicero, as all classical authors, the two terms were virtual synonyms for reflective inquiry. Nor are they greatly developed in the patristic period. In Bernard, consideratio in particular, which is a rare word in classical Latin, takes on an entirely new dimension, one which cannot be understood without relation to contemplatio. A discussion o f the two terms is also the simplest bridge to Bernard’s conception o f spiritual and material goals, and through them, if somewhat indirectly, to the real world o f action o f which he was a part.

Let us begin once again with simple distinction. Near the beginning o f De Consideratione, Bernard states:

Si quod vivis et sapis totum das actioni, considerationi nihil, laudo te? In hoc non laudo.... Certe nec ipsi actioni expedit considerationi non praeveniri.®'^I f you give everything that gives you life and pleasure to activity and nothing to consideration, do I praise you ? I do not

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bestow praise for this..., Nor indeed is it expedient for activity itself not to be preceded by consideration.

Clearly there are two types o f activity, planned and unplanned, and only the first, which relates to future goals, has any value.

A little later in book one, Bernard leads the reader more deeply into the idea o f consideration. He is praising piety as man’s most valuable asset, and he says:

Do you ask what piety is? To take time for consideration. Perhaps you will say that in this I differ from him who defined piety as the worship of God. It is not so. If you reflect carefully, I have expressed his sense, although in part, by my words. For what is so pertinent to the worship of God as what he himself urges in the Psalm [45:11] : ‘Take time iyacaté) and see that I am God’ - which exists especially in the parts of consideration. Moreover, what is as efficacious for all things as the parts of this very activity. By its beneficent presumption he performs his own acts, prearranging and preordering in a certain manner what is to be done, lest those things which were able to be foreseen and premeditated by sound and clear necessity might rather be precipitated by trial...

For consideration purifies the very fountain, that is, mind, from which it arises. Then it governs affections, directs actions, corrects excesses, forms manners, ennobles and orders life, and finally confers the knowledge (scientia) of divine as well as human affairs. It is [consideration] which confines what is disordered, closes what is opened, explores secrets, tracks down truths, examines the resemblances of the truth, and reveals what is counterfeit or dyed. Consideration is what preorders what is to be done and recogitates what has been done, so that nothing remains in the mind either uncorrected or wanting correction.*^

Chapter seven, from which this passage is quoted, is rhetorically constructed around the use and reuse o f a few central terms : pietas, consideratio, actio, the Pauline phrase ad omnia valens", and some terms for futurity like praevisa, praemeditata and praesentire. The initial question is simply, ‘what is essential for piety?’ Bernard is recalling the words o f Paul in 1 Timothy 4:7-9:

Ineptas autem et aniles fabulas devita; exerce autem teipsum ad pietatem. Nam corporalis exercitatio ad modicum utilis est; pietas autem ad omnia utilis est, promissionem habens vitae quae nunc est et futurae.Avoid moreover improper tales, fit for old women, and train yourself for piety. For bodily exercise is useful in a limited way ; but piety is useful for everything, since it holds promise not only for the life which now exists but also for that which is to come.


Paul makes two related statements, both modified by Bernard. First he says that one should practice piety above all; then he adds that piety is useful for all things, not only in this life but in the life to come. Bernard, in his discussion o f consideratio, makes reference to both o f these ideas, but changes them somewhat. As in Paul, the emphasis is on the practical achievement o f the good life, but Bernard, in consideratio, refers to only a part (licet ex parte) o f the whole. Paul, moreover, refers to the future in apocalyptic terms. Bernard, after all, is giving advice to a pope on how to plan his daily life. Paul therefore does not discuss the manner in which life may be structured in order, so far as possible, to insure future reward. Grace, in his mind, is a visionary, miraculous, supernatural event. Within Bernard’s thought, as we have noted, grace is also a gift o f God, but emphasis is placed on the foreordering o f conduct in this world. And from the analysis o f conduct in this world, Bernard infers certain aspects o f the conduct o f God directed downwards towards the world.

His point o f departure is ratio. What does “ irrefragable reason” show? That what is most valuable and potent for the future is pietas. The futurity o f Bernard’s interest is clear from the gerundives proferendam, collendam, and later, agenda. What then is piety? To have time for consideration {vacare considerationi), to have time for reflection upon experience directed towards the future, in short, to have time for planning. A t Job 28:28 in Bernard’s version o f the Vulgate, piety was defined as cultum Dei. But Bernard, as he states, interprets this in a special sense. The Psalmist says : ‘ Vacate et videte quoniam ego sum deus' [45:11]. In the use o f vacare, Bernard intends ‘to have time for reflection directed towards future goals.’ That, in effect, is what consideration is. For what, he adds, is so powerful as to do all things {quid... ad omnia valens [I Tim 4:8]), as the beneficent goodwill through which he performs all that is to be done : for he does this by bringing it about ahead and by ordering it ahead {praeagendo et praeordinando). I f God did not do this by clear necessity, what is foreseen and premeditated might fall to chance.

This statement must not be interpreted merely as a repetition, in rhetorical language, o f the classic Christian defence o f free will. It does o f course defend that thesis. But it does so within a framework o f everyday planning. To the question, how should a pope plan for the future, Bernard replies, by the imitation o f those divine actions by which God himself preordains what is to be done. God here is not a mathematician or an architect ;

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he too is a planner. Bernard may even be guilty o f seeing God in the image o f man as the perfect planner. He has, in a sense, utilized Scripture for legitimizing consideratio.

The first book o f De Consideratione, then, introduces the subject o f planning in significant depth. The other books refine and amplify the notion. Before turning to the other examples o f consideration, it may be useful to introduce the well-known contrast Bernard himself offers between consideratio and contemplatio. The initial distinction is made in book two, where he states;

First then, consider what I mean by the term consideratio. For I do not wish it to be understood as contemplation in all cases, since the former is concerned with the certitude of things, the latter rather with their investigation {inquisitio). According to this sense, contemplation can be defined as the true and certain intuition of the mind {intuitus animi) concerning any object whatever, or the apprehension without certainty of a truth, but consideration as the intense deliberation for the investigation of truth, or the exertion of the mind investigating truth. At the same time, it is customary for each to be used for the benefit of the other.®®

Bernard is here contrasting not aspects o f truth but ways o f approaching it. Contemplatio is intuitus. It is a process o f reasoning from cause to effect ; it is thought considered as thought alone, abstracted and detached from the process which has brought it about. Consideratio is intensio. It represents the activity o f the mind as it goes about its search for truth. Contemplatio represents the completion o f a system of thinking, whether it results in truth or just in a probability. Consideratio is the method o f deliberation, the exertion o f man’s problem-solving capacities. Contemplation may therefore be placed in the category o f thought divorced from action, consideration in the category o f dialectical reasoning, since, at every stage in the latter, thought must be guided by action and vice versa. Thus, although they are complementary, consideration and contemplation represent methods for different sorts o f sciences. Contemplation is reserved essentially for pure sciences; consideration for applied ones.

Like experience, knowledge, and reform, however, consideration has both a pragmatic and a mystical side. It has an earthly appUcation, in teaching the pope how to spend his time effectively, and a celestial one, in aiding the mind to rise above earthly cares. Bernard turns to these refinements in book five. In the following quotation he divides consideration into three types and indicates how it may help man ascend to the


divine. He also unites, through a series o f interlinked metaphors, his previous thinking on experience and knowledge:

Great is he who is content to measure out the experience of the senses, spending it, like the wealth of the citizens [of heaven], for his own and many others’ salvation. Nor is he less great who, in philosophizing, establishes this for himself as a step towards those invisible goals... But best of all is he who, having spurned the very experience of things and of the senses, insofar as it is permitted to human fragility, has formed the habit of flying aloft to those sublime heights from time to time through contemplation: not through ascending steps but through unexpected departures. I think those departures of Paul belong to the last kind... Moreover the three are attained as follows: when consideration, although in the place of its wandering, rises up through the desire of virtue and the assistance of grace, and either represses the appeal of the senses... or keeps it within bounds... or flees...

Do you wish to distinguish these species of consideration by their own names? If it please you, let us call the first distributive {dispensativam), the second estimative {aesti- mativani), the third speculative {speculativam). Definitions will illustrate the meanings of these terms. Distributive consideration is using the senses and sensible things in an orderly and sociable way for deserving God. Estimative consideration is scrutinizing and pondering those same things prudently and diligently for inquiring into God. Speculative consideration is collecting them in themselves, and, insofar as divine assistance is available, removing human matters in order to contemplate God. You note clearly, I think, that the last is the fruit of the others, and that the other two, if they are not referred to it, are not what they are said to seem to be...®'

Although the matter must be stated most tentatively, has not Bernard here presented the paradigm o f a simple social science? The three stages o f consideration represent the experience o f the senses or o f sensible things, organizing the impressions into a coherent whole, and evolving empirical generalizations based upon the data. What distinguishes this primitive social or applied science from a pure science is the third stage, which depends upon the other two. Bernard does not propose that an abstract or inductive model be imposed on experience ; he suggests that a model, if it is to have any validity, must continually be verified by the data o f experience.

Within the paradigm, other sorts o f relations are also indicated. The purpose o f consideration, first o f all, is spiritual, not material. The end o f planning is salvation. Secondly, the three stages correspond to the distinctions outlined above between discipline, nature, and grace. Thus it rephrases and presents in a more philosophical manner the pragmatic advice o f the sermons. Thirdly, the three stages are related, as elsewhere, to the three steps a man takes in his personal, sensorial awareness o f the world. At the end o f the above quotation Bernard states: “ Therefore the first desires, the second smells, and the third tastes.” Lastly, contemplatio.

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which Bernard, later in book five, subdivides into four types, is related to consideratio just as, earlier, thought is to action. Historians have sometimes wished to detach the notion o f contemplation from the real world and to present it as a pure idea. It is rather a generalization from a series o f empirical steps.

Consideration, then, may be described as a type o f problem solving, decision-making, or planning. It provides a simple and unsophisticated model o f how to improve the managerial skills o f the head o f a large complex organization. Elsewhere in De Consideratione, Bernard elaborates other aspects o f consideration, nowhere altering the overall thesis but presenting new and different sides. As in his sermons, it would be inaccurate to suggest that his observations form a consistent body o f theory; but it would be unjust to ignore the self-conscious design in his way o f thinking. On one occasion he suggests that man, as perceiver and decision-maker in his own moral universe achieves praxis by interrelating subject and object. He also makes it clear that consideration is the only type o f knowledge that can rescue man from his present state o f alienation and start him on the pathway to salvation. On the same occasion he summarizes his views on the useless or irrational pursuit o f knowledge in a brilliant statement relating reminiscence, alienation, and progress : “ Hence it is that men, alienated from themselves through oblivion, migrate through empty anxiety to other worlds which are not going to be o f use to them, indeed, which are not even going to be.” »8 There is also a whole series o f practical hints for the pope on issues like appeals to the papal court.»® Far from a philosophy, consideratio appears throughout with a sense o f immediacy, commonsense, and experiential relevance.

VI. c o n c l u s i o n : a c i s t e r c i a n c o n t r a d i c t i o n ?

The paradox o f Cistercian life and thought has recently been summarized as follows by Georges Duby:

Because they had refused to live from rents, because they had decided to draw their sustenance from the ground by their own labor, because they had chosen to instal themselves in solitude in the midst of pasture and forest, these communities found themselves established in spite of themselves, and, in accordance with the model they had incautiously taken as a rule of conduct (règle de conduite), in the avant-garde of the dominant economic system, in a position to produce in abundance the commodities that they did not consume themselves - wool, meat, iron and wood - which could be

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marketed better and better. Through a sort of ironic revenge on the part of the economy, these apostles of penury became rich. Doubtless, in the isolation in which they lived, they remained faithful to their ideal. But in the eyes of those who only saw them negotiating at the fairs, or, by successful overbidding, rounding out their heritage at the expense of their neighbors, in the eyes of those who, during this century, in the very bosom of a growing prosperity, supported all the worse that men of God were not, by way of compensation, really poor, the Cistercians ceased little by little to incarnate spiritual perfection; the same reverence was directed towards others, who went barefoot through the poorer parts of the towns, dressed in sackcloth, and who possessed nothing.®°

What Weber, writing over a half-century ago, called the monastic Lebensfiihrung, Duby, summarizing historical insights born in the same period, refers to as the règle de conduite. Thus, from different perspectives and with different aims, the sociologist and the historian are united in a common problem area. For many years, instead o f pursuing Weber’s genuine discoveries, debate centered on a single issue: whether economic events had a psychological determination, or whether, as Marxist critics o f Weber maintained, religious values were merely a superstructure o f economic and social change. Both views, as extremes are attempts to oversimplify a very complex phenomenon. Bernard’s notions o f experience, the functions o f knowledge, reform through praxis, work and planning, are not reducible to economic or social changes. They are rather the product o f a mind consciously reflecting on cultural values in a period o f change, which is quite a different matter. Yet they are clearly preceded by technological and material improvements which provoke a crisis o f inherited values, and they must not be artificially separated from their historical context. For idea-complexes as powerful as Bernard’s philosophy o f action, once articulated and institutionalized, have an internal life o f their own. They create a psycho-sociological ideal for lesser men to imitate. Few o f Bernard’s followers were capable o f his flights o f mysticism, but many could attempt to put his ideas into practice as they went about their everyday lives. And thus his thoughts, in part, could be translated into action.

In at least two areas Bernard’s ideas come close to reality. One is his doctrine o f the just war. In his eyes, where the cause was just, armed conflict was a legitimate side o f Christian expansion.® His letter to the templars uses the same phrases to describe the holy war as do other treatises to outline the stages by which a monk may achieve spiritual perfection.®^ The templar, he states, must observe all the ascetic principles o f other

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Cistercians. He must come and go at the order o f his chief, dress himself in what is given him, and presume to wear no other clothing. He must live in common with the other knights neither with wives nor other women. In order to attain evangelical perfection, he must live entirely without personal property. Like the monk, he must be o f one heart and one soul with the other members o f his community; his only desire must be to give allegiance with a free will. A t no time must he be otiosus or curiosus\ and on those rare occasions when he is not on the march, lest he should enjoy his bread without first working for it, he should repair his armor or the rents in his clothing, replace worn out equipment, reorganize what has become disordered, and, in general, serve community interests. Only rarely is a guest to be received; and when he is, the rule is "‘‘defertur meliori, non nobiliori.’’’’ Each knight should bear the other’s burdens, and each should try to outstrip his comrade in the rigor o f his service and the pursuit o f honor. The insolent word, the useless activity, the immoderate laugh, and even the hushed whisper are to be avoided. Games and dicing are forbidden along with hunting. Mimes, magicians, and tellers o f tales, together with risqué songs and the performance o f plays, are to be regarded as truthless forms o f madness. Hair must be cut short. In his choice o f horse, the templar like the cathedral builder, must studiously avoid ornament. His horse should be plain, but strong and swift. In battle he should not be impetuous, but like his Biblical ancestors, cautious, orderly and well organized. Although few in number, he must attack ferociously. The ideal templar, in short, must possess both the monachi mansuetudo and the militis fortitudo. Above all, he must beware, like the monk, o f yielding to vice, neither in exulting victory nor taking pride in killing. But he may, at the same time, possess a pure conscience, since, if victorious, he will further Christianity on earth, and if slain, will insure his own salvation in heaven.

A second area o f contact with reality occurred in his previously mentioned treatise o f counsel to Eugene III, De Consideratione. Here he not only touched upon the problems o f running a large bureaucracy, but also raised the moral question o f its involvement in the real world. How was the pope to use the world without using it? Differing from earlier monastic theorists and from critics in his own time like Joachim o f Flora, Bernard asserted that the Church’s essential mission lay in this world; only by fulfilling it could Christians insure their reward in the next. He expanded


the practical advice which he presented more rhetorically in the sermons, and made a notable attempt to give a logical structure to his thoughts. Typical is the following statement from book two:

We cannot deny that you have been raised up, but the reason is a subject for careful deliberation. Not, I think, for governing. For when the prophet was similarly raised up, he heard: ‘...in order to root up and to pull down, to lay waste and to destroy, to build and to plant’ [Jer 1:10]. What sounds like arrogance in this? Rather, in the metaphor of the peasant’s sweat, a spiritual labor is expressed...

Learn by the example of the prophet to be raised up not so much for giving orders as for practicing what the time requires. Learn that your work is with the hoe, not with the scepter, if you would do the work of the prophet. And to be sure he did not ascend in order to reign but in order to root out. Do you not think that you will find some labor to perform in the field of your lord? Indeed, much. Truly the prophets did not cleanse everything. They left something to be done by their sons, the apostles, and those relatives of yours something for you. Nor shall you be sufficient for everything. When you are done you will leave something to your successor, he to others, and others to others to the end of time. For this reason the laborers are reproved for idleness at the eleventh hour and sent to work in the vineyard [Matt 20:6-7]. Your predecessors, the apostles, heard that ‘the harvest is indeed great but the laborers few’ [Matt 9:37]. Claim for yourself your paternal inheritance. For, ‘if a son, also an heir’ [Gal 4:7].In order to prove your inheritance, awaken to responsibility; and do not waste your time in inactivity, lest it be said of you: ‘Why does he stand here the whole day idle’ [Matt 20:6].94

Bernard is here speaking o f spiritualis labor, and he places it in the context o f an historical inheritance from the prophets and apostles, an inheritance descended from the original ruin o f Jerusalem. The first sowing was in Eden, and the prophets, inheriting the labor undone, there both destroyed and recreated in order to sow anew. Like the Cistercians, in whose image they are now recreated, they rooted out the forests, cleared, and replanted. They achieved their ends not by focussing on intellectual utopias, but “ by practicing what the time requires.” This is what is meant by taking time, in the larger sense, for consideration, for proper decisionmaking, for planning. The prophets labored well, but they left something for the apostles, who, along with their predecessors, left something for the present age. Bernard focusses on the present, not like Augustine, to indicate a crushing debt from which man can only be released at the end o f time, but rather to indicate that progress, which has both a material and a non- material side, is a matter o f perpetual labor. I f one’s eye is fixed on the distant future, one’s hand is nonetheless bound to present servitude.

What is man bequeathed? Cura et opera. What must he avoid? Otium. How must he do this? Utens illis quasi non utens. The familiar phrases occur

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again and again. In book two o f De Consideratione, a single passage o f rare power and eloquence summarizes the doctrine o f spiritual progress which transforms the world:

Go out into the field of your lord and consider how much, even today, it runs wild with thistles and thorns from the ancient curse. Go out, I say, into the world. For the world is the field, and it has been entrusted to you. Go out into it, not as lord, but as steward, to look after it and take care of it, whence a reckoning shall be demanded of you. Go out,I repeat, with your feet of intense sollicitude and sollicitous intention. For even those who are commanded to go around the whole world [Mk 16:15] do not circuit the globe in their present body but in the providence of the mind. You, as well, raise the very eyes of your consideration and look out over the lands; see whether they are not rather dry for fire than white for harvest [lo 14:35]. How many lands, thought to be fruit- bearing, on close inspection, turn out to be brambles. Indeed, not even brambles. They are old and lifeless trees, either bearing no fruit at all or the kernels of husks, which pigs eat. How long will they occupy the land? If you go forth and see such things, will you not be ashamed that the axe is lying idle? Will you not be ashamed that you accepted the apostolic sickle with no end in view?

Long ago Isaac the patriarch went out into this field, when first Rebecca appeared before him; and, as the Bible says, he went forth meditating [Gen 24:63]. It is necessary that you go forth, not as he, for meditating, but for exstirpating. Meditation ought by now to have preceded you: it is time to act ‘for our hands’ [cf. Ps 118:126]. If you begin to hesitate now, you will do so later. Before, according to the counsel of the saviour, you ought to have sat down, estimated the work, measured your powers, weighed your wisdom, counted up our merits, computed the costs of virtues. Act therefore: think that ‘the time of pruning’ [Cant 2:12] is come, that the time of meditation has gone before. If you move your heart, your tongue is now to be moved and your hand s to be moved. Gird your sword, the sword of the spirit, which is the word of God. Glorify your hand and your right arm ‘to wreak vengeance on the nations and chastisement on the peoples, to bind their kings in chains, and their nobles with fetters of iron’ [Ps 149:7-8]... For it is a sin for you to know and not to act...®®

These lines summarize the fundamental ambivalence o f Bernard’s philosophy o f action. They achieve their profound effect through a series o f bald antitheses: in the first lines, in the contrast between the field, open for cultivation, and consideratio, man’s reflection on what is to be done; later, in the contrast between the spiritual and the physical voyage, also symbolized in the good and bad harvest, the fruit-bearing and the lifeless trees; lastly, in the two-sided image o f the sword o f the spirit, with its implications o f putting the word o f God into action. Consciously or unconsciously Bernard has summed up the tension in Cistercianism between spiritual values and material change. It was a tension, o f course, which he felt deeply and sincerely; but in the minds o f others, it could easily serve as a legitimation o f expansion, o f peaceful and unpeaceful colonization. The images are all sudden, abrupt and somewhat arbitrary, juxtaposing


conversion, settlement, the opening o f frontiers and the confrontation o f enemies. And as the images are violent, the message is direct and unequivocal. He urges the pope: “ ejc/ . . .et consideras.Go forth, he says, not as Paul, into the realm o f the spirit, but into the world: “ ex/, inquam, in mundum.” He ironically places side by side expressions o f spiritual barrenness and physical cultivation, the otiosa securis, the idle axe and the apostolica falcis, the apostolic sickle. In such statements Bernard cannot be considered only a mystic and theologian; he is a philosopher o f action, even a social planner, who sees man laboring in this world so that he may, in part, "ruinas Jerusalem restaurarent.” ^

The Pontifical Institute o f Mediaeval Studies, Toronto and Centre fo r Medieval Studies. University of Toronto

N O T E S

* This essay forms part of a study of religious values and economic changes in the medieval West which has been undertaken with the support of a Senior Killam Research Fellowship of the Canada Council. The translations from foreign languages, including Latin, are the author’s own.1 Die protestantische Ethik und der Geist des Kapitalismus, in Johannes Winckelmann, ed.. M ax Weber. Die protestantische Ethik I. Eine Aufsatzsammlung, 3rd ed., Hamburg, 1973, pp. 134-35.2 See in particular Wirtschaft und Gesellschaft. Grmdriss der verstehenden Soziologie, 5th ed., ed. Johannes Winckelmann, Tübingen, 1972, pp. 695-97 {=Economy and Society. An Outline o f Interpretive Sociology, ed. Guenther Roth and Claus Wittich, New York, 1968, vol. 3, pp. 1168-70). Weber’s other statements on monasticism are conveniently listed in the index to the English translation.3 S. N . Eisenstadt, ed.. The Protestant Ethic and Modernization. A Comparative View, New York, 1968, p. 3. But see Lynn White, Jr., ‘What Accelerated Technological Progress in the Western

Middle Ages?’ in A, C. Crombie, ed.. Scientific Change... Symposium on the History o f Science, University o f Oxford 9-15 July 1961, London, 1963, pp. 286-90, and ‘Cultural Climates and Technological Advance in the Middle Ages’, Viator 2 (1971). 186-93.® In addition to the volume by Eisenstadt, historical material relating to Weber’s thesis will be found in the bibliography of Benjamin Nelson, The Idea o f Usury. From Tribal Brotherhood to Universal Otherhood, 2nd ed., Chicago, 1969, pp. 161- T i l , and in David Little, Religion. Order, and Law. A Study in Pre-Revolutionary England, New York, 1969, pp. 226-37.* Eisenstadt, The Protestant Ethic..., pp. 4-8.’ Protestantische Ethik, ed, Winckelmann, p. 67; “ ...sie ist die unentbehrliche Natur- grundlage des Glaubenslebens, sittlich an sich indiflFerent wie Essen und Trinken.”8 Ibid., p. 132.» Ibid., p. 169.

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The Social Teaching o f the Christian Churches, New York, 1930, vol. 1, pp. 241-43. On Troeltsch’s relation to Weber, see Carlo Antoni, From History to Sociology, trans. H. White, Detroit, 1959, pp. 62-70. The study of Max Weber in this volume, although overlooked by the sociologists, is one of the most useful that has appeared; on the Protestant ethic, see pp. 147-61.

There is a single reference to St. Bernard; Religion and the Rise o f Capitalism, London, 1936, p. 29.

Aspects o f the Rise o f Economic Individualism. A Criticism o f M ax Weber and his School, Cambridge, 1933, pp. 6, 21, 117.

Historical work on the sociology of science is summarized by Eisenstadt, p. 40, n. 25. This is the chief imperfection of Gilson’s attempt to expose the ‘systematics’ of

Bernard’s thought; La théologie mystique de saint Bernard, Paris, 1934. cf. J. Monroux, L ’expérience chrétienne, Dijon, 1952.Sermones super Cantica Canticorum, éd., J. Leclercq, C. H. Talbot and H. M. Rochais

{S. Bernardi Opera, 1-2), Rome, 1957-58; Sermon 74.2.7. References to Bernard’s works are all from this edition and are cited by number.17 17.2.4.18 56.1.119 69.1.120 51.2.321 11.1.2 22 22.1.223 36.4.624 44.1.125 48.1.126 84.1.727 1.5.1028 1.6.1129 cf. 22.2.4; ''sentiri... et experiri.""30 cf. 3.1.131 4.1.132 5.1.133 5.1.334 5.1.335 5.1.5-6 3« 5.2.837 cf. C. Bodard, ‘La Bible, expression d’une expérience religieuse chez S. Bernard’, Analecta Sacri Ordinis Cisterciencis 9 (1953), 24-45.38 16.1.139 29.2.340 49.2.541 36.1.142 36.1.243 47.1.244 36.1.245 36.2.3-3.346 36.3.447 36.4.548 36.4.6


49 cf. E. Gilson, ‘Regio Dissimilitudinis de Platon à Saint Bernard de Clairvaux’, Mediaeval Studies 9 (1947), 108-30.50 In Vigilia Nativitatis Sermo 3.2 {Opera, vol. 4).51 Ibid.52 Ibid.53 3.354 Ibid.55 3.4 6« Ibid.57 Ibid.58 3.559 Ibid.60 Ibid.61 3.662 Ibid.63 Ibid.64 Ibid.65 In Cantica 25.A.166 82.2.267 17.4.868 23.2.369 23.2.470 23.3.671 23.3.772 23.3.873 23.4.974 23.4.1175 23.5.1476 74.2.677 85.3.878 46.2.579 47.1.280 50.1.2-381 26.5.782 Ibid., rusticus', cf. In Adventu Sermo 6.83 Acad., 2.41.12784 De Consideratione 1.5.6 (Opera, vol. 3.)85 1.8.886 2.2.587 5.2.3^88 2.10.1989 3.4.14; 4.6.1790 Des sociétés médiévales. Leçon inaugurale, Collège de France..., Paris, 1971, pp. 16-17. This view has recently been given an empirical foundation. See Richard Roehl, ‘Plan and Reality in a Medieval Monastic Economy; the Cistercians’, Studies in Medieval and Renaissance History 9 (1972), 83-113.91 Liber ad Milites Templi de Laude Novae Militiae 1.2.16 (Opera, vol. 3).92 This and the following details are drawn from the same book, 4.7.93 1.2

262 B. STOCK

De Consideratione 2.6.985 2.6.12

In Adventu 1.5

D IS C U S S IO N

B. stock ; My paper, which is incomplete and provisional, is primarily intended to be a point of departure for discussing some larger issues. They are both specific issues in medieval cultural development, and, I would argue, raise more general questions in the history of ideas, particularly in the history of science.

To date, it seems to me, with rare exceptions, the history of medieval science has explained change in one of two ways: by simply cataloguing scientific discoveries or inventions, or by utilizing the philological method, that is, by relating ideas to other ideas. I do not wish to belittle work of this kind, merely to make two observations on it. First, it is slowly growing out of touch with other currents of intellectual history, which, while not necessarily abandoning philological methods - 1 would stress that - are gradually augmenting them with more flexible tools of analysis. The new tools are offering more plausible explanations of change because they take account of mutations in material culture, that is, of economic and social transformations. Perhaps I may state this another way by saying that there is nothing wrong with the old teclmiques within their own frame of reference. The trouble is that the frame of reference is too small. In the history of science what is being explained by and large is change among a small group of literate people. Nothing is being said about the effects of change on larger groups. More specifically, in the period between the late eleventh and mid-fourteenth century, when a scientific rationality re-emerged in the West, we are not asking why large masses of people so fundamentally altered their views of reality.

How could one go about doing this? There is at least one method that cannot any longer be followed; a crude sociology of knowledge. The discussion of Rashed’s paper brought up a very important point, that one cannot reduce an abstract science to economic or social forces. The vulgar Marxist view, which sees in all idea-systems only the superstructures of economic and social factors, is not much use to the historian. But the retreat into a world of pure ideas, a frequent response, is perhaps just as bad. What became clear to me was that if I wanted to explain just some of these widespread changes, I had to abandon ideas of a theoretical nature, which have an internal development of their own. I had to deal with notions that were closer to the real fabric of life. In other words, after this roundabout route, I came to a conclusion which should have been obvious to me from the beginning; in order to write a concrete social history of ideas, one has to deal with ideas that have a concrete social history.

If we look at the period from the eleventh to the fourteenth century in terms of this problem orientation, I would argue that two questions have to be faced from the beginning. The first concerns techniques of communication. What were the techniques which aff'ected the spread of literacy and what is the relation between written culture and economic development? This is a fundamental problem in two respects. Unless facts are communicated, influence is impossible to determine. And the written, as opposed to the oral culture, anthropologists now know, imposes upon its members a certain kind of representation or externalization. In other words, when people adopt the norms of the written culture, they also adopt to some degree its processes of conceptualization, and, in an economic sense, its rules for decision-making.


The second question is very different; Is there a relation between religious values and economic or social change, and, if so, what is it? Why religion? For an obvious reason. In the Middle Ages, as in many countries right down to the Industrial Revolution, what one may call the ideal plan of living was almost always expressed in religious terms. In the light of recent anthropological field work, one may, I think, make this statement without appearing too reverently Weberian. In any traditional society there are a number of ways of facing uncertainty - by magic, witchcraft, folk medicine, miracles, or popular eschatology. By all these routes we are led back to religion. Moreover, by religion I do not mean theology, the systematization of its concepts, but rather the ideas that influenced religious movements, movements that have no meaning outside the economic and social context in which they arise. Now it seems to me that a study of this kind has some distinct advantages over a crude sociology of knowledge. First, its theoretical structure is fairly loose. It is what Merton would call a middle-range theory, and it can easily be adapted to historical situations. Secondly, there is plenty of evidence that there is some inter-relation. Thirdly, one does not need to go beyond the evidence and impose a pattern on events. The actors speak for themselves.

Let me summarize. There was a time when the only history was that of lords and lawmakers. Nowadays there is also a history of the people who shaped events from below. Similarly, intellectual history used to be concerned with big ideas alone, and now it has started looking at little ones. It is perhaps time that the history of science did the same. By its very nature the field will always have a large number of purely theoretical issues. But there is also a social history of medieval science.

T. GREGORY; M. Stock vient de souligner la méthodologie générale de son rapport. Je crois que l’exigence qu’il a posée est très juste; il faut poursuivre des recherches qui tentent d’établir des rapports entre certains mouvements d’idées et certains facteurs sociaux et économiques. Pour ma part, je me permettrai de soulever quelques doutes, de discuter de la possibilité d’établir des rapports directs entre certains textes de Bernard et certains des événements de l’économie de son temps et aussi de la réforme qu’il va développer au Xlle siècle.

M. Stock souligne, par exemple, la formule bernardienne utentes hoc mundo tanquam non utentes, et il établit un rapport entre cette formule et les textes de Bernard sur le thème de instrumentum corporis, nécessaire au développement spirituel de l’homme. Nous sommes ici en face de problèmes très importants. Mais je voudrais souligner que le thème de corporis instrumentum est lié à un discours plus large sur la nécessité du corps pour tous les esprits créés, et donc est utilisé par Bernard pour mieux souligner la difl’érence radicale entre les esprits créés et Dieu. Dans le texte de Bernard, la cor- poréité est la limite de la créature. La formule utentes tanquam non utentes est alors toujours liée à une perspective spirituelle ultra-mondaine. Parler d’une théologie du travail à propos de ces textes n’est peut-être pas très clarifiant, d’autant plus que l’expression même “théologie du travail” est en elle-même équivoque et recouvre des significations très différentes entre elles. On peut parler de théologie du travail à propos du récit biblique selon lequel Adam est condamné à travailler dans les champs conune à l’occasion de la justification théologique des prêtres-ouvriers. Il est, je crois, diflBcilede trouver chez Bernard de Clairvaux sur ce problème, une position originale et nouvelle dans son siècle si nous voulons éviter de moderniser sa position. Il faudrait encore éclaircir dans quelle mesure et où dans les écrits de S. Bernard on peut retrouver quelque référence à la réforme cistercienne touchant le travail dans les champs, la bonification des terres et l’exploitation des terres en friche. Je me demande, M. Stock, si chez Bernard le travail des moines, des conversi, dans les terres en friche a jamais été loué aussi

264 B. STOCK

fortement que la congrégation des templiers. J’ai l’impression que S. Bernard s’intéresse plus aux templiers qu’à la réforme et à la bonification des terres.

D ’autre part, il conviendrait de mettre en rapport la position de Bernard de Clair- vaux avec les autres ambiants de la vie monastique. Je pense à la célébration de la dignitas hominis etiam secundum corpus de Godefroid de Saint-Victor ou à la louange des arts mécaniques chez Hugues de Saint-Victor. En réalité, je crois qu’il est difficile de trouver chez Bernard une évaluation positive des réalités terrestres au delà de la traditionnelle contemplation religieuse du cosmos.

Enfin il est utile d’examiner de près un lieu des Sermones in cantica, souligné justement par mon ami Stock, en ce qui concerne la période entre nous et la fin du monde. Stock dit en passant que les problèmes éschatologiques restent en deuxième plan et que par contre apparaît au premier plan le problème de la réforme de l’homme dans sa vie terrestre. Il a raison. Mais je me demande si on peut amplifier ces considérations et dire qu’à l’intérieur de la spiritualité cistercienne de Bernard la tension éschatologique va diminuer en même temps que va augmenter l’attention pour la réforme de l’homme aujourd’hui sur la terre. On peut se demander dans quelle mesure la chute de la tension éschatologique dans la spiritualité monastique du Xlle siècle comporte une évaluation des réalités terrestres, et dans quelle mesure les ordres monastiques favorisent la chute de cette tension au profit d’un engagement au travail dans ce monde, et encore dans quelle mesure cette chute au Xlle siècle dans les ordres monastiques peut être mise en rapport avec la reprise polémique au XlIIe siècle de la tension éschatologique, a l’intérieur de rOrdre de S. François. On ne peut pas ignorer les rapports entre les problèmes de l’éschatologie et la modification profonde des conditions politiques, économiques, écclésiastiques. Dans les textes que M. Stock utilise la perspective, l’optique éschatologique de Bernard semble en réalité extrêmement mince et laisse seulement à l’homme la tache de suppléer aux ruines de la Jérusalem céleste. On profiterait à mettre en rapport la tension éschatologique, la réforme individuelle et la réforme de la communauté des croyants.

Ce sont là des problèmes qu’on doit se poser en lisant les pages de Stock. Il souligne la dimension sociale dans certaines thématiques de Bernard. Mais le doute demeure devant son affirmation que nous avons ici un modèle des sciences sociales. Il faudrait approfondir et voir de près ce problème. Je crois que cette thématique n’intéresse pas Bernard de Clairvaux, qui est surtout lié à des perspectives mystiques. Sans doute on ne doit pas toujours donner une signification purement mystique, allégorique aux textes de Bernard. Mais, il faut reconnaître qu’il est très difficile d’éloigner Bernard de son côté monastique et mystique.

M.-Th. d ’ALVERNY: Comme M. Gregory, je pense que vous avez diminué exagérément le côté tout de même obvious du sens spirituel et mystique des Sermons sur le Cantique. Ce que je vous reprocherais un peu ce sont vos traductions; elles sont, dirions-nous en français, “orientéer Traduire, par exemple, affectus par state o f mind, me paraît faible, mon cher ami. V affectus, en language mystique, c’est autre chose. Quant à Vexcessus mentis, c’est l’extase dans tous les traités du Xlle siècle, et même avant et après. Dire simplement departures n’est pas assez. Vous avez parlé de notre bon Bernard sans rappeler qu’il y a aussi Guillaume de Saint-Thierry, qu’il y a aussi le vocabulaire de Hugues de Saint-Victor, exactement son contemporain; c’est le vocabulaire du langage des spiritualités, du langage des mystiques.

B. STOCK ; Oui, mais celui qui étudie S. Bernard se trouve en face d’une véritable masse d’historiens qui, selon moi, ont beaucoup exagérés ses tendances mystiques. Le mot ‘mysticisme’ est un peu comme ‘démocratie’. On en fait ce qu’on veut, subjectivement.

OBSERVATIONS ON BERNARD OF C LAIRVAUX 265

selon la situation. Mais il me semble qu’il faut distinguer entre les mystiques qui se sont vraiment retirés et un mystique comme Bernard, qui a exercé une influence énorme dans le monde.

j. CADDEN : To tum to a somewhat broader question, I had some difficulties with your general method or approach. In particular, because I am conservative, I find that you have gone too far from what you call a purely philological approach. But on the other hand, because I am sympathetic with your goals, I find that you stayed too close to a purely philological approach. Too close, in the sense that, if what you are trying to establish is some relationship between certain kinds of ideas and certain kinds of social behaviors and organizations and changes, you really must go beyond a text like the Sermons which deals basically in ideas. All that you can establish by using these texts are relationships between ideas about behavior and other kinds of ideas. On the other hand, I find that you are too far from the philological approach in the sense that, in trying to bring some of these ideas to bear on social notions, you have used words like ‘activity’, ‘society’, etc. Now, a lot of these words clearly do belong to Bernard himself, but words like ‘life’, ‘activity’, ‘society’ need to be clarified, I think, by a traditional philological approach. A lot of the contentions that you make are ambiguous without such an approach. For example, it is not clear that when Bernard is talking about reform and about life that he is talking about anything beyond a purely psychological reform. If you are going to try to make the transition to a larger, social context, you really need to know how Bernard is using words like ‘activity’, and how the transition can be made to activity in the real world.

B. stock ; Yes, that is a valuable criticism. With a thinker like Bernard, whose interest is primarily psychological, who directs his views toward a monastic community, there is a tremendous distance between the texts themselves and the real world which surrounds them. In such instances I am not sure that the rapport is ever a direct one. But the challenge to the historian today is to attempt to look at the material and intellectual sides of culture at once, and not to separate them artificially. One of the problems with the social historians is that they won’t look at ideas except to reduce them; and the problem with the intellectual historians is that, even when they want to make connections, they are not trained to deal with the other side. I do see this as a real problem.

G. constable: Let me make a more specific conmient. You refer to Cistercian spirituality and Cistercian monasticism as something distinct and separate from the other monastic movements of the twelfth century. But I think that the emphasis that you place on work even occurs, for instance, in Cluny, which is so frequently contrasted with the Cistercians. I agree with your major point, but I think that some of your formulation may grow out of your concentration on Bernard at this point in your work. You might put a slightly different interpretation upon where the novelty is and wheie the distinctive locus is. On the role of technology among the Cistercians, there may be some question, but on the question of economic organization, I think that the originality and the advance of the Cistercians is very strongly questionable.

H, o berm an : Rather central to your paper is the question of the role of experience. Now relative to this there is the more specific point of whether you are right - and here I appeal to your own knowledge of Bernard of Clairvaux - in translating experientia and experimentum as synonyms. I am interested in this because in the later Middle Ages, in texts from the fourteenth and fifteenth centuries, a distinction is operative. Experientia is direct experience and experimentum is usually interpreted experience, rationally organized experience. Now it seems to me that this is of some interest because, when you emphasize experientia as a step in the direction of experimentum, at that point It

266 B. STOCK

starts to become pertinent to the history of science. And let me add to this another related point: You allude to the famous statement of the expertus novit about which there is a whole tradition. Theologians can use this notion to put laymen in their place, and a mystic can also speak about his world of experience in these terms and claim that no one else will be able to understand him as spiritual master and guide unless he is willing to be taken along this road. This expertus novit tradition becomes, then, very interesting when in the later Middle Ages we see that the nominalists use it as a defense of their insistence upon cognitio intuitiva. They use the same words for a completely different purpose. One has to know the individual thing in order to talk about it. Again, this seems to me to be a point in the history of this expertus rwvit tradition at which it becomes truly interesting in terms of the history of science. Now I wonder whether you would claim that you find all of this already in Bernard. I was inclined to agree with the criticism of Mr. Gregory. With Bernard there is more of the ultra-mundane direction; there is not yet this insistence on experientia as we find it in the later Middle Ages related to its fruition in experimentum.

B. stock : I have done some work on experiential experimentum, and as far as I can see the distinction you are making does not exist in St. Bernard. I am interested in what you say about the nominalists and cognitio, but Bernard, it seems to me, limits the range of experience to two sides. I have emphasized the pragmatic, but I tried to make clear that there is also the mystical side which everybody else has emphasized. Moreover in Bernard the two are not clearly distinguished ; one cannot understand the one apart from the other. In that sense you are partially right in seeing much that is ultra-mundane in Bernard. But Gregory also suggested that Bernard’s reduction of the eschatological might be related to the changing conditions of monastic life. That is worth pursuing. Although Bernard often speaks of paradise and the last day, he is really concentrating on the present and the not too distant future.

T. GREGORY: Par les mots experientia, experimentum et tous les mots qui sont liés au terme experientia, Bernard décrit un moment central de la vie religieuse, un contact direct et global avec la totalité de la réalité qui alimente la vie religieuse. Bien! Mais si l’usage constant de Bernard est très important, il serait bien de mettre en rapport l’usage de ces mots et les langages de la spiritualité chrétienne contemporaine. Une analyse historique du langage de Bernard peut faciliter la compréhension de la terminologie autour à'experientia utilisée par Bernard. Je crois qu’il n’apporte pas de nouveau à cette terminologie. En réalité, il est très difficile, je crois, à travers l’analyse du language d’isoler les thèmes tout à faits personnels de Bernard de Clairvaux.

B. sto ck : A u contraire, il est facilement démonstrable que Bernard est un innovateur dans le langage et les symboles de la spiritualité chrétienne. Mais ça n’est pas mon problème.

G. schmitt: Both philosophers and theologians used the terms ‘experience’ and ‘experiment’ during the Middle Ages and, it seems to me, that the contexts in which they were used furnish an important locus where we can investigate the interrelations between philosophy and theology. Yet I find that I am in disagreement with what Professor Oberman has said about the later Middle Ages. I had occasion some years ago to try to sort out some terms in Galileo. In investigating the background of the distinction between experientia and experimentum, I found in looking at the scientific literature (and I now realize that my approach was too narrow, for I looked merely in logical and scientific contexts and I should have looked in theological and mystical ones as well) that in the thirteenth century, for example, there was an order from one of the Dominican superiors which says that the monks are not to have books on necromancy, on


superstition, or libri experimentorum, a term which seems to indicate books of occultism. This sort of use of experimentum also occurs in Arnald of Villanova and Petrus Hispanus among others. That is, in the fourteenth and fifteenth centuries experimentum had strongly occult overtones while experientia didn’t, at least in the contexts which I have looked at. And if you look at the sixteenth century, you see that experientia (which seems to be a better classical term) gradually replaced experimentum. Moreover, if you look at the translations and commentaries on the Posterior Analytics, for example, during this whole period you find a continual shift from one term to the other. Some translate empeiria as experimentum, some as experientia. You see a shifting back and forth and, as far as I can see, no terminological consistency.

H. oberm an : Yes, this use of the word experimentum in exactly that context of something forbidden or occult goes back to St. Augustine and his interpretation of the devil tempting Jesus to jump from the pinnacle of the temple. That is then picked up as a theme throughout the Middle Ages. This interpretation of St. Augustine is quoted, when it is said that it is an experimentum to try to jump from the temple to see what happens. You are right, it is diabolical, but it is also to see what happens. That is the other aspect of it.

B. stock : What I would like to know is whether there is a clean break anywhere in the tradition in the use of the word experimentum, in (say) the fourteenth, fifteenth, or sixteenth centuries.

A. sabra : The difficulty with your question is what you would consider to count as an appearance of a real concept of experiment. Is it making experiments? Is it the occurrence of the word ‘experiment’, somebody using the word consistently to mean the same sort of thing? Or are you referring to the formulation of a theory of experiment as a methodological tool? These things are sometimes merged into one another. Take Galen. There you have the word peira which in some cases definitely means trial. He describes, for example, what he calls a geometrical proof of something to do with visual illusion and then says: “As for those who have no head for geometry, they can make the following peira." He then describes what we would readily call an experiment. But does that mean that Galen has presented us with a concept of experiment in the sense of trial? Well, yes and no. For he also has the word empeiria which means something quite different, and the two words are used interchangeably. So because of this confusion, because you don’t have one and the same word always attached to one and the same situation, perhaps one should conclude that we don’t have aproper concept of experiment in the sense of trial. One can make trials for all sorts of purposes, in order to prove something, in order to refute something, and so on. Which of these are you going to include? All?

Ptolemy, however, has the same concept of peira in the context of astronomy where one doesn’t make experiments in the sense of manipulating things, but where one does make tests. That is to say, you test observations that were made a long time ago by waiting until you can make an observation that you can compare with these earlier observations. Here the concept of comparison and peira are joined together. If you go on, then, to the optics of Alhazen, there you have the concept of experiment as trial and also as something implying manipulation. But now the whole situation is related or joined to a word that is not the word used by the Arabs to translate empeiria, nor the word used to translate peira in Galen, but a completely different word, the dictionary meaning of which would be something like “comparison.” Now I think this came about as a result of translating the particular text I mentioned of Ptolemy. There, in the Optics of Alhazen, you have terms corresponding to experimentum, to experimentator, and to

268 B. STOCK

experiri. And in the Latin translation these correspond exactly to three forms of one and the same Arabic root: ‘BR, from which i^tibâr is formed. It should be noted further that i^tibâr is a common word, used for many things. Indeed, I should stress the fact that it is used in different contexts to mean different things. For in the particular context I have in mind it is always used in the sense of testing with the purpose of proving something. Now this is, of course, taken over into the Latin translation. And it is in a way surprising that the Latin translator, working without a dictionary, would translate Vtibar by experimentum, but this is what he did. Obviously, it was the context that suggested the correct translation.

j. g a g n e ; Chez Bacon il y a une expression toujours liée à “expérience” : la confirmatio (ou la certificatio). L ’expérience, apparaît comme une confirmatio, comme dans l’expression experientia patet. Il s’agit d’une vérification; non pas d’une manipulation, et elle est très différente de Vempeiria grecque.

A. sabra : That is what I am saying: It is not empeiria, it is a different concept.

P A R T I I I

THE FOURTEENTH. FIFTEENTH, AND SIXTEENTH CENTURIES IN THE LATIN WEST

F R O M S O C I A L I N T O I N T E L L E C T U A L F A C T O R S :

A N A S P E C T O F T H E U N I T A R Y C H A R A C T E R

O F L A T E M E D I E V A L L E A R N I N G *

I N T RO D UC T IO N

The history o f medieval science has for some time now been o f age; it is not merely a recognizable, but a recognized area o f study. This is, to be sure, all to the good, especially in the eyes o f its practitioners. What is more, with this increased recognition has come a corresponding specialization. This too is all to the good, for what better means are there for the discovery, investigation, and understanding o f the primary sources o f medieval science than an active cadre o f historians whose training and interests are focused primarily on the Middle Ages?

Yet this necessary and welcome specialization has at the same time often been the bearer o f less fortunate separatist tendencies. As all historians o f science, those whose special burden has been the Middle Ages have been, and are, a relatively discriminable lot. Still, although this has undeniable virtues, I think one can now plausibly claim that this discrimination, this separatism, has gone too far. That is to say, there are any number o f other, “ non-scientific,” aspects o f medieval intellectual history whose appreciation and comprehension are so crucial to the historian o f medieval science that, for the good o f the discipline, traditional distinctions o f profession ought to be relaxed in order to facilitate their effective incorporation into scientific history. It is not that other pastures are greener; on the contrary, there is but one large plot to be tilled. The mistake has been, I think, to tend only certain parts o f the plot, to neglect what had been regarded (erroneously I would argue) as weeds in contrast to the more “ recognizably scientific” flora. As a remedy, all segments o f the plot should be cultivated, for each one can and will yield proper food for thought.

Thus, I have on an earlier occasion urged that a good part o f the history o f medieval science should not only heed the history o f medieval philosophy, but, properly understood, should be part o f the history o f medieval philosophy.^ I should now like to carry this counsel one step further and

JOHN E. MURDOCH


~ ” I»-*-»—•—

I l l J. MURDOCH

argue that historians o f medieval science should also enlist the assistance o f the historian o f medieval theology. Indeed, given the likelihood that those aspects o f medieval theology o f greatest interest to the former will not turn out to be a primary concern to the latter, historians o f science should even do some history o f theology o f their own. 2

Some o f this has been, and is being, done. Attention has not only been paid to philosophical sources but to theological ones as well, but often without sufficient appreciation o f the possible significance o f the kind o f source in question. O f historians o f medieval science, surely the late Anneliese Maier was acutely aware o f the benefits to be derived from broader contexts within the intellectual history o f the Middle Ages, and even Pierre Duhem was no stranger to medieval philosophical and theological texts (although he admittedly drew hasty and erroneous conclusions from many o f them^). Yet, even so, the bringing together o f the histories o f medieval science, philosophy, and theology needs further urging; it cannot help but enrich at least the first o f these disciplines, and probably the other two as well.

What is more, the unification I am urging has a very good basis in medieval fact. The most obvious elementis, o f course, the unity impressed upon medieval learning by the medieval university. As the predominant social factor effecting intellectual development and change in the Middle Ages, the university surely fostered a cohesive structure for learning. Not the least o f the reasons why it did so was its tradition o f having all those who progressed to the advanced studies o f theology, law, and medicine initially nurtured within the faculty o f arts. One could not help but derive at least some unity from this common artes origin. In fact, to judge from the condemnations that are found from the 1270’s onwards, perhaps more unity than the theological faculties had bargained for. I f this is coupled with the relatively common curricula advocated and followed in each o f the medieval faculties, the university seems the natural starting point for any inquiry into the unitary character o f medieval learning.

But it is only the starting point. Setting the institutional history o f medieval universities aside, even that part o f their intellectual history involving common sources, common teaching methods, and the often incredible continuity they gave rise to, is not enough. One must track down specific “ unifying” issues, ideas, and techniques that developed

U N ITA R Y CHARACTER OF MEDIEVAL LEARNING 273

within the university milieu and pursue them to a point o f detail most often o f only peripheral interest to the university historian proper. To be sure the university in the thirteenth and fourteenth centuries was the locus in which such developments occurred and insofar as any o f these developments are found to straddle the areas o f the arts, theology, medicine, and law, the university must have been a contributing factor in their occurrence. Nevertheless, at best, this ascribes to the university only the role o f a partial cause o f the unity or unification in question. Further, to gauge effectively the significance o f this or that unifying factor within medieval learning, one had best look to effects rather than causes. Besides, it seems unlikely that we should be able to establish much in detail about causal factors unless we first know with some intimacy the results they may be

held to explain.What follows then is intended as a preliminary and limited essay on the

level o f effects, not causes. It is preliminary insofar as the best one can do in the present state o f the historical sources is to outline the basic structure o f things and to suggest possible fruitful avenues o f investigation for the future. It is limited insofar as it addresses itself to but a single aspect o f the unitary character o f medieval learning and is further restricted to the

fourteenth century.

L THE NATURE OF THE UN IF IC A T IO N OF MEDIEVAL L EA RN IN G

A. A Spectrum o f Unities

There is no question but that one can discriminate a variety o f “ unities,” or better a variety o f ways to view unity, within medieval intellectual endeavor. To specify just which will be my primary concern is therefore in order.

To do so, let me indulge in the convenience o f restating some o f the conclusions I was led to in an earlier investigation.® In straightforward terms, one o f the theses I then suggested was that the most significant segments o f medieval science were, especially in the fourteenth century, but a part o f late medieval philosophy.® The unity I then had, and still have, in mind is a rather strong one. It is not merely that there was a good deal o f philosophy in most science; it is that most science was philosophy, natural philosophy to be specific, and that scientists were philosophers. For it seems to me that the most accurate and most adequate way o f describing the activity o f the likes o f Richard Swineshead and Nicole Oresme

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is that they were doing philosophy; they were, to put it in other terms, far more at one with other (to all historians, admittedly) philosophical activity in the later Middle Ages than they are with the activity o f a Ptolemy or a Newton. Considerably more mathematics may have been utilized in their enterprises than in those o f other medieval philosophers, but they were, in their way, philosophizing none the less."

In contrast to this strong unity, indeed identity, I would now like to take the additional step o f suggesting a weaker unity : that o f philosophy and theology in the fourteenth century.® In fact, although the claims I shall make in what follows about the unitary character o f late medieval learning will, a fortiori, apply to the stronger unity o f “ science” and natural philosophy that I have just mentioned, they are primarily meant to cover this weaker unity.

But let me explain what I mean by calling it “ weaker.” Simply put, the qualification derives from the fact that the unity in question is not one based on an inability to discriminate disciplines or areas o f intellectual endeavor (as is the case with most “ science” and natural philosophy). We can and do differentiate philosophy and theology, and the medievals themselves did the same.

On the other hand, there surely is a unity to late medieval philosophy and theology, weaker though it may be. To begin with, some o f the very best - indeed, the best - philosophy was done by theologians and in their theological works (Scotus, Ockham, and Robert Holcot, for example). That speaks for at least some kind o f unity. One should not, it suggests, distinguish between philosophers and theologians even though we can draw lines between philosophy and theology. Secondly, given the structure o f the medieval university, there was a built-in interchange between the two areas, especially in the fourteenth century. Thus, to say nothing o f content, the methodological input from the arts into theology scarcely needs mention. On the other hand, in return, one can discern the flow, not o f methods, but especially o f problems from theology into philosophy (that o f extra-mundane void space, o f the relative perfection o f species, and o f future contingents, for example).® O f course, movement from philosophy to theology was stronger and the nest o f common methods and conceptions that allowed one to pass with relative ease from faculty to faculty for the most part had an artes origin, but it seems to have been far from a one-way street.


What is more, in spite o f the frequent conservatism o f theological faculties and o f many theologians, one factor within late medieval theology appears to have made it quite receptive to arts material: the ever present Commentaries on the Sentences. There is a touch o f irony perhaps in what one might view as the relatively static requirement for every bachelor to lecture on Lombard’s Sentences. For the resulting Commentaries thereon were, over time, among the most dynamic o f medieval works. Apart from the increasing amount o f philosophical material that was, especially as one moves on into the fourteenth century, imported into the Sentences, there was a concomitant flexibility in just which distinctiones o f Lombard need treatment. Even the number o f questiones varies, dropping sharply from the hundreds to a mere ten to twenty, Few Aristotle commentaries ever saw such latitude o f treatment. And the different issues that were to find a home for examination in a single distinctio also testified the relative ease o f introducing external matters into this sine qua non for any aspiring theologian. We shall have ample opportunity to note even more with respect to the Sentences as a kind o f “ wild card” in the fourteenth century theological game, but merely from what has already been said it is clear that this work would be more likely than most others to reflect changes and developments in intellectual

interests and attitudes. ^In any event, I shall be treating the Sentences as the primary bearer o f

the weaker, secondary unity o f philosophy and theology o f which I have spoken. The justness o f considering it as such a bearer, and the accuracy o f my claim o f this unity, will become more evident, I trust, as I move on

to more specific details.

B. External Evidence o f the Secondary Unity

The few fourteenth century features o f the Sentence Commentary that have just been mentioned are in themselves presumptive evidence o f the kind o f unity I am u rg in g .S o are also the more institutional factors o f Arts dominance within the medieval university and the common core o f material and methods used in teaching. But there is other external testimony as well.

Codicological evidence, for example. Any number o f instances o f manuscripts that have duly collected philosophical and theological treatises side by side can easily be found. Yet, o f greater interest and significance is the evidence presented by the occasional “ student notebook”

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that we are fortunate enough to possess. Thus, it has recently been established that three bulging theological notebooks and what has long been regarded as the most important notebook o f fourteenth century science all belonged to the same student, presumably one Jean de Falisca.i^ Valuable materials for the intellectual biography o f a single fourteenth century figure are thus at hand. It will take completion o f the extremely difiScult task o f carefully analyzing all four o f these manuscripts to establish just what the yield o f these materials will be, but even a preliminary examination reveals traces o f the logical and natural philosophical conceptions and methods in the “ scientific” notebook in the theological ones. And other notebooks appear to hold promising evidence o f a similar sort.

Another external indication o f the unitary character o f philosophy and theology that I have in mind is the fact that genuine parts o f fourteenth century theological works have successfully masqueraded as straightforward tracts in natural philosophy. Thus, Gerard o f Odo’s examination o f the problem o f the composition o f continua was detached from the Sentence Commentary to which it belongs and circulated separately. So totally without specific theological relevance (it was shorn o f its introduction), it appears exactly as i f it could be the initial questio o f Book V I o f a commentary on Aristotle’s Physics.^^ Even more interesting is the opening questio o f the Commentaria sententiarum o f Roger Rosetus : its first article enjoyed an extensive separate career as a Tractatus de maximo et minimo. Originally theology, then circulating widely as natural philosophy, we also know that, coming full circle as it were, in its new guise it interested some whose primary preoccupation was the theology from whence it had come; for a copy o f it was owned by no one less than Peter o f Candia. '^

A final genre o f external evidence for the secondary unity o f philosophy and theology is that o f the complaints we witness about it. At minimum, condemnations from Etienne Tempier forward bewail the excessive incursion o f artes thinking into theology {studentes in artibus proprie facultatis limites exced en tes ).In the following century, essentially the same approach becomes more pointed and more specific: the University o f Paris statutes o f 1366 officially rule quod legentes Sententias non tractent quaestiones vel materias logicas vel philosophicas nisi quantum textus Sententiarum requiret.^^ And an echo o f this is found in the unofficial

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counsel to avoid, even to make a point o f avoiding, the logical and the mathematical, and to follow only speculative and moral philosophy, the metaphysical and the theological.^» Standing alone, such documents intrigue one’s historical imagination. When combined with what one can learn from the actual examination o f late medieval Sentence Commentaries o f the extent to which logic, mathematics, and philosophy (o f the wrong sort, presumably) had infiltrated theology, the substance o f the fears that they expressed becomes more real. It is to such an examination that we

must turn now.

C. Philosophical-Theological Unity ‘Materialiter’: The Importation o f

Philosophical ContentIt has already been pointed out that much o f the very best philosophizing in the fourteenth century was done by theologians, most often within Sentence Commentaries, less frequently in Quodlibetal Questions. To appreciate just how and why this was so one need not push very far into any number o f Sentences. Indeed, it is immediately clear from the slightest reading o f the various Prologues to Book I. For there one finds the locus classicus o f the investigation o f the nature o f scientia, o f its objects, its certitude, o f the notions o f evidentia, and o f the relation o f all o f these to relevant similar material within the Aristotelian tradition, Although the ultimate purpose o f these investigations is naturally that o f determining the status o f theology as scientia, there is little doubt that the fundamental issue at stake is a philosophical one and is accordingly treated as such. What is more, what was done in this, and in other similar, theological contexts in the fourteenth century is so recognizably philosophical that historians have been able without exaggeration to claim that its “ character and direction” were at one with modern philosophy. 22 That is to say, not only was the problem treated properly philosophical (though the way it was put may frequently have had a theological tinge), but the conceptions and methods utilized in examining and resolving it were also philosophical in the modern analytical, non-speculative, sense o f the term.

I f one returns for a moment to the dynamic character o f the Sentence Commentary that we have noted, one reason why such straightforward philosophizing was so often possible and, what is more, effective becomes evident. The text o f Peter Lombard upon which the young bachelor was asked to comment presented a quite different state o f affairs than, for

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example, some work o f Aristotle. In commenting or writing questiones on the latter, the medieval scholar was furnished with a battery o f conceptions and doctrines by the work itself and he not only treated these conceptions in setting down his commentary but operated with them as well. Not so with Lombard’s Sentences; frequently (and the more so in the fourteenth century) the conceptions with which a commentator operated were quite external to anything Lombard said in the text. Often they were his own. Surely, this not only allowed, but positively encouraged, the importation o f new material, material that was, as often as not, philosophical or artes derived.

The major concern o f this paper will be the importation o f such material on the methodological level. To that I shall turn in the next section. For the present I wish to underline that, in a great number o f contexts, a similar importing occurred materialiter, that is, on the level o f content. In most instances, what was imported was directly or indirectly relevant to the theological question into which it was inserted. One has to do with a unity, one might say, such that the same question was at once theological and philosophical. So for example the aforesaid question o f utrum theologia sit scientia. And the case is similar when the Baccalarius Sententiarus faced the issues o f God’s omniscience and future contingents or o f God’s omnipotence relative to the infinite. 3 In these, and numerous other, instances we expect to discover philosophical deliberation.

In other cases, one does not have such an expectation, at least not until one develops a tolerable familiarity with later medieval Sentence Commentaries. The introduction o f philosophical content appears somewhat forced; one has the suspicion that the theological point at hand is being used not as a genuine reason, but merely as an excuse, to discuss such and such a philosophical - even natural philosophical or “ scientific” - problem. Thus we find an elementary discussion o f light and the multiplication o f species or o f the rainbow inserted into the context o f the creation, an examination o f the problem o f the motion o f gravia et levia in a similar context, an elaborate consideration o f terms o f first and second intention in the context o f the Trinity, an extended investigation o f astrology relative to the problem o f whether creation occurs de necessitate, and even a major question creatione celi dealing with whether one can prove that there are nine spheres (for discussion o f the ninth sphere, can, and does, lead to the consideration o f the precession o f the equinoxes.


the rising and setting o f the signs, the astronomy o f eclipses and so on).^4 And such phenomena can be found almost ad infinitum.^^

This is not to say that these more unexpected imported matters had no relevance to the theology contexts in which they occurred; they did, even if in instances only marginally so. But it is to suggest that the quantum textus Sententiarum requiret o f the 1366 Paris Statutes was more than occasionally at low ebb and that this kind o f injection o f philosophical content into the Sentences may well have been one o f the things the authorities had in mind in promulgating this regulation. That other sorts o f abuses may also have troubled them will become apparent shortly.

However, a word is in order about the importation o f logic in particular into the Sentences before we leave the consideration o f the secondary unity o f philosophy and theology taken materialiter. Passing over the everywhere evident fact that logic is used throughout late medieval Sentences,^^ some attention should be paid to a slightly different phenomenon, namely an explicit awareness and discussion o f this use. Perhaps the most striking example is a set o f regule given by Egidius de Campis in his Lectura super primum Sententiarum. ' Put briefly, his concern was to set forth succinctly a series o f rules covering the theological terms commonly used in the discussion o f the Trinity and relating them, albeit somewhat crudely, to the logical doctrine o f suppositio. That he saw fit to make a special point o f this in his Sentences and, especially, that someone shortly thereafter thought it important enough to extract these regule alone from his Commentary is surely evidence o f the integral importance logic was felt to have in theological matters. Moreover, Egidius’s concern was not an unusual, let alone a unique, one. He belongs, I would suggest, in a tradition that, before him, includes Adam Wodeham’s discussion o f the relevance o f the art o f solving paralogisms intra materiam Trinitatis^^ and, after him, contains such relatively unstudied figures as Herman Lurtz de Nuremberg 29 and Petrus de Pulka.^o

Indeed, this kind o f worrying over the relevance o f logic to the Trinity was a tradition in the proper sense o f the term. But one comes upon other attempts to introduce logic into the Sentences in non-traditional, unique ways. Pierre Ceffons is a model o f how it might be done. He is also unusually informative, since he possessed the rather rare habit o f speaking quite directly about his motives for doing what he did and about the milieu in which he worked. He candidly tells us that friends had asked him

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to speak de logicalibus inasmuch as he was presumably reputed to be knowledgeable in such matters. The result consists in two rather lengthy prefatory questiones in Book II o f his Commentaria sententiarum: the first gives what is in effect a complete tract de scire et dubitare, a very current and fashionable logical topic, while the second does the same de insolubilibus.^ In the course o f his exposition he pauses to castigate those who despise logic (invariably those who are ignoramuses concerning it) and to praise its value for the faith.^^

Although taken as a whole, there are indications that CeflFons was unusually anxious to have, or to make, opportunities to display his knowledge,®^ the fact that he saw fit, and was even asked, to locate this display in his Sentences is but one other bit o f evidence o f the weaker unity o f philosophy and theology that I am suggesting as a frequent feature o f the fourteenth century. As evidence, it is unusual only in that it is more explicit than most.

D. Philosophical-Theological Unity ‘Formaliter’: Languages o f Analysis in the Fourteenth Century

In my earlier essay in which, I have mentioned, I sought to establish the “ strong unity’ ’ o f natural philosophy and science, I attempted to characterize what I believed to be one o f the most important aspects o f the change that occurred in natural philosophy between the thirteenth and fourteenth centuries in terms o f the development and application o f new conceptual languages and tools.34 “ Languages,” as I then put it, “ with which to treat the traditional problems o f natural philosophy on the one hand, and with which to invent and solve new problems on the other.” 35 Now, in addition to being instructive and fruitful in interpreting the evident thirteenth- fourteenth century shift in natural philosophy, I also believe that these new languages (their development and use as well as their existence) are among the primary bearers o f the unity o f science and natural philosophy as I see it. I should now like to maintain that these very same languages and tools played a similar role in the fourteenth century with respect to the weaker unity o f philosophy and theology.

This being so, it will be prudent to explain what I take these new languages and tools to be.^» To the “ tools” first; for they govern and assist the application o f the languages in a number o f important ways. I can begin with that which is well-known, to wit, those two principles so often


considered by historians as the very foundation o f “ Ockhamism” : (I) Deus potest facere omne quod fieri non includit contradictionem', (II ) Pluralitas nunquam ponenda est sine necessitate ponendi. ' Both function throughout fourteenth century philosophical literature (that which is genuinely Ockhamist and also much o f that which is non-Ockhamist in other significant ways) as analytical principles. The first is, o f course, a direct expression o f the potentia Dei absoluta. I realize that, on the one hand, one can and should probe further into its precise function and scope (especially with respect to theological matters) and, on the other hand, that within philosophy and theology some o f its most important applications as an analytical principle consist in its utilization in grounding the dispensability o f secondary causes and in assuring or denying putative distinctions among entities.^s However, within most o f natural philosophy, and within theology where the application o f the new languages that I shall shortly describe is concerned, its function is, in my view, at once broader and simpler. Its role is there thoroughly logical and it merely functions as a way o f pushing the analysis o f any given problem beyond the limits o f the physical possibilities licit, for example, within Aristotelian natural philosophy into the broader fabric o f all that is logically permissible. To put it another way, it is an absolutely valid warrant to argue secundum imaginationem. But more with respect to that later.

The predominant function o f the second analytical principle above, Ockham’s so called “ razor,” is reductionist. As such, when the application o f the new languages is at stake its role is secondary. It serves most frequently as a guarantor o f the universe o f particulars to which the languages are applied in the first place and plays but a minor part in governing how they are applied.

Again with the new languages in mind, it seems appropriate to add a third analytical principle to the foregoing two: non est maior ratio quare ...A quam Perhaps more a manner o f arguing than a principle, it is nevertheless o f considerable significance because it does enter into the moves one makes in applying the new languages.^!

One final conceptual tool should be mentioned before turning to the (by now much anticipated) languages. Unlike any o f the above three analytical principles it seldom, if ever, receives explicit statement. Properly speaking, itself neither a language nor a principle, it might best be termed a procedural rule consisting as it does in the prescription o f the effectiveness

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o f a second intentional point o f view in the analysis of problems. That is to say, in place o f analyzing a given problem in terms o f the entities or objective events involved, analysis is shifted to the terms and propositions which speak o f these entities and events. O f incredible importance within fourteenth century philosophy as a whole, for present purposes it is sujficient to note that the function o f this procedure is simply, and often most significantly, to transfer the analysis effected by means o f the new languages to the propositional level.^s

When one turns to the newly developed languages themselves, one has the tendency, as I did myself in my first interpretation o f them, to divide them into the logical and the mathematical. Now such a distinction is instructive, and does have more than a modicum of truth to it, most evidently because elementary mathematics is utilized in several o f the most important o f the languages. But it also has a tendency to make things a good deal neater than they actually were and to ignore features o f considerable significance. Put abstractly, it ignores the important fact that logic was not only central to the languages we would have no hesitation calling logical, but was also operative within those we would term mathematical. Just how this was so will become clear as we proceed.

Setting aside, then, any attempt at rigid pigeon-holing based on modern categories, we can begin by noting that the lion’s share o f these new, essentially fourteenth century, languages has to do with measure, provided we take ‘measure’ in an appropriately broad sense. How broad is best indicated by a description o f the languages themselves. (It is worthwhile even here to note the intimate connection with logic. For “ measure” to medievals was most frequently considered a matter o f denominatio and to elucidate the denominatio o f a subject was to delineate accurately the predicate or predicates that belong to it under such and such circumstances, be these predicates numerical or comparative ones involving “ measure” or more normal “ logical” ones, no matter.

One o f the most universally appUed o f the new “ measure” languages is that o f the intension and remission o f forms. As with all o f the languages, one can distinguish between its vocabulary and the algorithms or rules operative within it. In this instance the vocabulary consists o f intensus, intensior, intensissimus, intendere (and the corresponding terms for remissio), latitudo, gradus, uniformis, difformis, uniformiter difformis, difformiter difformis.^^ By the algorithms o f this intension and remission language I

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mean those rules that stipulate which relations can or cannot obtain between the entities for which the terms constituting their vocabularies stand. The most familiar such algorithm is that o f mean degree measure which states that for any uniformly dilformly qualified subject, its measure or denominatio relative to the quality in question is the same as if the whole subject were qualified uniformly with the degree o f that quality that is the arithmetic mean between the two extreme degrees it possesses in its uniformly difform state.^s Although this may be the most famous intension and remission algorithm, it is by no means the only, or even the most frequently applied, one. Others stipulate, for example, the possibility or impossibility o f the existence o f a most intense or a most remiss degree, the scale relative to which intensity and remissness is to be calculated, the determinate manners in which the highest degree o f a quality can be introduced into a subject already possessing a given ‘configuration” o f that quality but undergoing a certain specified alteration, and so on.^» Indeed, a whole treatise could be created through the mere tabulation o f the extensive vocabulary and numerous algorithms o f the intension and remission o f forms without even broaching the issue o f how they were utilized by the medieval scholar. In any event, it is worth emphasizing that, in this and all other cases, the vocabulary plus the algorithms constitute the analytical language in question.

Thus, the measure language o f proportiones draws its vocabulary from the relevant traditions within Greek and Arabic mathematics 4? and has as its algorithms many o f the established theorems within the theory o f proportion o f that tradition.^» Once again, however, there were appropriate medieval additions, one rather well known: Thomas Bradwardine’s so-called “ Dynamical Law” relating an arithmetic increase or decrease in velocities to a geometric increase or decrease in the force-resistance proportiones functioning as their causes." ® It too, even in face o f the goodly number o f algorithms lifted directly from Greek mathematics, is not the only medieval member o f such rules. Other medieval creations occur especially when there arose the attempt to include the infinite within the compass o f proportiones languages.^®

We must begin to stretch the notion o f measure when we come to the other new languages in this category. Fundamentally, they all “ measure” in that they ascribe limits to one or another entity, process, or event. There are, ignoring disguises, three languages that are enlisted to carry out

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this function. In medieval terms they are: (1) de incipit et desinit, (2) de primo et ultimo instanti, (3) de maximo et minimo.^^ For the most part, they derive from remarks o f Aristotle, but anything like their proper development only occurs in the Latin West, chiefly in the fourteenth century. 52 In contrast to the languages o f intension and remission and proportiones, their vocabulary is meager, consisting basically o f the terms just mentioned in labelling them. I f to these one adds such terms as quod sic or quod non (to specify the kinds o f maxima and minima involved), esse or non esse (to specify the limiting function o f the first and last instants in question), mediate or immediate, ante or post (relative to both instants and beginnings), and positio or remotio (o f the past, present, or future), one has a fairly complete catalogue o f what might be called the first level o f basic vocabulary for these three languages. A second level o f terminology deals directly with the entities to which the languages apply: res permanentes or res successive (re: de instanti and de incipit) and potentie active or potentie passive (for maxima and minima).^^

Given all o f this, it probably does not even need saying that the algorithms or rules o f these three “ limit” languages at bottom amount to the specification o f just when (and when not), and just which kind of, instants, beginnings, and endings or maxima and minima apply, or do not apply, correspondingly, to permanent vs. successive things or to active vs. passive potencies under such and such circumstances.®^

Complex as this might seem, there is one other item that needs adding to make the account o f the structure o f these limit languages complete. It is that the vocabulary and algorithms o f yet another language, the essentially logical language o f suppositio, is everywhere applied in formulating the algorithms o f these languages, in moving from one algorithm to another, and in establishing that they do indeed fit or apply to the casus under examination.

In point o f fact, the language o f suppositio is one o f the next that needs attention, but before attempting this, one final measure language requires mention. As we shall see in what follows its role is considerable and, in many ways, central. I refer to what might best be termed the language o f continuity and infinity. Here ‘measure’ must be taken in an even broader sense. For in addition to the normal sense o f measuring 6 and to that o f setting hmits, we find a special concern with what can be interpreted as extensions o f these senses; that is, with investigations focussing, on the

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one hand, upon the determination o f the number, relation, and order o f parts within continua and, on the other hand, upon the delineation o f the relations that can or cannot exist between entities that are, in one sense or another, infinitely distant or different from one another.^’

The precise function in the fourteenth century o f this whole continuity- infinity language and, particularly, its relation to the other five measure languages can be more adequately treated later. por the present it is sufiicient to note, first o f all, that its vocabulary was drawn largely from such traditional terminology as divisiones or divisibilitas, partes proportionales, excessus, pars, totum, etc. Medieval ingenuity was, to be sure, exercised in the invention o f new meanings or terms to describe the possible relations between parts o f continua^^ and the logical tradition was called upon to furnish ‘categorematic’ and ‘syncategorematic’ for the distinction o f types o f the infinite.®® But this is paltry little compared to the terminological (and hence conceptual) inventiveness one finds with respect to the intension and remission o f forms or even relative to the three “ limit setting” languages that have been noted.

Considering how much o f the vocabulary was not o f medieval creation, it may be initially surprising to realize that the algorithms o f the continuity- infinity language to a great extent did originate in the Middle Ages. Yet this surprise disappears when one reflects that the “ mathematics o f the infinite” with which this language so often dealt was not part o f the inherited mathematical tradition. Indeed, any self-respecting Greek mathematician would have regarded a good deal o f it with horror. When one also realizes that in many instances the medievals were attempting to fit algorithms designed for finite quantities to infinite ones, the problems that they faced immediately become apparent. It will be more fruitful, however, to postpone the examination o f some o f these difficulties as well as a sampling o f the algorithms themselves until after we have had the opportunity to observe the application o f all o f the measure languages within theology, since there the exemplication o f factors concerning continuity and infinity is a predominant feature.

It remains to examine one final analytical language; it is the most comprehensive o f all in its applications : the theory o f suppositio o f the so-called logica moderna. This is not the place to pause for even the most compendious description o f the theory or o f the service it was to philosophy in general. This, together with considerable detail about what I would call its

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vocabulary and rules or algorithms, can be gleaned from other sources.® For our purposes it is enough to note that, as an analytical language, it was used to treat any philosophical problem. My past interest has been in its application to problems within natural philosophy, most notably those de motu. But is was similarly applied in theology as well. As part o f logic, wherever is was brought to bear, it functioned metalinguistically. That is, its application amounted to an invocation o f the procedural rule to adopt a second intentional point o f view; one dealt not with individual entities, but with propositions and with terms within propositions that stood for {supponit pro) such entities. Accordingly, the elucidation o f the kind o f supposition that was had by the terms in a given problematic proposition was one o f the most common ways o f resolving the problem carried by the proposition, especially when that problem had to do with the analysis o f continuous processes or quantities, with the determination o f the proper order o f “ parts” within those processes or quantities, or with the setting o f limits for them.®^

These last phrases are the key to the importance o f supposition theory for our purposes. For they imply a rather direct connection between it as an analytical language and those languages I have characterized as mensu- rational. I have already indicated the central role played by suppositio in the three limit languages.®^ But it also did considerable service for the broader continuity-infinity language and, when questions o f the continuous were at stake, in the language o f intension and remission as well. Here, and equally within the three “ limit setting” languages, the medieval was eminently successful in clarifying conceptions o f what we would term the bounds or limits o f continuous series; and it was the “ metalanguage” o f suppositio that furnished the means more adequately to express those conceptions and, in the bargain, to test whether a given series instantiated this or that kind o f limit.® Supposition theory was, then, truly extensive in scope; indeed, o f all our languages, it seems that only that o f proportiones rarely suffered its intrusion.

One has to do, therefore, with what might be considered an order o f comprehensiveness among these languages. Proportiones, intension and remission, and the three limit languages are embraced, as it were, by that o f continuity and infinity, for the vocabulary and algorithms o f the latter are frequently applied to the former.®® The theory o f supposition, on the other hand, functions metalinguistically relative to these other languages


(save that o f proportiones). Perhaps the hierarchy stops there, but not so the intrusion o f one language into another. For one can find the rules o f the languages o f first and last instants and o f maxima and minima applied within the language o f the intension and remission o f forms ; so too, as one might expect, rules from the language o f proportiones. But the inverses o f these cross-applications also occur. ®' In fact, the translation o f one o f the fundamental algorithms o f proportiones, Bradwardine’s “ Dynamical Law,” into the language o f intension and remission was among the most important o f such occurrences. For it not only transferred a formulated relation from one language into another, but in so doing opened up a new and more effective technique o f handling that relation.®®

I have now spent so much time describing these languages (albeit only in outline form) and have so clearly implied their crucial importance for fourteenth century natural philosophy, that one can almost not help but ask how and why their application to all manner o f problems in philosophy and theology developed in the first place. Or, to ask the same thing in a slightly more limited way: how and why did the near frenzy to measure everything imaginable come about in the fourteenth century?®® Unfortunately, this is an extremely important question that I do not yet know how to answer with any adequacy. Here and there I believe I see a glimmer o f a solution, but nothing anywhere near being definitive. But perhaps these half-formed and unconfirmed suspicions are worth recording none the less.

In a category somewhat by itself is the language o f suppositio and the second intentional point o f view that is its concomitant. Their markedly increased application in the fourteenth century within philosophy and theology is most likely connected in some way, I would judge, with late thirteenth century concerns about evidence and certitude. Scotus is naturally the key figure, but Ockham carries these concerns further and puts an edge on them that might well have cut in the direction in which we are here interested. I have in mind in particular the form he brings to the confrontation between the required certitude o f scientia and the radical contingency o f individual res permanentes about which scientia must speak. To oversimply greatly, the point o f interest here lies in the realization that, since certitude cannot be grounded in the contingent individuals themselves, it is instead to be based within prepositional knowledge about these individuals. That is to say, the propositions become the bearers o f the requisite certitude and scientia is viewed as consisting o f

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such propositions (although it naturally still relates to individual physical things and events insofar as the terms in these propositions stand for {supponit pro) such individuals), Now this sort o f move demanded a more than usual reliance upon logic, in particular it demanded the assumption o f a second intentional point o f view. But to view scientia second intentionally accordingly urged one to view problems within it in a similar fashion; and to do that immediately opens the door for suppositio theory as a conceptual (and second intentional) tool to be utilized in analyzing these problems. Such is one possible explanation o f the rapid upsurge in applying the language o f supposition to philosophical and theological problems. I f it be a proper one, then one has to do with the interesting phenomenon o f having metascientific convictions, beliefs about science, materially ajffect which methods o f analysis are efficacious and should hence be operative within it.

Speculation about the origin o f the application o f the measure languages is not (at least in my head) even this developed and surely not as interesting. It is suggestive to conjecture that it too may be somehow connected with the concern for certitude, especially i f one could couple this with a parallel worry about precision. But for the present this must remain nothing more than an undocumented conjecture. Slightly less speculative is the possibility that the newly appearing measure-mania may have had a different sort o f logical origin, one connected with the medieval interpretation o f measure as denomination^ However, this also needs further probing and documentation.

I f we realize that the earlier and more effective application o f the measure languages occurred at Oxford in the fourteenth century, then another very attractive alternative lies in the fact that thirteenth century Oxford had scholars that were more versed in mathematics than Paris.'^ yet if we reflect on the further fact that the measurement tradition was at least as much an affair o f logic as it was o f mathematics, then this possibility seems less likely to have produced the phenomenon in question. A t least to any appreciable extent. For the development and exercise o f logic at Paris appears to have been at least equal, i f not superior, to that at Oxford.

One final suggestion: that o f a theological catalyst, i f not origin. Perhaps it was intra divinis that the tendency to measure found a primary moving force. The theological issue o f the augmentation o f caritas is already well established as one o f the classic contexts {Sent., I, dist. 17)


for the discussion o f the intension and remission o f form s.’ 3 Perhaps its role in urging the measure o f intension and remission is also o f appreciable significance, but in a way that we have not yet been able to discern adequately. More straightforward are suggestions concerning theological contributing causes in the case o f the “ measure” o f the infinite. For we can easily establish that later thirteenth century speculation about God’s infinity involved in the possibility o f an eternal world did contain elements found operative within the fourteenth century measurement tradition. And there is also the relevance o f the analysis o f continua within the discussion o f angelic motion.'^^ Yet with respect to all o f these suggestions one can only conclude that a good deal more work is required.

The detail concerning the new, fourteenth century, languages that I have felt it necessary to indulge in may perhaps seem excessive. But I have deemed it important to do so first as a kind o f prerequisite to the next section where their application in theology will be examined and secondly, and more importantly, because they are so very central to the major burden o f this whole paper. That is, that aspect o f the unitary character o f medieval learning that I hope to establish is located in the weaker unity o f philosophy and theology in the fourteenth century, taken formaliter. Moreover, to return to the very title o f the present section, that unity in that sense is expressed most adequately and precisely, I believe, by the common application o f those new languages o f analysis that have just now been des

cribed.

n. CHARACTERISTICS A N D EFFECTS OF THE A P P L IC A T IO N OF

L A N G U A G E S OF ANALYSIS

A. Some Features o f Their Application in Theology

There is little question that the application, often systematic application, o f the foregoing languages was more pervasive in natural philosophy than in theological contexts. Yet it is not only this difference in frequency which is noticeable at the “ first glance” level in the two disciplines. There is another distinction that strikes one even before a reading o f the specific arguments and problems: theology appears to lack the “ basic rule testing” that I have elsewhere taken to be one o f the central features o f exactly how the languages o f measure were applied in natural philosophy.^® Briefly described, I have maintained that, for every given measure language, one

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o f the most important ways in which it was applied consisted in the “ trying out” o f some fundamental algorithm within it (Bradwardine’s law relating velocities, forces, and resistances or the mean degree measure rule, for example) by applying this algorithm to all conceivable variant cases o f the quality, process, or other entity being measured under the language. By such a means there were even formulated complete brief tracts on individual algorithms or groups thereof. Logically speaking, the form that some o f these tracts assumed was that o f deducing a battery o f corrollary rules from the basic algorithm or rule from which they began. But when one looks beyond logical form, it seems proper to say that this deduction bore the feature o f testing the mettle, as it were, o f the basic algorithm, the deduced correlary rules being, in effect, the variant cases by means o f which the test was carried out. Moreover, this pattern o f application is found in all o f the various measure languages o f which I have spoken and should be considered, I maintained, as absolutely central to the thrust o f what is new and important in fourteenth century natural philosophy.’ ’

It is a pattern, however, that does not seem to be present in the application o f our languages in theology. But this is a distinction between theology and the major “ measurement o f motion” works in the natural philosophy o f the later Middle Ages, the works o f the likes o f Bradwardine, Heytes- bury, Swineshead, Oresme, and others. The languages o f measure are applied in all manner o f other works in natural philosophy {Questiones on the Physics, for example) and there one does not find “ basic algorithm testing” as the predominant feature o f their application. As one would expect in such works, the languages, or selected algorithms from them, are applied with the intention o f solving some particular given problem (a problem furnished in almost all instances, by the text or doctrine being commented upon). There may occur some deliberation establishing that the language is appropriate to the problem in the first place, but what is fundamental is the resolution o f the problem by its means.’ ® Now this pattern in the application o f languages in natural philosophy is the same as that which one finds in theology.

One might also wish to note, however, a difference in quality in this regard between theology and natural philosophy. That is, scholars like Swineshead and Oresme are incredibly more deft and competent in applying the languages and algorithms, no matter what the pattern o f application. Agreed. But this does not make the study o f their less


ingenious application within theology unimportant, even for historians o f science. For it seems to me that an investigation o f what happened in the utilization o f these languages within theology may well tell us things about their scope and character that we might not learn from our study o f the central works within fourteenth century natural philosophy. Thus even for the history o f science, let alone the history o f theology or o f late medieval learning in general, such an investigation has a good potential o f being beneficial.

None the less, no matter how convinced one may be o f this prospective benefit, the problem remains o f just how to structure this investigation and how best to limit, at least initially, its scope. For limitation is required, considering the mass o f fourteenth century theological material that does contain application o f the languages and the rather amazing variety o f problems with respect to which this application takes place. With this in view, I have chosen to exclude from consideration those theological contexts in which one would expect to find our languages appUed as a matter o f course (for example, problems dealing with the augmentation of caritas, the eternity o f the world, the possible infinity o f God’s power, future contingents, etc.). This may seem an odd choice to make. I think not. For to begin with, we will discover that the application in those areas that I shall treat is not necessarily any less extensive or informative than in the more “ naturally fitting” contexts that I shall exclude. Secondly, from the point o f view o f interest o f the history o f theology, who is to say that the employment o f these languages in “ non-obvious” matters was non-essential? That is, although the occurrence o f the languages in such contexts may initially seem forced and excessive (and would be regarded by some historians as positively silly and stupid), in the final analysis it may well prove to be the case that such a phenomenon was really very much part - even, perhaps, a necessary part - o f doing theology as it was then conceived. Finally, excluding the “ to be expected” cases o f application, one ends up with the very interesting result that the remaining major areas in which extensive application occurred are roughly coextensive with what we know to be the very heart o f theology in the period in question: namely, that o f the issues o f the will, justification, and grace.

In approaching the phenomenon o f the application o f the various analytical languages within theology, one o f the primary questions that demands attention is why fourteenth century theologians (or at least some

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o f the more important ones) felt urged to use them in their analysis o f certain issues in the first place (issues, o f course, that did not fit obviously with this kind o f analysis)."^® Similarly, in addition to the question o f why they may have thought it wise to apply these languages, what was it that made it possible for them to do so? Apart from the recognized general utihty and effectiveness o f philosophical methods and conceptions within theology (something that must have been present by this time in no small degree), it is interesting to speculate about the role fourteenth century voluntarism may have played in both these regards. I f it is true, for example, that one o f the effects o f this voluntarism was to weaken the ties that, in a theology that emphasized the primacy o f the intellect, harmonized God and the world, and as a consequence to lay bare the radical contingency o f all created beings and events,® then perhaps it is equally just to see at least one o f the reasons behind the newly found fondness for our languages in this same new kind o f relation that was held to obtain between God and his creatures. For the application o f these languages (in theology as in natural philosophy) proceeded secundum imaginationem and this, as we have seen, was permitted, even urged, by the invocation o f potentia Dei absoluta, a factor in turn at the very center o f the rising voluntarism. In other words, since God’s will can act with absolute contingency, it follows that, in a given problem, the entities or events involved can exist or can occur in all these imaginable ways, where ‘can’ is to be taken de potentia Dei absoluta and where ‘all these imaginable ways’ consist in the alternative casus that are analyzed by our languages. Furthermore, a specific question concerning the theological welcome that these languages received follows hard on the heels o f the preceding speculative suggestion: to what extent, i f any, did the new view o f the relation between God and creature encourage speculation, not about creatures as relata, but about their relations to God? For there was a good amount o f just such speculation within fourteenth century theology and a considerable part o f it took the form o f attempts to measure these Deus-creatura relations.®^ Hence again, o f course, the introduction o f our languages.

I have thus far considered only the possible unspoken reasons for the theological application o f our languages; only such it seems to me, will satisfactorily answer, howsoever partially, the general question o f motivation with which I began. There are, however, a variety o f texts concerned with showing that the languages can be so applied in this or that particular


case. A t bottom, these texts essentially tend to ground this application in the assertion o f a relatively direct connection between the theological matter at issue (for example, the action o f the will) and processes within the physical world insofar as these processes fall under determinate laws or rules as set forth in natural philosophy.®^ Often this connection is far from being merely implied or stated only in passing. Some time and effort may be expended in setting out the complete “ physics” into which the theological subject is to be inserted. Thus, we find the same problem o f the will’s action connected to the whole physics o f generation and corruption (both agents and patients being explicitly considered). Further, this is in turn related, via the necessary divisibility in one sense or another o f res creata, to the physics o f intension and remission.

The problem o f establishing the fit o f the language to be applied to specific subjects within theology also occurs in a more tacit, and simultaneously more important, way. It amounts to a demonstration o f the consistency o f the language, in particular o f its algorithms, with what might best be interpreted as the necessary theological principia governing the point or doctrine upon which the language is to be brought to bear. Foremost in this regard is God himself. To show the consistency o f a given language with the deity was tantamount to plugging God into natural philosophy. Perhaps the most astonishing display o f this procedure is Jean de Ripa. For when all is said and done is this not exactly what his relating o f God to the latitudo totalis entium, and hence to the language o f intension and remission, amounts to?®"* The result is one that was o f central importance to Ripa’s theology as a whole. However, attempts to relate God to something less comprehensive than the whole chain o f being also occur. At times, this takes the form o f fitting some sort o f human action amenable to treatment by our languages to some aspect o f the Divine essence. Or the fit in question might be that o f the human

action with a relation to God.®®Moreover, the same fitting o f the languages to theological principia

occurs in any number o f contexts other than God alone (although He is naturally almost always involved).®’ As evidence, let me briefly mention at least one other such additional area: that o f the whole complex o f grace, merit, reward, and sin and their determined relations. The ways in which the fit is accomplished are sometimes explicit, sometimes rather more implicit; but allow me to tabulate, as it were, a number o f examples

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without regard to such qualification. The augmentation, and hence intension, o f caritas through meritorious acts must be consistent with the fact that only a finite amount o f caritas is permitted man.®® Or, the intensibility and remissibility o f acts o f the will must not lead to the equation o f mortal and venial sin.®® Or, i f love for God and fellow-man is intensible and remissible and capable o f having proportiones between its degrees, then we must take care to avoid having this obliterate the required distinction between fruitio and usus. Or, the proportionabihty o f caritas and premia must fit with the fact that omni beato Deus est equatepremium.^'^ Or, more broadly now, the whole “ mechanics” o f merit, demerit, sin, reward, conscience, precepts, etc., must, because this “ mechanics” operates in time, mesh with the language o f first and last instants.® Or, finally, this same language o f instants must be made consistent with the simultaneous action o f God and the human will in each actus voluntatis, for otherwise man could sin mortally instantaneously after being in a state o f grace.

I f the imaginativeness o f these tests o f consistency seems impressive (or depressive as the case may be), then the reaction may well be next to overwhelming when it comes to the actual application o f our languages to particular instances. I f time would permit, it would be worthwhile to display at random a fair number o f these theological casus secundum imaginationem in all their complexity. Such would more accurately give a truer flavor o f the original sources. As it is, I shall have to treat the matter far more briefly. Unfortunately, there seems to be no striking overall pattern to the particular arguments in which the languages are invoked. Yet there are remarks that should be made about the ways the various appHcations are made, their scope, and the apparent repute in which they were held.

The first thing that needs saying is that all o f the measure languages are applied, those o f intension and remission and continuity-infinity most frequently so.® Secondly, it should be emphasized that, once the general fit o f the language to the context in question has been established (and it almost always is), then no matter what difficulties or logical peculiarities may be made to surface in the application o f the language in specific casus, the language is never, as far as I have been able to discover, rejected as inappropriate. Even when such difficulties reached the level o f near insurmountability, the languages are tenaciously retained, the maximum retreat being an occasional declaration o f a casus impossibilis.^^


Indeed, we even find “ theological retreat” in the abandonment o f a hitherto accepted authority. »6

As in the case o f almost any method, the application o f the languages occurs both in order to estabhsh the author’s position and to argue against it. Again as is usual in scholasticism, the arguments using the languages lead in any direction that will serve the author’s purpose: to confrontation with a theological principle, to a logical contradiction, or to a state o f affairs that is in some other way intolerable (usually, interestingly enough, involving the infinite). At times, the author argues immediately from the languages as applied to the entity under investigation directly to the point he wishes to make; but this is only occasional as is usual with most scholastic argument.®’

O f greater interest is precisely what it is that makes the languages an effective tool in each argument or casus ; what is, one might ask, the moving force or crucial step in each case? It is difficult to generahze, but there do appear to be several recurrent factors.®® In some instances, it is what might be called the “ additivity” invoked in the measure language being applied that gives rise to that being sought (usually a difficultas against the author’s view).®® At other times, the moving force derives from the attempt to fit the languages with one or another res in d iv is ib ilis .O f greatest frequency o f all - and also I think o f greatest interest - is the connection made between the freedom o f the will (both Divine and human) and the language o f continuity. In effect, the liberty or contingency postulated by the will allows o f the choice o f any one o f the infinity o f “ values” within a given continuum. Interestingly enough, the function o f the velle libere involved may be either to determine some particular value within a continuous interval or, more naturally, to show that an already determined value cannot stand (since another can be selected infinitely near it that will serve the same function).^®^ In addition to its intrinsic interest, to have the libertas voluntatis play such a role might be considered evidence relevant to my speculation about the importance o f voluntarism in general in the rise o f the application o f our languages.

I have above stated that in many instances (indeed, it seems in most) the measure languages were applied in arguments directed against the author’s opinio propria. In almost all such cases, the language was not, as I have said, compromised. Instead we almost always have to do with some alteration, some distinction, made with respect to the subjects to

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which the language is being applied.^o^ From time to time this tidying up o f the domain o f application becomes relatively systematic. One is witness to minor disquisitions on the permissible manners o f augmentation, or on the general applicability o f proportiones to entities o f a variety o f sorts.104 Jean Mirecourt, however, seems to be the most systematic and thorough o f all in this respect. He formulates, for example, what can appropriately be considered his own language o f proportiones and excessus, complete with its own vocabulary and algorithms, the whole o f it tailored in advance to fit his purposes. The “ alteration o f subjects” I have mentioned is, in other words, built into the language, Even more astonishing is the fact that in another Book o f his Sentences he devotes seven complete questiones to the elucidation o f whether, and just how, a whole battery o f theological conceptions fit with the languages o f intension and remission and first and last instants, lo® That he regarded this to be a serious undertaking receives confirmation from his own expUcit reference in his Apologia prima to its significance.^o' And this is not the only time that we find our languages implicated in Mirecourt’s condemnation. We even find him establishing his innocence o f an error his accusers had charged him with by explaining that, far from it being his intention to assert the notion in question, what he really meant to do was simply to determine the proper way to measure man’s meritorious goodness {Volebam igitur dicere, quod penes maximum gradum habitus meritorii attenditur bonitas hominis meritoria, et non penes maximum gradum actus \ it is worth noting that the terms penes quid attenditur were a standard, fourteenth century way o f asking for the measure o f a thing), lo®

Mirecourt is an extraordinarily explicit yardstick, it would seem, for the extent and importance o f our languages in theology. The frequency with which they occur in his Sentences surely would have put him at odds with the 1366 Statutes we have cited. But Mirecourt also represents a different level o f official displeasure. The Statutes, and the anonymous text I have cited o f roughly the same time, frowned on the use o f logic and mathematical conceptions; Mirecourt was condemned for asserting propositions that resulted from his use o f such tools, that is to say, from his application o f our languages.!®^

One might wonder if Mirecourt is not rather uncharacteristic in the apparently quite thorough penetration the new analytical languages had made into his theological work. Not so. There are numerous others who


exhibit the same pattern (save, o f course, for the condemnation). A ll o f the various theologians it has been, and will be, our occasion to cite are cases in point. For they apply the languages not merely in those contexts that are here referred to, but in all manner o f other corners o f their Sentence Commentaries. The proper conclusion is, I beheve, that utilization o f our languages was in no sense remarkable, but rather quite common.iio There is, moreover, one thing that should be said about the significance o f their use, even in face o f the fact that we naturally need far more work on the sources before anything like a definitive evaluation can be reached.

I have above drawn attention to the well-recognized role o f the potentia Dei absoluta in fourteenth century theology (and philosophy for that matter) and have noted its connection with rationes and casus secundum imaginationem. Let me reconsider this link in terms o f the language application I have described since that point. One should maintain, I think, that appeal to the potentia absoluta accounts for the fact that we have to do with secundum imaginationem procedures within theology, m But this is only half o f the story. We must explain not just that a greater number o f casus were treated de potentia Dei absoluta, but why it was that these new casus, or these kinds o f new casus, were treated. Now it seems to me that the application o f the new analytical languages takes care o f the second explicandum for a particular (but tolerably large) set o f these new casus. Further, I would urge this in the strong sense o f maintaining that these particular imaginationem elements in theology would not have been possible without the languages. Given this, at least two questions, or better two prospective avenues o f investigation, follow.

The first is to determine how many, or which sorts, o f these “ language- based” casus and rationes were new versions o f older, but substantially equivalent,ii2 casus and rationes, and how many, or which sorts, were totally new creations. (An educated guess would be that the latter would far outnumber the former.) Secondly, would it not be profitable to inquire whether the apphcation o f one or another o f the new languages may not have been the reason behind, not the origin, but the development and preservation o f some o f the major questiones in which this application occurs? Both o f these queries are, o f course, not subjects that can be treated here; they are, rather, a program for another paper.

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B. Extensive Concern with Continuity and the Infinite

The roster o f the new measure languages that has been given above included one labelled that o f “ continuity and infinity.” It was also pointed out that its function was more comprehensive than that o f the other measure languages and that its elements often embraced and found expression in the elements o f these other languages. I should now hke to examine this embracing at closer quarters and relate it to the preponderance o f continuum-infinity considerations that is immediately discernable in the “ language-application” segments o f theology.

It is best to begin with a brief overview o f this language’s constituents. On the one hand, it had to cover the infinitely great: cases o f entities infinitely distant from one another, the relation o f infinities to finîtes and o f finite values to (indivisible) zero values. On the other hand, infinity entered the field in a second way through the infinite divisibility o f continua, which was perhaps the factor most frequently behind the invocation o f this particular measure language. This divisibility, and hence the language in question, entailed consideration o f the order, the “ betweenness” properties, o f the divisions and parts resulting from it, o f the number o f these parts (how many in a part o f a continuum versus how many in the whole?) and of their relations (what are the ultimate parts o f a continuum and how do they “ fit together” in constituting it?). Further, it also considered the various manners o f characterizing this infinite divisibility {partes eiusdem quantitatis and/or partes eiusdem proportionis) and the problem o f what one must say o f its corresponding necessity in domains that were connected on other grounds (parallel divisibility, for example, for motion, time, and magnitude). Relative to all these considerations, a pertinent vocabulary was developed and appropriate algorithms set out,ii4 although to a greater degree than in the case o f the other measure languages such could be obtained from the inherited tradition, especially from the later books o f Aristotle’s Physics.

It will be evident even from this incomplete catalogue o f the contents o f the continuity-infinity language that it was broader than the other measure languages. Broader because the continuousness o f the subjects to which the languages were applied was a more fundamental or more primary property than others whose “ measure” might similarly, even simultaneously, be being taken, Thus, the continuity and hence the infinite

divisibility o f a static magnitude (a geometric line, for example) was one with that o f a continuous variation over time in (say) the heat o f some subject. But other properties that could be considered for measure might be nonisomorphic (for instance, the points or parts o f the line vs. the degrees or differences o f degrees over segments in the heat variation).

Now such a greater comprehensiveness in the subjects involved was directly reflected in the languages themselves. To begin with, one should realize that all three limit languages were themselves continuity-infinity languages, for if they were not always faced with representing the setting o f limits for continuous processes or entities, they consistently had to come to grips with the distinction between the continuous and the discrete no matter what they were being applied to.i^^ Secondly, the remaining two measure languages o f intension and remission and o f proportiones also fell under the jurisdiction o f that o f continuity-infinity. This took the form o f having what might appropriately be called derived algorithms in the former being legislated by the latter. Thus, for example, from the attempt to determine precisely how the initial point o f a line segment is related to the rest o f the line and the resulting algorithm that there is no point in the line immediately following its first point, one has the parallel attempt to determine the relation o f the non-gradus o f a given quality to the total latitudo o f that quality and the derived algorithm that there is no gradus remississimus o f that quality, Alternatively, one can observe similar derivations from the continuity-infinity domain when, from reasoning about the relation o f a line to a point, or a surface to a line, one set up algorithms de proportionibus quoad excessum infinitum, or when, from the divisibility o f a continuum into aliquot parts, one derived rules governing the partes o f p r o p o r t io n e s O f course, given such connection between languages, one had to keep a watchful eye on maintaining their consistency, and especially their consistency with one’s conception o f the subjects to which they could apply, something that occasionally gave rise to a certain amount o f trouble,

With these facts about the “ second level” position o f the continuity- infinity language and about its relation to the other measure languages in m i n d , l e t us now attempt to see in outline why and how this more comprehensive language was applied in theological contexts. Taking the two halves, as it were, o f the language one by one, the most obvious causal factors in this regard have to do with the presence o f God as an

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“ urger o f the infinite.” First in the order o f obviousness is the infinity o f God himself. Taken in almost any o f its various s e n s e s , 1 2 0 this automatically brought in one or another o f the languages in order to measure the infinite involved. It could be a question o f setting the yardstick to His infinity as such, to the kinds o f infinites He could possibly (i.e., logically) produce, or to His infinite “ distance” from res creata.^^^

On the other hand, in addition to infinitely great magnitudes and multitudes in general, God also served as the introducer o f the particular infinite multitude that arises from the infinite divisibility o f continua. By far the most common way He was called upon to serve this role was the de potentia Dei absoluta actual infinite division o f a continuum into all o f its proportional parts.122 The number o f secundum imaginationem rationes and casus that employ this “ proportional part matrix” is almost incalculable (in natural philosophy as well as in theology).

However, there was another way in which the infinite divisibility o f continua fell into theological contexts. It did not require an appeal to God, but arose so to say, secundum naturam. That is, many o f the processes that demanded theological consideration were either themselves continuous or necessarily occurred against some continuous background (usually the continuum o f time). In the first case, continuity-infinity derived algorithms o f intension and remission were directly pertinent ;i23 in the second, one invariably had recourse to one o f the limit languages.124

It bears mention, moreover, that precisely the same phenomenon occurred everywhere within natural philosophy, for the processes and entities it had to treat were also invariably continuous or took place within continuous time.^25 In contrast, however, natural philosophy usually did not possess the built-in infinity o f God for the benefit o f its deliberations. Infinite values did indeed permeate these deliberations, but they did not result from the presence o f God as infinite. A t most, they were assured through an appeal to His potentia absoluta, although in most instances natural philosophers were content to create infinite values by the simple secundum imaginationem exercise o f their wits.^^e

In any event, given the foregoing account o f how the language o f continuity-infinity was most often introduced into theology, it remains to consider what it looked like once there. Again the problem of elucidating some pattern is a formidable one. Nevertheless, one can sift out at least three themes that are recurrent enough to bear generalization.

The first is that secundum imaginationem casus applying our languages are repeatedly used to lead to the existence o f unacceptable infinites. These are almost always intensive infinites, and their possible existence either runs counter to theology (infinitely intense sin, merit, caritas, dilectio, or, more generally, actus) or to natural philosophy (infinite velocity, for example).^^’ There is also, fortunately, some pattern in how the existence o f these infinites is established. Sometimes the “ proportional part matrix” ploy is used, but more often it is either the libere action o f the will or the possibility o f indivisible values that affords the required ammunition. The freedom o f the will is made effective because its free action entails the intensibility and remissibility, and hence successiveness, o f its acts ; in turn, the rules for intension and remission then provide for the infinite increase in question.^2® Indivisible values, almost all o f which consist in the admission o f some kind o f change or action within an instant, lead to the undesirable infinites when they are plugged into the relevant algorithms governing the necessary increase in the effect o f an agent the longer it acts. 129

The implied existence o f all o f the foregoing infinites is always to be denied. But there were infinites that had to be admitted. Indeed, they constitute the ingredients within the second recurrent theme that is to be found in the theological application o f continuity-infinity language: that o f the accommodation o f certain types o f infinite excess into the fabric o f the languages, both that o f continuity-infinity and that o f proportiones. This accommodation was necessary for two reasons: to account for, or better to measure, the relation o f God to his creatures and to set up a proper scale for the required radical distinction between the different species o f these creatures. The first kind o f measuring had to be admitted not merely because it seemed required to say something about the relation o f God’s perfection to that o f inferiora, but also because man necessarily had the capacity o f being able to stand to God with the same kind, but different degree, o f relation (notably that o f dilectio and visio) as he was to other finite things. This required the permissibility o f infinite values in the measure o f at least those relations.

Such values were also required, however, even when God was excluded from the scale. For the radical distinction o f created species was consistently interpreted in the sense o f an infinite “ distance” between the members o f such species. Thus, consideration o f the perfection o f species went hand in hand with the problem o f making adjustments for the intro

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duction o f infinite excess into the relevant measure languages.iî But the revision and supplementing o f the languages did not end here. For i f one was under the obligation to allow infinite distance between God and creature and also between creature and creature, then clearly at least two kinds o f infinite excess must be accommodated. 1 2

Still another kind o f struggle with the infinite forms the third, and final, theme that I shall note. Less a matter o f having to effect an adjustment in the measure languages than was the problem o f infinite excess that I have just described, it nevertheless seems to have been believed that the languages would not be in proper order unless this additional factor could be encompassed as well. More o f a puzzle than a simple factor, their concern was with what we would term the problem o f relating infinite sets and subsets. The context was usually the discussion o f either the possible eternity o f the world or the kinds o f infinities licit under God’s omnipotence,i33 but it also appears as relevant to the kinds o f issues o f grace and the will that we have been concentrating upon.i34 Apparently, infinity and continuity had so thoroughly penetrated theology that all o f their aspects were regarded as o f significance, not merely those that one would have thought most relevant to theological debate. In at least one instance the penetration was so complete that a fair interpretation o f a whole Sentence Commentary would be to consider it a treatise on the continuum and the infinite. 135 An exaggerated case perhaps, but directly related to a general point that should be made. In as many, indeed in more, instances than not, whenever it was a question o f measure and measure languages, what was being measured involved some aspect o f the infinite, be it infinite distance, infinite multitudes, or the infinite denseness o f continua made no difference. I have above noted a specific instance o f the insertion o f a theological subject into the “ physics” relevant to it.iê But what kind o f “ physics” is it or what is the nature o f the elements that were considered in this “ physics” ? Basically, such elements have to do with considerations o f infinity and continuity: what is important, we are told, is whether the power o f the agents involved is finite or infinite, whether they act in time or instantaneously, whether the effect produced is divisible or indivisible, etc. But these are all pieces o f the continuity-infinity game.

Furthermore, it is not just in theology that measurement so often involves infinite values; the same is true within fourteenth century natural philosophy as well. ®' It is important that, as historians, we take this


preponderance o f continuity and infinity into account and appreciate its significance. 138 The medievals themselves did. For, to return again to theology, not only is the importance o f such revealed by its fit with the infinity o f God as its subiectum, but we find some theologians aware enough o f what they were doing to remark on the necessity o f examining the whole basis o f “ ad infinitum” arguments,

C. Sophismata and Unity

Were I at this point to attempt to formulate a one sentence resume o f what I have been trying to say and trying to assemble evidence for, it would claim, first o f all, that there existed a secondary (and hence weaker) methodological MViiiy o f philosophy and theology in the fourteenth century which resided in the common application o f the new analytical languages (largely measure languages) o f which I have been speaking and, secondly, that in both theology and natural philosophy in a very large number o f cases this application was concerned specifically with questions o f infinity and continuity, that, in other terms, the dominant kind o f measure at stake was one occupied with infinite values. I f all o f this, as methodological, speaks o f a second level unity, then what I should now like to treat briefly introduces a third level unity. For I shall be addressing myself to a description o f one o f the predominant ways in which the analytical languages were applied (again in both natural philosophy and theology). That way was through sophismata.

The terms ‘sophismata’ and ‘sophisma’ (let alone ‘sophistice’ , ‘ sophis- matice’ , etc) have a variety o f meanings in the Middle Ages, so it is well that I specify at the outset precisely what I have in mind. The simplest and most adequate way o f accomplishing this is, I think, merely to point to those elements called sophismata in, for example, the Summule logicales o f Peter o f Spain or in the Sophisma nuper emendata o f Albert o f Saxony. Looking at elements o f this sort, whatever other characteristics they may have or whatever role they may play in medieval intellectual history, it is fair to say that a sophisma is a proposition (often bizarre in some way) that can be interpreted in two different ways, one o f which is usually the proper one. A t times these “ two different ways” (appropriately displayed as probatur and improbatur) are reflected in the very enunciation o f the sophisma itself insofar as it contains, prima facie, both o f two seemingly contradictory elements.iô

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Whether sophismata taken in this sense are the disputationes de sophis- matibus articulated in university statutes, or whether one should consider them the Artes mate to the quodlibetal question o f the faculties o f theology, are problems that need not be resolved here.^^ For without such institutional support, there is more than adequate evidence in the logical literature o f the twelfth and thirteenth centuries revealing that sophismata (in precisely the sense I have in mind here) formed a frequent and well developed preoccupation. One has to do, therefore, with a tradition that is a good deal older than the analytical languages o f which I have been speaking. As we shall see, it was a tradition that can also be properly termed analytical.

For a concise statement o f how the medieval operated with sophismata, it seems to me that the most satisfactory interpretation is still that o f one o f the first historians to concern himself with the relevant literature. The literature in question is, o f course, more involved with logic and grammar, than with philosophy as a whole or with natural philosophy as a part o f it. We are told, in sum, that the treatment o f logical and grammatical sophismata can be interpreted as having the character o f the “ application o f a theory,” o f a set o f rules or distinctions. That is to say, their treatment has this character insofar as the sophismata themselves furnish (often rather strange) confirming examples o f the theory, the theory being applied in order to “ resolve” these examples. (Indeed, it is only after they have been resolved that they can appropriately be said to be confirming instances.)

In the thirteenth century, and in most instances in the fourteenth century as well, the “ theory” involved was naturally most often a logical one. It might have to do, for example, with something simple like the distinction between two kinds o f supposition (and between the types o f logical descent to singular propositions that is licit in each instance), or the “ theory” might consist o f more complicated matters such as the distinction between the composite and the divisive sense or such as the rules governing the modal context elicited by the presence o f cognitive verbs o f knowing, doubting, or believing.

The point I should like to make with respect to all o f this is that the pattern o f the application o f such a “ theory,” or o f such rules, was with few exceptions quite the same as that which we find in the application o f the new languages o f measure in the fourteenth century. This is

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especially clear in those instances in which the application o f these languages was set upon the testing o f a basic rule or algorithm o f the language in question (again Heytesbury, Swineshead, and the whole Mertonian clique in particular). For one can rightly interpret the outlandish variant cases invented to carry out this test as sophismata. A longstanding tradition in the exercise and development o f logical subtleties was bearing fruit, one might say, in the newer pastures o f subtilitates de

motuM'^What is more, this is also a profitable way to view things even in many

instances (in both natural philosophy and theology now) in which “ basic algorithm testing” is not the primary concern. In the cases I have in mind, the proof o f something external to the language being applied is that o f central importance. In establishing this external point (the freedom of the will, for example, or the fact that it necessarily acts successively), one faces a secundum imaginationem argument to the contrary in which a new measure language is applied; this argument is then in turn resolved in terms o f the same measure language. Now I believe that one can appropriately consider such an argument and its resolution as bearing an intriguing resemblance to a sophism. O f course this “ sophism” itself is almost never stated explicitly; but I think it can be elicited. Note first the usual procedure in the contrary argument: One moves from the idea being opposed to a secundum imaginationem casus that utilizes some measure language and from this one infers some absurd and unacceptable result (venial is equivalent to mortal sin, the soul o f Christ is comparable with the soul o f Judas, or what have you), this absurdity in turn naturally im p ly in g the rejection o f the initial idea. Consider now the resolution: To be sure, the absurdity is done away with or rendered innocuous, but in addition it is almost always simultaneously shown that the measure language used in the casus that gave rise to the absurdity still applies to the “ variables” in the casus (to mortal and venial sin, or to Christ and Judas, for example). Just how it applies is also shown.

Now the “ sophism” involved is not the absurdity alone,i45 but rather the whole procedure that I have just described. The fact that the absurdity is dissolved but nevertheless has the variables generating it taken into account by the language, corresponds, I would submit, to the two ways o f interpreting a genuine sophism (its probatur and improbatur phases, as it were). Finally, the “ theory” or “ set o f distinctions” involved in our less

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authentic “ sophism” is naturally the measure language in question, or some part o f it. For it is preserved; its terms are utilized in both the “ generating” argument and its resolution, This, then, is at least one possible way that the influence o f the sophismata tradition may be seen in a broader domain o f language application and not merely in that o f the Oxford calculatores and their confreres. I f nothing else, perhaps it might offer some explanation o f why it is that so many o f the measure language casus sound so very much like at least parts o f sophisms.

Let me now try to establish that my claim o f this pervasiveness o f sophismata-h2L Qà reasoning, especially in natural philosophy, is not an overworking o f the historical imagination. Attention should be drawn, to begin with, to the fact that it has for some time been recognized that a number o f sophismata physicalia occur in the fourteenth century literature.148 xhis discovery was based merely on the enunciations o f the sophismata in question and one could extend this kind o f evidence considerably. One can, however, confirm the connection in question in other, more substantial, ways.

There is, for example, the occurrence o f physicalia in a number o f the logical sophismata o f the thirteenth century, especially when it is a question o f ‘incipit’ and ‘desinit’ as syncategorematic terms.i^o There is also a good deal o f the physical, in particular much that is directly bound up with our measure languages, in fourteenth century sophisms that have been hitherto regarded as purely logical, gut even stronger evidence can be found in the fact that, within the most important natural philosophical treatises de motu in the fourteenth century, we find the variant cases o f change with which the author was dealing explicitly being called sophismata. What is more, i f we there examine the nature o f the sophisma so revealed, in many instances the measure it is concerned with is the familiar brand dealing with infinite values.

Turning to the bearing that all o f this has within theology, it is o f course true that we do not have any collections o f theological sophismata.^^ Nor do we have, as far as I have noticed, anything more than the incidental labeUing o f arguments in Sentence Commentaries as sophismata. This notwithstanding, it is proper, I think, to regard many o f the particular applications that I have noted o f the measure languages as just that. We have, as it were, '‘'‘sophismata without announcement.”

In both philosophy and theology they provided a convenient mold in


which to pour secundum imaginationem arguments and examples. One would imagine moreover, that the relative antiquity o f the tradition from which they came must also have given a certain amount o f expertise to their utilization. In concluding, I cannot resist quoting a couplet created in honor o f sophismata that a fourteenth century student was moved to inscribe in the margins o f his notebook: Concedat Cristus michi perlustrare sophisma, ut panis pistus reddat nullibi cisma.^^^

IIL CO NC LU SIO N

Every essay comes to an end, I would imagine, by its author trusting that what has been said has in some measure succeeded in showing how unnecessary was the reader’s willing suspension o f disbelief. In this case, I hope that any success has at least had the effect o f estabUshing that there was a secondary, methodological unity within fourteenth century philosophy and theology. In addition to this fact, I have o f course been concerned to spell out at least one form that this unity assumed, a form that was, I beUeve, an important one among those factors enabhng the fourteenth century scholar to move with relative ease, as I put it above, from faculty to faculty, and to do so with a reasonable confidence in his competence to deal with the tasks and questions asked o f him. How important has been at least partially indicated, I hope, by the particular points o f significance made in passing about the application o f the new analytical languages. In concluding, I should like to propose several additional remarks about the significance o f this phenomenon. They are remarks, unfortunately, that will have to be put in a general and abstract way and in part will be intended as more suggestive than conclusive.

The remarks are all, basically, ones o f comparison: what can be said o f the fourteenth century unity o f philosophy and theology with respect to that which preceded it? In the interests o f getting down to essentials quickly, let us concede the existence o f such a unity in both the fourteenth and thirteenth centuries, (from, say, 1260 on for the latter) and let us also grant that there occurred a shift from a fundamentally cosmological, speculative stance in the thirteenth to an analytic and critical one in the fourteenth. 155 Was there, let us now ask, any significant difference in the character o f the unity from century to century (i.e., an important difference beyond the fact that different things or problems may have been so uni-

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fied)? Intuitively, one would gather that there would be numerous differences. I should like to direct attention to one. It stands a good chance, I think, o f being the most important. Put abstractly, it amounts to claiming that that which did the unifying in the fourteenth century (or at least those unifiers o f which I have been speaking) was less touched, less changed, in carrying out the unification in question than was that which played the corresponding role in the thirteenth century. Let me try to fill in a few details.

Whatever unity there was to philosophy and theology in the thirteenth century, what was central to it can profitably be interpreted in terms o f the prevailing Aristotelianism.i^e Unification occurred, that is, by means o f the systematic application o f Aristotelian conceptions, definitions, and principles to theological subjects. But when these Aristotelian notions were apphed, as it were, to God and to the Christian universe, they were altered in a way, and to a degree, that the parallel “ unifying” algorithms o f the fourteenth century analytical languages were not.i^? The fourteenth century languages did not suifer, to put it in terms o f a metaphorical example, anything like the Avicennizing or Dionysianizing undergone by Aristotelianism.iss Or, to make another comparison, no algorithm o f a fourteenth century analytical language was ever prey to a debate as controversial and as extended as that surrounding the Omne quod movetur axiom.^^®

To this one might object that the accommodations made to allow the incorporation o f such new elements as infinite values consitute a fourteenth century analogue o f the thirteenth century Aristotelian alterations. Not quite. For these accommodations were almost always additions that did not violate the existing structure o f the language or change its algorithms.!®»

Another manner o f expressing the particular point I am attempting to make would, I suppose, be to claim that the unification o f philosophy and theology in the thirteenth century occurred magis materialiter quam formaliter. How could this be avoided, one might ask, i f a great part o f theology was to be expressed in Aristotelian terms and if this expression was to be carried out within the fabric o f all-encompassing philosophical- theological systems? This is not to maintain, by contrast, that all philosophy in fourteenth century theology was analytical languages (or analytical anything for that matter) and no Aristotle. But there was


much less o f Aristotle there and in a different way. For fourteenth century philosophy, especially natural philosophy, bore a largely reformulated Aristotle, reformulated in terms consistent with the new logical and epistemological requirements developed in that century (our analytical languages being involved in no small part, incidentally, o f these requirements).!®^ This in turn meant that one did not have to do so much with parts o f theology expressed in Aristotelian terms, but rather with Aristotelianism and parts o f theology expressed in a single terminology that stood apart from each. When to this one adds the fact that this terminology and the conceptual apparatus behind it were basically analytical, then a unity for theology and philosophy that is magis formaliter quam materialiter follows rather naturally. But such is just the unity that the new analytical languages, and my thesis, speak for.

I could finish with this confirming observation were it not for the fact that, save for occasional references to the importance o f the medieval university, I have said almost nothing about the first part o f my title. Yet I have not by this intended that social factors be removed from the scene by silence. I should like to offer at least some argument for the background position I have apparently assigned to them.

As is to perhaps a certain extent already implicit in some o f the things I have said, the unitary character o f medieval learning in general started socially, or had a social base. By this I mean to point not simply to the universities, but also to the monastic and cathedral schools before them, and to all other social elements o f tradition that went into constituting a Christian education and to producing Christian scholars. Nevertheless, although one can thus properly maintain that such a unitary character started socially, it seems to me undeniable that it developed intellectually. In particular, when it comes to the explanation o f the kind o f philosophical-theological unity that I have been describing, the relevant factors are overwhelmingly intellectual. A t best, social factors account for available possibilities; they seldom say anything about which ones were taken up and why. It may be true, for example, that social factors are intimately involved in a training in depth in logic within the thirteenth century, but they do not, as far as I can see, explain why this or that was done with it at the end o f the century, Furthermore, I do not really see that any non-intellectual ideology dictated, or perhaps even influenced, the development o f the kind o f unity I have been treating or o f the analytical langu

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ages that made it what it was. i^^Adequate investigation and explanation o f such developments demand, I believe, a detailed consideration o f just those kinds o f sources I have here utilized for documentation, and they are not, save with few exceptions, social ones. Yet I know o f no other way to proceed and to answer these kinds o f questions. As I have tried to indicate in the first, perhaps overly enigmatic, part o f the title to this paper, the historian must follow the path o f sources running from social into intellectual factors. The intellectual factors that I have found to be most relevant, however, are not ones specifically tied to individual works or accomplishments; they are largely common, methodological ones that can be seen as binding together whole groups o f scholars and, hence, as indicative o f broader intellectual characteristics and developments. As such, they are those factors most likely to be encountered in moving from the social to the intellectual.

One might reply to my belief in the necessity o f making this move that the analytical attitude that the new fourteenth century languages expressed can be viewed as a “ habit o f mind” characteristic o f a particular social group. Although I must admit to speaking with an appreciable ignorance o f most sociology o f knowledge, I do not think that this is o f much help. It cannot explain or account for the occurrence o f the phenomenon I have been concerned with if for no other reason because, as I see it, such a “ habit” or “ mentaUté” is an eflFect o f the development in question, not a cause. It is, i f one can so speak, the development developed or at least partially developed. As such, it may indeed explain the growth o f the attitude for which it stands, yet even here I would hazard that it would function more adequately in accounting merely for expansion in extension, both in the number o f new adherents and in the number o f new areas or problems in which the attitude can be discovered. Seldom would it explain, I think, a change or development in the attitude itself.

Further, a related point can be made in historiographic terms. It is that when we find a historian asserting the existence o f such a “ habit o f mind” (characterizing the fourteenth century, for example, as “ critical and analytic” ), the assertion is naturally almost always in the nature o f a conclusion drawn from a great deal o f previous research. Once it has been asserted (assuming it accurately describes the intellectual phenomenon in question), it can then serve the quite valuable function o f telling other historians what to expect and what to look for when they cover unexplored


ground o f the same territory. To be aware o f the “ critical and analytic habit” may well prove to be o f immeasurable assistance in properly interpreting such new material. Surely, however, we should not stop there. One should - to cite my own bias - inquire further into the “ habit” : given an analytic attitude, one ought to ask in precisely what way it was analytic and how it may have changed, grown, or passed into disuse. I have intended the present essay in part to do just that: to set forth one important aspect o f just how the fourteenth century attitude was analytic. But it is just one aspect. To follow this kind o f trail, however, is to continue the track from social into intellectual factors.

The results that I have reached over the short part o f the trail I have thus far managed to cover are intended as an instance (albeit quite one-sided) o f the cooperative history o f science-philosophy and theology that I recommended at the outset, so it is perhaps well that I conclude with a few reflections in this direction. Simply put, I should merely like to offer a few suggestions, or perhaps questions, o f how, apart from any historical value it may hold per se, the weaker unity o f philosophy and theology that I have been touting might prove o f interest to the histories o f medieval science and theology in general.

A t the most evident level, I would think that it would be appreciably instructive to the historian o f science to observe with some care exactly how languages and techniques developed largely in natural philosophy looked when disseminated to other areas or disciplines. One might even wish to summon enough courage to ask the rather intriguing question o f whether the “ results” obtained through the application o f the measure languages within theological contexts may not be viewed as in some sense being more important to the medieval scheme o f things as a whole than were those elicited in natural philosophy proper. Further, it would be well to sensitize one’s antennae for the discerning o f any possible change the languages may have suffered when transferred to the theological realm (one thinks for example, o f determining what may have been added to their development through their appUcation to “ theological in-finites” ).i65

The possible yield for the history o f theology is perhaps even greater. For in spite o f the separation o f faith and reason that is frequently to be found confidently asserted in so many h is to r i e s , i t seems to me that theology ended up being more philosophical in the fourteenth century

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than it had previously been. Setting aside those evaluations that have seen the fourteenth century as a whole as decadent and as guilty o f inducing the disintegration o f scholasticism, this theology has been pictured as one o f logicizing, as one of, to cite one o f the most expressive ways o f putting it, un usage extrêmement serré et touffu des procédés d ia le c tiq u e s .True. But the application o f the new analytical languages explains at least one way in which this thorough-going dialecticism occurs, one form which de potentia Dei absoluta secundum imaginationem machinations took. And there is much more to be appreciated along similar lines, especially the pervasive utilization o f a second intentional point o f view within theology.168 Finally, i f historians can muster the patience to trace, step by step, the application o f the new languages through all o f their convolutions, perhaps we shall learn better to appreciate the proper significance within theology o f what have sometimes been regarded as mere “ logical stunts” or the calculated display o f “ Oxonian sensationaUsm and casuistry.” ®® The application was not, I would suggest, simply the result o f trying to dazzle one’s audience by the ostentatious flaunting o f knowledge and know-how, at least no more so than in any number o f other scholastic philosophical and theological works in which the analytical attitude was not present. It was instead, I believe, a very serious way o f accomplishing things, o f contributing to the resolution o f important issues, in both natural philosophy and in theology. What is more, a more detailed inspection o f these languages and o f the way in which they developed and were disseminated will reveal that they were not a product o f “ an academic society which lacked... the impulse o f creative thought.” !' ® They were the result o f precisely what such a judgement denies.

Harvard University

N O T E S

* Much of the research into the primary sources upon which the present paper is based was supported by a research grant from the National Science Foundation.1 J, Murdoch, ‘Philosophy and the Enterprise of Science in the Later Middle Ages’, The Interaction between Science and Philosophy (ed. Y. Elkana, Atlantic Highlands, N.J., 1974), pp. 51-74. This paper, and a number of variant versions of it, have been both given as lectures on a number of occasions and circulated in manuscript form. The reaction and criticism that have resulted have naturally proved most valuable, especially that of Edith Sylla. Much in the revision that appears below of some of the


ideas of this earlier paper owes a great deal to discussions and correspondence we have had, as does much else in the present essay.2 Such interchange and cooperation should also be extended to the histories of law and medicine (the latter having been, for the most part, far too isolated from the rest of the history of medieval science).3 I have in mind the further investigation of why it is that such standard history of science topics as impetus theory often found expression in Sentence Commentaries (e.g., Peter John Olivi, Franciscus de Marchia) and whether such a context was of significant effect in the development and the nature of the ideas expressed,4 Such a conclusion would be, for example, Duhem’s view that the essentials of seventeenth century mechanics could be found in the fourteenth as a result of the Church’s 1277 condemnation of Aristotelianism.® Above, note 1. Revisions that I would now like to make of some of the views I then expressed are for the most part made below.® The medieval “ science” in question excludes mathematics, technical astronomy, formal logic, natural history, practical medicine, and (for somewhat different reasons) statics and optics. But this leaves the substantial area of so-called “kinematics and dynamics” in which the most creative thought of fourteenth century “science” is to be found.’ Much more than merely stating it is necessary to convince one that this is true. Some of what follows may serve this function, but I have tried to argue for the point somewhat more explicitly elsewhere (above, note 1).* Future research might address itself to the question of the “degree” of a similar unity with law and academic medicine.® Although there was naturally some material in Aristotle directly relevant to such problems (most notably, of course, De interpretatione, ch. 9 for future contingents), many important new elements in their treatment derived from their theological context.

See, for example, P. Glorieux, ‘Sentences (Commentaires sur les)’. Dictionnaire de théologie catholique, 14, col. 1875.

Such extreme sparseness in the number of questiones I have been able to find only in John Sharpe’s work on the Physics (he has - MS Balliol 93, 35v-91v - but one questio for each Book, save two for IV).

Book I, dist. 37, for example, whose concern is, to use St. Thomas’s words, quibus modis dicatur Deus esse in rebus, accommodates the examination of the possible infinite capacity of an entity like the soul (R. Killington, BN 14576, 150r-161r: Utrum omnis creatura sit sue nature cum certis limitibus circumscripta), a detailed discussion of the possible composition of continua out of indivisibles (Gerard of Odo; see note 16 below), and an extensive examination of imaginary infinite void space (Jean de Ripa; see Traditio 23 (1967) 191-267).

It is probably obvious that in claiming this unity, both here and in what follows, I do not wish to maintain that all fourteenth century Sentence Commentaries exhibit it. But many of the most important do, especially the anglicanae.

P. Glorieux, ‘Jean de Falisca: La formation d’un maître en théologie au XlVe siècle’. Archives d ’hist. doct. et litt. du moyen âge, 33 (1966) 23-104. The MSS are (for theology) BN 16408, BN 16409, BN 16535 and (for science) BN 16621. On the last see, for example, P. Duhem, Le système du monde, vol. 7 (Paris, 1956) p. 607ff; L. Thorndike, ‘Some Medieval and Renaissance Manuscripts on Physics’, Proceedings o f the American Philosophical Society 104 (1960) 189-191.

Thus, Worcester Cath. F.35, although it contains much more logic and natural

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philosophy than theology, is a good case in point. A preliminary analysis indicates that it should prove of considerable value in allowing us to construct the picture of the spread and utilization of “Mertonian” natural philosophy in the later fourteenth century.

For details, see Franciscan Studies 26 (1966) 213-214.On Rosetus and his Sent, in general see note 82 below. For MSS of Q.l, art, 1 as a

separate tract see Archivum franciscanum historicum 46 (1953) 91, to which one can add Oxford, Can. misc. 177, 17r-182r; Sevilla, Colomb. 7-7-29, 147r-167r. That one of these copies (viz. Erfurt, Ampl. Q° 107, 87r-10v) belonged to Peter of Candia is learned from its explicit: iste caternus... est ad usum fratris Petri de Candia ordinis Minorum provincie Romane.

Chartularium Univ. Paris., vol. 1, p. 543.19 Chartularium Univ. Paris., vol. 3, p. 144, cited by Glorieux op. cit. (above, note 10) col. 1876.

MS BN 16408,123r : In omnibus hiis, potissime in primo articulo, victa (!) et vitare te pretende cavendo processum logicum ac mathematicum, solum philosophicum speculativum ac moralem et processum methaphisicum et theologicum prosequendo.D. Trapp {Augustinianum 4 (1964) 403) has cited this text from its clean copy in BN 16409, 185r; but he has omitted the first six words and missed te, while the last six words do not appear in BN 16409. For the possible intention behind this note, see the table of contents of MS 16408 as published in Glorieux, op. cit. (above, note 14) p. 26.

See the incisive analysis of Ockham’s treatment of this problem by Robert Guelluy, Philosophie et théologie chez Guillaume d’Ockham (Louvain/Paris, 1947). For other fourteenth century treatments, see Josef Kiirzinger, Alfonsus Vargas Toletanus und seine theologische Einleitungslehre, Beit. z. Gesch. Phil. Mittelalters 22, Heft 5-6 (Münster, 1930).22 Ernest Moody, ‘Empiricism and Metaphysics in Medieval Philosophy’, Philosophical Review 67 (1958) 161.23 The standard contexts in which discussions of these problems usually occur in Book I of the Sentences were: Dist. 38-39, for future contingents; Dist. 42-44, for God’s omnipotence and infinity, where the infinity in question was introduced either by asking directly about God’s infinity itself (e.g., in vigore, in potentia, etc.) or about the kinds of infinities that He could possibly produce. Other frequent contexts for the introduction of the infinite were the discussion of the eternity of the world and the question of whether God could know the infinite. For still others, see Section II, B below.24 In Book II of his Sent. (MS. Valencia, Cated. 200), Gerard of Odo asks (dist. 13, Q Q l-2 ); Utrum lumen vel lux multiplicet speciem suam in instanti vel in tempore; Utrum lux ista que fuit facta prima die multiplicaverit lumen suum sicut modo sol multiplicat lumen suum (52r-53r), In dist. 15, Q. 1: Utrum yris sit unum de operibus 6 dierum (64r-65v). Finally, in Book I, dist. 23, Gerard asks no less than twelve questions directly relating to first and second intentions (MS Valencia, Cated. 139,88r-101v). For the introduction of gravia and levia, see the questiones of Franciscus Mayronis as reported in Franziskanische Studien 53 (1971) 207. For the investigation of astrology, see principium to Book II by Pierre CeflFons as cited by D. Trapp, ‘Peter Ceffons of Clair- vaux’. Recherches de théologie ancienne et médiévale 24 (1957) 105; Cf. p. 103, n. 2. The fascination with the ninth sphere is also that of Ceffons (in dist. 1 of Book II ; Trapp, op. cit., p. 104).2® For example, from work in progress on Henry of Hassia’s voluminous commentary on Genesis, Nicholas Steneck has reported the existence of a veritable avalanche of


scientific materials and questions. Indeed, even within Comm. Sent., the hexaemeron is a favorite context for the introduction of such matters.2« See, for example, the recent book of Fritz Hoffmann, Die theologische Methode des Oxforder Dominikanerlehrers Robert Holcot, Beit Gesch. Phil. Theol. Mittelalters, Neue Folge, 5 (Miinster, 1971).27 Egidius flourished at Paris ca. 1370-1395; student of theology at the College of Harcourt, attached to Norman Nation ca. 1371, lectured on Sentences 1377-1378, licentiate in theology 1384, Master of House of Navarre in 1389; made cardinal by John XXIII in 1411, died 15 March 1413. His Comm. Sent, has not yet been discovered. Inasmuch as the text of his regule is brief and interesting, I give it here in toto (from MS Vat. lat. 3088, 26r-26v):

Prima regula: Quod nomina supponentia pro essentia et supposito, que non supponerent pro essentia, si essentia et suppositum distingwerentur realiter, talia ut plurimi dicuntur de personis pluraliter. Verbi gratia: ista nomina: persona suppositum yposta- sis. Et ab illa regula debet excipi hoc nomen deus quod non dicitur pluraliter de personis divinis secundum usum doctorum.

Secunda regula: Nomina supponentia pro essentia et supposito, que non supponerent nisi pro essentia, si essentia et suppositum distingwerentur realiter, talia nomina dicuntur de tribus personis singulariter et non pluraliter. Verbi gratia: deitas, essentia, natura.

Tertia regula: Nomina substantiva absoluta supponentia pro essentia et supposito, et etiam sic supponerent, si distinguerentur realiter essentia et persona, talia nomina dicuntur de tribus personis pluraliter et singulariter. Ut est iste terminus res et iste terminus entitas prout dicit Robiton quod ego non assero ut tres persone sunt tres res et una res.

Quarta regula: Nomina adiectiva supponentia pro essentia et supposito quolibet, et ad huc sic supponerent, esto quod distingwerentur realiter, talia nomina dicuntur de tribus personis singulariter et non pluraliter. Verbi gratia: Creator eternus infinitus pater et filius et spiritus sanctus, unus eternus unus creator et non tres creatores.

Quinta regula: Nomina supponentia pro uno supposito et non pro alia nunquam dicuntur db tribus personis, licet bene dicantur de isto termino deus; ut iste terminus pater.

Sexta regula: Nomina supponentia pro supposito et non pro tribus suppositis non dicuntur de essentia, sumpto hoc nomine essentia vel deitas adiective, sed bene subiective, ut essentia et pater. Si pater capitur ( !) subiective est vera ; si adiective est falsa, quia valet tantum sicud essentia est generans.

Septima regula: Omnia nomina essentialia substantiva non numeralia vere dicuntur de essentia et quolibet supposito in singulari. Et dicunt essentialia que sic supponunt pro essentia quod non persona; vel si distingwerentur essentia et persona, adhuc supponerent pro essentia, ut iste terminus deitas; et sic conceditur pater et filius et spiritus sanctus sunt deitas (26v). Et dico notanter non numeraliter quare non conceditur pater est trinitas.

Octava regula: Nomina essentialia substantiva numeralia vere dicuntur de essentia singulariter et non de supposito, ut essentia est trinitas et non pater.

Nona regula: Nomina essentialia adiectiva dicuntur de essentia et non de supposito, ut essentia est communicabilis et non pater.

Decima huiusmodi: Nomina scilicet essentialia sive adiectiva sive substantiva veraciter dicuntur de nominibus communibus totius trinitatis et etiam isto termino deus.

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Undecima regula; Nomina personalia vere dicuntur de essentia et supposito, ut essentia est persona, pater est persona.

Duodecima: Nomina personalia propria abstracta, ut paternitas filiatio, dicuntur de essentia et aliquo supposito, ut essentia est paternitas et pater est paternitas.

Tredecima regula; Nomina personalia concreta dicuntur de essentia et supposito aliquo quando sumuntur substantive, sed non quando sumuntur adiective, ut pater dicitur de essentia substantive et non adiective, quia tunc valet tantum sicud generare,

Quartadecima regula: Nomina nocionalia, ut generatio et spiratio et cetera, dicuntur de essentia et supposito aliquo vel aliquibus, non autem de omnibus, ut essentia est generatio et pater est generatio et non spiritus sanctus est generatio et cetera.

Quinta decima regula; Omnia verba tam substantiva quam adiectiva communia dicuntur de essentia et quolibet supposito et eorum participia, ut essentia creat pater creat et cetera. Et dico notanter communia, quia propria non dicuntur de quolibet supposito, ut generare spirare et cetera.

Sexta decima regula: Verba adiectiva essentialia dicuntur de essentia et non de persona, ut communicare communicatur, ut essentia communicatur et non persona.

Decima septima regula: Verba adiectiva personalia dicuntur semper de persona et non de essentia, ut generare spirare, quia essentia non generat nec spiret sed pater.

Decima octava et ultima regula; Participia talium verborum dicuntur de persona et non essentia nisi cum aliquo adiuncto quod redit ipsum non adiectum ut generans sit adiectum huius quod est res in ista propositione: essentia sit res generans.

Istas regulas posuit reverendus magister egidius de campis in lectura sua super primum sententiarum quas cum labore ex diversis doctoribus collegit anno domini m ccc° 78 die sabbati ante purificationem gloriossime virginis marie. Amen.

Adam Wodeham, Comm. Sent., Abbreviatio Henr. de Oyta (I have not found this questio in the one copy of the versio longioris that I have examined). Book I, Q.30; Utrum aliqua sit regula vel ars per quam solvi possint communiter paralogismi intra materiam Trinitatis (BN 15894, 83v).

Lurtz (fl. ca. 1390) wrote a Tractatus de paralogismis consuetis fieri in materia Trinitatis (see L. Meier, ‘Contribution à l’histoire de la théologie à l’Université d’Erfurt’, Revue d'histoire ecclésiastique, 50 (1955) 455-470). He even cites Egidius and his regule {op. cit., p. 460).

Petrus de Pulka ffl. at Vienna, d. 1425) Comm. Sent., I (dist. 8?): Utrum regule silo- gizandi et paralogismes dissolvendi tradite a philosophis suflBciant christiano ad silo- gizandum et respondendum in materia benedicte Trinitatis (MS VI 4668, 133v-142r).

Bk. II, Q.2: Quia postulas amice dilectissime, o Bemarde, ut alica de logicalibus in huius secundi libri principio diligenter annectam, idcirco aJica logicalia que dudum multa velocitate composui que tibi in scolis non protuli hic annecto, que tuo prospicaci reliquuntur examini, nec correctionis limam diligentis horrescunt. Et quoniam in hiis diebus nonnulli dubitari videretur de scire et opinari, quero utrum circa idem scire et opinari contingat (MS Troyes 62, 87r-96r). Bk. II, Q.3: Quia petitur a me ut, si quidquam de insolubilibus novi, de ipsis aliquid hic pertractarem, idcirco in hac lectura secundi sententiarum quero utrum beatus augustinus vel etiam magister petrus lumbardus vel aliquis alius theologus fidelis per aliquod insolubile potuerunt ad inconveniens deduci (MS cit., 96r-101r). CeflFons was also willing to put together on the spot disquisitions de proportionibus and drop them into his Comm. Sent. ; See J. Murdoch, ^Mathesis in philosophiam scholasticam introducta-. The Rise and Development of the Application of Mathematics in Fourteenth Century Philosophy and Theology’, Arts libéraux et philosophie au moyen âge (Paris/Montréal, 1969) p. 233. Ceff’ons, in-


cidentally, seems to have been quite familiar with Oxford philosophy, citing Roger Swineshead, Killington and others.32 Hie est advertendum quod nulli {lege nonnulli?) logicam despiciunt totadie simien- tes: “ Linquo coax ranis, era corvis vanaque vanis, et cetera” ; et sumentes illud dictum senece: “Mus caseum rodit, et cetera.” Despiciuntque tam insolubilia que solvere nunquam noverint quam obligationes... Hic tamen bene aude astruere quod nunquam vidi peritum logicum qui logicam dilîameret, ignotos logicos logicam contempnere vidi... et propter ignorantiam logice multi in vanos prolabantur errores, sicut et olim nonnulli propter ignorantiam logice defeciunt pro ut scimus astrucxisse philosophum et eius commentatorem averoys (MS Troyes 62,96r-96v). The quotation from Seneca (Epist. ad Lucilium, 48) points a satirical finger at the triviality of “solving” the likes of: “ Mus syllaba est. Mus autem caseum rodit; syllaba ergo caseum rodit.” The other reference made by Ceffons is medieval: a couplet (the line not quoted by Ceffons is: “Ad logicam pergo, que mortis non timet ergo.”) ascribed to the twelfth century English scholar and poet Serlo of Wilton. The story is that Serlo composed the verses upon being converted from the vanities of a secular life to a monastic one. Cf. F.J.E. Raby, A History o f Christian-Latin Poetry from the Beginnings to the Close o f the Middle Ages, 2d. ed. (Oxford, 1953), pp. 340-41.38 Cf. supra, note 24.34 I also would maintain that the development of these languages is one of the factors that characterizes the shift from a cosmological and speculative attitude in the thirteenth century to a critical and analytic one in the fourteenth. The terms describing the shift are those of Ernest Moody (above, note 22).35 For much in the following paragraphs, compare my earlier essay (above, note 1). 3® I do not mean, of course, that what I shall here characterize as languages, their vocabulary, rules, and algorithms, were ever called that, or seen as exactly that, in the relevant sources. They are, however, intended as an accurate and instructive way of interpreting what transpired. Note that my present account of them is an expanded and slightly revised version of what I have said about them earlier.3’ For the sake of simplicity I have cited these principles as they appear in the pseudo- Ockham (but quite Ockhamist) Tractatus de principiis theologiae (ed. L. Baudry), pp. 45, 125.3® For the relevant texts, see P. Vignaux, ‘Nominalisme’, Dictionnaire de théologie catholique, 14, col. 767.3® This is not, to be sure, to deny that reductionism (often from connotative to absolute terms) was not of extreme importance in natural philosophy (see, for example, the De successivis compiled from Ockham’s writing [ed. P. Boelmer (St. Bonaventure, 1944)] and the analysis of it by Herman Shapiro, Motion, Time and Place According to William Ockham [St. Bonaventure, 1957]), Furthermore, it is also not to claim that the analytical languages in question could not, and were not, applied by those who did not adhere to Ockham’s “particularism.”

Cf. R. Guelluy (above, note 21) p. 220,It is especially important when the infinite divisibility of continua is at stake (as it

often is), since then there frequently is no reason to choose one, rather than another, of two “ infinitely close values,” or to select one, rather than the other, of two convergent infinite series that have the same limit. See below Section II, B.

For examples of this kind of analysis, see J. Murdoch, op. cit. (above, note 1) p. 61,43 Cf. J, Murdoch, op. cit. (above, note 1), 62-63. At times, one even finds the decision of when, and when not, to ascribe some property to a subject directly based upon the

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measurement of the degree of that property in the subject; see Nicole Oresme’s questio: Utrum quodlibet sit ita album sicut aliqua eius pars est alba, in his Quaestiones super geometriam Euclidis (ed. H. L. L. Busard; Leiden, 1961) pp. 41-45.

A convenient listing of such vocabulary can be found in the Summulus de motu incerti auctoris in M. Clagett, The Science o f Mechanics in the Middle Ages (Madison, 1959) pp. 445-462. For the development of different meanings for some of the vocabulary, and for the whole intension and remission language in general, see the articles of Edith Sylla, ‘Medieval Quantifications of Qualities: The “Merton School’” , Archive fo r History o f Exact Sciences 8 (1971) 9-39; and ‘Medieval Concepts of the Latitude of Forms: The Oxford Calculators’, Archives d’hist. doct. et litt. du moyen âge 30 (1973) 223-283. Note should also be made of the fact that terms for the subjects to which the languages were applied also formed part of the relevant vocabulary, but it is best seen - save in the instances of the three “limit” languages to be described below - as separate from the vocabulary of the language applied. Thus, for the most part, such “subjectum” vocabulary will be ignored in what follows.'*5 Thus, a subject that varies uniformly in heat from zero degrees at one extreme to 8 degrees at the other is “just as hot” as if it were uniformly hot in degree 4 throughout. A special case of this “mean degree” algorithm is, of course, the familiar Mean Speed Theorem of the Middle Ages. On the whole, see M. Clagett, op. cit. (above, note 44) ch. 5.

For the three examples given: (1) Thomas Bradwardine, Tractatus de continuo (MS Torun, R 4° 2, p. 166): Nullius forme suscipientis magis et minus remississimum gradum esse; (2) Richard Swineshead, Liber calculationum (ed. Venice, 1520,2r): Intensio habet attendi penes distantiam a non gradu et remissio penes approprinquationem ad non gradum (there was considerable controversy concerning this algorithm and its alternatives: See M. Clagett, ‘Richard Swineshead and Late Medieval Physics’, Osiris 9 (1950) 131-161; and E. Sylla, “Medieval Concepts...” {above, note 44]); (3) Richard Swineshead, op. cit., 54v: Si subiectum uniformiter difforme terminatum ad summum alteretur uno gradu uniformi per totum, isto subiecto aliunde non moto nec facta mutatione illius alterationis, per illud subiectum gradus summus uniformiter inducetur.

That is, basically the vocabulary relevant to Book V of Euclid’s Elements, that found in various treatises on composed ratios translated from the Arabic, plus several medieval Latin additions, such as denominatio (sc. proportionis), excessus secundum proportionem vs. excessus sec. quantitatem, etc.

Again, the primary source for such algorithms was Book V of Euclid. Medieval versions and supplements can be seen from Thomas Bradwardine’s Tractatus de proportionibus, ed. L. Crosby (Madison, 1955) pp. 76-80.

See L. Crosby, op. cit. (above, note 48) and M. Clagett, op. cit. (above, note 44) ch. 7. A similar algorithm was applied within medieval pharmacology: See M. McVaugh, ‘Arnald of Villanova and Bradwardine’s Law’, Isis 58 (1967) 56-64,

See below. Section II, B.51 On all three languages: Curtis Wilson, William Heytesbury: Medieval Logic and the Rise o f Mathematical Physics (Madison, 1956) ch. 2-3. Herman and Charlotte Shapiro have edited Walter Burley’s De primo et ultimo instanti [Archiv fü r Geschichte der Philosophie 47 (1965) pp. 157-173], but it contains a number of errors and should be consulted with care.

The pertinent Aristotelian background is given in Wilson, op. cit. (above, note 51) pp. 29-32, 59-62.

I have here included within the vocabulary terms referring to that to which the


languages are applied since the subjects suffering application are more intimately related to the determination of the relevant algorithms than is the case in the other languages.

A good number of examples can be found in the references cited in note 51 above.See the example cited in Wilson (above, note 51) pp. 43-44.Such “normal measure” for the medieval made no use at all of standard units or

constants, but relied, in proper Greek fashion, upon the theory of proportion.Examples of relevant algorithms would be (here conflated from any number of

works): (I ) On the number of parts in continua: Tot sunt partes in quolibet toto continuo quot sunt in eiusdem medietate; (2) On the relation of parts in continua: In nullo continuo sunt partes immediate ad invicem; (3) On the order of parts in continua: Inter primum punctum linee et omnem alium punctum eiusdem linee cognitum a Deo est linea media; (4) On the relation between things infinitely “different” : Nulla est proportio inter finitum et infinitum. Attention should be drawn to the fact that there was frequent disagreement about algorithms such as these (e.g., one might deny the first example given above and substitute ‘plures... quam’ for ‘tot... quot’). Much of the disagreement arose because of an imperfect understanding of what we would consider the “part-whole” relations for infinite sets. At times, this misunderstanding took the form of considering infinite magnitudes and infinite multitudes on the same level with respect to part-whole relations (e.g., considering one foot of an infinitely long line as analogous to all even nimibers in the infinite set of all positive integers).

Section II, B below.See, in particular, J. Murdoch, ‘Superposition, Congruence and Continuity in the

Middle Ages’, Mélanges Koyré (Paris, 1964) 1, 416-441.Treatment of ‘infinita’ as a logical term can be found in Peter of Spain, Summule

logicales, ed. L. M. DeRijk (Assen, 1972) pp. 230-32 and in William of Sherwood, Syncategoremata, ed. J. R. O ’Donnell, Mediaeval Studies, 3 (1941) 54-55. Relevant secondary literature on the “categorematic vs. syncategorematic” infinite is: P. Duhem, op. cit. (above, note 14) vol. 7, pp. 3-157; Anneliese Maier, Ausgehendes Mittelalter, vol. 1 (Rome, 1964), pp. 41-85, 460-62. A later, but still thoroughly medieval, source is Jean Mair, Le traité de l ’infini, ed. & tr. H. Elie (Paris, 1938).

William & Martha Kneale, The Development o f Logic (Oxford, 1962) pp. 246-274; Ernest Moody, Truth and Consequence in Mediaeval Logic (Amsterdam, 1953) ch. 1-3; Philotheus Boehner, Collected Articles on Ockham (St. Bonaventure, 1958) pp. 174-267; L. M. De Rijk, ‘The Development of Suppositio naturalism Mediaeval Logic’, Vivarium,9 (1971) 71-107; 11 (1973) 43-79 and the other articles of De Rijk cited in the bibliography to his recent edition of Peter of Spain (above, note 60).

Since suppositio is a significative relation had by terms only as they occur in propositions, this qualification is necessary.

Any number of examples of this application of supposition in the resolution of problems within natural philosophy could be cited, but an abstract account of how such applications worked would perhaps be more useful. Thus, omitting for the present a number of important qualifications, one can fairly describe the procedure at hand in the following way: Given two propositions (say) p and q, where q is being offered as an interpretation, analysis, or explanation of p (and hence where one often regards p as logically implying q), attention is directed to the supposition of some single term occurring in both p and q. Most frequently, it is noted that this same term has one kind of supposition in proposition p, another in proposition q. Given this additional information, on grounds of the logic of supposition theory alone and without any regard

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for the particular problem of which p and q speak, one determines whether a licit inference can be made from a term (indeed any term) having the first kind of supposition (i.e., that had by the term in questionin p ) to a term having the second kind of supposition (i.e., that had in q). If the inference is not licit, then q is not an admissible analysis or interpretation of p and the attempted explanation of the problem at hand must be rejected. If, on the other hand, the inference is licit, then the analysis is a (logically) proper one (although, admittedly, other considerations may have to be invoked in order to determine whether it is an informative one). In a rather rarefied form this gives, I believe, the basic structure of how the new conceptual tool or language that was supposition theory was applied.«4 See above, note 55.*5 To distinguish, for example, between some single determinate element falling between the first element of a series and all other elements in the series and the quite different case in which there is merely always some element falling between the first element and all others. Now the medieval would say that, in the first case, the term ‘some single determinate element’ has determinate supposition, while ‘some element’ in the second case has merely confused supposition (in an actual example the terms in both cases would merely read ‘some element’, but I have added qualifications in the first case for the sake of clarification). But we know from our logical primer, as it were, that from any term having determinate supposition we can make a direct inference to singulars, while in the case of merely confused supposition one cannot, which means that one cannot argue from the latter state of affairs to the former. Hence, the two cases are quite different. For the kind of text this example represents, see J. Murdoch, op. cit. (above, note 31) p. 220. (The whole procedure is, incidentally, an instance of the type of utilization of supposition theory that has been outlined above in note 63).«« See Section II, B below.

For examples, see Wilson, op. cit. (above, note 51) p. 79 ; Burley, op. cit. (above, note 51) p. 170; Oresme, op. cit. (above, note 43) p. 44.*8 The translation of Bradwardine’s rule that I have in mind is that of John Dumbleton. In effect, what Dumbleton does amounts to observing that the latitudines involved in the language of intension and remission apply to both motion (or velocities) and the force-resistance proportiones causally related to these motions. This is permissible because not only are there parts to the (ordered) range of available motions or velocities but also to the range of proportiones. However, equal parts of the latitudo motus proceed arithmetically over their range while equal parts of the latitudo proportionis must proceed geometrically (since such are the only kind of parts obtained when one divides a proportio). Therefore, to correlate equal parts in one latitudo with equal parts in the other is to restate Bradwardine’s law in terms of the language of intension and remission; Latitudo proportionis et motus inter se equaliter adquiruntur et deperduntur (Dumbleton, Summa natural., MS Cambridge, Peterhouse 272, 24v). On ail of this, see E. Sylla, ‘Medieval Concepts...’ (above, note 44).

The problem is not basically one of the possible origins of the languages themselves, but rather that of the origins of their wholesale application. Of course, a great deal of the substance (i.e., the vocabulary and algorithms) of these languages developed, even originated, during the course of this application, but it is also true that a good deal existed beforehand. One can point, for example, to an unravelling of the notion of latitudo before it was used to measure things, or to the availability of the notion of first and last instants in Aristotle before they were made to serve a similar role. On this “preapplication” stage of the development of some of the languages see: Anneliese Maier,


Zwei Grundprobleme der scholastischen Naturphilosophie, 3 Aufi. (Rome, 1968); E. Sylla, ‘Medieval Quantifications...’ (above, note 44); C. Wilson, references in note 52 above; L. M. De Rijk, Logica modernorum, 2 vols, in 3 (Assen, 1962-1967).70 See particularly Ockham’s Prologue to his Expositio on the Jp/l>’ IC (inhisP/»7o 'opA- ICûl/ Writings [ed. &tr. P. Boehner; Edinburgh, 1957] pp. 2-16); cf. note 42 above. All of this also bears directly on the problem of the “object” of a proposition (the dictum sive significatum propositionis). For the latest literature on this: E. A. Moody, ‘A Quodlibetal Question of Robert Holcot, O. P., on the Problem of the Objects of Knowledge and Belief’, Speculum 39 (1964) 53-74; T. K. Scott, ‘John Buridan on the Objects of Demonstrative Science’, Speculum 40 (1965) 654-73 ; H. Schepers, ‘Holkot contra dicta Crathom’, Philosophisches Jahrbuch 79 (1972) 106-136.

Cf. above, note 43.Guy Beaujouan, ‘Motives and Opportunities for Science in the Medieval Universities’,

Scientific Change, ed. A. C. Crombie (London, 1963) pp. 220-21.A. Maier, op. cit. (above, note 69).J.Murdoch, op. cit. (above, note 31) pp. 221-24. It appears that the “ infinity” in

volved in measuring the “distance” of creatures to God was a later development (see Section II, A -B below). It is interesting to speculate whether, and to what extent, various elements in that development may have been the effect of the existence of our measure languages.

Duns Scotus {Sent. II, dist. 9, q. 2) was the locus classicus for such a connection. On the whole continuimi-composition problem see; J. Murdoch & E. Synan, ‘Two Questions on the Continuum: Walter Chatton (?), OEM and Adam Wodeham, OEM’, Franciscan Studies 26 (1966) 212-288; Of. J. Murdoch, op. cit. (above, note 31) pp. 216-221 and ‘Naissance et développement de l’atomisme au bas moyen âge latin’. Cahiers d'études médiévales, vol. 2; La Science de la nature: théories et pratiques (Montreal/Paris. 1974), pp. 11-32. I must admit, however, to a certain degree of skepticism about the explanation of angelic motion as a context for these discussions: Was it truly a “cause” for them, or merely mostly an “excuse” ?

J. Murdoch, op. cit. (above, notes 1 & 31).” It also does much to confirm the view that the procedure of the fourteenth century “scientists” who made these applications was a philosophical procedure very much in harmony with other medieval philosophical activity (cf. reference in note 1, p. 74).

If one compares this more “ordinary” use of the measure languages in natural philosophy with that of Swineshead and other Mertonians, then another way of viewing the distinction is to say that the former imports the language and its rules to solve the problem, while the latter imports (or invents) the problem to test or confirm the rule.

In all of what follows, unless stated to the contrary, the theological issues or contexts of which I shall be speaking are these “non-obvious” ones and will consequently exclude those I have mentioned above as holding a natural expectation that the languages will be found to be applied within them.

P. Vignaux, op. cit. (above, note 38) col. 763 and Nominalisme au X lV e siècle (Montréal, 1948) pp. 22-26; H. Oberman, ‘Some Notes on the Theology of Nominalism’, Harvard Theological Review S3 (1960) 60-61 ; David Knowles, The Religious Orders in England, vol. 2 (Cambridge, 1955) p. 76.

See above, note 74. To make things even neater, can we establish a defiinite connection between voluntarism and interest in the perfection of species?

The example in question is from Roger Rosetus and the physical process with which the connection is made is that of an agent or potency acting through time (where

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the effect increases in proportion to the time). The context is Book I of Roger’s Sent, (ca, dist. 1) Q.2, art. 2: Circa secundum articulum, supposito quod voluntas causet aliquos actus suos, <queritur> utrum causet illos subito vel successive... Primo ponam alicas conclusiones... Prima conclusio: Quod voluntas, quando causat actos suos, solum causat illos successive et nullos instantanée ita quod sit dare aliquem actum voluntatis quem actum voluntas causet totum simul et non per partem ante partem... sicut alie qualitates corporales successive causantur... Istam conclusionem probo sic: quia si posset actum suum volendi causare instantanée, sequitur quod voluntas posset causare actum infinitum intensive; patet, nam ponatur quod voluntas eliciat unum actum volendi in A mediante alico conatu, et cum hoc quod voluntas intendat actum suum immediate postea mediante eodem conatu per aliquod tempus; quo posito, sequitur quod voluntas mediante illo conatu in qualibet parte huius temporis tantum causabit de actu et hoc totaliter distinctum ab illo quod causabatur in A ; et cum sint infinite partes in illo tempore per quod sic continue intendet actum suum, sequitur quod infinite partes in tali actu erunt quarum quelibet erit equalis illi parti que precise causabitur (!) in A et ab invicem totaliter distincte; igitur per consequens erit actus infinitus (MS Bruges 192, 28r). Almost nothing is known of Rosetus, save that his Sent, are at least as early as 1337, at which time they were read at Norwich (perhaps by Roger himself). On Rosetus see: V. Doucet, ‘Le Studium franciscain de Norwich en 1337 d’après le MS Chigi B.V.66 de la Bibliothèque Vaticane’, Archivum franciscanum historicum 46 (1953) 88-93; cf. note 17 above. (I might note here that in many of the examples and references that I shall give below, I have often not troubled to indicate whether the example in question is being employed for or against the author from whose work it is drawn or to cite the additional text necessary to establish the author’s reply if its use is negative. I have done this not merely to keep my citations as compendious as possible, but primarily because indication of such a pro-contra distinction is not necessary for my purpose, viz., to illustrate the application of this or that analytical language.)

Robert Halifax, Comm. Sent., Q.5: Utrum aliquis actus voluntatis possit subito esse productus a voluntate (MS VA 1111, 34v)... Circa istum articulum... primo ponam aliquas suppositiones, secundo conclusiones... Prima suppositio est (1) quod omnis G7v) res quocunque modo de non esse ad esse producta - quod dico pro generatione Filii in divinis et pro processione S. S. quia ibi non est productio de non esse ad esse- per motum vel mutationem producitur... (2) quod omnis res quocunque modo corrupta per motum vel mutationem corrumpitur; et accipio motum et mutationem proprie secundum quod eos distinguit Philosophus 5 et 6 Phisicorum... (3) quod omnis res producibilis vel corruptibilis per motum habet partes et divisibilis est... (4) omnis res habens partes est divisibilis secundum extensionem tantum vel secundum intensionem vel secundum utrumque; secundum extensionem ut forme substantiales in subiecto quanto que non decipiunt (! sed lege suscipiunt) magis vel minus, et materia prima; secundum intensionem tantum ut qualitates spirituales in subiecto non quanto cuius- modi sunt omnes actus ipsius intellectus et omnes actus et habitus ipsius voluntatis; secundum utrumque sunt ut omnes qualitates et omnes actus in subiecto quanto corporali... (5) rem aliquam intendi non est aliud nisi immediate ante hoc aliquam partem eiusdum speciei in eodem situ non habuisse quam modo habet et immediate post hoc aliquam partem fore habituram precise in eodem situ quam non habet modo, quia additio partis et non in eodem situ non est proprie intensio sed augmentatio... (6) quod rem aliquam remitti non est aliud quam immediate hoc... (and so on, corresponding to suppositio 5)... [Conclusiones]: (1) omnis res producta vel


corrupta ab alica potentia finita per motum producitur vel corrumpitur... (2) nulla res carens partibus est producibilis a potentia finita... (3) nulla res producta a potentia finita producitur subito et in instanti... (4) nulla res divisibilis solum secundum extensionem est intensibilis vel remissibilis... (5) onmis res divisibilis secundum intensionem sive in partes non distinctas secundum situm est intensibilis et remissibilis... (6) omnis actus elicitus a voluntate est productus a potentia finita... (sc. a voluntate)... (7) omnis talis actus producitur in tempore... (8) 8a conclusio est quod ad bonum intellectum hecest vera: quod omnis actus voluntatis potest intendi et remitti; ista patet quia omnis actus voluntatis habet partes non distinctas secundum situm et cuilibet tali actui possunt addi per motum partes eiusdem speciei. A Franciscan, very little is known about Halifax, for he has hardly been studied. We do know that his Lect. Sent, were before 1332. For this, and other facts and references, see A. B. Emden, A Biographical Register o f the University o f Oxford to A.D. 1500, vol. 2 (Oxford, 1958) pp. 850-51. (See now, however, W. J. Courtenay, ‘Some Notes on Robert of Halifax, O.F.M.’, Franciscan Studies 33 (1973) 135-142, who dates his Sent, slightly later.) In addition to the specific connections the foregoing text makes between generation, potencies, divisibility, intensibility, etc., it also illustrates another frequent preoccupation; namely, establishing that the theological entity at hand fits into the doctrine of intensio and remissio. Frequently, as here, this is accomplished by showing that the entity in question possesses partes.84 This theme is so central to Ripa that one comes upon it throughout his works. The late André Combes published (at times with the assistance of P. Vignaux or F. Ruello) a good amount of Ripa: Determinationes (Paris, 1957), Conclusiones (1957), Lect. Sent.I, QQ Prol. (1961-1970), De gradu Supremo (1964). They are all relevant to the point at issue here. To this one should add Combes’s posthumous article ‘L ’intensité des formes d’après Jean de Ripa’, Archives hist. doct. litt. du moyen âge 27 (1970) 17-147. Cf. J. Murdoch, op. cit. (above, note 31) pp. 241, 246.

For example, the fitting of the action of the human will with the infinite virtus of God. Roger Rosetus, Sent., Q.2, art. 2 (in another proof of the same conclusion cited above in note 82): si volitio possit sic causari in instanti, sequitur quod virtus infinita non posset citius producere talem quam virtus finita; hec consequentia [MS consequens!] est bona et consequens falsum, igitur antecedens; probo consequentiam, quia Deus, qui est virtutis infinite, non potest citius producere effectum suum quam in instanti ex quo nulla est mensura minor; et sic potest voluntas effectum suum, igitur et cetera. Consequentis falsitatem probo, quia si alica virtus potest producere effectum aliquem in alica mensura, et maior virtus potest illum effectum in minori mensura producere; hoc videtur esse de intentione Philosophi 7° Phisicorum; ergo si voluntas potest producere in instanti voiitionem, sequitur quod Deus potest illam producere in minori mensura quam sit in instanti, quod non potest dari (MS Bruges 192, 28r). Note once again the fitting with the rules governing physical processses. Rosetus is here tacitly using proportiones thinking in his argument, but he goes on to fit the action of the will into intensio and remissio language (see below, note 97). A more curious kind of “fitting” of God is found in the Centiloquium theologicum attributed (wrongly) to Ockham (ed. P. Boehner, Franciscan Studies 23 (1942) 262-63) where God’s eternal existence outside time and His creation o/'time are put together with the temporal language of de incipit et desinit.

Richard Killington, Comm. Sent., Q .l: Utrum Deus sit super omnia diligendus... [Conclusiones]: (1) Quod quecumque dilectio Dei super omnia quam habet quis, est maior dilectio quam sit dilectio eiusdem meritoria respectu alicuius creature... (2) Quod quecumque dilectio Dei super omnia in alico infinite excedit dilectionem creature in eodem... (3) Quod non est possible amplius diligere Deum super omnia propter bene-

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ficium factum sibi vel proximo... (4) Secundum nullam proportionem que est vel esse posset inter finitum et finitum eiusdem rationis vel speciei est Deus amplius diligendus quam alias foret sine beneficiis (MSS VA 4353, lr-2r; Bruges 503, 80r-80v).87 In addition to the various contexts cited above and below, the following examples (all of them, again, not “ to be expected” contexts) from fourteenth century Comm. Sent, might be mentioned (ignoring MSS): Adam Wodeham: Utrum solus Deus sit immutabilis (I, Q. 21); Utrum anima Christi possit in verbo cui unitur distincte cognoscere minimas partes accidentium sibi inherentium vel minima»; particulas corporis quod informat (III, Q. 11); Richard Killington: Utrum peccans solum per instans mereatur premiari per infinita instantia interpellata (Q. 5); Robert Halifax: Utrum commensuratio premii ad meritum et pene ad peccatum, que per studium theologie ex scriptura possit cognosci, sit iuste a Deo ordinata (I, Q. 1) Thomas Buckingham'. Utrum sit dare primum instans meriti vel demeriti (Q. 4); Roger Rosetus: Utrum aliquis in casu possit ex precepto obligari ad aliquid quod est contra conscientiam suam (Q, 1 ; this the questio the first article of which circulated as De maximo et minimo ; see above, note 17) ; Anon. VA 986: Utrumsit(!)aliquodenscitraprimumequesecundum perfectionem distare a summo esse, scilicet Deo, et ad simpliciter non esse seu non gradu entitatis, etc.

Roger Rosetus, Sent., Q. 5: Utrum caritas augeatur per opera meritoria... Secundus articulus erit quod tangitur in secundo argumento quod caritas potest esse infinite (proved in that argument by considering meritorious acts over the infinity of proportional parts in a day), ideo queritur utrum alica creatura posset esse infinita (MS Bruges 192, 42r-44r).89 R. Halifax, Sent., Q. 5: Within the same questio cited above (note 83), Halifax asks the following subordinate question: Utrum actus voluntatis create possit intendi vel remitti; His own position is quod sic, but he sets forth a number of argumenta principalia to the contrary, among them the followmg: Capio aliquem actus voluntatis qui est mortale peccatum et sit idem A, et capio alium actum qui est veniale peccatum et sitB, et sit C aggregatum ex A et B; tunc arguitur sic: C excedit A, quia est totum respectu A... tunc quero aut C excedit A finite vel infinite; non infinite patet, igitur finite, igitur in aliqua certa proportione, sit quod in sexquialtera proportione; capio tunc aliquod peccatum mortale quod in eadem proportione excedit A sicut C excedit A et sit idem D ; <et> smt due partes illius G et F ita quod G sit equalis A ; tunc arguitur sic: eandem proportionem habuerint G et F ad A quam habet C ad A, quia C et D habeant eandem proportionem ad A ; igitur A et G et F et B sunt equalia... cum igitur onmis pars peccati mortalis est peccatum mortale, ut prius probatum est; sed F erit pars peccati mortalis, quia pars D, et B est peccatum veniale; igitur peccatum veniale et mortale erunt equalia (MS VA 1111,36r). The effect of the whole argument is to show that the radical distinction between mortal and venial sin (as actus voluntatis) must be taken into account if we are to apply the language of proportiones to actus voluntatis (which is entailed by the latter being intensible and remissible).

Richard Killington, Sent. Q1 (the proof of Concl. 2 cited in note 86 above): Sit A alica dilectio Dei super omnia que ponitur non excedere nisi solum finite dilectionem creature B; et sit quod A excedat B dilectionem in duplo precise, et sit C dilectio Dei in duplo precise remissior quam A ; tunc A equaliter excedit B et C, igitur B et C sunt dilectiones equales et C est fruitio et B est usus vel dilectio creature; igitur dilectio alica creature est equalis dilectioni Dei super omnia, quod est contra primam conclusionem probatam (MSS VA 4353, 2r; Bruges 503, 80vX The implication of this is, that if the languages of intension and remission and proportiones are to be applied to dilectiones, then either there will have to be two separate “scales” (one for usus, one for fruitio)


or one will have to maintain (as Killington does) that dilectio Dei infinitely exceeds dilectio creature.»1 Adam Wodeham, Sent. (Abbrev. Oyta), II, Q8: Utrum secundum proportionem charitatis vie succedat pro premio proportionabiliter magnitudo glorie... Videtur quod non: Deus est premium cuiuslibet beati non solum objectivum sed formale; igitur omnium beatorum est penitus idem et equale premium; non autem in via erat caritas eadem vel equalis (ed. Paris, 1512; 107r).92 This is the thrust of a whole battery of arguments against a particular conclusio (Quod nullus potest mereri precise in instanti ita quod non per tempus) and their resolutions (the text of which is too long to cite here): Roger Rosetus, Sent. Q. 2, art 2., MS Bruges 192, 31r-33r.93 Jean Mirecourt, Apologia prima, ed. F. Stegmiiller, Recherches de théologie ancienne et médiévale 5 (1933) 71-72. Note should be made of the fact that, although one could occasionally disagree with the applicability of the measure languages of intensio and remissio and of proportiones to a given theological subject, one almost always had to explain the consistency and application of the “ limit” languages to such subjects. For they invariably existed or occurred in time, and this automatically and irrevocably brought in the languages of incipit et desinit and of first and last instants. Cf. note 124 below.94 Save that the language o f suppositio is perhaps of even more frequent occurrence; but I am ignoring its pervasive application in the present investigation.95 That is, the claim is made that, utilizing a given language, one has set up a situation in the casus that amounts to a contradiction. The following is a good example of such a casus impossibilis (explicitly recognized as such): R. Rosetus, Sent., Q. 2, art. 1 : Pono quod Sortes velit currere si Plato velit currere et aliter non, et quod Plato velit currere si Sortes non velit currere et aliter non (MS Oriel 15, 265v). See also note 101 below. 9« Robert Holcot, Sent. I, Q. 3, arg. prin. 8 (ed. Lyon, 1518 reprt. Frankfurt, 1967 fol. biiii^): It is argued that, if the will has a libertas contradictionis with respect to fru i and uti, then it can elicere duos actus oppositos successive et immediate ; but this is not permissible, the argument proceeds, because on the authority of Anselm omne quod aliquid vult libere, prius movet se ad volendum illud. In his reply to this Holcot simply says that we should dispense with this “authority” : Dico quod argumentum stat in pondere auctoritatis Anselmi; ideo videtur quod facile est homini volenti illo onusto pondere seipsum deonerare, negare illam auctoritatem (ad sign, in mg. EE).97 Thus, one can argue directly from the fact of the intensibility and remissibility of something to its necessary successiveness (which is that to be established): R.Rosetus, Sent. Q2, art. 2: Preterea, tales actus (scil. voluntatis) sunt intensibiles et reniissibiles, quia aliter non posset quis uno tempore intensius diligere quam alio; et si sic, igitur potest talis actus diligendi successive causaii, quia omne intensibile et remissibile potest sic causari (MS Bruges 192, 28v).98 Other general factors will be treated in the following section.99 R. Killington, Sent., Q. 1, secundo ad principale: The point is made that : Deus est plus diligendus quam frater vel proximus; aut igitur finite plus aut infinite. After rejection of the possibility of a finite excess, the attack is made on the possibility of an infinite excess as well : Ponatur quod A sit dilectio qua quis diligit Deum propter Deum et sit B illa pars latitudinis qua quis diligit Deum propter beneficium exhibitum proximo; tunc A non est incomparabiliter maior quam B, quia tunc in nulla proportione fieret dilectio composita ex A <et> B maior quam B; ymmo sequitur quod talis dilectio composita ex A et B fieret infinita intensive, quia componitur ex duabus partibus qualitativis quarum

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una excedit aliam infinite; ergo tota est infinita intensive (MS Bruges 503, 80v). Note that the assumption allowing the formulation of this particular casus is: Licet augere dilectionem Dei simpliciter ad alium gradum propter beneficium exhibitum creature vel proximo (jb id )10“ R. Holcot, Sent. I, Q. 3, art 7 (ed, Lyon, 1518, sign, mg, I-K): Septimus articulus est an volitio fiat subito an successive... Quod autem nulla volitio causata possit esse subito declaratur, quia si sic, tunc foret possibile quod angelus peccaret sive pecasset in instanti sue creationis. Consequentia patet, quia si in instanti haberet cognitionem boni et mali et usum liberi arbitrii, tuncin illo instanti posset bene vel male velle et peccaret. Falsitas consequentis ostenditur multipliciter... Preterea, si actus voluntatis fiat subito, aliquis angelus necessario peccaret et invitus; quia supposito quod Deus creet in hoc instanti angelum, et precipiat sibi actualiter quod diligat quam citissime poterit, et sequestret actum voluntatis sue per hoc instans precise; quo facto, iste in aliquo instanti amabit Deum, et sit illud instans A. Et arguo sic: inter A et hoc instans fuit tempus medium in quo ille angelus non amavit Deum; ergo tunc peccavit, et tamen hoc vitare non potuit; ergo invitus et necessario peccavit. The “moving force” behind this particular argument is the inconsistency of indivisible (i.e., instantaneously occurring) actions and the continuity of time (together with the language therefore) in which these actions must occur. Another, more straightforward, example of the problem of indivisibles and a language is R. Halifax, Sent, Q. 5 (Cf. note 83 above): Si voluntas potest producere actum suvun in instanti; sequeretur quod, si voluntas intenderit actum suum per aliquod tempus, in fine temporis actus voluntatis esset infinitus intensive (MS VA 1111, 35v). For other instances of difficulties with indivisibles see note 82.101 The role played by the libera volitio is evident in general from the whole context (i.e., usually some aspect of the freedom of the will itself). On the other hand, the specific role that it plays in allowing or determining choices within a continuous interval is usually hidden within the twists and turns of an often complex argument; but it is there none the less. A good example is Roger Rosetus, Sent., Q. 2, art. 1 : The questio principalis is : Utrum voluntas creata libere vel necessario causet actum fruendi respectu Dei... Primus articulus est utrum voluntas sit causa sui actus... pono alicas conclusiones. Prima conclusio est quod cuiuscumque sue libere volitionis est voluntas cause... (After two further conclusiones, there follows a series of argiunents contra conclusionem primam, among which is the following): Preterea, si conclusio foret vera, tunc voluntas libere posset in actum indifferentem, puta moveri. Tunc pono quod quilibet movens localiter motu uniformi premiabitur alico premio sic quod velocius movens et uniformiter magis premiabitur; et volo quod cum hoc Sortes summe appetit premiari. Tunc arguitur sic: Nullus est velocissimus motus uniformis quo Sortes potest moveri, igitur est remississimus quo non potest moveri; sit igitur talis motus A. Tunc arguitur sic: Sortes efiicaciter vult premium et Sortes non potest habere premium, ut suppono, nisi moveatur localiter; igitur Sortes movetur localiter propter premium; igitur Sortes per casum movebitur uniformiter et per consequens alico gradu uniformi; sit ille gradus B, Queritur tunc utrum B et A sint gradus equales vel non. Si sic, igitur cum Sortes movebitur B, sequitur quod possit moveri A gradu, quod est contra prius assumptum. Si autem B sit gradus remissior quam A sicut oportet positione, ergo inter B et A erit vel saltem est possibile gradum medium quem suppono esse C. Et arguitur sic: Si Sortes summe appetat premium et per C gradum magis potest moveri quam per B cum C sit gradus intensior quam B, et voluntas Sortis fuit libera ut eliceret C gradum; igitur eliciebat C gradum, non B gradum, cuius oppositum fuit positum. lam restat probare quod nullus erit intensissimus gradus velocitatis uniformis quo Sortes potest moveri... (MSS


V A nos, Ir, 3v; Oriel 15, 264v, 256v; Chigi B. V. 66, 38v, 40r). [In passing, one might note that a good part of Rosetus’s reply to this argument is devoted to showing that it is a casus impossibilis (necessario Sortes non movebitur illo casu posito).]

In other instances, the function of the libera volitio is not even as explicit as it is here (as indicated by the italicized words in the text above); but it can, and should, be inferred. For example. Adam Wodeham, Sent. I, Q. 21 (for context, see note 87 above): Deus est primus motor; aut ergo modo nature vel libere... non igitur est Deus primus motor nature quin ipse sit mutatus vel mutabilis; ergo si est primus motor, ipse movet libere contingenti libertate. Sed hoc videtur falsum, quia tunc posset omne mobile, immo omnia mobilia, movere sicud vellet. Consequens falsum, ut videtur; quia volo tunc quod sint hic duo mobilia equalia per omnia et incipiant simul moveri super spacia equalia; et sit unum A et aliud B, et volo quod Deus moveat A et B per istum modum quod cum A precise pertransivit primam partem proportionalem sui spacii, id est primam eius medietatem, quod B de suo spacio pertransivit precise duas, scilicet primam eius medietatem et primam medietatem residui, et cum A duas B quatuor, et sic deinceps semper duplo plures donec totum spacium sit pertransitum. Et tunc quero utrum A citius pertingeret ad terminum sui spacii quam B vel tardius vel simul... (MS V A 955,123r). Here, the casus involving what are in effect two convergent infinite series with the same iimit is made possible by fact that God posset omnia movere sicud vellet.

In a final example, the role of a free will as an “actualizer” of the infinite divisibility of a continuum is even less evident. R. Holcot, Sent. I, Q. 3, arg. prin. 8 (ed. Lyon, 1518, fol. b iiii'^): Si sic (scil. si voluntas hominis esset libera), sequitur quod voluntas posset simul mereri et demereri libere. Consequens falsum. Quod probo multipliciter. Primo sic: Ponatur quod aliquis homo in prima parte proportionabili unius hore mereatur et in secunda peccet et in tertia mereatur et in quarta peccet et sic semper alternatim secundum omnes partes proportionabiles huius hore, in cuius hore ultimo instanti moriatur; et sit illud instans A. Tunc sequitur quod istum hominem non potest Deus premiare nec punire, quia nec fuit finaliter malus nec finaliter bonus; ergo tale non potest Deus nec sciet indicare... (and there follow eight other similar proofs). Here it is man’s, not God’s, will that realizes the infinite series. It is worthwhile noting that in his resolution of these nine arguments, Holcot applies the languages of maxima and minima and first and last instants {ed. cit., ad sign. mg. FF).102 xhe following can be cited as examples of such alteration: (1) R. Rosetus, Sent., Q. 2, art. 2 : A series of arguments directed against Rosetus’s conclusio prima (see above, note 82) to a great extent revolve about the possibility of applying the will (as a potency) to proportiones algorithms relevant to potencies acting against resistances and the corresponding effects so produced. The difficulty is, of course, that the will acts with no resistance. In place of changing the algorithms or denying their applicability, Rosetus “alters the subjects,” i.e., he makes a distinction with respect to resistances: Dico quod duplex potest poni successio: una causata ex contrarietate que est in passo ad effectum producendum; et sic est successio in productione caloris in passo alico propter frigiditatem que est in passo... et talis successio que sic causaretur ex tali contrarietate non est in productione successiva volitionis. Alia autem est successio in productione alicuius effectus in passo... propter limitationem agentis, quia agens respectu talis actionis est finite virtutis. Et talis successio... est in voluntate respectu productionis actus voluntatis (MS Bruges 192,28v). (2) Adam Wodeham, Sent., Abbrev. Oyta, I. Q. 3 ( =dist. 1, Q1): In the context of a discussion of one condition under which man might merit visio Dei (scil. Utrum pro studio sacre theologie ex caritate procedente debeatur pro mercede visio Dei et eius fruitio), a number of argumenta principalia are brought to bear to show

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the untenability of such a visio\ all of them, in effect, reject the possibility because, following the required proportionability between visiones and obiecta visionis, the visio D ei would be of infinite perfection, which is an unacceptable result. In reply, Wodeham allows the formulating of proportiones, but only within latitudines within the same species. Given this, it is a simple matter to resolve the arguments in question by showing that the subjects that were held to be proportionable in the arguments belong to different “scales” ; Nullum obiectum quantecumque perfectionis etiam naturaliter agens potest producere visionem sue speciei in eadem anima perfectiorem seu meliorem quam visio mille graduum [the particular value is not important, this one deriving from its chance occurrence in a previous casus] in eadem specie... Correlarium: ceteris paribus ex parte intellectus et certitudinis vel evidentie actuum et obiectorum perceptorum, non oportet quod actus in eadem proportione se excedant in qua obiecta quo ad perfectionem specificam, quia tunc visio mille graduum respectu Dei esset in infinitum perfectior visioni mille graduum respectu cuiuscumque obiecti creati... Unde dicendum est quod tota latitudo specierum visionis possibilium equalium semper graduum cuilibet in sua specie est semper finita ita quod sunmium gradum tenet visio obiecti infiniti (ed. Paris, 1512; 8v-9r).

R. Rosetus, Sent., Q. 4 (Utrum caritas possit augeri), art. 2 (Utrum caritas possit augeri in perfectione sine alico alio novo adveniente): Primo ponam unam divisionem de isto termino ‘augeri in perfectione’, postea eliciam aliquas conclusiones... Distinctio est ista : Quod aliquid augeri in perfectione potest esse dupliciter : uno modo potest aliquid augeri in perfectione quia unum et idem est primo minus perfectum et postea magis perfectum, et hoc est proprie augeri in perfectione. Alio modo dicitur aliquid augmentari in perfectione, sed improprie, quia ipsum precedit et postea adveniente aliquo eiusdem speciei fit unum perfectius in illa specie ex precendente quam illud quod precessit in tali specie, et ideo dicitur illud precedente augeri... [Conclusiones] (1) Quod nullum inanimatum augetur in perfectione primo modo loquendo de augmentatione ita quod idem sit prius minus perfectum et postea magis perfectum... (2) Quod aliquod inanimatum potest augeri in perfectione secundo modo, scilicet improprie, loquendo de augmentatione... (3) Quod aliquod animatum in perfectione augmentatur primo modo, puta homo, quia adveniente continue nova et nova perfectione, dummodo maneat eadem anima, semper est idem homo quod prius, et per consequens idem animatum primo est imperfectius et postea perfectius... (4) Quod non omne animatum potest sic augeri quod ipsum sit primo imperfectius et postea perfectius, quia nullum animatum aliud ab anima intellectiva potest sic augeri... (5) Quod caritas ex quo est quid inanimatum non augmentatur sic quod alica eadem caritas s:t prius minus perfecta et postea magis perfecta. .. (6) Quod caritas secundo modo loquendo de augmentatione augetur improprie... (MSS Bruges 192, 36v-37r; Chigi B. V. 66, 66v-67v).104 jh e text in question is a theological questio by an otherwise unknown Haverel Norvici. The most we can say until we have studied the few questiones that we know to be by him, is that he flourished at the Franciscan convent in Norwich ca. 1337-1339 (on the MS of the questiones and on HavereJ, see V. Doucet, op. cit. [above, note 82] pp. 93-95). The context is thoroughly theological: Utrum aliquis possit meritorie frui Deo et eidem venialiter displicere vel peccare venialiter. However, the extent to which our languages are present is unexpected. Because several of the argumenta principalia employ casus involving proportiones, Haverel decides that some judgment must be made concerning the propriety of their use. Beginning from the observation that proportio non est nisi inter quantitates (which is supported by references to Euclid and Aristotle), he replies by all manner of other passages in Aristotle that do maintain, in his eyes, a


broader domain for proportiones, for example, one including virtutes elementorum, velocities, motive powers, qualitates alterationis, etc. All very well, but precisely how do proportiones apply to such entities? Haverel does not answer in general, but he does examine their relevance to velocities, especially those of alteration. The major point at issue in his view is how one should measure such velocities; he attempts its resolution by giving four opiniones: (1) Quod nulla velocitas alterationis est velocior alia... (2) Quod velocitas attenditur penes maximam latitudinem acquisitam in maiori tempore vel minori... (3) Quod velocitas alterationis debet attendi penes maximum gradum inductum vel inducendum ita quod illa alteratio sit velocior per quam acquiritur gradus intensior... (4) Quarta opinio est, et verior inter istas, quod duplex est velocitas alterationis: una est per se et qualitativa, alia est materialis et quantitativa. Illa que est per se et qualitativa adtenditur penes maximam latitudinem forme acquisitam; illa que est materialis et quantitativa attenditur per comparationem ad subiectum (MS Chigi B. V. 66,105r-106r).

J. Mirecourt, Sent., I, Q. 10; Utrum cognitiones excedant se perfectione propor- tionaliter per excessum obiectorum... Respondeo premittendo unam distinctionem quod unam rem excedere aliam intelligitur dupliciter: uno modo quidditative seu essentialiter, alio modo accidentaliter. Res una dicitur excedere aliam essentialiter quando sic excedit quod etiam quodlibet illius speciei excedit illud nec est possibile quod aliquid sue speciei sit et non sic excedit iliud... Accidentaliter vero dicitur una res excedere aliam quando sic excedit quod possibile est aliquam rem eiusdem rationis esse quam non sic excedet vel non sic excedet aliam... Excedere etiam accidentaliter dicitur dupliciter, uno modo intrinsece, alio modo extrinsece. Res una dicitur excedere aliam intrinsece accidentaliter quando hoc sit propter aliquam rem que non est extra ipsum... Res dicitur excedere aliam extrinsece accidentaliter quando comparatur ad aliam vel comparari potest penes excessum propter rem aliquam que non est ipsa nec aliquid ipsius nec in ipsa... Tunc pono conclusiones: (1) Prima est quod nulla cognitio nec aliqua res creata excedit aliam rem creatam infinite quidditative vel essentialiter... (2) Nulla cognitio nec res creata finita permanens excedit vel excedere potest rem aliquam creatam infinite accidentaliter et extrinsece... (3) Quod aliqua cognitio vel aliqua res creata excedit vel excedere potest aliam infinite accidentaliter extrinsece... (4) Quod quelibet cognitio et universaliter quelibet res quamlibet aliam rem excedere potest vel excedi potest ab eadem vel quidditative vel accidentaliter intrinsece vel extrinsece... (5) Quod una res potest excedere aliam in duplo quidditative vel in alia proportione finita vel infinita, et tamen non oportet cognitionem eius excedere cognitionem alterius propriam et distinctam in duplo accidentaliter vel in aliqua proportione et tamen non oportet cognitionem eius excedere cognitionem propriam et distinctam alterius (MS Napoli, BN V il . C. 28, 17r-18v). Several observations are in order. First, Mirecourt carries systematics further when for each of his conclusiones (save the last) he gives proofs, arguments contra, a series o f propositiones, and resolutions o f the contrary arguments by means of these propositiones. I mention this because these propositiones add to his little “language of proportiones" in that, in addition to the conclusiones, they too furnish algorithms, often of a more specific nature. Secondly, note should be made of the fact that infinite excessus and infinite proportiones have been incorporated into Mire- court’s system, as well as other different kinds of excess that will allow the simultaneous proportio of a given thing to another in various senses. This naturally allowed of a broader application of the language in theology. Thus, Conclusio 3 permitted him to accoimt for the proper proportio of dilectio D ei to dilectio creature, a problem that we have abeady seen giving Richard Killington much exercise (above, notes 86, 90, 99)

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Alternatively, Conclusiones 5-6 enabled him to treat the kind of issue that had troubled Wodeham in separating visiones from thcir obiecta (above, note 102). Finally, attention should be drawn to the fact that the combining of the scale of perfections, their mutual excessus and proportiones, with cognitiones or mental contents was also carried out by Pierre Ceffons, Sent. I. Q. 6 circa prol: Utrum necesse sit quod generaliter scientie se excedant in perfectione secundum quod subiecta (MS Troyes 62,19v-24r). Considering that Ceffons apparently knew Mirecourt well, the two accounts would bear comparison. (For some of the material contained in the Ceffons questio, see J. Murdoch, op. cit. [above, note 31] pp. 243-46).108 J. Mirecourt, Sent. Ill, QQ 4,6-11 (MSS Paris, B N 15883,113r-133r; Praha, Univ. III. B. 10 (41g) 85v-88r, 91v-105v, et 112v-113r tabula). It is difficuU to indicate in a single footnote the scope of what Mirecourt tried to accomplish, but at least some of the pains he went to in order to fit the various measure languages into theology can be revealed by citing the relevant questiones and a few of the conclusiones he established within them. Quest. 4: Utrum voluntas per additionem partis ad partem vel per diminuti onem partis a parte meritum vel demeritum suum possit intendere vel remittere: Conci. 1 ; Intensio actus meritorii ipsius voluntatis fit per additionem partis ad partem. Quest. 6: Utrum voluntas creata posset intendere vel remittere meritum suum vel demeritum (this questio appears only in the Paris MS - where the order of questiones differs and all are collected together in a single series at the very end of Book III - and the Praha tabula): Concl. 5: Non solum quilibet actus voluntatis sic potest intendi et remitti, ymmo etiam quilibet actus intellectus et quilibet actus animo ; Concl. 6 : Quodibet accidens in anima receptum naturaliter vel supernaturaliter potest intendi et potest remitti. Quest. 7: Utrum ahqua creatura possit aliquod instantanée precise producere. All four conclusiones deny the existence of a primum instans esse for various physical and intellective processes; for example: Concl. 3: Non est dare primum instans in quo luminosum primo illuminet medium. Quest. 8 : Utrum creatura a solo Deo per solum instans possit conservari. Immediately preceding the assertion of his first conclusio Mirecourt neatly reveals the fact that he was consciously applying the measure languages at hand: De questione proposita supponendo modos communes loquendi secundum quod dicimus res esse in tempore vel in instanti, pono aliquas conclusiones... Concl. 1 : Nulla res indivisibilis potest esse vel non esse precise per instans sic quod non per tempus. Concl. 3: Hec propositio non est possibilis: Hec res permanens est, sive sit divisi bilis sive indivisibilis, et immediate post hoc nec ipsa nec aliquid ipsius erit. Concl. 6 : Hec est possibilis : Aliqualiter res non est talis in hoc instanti, qualiter talis erit immediate post hoc; similiter aliqualiter res est talis, qualiter talis non erit immediate post hoc. Quest. 9 : Utrum voluntas creata mereri vel demereri possit in instanti precise per instans. Concl. 1 : Si voluntas meretur in hoc instanti, illa voluntas immediate ante hoc merebatur. Concl. 3: Possibile est quod in instanti in quo voluntas desinit mereri ipsa incipiat demereri. (In the discussion of this conclusio Mirecourt considers the example of a bean thrown upward being met by a falling millstone, a casus frequently invoked in treatments of the problem of a quies media.) Concl. 4: Quod immediate post intensionem meriti potest aliquis remittere meritum vel demeritum. Concl. 5 : In alico instanti potest quis incipere peccare mortaliter qui immediate ante erat in caritate. Concl. 6: Quod non est dare ultimum instans caritatis. Quest. 10: Utrum voluntas creata, que in hoc instanti non meretur vel in hoc instanti non demeretur, immediate post hoc instans possit mereri vel demereri. Concl. 1 : Si voluntas in hoc instanti meretur, ipsa immediate post hoc merebitur. Concl. 3 : Possibile est quod voluntas nunc non mereatur vel demereatur que immediate ante merebatur vel demerebatur. Concl. 4: Pro nullo instanti quo quis mere


tur debetur aliquod premium cuius nulla pars prius debeatur. Concl. 5 : Cuiuslibet meriti vel demeriti est primum instans sui esse (this conclusio and the following should be compared with those dealing with physical processes given in quest. 1). Concl. 6: Contingit dare primum instans in quo aliquis mereatur hoc merito et primum in quo demereatur hoc demerito. Quest. 11 : Utrum voluntas creata ad quemcumque gradum meriti possit intendere vel remittere actum suum. Concl. 1 : Voluntas creata per aliquod tempus rationale potest eligere actus meritorios equalis intensionis. Concl. 2: Aliquis est gradus ymaginabilis meriti tam intensus quod hec voluntas cum gratia quam habet vel habitura est ex ordinatione Dei et in tempore quo potest esse in statu merendi ad illum non posset intendere meritum suum et aliquis est gradus ymaginabilis tam remissus quod hec voluntas cum gratia quam habet vel habitura est ex conatu suo quantumcumque modico non posset illum habere per se sic quod illo habito cessaret ulteriorem habere. Concl 3: Nullus est gradus meriti ita intensus quod voluntas cum gratia habita vel habenda posset acquirere quin posset intensiorem acquirere nec aliquem gradum ita remissum quin possit remissiorem. Concl. 4: Non semper ad quemcumque gradum voluntas vult intendere vel remittere meritum suum intendit vel remittit meritum suum. Again, several observations: I have cited but some 20 of the 36 conclusiones that Mirecourt formulates in these questiones (I have concentrated mostly on those with theological referents), but in addition to this, following his usual pattern (see note 105), Mirecourt sets forth numerous propositiones that also serve as algorithms for the languages with which he is dealing. One final, incidental, remark about Mirecourt’s possible sources: Before proceeding to the drawing out of conclusiones in quest. 7 (BN 15883, 112v), he sets down duas propositiones. Now, save for three repeated words and a few transpositions, these propositiones are precisely the same as two suppositiones of Robert Halifax that were cited above (note 83), even to the point of excluding the Son and the Holy Spirit in exactly the same terms. Moreover, in another place (BN 15883, 118v) suppositiones 5 and 6 of Halifax (again note 83) are used verbatim by Mirecourt. In neither case is Halifax mentioned, at least in the MSS I have consulted. In any event, the relation of the two thinkers bears further investigation.

Apologia prima, ed. Stegmiiller (above, note 93) pp. 71-72: et hoc (scil. de primo et ultimo instanti) diffuse satis pertractavi in aliquibus questionibus tertii libri.1”® Apologia prima, ed. Stegmiiller (above, note 93), p. 61.

That this is not too strong a claim is evident from the fact that a careful examination of the condemned proposition reveals that, although some equivalent proposition might have been formulated in another way, that particular proposition could not have resulted without the languages. See, for example, the proposition to which the foregoing note refers: Non peior est moraliter vel demeritorie habens habitum malum cum actu quam habens habitum malum eiusdem intensionis sine actu; nec melior est moraliter vel meritorie habens habitum bonum cum actu quam habens habitum bonum eiusdem intensionis sine actu. Cf. Chartularium Univ. Paris., II, p. 611, prop. 20-23.

Thus, for example, Adam Wodeham brings in intensio and remissio in an astounding number of questiones and Richard Killington commences a questio that makes liberal use of measure language (e.g., above, notes 86,90,99) by remarking that his discussion will proceed nihil penitus asserendo ignotum (MS Bruges 503, 80r). This is not to say, to repeat my eariier caution, that the languages were so popular that all fourteenth century theologians used them freely.m By this I mean not merely that the potentia absoluta accounts for the possibility of these procedures, but also for the fact of these procedures.112 By ‘equivalent’ I mean, of course, that the rationes or casus themselves are some

332 J. MURDOCH U N ITA R Y CHARACTER OF MEDIEVAL LEARNING 333

how similar, and not simply that they are concerned with establishing the same point. I have in mind, for instance, something in the nature of a “translation” of an earlier, non-language based, ratio or casus into one that did apply the languages.

To what extent, for example, was the problem of the instantaneous vs. the successive action of the will an issue that was developed or “egged on” by the fact that the languages were available to treat it? It certainly was a frequent context for their exercise; beyond the instances that have been cited above (notes 82, 83, 100, 106), one could add Wodeham, Sent. I, QQ. 10-11, Richard Fitzralph, Sent. I, Q. 9, art. 2[cf. Gordon Leff, Richard Fitzralph, Commentator o f the Sentences (Manchester, 1963) pp. 93-96], Killington, Sent., Q. 5, and many others.

See above, note 57.With respect to the languages of first and last instants and of de incipit et desinit

this is also evident from the fact that they had roots going back to Aristotle’s discussions of continuity and continuous change. (For these roots see note 52 above.)

For such a parallel compare the citation from Bradwardine in note 46 with that involved in note 65.11' Thus: (1) In his discussion in Sent. 1, Q. 3 about the latitudo visionum and their obiecta (above, note 102), Wodeham is led to consider the infinite excess of any rectilinear angle over a hom-angle (viz., that formed by any circle and a tangent to it). He grants that the latter is infinitely more acute than the former, but claims that, even so, it does not infinitely exceed it in acuteness. For proper infinite excess (which is the kind at issue in this questio) one must appeal to the excess of a line over a point; Dico quod licet quod angulus contingentie {ed. continentie!) in infinitum sit acutior rectilineo, cum sit solum circumferentialiter divisibilis et rectitudinaliter indivisibilis, non tamen conceditur quod infinite excedat in parvitate vel acutie angulum rectilineum, quod tamen oporteret si directe valeat ad probandum unam intellectionem finitam excedere aliam infinite. Unde si poneretur punctus indivisibilis linea in infinitum esset maior, ipso accipiendo comparationem proprie (ed. Paris, 1512, 9v). (2) Just as one could divide a continuous line into (say) 5 equal parts, so one could divide a proportio into 5 equal parts (e.g. 32/1 into five 2/1 parts). And just as three such equal parts of the line are to the whole line, so three such equal parts of the proportio are to the whole proportio [which, in our terms, amounts to (8/1)®/® = 32/1]. Nicole Oresme went so far as to generalize the existence of incommensurable parts for a proportio. On all of this, see Nicole Oresme, De proportionibus proportionum and Ad Pauca respicientes, éd., transi., comm, by Edward Grant (Madison, 1966), although the parallel between the division of continuous quantities and the division of proportiones is not emphasized there.11® For example, Walter Burley seems to have had more problems than he realized in fitting the “indivisibilism” of his view of the intension and remission of forms with the necessary continuity of time in which intending and remitting took place; see E. Sylla, ‘Medieval Concepts...’ (above, note 44). Another way of viewing phenomena such as this, is to note that the new analytical languages were “content loaded.” That is, simply to apply them to some subject often implied something about the nature of that subject, what properties it might have other than those eliciting the application, what relations it might have to other entities, etc. For example, the application of intensio-remissio language was usually seen to entail that the subject had parts (whence Burley’s problem). Or one might even claim that the utilization of personal suppositio and the rules that went with it implied a domain taken in extension. O f course this “content loaded” character of the languages is really what is behind much of the concern over their “fit” with theological principia and subjects.

119 Recall, also, the function of suppositio with respect to continuity-infinity. See note65 above.120 See above, note 23.121 J. Murdoch, op. cit. (above, note 31) pp. 221-224, 238-246.122 This technique is of extremely wide use. It is even employed by those who would argue against there being an infinity of proportional parts in a continuum: Roger Rosetus, Sent., Q. 4, art. 2 (MS Bruges 192, 37r-37v): A series of arguments directed against Roger’s second conclusio (above, note 103) of this article all center around proving quod in nullo inanimato sunt infinite partes proportionales. To show that there is no such infinite, one invokes it (via God) to see what happens: Volo quod Deus faciat unum continuum cuius prima pars proportionalis sit alba, secunda nigra, tertia alba, quarta nigra et sic deinceps alternatim in infinitum; et pono quod in extremitate illius continui, versus quod divisio fit, ponatur stilus; tunc queritur utrum illa pars que tangit stilum sit alba vel nigra vel composita... We need not pursue the argument further to appreciate its thrust. Our specific interest is merely to reveal God’s role in playing the “ infinity of proportional parts game.” This role is made even more explicit in Roger’s reply to another move in this particular series of arguments. We do not need to know the argument itself, since Roger makes everything involved admirably clear in his reply : Quamvis ita sit quod nullum agens naturale posset sic se movere quod tantum precise quiesceret in fine cuiuslibet partis proportionalis, tamen Deus posset sic movere unum mobile quod mobile moveretur sic uniformiter per aliquod spacium quandocumque movebitur super illud spacium et quod quiescat in fine cuiuslibet partis proportionalis precise per tantum tempus per quantum movebatur super illam partem proportionalem quantumcumque parvum, quia Deus habet notitiam distinctam de illa parte proportionali, et fiat argumentum ut prius. Ideo dicitur aliter, scilicet, quod casus est possibilis de potentia Dei et per consequens possibilis, quia ut mihi videtur non includit contradictionem quod sic moveatur, quia mihi apparet Deus potest hoc facere, ideo possibile... Roger’s specific reply from this point on need not concern us. What does concern us is made perfectly clear (Roger bothered to say it only three times!): God is the Master of the proportional parts. In most instances, not so much attention is drawn to God’s function; but it is usually there. Cf. Wodeham in note 101 above.123 This is clear in many of the texts cited above; so for example Halifax’s suppositio5 (note 83), Rosetus’s argument about Sortes movens propter premium (note 101), and of course especially Mirecourt’s systematizing of the will, merit, and demerit in terms of intension and remission (note 106; Cf. note 108). The connection between intension- remission and continuity is even more direct and evident in those “naturally fitting” contexts that I have tried, for the most part, to exclude from present consideration. The augmentation of caritas is an excellent case in point. Once again, one of the clearest examples is presented by Rosetus: Sent., Q. 4 (Utrum caritas possit augeri), art. 1: Utrum tot sint partes in medietate alicuius caritatis sicut in tota caritate... Circa primum articulum sic procedam: Primo ponam alicas conclusiones ex quibus patebit quid sit dicendum ad articulum... (1) Non sunt plures partes in alica tota caritate quam in eius medietate... (2) Demonstrata alica caritate totali, quod in illa tota caritate non sunt tot partes quot sunt in medietate illius caritatis... (3) Quibuscumque partibus medietatis illius demonstratis, adhuc plures sunt partes in tota illa caritate et in quacumque parte... (MS Bruges 192, 35r-35v). Ignoring as not relevant to present purposes Roger’s intriguing distinctions concerning “equality” and “ inequality” between numbers of parts, it is quite pertinent to ask why Roger found it proper and necessary to move so quickly from the augmentation of caritas, and hence its intension and remission, directly to such

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puzzles about continua. Once more the answer is unambiguous ; because the connection was made in the (single) argumentum principale. For if, this argument urged, caritas is capable of augment and intension, then this occurs either with or without the addition of new parts (for without see note 103 above). If new parts are acquired the augmentation, like any intensification, occurs continuously and not by leaps and bounds, then there will be as many new parts acquired - to wit, an infinite number - in half a day as in a whole day (since there are an infinity of parts in both such intervals of time) ; therefore, etc. Although the connection in question is made more explicitly than most, it should not surprise us. For intension and remission does occur continuously, so the shift to considerations about that continuity should follow almost as a matter of course.124 The most evident examples here are all of those dealing with the will, since it necessarily acts in the continuum of time, even if it be held to do so instantaneously. Note that almost all instances of intension and remission also fall into this category, since once again action in time is involved.125 Cf. C. Wilson, op. cit. (above, note 51).126 por examples of appeal to the potentia absoluta in questiones on ih.Q Physics, see Jean Buridan (ed. Paris, 1509) 64r, 72v, 73v, etc; Marsilius of Inghen (ed. Lyon, 1518; repr, Frankfurt, 1964) 41v, 43v, 54r, etc.127 See, for examples, the texts cited above of Rosetus (note 82), Killington (note 99), Halifax (note 100), and Wodeham (notes 102 and 128).128 As a sub-class of the examples just cited, see Rosetus (note 82) and Halifax (note 1(X)). To this one can add A. Wodeham, Sent. I, Q. 8 (Utrum voluntas necessario vel libere principiet suos actus): In a series of dubia directed against the actio libera of the will, implication of an unacceptable infinite is one of the most recurrent themes: Dub. 2: Tunc (i.e., si voluntas causat actus suos libere) voluntas posset libere peccare sine causa movente, et tunc peccaret peccato infinito secundum intensionem malitie, quod est impossibile... Dub. 4: Tunc voluntas libere posset se conformare rationi recte, et quia illa dictat quod Deus est diligendus quod quanto aliquid est melius tanto ceteris paribus est magis diligendum, sequitur quod voluntas posset diligere Deum infinite, quod est impossibile cum sit virtus finita... Dub. 1 : Tunc possem tantum diligere Deum quod vellem sibi dare gloriam infinitam... £)m6. 9: Si voluntas aget libere, igitur potest efiicacius et velocius agere et sic in infinitum (ed. Paris. 1512; I8r-19r).129 Again instantiation from Rosetus (note 82) and Halifax (note looi130 See in particular the citations of Killington (notes 86,90) and of the conclusiones of Mirecourt (note 105). Cf. the references above in note 84.131 One of the most striking examples is an anonymous Utrum per debitam suceptionem sacramentorum Christi remittatur culpa et gratia confertur (MS BM Harley 3243, 91r- lOOv). The author confesses to three difficultates principales, each of which in turn forms an article: Prima erit numquid aliquod peccatum finitum aliud peccatum finitum vel gratia gratiam vel quecumque res finita aliam rem finitam excedere possit infinite. Reversing the usual direction of subordination, the discussion contains an elaborate examination of the problem of the perfections of species and the “ infinite excesses” that obtain between them. (The second article of this questio is also relevant to present concerns: Numquid intensio gratie vel alicuius forme sic possit esse sine additione cuiuscumque forme noviter adquisite.) Other instances of the connection reverse the order of treatment and approach infinity via perfections; thus, Mirecourt (note 105) and Wodeham (note 102).132 Specifically, inasmuch as variation was allowed within each species, the problem was to establish some kind of “ infinite increase” or variability that remained within the


species, that is, an “infinite increase” (and “decrease” for that matter) with a “ limit.” The “limit” was another species, and the “infinite increase” expressed the required infinite excess between species that was grounded in their radical distinctness. But there remained an additional problem: there is no single “next” species that can function as such a “limit” ; for between any two species God can always create another. Thus we must have an infinite number of species within a finite latitude each one of which is (a) infinitely distant from all others, (b) of a greater distance from some than it is from others, and (c) equally distant with all others from God in an amount greater - infinitely greater - than the equal infinite distance of each from all others. To construct a scale of measure to satisfy such conditions is what, for example, might be seen as the fundamental theme in Jean de Ripa’s enormous output (see above, note 84). But one of the most ingenious, if rather fanciful, attempts to solve the puzzle was that of Pierre Cef- fons who applied the divisibility properties of horn-angles and other curvilinear angles relative to the divisibility properties of rectilinear angles as a model (see J. Murdoch, op. cit. above, note 31 pp. 243-246). Cf. Wodeham in note 117.133 Cf. J. Murdoch, op. cit. (above, note 31) pp. 221-224.134 See Rosetus (note 122). Killington also treats the problem (Hie forte videtur unum dubium numquid unum infinitum extensive est maius alio; MS Bruges 503, 81r) in the questio on dilectio Dei that we have mentioned above.135 The Comm. Sent, of Roger Rosetus. Not of especially great length, it consists of five questiones principales (see above, notes 87, 82,103, 88) each divided into sub-questions corresponding to the various articuli. But only one questio principalis (Q. 3 : Utrum de essentia Dei, que est creatrix omnium, possit aliquid ostendi) does not contain an extensive application of the measure languages that concentrates on issues of infinity and continuity. And this one is not one-fifth of the whole, but only some five per-cent.136 Above, note 83.137 A particularly striking example is Richard Swineshead’s development of what we would regard a divergent out of a convergent infinite series (see J. Murdoch, op. cit. [above, note 1], note 39). But this is only an instance, there are countless others that, qua their consideration of infinite values, await analysis.138 cf. the references in J. Murdoch, op. cit. (above, note 1) note 54.139 Adam Wodeham addresses himself to the importance of rejecting the actm l division of a continuum into all of its proportional parts in Sent. Ill, Q. 10 (ed. Paris, 1512; 123v), while Robert Halifax develops extensive arguments relative to the same problem in Questio 6 of his Sent. (MS V A 1111, 62v-70r). But Robert Holcot addressed the issue differently and rather more directly: In a Quodlibetal Question on grace and justification he claims that : circa istam questionem, si tempus permiserit, ciuinque fient... Tertio videbitur an ista forma arguendi sit bona: A excedit B in duplo, in triplo, quadruplo et sic in infinitum, ergo est infinitum [in Paolo Molteni, Roberto Holcot o.p. Dottrina della grazia et della giustificazione con due questioni quodlibetali inedite (Pi- nerio, preface dated 1967) p. 179]. Unfortunately, perhaps time did not permit, for this part of Holcot’s questio does not seem to be in any of its MSS.1 0 At times the term sophismata was taken generically to cover insolubilia (closer to what we would regard as, for example, logical paradoxes), but this is not the “contradictory” character I have in mind. Rather, I mean, the “contradiction” apparently present in the likes of : ‘Si nullum tempus est, aliquod tempus est’ ; ‘Infinita sunt finita’, etc.1 1 See J. A. Weisheipl, ‘Curriculum of the Faculty of Arts at Oxford in the Early Fourteenth Century’, Mediaeval Studies 26 (1964) 154-156,177-181. Themajor problem

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is that there are questiones explicitly called sophismata in their opening lines or explicits, but save for a missing ‘Utrum’ differ in no way at all from the usual scholastic questio. Grabmann appears to have been the originator of the suggestion that sophismata were the quodli^tal questions of the Faculties of Arts (Weisheipl, op. cit., p. 182). •*2 For some indication of this literature see Martin Grabmann, Die Sophismataliteratur

des 12. und 13. Jahrhunderts. Beit. z. Gesch. d. Phil. u. Theol. Mittelalters 36, Heft 1 (Münster, 1940).143 G. Wallerand, Les oeuvres de Siger de Courtrai (Louvain, 1913) pp. 20-33. What follows represents a slight revision and shift in emphasis with respect to Wallerand’s views.

Of course, this is not to say that Swineshead, Heytesbury, and others simply transferred the form of the procedures they found in logical sophisms to new ground. There are differences, but in no case so serious as to damage the filiation I am suggesting. What is more, the differences are explicable ones. We can rapidly pass over the fact that the literature of the measurement tradition (Swineshead in particular) often “resolves” the variant cases or confirming examples by a kind of deduction from the basic rule being applied or tested; this is to be expected when the rule itself is mathematical in character and measurement is its function. A more tantalizing difference lies in the fact that in our treatises on scientia de motu quite frequently it is a single rule or algorithm that is being examined. Or at least one such rule per chapter or tract. Although this kind of procedure also appears in the more strictly logical sophismata literature, more often a whole series of rules are “tested” in rapid succession over consecutive sophisms. At times, the grouping is not by types of rules, but rather by kinds of examples, that is, sophismata, that are connected in other, external ways. We even find a number of rules being applied within the resolution of a single sophism. Again, 1 think that this difference is to be expected. The easy mix and move from rule to rule in logical sophismata follows, I believe, from the fact that the rules in question were part of a larger, more systematic and unified logical theory. They were, that is to say, a good share of the sum and substance of the logica moderna, especially of that part of it falling collectively under the rubric de proprietatibus terminorum. When we tum to the measurement tradition, we do not find such imity or such system. There is a oneness, to be sure, insofar as all of the rules here belong to this measurement tradition. But there is no attempt to spell out the logical connections of the various rules on mean degree measure, on proportiones velocitatum in motibus, on maxima quod sic and minima quod non or de primo et ultimo instanti. And no wonder. For in most cases there was no logical connection. In any event, I would suggest that it is this lack of a higher, more unified theory that makes a procedure of “ take it one rule at a time” quite natural within the measurement tradition.

For an example of a sophisma from a work of natural philosophy consider the following from Richard Swineshead’s Liber Calculationum (ed. Venice, 1520; Fr): A nunc est solum finite intensum, et per rarefactionem finitam solum subito fiet infinite intensum. For its “resolution” see the reference in note 137. Cf. below, note 152.145 To do so would make almost all indirect arguments ending with a bizarre absurdity something like sophismata, which is certainly not my intention.146 To cite several examples merely from texts quoted above: (1) Rosetus (note 102) has a contrary argument that moves from the successive action of the will in time to a casus (in which proportiones language is applied to the variables of agent, resistance, and time) in turn leading to the absurdity that something that acts against no resistance also acts in time; this is in turn resolved by Rosetus’s introduction of an alternate way of viewing resistance that simultaneously renders the absurdity innocuous and shows how one can


still apply proportiones to the variables in the casus. (2) In another place Rosetus (note 103, where only fragments of the total relevant text are given) has the following pattern : Augmentation by parts - casus with continuity language finfinity of proportional parts) - absurdity: X belongs to the set of black and white things but is neither black nor white; resolution: amounts to showing that a proper understanding of what is truly involved in the infinity of proportional parts in a continuum does not allow the element (viz., an ultimate part) giving rise to the absurdity, but that it can still cover the variables (alternating black and white parts) in the casus. Similar patterns can be found in still other Rosetus texts (note 101), Halifax (note 89), and Holcot (note 101).14’ There are other instances of arguments applying measure languages in natural philosophy that are sophismata in a more straightforward sense inasmuch as they transfer the substance of more genuine sophisms to the context of some more general problem under investigation. This occurs quite frequently in investigations of the composition of continua. For an example, see note 65 above. One can compare this kind of discussion of the “continuum problem” with the numerous sophisms dealing with the term ‘infinitum’ (found from the thirteenth century on) and especially with the likes of Immediate sunt partes continui (Albert of Saxony [ed. Paris, 1494], Sophisma 178).148 This was first noted by K. Michalski, but see the relevant reference to him and others in Weisheipl, op. cit. (above, note 141), p. 178, n. 96.149 See, for example, the work called A est unum calidum, apparently by one Johannes Bode: H. L. L. Busard, ‘Unendliche Reihen in A est unum calidum'. Archive fo r History o f Exact Sciences 2 (1965) 387-397.1®“ See, for example, the sophisms dealing with these terms in the works of Peter of Spain and William of Sherwood cited above (note 60).i®i Thus, elaborate considerations of intension and remission, of first and last instants, of maxima and minima, and of velocities, etc. occur in a substantial number of Heytes- bury’s Sophismata (ed. Venice, 1494), especially V, VI, VIII, IX, X IX and XXFV. In each case the sophisma itself is a standard logical one. It is interesting to couple with this the fact that Heytesbury’s Mertonian colleague, John Dumbleton, also thought it most appropriate to inject physicalia into the logical pars prima for his Summa. He speaks and argues, for example, about the intension and remission, and the latitudes and degrees, of scientia, credulitas, evidentia and hesitatio, and treats such standard Aristotelian issues as the magis nota nobis character of a proposition in terms of ita intensus gradus scientie and unum intensius scitur quam alio (MS Cambridge, Peter- house 272, 9v-llr).i®2 The casus are not all explicitly labelled sophisma, but in the course of an argument the words in hoc sophismate are often used, or at the end of some secundum imaginationem case there occurs some such phrase as de hoc multa fieri passent sophismata. See, for example, William Heytesbury, Regule solveruii sophismata (ed. Venice, 1494) 26r, 27r, 31r, 32v, 41 v, 42r, 44r, etc.; Richard Swineshead, Liber calculationum (ed. Venice, 1520), 9r, 15r, 16v, 22r, etc.1® However, the investigation of such works as the Tractatus de paralogismis of Herman Lurtz (above, note 29) might alter the situation slightly. Further, such anonymous treatises as that in BN 16401,178r-198r (/«c: In hoc tractatulo aliqua sophismata communia conscribam quorum primum est hoc: Deus est, quod sine probatione aliqua ex fide nostra suppono esse verum... Sophisma secundum (191r)... Homo est asinus) bear further examination in order to determine how “theological” they may be and whether or not they belong to the sophismata tradition proper or are merely rather ordinary questiones disputate so labelled.

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MS Worcester Cathed. F. 118, 136r.155 xhe terms are those of Ernest Moody, op. cit. (above, note 22) p. 161.156 I realize that, for purposes of brevity and simplicity, I am ignoring the importance of Platonic and Augustinian elements, but the point I wish to urge can be made, mutatis mutandis, with respect to them as well. Similarly, I also realize that I shall be concentrating rather more on the unity of theology with natural philosophy than withepistemology or metaphysics, and that I shall have in my mind chiefly St. Thomas as an example, but once again I do not believe these restrictions affect my point. Finally, I should draw attention to the fact that I shall be deliberately excluding (as I have throughout this essay) the use of the logic of syllogisms or consequentie within theology; for that gives, I think, a rather trivial, certainly less interesting, kind of unity.

This “alteration” had good precedent, of course, in Aristotle himself who was something of an expert “model bender” when it came to working out a fit with a new area or topic.1®® By this I do not mean to imply anything about elements in the fourteenth century other than the analytical languages suffering or not suffering such alteration.159 See Roy Effler, John Duns Scotus and the Principle ‘Omne quod movetur ab alio movetur” (St. Bonaventure, N.Y., 1962).

That is to say, such algorithms as Nulla est proportio inter infinitum et finitum already existed, or fit into the tradition (e.g., Aristotle or Euclid). And even the incorporation of such essentially new problems as that of infinite sets and sub-sets did not cause a great deal of disturbance among algorithms. The kind of excess here involved was either (wrongly) assimilated to the Omne totum est maius sua parte algorithm for finite quantities or, when the issue was properly appreciated, a new alogrithm of set/sub-set relations was added without affiecting previously existing ones.

This reformulation often carried with it what might be viewed as a reversal in the “direction of argument.” For example, in the thirteenth century one frequently analyzed a given problem beginning from and operating with and within its authoritative formulation (in, say, Aristotle una cum Averroes or Avicenna), where this authoritative formulation provided almost all of the variables and conceptions to be utilized in examining the problem. In the fourteenth century, on the other hand, one often finds the same problem analyzed where the operation is with and within an Aristotelianism reformulated in new terms and where the analysis essentially works toward the pertinent issues to be treated in the authoritative formulation of the problem. Compare, for example, Albertus Magnus’s treatment of the problem of the nature of motion in his Comm. Phys. (Book III, tract. I, ch. 3) with that of Ockham in the De successivis (above, note 39).i®2 They do not account, for instance, for the rise of the application of a second intentional point of view within philosophy or theology. Much more relevant are, I believe, such considerations as those which I suggested above (pp. 287-288). i®3 I am much less convinced of the importance of the 1277 condemnations than many other historians of science and philosophy. They may have indeed lent a helping hand in the rising criticism of Aristotelian notions, but I am skeptical about their “causing” this criticism in any substantial way. Often it seems that the criticism was “ready to go” before 1277 (e.g., about the eternity of the world) and would have come to a healthy state of development without Tempier’s assistance. In any event, we need far more work on the relevant literature just preceding 1277 to be able to tell.1® One must also be careful, incidentally, not to make the relevant social groups too “particular.” To operate with modern ideas of professionalism and specialization and


thence to be led to such conceptions as that of fourteenth century philosophers as a socially “distinct and self-conscious group” (Joseph Ben-David, The Scientist’s Role in Society, Englewood Cliffs, 1971) misrepresents the situation.165 See for example Pierre Ceffons’s multiplication of algorithms for curvilinear angles (above, note 132X Indeed, in general one might not be wrong to make the claim that more was accomplished in the various discussions of infinity in theological literature than in that of natural philosophy.186 See, for example, that of Maurice De Wulf, or better, Philotheus Boehner’s attack on it {pp. cit., above, note 61) espec. pp. 155-156.167 H. D. Simonin as quoted by P. Vignaux, ‘Occam (Originalité philosophique et théologique)’. Dictionnaire de théologie catholique, 14, col. 882.168 Frequent as the occurrence of such a point of view is within late medieval theology, it is hard to escape noticing it. But to interpret it as something like “the inferential logic expressed in consequentiae” (E. Synan, Mediaeval Studies 25 (1963) 261) misses what it is and what importance it held.169 The terms are those of Damasus Trapp (Augustinianum4(1964) 404; 5 (1965) 269). One should also note Trapp’s unappreciative evaluation of the measurement tradition in his ‘Augustinian Theology of the 14th Century’, Augustiniana 6 (1956) 148-149.170 David Knowles, op. cit. (above, note 80), p. 83.

D I S C U S S I O N

H. o berm an: I have noted a series of questions that came to me while rereading your paper a number of times, and the first of them has to do with the “social factors” that you mentioned in your title. That the unities you are after stemmed from those social factors that constituted the university context goes without saying. It is perhaps more important to keep in mind that many of these people were simultaneously both theologians and natural philosophers. But where the question becomes critical is when we try to explain how it is that there emerges such a new climate in the fourteenth century That is to say, perhaps we should ask the question : ‘ ‘What are the social factors that led to this new profile in the fourteenth century?” And here we are very much at the beginning of things, as we should be. We should not overreach ourselves because, whether we approach it from the level of the sciences and natural philosophy or from that of theology, we are - to compare our work, for instance, with Renaissance studies - in the very initia. Perhaps we should try to avoid the temptation of considering social factors until we have more fully catalogued what is going on. That you can suddenly, as John does, open up a whole new series of sources to be looked at by the historian of science shows what can still happen.

That is the first observation. The second relates to another aspect of the unities you speak of. There is indeed a weaker unity, to use your vocabulary, between theology and natural philosophy than there is between philosophy and science. The whole idea is for me a very urgent one. For while it is true that one of the achievements of the fourteenth century is the clear distinction between philosophy and theology (and I think that your paper also points in that direction) why is there at the same time so much natural philosophy in theology? I have come up with the answer that the traditional, thirteenth century Sentence Commentaries comprised a totality of theology and metaphysics that was no longer accepted. That is to say, by means of potentia absoluta arguments, fourteenth century authors became interested in showing that in the traditional treatment of

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theological problems there were only certain elements that could be considered properly theological. Now, just as their thirteenth century predecessors, they also had to comment on Lombard’s Sentences. They had a whole series of Sentences o f ih&h Masters and of the teachers of their Masters before them, and they now had to distinguish within earlier Commentaries a whole set of subjects that were not properly theological. But they still had to deal with these subjects bôause as the members of this new generation they were still very much in debate with the former generation. That seems to me a sli^tly different way of interpreting the fact that we have so much natural philosophy within theological Sentence Commentaries.

Finally, let me say something about one of the questions you yourself raise in your paper: it is that of the origin of, as you put it, the near frenzy to measure everything imaginable. To me, this jibes with the tendency to translate quantitas into res quanta, creatio into res creata, motus into mobile and so on. That is, in the fourteenth century you see everywhere an eflfort to translate abstractions into the concrete. And it seems to me that this use of “measure languages” (as you interpret them) is due to the fact that it is part of a campaign against a metaphysics that is based on abstractions and that therefore removes one from reality. Whether the basis of this campaign is in natural philosophy or in theology we can perhaps leave open. I am inclined to believe that it has a theological impetus behind it and that it is an impatience with earlier thinkers who, by an erroneous interpretation of Aristotle, have fractured or threatened the unity of theology by concentrating their speculations on abstractions and therefore moving away from reality.

Now when we try to answer the question of why there is this near frenzy to measure, my suggestion is that part of the answer is to be found in the fact that all abstractions are translated into things concrete. You are then already halfway in the direction of describing the individual res in a new way. You no longer describe it as placed in an ontological hierarchy, or as belonging somewhere on the Porphyrean Tree, but you have to describe it now in terms of itself and how it is distinguished from other individual things. This at least relates these new measure languages to the whole climate of the time. This is a point to be kept in mind.

j. MURDOCH: Well, I take it that what you are saying, Heiko, is something like the following (and let me put it in terms of a concrete example) : We move from abstraction, as you put it, to the concrete, to particulars, to a particularism. We would then say, for example, this individual thing is whiter than that other individual thing and, therefore, if you want to describe just how this is whiter than that, you are led to “measure.” Is this the kind of thing that you are talking about? This is a possibility, but then where do you find evidence for this in writers at the end of the thirteenth and the beginning of the fourteenth century? It doesn’t seem to me that it is an hypothesis that has any more, perhaps even less, substantial support behind it than the conjectural ones that I have put forth in trying to connect measure somehow with the new-found emphasis on evidence and certitude and so on.

E. s ylla : Can’t you say that all three things fit together? You want to be certain, so you want to reject metaphysics and rely only on the concrete and so you get this exactness that we call measuring. In other words, you could say that certitude is what caused the effort to be more concrete.

H. OBERMAN : I don’t think that these are competing interpretations. I have myself tried to show that everywhere there is a hunger for reality, a search for certainty. I think that you find it, for example, with Holcot in many passages and with Gregory of Rimini very explicitly in the prologue to his Sentences. In fact, one of the reasons why he hails


Ockham and why he can be called a nominalist is because, he says, we have always been debating general propositions, we have been debating what quantitas is (and then comes the example, of course, of the Eucharist), but we should instead ask what a res quanta is.

J. mxjrdoch: Y ou see, I have been looking for the origin of this “measure mania.” One of my problems is that, in looking for texts that will help me, I keep finding very suggestive ones that are later than 1330, but that’s not early enough because the frenzy is already there. I would like to find somethingin the 1320’s or even earlier - and this is why I have moved back to Scotus - that would lead in this direction. If you use someone like Holcot or Rosetus (who is presumably also in the 1330’s) you are presented with zfa it accompli-, they are already running around measuring everything, particularly Rosetus, less so Holcot. You have this put together with the other elements we have just mentioned: particularism, emphasis upon certitude, and so on and so forth. I want to see what the beginning of it all is.

H. OBERMAN : John, I think there are perhaps two ways to do this. You would like to have the earliest in time. But in later generations - in the 40’s, in the 50’s, even in the 60’s and the 70’s - you see that people are then able to verbalize why they opted for this, and what they say may be an indication of why it originated.

}. MURDOCH: Good. Yet given these suggestions by later people, it seems to me that it is imperative for me to try to find what they are talking about in earlier material, and in that I have been unsuccessful.

G. beaujouan : Sans vouloir rabaisser la valeur de recherche de ce langage des calculationes, je crois qu’on peut dire qu’il y a une mode aussi dans son adoption; je n’irai pas jusqu’à dire que c’est comme la mini-jupe ou le structuralisme de nos jours. Ce qui me semble important cependant, c’est de savoir pourquoi, dans certains milieux, cette mode prend, pourquoi elle se démode; plus concrètement, pourquoi par exemple cette mode a-t-elle pris à Paris au milieu du XlVe siècle avec une telle virulence, alors que, en Italie, elle n’a pas pris?

M.-Th. d ’ALVERNY: C’cst là où malgré tout les facteurs sociaux peuvent entrer.b . stock : John, in suggesting that we might examine this rising frenzy to measure in

connection with the emphasis on evidence and certitude, perhaps we should consider things such as textual criticism, bookkeeping, legal documents, and the like. Certainly evidence and certitude and other nominalistic tendencies can be discerned in some of these areas. I would agree with Professor Oberman that we are perhaps not ready to examine some of these things. But backing away from the question doesn’t make it any better, you know.

J. MURDOCH: Well, I wouldn’t want to commit myself one way or the other; this might be fruitful or it might be sheer nonsense. But at best I would think that any connection between bookkeeping, legal things, on the one hand, and certitude on the other would be a very general one. What I am interested in, however, is a connection between some social or institutional factors and this particular push toward certitude. But I have not been able to find them; “internal” factors seem to give a more plausible explanation of the specific kind of certitude we have to do with here.

J. g a g n e : Parlant de textes assez anciens qui pouvaient être reliés à cette question de frenzy to measure, un point et une série de textes m’ont frappé: ce sont les textes de Roger Bacon sur l’emploi des mathématiques. Us sont tous marqués de près ou de loin par un propos didactique; non pas la certitude, non pas le rejet d’une méthode antérieure, mais l’utilité. Il appelle d’ailleurs ça l’utilité des mathématiques pour la clarté de l’exposé. Lorsque tous ces textes sont rassemblés, il devient manifeste que c’est là

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une ligne caractéristique: utiliser des exemples, utiliser la mesure, utiliser le schéma géométrique, simplement pour faire comprendre. D ’autres textes qui me paraissent intéréssants aussi, à peu près aussi anciens que ceux de Roger Bacon, ceux de S. Thomas où, à l’aide d’exemples, il veut faire comprendre. Je me demande si on n’a pas là déjà une somme importante de textes pour mettre en relief la simple utilité didactique de la mesure, du schéma géométrique ou de l’argument philosophique, ou même de l’argument scientifique. Lorsque au début de la Summa S. Thomas parle des épicycles et de la querelle des épicycles, il entend mieux faire comprendre son propos: quelle sorte de science est la théologie? Et il se sert d’arguments connus, clairs, facilement compréhensibles.

j. MURDOCH: To these texts I would add Grosseteste who specifically introduces measure, even calls God a Primus Mensurator. But there is a different sense involved here, it seems to me. As I look at Bacon and Grosseteste - 1 do not have any feeling at the moment for the St. Thomas that you refer to - what they say about the application of mathematics and its utility is essentially different in spirit from the people in the fourteenth century. For one thing, it lacks this application of analytical languages whichI think is characteristic, and it lacks the sophismata flavor that I think one finds in the Mertonians. There is something wrong, I think, with putting Bacon and Grosseteste together with the Mertonian calculatores.

j. g a g n e : Je crois que l’utilisation des mathématiques est beaucoup plus simple et plus spontanée. Je me demande, en parlant de facteurs sociaux, si ce n’est pas simplement la tâche d’enseigner qui crée cette relation et non pas un raisonnement abstrait qui dit: sur la base de l’unité, on peut illustrer de cette façon-là. Je ne connais pas d’arguments de ce genre dans la deuxième partie du XlIIe siècle.

s. victo r : I think that the big difference you are going to see in these uses of measure in the thirteenth and fourteenth centuries is their function. I don’t see the fourteenth century materials that are talked about in this paper as didactic examples but as research. The universal or general languages are research tools, not didactic ones.

J. g a g n e : I agree with that; it’s different. But isn’t there some continuity at least with respect to content, materialiter, to take your category?

s. victo r : If there is a connection seen by people in the fourteenth century between mathematical methods and logical methods, might not the application of these new languages in theology be seen as an attempt to make theology an exact science? This move toward a kind of specification or particularization within theology might be viewed as a striving toward exactitude.

J. MURDOCH : But if you look at the theological works in which these languages occur, and then at the same time look at what they have to say about utrum theologia sit scientia, their answer is that, not only is it not an exact science, but it is not scientia in any proper sense of the term.

R. mckeon: May I suggest a different way of raising your question, a less argumentative and controversial one? Suppose in the thirteenth and the early fourteenth century that one were trying to make theology scientific. If one of the results of this attempt was to disclose a difference between natural science and theology as a supposed science, the distinction would be one of the results of trying to make theology scientific and therefore not against your position but a stage in the evolution of it.

J. MURDOCH: Well, if they were going to try to make theology a science, they would presumably have tried to get their heads clear about what a science was, or scientia was, in the first place. That is exactly, as a matter of fact, what did happen. And one of the results of this is, I have suggested, this new development of analytical languages,


or at least one of the results may have been this. Perhaps, somewhat more surely one of the results was at least the utilization of a second intentional point of view.

E. s ylla : Could we not say - and perhaps this is what Steve has in mind - that theologians were trying to be more scientific? A theologian who was seeking certainty might try to be more scientific in his theological work even though when he was being more scientific what resulted wasn’t theology, but, for example, philosophy.

c. SCHMITT: These languages that you speak about, although they continue on - you can still see intension and remission notions in Newton and so forth - it seems to me that in many ways they have a very short history. The internal development somehow comes to an end very abruptly in the middle third of the fourteenth century. Is there anything that you can say about this problem? Do they raise internal problems that can’t be resolved and then have to move into new developments?

E. s ylla : I don’t think that there was an intrinsic limit to them. It seems rather that their demise was caused by something like a humanist or anti-intellectual reaction.

c. SCHMITT : Well, this is the sort of argument that people usually put forth. But if you look at the matter specifically - take Oxford for example - humanism only came to Oxford at the beginning of the sixteenth century and this use of analytical languages ended much before that. The same thing is true at Paris. I can’t see any connection whatever between humanism and the end of this phenomenon.

E. s ylla : Well, what about Gerson? Or someone like him, who claims that when this kind of approach or material falls into the hands of second-rate thinkers, it is a waste of time and is even liable to mislead people. One should stick to simpler and more religious concerns.

c. SCHMITT: Well, why are there no first-rate thinkers? Do we have a situation in which a number of very intelligent people come together and develop something and then in the next generation there are no people intelligent enough to carry it on? This is to me a very significant problem with this whole development.

J. MURDOCH: I can’t think of any internal problem that made it stop short. You are quite right in claiming that after the 1370’s or 1380’s not much new is done with these things (although there is a little flourish at Paris about 1500 when someone like Alvarus Thomas put together a good deal of the material in a rather unique way). But throughout most of the fifteenth century what you find in terms of these languages is repetition on the one hand and, on the other hand, an inability to understand them.

H. oberm an : But if it is true that the theologians - let us say some kind of commentator on Lombard’s Sentences in the 30’s or 40’s of the fourteenth century - had first of all to do the basic job of indicating that in the traditional discussion of a given question, three-fourths of it really belongs to natural philosophy and only one-fourth to theology, then it is very understandable that only in the next phase there is a man like Gerson who had a lot to say about the reforms of the University of Paris and who advised that for theology it is important to concentrate on matters of the spiritual life, biblical interpretation, etc. Let the other faculties, he would urge, deal with this other material. One is at the next stage, then, in the fight to establish the lines of demarcation.

c. scHMirr: Well, this raises another question: Do you see a shift of emphasis in the development of Sentence Commentaries! Are certain questions given preferred treatment? Do you see an increasing emphasis, for example, on moral problems as against theoretical problems?

H. oberman: Y ou see something very significant. They shrivel. Fewer and fewer questions are being dealt with. And again, this is understandable. For after you have this whole debate in which you have come to discover the earlier confusion tetween theo

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logy on the one hand and this theological natural philosophy on the other, then the traditional Sentence Commentaries can no longer do a proper job in providing a framework for either one. Then it splits up into a treatise on proportions, for example, on the one hand and writings on the spiritual life on the other hand,

T. GREGORY; Notte ami Murdoch a bien souligné qu’il est nécessaire pour faire de l’histoire des sciences de puiser à l’intérieur de la théologie. Mais on peut élargir un peu sa considération et dire qu’on ne peut pas faire de l’histoire de la théologie si on ne connaît pas ces questions de science. Nous sommes habitués aujourd’hui à une façon de faire de l’histoire de la théologie en prenant le problème de Dieu, les problèmes de la chute d’Adam, la rédemption, la fin des temps, etc. Nous avons pour ainsi dire purifié certaines conceptions historiques de tous les éléments qui se réfèrent à une certaine mentalité, à certains matériaux de caractère philosophique, scientifique, qui ont été, quand même, toujours utilisés par des théologiens. Et nous avons fait une histoire de la tiiéologie en présupposant que les problèmes sont toujours les mêmes, que le problème de Dieu, par exemple, se pose d’une façon égale chez Origène, chez S. Augustin, chez S. Thomas, chez Duns Scot, chez Occam, etc. Par contre, chaque période, chaque homme aussi, est toujours conditionné par un certain tableau mental où entrent de plein droit toutes les conceptions philosophiques et scientifiques. On ne peut pas faire de l’histoire de la théologie si on ne comprend pas l’importance fondamentale des problèmes que posent les théologiens du XlVe siècle et qui font de leur théologie une théologie tout à fait différente de la théologie du Xlle siècle et du XlIIe siècle. On ne peut pas comprendre autrement ce qu’est la théologie au XIV siècle.

H. oberm an : Before we go on, may I just come back to the last part of the question that Charles raised, namely, whether these shriveled Sentence Commentaries at the end of the Middle Ages any longer have anything to contribute to moral issues. Now two of the Sentence Commentaries from the end of the fifteenth century - those of Gabriel Biel and Wendelin Steinbach - say explicitly that they have used everything they could from Ockham and the nominalists, but that in moral issues, that is to say in Book IV, they are almost ninety per cent dependent on Duns Scotus because the nominalists have not made independent contributions to moral theology. We may not agree with it, but this is an interesting evaluation. Thus, theologians who are very consciously nominalists use a purified Scotus when it comes to ethics. In general 1 think it is important to realize that we have made our own work in the history of theology so difficult because we have elevated St. Thomas to a level beyond his true medieval status. That is a seventeenth century invention; the fourteenth and fifteenth centuries pass him by. They tip theh- hats politely, they will quote him on certain issues, but the main thrust of theology in the fourteenth and fifteenth centuries is not Thomistic; Thomism lies in waiting till the Counter-Reformation.

R. rashed: Au début de son rapport John a eu la sagesse de limiter ce qu’il appelle une unité forte à un certain domaine, celui du mouvement. On peut donc exclure de l’exposé général des problèmes comme l’optique, la statique, etc., ou l’on peut dire au moins que déjà dans cette période le rapport entre philosophie et mathématique en tant que science est assez limité; nous avons pour ainsi dire une optique scientifique où la philosophie intervient peu. Ensuite Jean a parlé de l’application des mathématiques au Xllle siècle, avec l’optique, Grosseteste, l’arc-en-ciel. A ce moment-là John a répondu que ce n’est pas la même chose que l’application des mathématiques courante au XlVe siècle. Ma question aux spécialistes du XlVe siècle est la suivante: comment différencient-ils ces deux types d’application des mathématiques? Qu’est-ce qu’ils veulent dire exactement par le mot “mesure” chez les auteurs?


3. MURDOCH; Let me start with your remark about the non-penetration of philosophy into optics. Yes, I did exclude optics from the “strong unity” of philosophy and science primarily because in such texts as Alhazen and Witelo the importance of philosophical factors is much, even drastically, less. On the other hand, I think that one can show the penetration of philosophy into optics if one reads other texts. Do not consider Alhazen as the central or the most important optical text for the Latin West, because it wasn’t. John Peckham was, something that can be established simply by appealing to the number of manuscripts and the number of marginalia within them testifying to their use. So we have Peckham. And there are philosophical elements there. What is more, as one moves into the fourteenth century - I think of such works as the Questiones of Blasius of Parma on optics - the philosophical elements become more dominant. So that I think one could establish a unity - perhaps it would be less strong - also within fourteenth century optics,

A. sabra: YeSÿ in the Latin tradition the situation is a bit different from what one finds in the Arabic, Alhazen is not known to have had any influence on Grosseteste, but he certainly did influence Bacon and Peckham, and in the work of these two you find the doctrine of the multiplication of species joined to the optics of Alhazen. Now that doctrine is completely extraneous to Alhazen, Yet it affects his theory as one has it in the Latin tradition in a very fundamental way.

R. hashed : Ce n’est pas ça que j ’essaye de nier. Mais prenons l’exemple de Thierry de Freiberg. En dépit de toutes les spéculations de l’allure du De multiplicatione specierum, dès qu’on commence à élaborer le modèle de la sphère ou à traiter de l’arc-en-ciel, ces spéculations n’interviennent plus. Je ne nie absolument pas l’importance de ces considérations dans l’histoire des sciences. J’essaye simplement de réagir contre un danger. Ce danger consiste à rendre l’histoire des sciences - je ne dit pas que John fait cela - une histoire de la philosophie des sciences. Une histoire des sciences n’est pas ime histoire de la philosophie des sciences; quoi qu’on en dise, une histoire des sciences doit répondre aussi à des problèmes techniques posés et à des problèmes techniques à résoudre. Par exemple, le problème de l’arc-en-ciel ou le problème de la double réfraction.

G. beaujouan : Mais alors vous faites ce contre quoi John Murdoch lutte depuis déjà longtemps, c’est-à-dire que vous ne résistez pas à la tentation d’inclure dans le moyen âge occidental une conception de la science qui, malgré tout, est une conception moderne de la science. Evidemment une expérience comme celle de Thierry de Freiberg sur l’arc- en-ciel est pour vous un bon exemple parce qu’elle correspond davantage à notre catégorie de science. Le problème justement posé par le rapport que nous discutons, c’est précisément de penser la science médiévale avec un cerveau totalement médiéval et de ne pas la penser, plus ou moins malgré soi, avec un cerveau influencé par la science moderne.

R. rashed ; Non, il y a une question nette avant cela : doit-on parler de “science médiévale” ou de “sciences médiévales” ? Est-ce que vous pouvez grouper l’optique et ce que j ’appelle, entre guillemets, “ la théorie du mouvement du XlVe siècle” telle qu’elle est traitée par “ l’école de Harvard” ? Est-ce que je peux grouper cela sous les mots “ la science médiévale” ?

E. s ylla : If you are saying that there are categories of things that are different and that the unity only belongs to things within natural philosophy and not to the more mathematicized sciences, like optics and statics, which were inherited from the Greeks and also from Islam, isn’t it the case that, when they came to the Latin West, they were always changed in the direction of becoming more similar to natural philosophy?

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R, rashed; Mais, je possède par contre un exemple différent, c’est l’exemple de l’étude de l’arc-en-ciel.

E. s ylla : But in Theodoric of Freiberg, do we really have a counterexample? True, he does those experiments, but that is just an excerpt. The whole is not a purely experimental treatise, it contains natural philosophy as well. But can we not put the whole problem in another way? If you were just a natural historian and you never knew about the seventeenth century, and you looked at the manuscripts of the thirteenth and fourteenth centuries, you examined Witelo and Swineshead’s Liber calculationum, then what classifications would you make within these centuries? What did they really think about such works on optics? How did they fit in with such other works on motion? Were they kept in a separate category? What were they there for? Why were they commenting on them? Where did they fit into the university rubric?

c. SCHMITT: One of the problems that an historian has to face is that they did put them in categories different from ours. But it is very difiicult to sort out just how they are different and what difference this makes in our interpretation. And it seems to me that the reason for the argument here between Roshdi and others is that he sees science in a particular way, I would say perhaps in a twentieth century way. But if we look at the fourteenth century and see what these people thought science was, it’s a very different range of things; it includes theology and a great number of other things. And it seems to me that you can shed light on this question by looking at it from both points of view. That is, there is a certain continuity between fourteenth and (say) nineteenth century discussions of astronomy and optics. On the other hand, if you look at science in a generalized way in the fourteenth century, there is a perspective in which physics, optics, and so forth are somehow related to theology.

E. s ylla ; M. Beaujouan said something to me yesterday that is relevant to this. In the Middle Ages there is some mathematics and astronomy that serves the purposes of astrology or of computus treatises, and it is different because it had a different destination within the medieval context, not because, as seen from our point of view, it is more scientific, but because it fits in differently with what they were doing. There were, then, mathematical treatises for calculating the date of Easter and not at all for mathematics as such or for natural philosophy.

G. beaujouan : Je crois que la position de M. Rashed s’explique un petit peu par sa propre spécialité. En effet l’algèbre ou l’optique sont des traditions que même à l’intérieur du moyen âge, il est relativement possible de suivre de façon indépendante. Ce n’est pas la même chose pour, par exemple, la philosophie naturelle ou tout ce qui tourne autour de l’astronomie et de l’astrologie, il y a là, si j’ose dire, de véritables paquets qu’on est obligé de penser globalement, c’est-à-dire avec la forte intégration que préconise John Murdoch.

j. MURDOCH: But we still have to answer Roshdi’s question about the different ways in which mathematics is applied. It can’t be done properly save ostensively; one has to do it case by case. And if one does this, it seems to me that one of the things that can be claimed for the case of the application of mathematical measure languages within natural philosophy, within scientia de motu, is that here the application often serves the function, as I have put it, of testing a basic rule. Namely, you test a basic rule by applying it to all conceivable variations, particularly variations where subtle issues of continuity, infinity, and the like are involved. Such tests often amounted to working out sophismata. Now in the kind of optics that you are talking about - Theodoric of Freiberg, for example - where you do have an application of mathematics, this kind of application or measuring doesn’t occur. Yet there are optical treatises where this does


occur, at times even mixed with the more traditional way of applying mathematics, but they are not the optical works that you have in mind.

E. s ylla : I think that when we talk about “measure” in late medieval natural philosophy it is really not measure in its usual sense at all. Although I am not very familiar with the procedure, it seems to me that it is closer to the social sciences where you have a general equation, for instance in economics, but don’t really know what capital (or something of this sort) is. You have to specify the variable in question. You don’t call that measuring so much as making precise what is it in the real world that corresponds to the theoretical terms at hand.

j. MURDOCH: Put that together with the incredible variations and you have your answer.

R. RASHED : That is the Harvard School !A. sabra : John, there is quite a lot that can be said and should be said for the way

you want the history of medieval science to be done, but there is another way as well. There are these historians - and here I am playing the devil’s advocate for a while - namely, historians who have been writing on fourteenth century science, or on medieval science in general, from the viewpoint of the seventeenth century. They would say, we are working on the assumption that sometimes people read books and that sometimes when they read books they are influenced by what they read. Now what is wrong with telling their story, the story of the transmission and development of ideas, without this necessarily being contradictory to what you want to do? Why can’t I tell that story? It’s not the story you want to tell, but what’s wrong with it?

J. MURDOCH: Not only is there nothing wrong with it, it is quite consistent with what I am advocating. But the problem is that, first of all, doing it only from the seventeenth century point of view, the results may be, indeed often are, taken to be the sum and substance of fourteenth century or medieval science, what medieval science amounts to. Furthermore, in using the seventeenth century point of view one often positively misinterprets some of the fourteenth century material. That would be a second charge against it.

H. oberm an : Are you not granting too much when you say that it can also be done that way? It seems to me that only by going through this very laborious and detailed investigation of the fourteenth century on a much broader level would you then also be able to write the story of the seventeenth century. Only then will you be able to show that there occvirred a misunderstanding of the medieval material and to show exactly where and how it took place. I don’t think that you can take the shortcut of simply looking back from the seventeenth century; you have to do it on this broader front.

J. c a d d e n : Because what you have set up as the explanandum in the seventeenth century is really much too narrow, John. You need not only to explain the origins of specific theories, but you need to explain why, if seventeenth century people did read fourteenth century texts, they were able to transform these fourteenth century texts. What was the shift in understanding and expectations that allowed this?

A. sabra : Yes, but whatever your answer to these questions, my explanation would still be an element in the overall picture. I am not eliminating these other things, but if they are such that they led Galileo to read a text in such a way that he transformed it, then it meant something to him which it would not have meant to someone in the fourteenth century. This, then, is part of the explanation of Galileo, whatever else this explanation may include.

s. victo r : ‘Part’ is the operative word. And the important thing about history is not its analytic nature, but the way it grasps on to more and more and more. And the ex

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planation of why Galileo read fourteenth century texts in this funny way is probably even more interesting for our understanding of Galileo than the positive contributions that the fourteenth century may have made to Galileo. Yes, there are broader questions than the vertical one that Bashy is asking.

A U T O N O M O U S A N D H A N D M A ID E N S C IE N C E :

ST. T H O M A S A Q U IN A S A N D W IL L IA M O F O C K H A M

O N T H E P H Y S IC S O F T H E E U C H A R IS T

I. IN T R O D UC T IO N

It is a commonplace o f the history o f science that the rise o f modern science involved the breaking off o f the specific disciplines o f modern science from theology and from philosophy in general.^ This is supposed by some to have occurred mainly in the seventeenth century and later and by others to have had its origins in the Middle Ages or earlier. Sociologists o f science have suggested various external social or cultural factors that might have allowed or supported such specialization. In his classical study o f seventeenth century England, Robert Merton pointed to religious, economic, and technological factors.^ In a more recent study extending to the medieval origins o f specialization, Joseph Ben-David suggests that the medieval university guilds acted as a buffer between the practical goals o f public service set by outside society for university graduates and the individual professor who might be inclined to pursue his special interests in conjunction with colleagues.^

In general, however, it is assumed that the natural sciences^ did not have autonomous status within medieval society and that their specialized development was therefore necessarily limited.® Aside from a few noble or royal patrons o f learning, the church was the main source o f support for medieval scholars, and it, naturally, set religious goals for scholarship. Secular arts and sciences were considered at worst as useless and distracting and at best as handmaids providing some slight assistance to the religious learning which was o f primary concern. Thus within medieval universities most students and professors had ultimately religious goals. A man might do work in logic or physics, but he would also teach or write on theology, ethics, canon law, or other more strictly religious subjects.

I f one looks, however, for at least nascent specialization in the secular sciences, one can point to the division o f many universities into faculties o f arts, theology, law, and medicine, and suggest that some professors may have confined themselves to topics proper to their own faculties. In the

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J. E. Murdock and E. D. Sylla (eds.). The Cultural Context o f Medieval Learning. 349-396. All Rights Reserved.

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time o f Buridan at Paris there was a regulation that professors o f arts or philosophy should not treat specifically theological subjects.® But since the same regulation also stated that if a professor o f arts should find it necessary to treat a subject bearing on theology and faith, he should resolve it in accordance with faith, it was assumed that such an arts professor would also know his theology.'^ In the reverse direction, professors o f theology often assumed it was their right to treat questions bearing on the arts. Although this was perhaps supposed to occur only where the arts were relevant to theology, in various cases theologians were accused, with some justice, o f an excessive interest in non-theological material.^

So the division o f the medieval university into faculties provided only a weak basis for specialization in the secular arts and sciences.

A second possible source within medieval universities o f at least temporary specialization in the arts might have been the fact that the medieval student studied and perhaps even taught arts before he went on to theology or one o f the other higher faculties, so that he might in a sense be said to be a temporary specialist in the arts before he went on to higher studies. In many cases, however, the earliest work we have o f a medieval professor is his Sentence Commentary, whereas his lectures on arts topics, logic, physics, or the like were at least revised if not originally produced after his first work in theology, so it is difficult to determine what his views were before the possible influence o f theological studies. In addition, because the arts were widely considered to be o f value only insofar as they were handmaids to theology, theological concerns were very likely to influence what was taught in the arts even at an elementary level. Arts courses in medieval universities, like their counterparts in some modern universities, namely the “ service courses” that students may be required to take in addition to courses in their major departments o f study, tended to be elementary and directed either to basic information that every student must know (how to read and write well, for instance) or to more specialized tools that would be useful in the student’s intended major field o f study. So medieval university structure in general provided only a very limited place for specialization in secular arts and sciences.

On the whole, the surviving medieval works on secular subjects tend to confirm this view. Given the primary role o f the arts in medieval universities as service disciplines, one would expect that most medieval works written on the arts would be directed either to teaching elementary courses

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or to providing the theologian or canon lawyer with the tools needed for his work.i® Since much teaching in medieval universities was based on standard texts, one would expect to find primarily commentaries on these standard texts, questions related to the texts, or elementary compendia related to the various arts. One would not expect to find many advanced specialized treatises in the arts although one might find these in theology and perhaps in law and medicine.

When one surveys the extant medieval works on the arts, one does, in fact, find mostly elementary compendia and commentaries. There are, however, some notable exceptions. Logic, perhaps, attracted more advanced work than any other secular field. William Heytesbury’s Regule Solvendi Sophismata, just to pick one example, although it claims to be a work directed to first year students o f logic, has seemed to some historians too difficult for that purpose. The sophismata hterature in general, in fact, seems to assume advanced proficiency in logic.^^ There is, however, a likely institutional explanation for this apparent exception. Logic or dialectic held in the medieval university the place that mathematics holds in the modern university: it was considered the basic key to many other areas o f knowledge.^® It might have been a discipline primarily o f interest because o f its use in other disciplines, but its use was so widespread and considered so necessary in other disciplines, that it outgrew its service role. Since there were many competing service functions, no one other discipline could control the teaching o f logic, and logicians could control the development o f their own discipline. There were also large enough numbers o f teachers o f logic that they could provide an audience for each other and mutual stimulation. Thus logic in the medieval university, as mathematics in the modern university, could become not a mere handmaid biit something like the “ queen and servant o f the sciences.”

Besides logic, other secular arts could also gain greater acceptance because o f a recognition o f their special service. In numerous appealing and convincing studies, M.-D. Chenu has described the use and acceptance o f various arts within theology. First grammar, then logic, and then the Aristotelian conception o f science were applied to theology.^^ Despite worry and rejection o f these tools by some, it was those who were most expert in the arts that had the chance o f being the best theologians, as Chenu has argued so persuasively. Rather than restricting the role o f the arts, these theologians allowed the arts to be o f utmost assistance in the

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unfolding o f theological insight. Thus in addition to gaining acceptance because o f its very widespread applicability to other disciplines as in the case o f logic, an area o f secular knowledge could gain greater acceptance by proving its value within theology in particular.

Theology must be dependent on the state o f the contemporary disciplines o f textual analysis, Chenu argues, because the word o f God is revealed in human language.^’ Only to the extent that men are able to understand and interpret human language will they be able to derive the utmost benefit from the revealed word o f God. Thus as the arts o f the trivium were accepted into use in theology, one would expect to see a more and more advanced development o f these arts. In fact, new insights into the arts o f the trivium were often developed hand-in-hand with solutions to theological problems, so that the theological motivation in the development o f grammar or logic is readily apparent.^» This might mean that the autonomy o f the arts would be submerged and that the principles o f the arts would be distorted by theological considerations, but, Chenu argues, in the best cases the arts were allowed their own autonomy and dynamisni and thus contributed even more to the benefit o f theology,

Before the arrival o f Aristotle’s physical works in the West, the real sciences, in particular the quadrivium and physics, may not have seemed to have as much to offer to the development o f theology. With Thomas Aquinas, Aristotle’s theory o f science (i.e. his description o f what makes something genuinely scientific) and to a lesser extent Aristotle’s science itself was applied in theology. 20 It is probably in the fourteenth century, however, that one finds the greatest use o f the natural sciences in theology. One can point to numerous Sentence Commentaries in which natural science is used extensively, and there are some Sentence Commentaries which in fact seem to be works on logic and natural science in disguise - in response to each theological question raised, the author immediately launches into a logical-mathematical-physical disquisition and then returns only briefly at the end to the theological question at hand. 21 One can also point in the fourteenth century to the simultaneous, apparently autonomous development o f logical-mathematical-physical science at Oxford, Paris, and elsewhere.

This paper, then, is directed to the following questions: can one show that as grammar and logic beginning in the twelfth century if not earUer, and the Aristotelian theory o f science beginning in the thirteenth century.


so the physical sciences and mathematics beginning in the late thirteenth century and especially in the fourteenth century proved their value as handmaids to theology to the extent that their further autonomous - i.e. theologically undistorted - development was stimulated? Physical science was certainly applied to theology, but was it useful and did it prove its value, or was it in fact, even at this early date, mainly a competitor for men’s attention and a distraction from the higher truths o f theology? Were apparently purely secular advanced treatises on natural science - for instance, Richard Swineshead’s Calculationes ~ justified by their supposed applicability to and usefulness in theology?

When logic became important in the medieval universities because o f its service to other disciplines, it was chiefly the methods o f logic that were applicable and received further development - how does one, for instance, use rules o f logic to solve sophisms arising in the various disciplines? I f natural philosophy received a similar increase o f importance because o f applicability to theology, it was not only the methods o f natural philosophy that were applicable - although as I have said, St. Thomas did apply the Aristotelian theory o f science to theology - but also the results or content o f natural philosophy. So, as in St. Thomas’s case, one might look to natural philosophy to see what it had to say about the eternity o f the world versus its special creation by God .22 Although even where use as a method was concerned one might need to look to theology to see what parts o f the available methods might be likely to be useful, it was more clearly the case where content or conclusions were concerned that theology would have to be the guide as to which areas o f natural science were applicable and therefore worthy o f further development.

Thus one might expect that in the case o f natural philosophy the greatest development would come in contexts closely connected with theology. One might indeed have commentaries on Aristotle’s works or other standard texts for the elementary courses on natural philosophy, but the advanced treatises might spin off" not so much from Aristotle’s works as from theological texts or contexts. In discussions comparing the “ Augus- tinian” attitude toward natural philosophy with the Thomistic attitude, it has been stated that the Augustinians provide very little scope for a natural philosphy separate from theology, whereas St. Thomas uses a separable philosophy.23 Despite this, however, even those in the Thomistic tradition might not be expected to devote themselves wholeheartedly to

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the further development o f secular philosophy - after all such philosophy even for non-Augustinians maybe assumed to be o f secondary importance. But if an autonomous secular philosophy is shown to be o f important help w ithin theology, then one might look for greater interest and attention. 24

So one might expect the most advanced philosophical work done in the thirteenth and fourteenth centuries to have been done in a theological context. This expectation would be reinforced by the fact that most people did their work in philosophy proper when they were young and then did work in theology when they were more mature and might be expected to have deeper insights.25 Against this expectation would be the possibility that the theological context would lead to a superficial treatment o f the philosophical issues. But were there not, at least in the fourteenth century, some extended and insightful philosophical discussions within theological works?

In the rest of this paper I will try to investigate these sorts o f questions by looking primarily at two o f the best known theologians o f the thirteenth and fourteenth centuries to review their theories o f the relations o f theology and philosophy and to examine how in practice they carry out the cooperation o f theology and philosophy. For the thirteenth century I will look at the ideas o f St. Thomas Aquinas and for the fourteenth century I will treat William o f Ockham. I hope to show that even though Aquinas may have acknowledged the value o f an autonomous philosophy, his use o f philosophy within theology prevented philosophy from receiving the autonomous development to which Ockham’s use entitled it.

IL THEORETICAL RELATIONS OF PHILOSOPHY A N D THEOLOGY

How then did Aquinas and Ockham conceive o f the relations o f theology and natural philosophy? I f the application o f the trivium is justified, as Chenu argues, because God’s revelation appears in human language, what is the justification o f the application o f the quadrivium or natural philosophy? To answer these questions I can rely mainly on the researches o f other historians.

In the work o f Aquinas, reason and physics or metaphysics were used to elaborate theological conclusions. Thus, according to Aquinas, there are three ways in which philosophy can be o f use to theology: first it can


demonstrate various preambles to faith, such as the existence and uniqueness o f God; second it can clarify matters o f faith by analogies with philosophical doctrines; third it can refute objections against faith.^s It is the second o f these uses, however, which is particularly characteristic o f Aquinas’s theology.

This is an important point and deserves elaboration, for Aquinas’s notion o f theology as a science was based on an adaptation o f Aristotle’s notion o f subalternate sciences that was quite different from Aristotle’s original conception. In the Posterior Analytics Aristotle had stated that a genuine science must be based on logical deductions from self-evident axioms. In some cases, however, he allowed that when one science naturally fell under another, the subalternate science could use as its axioms not self-evident propositions but conclusions o f the higher science. Thus optics or perspective is subalternate to geometry and can use geometrical conclusions or theorems as premises without tracing these back to the self-evident axioms by which they are demonstrated in geometry. A subalter«afe science can demonstrate that things are so (demonstrations quia) while the suhalternating science demonstrates why {propter quid) they are so.

As a rule the subject matters o f the subalternating and subalternate sciences are not the same - if they were exactly the same, one would have a single science and not two separate sciences. So, for example, the subject matter o f geometry is lines, whereas the subject matter o f optics is visual lines. Since a visusal line naturally is a type o f line, optics falls under geometry. Geometry, then, can be used as a tool o f optics. ' Combining premises from geometry and optics, one can draw optical conclusions. The subalternating science alone, however, cannot provide a complete propter quid demonstration o f a conclusion o f the subalternate science because its subject matter is not identical, Thus geometry alone cannot demonstrate conclusions about visual lines. To demonstrate propter quid the conclusion o f the subalternate science, therefore, one must combine the conclusions o f the subalternating science with premises proper to the subalternate science. The conclusions o f the subalternate science will be genuinely scientific since they could be traced back, i f necessary, through the subalternating science in part, to self-evident propositions.

In Aquinas’s modification o f the notion o f subalternate sciences, on the other hand, it is only a matter o f faith that the premises taken from reve

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lation are self-evident or truths known to God. The analogy that Aquinas sees is that in both cases one takes from a higher science premises whose truth is guaranteed by the higher science. Aquinas wants to point out that there is not such a great disparity between theology based on faith and science based on axioms because in many sciences-i.e., in the subalternate sciences - one also takes one’s premises “ on faith” assuming that the subaltemating science has proved them starting from self-evident axioms. The difference is that whereas in Artistotle’s case the premises taken from the higher science can be demonstrated by man, in Aquinas’s theological science this truth cannot be demonstrated rationally. Nevertheless, in both cases, one presumably has a soUd foundation o f truth to base one’s reasoning on.

A second difference between Aristotle’s and Aquinas’s notions o f subalternate sciences is that whereas for Aristotle the subaltemating and subaltemate sciences have different subject matters as a rule-e.g., lines versus visual lines for geometry and optics - for Aquinas Divine science and theology as subalternate to it have the same subject matter. Theology, therefore, really forms one science together with Divine science, although Divine science cannot be known directly to man. Whereas the separate subject matters o f Aristotle’s subalternate sciences provide for these sciences some degree o f autonomy and separation from the subaltemating sciences, Aquinas’s theology does not have this autonomy and separateness.

A third difference between Aristotle’s and Aquinas’s notions is that whereas for Aristotle the principles o f inference o f the higher and lower sciences tend to be the same - and tend to be simply the rules o f logic or reason -, for Aquinas the principles o f inference may be diflferent. Divine science is presumably known immediately and non-discursively to God and to the Blessed. Theology, on the other hand, draws its conclusions by reason, although perhaps, in view o f its subject matter, it must make use o f a purified and circumspect reason. This last point - the possible need to “ purify” one’s reason for use in theology - can be crucial in undermining the autonomous status o f secular sciences in their use within theology.^® This point will be made clearer in the example which forms the third section o f this paper.

Thus there are crucial differences between the status o f theology for Aquinas and the status o f the usual sub alternate science for Aristotle -


differences great enough so that even Aquinas himself called theology “ quasi-subalternate” to Divine science.^o Nevertheless, Aquinas felt enough confidence in his view o f theology as a science that he was willing to make extensive use o f reason in his works to draw further conclusions from revealed premises. In doing this he claimed he was not introducing an alien philosophical element into sacred doctrine, but using a purified reason that combined with revelation to make a single sacred science - the water o f philosophy when mixed with the wine o f revelation was turned into wine.®i

In the work o f Ockham and other nominaUsts, by contrast, this unified sacred science was, for better or worse, split apart to a great extent.32 Thus o f Aquinas’s three uses o f philosophy in matters o f sacred doctrine, Ockham generally allows only the first and third, external uses. He believes one can prove certain propositions preliminary to faith, such as the existence o f a Prime Mover,^^ but far fewer such propositions than Aquinas thought he could prove. His most extended use o f philosophy in theology is to refute objections against the faith or to refute false views in theology. He does not think that it is possible to any great extent to elaborate a rational theology based on revealed premises (in other words he greatly downplays the value o f speculative theology).

The guiding principle o f Ockham’s distinction between divine and natural knowledge is the distinction between God’s absolute power (potentia Dei absoluta) and His ordained power {potentia Dei ordinata). Although historians still disagree about the interrelations o f these two potentiae and about whether one or the other represents what a given author is really committed to,^4 it is fairly certain that in the work o f Ockham both had their own intrinsic validity. Thus God’s absolute power represents the possibilities open to God - and these are limited only by the laws o f logical contradiction - whereas God’s ordained power represents what He has in fact chosen to do. Happily for the possibility o f natural science, God has chosen to act in regular ways for the most part. Man knows how He has chosen to act through experience and intuitive cognition or through revelation. On the basis o f his intuitive cognition and by his memory o f previous intuitive cognitions man can formulate true propositions about what exists. God could, by His absolute power, create the intuitive cognition in a man’s mind o f something that did not exist, but this would be an exception to the ordinary course o f nature. In Ock

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ham’s own view, although he was not followed in this by other nominalists, the man would probably recognize that, contrary to the case o f most intuitive cognitions, the thing did not exist.^s Ockham never satisfactorily explains how, if one had the intuitive cognition o f a non-existent thing, one would be able to judge that it did not exist,^ but, i f this is so, it indicates that the intuitive cognitions that men have had and on the basis o f which they have judged things to exist, were in fact natural intuitive cognitions o f existing things - if they had been intuitive cognitions o f nonexistent things, this would have been obvious.

Thus on the basis o f perceptions (intuitive cognitions) o f what exists (which in the ordinary course o f nature for human beings are always accompam’ed by sensations o f external things or else involve perception o f one’s own mental processes), one can develop natural science based on the ordinary course o f nature (ex puribus naturalibus) and God’s ordained power. On the basis o f direct revelation, scripture, and authoritative Christian doctrine, one can receive gUmpses o f God’s absolute power. Paradoxically, since God never changes. He must always have ordained that these exceptions were going to occur at a particular time, but nevertheless they are considered to be in some respects special interventions into the ordinary course o f nature.^^ The point is that, although God has freely decided to act in regular ways. He is also free to act in other ways. Although in the normal course o f events, for instance, a man cannot attain salvation except if he is in a state o f Grace when he dies, God could save a man who died without Grace if He so chose. The only Umit to God’s absolute power is the law o f non-contradiction - He cannot choose to do something that is logically impossible.

Thus for Ockham one has three main sources o f knowledge: intuitive cognition as the basis o f natural science, revelation, which is contained in scripture or other authentic Christian writings as determined by the church (thus in this case there are two bearers, scriptures and the Church, o f one type o f knowledge), and reason or self-evident truths, as exemplified in the law o f non-contradiction and other laws o f logic. A ll three sources o f knowledge are sufficiently reliable in their own domains.

Nicholas o f Autrecourt later argued that i f intuitive cognition o f non- existents is ever possible, then intuitive cognition is not a reliable source o f knowledge. Rather than accept this alternative, he proposed as a postulate (if he had arguments for his postulate, they are not known) that in


tuitive cognition or sense experience o f the world is always reliable but that its rehability is limited to what is directly perceived - the inference from quality to substance or from cause to effect or vice versa is not certain.38 Given Ockham’s theory o f sensation and perception, it would be natural to expect him to conclude that if there were an intuitive cognition o f a non-existent, one would judge the thing to exist as in normal cases. Then Nicholas’s dilemma would be a telling one. Because Ockham began from the view that intuitive cognition provides evident knowledge o f the existence o f objects and because he thought it a contradiction in terms for evident knowledge to be false, however, he concluded that intuitive cognition o f a non-existent would lead one to conclude that the thing did not exist. He did not have to face directly, therefore, the problem o f the unreliability o f intuitive cognition. In fact, although the intervention o f God’s absolute power is always a possibility, Ockham proceeds in doing natural philosophy as if God does not intervene except in those cases where Scripture or the Church specifically states that it has been revealed to be otherwise.

In the work o f Ockham, therefore, the role o f natural knowledge was almost the reverse o f its main role for Aquinas. Rather than using philosophy to build and extend theology, he uses it to limit the area in which theology and special revelation is necessary. Thus to take a very simple case, natural explanations could be found for some apparently non-natural phenomena, and make the hypothesis o f supernatural or miraculous intervention unnecessary. Despite God’s absolute power hovering in the background, natural science could be essentially autonomous in its own sphere. Heiko Oberman has described how, in his view, the autonomy o f man was one o f the four basic principles o f nominalistic theology, along with the sovereignty o f God, immediacy, and secularization.^» To reconcile the apparent contradiction between the sovereignty o f God and the autonomy o f man, Oberman uses the image o f a dome within which man’s autonomy prevails.^» The autonomy o f natural philosophy is, I think, the partner o f the autonomy o f man, and is also an autonomy within limits or within the “ dome.”

Thus the kind o f relationship between theology and natural philosophy that one would expect in the work o f Ockham is a relationship o f mutual cooperation where each type o f knowledge has its own proper sphere within which it is autonomous. It is, o f course, assumed that God is the

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first cause o f all events within the natural sphere and not only o f supernatural events de potentia Dei absoluta. Since, however, man knows by experience that God has chosen to act in regular ways, the ultimate causality o f God can be kept in the background within the natural realm. In line with Ockham’s famous razor, Ockham also states that one should not multiply miracles beyond necessity - although even here Ockham admits that sometimes it may please God to cause more miracles when fewer would do!

It is a trademark o f Ockham and other nominalists to introduce possibilities de potentia Dei absoluta into natural science. This is often supposed to have been partly the result o f the 1277 condemnation o f propositions implying that God could not violate the laws o f physics. The actual function o f the reference to God’s absolute power in most natural contexts, however, is essentially equivalent to an appeal to reason and almost always is made to determine what are the real and distinct entities {res) involved in the situation.

Both Aquinas and Ockham commented on Aristotle’s Physics, Ockham several different times. For both authors, however, theological contexts are more likely to be important and to reveal the nuances o f how the author conceives the interrelations o f theology and natural science. In such contexts one has to do not only with what God might have done without logical inconsistency although in fact He has not done it: in addition one has to do with cases in which Scripture or Church authority indicates that God has in fact done something outside o f the ordinary laws o f nature. How can one use natural science to help explain a situation in which it is agreed that the laws o f natural science have been violated?

In the third main section o f this paper, therefore, I will look at how in practice Aquinas and Ockham resolved the conflicting claims o f revelation and natural philosophy within a theological context. Good contexts to look at would be the ones in which Aristotle and the Church disagreed, such as concerning the eternity versus the creation o f the world, or concerning the nature and possible inxmortality o f the human soul. For Aquinas and Ockham in particular, however, perhaps the best problem to look at is that o f the Eucharist. In the sacrament o f the Eucharist one had a strange middle ground where, as both Aquinas and Ockham agreed although they may not have put it quite this way, God had freely agreed consistently to produce a miracle whenever the words o f the Mass were


spoken in the proper circumstances. Thus the Mass involved not God’s usual ordained power, but a kind o f second order ordained power, which, as Ockham would emphasize. He could again abrogate by His absolutepower.‘*2

in . THE EUCHARIST

That there was a direct conflict between natural philosophy and theology concerning the Eucharist was signalled directly by Peter Lombard at the beginning o f Distinction 10 o f Book Four o f the Sentences. There are some insane people, he said, who, measuring the power o f God by natural means, audaciously and dangerously contradict the truth, asserting that the body and blood o f Christ are not actually present and that when Christ said, “ This is my body,” he was speaking only metaphorically.

In fact, as determined by Pope Innocent III and the Fourth Lateran Council, one has in the Eucharist the substance o f Christ accompanied by the accidents o f the bread, but without the substance o f the bread. Contrary to Aristotle, therefore, the accidents o f the bread do not inhere in any substance - it would be absurd and irreverent to suppose that they inhere in Christ - and yet it is obvious to the senses that the qualities behave physically just as i f the substance o f the bread were still underlying them. How this could be so required explanation.

Aside from problems concerning the remaining accidents o f the bread, there were problems concerning the accidents inhering in Christ: i f Christ was really present in the Eucharist, what was the status o f the qualities inhering in Him - why can’t He be seen, for instance - and how was His quantity present - how could Christ’s extension be present in the Eucharist, and was Christ in place in the Eucharist so that He could move locally with the Eucharist? A further problem concerned transubstantiation - how exactly did Christ come to be present in the Eucharist and what exactly happened to the substance o f the bread?

Aquinas and Ockham each consider the physics o f the Eucharist in several different works, but each also repeats essentially the same view in the different contexts so it is not necessary here to distinguish between their separate treatments. Aquinas’s two most important treatments o f the problems are in his Sentence Commentary, Book IV, Distinctions 10-12 and in his Summa Theologiae, I I I “, Questions 75-77. Ockham has three important treatments - in his Sentence Commentary, Book IV, Questions

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4-7 ; in his separate treatise De Sacramento Altaris (actually two separate works on the same subject); and in his Quodlibet Quartum, Questions 20-39. For convenience sake, I will follow primarily the parallel discussions o f the two authors’ Sentence Commentaries, referring in footnotes to parallel texts from the other works. Thus in the order that they are discussed by Peter Lombard the five main problems are: concerning Christ,(1) His quantity and (2) His qualities (Distinction 10); (3) transubstantiation (Distinction 11); and (4) the qualities o f the bread and (5) the quantity o f the bread (Distinction 12).

In his Sentences, Book IV, Distinction 10 Peter Lombard treats the real presence o f Christ in the Eucharist. Both Aquinas and Ockham naturally accept the fact o f Christ’s real presence and their discussions concern subsidiary aspects o f this presence - in particular the quaUties, quantity, place, and possible motion including action and passion o f Christ in the Eucharist. Both authors agree that Christ is entirely present in the Eucharist - including his soul as well as his body - but that He still remains in Heaven also. Both authors agree that He is not in the Eucharist circumscriptively with His parts extended in space, but rather that He is entirely at every part o f the Eucharist. They agree that Christ cannot be sensed or perceived in the Eucharist although it is known by revelation that He is there.

Beyond these points o f agreement, however, the two authors diverge. Aquinas emphasizes that Christ is not really in place per se in the Eucharist because His dimensions are not extended with the dimensions o f the Eucharist. Since the bread was previously in place, however, Christ is now within the former place o f the bread as if by accident and indirectly because the substance o f the bread was converted into His body.^4 Although Christ is now present where He was not present before, it is not necessary that He was changed or moved in any way to become present in the Eucharist.45 The substance o f the bread is changed directly into the body o f Christ, Aquinas says, and the rest o f Christ - for instance His blood, soul, and accidents like quantity - are present by natural concomitance.^®

Christ cannot be seen in the Eucharist because He is not there quantitatively and action by qualities presupposes quantitative presence and contact." ’ Like Christ’s quantity. His qualities in the Eucharist are present only mediately through His substance and hence have no immediate relationship to the species o f bread or surrounding bodies.^»


Ockham opens his discussion o f Christ’s presence in the Eucharist with a refutation o f Aquinas’s view.'*® Christ cannot be present precisely because o f the conversion o f the bread into His body, Ockham says, because God could have caused Him to be present beneath the accidents o f the bread even if the substance o f the bread had never been there. Since Christ is now present where He was not present before, there must be a change involved and Christ must be moved. Contrary to Aquinas, Christ is in place definitively i f not circumscriptively beneath the species o f bread - it is not contradictory for Christ to be definitively present in the Eucharist and at the same time circumscriptively present in Heaven. Furthermore Christ is in place immediately and not only via the species o f the bread or because o f the conversion - all things are immediately present in a given location and not one via the other unless there is some special union o f one thing with another. So if Christ were present only via the species o f bread, He would have to have some special union with the species o f bread, which He does not have.®®

Ockham’s points here are, from the point o f view o f natural philosophy, all well-taken. Leaving aside the question o f conversion which will be considered below, Aquinas’s views on the lack o f change in Christ’s body and the relation o f Christ to the place o f the Eucharist clearly go against the Aristotelian doctrines concerning change and place, the vocabulary at least o f which both authors are using. Aquinas, in fact, admits that his view o f how Christ is in place does not correspond to any o f the philosophically recognized ways o f being in place.® Yet his use o f Aristotelian philosophical terminology would make one think he was doing philosophy.

Thus right from the start the basic difference between Aquinas’s procedure and Ockham’s procedure is clear. In almost every important case Aquinas modifies or “ sublimates” natural philosophy to explain the Eucharist whereas Ockham allows natural philosophy its own autonomy- where natural philosophy is not applicable Ockham refers to God’s direct intervention rather than assuming a modified physics. Thus in Ockham, but not in Aquinas, natural philosophy has its proper autonomy even within theological contexts.

Ockham prefaces his own view of the physics o f Christ’s presence in the Eucharist with a long excursus expounding his famous and well-known view o f quantity, according to which quantity is not a separate entity, but

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only a connotative term.^^ There were two contexts within discussions o f the Eucharist that led authors to discuss quantity - this context concerning Christ’s quantity or lack thereof in the Eucharist and the context o f the quantity o f the species o f bread. Aegidius Romanus’s brilliant insights concerning quantity were developed in the second o f these contexts and resolved serious problems concerning the quantity o f the species o f bread as he viewed it.s4 Ockham’s analysis o f quantity, on the other hand, is developed to solve the problem o f Christ’s quantity in the Eucharist. Since it clearly does remove the very great inadequacies o f both Aquinas’s and Duns Scotus’s views concerning the quantity o f Christ in the Eucharist, it seems to me very likely that Ockham’s theory o f quantity was first developed for this purpose and not solely as a logical-ontological excer- cise in the avoidance o f multiplying entities beyond necessity.

As Anneliese Maier has shown,5s Ockham’s equation o f quantity with substance (or quality) was not new with him, but had been expounded earlier in several contexts by Peter John Olivi, perhaps originally in the context o f the quantity o f the species o f bread. Other authors before Ockham, in particular Richard o f Mediavilla, had sharply attacked Olivi’s view and Ockham was familiar with their attacks.^® This may explain why, even before Lutterell initiated censure proceedings against Ockham, including in his list o f errors Ockham’s view o f quantity in its relationship to the Eucharist, Ockham seems to have been particularly on the defensive about his theory o f quantity.^’ Since the order o f Ockham’s works is not known with certainty, it cannot be established absolutely whether Ockham first developed his version o f OUvi’s view o f quantity in a theological context, but it seems very plausible that it was in fact either in the context o f the earlier o f his separate treatises on the Eucharist, as Maier argues, or in his Sentence Commentary. S i n c e Ockham says twice in the earlier separate treatise on the Eucharist that he is resolving issues that arose when he was expounding the Sentences, the Sentence Commentary would seem to be the most probable original context.5® Whether Ockham’s view o f quantity had a theological origin or not, Ockham extends it to quantity in general and makes it an important and truly philosophical doctrine - unlike Aquinas’s view o f the quantity o f Christ in the Eucharist which is used solely in that context and which, although expressed in philosophical language, has little philosophical plausibility.


The role o f Ockham’s theory o f quantity in solving the problem of Christ’s quantity in the Eucharist is the following. It was generally agreed that Christ is present in the Eucharist with all his essential and accidental properties just as He then exists in heaven.®» But Christ’s quantity or extension, it was generally thought, is present in Him in Heaven and must therefore also be present in the Eucharist. Yet in the Eucharist Christ is wholly present in every part - otherwise He would not be present in every part o f the host after it was broken, and furthermore He would be broken apart when the host was eaten which, all agreed, was an irreverent thought. How, therefore, can Christ’s quantity be in the host when He is not extended in the host?

Aquinas simply declared that since only the substance o f Christ is present in the Eucharist by virtue o f the sacrament whereas the dimensions o f Christ are present by natural concomitance, it followed that contrary to the usual situation in which extension precedes substance (the extension preceding substance being Averroes’s “ indeterminate dimensions” and not determinate extension), here the substance o f Christ is immediately present and the extension o f Christ is only subsequently and accidentally present. Ordinarily the mode o f being o f substance is determined by the preceding indeterminate dimensions and thus the substance, in itself intrinsically unextended, is extended. In the Eucharist the mode o f being o f Christ’s dimensions is determined by the preceding unextended substance, and hence the dimensions are unextended. Thus the dimensions o f Christ are not directly comparable to the dimensions o f the species o f bread and in fact they are not extended. Philosophically speaking, this is a contradiction in terms - a non-extended extension - whatever its theological value may be.® Aegidius Romanus later made good philosophical sense out o f this approach to Christ’s quantity by distinguishing between what today would be called quantity as mass and quantity as extension.®^ Christ’s mass-quantity could be present in the Eucharist without extension without supposing anything self-contradictory. Aquinas does not try to elaborate or justify his view philosophically along the lines o f Aegidius’s approach or any other.

Ockham who, like most o f his contemporaries, was peculiarly unable to conceive o f a quantity o f matter distinct from extension o f matter as Aegidius did, cut the Gordian knot concerning Christ’s quantity in the host simply by arguing that quantity is not a distinct absolute or relative

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entity so that it is not necessary to suppose that Christ’s quantity is present in the Eucharist. Since all o f Christ’s parts are together in every part o f the host, Christ is not extended, or not a quantum, in the Euchar i s t , but since Christ’s quantity is nothing else but His substance in any case. He is not lacking any real attribute in the Eucharist.®® Thus Ockham saves the basic theological doctrines concerning Christ’s presence in the Eucharist without having to invent a non-extended mode o f existence for extension. To show naturally that Christ’s parts can be together in the Eucharist Ockham refers to condensation, where parts that existed separately in the rare substance now exist together. To show naturally that a single indivisible thing, as Christ is when all o f His parts are together, can exist simultaneously in distinct places, Ockham refers to the intellective soul which was thought to exist entirely in every part o f the body. He also provides theological parallels for each o f these two aspects o f Christ’s presence in the Eucharist. So concerning the quantity o f Christ in the Eucharist, Ockham has a view that makes philosophical sense, and he tries to show that it makes sense in natural contexts,®» whereas Aquinas does not.

Concerning the other aspects o f Christ’s presence in the Eucharist, Ockham also preserves the tenets o f Aristotelian natural philosophy far more carefully than Aquinas. He allows that in the Eucharist Christ is in place definitively, one o f the two natural ways to be in place.®® He admits that Christ is moved locally when the Eucharist is moved - which seems obviously to be the case philosophically speaking if Christ is present in the host - whereas Aquinas tries to avoid this by saying that since Christ is not strictly speaking in place He does not move locally unless by accident.70 Ockham even takes Christ’s motion with the Eucharist seriously enough to worry how the Aristotehan dynamics o f motion will be fulfilled - it would appear that a mover naturally proportioned to move the species o f bread will not be in proportion to move Christ with the same velocity. He solves this by saying that Christ moves voluntarily - or i f He does not do it voluntarily God moves Him - with the species o f bread.

Concerning Christ’s quaUties in the Eucharist and the possibihty o f Christ having sense perception there, Ockham again allows natural philosophy its proper autonomy. According to the usual Aristotelian analysis o f action and passion, he concludes that Christ’s definitive rather


than circumscriptive presence in the Eucharist should not hinder action and passion.'^2 After all, the physical proximity necessary for action is still present. One should not deny, he says, the common proposition o f physics that when an agent is approximated to a properly disposed patient action follows unless this denial is compelled by reason, authority, or experience.’ So it should naturally be possible to perceive Christ in the Eucharist - although the fact that the colors, for instance, o f all o f the parts o f Christ’s body are now superimposed at each point o f the Eucharist might mean that only one dominant color would be seen.’ Since it is a fact o f sense experience that Christ is not visible in the host, the only possible conclusion is that God has chosen to suspend miraculously His normal concurring causality in this case, so that Christ is not seen.’ Concerning the possibility o f Christ’s own sense perceptions in the host, Ockham concludes that there is no reason or experience sufficient to convince him one way or another but that it seems more reasonable to assume that Christ knows where He is when in the Eucharist.’ ®

Thus concerning the physical conditions o f Christ’s presence in the Eucharist, Aquinas proposed a “ sublimated” philosophy, which, from a purely natural point o f view, does not always make good sense. It may be a kind o f metaphysics but it is not physics. Thus Aquinas’s assertion that Christ’s extension is present in a non-extended way in the Eucharist is essentially self-contradictory from a purely natural point o f view. Aquinas was certainly capable o f doing good philosophy as he shows in purely natural contexts, such as commenting on Aristotle’s works, so his proposal o f such apparently self-contradictory ideas was not a simple mistake on his part. Near the end o f his discussion o f the real presence in the Summa Theologiae, he in a way acknowledged that his concept o f the real presence did not make good sense from a purely natural point o f view by saying that the mode o f Christ’s presence was wholly supernatural {penitus supernaturalis) '^ Thomas’s primary goal, however, was not to prove the consistency o f the real presence from a purely natural point o f view nor to follow the principles o f natural philosophy wherever they might lead, but to explain and clarify, to sustain, the dogmas o f Christianity in a reverent way. When explained in the proper way, there should be nothing in sacred doctrine that would seem unreasonable - reason is from God as well as revelation and God would not be contrary to Himself- but faith can be above reason, supra rationemJ^

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Ockham, by contrast, explains the real presence in a way that makes good philosophical sense. Where there is some aspect o f the real presence that he cannot deal with from a purely natural point o f view, he simply says so - as when he says that reason cannot conclude whether Christ perceives things as He is present in the Eucharist. Where revelation contradicts normal experience and natural philosophy he also says so openly and gives the priority to revelation. He does not, as Aquinas, develop a “ reverent” or “ sublimated” philosophy or metaphysics. In a spirit similar to that o f the twentieth century logical empiricists, his attitude seems to be that there are no sufficient grounds - neither experience nor revelation nor self-evident axioms - to establish the validity o f such “ sublimated” philosophy. He limits himself instead to statements for which he thinks he has evidence and labels these statements according to the type o f evidence in their favor, whether it be reason, revelation, or experience.

Having made clear, I hope, the differences between Aquinas’s and Ockham’s uses o f philosophy within theology in the context o f Distinction 10, let me indicate more briefly that similar differences can be found concerning the subject matters o f Distinctions 11 and 12. In Distinction 11 Peter Lombard treats the process o f transubstantiation. Both Aquinas and Ockham hold that transubstantiation occurs and that it involves the replacement o f the substance o f the bread by the substance o f Christ while the species or accidents o f the bread remain. Both agree that this replacement takes place at the last instant o f the priest’ s pronunciation o f the words o f the sacrament and that there is a first instant o f Christ’s presence and no last instant o f the existence o f the substance o f bread. Both agree that the accidents o f the bread cannot inhere in the air as some, including Peter Abelard, had proposed previously since this would involve physical implausibilities - such as that the air would have to rush into the space previously occupied by the bread instantaneously whereas no such motion o f the air is observed, i f indeed such instantaneous translation were physically possible. Thus both authors use natural philosophical principles to clarify the conditions o f transubstantiation. Beyond this, however, Aquinas makes several strong arguments which, from Ockham’s point o f view, involve an improper confusion o f the realms o f theology and philosophy.

First, Aquinas asserts that there are only two ways in which Christ can come to be present in the Eucharist - either He must be brought there


from heaven by local motion or the previously existing bread must be converted into Him.®i Since, among other reasons, Christ remains in heaven. He is not moved locally from heaven, so the bread must be converted into Him.82 Aquinas draws two consequences from this understanding o f transubstantiation. First, the substance o f bread can not be present when the substance o f Christ is present - it must have been converted into Christ for Christ to be present.^ Second, the substance o f bread cannot be said to be annihilated since it is converted into the substance o f Christ and not into nothing. 4

Ockham, by contrast, interprets transubstantiation as the annihilation o f the bread along with the concomitant creation o f Christ in the former position o f the bread. He denies that the first o f Aquinas’s consequences o f his theory can be shown on the basis o f revelation or reason. No authentic scripture expressly says that the substance o f the bread is no longer present, he says. Furthermore many aspects o f the Eucharist could be explained much more easily by the normal processes o f nature if the substance o f the bread did remain, since then there would not be accidents present not inhering in a substance. It is naturally possible for two substances to be present in the same place. One should not, he argues, posit more miracles when fewer would do. He eventually accedes, however, to the view that the substance o f the bread is not present in the consecrated Eucharist not on the grounds o f reason but because the church (Innocent III) had so determined.®®

Ockham similarly refuses to give any weight to Aquinas’s argument that the bread is not annihilated. In transubstantiation, he says, the bread simply ceases to exist (except in the sense that God has the power to recreate it) and Christ begins to be present in the Eucharist, ss Indeed, according to well-established principles o f Aristotelian physics, for one thing to be converted into another there should be a subject or substrate which is the same throughout the process. Thus in accidental change the substance is said to be changed because its qualities or quantity change, the substance remaining the same, and in substantial change, as when water is converted into air, the matter remains the same throughout the process. In transubstantiation, on the other hand, there is no substrate that remains the same. Although the accidents o f the bread remain the same throughout, they are not involved in transubstantiation - God could equally well cause Christ to be present without them. Since God is capable

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o f creation ex nihilo, Aquinas is wrong to limit the ways in which Christ could come to be present in the Eucharist to local motion or conversion o f the bread - God is not limited to obeying the laws o f normal physics.®’

One o f Aquinas’s major motivations for his view was apparently the desire to avoid having to say that Christ is moved or changed in coming to be present in the Eucharist. A change has occurred when Christ comes to be present and it is not in Christ, so it must be a change in the bread, since this is the only alternative left. Ockham simply asserts that Christ has changed or moved in coming to be present in the Eucharist - or at least has moved in a broad sense o f the term since He still remains in heaven. Again, from the point o f view o f Aristotelian natural philosophy, Aquinas’s view that Christ can come to be present and later cease to be present when the species are destroyed without any intrinsic motion or change in Christ himself seems to be a contradiction in terms.®®

In Distinction 12 Peter Lombard discusses the remaining species o f the bread. Concerning these species the main problems faced by Aquinas and Ockham were first, quite simply, Aristotle’s view that accidents must inhere in substance, and, second, Aristotle’s view that it is not qualities primarily that cause and suffer change, but the substance underlying the qualities.

Aquinas solved the first o f these problems by declaring that the First Cause is more important as a cause than the second cause and hence that God as the First Cause o f accidents can take the place o f substance, which is the normal secondary cause o f accidents.®® The definition o f accidents, he claims, is not that they inhere in a subject, but that they ought to be in something else. This latter quiddity o f an accident is not removed from an accident even i f by divine power the accident does not inhere in a substance.® To the argument that a disembodied form would not be individuated because forms are individuated by matter, Aquinas replies that in this case the accidents are individuated by the quantity remaining (thus introducing a different cause o f individuation than the normal one).® Concerning the special case o f density and rarity which would seem to include matter in their definitions, he claims that density and rarity can remain without matter because the true essence o f density is not that much material is contained in small dimensions. Density is instead a property consequent upon the fact that matter is thus disposed and hence God can create this property without matter.


For the second o f the problems concerning the species Aquinas replies that in the consecrated host the only accident without a subject is the quantity o f the (former) bread and that the other, quahtative accidents inhere in the quantity as in a subject. God gives to the quantity all the properties and capabilities for action and passion that the substance o f the bread formerly had and, after He does this, action and passion occur as before, only with the quantity acting as substance, and with no need for further intervention by God - it is like the situation in which God gives sight to the blind - once the bhnd are given sight they see normally like anyone else.

Ockham agrees with Aquinas in allowing that God by His absolute power can create accidents without a substance. Indeed Ockham allows consistently in his logical and physical as well as theological writings that the two types o f distinct real things {res) in the universe are substances and qualities. God can create any such distinct things separately since it involves no logical contradiction, although in the normal course o f nature qualities always inhere in substances.®®

It is at least arguable that had it not been for the Eucharist, Ockham would have concluded that the only distinct res in the universe are substances.®® Although the condemnations o f 1277 did include the proposition that God could not create a quality not inhering in a substance - and hence Ockham might have been led by the condemnations to treat qualities as distinct res - probably the proposition appeared in the 1277 condemnation because o f its connection with the Eucharist.®’ As in the case o f his doctrine o f quantity, therefore, here too Ockham may have adopted his view for ultimately theological reasons. In this theological and non- theological works, however, he consistently develops his view o f substance and quality as the two distinct types o f res and makes it a genuinely natural philosophical doctrine. So a theological origin may tend to lead to “ sublimated” philosophical doctrines in Aquinas’s work, but in Ockham’s system a theological origin can lead to an autonomous philosophical doctrine. Ockham does not think that the qualities inhere in the quantity, but, if anything, the reverse - the quantity o f the species o f bread is only a connotative term referring to the qualities directly and to their coextension in space with other bodies indirectly.

Concerning the action and passion o f the species o f bread, Ockham says very plainly that naturally there cannot be action or passion where

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there is no substance, but we see that action and passion occur, so such action and passion must be caused directly by God’s absolute power.®» Indeed, Aquinas’s assertion that God gives the quantity the power to act as a substance had been simply that - an assertion with no elaboration as to how a quantity could act as a substance. Again it seems clear that from the point o f view o f natural philosophy Ockham has by far the better argument. Aquinas, to be sure, may have a theologically more suitable conclusion - he rejects the argument that God may cause directly the action and passion o f the species o f bread basically because such action and passion eventually lead to the annihilation o f the species o f bread, and God never acts directly to annihilate anything.®® Ockham, however, follows the logic o f his philosophical argument even when it leads to a theologically disturbing conclusion.

IV. CONCLUSIONS

Thus in their Sentence Commentaries both Aquinas and Ockham use philosophy to clarify theology. Unlike the so-called “ Augustinian” or anti-philosophical theologians, both believe that philosophy as pure reason has an important role. Aquinas’s philosophy, however, is often “ sublimated” to the special demands o f theological doctrine with little attempt to preserve the conclusions o f normal, natural, non-theological philosophy or to reconcile what is said in the theological context with what might be said in a purely natural context. Ockham, on the other hand, very carefully preserves the autonomy o f the natural philosophy he uses. Whether or not a philosophical proposition may have an ultimately theological origin, he is always sure that the philosophy he uses preserves its philosophical validity. To be sure, where there are contradictions between philosophy and revelation, revelation is given the superior authority, but this is done without destroying the autonomy o f the purely philosophical - an exception de potentia Dei absoluta to the normal order o f things is recognized as such but this does not change the fact that there is a normal order.

The autonomy o f Ockham’s physics was not, I believe, the result o f a great interest in and commitment to physics on his part. Among later nominalists, Buridan does seem to have genuinely physical interests, but Ockham devotes too little attention to everyday physical observations for


this to have been one o f his main interests. Ockham’s two main commitments in his early theological, logical, and physical works seem to have been instead to emphasizing the absolute power o f God, on the one hand, and to demonstrating how the sense o f propositions can be explained without multiplying entities on the other. Other authors who do creative and autonomous physics in the context o f problems o f the Eucharist - including Aegidius Romanus who developed his concept o f quantity o f mass and Walter Burley who showed how qualities could produce substantial forms without the aid o f previous substantial forms - were not nominalists. Rather than empiricism or nominalism, then, I think that the desire to have ostensive or demonstrable grounds, whether experiential, rational, scriptural, or even authoritative, for one’s assertions was probably the common motivation behind recognition o f the autonomy o f natural philosophy in the fourteenth century,

Ockham’s way o f respecting the autonomy o f philosophy and theology has been considered by some to involve skepticism and the disintegration o f the medieval synthesis represented pre-eminently by the work o f Aquinas.103 Some historians have interpreted his views as involving the abandonment o f the rational search for truth about the universe and the substitution for it o f simple faith. Others, however, studying Ockham’s purely physical works have concluded that Ockham wanted to restore pure Aristotelian physics undistorted by Islamic or Christian theology.In advocating simple faith on the one hand and purely Aristotelian physics on the other, Ockham would seem to come dangerously close to what has been called the doctrine o f the “ double truth.” !®®

Some at least o f these labels applied to Ockham are, however, seriously misplaced. The tone o f Ockham’s writings, for instance, is not at all skeptical.!®® on the contrary, within each separate realm, be it theology, logic, or physics, Ockham appears to be committed to the validity o f his ideas and not at all doubtful about the possibility o f achieving knowledge.i®'^

How the various facets o f Ockham’s views fit together while retaining their separate autonomy and sometimes apparent contradiction can perhaps best be seen by recognizing the similarity o f Ockham’s epistemological position to that o f some modern pragmatic philosophers. I have in mind, for instance, the views on the relations o f science and spiritual values expressed by James B. Conant, the chemist and former president o f

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Harvard. Starting from science and trying to reconcile modern science with spiritual values, Conant argues that we have at present no sufficient grounds for formulating a “ cosmic creed” or “ world hypothesis” combining in a single conceptual scheme the findings o f the various sciences, common sense, religious views, and so forth. We do have, however, sciences which have been successful within their own limited areas and similarly ethical codes or religious insights which have been successful. In this situation, then, Conant advocates using our separate conceptual schemes in the areas where they have proved successful without trying to combine them in a “ world hypothesis” o f doubtful validity. I f separate conceptual schemes can be applied to the same problem, then by all means let them be applied and compared, and let the conceptual scheme which provides better results take precedence over the conceptual scheme that fails. I f conceptual schemes do not overlap in applicabihty to the same problem, then let them remain separate. Each conceptual scheme can be developed and expanded in the area o f its applicabihty but should not be extrapolated to areas where it has no competence,

Conant’s position, I would argue, is the same in spirit as Ockham’s. Although neither attempts the grand synthesis, neither is in any way a genuine skeptic. Both are devoted to the advancement o f the separate areas o f knowledge and to maintaining the close relationship o f each conceptual scheme to the grounds for its validity. For Conant the pre-eminent sources o f validation are agreement with empirical facts and usefulness in action. For Ockham the preeminent sources o f validation are, in order o f decreasing weight, revelation, the Bible, and ecclesiatical authority in theology, intuitive cognition and reason or the laws o f logic in natural philosophy. 109 For Ockham, but not for Conant, there is a clear ranking o f validity between the separate types o f knowledge - revelation or truly authoritative sacred doctrine takes precedence over natural philosophy. But the precedence o f revelation for Ockham should not obscure the essential similarity o f his view to Conant’s because the precedence o f revelation for Ockham leaves the autonomy and intrinsic validity o f natural philosophy intact.iio And Ockham is not at all shy about trimming the feathers o f theology, reducing it from the full display o f contemporary theological opinion to the minimum certified and authoritative Christian doctrines.

Ockham’s two treatises De Sacramento Altaris^ and in particular the


treatise usually printed second although probably written first, are excellent examples o f the working out in practice o f this epistemological position. These works are written like legal briefs, indicating the exact degree o f authority or probability to be attached to each proposition. Like Peter John Olivi before him,m Ockham repeats several times that when he goes beyond the teachings o f the Catholic church he is only reciting opinions for the sake o f mental exercise.^^ But he also makes careful, essentially lawyerhke distinctions between types o f religious documents and the degrees o f authority to be ascribed to them. What the Bible says has greater weight than what the saints say, and what the saints say has greater weight than the opinions o f modern theologians. When modern theologians disagree one is perfectly free to reject their opinions. Canon law is to be respected, but not necessarily the opinions o f any bishop. Only the Pope, Ockham says, can decide when theologians disagree concerning Christian faith. The Inquisition is often staffed by simple men and hence it would be absurd to submit to it difficult and profound matters on which university professors d i s a g r e e .

Thus, unless the view that quantity is really distinct from substance and quality can be shown to have church authority o f the strongest type backing it, Ockham is not prepared to go against his own reason merely because it differs from common opinion.^^^ A view that is different from common theological opinion need not be heretical. A search o f authoritative church documents, Ockham claims, does not reveal that his view o f quantity is heretical.^!®

It is perfectly true, therefore, that Ockham does not claim absolute certainty for the conclusions o f natural philosophy, reserving such certainty for authoritative doctrines o f the Church. Anneliese Maier has shown that Buridan and the other nominahsts at Paris take a similar standpoint - although they may at times sound like exponents o f the “ double truth,” in fact they are not since they assign only probability and not certainty to the conclusions o f natural philosophy.^^^ But both Ockham and Buridan, as well as other nominalists at Oxford and Paris, take their natural philosophy very seriously and are by no means skeptical about it.

Their position does not, it should be emphasized, involve any loss o f integrity as far as respect for the conclusions o f natural philosophy is concerned. Here, I think, some historians fail to give Ockham and other

Wi

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medieval authors their just credit because they think that a loss o f integrity is involved. When Pierre Duhem proposed Christian positivism as the proper attitude toward science and as the medieval attitude leading to modern science, some other historians were quick to point out that Duhem himself was a Catholic and might therefore be suspected o f bias in favor o f medieval churchmen.i^^ Duhem himself, however, did not arrive at his positivism concerning science simply from his Catholicism and from the need to downplay the certainty o f science to protect the certainty o f religion. Duhem’s book on The Aim and Structure o f Physical Theory has won the deserved respect o f many non-believing philosophers o f science purely on the grounds o f the cogency o f its philosophical arguments.^^®

The same can be said for Ockham, Buridan, and the others like them. I f they denied the absolute certainty o f natural philosophy, they had good purely philosophical reasons for it. Many o f the best modern philosophers o f science - and I take Conant as my example but there are many others - arrive at the same conclusion. When, from within the philosophical disciplines themselves, one concludes that absolute certainty cannot be ascribed to philosophy, this in no way involves a loss o f autonomy or integrity - in fact to assert the certainty o f philosophy without sufficient grounds would seem to involve the greater loss o f integrity.^^o j f natural philosopher consistently reaches conclusions that contemporary theologians would like him to reach, one is entitled to be suspicious - especially, as in the case o f Ockham, when the philosopher himself is a theologian. But when, as in Ockham’s case, the philosopher lays his philosophical arguments meticulously on the line and proves their intrinsic philosophical worth, the evidence should be sufficient to allay such suspicions.

There is no reason why, given Ockham’s approach, the best theologian cannot also be the best natural philosopher. Whether conversely, the best natural philosopher can be the best theologian is a matter which is much more difficult to decide. Fernand Van Steenberghen has argued that Aquinas was a great theologian because he was a great philosopher.121 I f this is true, however, it is because Aquinas uses his philosophy in his theology. Although this may compromise the autonomy o f natural philosophy, as I have argued above - replacing physics by a kind o f metaphysics valuable to theology but not to natural philosophy - it may, but this is a matter o f opinion, make good theology. Many people would indeed argue that if Ockham was the better natural scientist, Aquinas was

the better theologian. The question that I asked at the start o f this paper, therefore, whether the best natural philosophers were the best theologians in the fourteenth century, remains an open one. It is, I think, an historical fact that Ockham represents a way o f combining theology and natural philosophy that allows both theology and natural philosophy a proper autonomy. One also finds historically the development o f an autonomous advanced natural philosophy separate from theological contexts among men who have been labelled nominalists or Ockhamists at Oxford and

Paris.Some historians may judge that this approach also led to the best theo

logy. The contemporary reaction to Ockham’s theology was, however, often negative, although the reaction was complicated by Ockham’s subsequent anti-papal activities.122 Some historians think that Ockham’s theology leads at least indirectly to Martin Luther’s theology and the Reformation.123 To the question, therefore, o f whether in the fourteenth century the best natural philosophers had the chance o f being the best theologians, this historian must answer that it depends on what you think is the best theology. Thus although some Franciscan historians and some Protestant historians may answer the question in the affirmative, modern followers o f St. Thomas Aquinas may well be expected to have the opposite viewpoint.124

Concerning the autonomy o f the sciences or the separation o f philosophy from theology with which I began this paper, I think the above investigation demonstrates that autonomy or its lack was not solely a matter o f social or institutional factors. Both Aquinas and Ockham produced their commentaries on the Sentences in essentially the same institutional framework, that, namely, o f the medieval university. That Aquinas produced a “ sublimated” philosophy and Ockham an autonomous natural philosophy must have been caused, therefore, not so much by external factors as by their different epistemological positions. I f external factors were influential, they must have operated directly on this epistemology and only indirectly on the content o f philosophy. Since with Ockham’s approach there is still a single person using the diverse autonomous sciences, it would be very unlikely that an institutional separation could

occur.

North Carolina State University at Raleigh

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N O T E S

1 Many of the ideas lying behind or expressed in this paper were first developed during conversations and correspondance on the nature of fourteenth century philosophy between the author and John Murdoch. In many cases I can no longer recall whether a given idea was my own or suggested to me. In any case I want to express my indebtedness for his contribution while absolving him of any responsibility for errors that may remain.2 Robert K. Merton, Science, Technology and Society in Seventeenth-Century England (New York: Harper Torchbooks, 1970). Originally published in Osiris 4, Part II (1938). ® Joseph Ben-David, The Scientist’s Role in Society. A Comparative Study (Englewood Cliffs, N.J. : Prentice Hall, 1971), pp. 46-55.

I here use the terms ‘natural science,’ ‘natural philosophy,’ and ‘physics,’ as if they were synonymous although obviously in many medieval contexts it would be important to distinguish between them. I similarly use the terms ‘arts,’ ‘philosophy,’ and ‘secular sciences’ as if they were synonyms and included the natural or real sciences plus the trivium. I do not think that for my purposes a more precise terminology is necessary. 5 Cf. Fernand Van Steenberghen, The Philosophical Movement o f the Thirteenth Century (Edinburgh: Nelson, 1955), p. 112:... the rationalist historians have long denied that the philosophy of the Middle Ages had arrived at this scientific autonomy ; they maintained that during this long period there was only a philosophical-religious syncretism, a speculation dominated by dogmas and watched by ecclesiastical authority. « Anneliese Maier, Metaphysische Hintergriinde der Spatscholastischen Naturphiloso- phie (Rome: Edizioni di Storia e Letteratura, 1955), pp. 3-4.’ Cf. Paul Wilpert, ‘Boethius von Dacien - Die Autonomie des Philosophen’, Bei- trage zum Berufsbewusstsein des Mittelalterlichen Menschen, Miscellanea mediaevalia, vol. 3 (Berlin: Walter de Gruyter and Co., 1964), pp. 136-7, referring to a 1272 University of Paris statute on this topic.* Cf. Pope Gregory IX’s admonitions to the faculty of the University of Paris in 1231. Étienne Gilson, History o f Christian Philosophy in the Middle Ages. (London: Sheed and Ward, 1955), p. 246,250. The statutes of the University of Paris of 1366-1389 also say that Sentence Commentaries should not include discussions of logic or philosophy unless absolutely necessary. (P. Glorieux, ‘Sentences’, Dictionnaire de théologie catholique, tome 14, part 2, col. 1876). For theologians’ limitations of themselves from treating philosophical questions, see Daniel A. Callus, ‘The Function of the Philosopher in thirteenth-century Oxford’, Beitrage zum Berufsbewusstsein des Mittelalterlichen Menschen, Miscellanea Mediaevalia, Vol. 3 (Berlin: Walter de Gruyter, 1964), pp. 156-158.* Cf. Van Steenberghen, The Philosophical Movement o f the Thirteenth Century, p. 114: ...we know that, in virtue of the organization of teaching in the medieval universities, “one had not to grow old in the Arts Faculty” ; you taught there for a few years, before starting theology studies; the young masters of the Arts Faculty thus had no opportunity to acquire full philosophical maturity; they only gained that at the time of their theological teaching and, most often, they no longer had the opportunity to express their philosophical ideas except in theological works.

As a result, their philosophy has almost always to be separated from their theological writings and, consequently, a good historian of medieval philosophy must also be a good historian of scholastic theology.

There do not seem to have been many arts textbooks specifically slanted to the pro


spective medical student. Perhaps there were not enough pre-medical students, at least at Oxford and Paris, to provide a sufficient demand, as compared to the larger numbers of students destined for theology or law.

Cf. James A. Weisheipl, ‘Ockham and Some Mertonians’, Mediaeval Studies 30 (1968), 197.

Cf. Theodore Kermit Scott, (ed.), John Buridan: Sophisms on Meaning and Truth (New York: Appleton-Century-Crofts, 1966), p. 5: As is evident in Buridan’s work, by the fourteenth century, the sophism had taken on major philosophical importance and its scope had been restricted, by and large, to a consideration of logical and semantical questions. The impossibilia, as merely formal exercises, are ignored by Buridan, and the insolubles are retained only as sophisms of a special sort. This is because the development of the logical summa as an introduction to logic freed the sophisms from more menial duties and allowed them to serve as tests of logical rules and as devices for extending the application of basic principles expounded in the summae. And since logic was understood very broadly as including questions of meaning and truth, as well as structure and inference, Buridan’s sophisms are anything but a mere dialectical exercise and are arranged so as to constitute an advanced treatise in the theory of language.1* Cf. Robert W . Schmidt, S. J., The Domain o f Logic According to Saint Thomas Aquinas (The Hague: Martinus Nijhoff, 1966), pp. 25-26. Aquinas says, for instance, (JExpositio super librium Boethij De Trinitate, 6,1, sol. 2 ad 3): In addiscendo incipimus ab eo quod est magis facile, nisi necessitas aliud requirat. Quandoque enim necessarium est in addiscendo non incipere ab eo quod est facilius, sed ab eo a cuius cognitione sequentium cognitio dependet. Et hac ratione oportet in addiscendo a logica incipere ...quia aliae scientiae ab ipsa dependent. Aquinas also says {In II. Met., 5, n 335): Et propter hoc debet prius addiscere logicam quam alias scientias, quia logica tradit communem modum procedendi in omnibus aliis scientiis.

Cf. Ben-David, The Scientist’s Role in Society, pp. 46-55. This audience or demand factor would hold true even if professors of logic were only temporarily so before going on to theology and even if professors of logic had many other simultaneous non-logical interests.15 Cf. M.-D. Chenu, La Théologie au douzième siècle (Paris: J. Vrin, 1957), especially Chapter 4, ‘Grammaire et théologie’, originally published in Archives d ’histoire doctrinale et littéraire du moyen âge, 20 (1935-36), pp. 5-28, and Chapter 15, “Les Magistri. La ‘science’ théologique.” Also by Chenu, La Théologie comme science au X lIIe . siècle, 3rd. edit. (Paris: J. Vrin, 1957).1* Chenu, La Théologie au douzième siècle, p. 91 : Lès regies de Donat ne commandent pas en théologie, car le mystère les met en échec; la doctrina sacra les emploie comme des “servantes”, comme des moyens, pour pénétrer dans la parole de Dieu. Mais plus la théologie est fidele à son objet transcendant, plus, chez elle, la grammaire joue selon ses lois propres. Ainsi dans la parole de Dieu elle-même. Au Xlle siècle, ce sont ceux qui pratiquèrent la meilleure critique grammaticale, qui avaient chance d’être les meilleurs théologiens.1 Chenu, La Théologie comme science, pp. 15-16.1* Cf. Chenu, La Théologie au douzième siècle, p. 353.1* Ibid., pp. 90-91: ... les “ sept arts”, en entrant au service de la sacra doctrina, y apportent leurs lois et leur dynamisme, ce qui les amène à réclamer un jour, jusque dans le plus fidèle service, l’autonomie de leurs démarches et de leurs méthodes... La même histoire montra que le triomphe de la théologie a consisté précisément à traiter la

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grammaire - comme la dialectique, comme la métaphysique - non en esclave asservie, entendez en simple outillage, mais en discipline majeure, dont les lois et les méthodes sont d’autant plus valables religieusement, en expression de la parole de Dieu, que leur humaine vérité est loyalement reconnue.20 Chenu, La Théologie comme science, pp. 11,67-92.21 See, e.g. the anonymous Sentence Commentary in MS. Vat. lat. 986, which is thought to be associated with fourteenth century Oxford. Also the Sentence Commentaries of Grerard of Odo, Roger Rosetus, and Pierre Ceffons contain a great deal of natural philosophy; see, for example, J. Murdoch, '^Mathesis in philosophiam scholasticam introducta. Arts libéraux et philosophie au moyen âge (Montreal/Paris, 1969) pp. 217, 232-33,238,242-46,249.22 Etienne Gilson, History o f Christian Philosophy in the Middle Ages, pp. 372-375. Cf. also Wilpert, “Boethius von Dacien,” (note 7) for Boethius of Dacia’s treatment of the relations of theology and philosophy particularly as applied to the question of the eternity of the world.23 Gilson, History o f Christian Philosophy, p. 331flf, 366. Van Steenberghen, The Philosophical Movement o f the Thirteenth Century, pp. 63-64,68fF.24 Cf. Van Steenberghen, The Philosophical Movement o f the Thirteenth Century, pp.113-114: Theology is a science whose essential characteristic is that it takes as its principles or as its starting point, the data of divine revelation... Speculative theology... studies the data of revelation with the aid of a philosophy, which serves as its instrument: hence the well-known scholastic expression: “philosophia ancilla theologiae” (“philosophy is the handmaid of theology”). The data of revelation being the same for all, the theological systems differ essentially by the philosophies which serve as their instrument in the interpretation of revealed truths; and the richer and more profound the philosophy a theologian utilizes, the greater the chance that his theology will be excellent.

This is just what one finds in the Middle Ages; the systems of speculative theology constructed by the scholastics are worth exactly what the philosophies utilized in these systems are worth; their variety and originality are above all of the philosophical order.25 Cf. Van Steenbergen, The Philosophical Movement o f the Thirteenth Century, pp.114-115 : Professor Gilson was struck by the fact that the most noteworthy philosophies of the Middle Ages were created by theologians. It is a fact, but it must be understood accurately. If the masters of the Theology Faculty pushed philosophical research further than their colleagues of the Arts Faculty, it was not because they were theologians, but simply because they were older and possessed greater maturity of intellect.... 28 Chenu, La Théologie comme science, p. 89. My discussion of the relations of theology and philosophy for St. Thomas is based mainly on this study by Chenu.27 It is worth noting that in this relationship of subaltemating and subaltemate sciences, it is the superior science which is a tool in the inferior science and not the reverse.28 Cf. A. C. Crombie, Robert Grosseteste and the Origins o f Experimental Science 1100-1700 (Oxford: The Clarendon Press, 1953), pp. 91-96.29 Cf. Chenu, La Théologie comme science, p. 87. Gilson, History o f Christian Philosophy, says ; p. 365 : Thomism was not the upshot of a better vmderstanding of Aristotle. It did not come out of Aristotelianism by way of evolution, but of revolution. Thomas uses the languge of Aristotle everywhere to make the Philosopher say that there is only one God, the pure act of Being, Creator of the world, infinite and onmipotent, a providence for all that which is, intimately present to every one of his creatures, especially to men, every one of whom is endowed with a personally immortal soul naturally able to


survive the death of its body. The best way to make Aristotle say so many things he never said was not to show that, had he understood himself better than he did, he could have said them. For indeed Aristotle seems to have understood himself pretty well. He has said what he had to say, given the meaning which he himself attributed to the principles of his own philosophy. Even the dialecticial acumen of Saint Thomas Aquinas could not have extracted from the principles of Aristotle more than what they could possibly yield. The true reason why his conclusions were different from those of Aristotle was that his own principles themselves were different. As will be seen, in order to metamorphose the doctrine of Aristotle, Thomas has ascribed a new meaning to the principles of Aristotle. As a philosophy, Thomism is essentially a metaphysics. Cf. p. 708, fn. 90.3“ Chenu, La Théologie comme science, p. 82.31 Ibid., p. 86.32 For Ockham’s views of the relations of philosophy and theology in general, see Robert Guelluy, Philosophie et théologie chez Guillaume d ’Ockham (Louvain: Nauwe- laerts, 1947).33 Cf. Philotheus Boehner, éd., Ockham. Philosophical Writings (Edinburgh: Thomas Nelson and Sons, 1957), pp. xliii-xlvi.34 Cf, Heiko Oberman, The Harvest o f Medieval Theology. Gabriel Biel and Late Me /jeva/iVom/nfl/w/n (Cambridge, Mass.: Harvard University Press, 1963), pp. 30-56.35 OF. Anneliese Maier, Ausgehendes Mittelalter, Vol. 2 (Rome: Edizioni di Storia e Letteratura, 1967), pp. 373-376. Philotheus Boehner, ‘The Notitia intuitiva of Non- Existents According to William Ockham’, reprinted in Boehner’s Collected Articles on Ockham, Eligius Buytaert (ed.), (St. Bonaventure, N .Y .: The Franciscan Institute, 1958), pp. 268-300.3« Cf. Maier, Ausgehendes Mittelalter, vol. 2, p. 520, for Gabriel Biel’s attempt to fill this gap.3’ Cf. Ockham, Super Quatuor Libros Sententiarum, Book IV, Q. 7 S in Opera Plurima (Lyon, 1494-96, reprinted Gregg Press Ltd., 1962).38 Cf. Maier, Ausgehendes Mittelalter, Vol. 2, pp. 376-391. Gilson, History o f Christian Philosophy, pp. 505-511.39 Heiko Oberman, ‘Some Notes on the Theology of Nominalism with Attention to its Relationship to the Renaissance’, Harvard Theological Review, 53 (1960), 47-76.40 Ibid., p. 63: The supernatural world, instead of accompanying and nourishing the viator, has receded and has become a hemisphere, a dome.

This dome shuts out the world of God’s non-realized possibilities and provides room on the inside for man’s own realm, in which he, as the image of God, thinks and acts.41 Quodlibeta Septem (Strasbourg, 1491, Réimpression en fac-similé, Louvain: Editions de la Bibliothèque S.J., 1962), Quodl. IV, Q. 35.42 Cf. Aquinas, Sentence Commentary, Book IV, Dist. 12 (in Opera Omnia, Parma: Petrus Fiaccadorus, 1852-1873, Photolithographice Reimpressa, New York: Musurgia, 1948), Vol. 7, p. 654: ... divina dispositio quae aliquid ordinat secundum legem communem, etiam sibi aliqua reservat praeter legem communem facienda ad aliquod privilegium gratiae communicandum; nec ex hoc sequitur aliqua inordinatio, quia divina dispositio unicuique rei ordinem imponit. Also Summa Theologiae, Illa, Q. 77, art. 1 (Blackfriars, 1965), Vol. LVIII, p. 128: ... dicendum quod nihil prohibet aliquid esse ordinatum secundum communem legem naturae, cuius tamen contrarium est ordinatum secundum speciale privilegium gratiae....

Ockham says, for instance, concerning the motion of Christ with the consecrated

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host {Sentence Commentary, Bk. IV, Q. 5F): Sed potest ne anima intellectiva Christi in hostia separari ab hostia ita quod non moveretur ad motum hostie. Dico quod sic nisi esset ordinatio divina in contrarium que de facto ordinat semper illud corpus moveri ad motum hostie. Sed non obstante illa ordinatione potest separare se ab hostia et hoc volendo quiescere hostia mota vel hostia quiescente volendo recedere et moveri ad alium locum. Tunc esset causa partialis concurrens cum deo ad causandum istum motum. Et eodem modo potest separari illud corpus ab hostia predictis modis sicut causa totalis.

As in Aquinas’s Sentence Commentary, p. 616; Sunt item alii praecedentium insaniam transcendentes; qui Dei virtutem juxta modum naturalium rerum metientes, audacius ac periculosius veritati contradicunt....44 Dist. X, Q. I, Art. 1, and 5, p. 619.45 Dist. X, Q. I, Art. 1, ad 4, p. 619.4« Dist. X, Q. I, Art. 2, Quaestiuncula 1, Solutio, p. 620-621.47 Dist. X. Q, I, Art. 4, Quaestiuncula 5, Solutio, p. 625.48 Summa Theologiae, III®, Q. 76, art. 7, p. 116.49 Sentence Commentary, Bk. IV, Q. 4 B-C. This is followed by a refutation of Scotus’s views, which is not relevant to the comparison being made here. Ockham says: Est igitur una opinio que ponit quod corpus Christi est ibi ex vi conversionis substantie panis in corpus Christi et ideo locus non habet immediate ordinem ad corpus Christi, sed mediantibus speciebus sub quibus fuit substantia panis; et ita non est ibi sicut in loco proprie: sed sicut in sacramento; quia ex vi conversionis est sub speciebus substantie panis. Secundo declaratur quomodo est ibi quantitas corporis Christi: quia non est ibi ex vi conversionis; sed tantum ex naturali concomitantia; et ideo contrario ordine sunt ibi dimensiones corporis Christi et dimensiones corporis locati in loco: quia substantia non potest esse alicubi sine dimensionibus suis, et ideo una substantia non potest esse cum alia: nisi quia dimensiones sue possunt esse cum dimensionibus alterius: sic est in proposito, et sic est ibi quantitas corporis Christi.

Contra istam opinionem primo quia non videtur ibi esse precise corpus Christi ex vi conversionis: quia quicquid potest deus conservare circumscripto quocimque alio illud potest facere sine alio, igitur sicut potest corpus Christi sub illis speciebus sine substantia panis: ita ibi potest facere corpus Christi sub illis speciebus et tamen quod ibi nunquam fuit substantia panis, quia si nunquam fuisset ibi nunquam fuisset conversa in corpus Christi: et tamen eodem modo foret ibi tunc sicut nunc. Et tunc non foret ibi ex vi conversionis; igitur nec nunc. Si dicas quod non potest ibi fieri corpus Christi sine mutatione: quia tunc corpus Christi mutaretur localiter et haberet diversa ubi. Contra non obstante conversione ignis in aerem posito quod si talis conversio esset ibi mutatio localis aeris igitur eodem modo in proposito. Nam sicut materia non potest habere novam formam sine mutatione sic nec corpus potest habere esse quod prius non habuit sine mutatione illius corporis. Mutatur igitur corpus Christi sed non secundum perditionem loci prioris, sed per acquisitionem loci prius non habiti, quia nunc est presens illi loco qui prius non fuit presens, et tamen cum hoc est presens illi corpori cui prius fuit presens.... Tunc sic: illud cui primo acquhitur respectus primo mutatur, corpus Christi est huiusmodi, igitur etc. Item aut corpus Christi ibi est in loco immediate aut mediate, si immediate habetur propositum, si mediate contra: omne quod competit alicui mediante alio cui primo competit non competit illi nisi propter specialem unionem unius ad alterum quam prius non habuit.... sed unio corporis Christi ad illas species non est unio specialis....50 Cf. Ockham’s Quodl. 6, Q. 3. Ockham concedes to Aquinas that if motion is defined


strictly as not only gaining a new place but also leaving the old one - and Aristotle uses the word in this way - then Christ is not moved since He remains in heaven.51 Dist. X, Q. I, Art. 3, Solutio 1, p. 623: ... dicendum quod comparatio corporis Christi ad species sub quibus est, non est similis alicui comparationi naturali; et ideo non potest reduci, proprie loquendo, ad aliquem modorum a Philosopho assignatorum; tamen habet aliquam similitudinem cum illo modo quo aliquid dicitur esse in loco secundum quod esse in loco est esse in aliquo separato extra substantiam suam, quod non est ejus causa.... Cf. Ockham, Sent., Bk IV, Q. 4 N : Item hec opinio ponit modum essendi in loco qui non competit creature....52 This may not be the best word to use, but I hope my meaning is clear enough. Aquinas creates new metaphysical distinctions using the old Aristotelian vocabulary in a “pxirified” or extrapolated sense.53 Cf. Maier, Metaphysische Hintergriinde, pp. 176-198.54 Cf. Anneliese Maier. Die Vorlaufer Galileis im 14. Jahrhundert, 2nd edit., (Rome: Edizioni di Storia e Letteratura, 1966), pp. 29-41.®5 Maier, Metaphysische Hintergriinde, pp. 159-175.5« Ibid., pp. 151-158.

Cf. A. Pelzer, ‘Les 51 articles de Guillaume Occam censures, en Avignon, en 1326’, Revue d ’histoire ecclésiastique, 28 (1922), 261 (art. 21): Recitat opinionem dicentem quod substantia et quantitas sunt eadem res nec tamen reprobat, immo secundum ea Respondet in diversis locis ad argumenta et in ea in uno loco residet. Magistri-. Dicimus quod ponere quantitatem non esse rem distinctam a substantia est contra communem sententiam sanctorum, doctorum et philosophorum, quam reputamus veram. Quo supposito dicimus esse erroneum et periculosum et contra determinationem ecclesie, que ponit in sacramento altaris solam substantiam converti, quantitate et ceteris accidentis remanentibus.

Maier, Metaphysische Hintergriinde, pp. 176-177.59 Ockham, De Sacramento Altaris, ed. T. Bruce Birch, (Burlington, lowa: The Lutheran Literary Board, 1930), pp. 160,210. Although this edition has been criticized, it seems adequate for my purposes. I have occasionally checked it against the version printed with Ockham’s quodlibetal questions. Anneliese Maier (Metaphysische Hintergriinde, p. 177; Ausgehendes Mittelalter, vol I, p. 221, fa. 28) argues that the existing version of Ockham’s Sentence Commentary, Bk. IV, cannot be the one to which Ockham refers and that Ockham may have commented on the Sentences in the Franciscan studium at Oxford previous to giving his public lectures.

It was also agreed that if the sacrament had been celebrated during the days when Christ was in the tomb, then only His body would have been present in the Eucharist and not His soul. Cf. Ockham, Sent. IV, Q. 6 E.

Dist. X, Q. I, Art. 2, Solutio 3, ad secundum, p. 621 : Cf. S. T., III“, Q. 76, art. 5, Responsio, p. 108.

The editor of the Summa Theologiae remarks, p. 108, fn. b : The substance is envisaged as contained by the dimensions or the quantity. This ‘being contained' is understood as prior to ‘being the subject ’ which the quantity affects by dividing it into integral parts. This metaphysical distinction is solely an insight of Eucharistie theology; it is the key to an understanding of the Real Presence.

See Anneliese Maier, Die Vorlâufer Galileis im 14. Jahrhundert, pp. 29-41.®4 In the De Sacramento Altaris but not in his Sentence Commentary, Ockham does approach Aegidius’s view of a quantity of matter not identical to extension by saying that if one calls a quantum whatever has really distinct parts that are dfôigned to be

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distant locally (natas distaré) and to be produced {natas produci) by a natviral agent in distinct locations, then Christ can be conceded to be a quantum in the Eucharist. (Ock- ham-Birch, p. 344). He obviously does not see the appeal of this view, however, and usually identifies being a quantum and being extended. Cf. Sentence Commentary, Book III, Q.6E.85 Senf.,Bk.IV,Q.4K.®® Q. 4 L, ad quartum; cf. Quodl. 7, Q. 25.67 Q .4H .

Also in his non-theological works. Cf. Maier, Metaphysische Hintergriinde, pp. 192-198. In his Summa logicae, P. I. Ch. 44 (Ed. Philotheus Boehner, Franciscan Institute Publications, Text Series No. 2, St. Bonaventure, N .Y .: The Franciscan Institute, 1957), Ockham repeats several times that Aristotle held this view of quantity: ...recitabo opinionem... quae mihi videtur esse de mento Aristotelis, sive sit vera sive falsa, sive catholica sive haeretica (p. 122); Propter quod mihi videtur, quod de intentionis Aristotelis est, quod quantitas continua non est res absoluta realiter et totaliter distincta a corpore. Ideo contra istam opinionem communem modernorum intendo aliquas rationes, etiam theologicas recitare, sive concludant, sive non, saltem valeant, quantum valere possunt (p. 123); Ideo est alia opinio de quantitate, quae mihi videtur esse de mente Aristotelis, sive sit haeretica sive Catholica, quam volo nunc recitare, quamvis nolim eam asserere. Et ideo quando illam opinionem posui, et scripsi super Philosophiam, non scripsi eam tanquam meam, sed tamquam Aristotelis, quam exposui, ut mihi videbatur. Et eodem modo nunc sine assertione recitabo eam. Est autem ista opinio, quam etiam multi theologi tenent et tenuerunt, quod scilicet nulla quantitas est realiter distincta a substantia et qualitate.... (p. 125). Leaving aside the question of why Ockham does not want to give his personal backing to the view that quantity is not a distinct res, it is clear that he wants to show that the concept is philosophically respectable.«9 Q.4N;cf.G«oi//.4,Q.36.’0 Cf. S. T., III“, Q. 76,6, pp. 112,114.’1 Quodl. 4, Q. 21 ; Sent. IV, Q. 5 II, ad tertium. Cf. Sent. IV, Q. 5 F.’2 Sent. IV, Q. 5 D.

Sent. IV, Q. 5 D : Aliter ergo dico ad articulos predictos quod sepositis illis que sunt fidei non potest probari per rationem quin omnem actionem et passionem terminatam ad formam absolutam quam potest corpus habere existens in loco circumscriptive habeat in loco diffinitive et non quantitative.... Unde videtur quod ista propositio communis quod agente approximato et passo disposito sequitur actio non est neganda nisi obviet sibi vel auctoritas vel experientia.... Sent. IV, Q. 5G: Hec patet quia posito activo sufficiente et passivo disposito et approximato sequitur actio. Hoc non est neganda nisi appareat ratio evidens in contrarium vel experientia certa vel auctoritas quorum nullum patet in proposito sicut supra dictum est.... Ideo teneo quod omnem actionem et passionem quam potest habere quando existit circumcriptive in loco potest habere in eucharistia nisi aliud impediret puta voluntas divina sicut supra dictum est.’4 Sent. IV, Q. 5 K.’5 Sent. IV, Q. 5, D and G ; Quodl. 4, Q. 20: Secundo dico quod Christus in eucharistia posset videre oculo corporali illa que fiunt in altari et similiter posset videri consimili visione ab aliis nisi esset speciale impedimentum. Quod patet tum quia posito activo sufficienti et passivo potest sequi actio sicut supra dictum est. Nec est ista propositio neganda nisi propter rationem que hic non apparet, vel propter auctoritatem scripture que etiam non apparet hic, vel experientiam que hic non concludit, quia deus suspendit


actionem qualitatum ne agant. Tum quia non repugnat intellectui pati non habente modum quantitativum sicut patet de intellectu meo vidente albedinem extra. Nec etiam ab obiecto non habente modum quantitavum sicut patet quando intelligit se et suam cognitionem, ergo ad hoc quod naturaliter intelligat aliquid non refert an habeat modum quantitativum vel non. Tertio dico quod de facto corpus Christi et accidentia eius corporalia non videntur naturaliter ab homine, licet forte videantur ab angelo. Sed hoc solum scimus per experientiam. Et causa quare non videtur de facto est quia deus non coagit naturali influentia illis qualitatibus ut videantur ab homine. Unde si deus coa- geret illis qualitatibus generali influentia sicut coagit aliis, tunc de facto naturaliter viderentur et ideo videtur quod Deus miraculose suspendit illas actiones sicut fecit actioni ignis in camino. Sed utrum Christus videat oculo corporali illa et visione intellectuali vel non nescio quia non habeo rationem ad hoc convincentem nec experientiam sed ipse novit quomodo. Rationabilius tamen est dicere quod sic etiam loquendo de facto quia satis videtur mirabile et extraneum quod Christus sit in eucharistia et tamen nesciat ubi sit.78 Sent. IV, Q. 5 G ; Quodl. 4, Q. 20.” S. T., 111% Q. 76, Art. 7, p. 116.

Dist. X, Expositio textus, p. 627; Quid ergo hic quaeris naturae ordinem! Ergo videtur quod non licet disputare per rationes de hoc sacramento. - Et dicendum quod loquitur contra illos qui nihil in hoc sacramento, et in aliis quae sunt fidei, volunt credere, nisi hoc quod per naturalem rationem probari potest; non autem contra illos qui ex principiis fidei disputant, et qui ex principiis naturalibus non volunt probare quae sunt fidei, sed sustinere: quia quae sunt fidei, quamvis sint supra rationem, non tamen sunt contra rationem: alias Deus esset sibi contrarius, si alia posuisset in ratione quam rei veritas habet.’ 9 Aquinas, Sent. IV, Dist. XI, Q. I, Art. 3, Solutio 2, pp. 655-657; S. T., III“, Q. 75, art. 7. Ockham, Quodl. 2, A. 19. Since Ockham does not think that instants as such exist, he does not emphasize the second half of this proposition. Cf. Ockham-Birch, De Sacramento Altaris, p. 306 for the relevant passage from canon law.80 Aquinas, Sent IV. Dist. XII, Q. I, Art 1, Solutio 3, p. 654 and Art. 2, Solutio 4, p. 658; S. T., III^, Q. 77, art. 1. The identification of A W ard as a holder of this view is made by the editor of the S. T., p. 126, fn. 6.81 Dist. XI, Q. I, Art. 1, Solutio I, p. 631.82 S. T., III», Q. 75, Art. 2, pp. 60,62.83 Sent. IV, Dist. XI, Q. I., Art 1, Solutio 1 ; S.T., 111% Q. 75, Art. 2.84 Dist. XI, Q. I, Art. II, pp. 632-633 ; S.T., IIP, Q. 75, Art. 3.85 Sent. IV, Q. 6 D. Cf. Quodl. 4, Q. 35: Tertia opinio (that the substance of bread remains) esset multum rationabilis nisi esset determinatio ecclesie in contrarium. Quia ilia opinio salvat et vitat omnes diflîcultates que consequuntur ex separatione accidentium ex subiecto. Nec contrarium illius habetur in canone biblie. Nec includit aliquam contradictionem corpus Christi plus coexistere substantie panis quam eius accidentibus. Nec repugnat rationi. Tum quia tantum repugnat quantitas quantitati quantum substantia substantie. Sed due quantitates possunt simul existere in eodem loco sicut patet de duobus corporibus existentibus in eodem loco. Tum quia substantia Christi potest esse in eodem loco cum quantitate hostie. Ergo eadem ratione cum substantia eiusdem. Ockham concludes : Ad argumentum principale dico quod aliquando sunt ponenda plura miracula circa aliquod ubi posset fieri per pauciora et hoc placet deo et hoc constat ecclesie per aliquam revelationem ut suppono et ideo sic determinavit. The insertion “ ut suppono” appears to me to indicate Ockham’s preference

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for the view rejected by the church. Cf. Ockham-Birch, De Sacramento Altaris, pp. 172-186.8® Sent. IV, Q. 6 F: Ideo dico quod duplex est mutatio, una acquisitiva alia deperditiva. Aquisitiva est in corpore Christi quia accipit esse ubi prius non habuit esse. Sed deperditiva est ipsius substantie panis que non manet et prius mansit. Ockham here follows Duns Scotus’s view of transubstantiation. The Thomist and Scotist interpretations of transubstantiation are both considered orthodox. Cf. S.T., p. 66, fn. e. See also Gabriel N. Buescher, O.F.M., The Eucharistie Teaching o f William o f Ockham (Washington,D. C. : The Catholic University of America, 1950).»7 D ist .X II,Q .4C ;Q .6F ,K .88 Cf. 5. r., 111“ A. 76, Art. 6.89 Sent. IV, Dist. XII, Q. I, Art 1, Solutio 1, p. 653.90 Dist. XII, Q. I, Art 1, Solutio 1, ad secundum, p. 654.»1 Dist. XII, Q. I, Art. 1, Solutio 3, ad tertium, p. 635. Cf. S.T., III“, Q. 77, Art. 1, ad 3 where he gives a different answer. Jfames A. Weisheipl, ‘Matter in Fourteenth Century Science’, in Ernan McMullin, (ed,). The Concept o f Matter, (Notre Dame, Indiana: The University of Notre Dame Press, 1965), p. 153, fn. 18, remarks : only in speaking of the Eucharist, in which there is no primary matter, does St. Thomas call dimensive quantity a “quoddam individuationis principium” {Sum. Theol. Ill, q. 77, a. 2), but this does not mean that quantity is an independent source of individuality....»2 Dist. XII, Q. I, Art 1, Solutio 3, ad 6, p. 655; S.T., 111% A. 77, Art. 2, ad 3, p. 134.93 Dist. XII, Q. I, Art 2, Solutiones 1-3, pp. 657-8 ; S.T., III», Q. 77, Art. 2.94 Sent. IV ,Q .6C .95 Cf., e.g. Summa Logicae, P. I., Ch. 49, p. 141.9« Cf. James A. Weisheipl, ‘Matter in Fourteenth Century Science’, pp. 157-8: Were it not for the Eucharist, Ockham would have denied absolute reality to every accident. But the Christian faith teaches that sensible qualities such as color, taste and weight, remain per se subsistentia in the Eucharist without any subject.97 H. Denifle and A. Chatelain (eds.). Chartularium Universitatis Parisiensis (Paris: 1889-1897), vol. 1, p. 551: Quod Deus non potest facere accidens sine subiecto nec plures dimensiones simul esse.98 Sent. IV, Q. 7M, N ; Quodl. 4, Q. 31 : Quarto sic. Causa naturalis potest qualitatem in hostia consecrata de novo producere et priores augmentare quia hoc negare est tollere omnem certitudinem quam habemus via sensus et dare infideli occasionem errandi et non credendi eo quod ad presentiam ignis videmus illas species calefieri post consecrationem sicut ante sed causa creata non potest aliquid agere sine passo et substantia non est ibi quantitas....

Ad quartam dico quod illud argumentum est contra te ponendo quantitatem de rarefactione et condensatione quantitatis ubi non potes dare subiectum. Ideo potest de omnibus talibus dici quod omnia apparentia sensui que fiunt circa hostiam non consecratam per ordinationem divinam fiunt circa hostiam consecratam immediate a deo ex quo non possunt fieri a potentia creata. Dico ergo quod tam augmentatio quam productio nove qualitatis fiunt totaliter et immediate a deo sicut tu ponis de rarefactione. Non plus tollitur hic certitudo que habetur in via sensus, nec datur infideli occasio errandi vel non credendi plus quam per rarefactionem et condensationem quantitatis. Unde ista constant partim ex fide et partim ex ratione. Ex fide tenemus quod substantia panis non remanet post consecrationem. Per rationem tenemus quod quantitas non distinguitur a substantia et qualitate. Et per experientiam tenemus quod causa creata presupponit passum in sua actione. Ex quibus sequitur quod omnia talia fiunt immedia


te a deo. Ockham-Birch, De Sae. Alt., p. 478: ...potest aeque faciliter dici quod Deus ordinavit quod omnia apparentia sensui quae fiunt circa hostiam non consecratam, fiant etiam circa hostiam consecratam. Et ideo illa, quae non possunt fieri virtute creata, disposuit facere inunediate per seipsum.

Ex predictis colligi potest quomodo illa accidentia manent simul, quamvis non sint in aliquo uno subiective nec unum sit subiectum alterius; quia sive hoc possit fieri virtute creata sive non, non debet esse dubium quin possit fieri virtute divina.... Sic etiam omnes transmutationes, quas videmus fieri circa qualitates remanentes in sacramento altaris, possumus salvare quod illae, quae non possunt fieri virtute creata, possunt fieri virtute Dei, sicut multi ponunt de multis.99 Sent. IV, Dist. XII, Q. I, Art. 2, Quaestiuncula 3, argument 3 and reply, pp. 656,658.

Cf. Guelluy, Philosophie et théologie chez Guillaume d ’Ockham, p. 365: Notre auteur semble avoir repris, avec la seule préoccupation de n’avancer que des idées claires et des raisonnements rigoureux, les problèmes que le Docteur subtil avait traités avec une âme plus religieuse et le souci de montrer que la pensée paienne n’epuisait pas ledomaine du savoir possible.

For Aegidius Romanus, see Anneliese Maier, Die Vorlaufer Galileis, pp. 28-41. Walter Burley’s treatment of this aspect of the physics of the Eucharist occurs in his Tractatus Primus. Cf. Anneliese Maier, Ausgehendes Mittelalter, vol. 1, pp. 219-226, and Edith Sylla, The Oxford Calculators and the Mathematics o f Motion, 1320-1350, Unpublished Dissertation, Harvard University, 1971.192 The importance of the quest for certainty was suggested to me by John Murdoch. Cf. also Heiko Oberman, The Harvest o f Medieval Theology, p. 35: The issue of certitude and security, for all kinds of non-theological reasons, may have become so central that this has led to the questioning of the reliability of traditional physics, metaphysics, and theology.193 Gilson, History o f Christian Philosophy, p. 489: Like Thomas Aquinas and Duns Scotus, Ockham was first and last a theologian using certain philosophical doctrines in order to elaborate his own understanding of Christian faith. The dissolving influence excercised by his doctrine in the history of mediaeval scholasticism is due to the fact that, professing as he did a radical empiricism in philosophy, he had to reduce the understanding of faith to a bare minimum. An Ockhamist intellect is as badly equipped as possible for metaphysical cognition, and since where there is no metaphysical knowledge theology can expect little help from philosophy, the consequence of Ockhamism was to substitute for the positive collaboration of faith and reason which obtained in the golden age of scholasticism, a new and much looser regime in which the absolute and self-sufiicient certitude of faith was only backed by mere philosophical probabilities. Cf. also by the same author, Reason and Revelation in the Middle Ages, (New York: Charles Scribner’s Sons, 1938) pp. 87-88: The influence of Ockham is everywhere present in the fourteenth century; it progressively invaded Oxford, Paris, and practically all the European universities. Some would profess it, others would refute it, but nobody was allowed to ignore it. The late Middle Ages were then called upon to witness the total wreck of both scholastic philosophy and scholastic theology as the necessary upshot of the final divorce of reason and Revelation.

Cf. Guelluy, Philosophie et Théologie, pp. 14-21.For the “double truth” see Gilson, Reason and Revelation in the Middle Ages,

pp. 58-66. Also Wilpert, “Boethius von Dacien,” p. 149flF.; Maier, MetaphysischeHintergriinde, pp. 3-44.

I think that Philotheus Boehner’s views on this issue - that Ockham was by no

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means a skeptic - are generally correct. Cf. also Guelluy, Philosophie et Théologie, p. 359.

Interestingly, for Ockham’s procedure to be useful there must exist separate sciences that have clear procedures for establishing their own validity. Ockham would have little use for simple speculations or hypotheses without proof and indeed he discounts much such speculation by means of a nominalistic analysis. Conversely, any methods successfully applied to defeite areas would be likely to receive enthusiastic use by those taking Ockham’s approach wherever they were applicable. This would help explain the popularity of the Mertonian mathematical and logical techniques and of the new “conceptual languages” of the fourteenth century. Cf. John Murdoch, ‘Philosophy and the Enterprise of Science in the Later Middle Ages’, The Interaction between Science and Philosophy, ed. Y. Elkana, Atlantic Highlands, N.J.: Humanities Press 1974, pp. 51-74.1'’* James B. Conant, Modem Science and Modern Man (Garden City, N .Y. ; Doubleday and Company, Anchor Books, 1953), pp. 166-178 : As to the unifying, materialistic World Hypothesis, my doubt stems from its manifest inadequacy. As a conceptual scheme attempting to account for everything in the whole universe, it seems to me unsatisfactory because it is incomplete. It fails to provide for the altruistic and idealistic side of human nature. It fails to accommodate what I regard as highly significant facts, not facts of science but facts of human history.... On the other hand, the formulations that attempt to include spiritual values, modem physics, biology, and cosmology within one total consistent scheme attempt, to my mind, far too much. Whether the unifying principle can be a dualism of matter and spirit, mechanism, formism, or some form of idealism, the whole attempt seems to me to be in the wrong direction. My preference would be for more adequate exploration of special limited areas of experience; one of these would include those experiences which can be ordered in terms of a system of spiritual values.

Each of these restricted areas of exploration I venture to designate a universe of inquiry. I do so only to underline my objection to those who insist on using the “in principle” argument to relate concepts in one set of inquiries to those used in another. Such insistence is, of course, almost second nature for those who regard a scientific theory as a creed or a map of at least a portion of the universe. But for those who regard scientific concepts and conceptual schemes as policies and guides for action, the need for an “ in principle” consistency between inquiries in different areas disappears. If two policies in two areas (universes of inquiry, to use my phrase) can actually be brought into conflict as guides to action, then an observational or experimental test between them becomes possible. The conflict generates, so to speak, a series of limited working hypotheses, a chain of reasoning that finally eventuates in a hypothesis so restricted that a fairly clean-cut yes or no answer can be obtained. But if attempts to bring the two policies into conflict fail, as in the case of the corpuscular and wave theories of light, then one may say that the two theories are so dissimilar as to constitute incompatible universes of inquiry....

Within the general field of the natural sciences, I suggest that those inquiries that involve the assumption of the uniformity of nature over long periods of time constitute a special universe of inquiry (or perhaps a group of such universes)....

The point of view I have presented regards scientific theories as restricted policies, not parts of a unified cosmic creed. I am well aware that it can be attacked in the name of man as a rational being. It can be labeled defeatist, obscurantist, or just a lazy man’s way out of embarrassing difliculties....


A view of the universe that rejects the necessity for a imified World Hypothesis consistent in principle throughout is not defeatist as regards the advance of science. For if one regards scientific theories as guides to investigations, each theory is continuously open to testing by experiment and observation. Such a view leads to suspicion of all assumptions carried over from one area of investigation to another.... There is nothing in such an outlook to discourage attempts to bring different scientific theories into close relation....

As a man of action, each of us must not only manipulate a world of inanimate nature full of all sorts of plants and animals..., but also accommodate ourselves to other people....

For many people in the Western World the concepts that are particularly relevant to human intercourse are religious doctrines....

Cf. L. Baudry, ed.. Le Tractatus de Principiis Theologiae attribué a G. d ’Occam (Études de Philosophie Mediévale, 13, Paris: J. Vrin, 1936), p. 125 : Pluralitas nunquam ponenda est sine necessitate ponendi. Exponit autem quid vocat necessitatem ponendi et dicit quod est ratio vel experientia vel auctoritas scripture, cui contradicere non licet, et auctoritas ecclesie. Hoc autem rationabile principium est quia sine istis liceret res ad placitum multiplicare.

An earlier thinker with a position similar to Ockham’s was Boethius of Dacia. Cf. Wilpert, ‘Boethius von Dacien’, pp. 145-146: Die Position des Boethius is klar um- rissen. Jede Wissenschaft ist auf ihre Voraussetzungen und auf die Reichweite ihrer Methode angewiesen. Wo die Philosophie aufhort nicht mehr mit rationalen Argu- menten zu arbeiten, oder wo sie auf etwas anderes sich stiitzt als auf die erfahrbaren Phanomene, da hat sie sich selbst preisgegeben.... Worum es Boethius geht, das ist nicht die Trennung der Person, hier wissenschaftlicher Forscher, dort glaubiger Christ, sondem die saubere Trennung der Bereiche. Es ist nicht wichtig, wer eine Aussage macht, aber ist diese Aussage gestiizt auf die Phanomene und auf rationale Deutung dieser Phânomene, so handelt es sich um eine philosophische Wahrheit. 1st sie gestiitzt auf Off'enbarung, so ist est eine Glaubenswahrheit. Es its nicht wichtig, ob eine philosophische Wahrheit von einem theologen ausgesprochen wird oder eine theologische Wahrheit von einem Philosophen. Nicht wer sie ausspricht, des bestimmt den Charakter einer Wahrheit, sondern mit welchen Begründungen und mit welchem Recht er sie Ausspricht, davon hângt die Einordnung dieser Wahrheit in das Gebaude der Wissenschaft ab. Among earlier authors at Oxford a somewhat similar position may have been taken by Geoffrey of Aspall. Cf. Daniel Callus, “The Function of the Philosopher in thirteenth-century Oxford,” pp. 159,161. The 1277 Paris condemnations were directed in part against Boethius’s view. That Ockham writes after 1277 may account for his frequent repetition that when he speaks philosophically he is only reciting hypotheses. Both Boethius and Ockham, however, assume that certified Christian belief is absolutely true whereas the results of natural philosophy are probable.

Cf. Maier, Metaphysische Hintergründe, pp. 159-160,166, fn. 34,167.Ockham-Birch, De Sacramento Altaris, p. 336: Ista sunt subtiliter dicta, nullus

tamen amator veritatis debet offendi si causa veritatis inquirendae et exercitii impugnentur. Si enim vera sunt, expedit audire obiectiones ut solvantur ut sic veritas clarius innotescat. Si falsas sunt, expedit ut convincantur. See also pp. 158-160,196, 210, 240.

Ibid., p. 378: Et certe fateor numquam me legisse nec in scripturis canonicis nec in originalibus sanctorum nec in decretis alicuius summi pontificis, nec in aliquo concilio generali, nec in aliquo authentico scripto talem propositionem, ‘quantitas non convertitur in corpus Christi,’ .... quamvis sententiam contrariam multos doctores

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modernos se mutuo reprobantes video ponere, et ideo eorum scripta non sunt authentica; immo etiam aliquorum multae opiniones in universitatibus solemnibus sunt damnatae quia tales propositiones approbare praesumpserunt.... Cf. also pp. 356,360,444-6.

Ibid., p. 442: Patet igitur quod cum controversia sit inter theologos de aliquo articulo an sit consonus an dissonus fidei Chriatianae, ad summum pontificem est recurrendum. Cum enim ofScium inquisitionis de haeretica pravitate aliquando simplicibus vel non magnis doctoribus committatur, absurdum videtur quod ad talem inquisitionem pertinet quamcumque quaestionem difficilem et profundam de articulis quibuscumque pertinentibus ad theologiam auctoritate propia terminare, et quemcumque magnum et in theologia famosum et dignum tam ratione vitae quam scientiae doctoris officio per universitatem solemnem approbatum, si suae opinioni contradiceret, tamquam haereticum condemnare. Videtur igitur ad Romanum pontificem recurrendum, quando quaestio ventilatur de aliquo quod non est in scripturis canonicis expressum, nec est per Romanam Ecclesiam determinatum, quod etiam videmus fieri modernis temporibus.... Not long after this Ockham decided that the Pope himself was unreliable.

Ibid., p. 126: ...doctores modernos mutuo se reprobantes publice et occulte et etiam in scriptis.... Nihil enim quod dicunt est recipiendum nisi quod possunt probare per rationem evidentem vel per auctoritatem sacrae scripturae vel per determinationem ecclesiae vel per doctores approbatos ab ecclesia.... Immo periculosum et temerarium aestimo velle artare quamcumque ad captivandum ingenium suum et ad credendum aliquod quod ratio dictat sibi esse falsum, nisi possit elici ex scriptura sacra vel ex determinatione Ecclesiae Romanae vel ex dictis doctorum approbatonmi.... Si tamen possit probari, quod sit de mente alicuius sancti vel doctoris approbati ab ecclesia quem negare non est licitum, propter eum volo ingenium captivare et concedere quod sit alia res a substantia et qualitate. Earlier in the same passage Ockham says that if authors are found who seem to contradict his view their statements should be expounded to show how they can be reconciled with the truth. Cf. p. 450 for a similar passage in the second treatise.11« Ibid., pp. 276,360,370,378,436,440.11’ Maier, Metaphysische Hintergriinde, pp. 3-44.11® Cf., e.g., Stanley Jaki’s introductory essay in Pierre Duhem, To Save the Phenomena. An Essay on the Idea o f Physical Theory from Plato to Galileo (Chicago: The University of Chicago Press, 1969), pp. xix-xxii. Also Pierre Duhem, ‘Physics of a Believer’, published as an appendix to Duhem’s, The Aim and Structure o f Physical Theory (New York: Atheneum, 1962).11® Originally, La Théorie Physique'. Son Objet, Sa Structure, 2nd edit., (Paris: Marcel Riviere, 1914).120 Cf. Wilpert, ‘Boethius von Dacien’, p. 150: Doch gerade dann miisste er die Be- reiche sauber auseinanderhalten. Was er als Wissenschaftler bestreiten muss, mag er als Christ glauben. 1st das nicht doch das Verlangen einer schizophrenen Geisteshaltung gegen die Tempier den gesunden Menschenverstand verteidigt? Ich meine im Gegenteil, was Boethius hier vertritt ist, um mit Nietzsche zu sprechen, die Forderung der intel- lektuellen Redlichkeit.121 Cf. Van Steenberghen, The Philosophical Movement o f the Thirteenth Century, pp.114-115: (After agreeing with Gilson that the best medieval philosophy was done by theologians. Van Steenberghen goes on) But that in no way implies, as Professor Gilson would have it, that these philosophies owed their worth and interest to the theologies in which they were incorporated. In my opinion, good scholastic philosophers make good theologians ; and not, good theologians make good philosophers.


This thesis seems capital to me. ...even if he (St. Thomas) was a theologian by profession rather than a philosopher, I am sure that he was a great theologian because he was a great philosopher, and not vice versa.122 For the opposition to Ockham see A. Pelzer, ‘Les 51 articles de Guillaume Occam censurés, en Avignon, in 1326’, Revue d ’histoire ecclésiastique, 28 (1922), 240-270; J, Koch, ‘Neue Aktenstiicke zu dem gegen Wilhelm Ockham in Avignon gefiihrten Pro- zess’. Récherches de théologie ancienne et médiévale, 7 (1935), 353-380, 8 (1936), 79-93, 168-197 ; F. Hoffmann, Die erste Kritik des Ockhamismus durch den Oxforder Kanzler Johannes Lutterell, Breslauer Studien zur historischen Théologie, N.S. 9 (1941); ErnestA. Moody, ‘Ockham, Buridan, and Nicholas of Autrecourt. The Parisian Statutes of 1339 and 1340’, Franciscan Studies, 7 (1947), 113-146; Ruprecht Paque, Das Pariser Nominalistenstatut zur Entstehung des Realitatsbegriffs der Neuzeitlichen Naturwissen- schaft (Berlin: Walter de Gruyter, 1970). Despite Paqué’s efforts to correlate the Parisian statute of 1340 with Ockham’s views, I believe that Moody was essentially correct and that on the whole the errors listed in the 1340 statute were not Ockham’s views. They do, however, represent another way in which fourteenth century authors attempted to attain certainty.123 Cf. Gilson, Reason and Revelation in the Middle Ages, pp. 86-95.124 por instance, Philotheus Boehner, although he concentrates on Ockham’s philosophy rather than on his theology, seems not unfavorably disposed to Ockham’s achievements. Cf. Boehner’s quotation from Luke Wadding, Annales Minorum (Collected Articles on Ockham, p. 319): Neque vero depravatorem theologiae... aut philosophiae fuisse Occhamum, probant ipsa eius scripta philosophica et theologica, quae passim in scholis leguntur, approbantur, commandantur: confirmantque destinata sibi subsellia in quibusdam orthodoxis academiis, ex quibus solae Occhami sententiae tum philosophicae, tum theologicae, designatis stipendiis edocentur....

D IS C U S S IO N

c. scHMmr: I’m quite in agreement with you that everything cannot be explained by social and institutional factors as some historians and sociologists would want it. On the other hand, I’m not certain whether you haven’t made their argument sort of a straw man. If there were a strong social and institutional historian here, I think he might be able to answer some of your questions. You say, for example, that Thomas Aquinas and William of Ockham were were both members of the same institution, the university of Paris. This is important, but I think that there were also other institutional factors, for example one of them was a Franciscan and the other was a Dominican, a fact which certainly must be taken into account in any discussion of this sort.

Secondly, I think that your work is a good example of a view of medieval philosophy, science, and theology based upon accepting Oxford and Paris as typical universities of the time and leaving out not only the whole Italian tradition but also the tradition of a place like Montf>ellier, where the orientation was very different. Our general studies of medieval universities are somehow distorted by taking Paris and Oxford as much more important than anyplace else. Perhaps they were the two most important universities, but Bologna, Padua, Montpellier, and others were also extremely important and must be given serious consideration.

A third question concerns the function of the law and medical faculties. Medieval universities were essentially set up for very practical reasons, to produce theologians.

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physicians, and lawyers for society. The law faculties were very large and dominated a number of universities, not only Italian ones such as Bologna, but northern ones such as Toulouse. We must also pay more attention to the medical traditions in universities. The scholars who began studying the history of universities in the last century were primarily interested in theology and, to some extent, in philosophy, particularly the philosophical problems related to theology. Much of the impetus for the study of medieval intellectual history and medieval universities, it seems to me, resulted from the revival of interest in medieval philosophy and theology with the Aeterni patris with its emphasis on Thomism, and so forth. This provided an incentive for others who didn't agree with this emphasis to study the Franciscan tradition and yet others to study the proto-Protestant movements of the Middle Ages, but the focus of the study of medieval intellectual history has up to now, or up to very recently, been on the study of theology and those aspects of philosophy directly touching on theology, such as metaphysics. Only within the last couple of generations, with the work of Anneliese Maier, Marshall Clagett, and some of the people here, has a strong interest been taken in the very vast literature of natural philosophy. The medical literature of the Middle Ages has largely remained unstudied. I am not attempting to say that the theological and metaphysical issues are not important, but I think that perhaps they have been unduly emphasized.

B. STOCK : I don’t want to bring in a lot of institutional factors here, but let me ask whether you would distinguish between “specialization,” as you use it, and what might be called “professionalization” ? What distinction would you make? It seems to me that the two ideas are distinct, although, when you are dealing with the institutional context, they have to be considered together as well. We are dealing here with a period of increasing professionalization. It is also a period of increasing specialization in terms of classification of sciences and of divisions of labor among people who are working in intellectual disciplines. Would you see these developments as related?

E. sylla : I don’t know what the profession involved would be except Master of Arts or Master or Doctor of Theology.

B. stock : Take the lawyers; they became specialized.E. s ylla : But do you think there were very many specialist mathematicians or specia

list physicists? It would be very hard, I think, to pick out very many people in the thirteenth century or in the fourteenth century who are specialists in one branch of physical science. Bradwardine can write the De proportionibus, which is an entirely physical work, but he also wrote the De causa Dei, so be cannot be a scientific specialist or professional mathematician.

c. SCHMITT: But there is an increasing professionalization, it seems to me, with the rise of new universities. There are more positions for someone who is a theologian, for someone who teaches in the Arts Faculty, for the physician who teaches natural philosophy, and so forth. There would seem to be is a new professional class rising during this period.

E. sylla : But aren’t the major categories physician, lawyer, and theologian?c. SCHMITT: Yes, there doesn’t seem to be scientific specialization, but it may begin

taking place in the sixteenth century universities. But let’s look at the situation, say, at Padua rather than Paris.

j. MURDOCH: In the fourteenth century?c. SCHMITT: Yes, in the fourteenth or the fifteenth century there are people who teach

natural philosophy and logic in Italian universities to prepare students to study medicine, that is in the first two or so years of medical studies.


E. s ylla : Would these people have been medical doctors?c. schmitt: Most of them became medical doctors. It was a higher profession with

greater prestige and greater salary. Most people taught logic for a couple of years, then natural philosophy, and finally teach medicine as they become older, ^tter known andcould move to higher positions.

j. MURDOCH: I agree with you that you wouldn’t want to call Buridan or others who never did theology theologians, but isn’t there a problem in moving from what you just said, somebody doing X, Y, or Z, to calling him an X-ist, Y-ist, or Z-ist? You are making an assumption that has to be justified. If you take the major philosophers of the fourteenth century, almost all of them were theologians as well, Now, are they both at the same time?

c. SCHMITT: Well, Siger of Brabant, for example, taught in the Arts Faculty, and I would say that he was a philosopher and taught philosophy in the Arts Faculty, whereas Duns Scotus and Thomas Aquinas did philosophy, but I would call them theologians, if I had to choose one or the other. It is a difficult distinction.

J. Mu r d o c h : A curious thing, of course, is that, with the possible exception of Buridan, those philosophers who didn’t do theology seem to me to be quite inferior, as philosophers, to those who did theology as well. Why this is so, I don’t know.

c. Schm itt : That may also be tied with the basic social factor of prestige. I mentioned before that in Italy those who were good philosophers and good logicians, later stepped up to the more prestigious job of being a physician. Perhaps in Paris those who were rather mediocre philosophers never got to be theologians because this was a higher calling. The social historians may be able to shed some light on this.

M.-Th. d’ALVERNY: Let me make a comment more directly related to the paper. I think that to understand and to appreciate St. Thomas’s position on the Eucharist you cannot entirely leave out the historical background. The question is already treated in Lombard, of course, and in many of the theologians. St. Thomas is only one link - he may have tried to give a better explanation, but he is only one link in a long trend of discussions which took place in the Western Church. There is the controversy between Paschasius Radbertus and Ratramnus in the Carolingian era and of course the Beren- garian quarrel. What is important is that the terms used - ‘substantia’, for instance, and ‘accidentia’ - are Aristotelian right from the beginning, even at a time when Aristotelian physics was known only by the short quotations or allusions in Boethius or in the Greek Fathers. So I don’t think that St. Thomas’s terminology is new by any means. His explanation is clearer, I think, but it is not entirely different even in terminology from that of some of his predecessors. I shall not read the text, but I have brought Peter Cantor, who is a rather good example of late twelfth century theology, because he did not try to do anything new. He describes the current opinion of his times and the terminology is the same. I think that you are right to say that St. Thomas was more definite and precise and so on, but I think that he was fairly traditional and not so influenced in that respect by Aristotle’s Physics in particular.

E. s ylla : But would it really count against my argument if St. Thomas were not original in this? Whether Thomas was original or not, it seems to me that there were some people before him who didn’t even claim to be using physics, but claim instead to be thoroughly religious. They don’t claim that they are using natural reason, they just claim to be expounding the doctrine of the Church. So that would be one thing.But Aquinas claims to be rational.

R. f r a n k : Aquinas is, I think, here fully consistent with his own philosophical principles - that is to say with his conception of the ontological relationship of

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quantity with the other accidents, etc. This is a thoroughly theological section of the Summa.

The only question is whether as a theologian Thomas is consistent with his own metaphysics. Now you can dislike metaphysics or like it, but the real question is whether he maintains the integrity of the metaphysics which is the base of his philosophy at this point.

c. SCHMITT : In preparing for this discussion I looked through Denziger and so forth, and it seems to me that the substance-accident terminology and the discussion of change in the Aristotelian sense really comes in in a strong sense only with the introduction of Aristotle’s own works.

M.-Th. d’ALVERNY: In a strong sense, maybe, but it was used earlier. You find it in Lanfranc, Berengar, and so on.

j. MURDOCH; I agree with you that the Aristotelian tradition and terminology does occur earlier, but more Aristotelian terminology, if I remember correctly, occurs in the «<?n-transubstantiationist solutions deriving from St. Augustine, Berengar, and others than is the case with the Ambrosian-inspired transubstantiationist view that finally won out. Consequently, one might claim that Thomas, falling within the transubstantiationist view, is more Aristotelian than some of the others who shared this view.

H. oberm an : I think that it is perfectly proper to work with two case studies where you don’t want to work with the historical background. For Thomas one might ask whether it is right to refer to the Sentence Commentary, the young Thomas, rather than the mature Thomas who really had the major influence. But that does not touch on the heart of the paper, it seems to me, where you compare major representatives of the thirteenth and fourteenth centuries and show something that we have hitherto assumed, namely that something very new took place in the fourteenth century. That, it seems to me, is the excitement of this paper. And you dare to speak of the nominalists in positive terms. It is perhaps not absolutely necessary to define nominalism, but we can agree that nominalists were first of all those who emphasized the distinction between potentia absoluta and potentia ordinata, and used that distinction as a conscious tool to separate fields of scholarly enterprise. And secondly, nominalists emphasized cognitio intuitiva as the primary and reliable knowledge of the individual thing. Then you can start to argue whether you should call them Ockhamists or nominalists. In the fifteenth century, there is a whole group of followers of Ockham whom you can call Ockhamists. But there are other nominalists who share many basic assumptions, but who are so critical of particular positions of Ockham’s that you should distinguish them from the Ockhamists. Therefore “nominalist” might be a more comprehensive title for a number of schools.

Now I would like to ask you about one of the first points in your paper where I stumbled, and that challenged me very much because you are saying something thatI would not have expected: “thus the Mass involved not God’s usual ordained power, but a kind of second order ordained power, which, as Ockham would emphasize. He could again abrogate by His absolute power.” That surprised me. I don’t think I ever read that Ockham said that, after God had made the pactum cum ecclesia, after His contract with the Church, He could retract His promise that when the words of the Mass were said He would proceed to bring about transubstantiation. This would very much impinge on larger issues concerning Ockham’s time. There is a school of scholarship, e.g., Knowles and Leff, who claim that Ockham is a skeptic, and you very appropriately oppose this view. But if indeed God could retract what He has decided to do - not according to the course of nature, but in a covenant with the church - then the covenant would be uiyeliable.


E. s ylla : I don’t know enough about theology so I may be wrong here, but what I was thinking about is the kind of discussion where Ockham says that, for instance, God could take a sinner to heaven - even though ordinarily to go to heaven one must be in a state of grace when he dies, God could, even so, save someone not in a state of grace.

H. oberm an : Yes, but then you have to be extremely careful and realize that this is not a real statement about what could happen in the future. Ockham wants to show that there is no necessity on God’s part of accepting someone who has a certain amount of charity, a certain amount of merit ; but God has freely committed Himself in a pactum cum ecclesia to reward everyone who has this amount of charity with acceptatio, with accepting into heaven, and that commitment is absolutely reliable. Ockham emphasizes this in opposition to those we would call the Averroists who try to construct a necessary framework for God’s actions and who want to explain the principles of theology on the basis of natural reason, showing why God has to do this or has to do that. Tempier’s condemnations fit in here. Ockham’s statement is not a statement about what God is really going to do; it is a statement showing that we could never have outguessed God’s pactum, since there is no necessity (Averroist) for God to have established it. You cannot give reasons why God has established things as He did - that is the point of the potentia absoluta. He could have done things very differently, but He won’t.

E. SYLLA : I was thinking about this when I was reading about the potentia Dei absoluta, because it seems, when you start thinking about God’s foreknowledge and all, that really God has already made His decisions. The potentia D ei absoluta seems in some contexts to be counter-factual: He could have done it otherwise, but actually it is all laid out.

H. oberm an ; Yes, that is the problem De futuris contingentibus: to what extent is the whole future already sketched out, and do we have freedom of action in it? In that context, one tries with all logical means to show that man can make free decisions even though they are already a part of God’s eternal plan.

j. MURDOCH: Heiko, there is a difference between saying “He could have done it otherwise, but He won’t” and saying “He could have done it otherwise, but now He can’t,” Saying that X = Y is always the case, is now the case and always will be the case, is, logically speaking, not at all equivalent to saying that it must be the case. Saying “He won’t” is much, much weaker than saying “but now He can’t,” once He has made the

pact.H. oberm an : Yes, the medieval theologian would avoid saying “He can’t,” because

that would limit God; it is rather a voluntary decision on the part of God to make this contract. But when you say “He can’t” you mean that now that He has made the pact. He will not deviate from it, because He, of his free will, is reliable.

J, v a n ess; May I ask, do these theologians ever introduce the concept of time into this? The future is our category. It has nothing to do with God. God is eternal and there is no time in the eternal ; there is no future. So the problem of God’s foreknowledge is our problem, not God’s problem.

H. oberm an : That was a commonplace: that God is a mirror in which all times - the past, the present, and the future - are mirrored, and that for us this mirror is fractured. This is an image that is always repeated. But perhaps the problem of future contingents could be for a moment eliminated - we have our hands full with the Eucharist. The Eucharist is such a good case because there Ockham could show that what Thomas has done (although Ockham would more often talk about Scotus and other theologians) is to take the doctrine of the Church and show why it is metaphysically right and sound and has to be that way. By contrast, Ockham himself says that, although this is the

396 E. SYLLA HEIKO A. OBERMAN

doctrine of the Church, there are many other ways that God could have done it, as it were, much more prudently (d’Ailly and later nominalists will almost go that fax). We have to accept Church doctrine; it is a decision of God, it is absolutely reliable. But de potentia absoluta God could have done it differently and we should not be so arrogant in our theologizing that we forget to take into account that it could have been set up very differently.

R. mckeon: Let’s leave science and turn to morals since moral questions have been brought up. Questions were raised whether God could will the opposite of the Ten Commandments. In the thirteenth century Thomas Aquinas argued that He could not have; Duns Scotus held that He could have willed the opposite of the last eight, but not the first two; William of Ockham took the position that He could have willed the opposite of all ten. The evolution of positions on the Ten Commandments bears on the question of the absolute power of God and the ordained power of God. According to William of Ockham, we can say nothing about the absolute power of God. Our propositions are only about His ordained power. The absolute power of God is, as it were, the first principle from which these ordained powers result. Therefore both in the pact with the Church and in the natural sciences, working with human minds, we start from ordained powers, and the statement of absolute power is an inference to the necessary first principle about which we can say nothing. In science, therefore, it is conceivable that any scientific conclusion might be different - it is even conceivable, when you move out of our present human understanding, that God could have set up not only a different science but a different logic, even one in which the principle of contradiction didn’t hold.

H. OBERMAN: Let me add this one point, because your example on the level of morals is very well taken: the real point of the pactum cum ecclesia is not clear unless you see it in contrast to an earlier tradition where the highest that can be grasped is God as Being and as an ontological structure of one piece with the world, so that theologians who understand God have an insight into all lower levels of reality. In the fourteenth century, however, for Ockham and the nominalists, what lies beyond the pactum cum ecclesia is just the will of God which does not allow further penetration. Now you no longer talk about Being; you talk about what God has decided - it is the business of the theologians to interpret and to preach God’s will.To understand reality, on the other hand, it is no longer a help to be a theologian, you have to be a “technician.” You have to be a man who relies on his experientia to discover reality. This world is held together by natural laws (since parallel to the pactum cum ecclesia, there are natural laws that are reliable which God has grafted into this world). But these laws are not revealed, we have to discover them by experientia. D ’Ailly and Gerson have a whole series of statements in treatises where they sing the praises of the new task of discovering these natural laws.

R E F O R M A T I O N A N D R E V O L U T I O N :

C O P E R N I C U S ’ S D I S C O V E R Y I N A N E R A O F C H A N G E *.-4

This paper is not to be just an interesting commemoration o f the historical past. Copernicus has become more than a private scholar who made a scientific discovery. Copernicus has become a symbol if not a syndrome; and it is not easy to define exactly what this symbol stands for, so varied is the reaction to his name and the associations it evokes. The nerves o f Western man are hit, titillated, or hurt, and sometimes all o f these at once. By no means without precedent, but certainly most intensively, today’s community o f scholars and - with a remarkable intuition for essentials - society at large is probing the ultimate questions o f man and matter, o f

time and space.The inability to present the Copernican Revolution in a more or less

objective-descriptive fashion, myth-proof as it were, was obvious in the series o f articles and television programs commemorating the five hundredth anniversary o f Copernicus’s birth. But the serious scholarly tradition on which these popularizations had to rely gave ample occasion, reason, and cause for the spread o f myth. With ill-hidden ideological passion the name o f Copernicus has been used to propagate the values o f the French or Russian Revolution as his legitimate heirs. Replacing the Aristotelian hierarchy o f multiple spheres, Copernicus then would mark the end o f feudahsm and emerge as the herald o f our modern society. Or his name suffices to connect the Christian faith with the dark Middle Ages. Pre-Copernican man is seen as caught in the blinding spiritual captivity o f the “ Ptolemaic Church” from which this astronomical giant hberated us to lead us into the promised land o f modern times.

Furthermore, what is at stake in this complex issue-indeed a central issue underlying our Western Copernican complex - is the question what the access-route to knowledge is and, concomitantly, what the universities on the tightrope, tottering between impatient relevance and vain curiosity,^ can do and should do. It concerns the question o f theory and practice, o f reason

J. E. Murdoch and E. D. Sylla (eds.). The Cultural Context o f Medieval Learning, 397-435. All Rights Reserved.

398 H. OBERMAN

and test, speculation and experience. It is the classical clash between Plato and Aristotle, today intermittently illuminated by tensions between the German and the Anglo-American tradition o f scholarship and research - underlying in parallel but different ways the student revolution o f our times.

And finally, the Copernican Revolution touches upon - and is rooted in - man’s new relation to nature, suggested by the development from pre- historical animistic veneration to the classical adoration o f nature, and via Christian admiration to the post-Christian administration o f nature - therefore implying man’s own changing role.

The five hundredth anniversary celebrations may appear as a feast for fools ; after all, Copernicus’s heliocentric cosmology places man off center and unmasks him as cosmically eccentric. Yet we have to reconcile this with another phenomenon, on the level o f anthropology, where we see a geocentricity reemerging in a sublimated form as anthropocentricity, since man in a succession o f stages developed from the microcosm and image o f God into the homo faber^ and partner o f God, to end up, finally, as the homo manipulator, God in his own realm. A t that very point, what used to be the mysterious dwelling place o f man and dewed path for the feet o f God becomes the secular “ environment” - the mechanical context o f Man’s survival. That is : the contemporary sore point where cosmological, behavioral, and environmental studies converge.

Even this short tour d’horizon suggests the range o f concerns and apperceptions with which I have approached the given theme. I f done well this paper will be a festive historical commemoration, but at the same time something o f an acupuncture o f nervous centers without the Chinese promise that it will not hurt.

We begin by looking into the first encounter between the two sixteenth century reform movements - in theology and in cosmology - for a time suspended in a precious but precarious balance between partnership and rivalry. In a second part we gain historical perspective and distance by dealing with the preceding late medieval phase in which both the modern sciences and the modern cowsciences prove to evolve simultaneously, in terms awaiting translation to reveal their effect on modern man.

II

In his play, The Life o f Galileo, Bertolt Brecht has the old cardinal say

REFORMATION AND REVOLUTION 399

to Galileo: 3 “ You want to degrade the earth, although you live on it and receive everything from it. You dirty your own nest! But I for one am not going to stand for it! I am not just some being on some little star which circles somewhere for a short time. I pace on a firm earth with a firm foot, and the earth does not move. It is the center o f the universe. I stand at that center and the eye o f the creator rests on me and on me alone. Around me, fixed to eight crystal spheres, revolve the fixed stars and the mighty sun, which exists to light my surroundings. And me too, so that God can see me. It is certain and beyond dispute that everyting is aimed at me, at man, the achievement o f God, the creature at the center, the very image o f God.” 4

The scene here presented by Bertolt Brecht is as moving as it is misleading. Granted, there is some truth in seeing in Galileo’s plight the clash o f science and faith; and therefore we cannot avoid asking whether the same applies in the case o f Copernicus, whether just as the Roman Catholic Church forced Galileo to recant, so - some twenty years after Luther’s appeal to his conscience at Worms - the Reformation did not unmask itself as an intolerant, repressive, and anti-conscientious movement which tried to suppress, and for a time succeeded in subverting, the Copernican Revolution.

However, it is to be said with all possible clarity that pre-Copernican cosmology did not posit the earth at the static center as a place o f glory but as a place o f inertia, the farthest removed from divine movement so perfectly reflected in the circular movement o f the stars. Man, not his earth, held the cosmic place o f honor, reaching in the summit o f his soul {apex mentis) the greatest proximity to God. As far as I can see, we owe it to the mystical tradition that ‘center’ and ‘summit’ could become interchangeable and equivalent in dignity® - as can still be noticed in the parallel mixture o f spatial and anthropological components in the words ‘depth’ or ‘profundity’ .

The resistance against Copernicus may have had other causes than the normal healthy resistance in intellectual man to novelty - it might have been furthered by a mystical sense o f the cohesion o f man and his cosmic environment. But this resistance cannot be explained in terms o f hurt pride as the defence mechanism o f Ptolemaic-medieval man. To the contrary, Copernicus gave the earth a cosmic dignity in keeping with the ontological rank o f man, its divine inhabitant.

400 H. OBERMAN REFORMATION AND REVOLUTION 401

It is thus all the more important to analyze the first reactions to Copernicus from close quarters. In order to test the traditional story o f Copernicus’s lone-battle-against-the-mighty-Church we have to listen to Luther’s oft-quoted (“ Tabletalk” ) and weigh more extensively the arguments in the famous case o f Osiander’s “ fraud.”

I f this story could be substantiated Luther and the Reformation would stand against the new science: it would imply the withdrawal o f faith into the intimacy o f the heart. And Copernicus would have a valid claim on the gratitude o f all those who see in the emancipation from Christian faith the basis for the cultural progress o f Western man. More gratitude, at least, than is owed to Galileo, whose similar claim is convincingly rejected by Friedrich von Weizsacker® and - for very different reasons - by Bertolt Brecht himself.'^

Subjectively the case is clear: Copernicus felt intimidated by the anticipation o f the charge o f innovation: the very fact and the carefully worded content o f his letter o f dedication to Pope Paul I I I make this abundantly clear. (See Appendix I). This is the element o f truth in Arthur Koestler’s Sleepwalkers^ where he casts Copernicus as a fearful and submissive weakling.

But objectively seen Copernicus’s expectation o f a curt, i f uninformed, rejection seems to be well founded. On hearing the advance rumor, Luther spontaneously exclaims: “ Nowadays people try to show their genius by producing new deviating ideas; this man subverts the whole field o f astronomy. Even when that whole field stands topsy turvy I believe Holy Scripture. After all Joshua (10:13) commanded the sun to stand still and not the earth.” ®

Calvin - who without documentation and basis in fact is held by recent scholarship to have been a critic o f Copernicus - seems to present an alternative to Luther by introducing another relation between revelation (in Scripture) and (experienced) reality. After all, as Calvin points out in his commentary on Genesis}^ the story o f creation does not compete with the “ great art o f astronomy,” but accommodates to and speaks in terms o f the unlettered idiota, the common man. 12 Exactly the same argument we find a hundred years later with Kepler, when this admirer o f Copernicus reconciles Joshua with his new cosmology.^^

Since we touch here, in this difference between Luther and Calvin, upon one o f the main phenomena o f change in the Copernican era, we

want to take a closer look. For those who know this period Luther’s reaction is predictable: he does not give his considered opinion o f the Copernican thesis; he sees him merely as an instance o f the sickness o f the times, o f the so-called vana curiositas. Luther stands in a late medieval tradition contra curiositatem which is pre- and supra-confessional, as can be seen from the identical views o f Gerson and Erasmus. More generally a characteristic o f the via moderna and devotio moderna, this acute aversion to curiositas is the awareness o f the danger o f one-sided intellectualism.

A t its worst this “ modern” attitude is pietistic and anti-intellectualistic, reeling back from secular scholarship as a threat to the sacrality o f the inner life. As its best - and closer to its historical origins and main thrust- it calls for a reform o f the universities to discard intellectual games, far removed from experienced reality. And exactly here Luther stands. As we shall see, this very thrust o f seeming obscurantism but de facto antispecu- lative empiricism proves to be the great wedge which is to provide Copernicus with the metaphysical antidote and the intellectual antecedents presupposed in his discovery: it is the contra vanam curiositatem critique o f time-honored truths not verified by experience.

The appropriate slogan for this campaign contra curiositatem we find in the Adagia o f Erasmus: “ Quae supra nos nihil ad nos.’ ’ ^ Erasmus found it as a dictum socraticum (Socratic saying) with the Church-father Lactantius (f320) and knows that its main thrust is directed against cosmic speculation as “ the curious investigation o f things celestial and the secrets o f nature.” After Lactantius Augustine had dedicated an excursus in his Confessions to the dangers o f curiosity,1® but left the deepest impression in a more direct parallel to Lactantius in his Enchiridion,' '^ confronting the Greek metaphysical-cosmological speculation by arguing that to know the cosmic forces, the causas motionum, does not bring happiness: what we should know are the causes o f good and evil; hence not metaphysics, but ethics deserves our dedication and intellectual pur

suit.This Augustinian legacy o f the contrast, antithesis, and even mutual

exclusiveness o f metaphysics and ethics, o f cosmology and theology, had been submerged and was lying dormant throughout the era o f the successful Aristotelian band wagon - till in the fourteenth century human experience in physics and theology started to pull at the dogmatic Aristotelian chains. It is this pulling which is expressed in the campaign contra

402 H. OBERMAN

vanam curiositatem, the campaign that would provide both Luther and Copernicus with their initial thrust. Seen in this perspective Luther and Copernicus are kindred minds related by force o f a common origin.

It would be a fatal mistake to see in this campaign the high tide o f medieval obscurantism thwarting the emergence o f modern science. On the contrary, contra vanam curiositatem is best translated as “ against the ivory tower o f dogmatic intellectualism” and marks the revolt which not only paved the way, but also provided method and models, for the coming era o f science.

Before reform and revolt grew into religious reformation and scientific revolution as two distinguishable movements, we see how a man like Gerson can hold together the threads o f renewal in both fields. The common impetus is the call for experience as the best antidote against curiosity. On the one hand the reform of religion. Church, and theology urged a return to mystical piety (Bonaventure!) and thus stressed experience as the hallmark o f the true Christian. On the other hand the renewal o f the sciences called for a revolt against metaphysics and thus based the new physics on the sources (fontes) o f experience, a similar return to the sources (adfontes) as energized humanists throughout Europe.

Less than a century and a half later, the common impetus is severely tested when the experience o f faith and the experience o f science are in the process o f turning against each other as alternative bridges to the future. It is here that the voice o f John Calvin carries particular weight. Calvin applies the slogan “ Quae supra nos nihil ad nos” not to the reader o f Scripture, but to the intention o f Moses as the author o f Scripture, who did not intend to provide a chart o f the heavens.

The discrepancy between the story o f creation and the secured data o f astronomy is not to be solved by condemning astronomy as the obscurantists {phrenetici) do, who arrogantly reject everything unknown to them. Nor should the data o f astronomy be taken as proof that Moses erred. Moses was not a teacher o f astronomy, but a theologian, hence concerned with the glory o f God which - contrary to vain curiosity - is most useful to man. In his field the astronomer does exactly the same: his field is not only exciting, but also most useful providing access to the breathtaking wisdom of God; “ nam astrologia non modo iucunda est cognitu, sed apprime quoque utilis ; negari non potest quin admirabilem Dei sapientiam explicet ars illa.”


In words almost identical with Kepler’s in his Astronomia Nova,^^ Calvin sees astronomy no longer in competition with theology or as sacrilegious penetration o f the heavens traditionally rejected with the charge o f vain curiosity and audacious preoccupation with the things supra nos. The sky above us is no longer the realm beyond us, beyond our ken, supra nos. Calvin’s solution is not the obscurantist rejection o f astronomy, nor does he go along with the adherents o f the doctrine o f “ double truth” who say that what is true in theology is not true in philosophy. His point is rather that one has to respect the limits. To stay within one’s personal limits - the medieval definition o f humility and the alternative to proud curiosity 21 - means now to stay within the limits o f one’s field o f competence. The medieval differentiation between the university faculties - programmatically transcended in the preceding stages o f the Renaissance - is here recaptured by Calvin to defend and respect the different methods o f illuminating the common object, the glory o f God.

It is in Calvin’s new hermeneutics that I find the historical basis for the early latitude in Calvinism to favor or reject the Copernican vision. And this stance helps to explain as well why - against all expectations - the relationship between Puritanism and science is to be a most intensive and fruitful un ion .22 After all, before the Restoration the Puritans “ were the main support o f the new science.” 23

The so-called fraud o f Osiander, who in his introduction to De Revolutionibus tried to pass Copernicus’s heliocentricity thesis off as “ hypotheses,” 24 as it is usually put, was intended to raise the toleration-level in the scholarly world (See Appendix II). It may explain Melanchthon’s shift from early condemnation to cautious support 25 - it could o f course not provide a more lasting basis for welding together the new science and rehgion. Such a basis could only be found in the conviction formulated by Calvin that Scripture is not a supernaturally revealed book o f nature, so that religious experience and scientific experience can go hand in hand.

Only after Darwinism as the scientific “ arm” o f Cartesianism programmatically separated these two hands, was the threat o f Descartes to Christian faith met with obscurantist fanaticism.26 One reaction was to hold the book o f Genesis against the book o f Darwin and to match God’s Adam with Darwin’s ape, hence falling back into a pre-Calvin stage o f unenUghtened obscurantism, all the more offensive since science had made such remarkable progress in the meantime.

404 H. OBERMAN

It is a serious mistake, however, - and very often made - to read the reactions against Copernicus in the Hght o f the anti-Darwin crusade. Even the seventeenth century stir over GaUleo is a misleading paradigm. Apart from the over-cautious suspicion o f vain curiosity which all that emerged from academic circles had to face in late medieval society, the opposition to Copernicanism was rather due to weaknesses and obscurities immanent in the Copernican system itself, as well as to his assumptions ( = hypotheses!) which were not to be substantiated until the time o f Kepler, Galileo, and Newton.

“ It is safe to say that even had there been no religious scruples whatever against the Copernican astronomy, sensible men all over Europe, especially the most empirically minded, would have pronounced it a wild appeal to accept the premature fruits o f an uncontrolled imagination, in preference to the solid inductions, built up gradually through the ages, o f man’s confirmed sense experience.... Contemporary empiricists, had they lived in the sixteenth century, would have been [the] first to scoff out o f court the new philosophy o f the universe.” 7

III

The unauthorized preface to De Revolutionibus by the first Lutheran Minister and astronomer in Nürnberg, Andreas Osiander, has been characterized by Bishop Tideman Gisius as a “ fraud” 28 and has, ever since, drawn a major portion o f research energy away from the real subject Copernicus. Some o f the charges against Osiander can be easily disposed of. There is no sly effort on his part to suggest that his Preface is actually written by Copernicus. Content and style - he speaks about the author in the third person - clearly pointed to a third person, often a friend o f the author who introduced the book to the reader, as was often the case in this genre during the sixteenth century. 2»

One more aspect o f Osiander’s subjective honesty: the basic structure o f his Preface can be found in a letter sent two years earlier to Copernicus and to the first Copernican and original editor, Joachim Rheticus. Here we already find the proposal to placate and then win the Aristotelians and theologians by emphasizing that the Copernican theory is based on a series o f assumptions (hypotheses) and hence cannot claim ultimate truth. Since several hypotheses can be offered to explain one and the same


phenomenon, it should be regarded as belonging to scholarly freedom ( “ Freiheit in Forschung und Lehre” ) that more convincing hypotheses can be always advanced: “ In that way the potential opponents will be lured away from massive criticism to more intensive research; and, through newly gained respect and a lack o f counter arguments, they will be moved to fairness and ultimately to acceptance.”

Finally, the word ‘hypotheses’ should not be as offensive to us as it was to Kepler and many a Copernicus scholar since.^i In one o f the most concise but also most accurate treatments o f the Copernican discovery Edward Rosen 32 has established Copernicus’s own use o f the term in his main works. And the first beUever, Rheticus, describes the achievement o f his beloved master as “ renovare hypotheses.” 33 in his own dedicatory letter to Pope Paul II I Copernicus describes the genesis o f his breakthrough and provides us with a number o f significant parallels with Osiander’s Preface. But more importantly the letter lays the basis for our effort to place the Copernican Revolution in an era o f change.

The point o f departure for Copernicus is that the hypotheses o f preceding astronomy, the theoretical explanations o f the postulated mathematical astral movements, did not jibe with observed reality: the actual forecasts o f future movements o f sun and moon on the basis o f the assumption o f concentric circles did not prove true. Above all - and now comes the explicit goal which Copernicus had set for himself - earlier assumed explanations did not lead to the discovery o f the forma mundi, the true shape o f the universe, or to the symmetry o f its structure {partium eius certam symmetriam). What had been lacking was a blueprint explaining the inner workings o f the universe (ratio motuum machinae mundi) - the world machine which, after all, the greatest and the most orderly machinist has produced because o f us (propter nos). Encouraged by the witness o f classical authors “ I too began to think seriously about the mobility o f the earth. And although this still seemed to me an absurd point o f view (o p in io ) , I knew that others before me had been granted the liberty o f postulating whatever cycles they pleased in order to explain astral phenomena. Therefore, I thought that I too would be readily permitted to test (ut experirer), on the assumption that the earth has some movement (an posito terrae aliquo motu), whether a more convincing explanation, less shaky than those o f my predecessors, could be found for the revolutions o f the celestial spheres.” (See Appendix I)

406 H. OBERMAN

Up to this point there is a striking double parallel with Osiander. First, the appeal to the freedom o f scholarly investigation in a time o f emancipation from the homogenizing weight o f tradition. This is the very juncture at which the ideal o f self-directed research frees the true scholar from the pious shackles o f metaphysical orthodoxy. This is an implicit plea against vain curiosity and a call for acknowledgement o f the limits o f each discipline. For Copernicus it is the piety o f the Church-father Lactantius that leads to obscurantism - quite audaciously put in a letter to the Pope! But appropriately so, since it was Lactantius, who handed down to posterity the slogan “ Quae supra nos, nihil ad nos” (“ The things above us do not concern us” ) to ridicule those who discovered the rotundity o f the earth.

Secondly, there is the common description o f the Copernican research- process in terms o f “ hypotheses.” This is as far as the parallel goes. What Copernicus now discovers remains for Osiander on the level o f opinio, that is assumption, hypothesis, without an ultimate claim to a true explanation o f cosmological causality - o f what makes the universe tick. For Osiander that is the sole domain o f God and o f those with whom he cares to share his wisdom.^s After all, Osiander is a nominalist who knows that science develops models, not eternal laws, Osiander the nominalist was in a position to distinguish between cosmology and astronomy, between final causality and efficient causality. Copernicus, on the other hand, claims to have surpassed the level o f assumptions at the moment when he made his breakthrough: at that moment, namely, when his hypothesis o f the movement o f the earth is hardened, as he argues, by experience and confirmed by observations (multa et longa observatione tandem repperi). Sense-data suddenly fall into place, and above all, show a universal p a t t e r n , a true cosmos: blueprint and global machine fit perfectly together.

We are now in a better position to assess the charge o f fraud against Osiander. Osiander is not a misleading guide to the world o f Copernicus. Yet without questioning the former’s good intentions, the worlds o f Osiander and o f Copernicus are not identical and clearly to be differentiated. Yet we would miss the true nature o f science’s advance if we cede traditional scholarship the point that these two worlds are to be designated as “ medieval” and “ modern.” With great erudition as well as with dizzying rhetorical magnetism Hans Blumenberg has advanced the thesis that


Osiander embodies a basically nominalist position. As Blumenberg sees it, the nominalist stands in an alien, unreachable universe, which is metaphysically systematized by him as “ astronomical resignation.” ®’ Out o f this heteronomous world, the great humanist Copernicus, as it is claimed, freed us to relate man to his Umwelt within which he is to gain his con

scious autonomy.In a last section, I shall attempt to show that where the Copernican

Revolution is a cause o f celebration for modern man, it presupposes and is based on a nominalist platform - and that, when we let ourselves be waylaid and lured away from this platform, we are bound to fall back into worse, to confuse again astrology and cosmology, Weltbild and Weltanschauung. Not Protestantism, nor Roman Catholicism - and much less Blumenberg’s philosophical humanism - gave birth to modern science. For that we have to look at a preceding stage, a true fertile crescent.

IV

“ ... nous avons du ciel trop peu d’experience.” ®» That is an exclamation, a cri de coeur o f the leading nominalist philosopher in the generation between Ockham and Gerson (fl429), Nicolas Oresme (|1382), one hundred and fifty years before Copernicus, younger contemporary o f Thomas Bradwardine ( f 1349) and disciple o f Jean Buridan ( t 1348). We do not quote him here because we believe that he influenced Copernicus directly, though Copernicus had in his library besides some Bradwardine at least one nominahst source, the Quaestiones o f Pierre d’Ailly ( f 1420).4o

Copernicus probably did not know French. And it is in beautiful, indeed creative French that Oresme made available the works o f Aristotle - in translation, commentary, and critique. But in France we find Oresme quoted by d’Ailly and Gerson. And his name was soon respected both in Germany and in Italy. Moreover nominalism is such a powerful and all pervasive movement that we cannot ignore Oresme, one o f its pacesetting spokesmen, if we want to catch at least a glimpse o f its originality and

constructive revolt."*!It is by no means a novelty to introduce Oresme’s name in our attempt

to understand the significance o f Copernicus. Since Pierre Duhem modern scholarship has been very aware o f this point: among others, Lynn Thorn- dike,42 Anneliese Maier, and Marshall Clagett have furthered our knowl

408 H. OBERMAN

edge o f Oresme significantly. Yet the high claims o f Duhem for Oresme’s role as precursor and even as preemptor o f later discoveries have now generally led to an overcautious reaction. With their usual nod to Anne- liese Maier’s impressive phalanx o f manuscript-based evidence,scholars invariably tend to come to the conclusion that Oresme may have had some theoretical insights but remained “ Aristotelian” and offered mere speculative possibiUties without relation to fact and reality.'^^

It is, however, misleading to speak here o f “ mere speculation,” for we then miss, I believe, the decisive access-route to the phenomenon o f modernity. Hence we should be prepared to listen more patiently to the sources.

The systematic application o f the theological distinction between potentia absoluta (what God could have done without contradiction) and potentia ordinata (what God de facto did or, as Oresme puts it, “ selon vérité,” actually revealed, decided to do, or ordained) functioned, in line with the condemnations o f Averroism in 1277, to place God beyond the fangs o f necessity in thought or action. In other words, the transcendence o f God is what really concerned the nominalists here.

The distinction - and this we have not realized before - works itself out in two different ways in theology and physics - which includes o f course astronomy. In theology it goes to show the irrelevance and irreverence o f speculative theology and man’s absolute dependence on God’s own revelation. Speculation makes us leave reality behind, and orbit in the infinite realm o f the potentia absoluta, disoriented and lost amongst the infinite number o f possibilities God could have decided to realize. To penetrate this realm o f the Deus absconditus is vana curiositas, to fathom the thoughts o f God is vain curiosity, whereas it is the task o f religion and faith to base itself on God’s own revelation, the potentia ordinata. Together with the humanist quest for authentic sources {fontes), the insistence on nothing but God’s commitment, the sola potentia ordinata, may evolve into a sola scriptura, the Reformation principle “ Scripture alone.” But as history can document, nominalism has left its profound impact not only on Luther, but also on Erasmus and the decrees o f the Council o f Trent.

In both theology and physics the distinction between possibility and reality helped to free man from the smothering embrace o f metaphysics. Yet in physics the same distinction works itself out in a different way. Here the main shift over against preceding tradition is that the investigation o f


final causality is recast in terms o f efficient causality, This means that the Weltbild, the experienced world, is set free from the fangs o f a Weltanschauung, the postulated world. Simultaneously the unmoved Mover thus cedes his place to the inscrutable Lawgiver. Here the potentia ordinata stands for the realm o f nature, the “ present order,” or as Oresme puts it, “ le cours de nature.” Whereas in theology the established order (e.g. o f the Church, Sacraments) is at the same time the revealed order (through Holy Scripture, and/or Tradition), in the realm o f physics the established order is the order o f the established laws o f nature,sti l l to be investigated and freed from the babylonian captivity o f metaphysical a priori.

In this climate there emerge before our eyes the beginnings o f the new science. We see the first contours o f this science in a double thrust:

(1) The conscious and intellectually ascetic reduction and concentration on experientia both as collective experience entered in the historical record o f mankind; andasjenje or test-tube'’ (cognitio intuitiva) experience which allows for general conclusions and the discovery o f laws, and such only by induction.^»

(2) The discovery o f the scientific role o f imagination^^ that allows for mental experiments. Where facts are not in the reach o f experience, we grope for the facts with our imagination, the realm o f the potentia absoluta, the terra incognita, the unknown realm o f logical possibilities. In the field o f theology this would be vain curiosity; in the field o f natural philosophy this is research, investigation. This is the breeding ground o f the so-called hypotheses which are completely misunderstood when seen as “ mere speculation” ; hypotheses are at once the feast o f free research unhampered by a priori, unassailable assumptions and the forecast o f possibilities based on experiments, the formulations o f scientific expectations. The nominalist scientific revolution cannot be sufficiently measured when one merely looks at the research results, even though these are most impressive; but nominalism brings about a revolution in research methodology, which is strictly oriented to experiment and

experience.In the field o f astronomy the nominalist hunger for reality is all the

more acute, since the heavens are so far removed from collective (the records o f observations made by preceding scholarship) and one’s own individual experience. Hence the cri de coeur o f Oresme: nous avons du ciel trop peu d’experience.” While this very hunger will lead to the

410 H. OBERMAN

development o f such instruments as the telescope and microscope, the needed extensions o f the human sense, in the meantime imagination has to fill the gap left by actual experiments, in a conscious suspension o f final judgement. A ll in all the mental hypotheses reach out to reality and expect to be verified by it.

When the distinction is allowed between microcosm (for man), macrocosm (for the universe), and metacosm (for the realm o f God) we may say :

(1) Nominahsm has discovered “ space” by transforming the metacosm from the “ heavenly abode” o f God into the infinite extension o f the macrocosm,^^ hence placing His presence squarely in the macrocosm - an aspect pursued in Luther’s theology and particularly in his doctrine o fthe Eucharist; 52

(2) After the elimination o f the metacosmos as sheer speculation, all attention is given to the natural laws grafted by God into his creation. In concentrating on the macrocosm as machina mundi or the reliable clock set by God,®^ the demarcation line between God and nature is clearly marked and hence space is demythologized and dedivinized.^^ The thrust o f this development is better expressed in the designation “ naturalization o f the universe” than in the more depreciating two-dimensional “ mechanization o f the universe;”

(3) The demarcation line drawn by God himself between his own being and his creation terminates the centuries-long argument that the very existence o f God requires celestial movement including the orbiting o f the sun. 55

The very example from the book o f Joshua that was going to be used as a biblical argument against Copernicus to prove that the sun moves - “ Sun stand still” 10:13 - is adduced by Oresme to show that creation is not a necessary function o f the Highest Being but the result o f a voluntary decision o f the Highest Person.56 It is important to note that for Oresme Scripture admits the possibility that the earth moves - “ qui commovet terram de loco suo” (Job. 9:6) - so that henceforth the investigator is forced to offer a physical instead o f a theological solution.57

For Oresme as well as for those who stand in his tradition the issue o f the heavenly movements - o f the orbits o f the sun, the moon, the moving stars, and the earth - is no longer to be solved in terms o f a deductive speculative cosmology, but in terms o f an experiental inductive cosmo- nomy - with the aid o f imagination, but without claim on scientific accu


racy until the mental experiments are confirmed by experience. It is impressive to see how far Oresme - drawing on advances made by the preceding generation o f scholars in Oxford and Paris - has opened up the realm o f imagination, and o f theoretical astrophysics - the impetus theory, the three-point-requirement in perspectives, the diurnal rotation o f the earth - thus “ homing” significant pieces (i.e. assigning their proper place) in the puzzle that would reveal to Copernicus the vision o f heliocentricity.

But again, outlasting by far the significance in material progress, we emphasize the advance in scientific attitude an - attitude which is not tagged on but integrally related to the new religious and theological attitude: vain curiosity is the effort to penetrate the unknown realm o f God omnipotent {qui supra nos; potentia absoluta) - true and valid curiosity is concerned with the whole machina mundi which includes earth and heaven {quae supra nos; Vordre selon nature). Programmatically God and the heavens are separated. The fifteenth century heirs o f the wise Greek Thales - once the laughing stock and object o f jokes about dangers o f the ivory tower o f speculative Platonism - may still stumble, but now because o f proud penetration o f the God beyond God, the deus absconditus o f the unrevealed mysteries, no longer because o f astronomical curiosity. Put in our modern parlance: the mysteries o f the heavens have

been “ declassified.”

We have presented a sketch o f Oresme because we sense here a remarkable proximity to the birth o f the modern theory o f research in the natural sciences. With much truth yet with little humility and hence in a strikingly post-medieval way Oresme concludes his Livre du ciel et du monde with the words: “ I dare say and insist that there is no human being who has seen a better book on natural philosophy than this one.” 58 59

We have not dealt with Oresme, the Parisian master, to reopen the issue o f the forerunners o f Copernicus. Though it may have become clear that we do not support the theory o f “ spontaneous combustion,” ®® the point is rather that we thus gain a revealing perspective on Copernicus, and this evaluation necessarily includes his two unfortunate editors. To begin with there is Joachim Rheticus - who had cause to feel sUghted by his beloved master Copernicus when the latter decided not to mention this Protestant disciple in his dedicatory letter to Pope Paul III.

412 H. OBERMAN

In a letter to Peter Ramus, dated Krakow 1568, Rheticus describes his future program as the task o f liberating astronomy from hypotheses; henceforth astronomy was to be, as he insists, solely based on observation (jsolis observationibus)’, in the field o f physics modern research should be freed from the shackles o f tradition and be allowed a direct approach, based only on the analysis o f the phenomena o f nature {ex sola naturae contemplatione).

We find here some two centuries after Oresme a reformulation o f the nominahstic anti-metaphysical program which envisioned the replacement o f metaphysical a priori assumptions by experiment and experience. In discarding classical sources as a hindrance to progress, Rheticus proves that he has outgrown the scientifically unproductive phase o f the Renaissance which, with its sun-symbolism and magi, blinded many a scholar until our own day.®^

As far as Osiander is concerned we are, I think, now in a position to do justice to his vision o f reality and to see the element o f truth in his Preface. Better, I believe, than either those who are understandably irritated by his face-saving (but not faith-saving!) devices or those who have opted for the via antiqua and reject the nominalist stance on principle.

However harsh it may sound, astronomy cannot reveal the “ true causes” o f astral phenomena in so far as final causality Hes beyond its purview. It can deal with efiicient causality - what is called in German “ system-immanente Faktoren.” Put in our terms it can deal with cosmo- nomy in contrast with cosmology. But even here astronomy and science in general provide hypotheses whose validity cannot be established without experiment and experience, which, most literally, were not yet “ in sight” in Osiander’s day. Whatever we may hold concerning his claims for the Christian faith, I for one am prepared to grant that the goal o f the natural sciences is validity in the sense o f accuracy, whereas that o f the humanities, particularly o f philosophy and theology, is validity in the sense o f truth. Where this distinction is lost, a mechanized and not a naturalized world view has emerged out o f the process o f nominalist demythologization.

And now finally the case o f Copernicus himself. In the first place heliocentricity is a significant advance and break-through in the accurate charting o f the universe. Before Copernicus, the theological, philosophical, and physical possibility o f the daily and yearly (dual) movement o f


the earth had been probed and approved - but indeed only as possible. Hindrances in all three fields had been cleared to make Copernicus’s theory conceivable, a Denkmoglichkeit.^^ But it was Copernicus who formulated heliocentricity with clarity and audacity, particularly when the limited basis o f facts established by experience is taken into consideration.

Yet, on that very point Copernicus, though materially an advance, is formally a step backwards in comparison to nominalistic research standards.® Copernicus presented a system mathematically equivalent to that o f Ptolemy and based on the AristoteUan, pre-Newtonian hypothesis o f the circular movement o f the planets without the substantial addition o f new ol3servations (experience). In describing the road to his discovery Copernicus mentions heliocentricity as an initial assumption which then, however, becomes conviction and certainty {repperiï).

Until hard proof had been ascertained by Galileo, Kepler, and Newton, Copernicus asked from his readers a faith in his intuition {fides implicita); from such faith the nominalists had wanted to free science in their crusade against metaphysics, against arguments drawn from a dimension o f faith beyond the test o f experience. Copernicus’s discovery would not have been less but more modern i f he had highlighted the gap between his heliocentric “ imagination” - as Oresme would have termed it - and the compound o f experiment and experience interpreted by it. Such a procedure might have made Osiander’s “ fraud” redundant, it most certainly would have made early Copernicanism more difficult to combat. Whatever the differences in goals and methods, common to the natural sciences and the humanities is the accurate description o f the credibility-gap between conceived and sensed reality as a precondition for every advance in our different accesses to reality.

The most significant and lasting aspect o f the Copernican discovery is that Copernicus crowned an era hungry for reahty, groping for answers, and seeking to initiate change. By the very fact that the earth is launched as a planet into space, the macrocosm is drawn into the orbit o f man: heliocentricity is the extension o f creation in space and infinity.

This projection into space is the part o f the revolution o f Copernicus that has not yet been “ received” and absorbed by modern man, it is the part that psychologically, i.e., effectively, is still ahead o f us. A t the historical beginnings o f our conception o f the universe the Greeks projected their polis, their city-state, into the skies as the model o f the cosmos.®^

414 H. OBERMAN

That was at the same time the beginning o f a long process o f demythologization o f the divinized planets. Yet the older view proved to be virile, indomitable, time- and science-resistant: the gods jealously contested Man’s access to space: “ What is above you, man, is none o f your business {Quae supra vos nihil ad vo5)” ! The Icarus complex or space-angst - the hidden motive in the Icarus story - is so fundamental a trait o f man that faith, science, and superstition combined to stage the fundamental antithesis between Mother Earth and Father Cosmos. This is what was and is blocking the medieval emancipation o f astral physics from cosmology and obscuring the distinction between Weltbild and Weltanschauung, between astronomy and astrology, and finally, between legitimate research and vain curiosity.

In this long drawn-out intellectual dawn, Copernican heliocentricity is at the same time a manifesto proclaiming the secular cosmos and a call for the radical colonization o f space: '‘'Quae circa nos tota ad nos,"’ (the cosmos around us is our immediate concern). Till this very day we modern men have not been existentially able to absorb this vision o f reality, as is clear from the fact that the designation “ cosmopolitan” has been reduced to the tourist badge for the well-travelled on this very small globe.

With an allusion to Paul Tillich’s book The Courage To Be, we may conclude by saying that Copernicus is properly celebrated when in the name o f the survival o f man (Copernicus: “ propter nos” ) the dediviniza- tion o f space finds its completion in the exorcism o f our residual space- angst, thus freeing us to face the future with the courage to be in space.

Universitat Tubingen

APP ENDIX I

Copernicus's Dedication to Pope Paul I I I

“ After I had pondered at length this lack o f certainty in traditional mathematics concerning the movements o f the spheres o f the world, I became increasingly annoyed that the philosophers, who in other respects made such a careful scrutiny o f the smallest details o f the world, had nothing better to offer to explain the workings o f the machinery o f the world, which is after all built for us by the Best and Most Orderly Workman o f all. Hence I assigned myself the task o f reading and rereading all


the philosophers whose books I could lay my hands on, to see if anyone ever advanced the view that the movements o f the spheres o f the world are different from those postulated by the specialists in the field o f mathematics.

As a matter o f fact I first discovered in Cicero that Nicetas thought that the earth moved. Afterwards I also found in Plutarch that there were others o f the same opinion. I shall quote his words here, so that they may be known to all:

Whereas the others hold that the earth is immobile, Philolaus, the Pythagorean, claims that it moves around the fire with a nearly circular motion, not unlike the sun and the moon, Herakleides of Pontus and Ekphantus, the Pythagorean, do not assign to the earth any movement of locomotion. Instead they think in terms of a limited movement, rising and setting around its center, like a wheel.

This was reason enough so that I too began to think seriously about the mobility o f the earth. And although this still seemed to me an absurd point o f view, I knew that others before me had been granted the liberty o f postulating whatever cycles they pleased in order to explain astral phenomena. Therefore, I thought that I too would be readily permitted to test, on the assumption that the earth has some movement, whether a more convincing explanation, less shaky than those o f my predecessors, could be found for the revolutions o f the celestial spheres.”

Translated from Nicolai Copernici Thorunensis, De Revolutionibus Orbium Caelestium libri sex. Vol. 2, ed. Franciscus Zeller and Carolus Zeller (München, 1949), pp. 5,18-6, 3.

APP ENDIX II

Osiander's Preface

“ Since the newness o f this work’s hypotheses which assume that the earth is in motion and that there is an immovable sun at the center o f the universe, has already received a great deal o f advance publicity, I do not doubt that some scholars will have taken grave offense and think it wrong to raise havoc among the liberal arts with their properly time-honored classical tradition.*

* It has not yet been noted, as far as I can see, that this passage reflects, almost verbatim, Luther’s Tischrede quoted in note 9.

416 H. OBERMAN

Yet, i f they are willing to ponder the matter seriously {exacte), they will come to the conclusion that the author o f this work has done nothing which merits blame. For it is the specific task o f the astronomer through patient and refined observations to chart the course o f the stars and planets. On this basis he has to compute the causes or, rather, develop hypotheses, since he cannot possibly establish the final causes o f these movements. By these assumptions past and future heavenly movements can be calculated with the help o f geometry.

This scientist has done a first-rate job in both respects. After all, it is not necessary that his hypotheses should be true, or even probable. This alone suffices: that they provide a computation which tallies with the observations....

And if scholars in the field construct and think up causes - and they have certainly thought up a good many - nevertheless they advance their models not in order to make a claim o f unshakable truth, but to present a correct basis for calculation.

Since, then, for one and the same movement several hypotheses, such as eccentricity or epicycles for the movement o f the sun, have been advanced in the course o f time, the astronomer will be inclined to accept that one which has the highest degree o f prima facie consistency. The philosopher is more likely to insist on probability; but neither o f them will be able to learn or teach anything that claims to be ultimate truth, unless it has been divinely revealed to him.

Therefore, let us allow these new hypotheses to take their place among the old ones - which were by no means more probable - especially since these are impressive, crystal clear, and based upon a vast amount o f learned observations.

But, as far as the hypotheses are concerned, let no one expect absolute certainty from astronomy, since astronomy cannot provide this. Otherwise, i f one takes models, which have their own good purpose, to stand for reality, one becomes through involvement in this discipline more ignorant than before.”

Translated from Nicolai Copernici Thorunensis, De Revolutionibus^ Vol. 2, ed. cit., pp. 403, 3-404, 7.


APPENDIX III

“ Thus Kepler and Galileo, in contrast to Plato, put forward a mathematical empiricism. This was quite evident in one o f the most decisive moments in the history o f science. It had been a dogma o f the ‘church scientific,’ up to the time o f Kepler, that movements in the heavens could be nothing but uniform and circular. Everywhere, everybody had always held this to be true a priori', Platonists and Aristotelians, Idealists and Nominalists, Copernicus and Galileo had accepted this dogma and Kepler himself was thoroughly convinced o f its truth.

Yet a difference o f eight minutes between observation and calculation o f the orbit o f the planet Mars forced him, after a struggle o f several years, to abandon this dogma o f circularity and to postulate a non-uni

form motion in elliptical orbits.He submitted to given facts rather than maintaining an age-old preju

dice; in his mind a Christian empiricism gained the victory over platonic rationalism; a lonely man submitted to facts and broke away from a tradition o f two thousand years. With full justice he could declare: ‘These eight minutes paved the way for the reformation o f the whole o f astronomy,’ and it was with full justice, too, that in 1609 he gave to his

book the title New Astronomy.^'

R. Hooykaas, Religion and the Rise o f Modern Science (Edinburgh-

London,1972)p.35f.

N O T E S

* With the permission of the Smithsonian Institution Press, the present paper is reprinted, with changes, from The Nature o f Scientific Discovery, edited by Owen Ginge- rich, Smithsonian Institution Press, Washington, D.C., 1974. The association of astral (meta) physics and irrelevance has a classical root. Cf. the

wise Thales falling in a pit while watching the heavens; Werner Jaeger, Paideia. Die Form m g des griechischen Menschen, Vol. 1, 2nd ed. (Berlin, 1954), p. 211. This association is reflected in Christian antiquity when St. Augustine applied to it the term curiositas [see note 16]. Since that time the growth - and stagnation - of intellectual European man is reflected in his attitude to “the heavens,” “quae supra nos.” With the expression “vain curiosity” I allude to the title of the November 1402 sermon and manifesto calling for university reform by Jean Gerson (t 1429) as Chancellor of the University of Paris. Cf. Steven E. Ozment ‘The University and the Church. Patterns of Reform in Jean Gerson’, Medievalia et Humanistica New Series 1 (1970), pp. 111-126; p. 113. Edition and English translation by Steven E. Ozment. Jean Gerson, Textus

418 H. OBERMAN

Minores, Vol. 38 (Leiden, 1969), pp. 26-45; p. 82ff. I emphasize and cherish Gerson’s adjective “vain,” because of the heahhy ambiguity of “curiosity” in the western tradition. For Hans Blumenberg’s learned but illegitimate identification of curiositas with true learning and therefore his identification of the campaign contra vanam curiositatem as medieval (non-modern) obscurantism, see his Die Legitimitat der Neuzeit (Frank-\ furt a. M., 1966), pp. 201-432; esp. pp. 350-352. However, Gerson could harmoniously have reconciled his attack “contra vanam curiositatem” with Adam Ulam’s description of the lasting task of the university: “A liberal education seeks to indoctrinate the student in cu rio s ity ...The Fall o f the American University (London, 1972), p. 31. For a description and documentation of the history of ‘curiositas’ see my "Contra vanam curiositatem: Ein Kapitel der Theologie zwischen Seelenwinkel und Weltall {Znnch., 1974),2 “During the first Christian millennium, in both East and West, God at the moment of creation is represented in passive majesty, actualizing the cosmos by pure power of thought, Platonically. Then, shortly after the year 1000, a Gospel book was produced at Winchester which made a great innovation: inspired by Wisdom 11.20, ‘Omnia in mensura et numero et pondere disposuisti,’ the monastic illuminator showed the hand of God - now the master craftsman - holding scales, a carpenter’s square, and a pair of compasses. This new representation spread and, probably under the influence of Proverbs 8.27, ‘certe lege et gyro vallabat abysses,’ the scales and square were eliminated leaving only the compasses - the normal medieval and renaissance symbol of the engineer - held in God’s hand.” Lynn White, Jr., ‘Cultural Climates and Technological Advance in the Middle Ages’, Viator 2 (1971), 171-201,189.3 Bertolt Brecht, Gesammelte Werke, Vol. 3, “Leben des Galilei” (Frankfurt a. M.,1967), pp. 1229-1345; p. 1282.4 The Laughton translation authorized by B. Brecht was not available to me in a European library. Mr. Philip J, Rosato made this elegant translation. Generally, I am most indebted for his critical perusal of my English efforts.5 “ ‘Centrum’ est terrae medium magis presse, est punctum quoddam defixum in totius mundi parte infirma, unde ad superficiem caeli aequales undique lineae producuntur. Hinc transfertur ad significandum medium vel imum quodlibet, vel proprium, aut improprium, in corpore, vel in anima. Nam in hac quoque medium et imum agnoscunt Mystici. Et est idem quod Animae apex... Theologiae Mysticae Clavis, ed. Maximilia- nus Sandaeus (Cologne, 1640), fol. 12.

For ‘centrum’ as image of the spirit that is free from the body within all directions ( = in every respect) with a unique immediacy ( = same distance) to reality, see Nicolaus Cusanus, Liber de mente, cap. VII, ed. Ernst Cassirer, Individuum und Kosmos in der Philosophie der Renaissance, 3rd ed. (Darmstadt, 1963, [1st ed., Leipzig, 1921]), p. 248, lines 18-21. See further Norbert Schiffers, Fragen der Physik an die Theologie. Die Sakularisierung der Wissenschaft und das Heilsverlangen nach Freiheit (Düsseldorf1968), p. 14 ff.

The problem of Cusanus as forerunner of Copernicus is best presented by A. Koyré, in a fashion which deserves a full quotation: “On pourrait m’objecter, sans doute, que, cent ans avant Copernic, en 1440, Nicolas de Cues, dans sa Docte Ignorance {De docta ignorantia, II, 17) avait déjà proclamé que la ‘Terre est une étoile noble’ (terra est stella nobilis) et l’a enlevée du centre du monde, en proclamant, au surplus, que ce centre n’existe pas, vu que le monde est ‘une sphère infinie ayant son centre partout et sa circonférence nulle part’ ; et que son oeuvre, que Copernic avait probablement connue, a pu, ou dû, influencer sa pensée (R. Klibansky, ‘Copernic et Nicolas de Cues’, in Léonard de Vinci et l ’expérience scientifique du XVIe Siècle [Paris, 1953]), Je n’en discon


viens pas. Il n’en reste pas moins vrai que le conception, métaphysiquement très hardie, de Nicolas de Cues, à savoir celle d’un Univers indéfini sinon infini, n’a pas été acceptée par Copernic (ni personne d’autre, avant Giordano Bruno); que sa cosmologie, scientifiquement parlant, est inexistante; que, s’il attribue un mouvement à la Terre, il ne lui attribue pas de mouvement autour du Soleil et que, en général, ses conceptions astronomiques sont tellement vagues et souvent tellement erronées (il attribue par exemple, une lumière propre aussi bien à la Lune qu’à la Terre) que Nicolas de Cues - sauf en dynamique - ne peut d’aucune façon être classé parmi les précurseurs de Copernic, ni même prétendre à une place dans l’histoire de l’astronomie.” La Révolution astronomique. Copernic, Kepler, Borelli, Histoire de la Pensée, Vol. 3 (Paris, 1961), p, 75.® “Wir kônnen also sogar behaupten, dass die Inquisition von Galilei nicht mehr ver- langte, als dass er nicht mehr sagen solle als er beweisen konnte. Er war der Fanatiker in dieser Auseinandersetzimg.” Weizsâcker’s radicalization - and romanticization of Inquisitional objectives - is decisively mitigated, when he introduces his views on the parallel between faith and science: “ ... Er hatte damit recht, dass er der Fanatiker war. Die grossen Fortschritte der Wissenschaft geschehen nicht, indem man angstlich am Beweisbaren klebt, Sie geschehen durch kiihne Behauptungen, die den Weg zu ihrer eigenen Bestatigung oder Widerlegung selbst erst off nen. Allés was ich iiber den Fall der Korper und über das Tràgheitsgesetz gesagt habe, erlautert dieser Satz, und wir kônnen nicht zweifeln, dass Galilei sich dieser methodologischen Situation voll be- wusst war. Die Wissenschaft braucht Glauben so gut wie die Religion, und beide Weisen des Glaubens unterwerfen sich, wenn sie sich selbst verstehen, der ihnen jeweils eigen- tiimlichen Probe: der religiose Glaube in menschlichen Leben, der wissenschaftliche im Weiterforschen,” ‘Kopernikus, Kepler, Galilei. Zur Entstehung der neuzeitlichen Naturwissenschaft’, in Einsichten, Gerhard Kruger zum 60. Geburtstag, ed. Klaus Oehler and Richard Schaeffler (Frankfurt a. M., 1962), pp. 376-394; p. 392. Galileo as the “glorious fanatic” is also reflected in the words of Albert Einstein. See his Foreword to a translation of Galileo’s Dialogue: “A man who possessed the passionate will, the intelligence, and the courage to stand up as the representative of rational thinking against the host of those who, relying on the ignorance of the people and the indolence of teachers in priestly and scholarly garb, maintained and defended their positions of authority. His unusual literary gift enabled him to address the educated man of his age in such clear and convincing language as to overcome the anthropocentric and myth- ridden thinking of his contemporaries.” Quoted by Stillman Drake, Galileo Studies. Personality, Tradition, and Revolution (Ann Arbor, 1970), p. 65. The puzzling complexity of the assessment of the significance and “human dimension” of Galilei’s achievement may be seen in the fact that exactly the anthropocentrism of Copernicus, as basis for his faith in the cosmic order, marked the path toward his discovery. See his Dedication to Pope Paul III (Appendix I).

“ In Wirklichkeit hat Galilei die Astronomie und die Physik beteichert, indem er diese Wissenschaften zugleich eines Grossteils ihrer geseUschaftlichen Bedeutung beraubte. Mit ihrer Diskreditierung der Bibel und der Kirche standen sie eine Zeitlang auf der Barrikade fiir alien Fortschritt, Es ist wahr, der Umschwung vollzog sich trotzdem in den folgenden Jahrhunderten, und sie waren daran beteiligt, aber es war eben ein Umschwung anstatt einer Revolution, der Skandal artete sozusagen in einen Disput aus, unter Fachleuten, Die Kirche und mit ihr die gesamte Reaktion konnte einen geordneten Riickzug vollziehen und ihre Macht mehr oder weniger behaupten. Was diese Wissenschaften selber betrifl't, erklommen sie nie mehr die damalige grosse Stellung in der Gesellschaft, kamen nie mehr in solche Nâhe zum Volk.

420 H. OBERMAN

Galileis VerbreChen kann aïs die ‘Erbsünde’ der modernen Naturwissenschaften betrachtet werden. Aus der neuen Astronomie, die eine neue Klasse, das Bürgertum, zutiefst interessierte, da sie den revolutionâren sozialen Strômungen der Zeit Vorschub leistete, machte er eine scharf begrenzte Spezialwissenschaft, die sich freilich gerade durch ihre ‘Reinheit,’ das heisst ihre Indifferenz zu der Produktionsweise, verliâltnis- massig ungestôrt entwickeln konnte.

Die Atombombe ist sowohl als technisches als auch soziales Phânomen das klassische Endprodukt seiner wissenschaftlichen Leistung und seines sozialen Versagens.” Bertolt Brecht, Gesammelte Werke, Vol. 17 (Frankfurt a. M., 1967), p. 1108 f.® Koestler ponders a number of explanations why Copernicus did not object to or have Osiander’s Preface removed and concludes: it is more likely that he submitted to Osiander’s proposal since he had already submitted his whole life long, more likely he procrastinated, as he had done all his life.” Arthur Koestler, The Sleepwalkers, 2nd ed. (Harmondsworth, Middlesex, 1964 [Penguin Book]), p. 175.® In the reading of Lauterbach, with a better claim to authenticity than Aurifaber’s: “De novo quodam astrologo fiebat mentio, qui probaret terram moveri et non coelum, solem et lunam, ac si quis in curru aut navi moveretur, putaret se quiescere et terram et arbores moveri. Aber es gehet jetzunder also: Wer do w’l klug sein, der sol ihme nichts lassen gefallen, das andere achten; er mus ihme etwas eigen machen, sicut ille facit, qui totam astrologiam [alias: astronomiam] invertere vult. Etiam illa confusa, tamen ego credo sacrae scripturae, nam losua iussit solem stare, non terram.” D. Martin Luthers Werke. Tischreden 4.4638. Cf. Ibid., 1. 855.

Basic literature: Werner Elert, Morphologie des Luthertums, Vol. 1, Theologie und Weltanschauung des Luthertums hauptsâchlich im 16. und 17. Jahrhundert, 2nd ed. (München, 1958), pp. 363-393. Heinrich Bornkamm, ‘Kopernikus im Urteil der Refor- matoren’, Archiv fü r Reformationsgeschichte 40 (1943), 171-183; repr. in Das Jahr- hundert der Reformation. Gestalten und Kràfte, 2nd ed. (Gottingen, 1966), pp. 177-185. John Dillenberger, Protestant Thought and Natural Science. A historical interpretation o f the issues behind the 500-year-old debate (New York, 1960), pp. 28-49. Klaus Scholder, in a large cultural and historical setting: Urspriinge undProbleme der Bibelkritik im 17. JahrhuTukrt. Ein Beitrag zur Entstehung der historisch-kritischen Theologie (München, 1966), pp. 57-65.

See Thomas S. Kuhn, The Copernican Revolution. Planetary Astronomy in the Development o f Western Thought (Cambridge, Mass., 1957), p. 196: “Protestant leaders like Luther, Calvin, and Melanchthon led in citing Scripture against Copernicus and in urging the repression of Copemicans. Since the Protestants never possessed the police apparatus available to the Catholic Church, their repressive measures were seldom so effective as those taken later by the Catholics, and they were more readily abandoned when the evidence for Copernicanism became overwhelming. But Protestants nevertheless provided the first effective institutionalized opposition.”

Since the Protestant “attack” is interpreted as being due to its “ sola scriptura,” the Catholic reaction to Galilei has to be explained in different terms - and much to the historian’s surprise - it is presented as anti-protestant reaction and part of Catholic reform.

R. Hooykaas has eloquently opposed the myth that Calvin mentioned - and rejected - Copernicus in his works “ ‘There is no lie so good as the precise and well-detailed one’ and this one has been repeated again and again, quotation marks included, by writers on the history of science, who evidently did not make the effort to verify the statement. For fifteen years, I have pointed out in several periodicals concerned with the history of


science that the ‘quotation’ [Ps 93:1] from Calvin is imaginary and that Calvin never mentioned Copernicus; but the legend dies hard.” Religion and the Rise o f Modem Science (Edinburgh-London, 1972), p. 121.

Furthermore, Hooykaas dealt with the theological thrust of Calvin’s Genesis commentary by pointing to another aspect: “Thus Calvin’s exegetical method was based on the Reformation doctrine which held that the religious message of the Bible is accessible to everybody. The Spirit of God, as he put it, has opened a common school for all, and has therefore chosen subjects intelligible to all. Moses was ordained a teacher of the unlearned as well as of the learned; had he spoken of things generally unknown, the uneducated might have pleaded in excuse that such subjects were beyond their capacity; therefore, Moses ‘rather adapted his writing to common usage.’” p. 118.

See Corpus Reformatorum, Vol. 51 (Calvini Opera 23), col. 20-22.12 “Tenendum est illud, Mosen non acute Philosophari de occultis mysteriis: sed referre quae passim etiam rudibus nota sunt, et posita in vulgari usu.” Calvin, loc. cit. Cf. “ Moses duo facit magna luminaria: atqui astrologi firmis rationibus probant, Saturni sidus, quod omnium minimum propter longinquitatem apparet, lunari esse maius. Hoc interest, quod Moses populariter scripsit quae sine doctrina et literis onmes idiotae communi sensu percipunt: illi autem magno labore investigant quidquid himia- ni ingenii acumen assequi potest. Nec vero aut studium illud improbandum est, aut damnanda scientia, ut phrenetici quidam solent audacter reiicere quidquid est illis incognitum. Nam astrologia non modo iucunda est cognitu, sed apprime quoque utilis: negari non potest quin admirabilem Dei sapientiam explicet ars illa.” Calvin, loc. cit.13 See K. Scholder, op. cit., p. 68 ff. and Heinrich Karpp, ‘Der Beitrag Keplers und Galileis zum neuzeitlichen Schriftverstandnis’, Zeitschrift f i ir Theologie und Kirche 67 (1970), 40-55; 46 f.1 Adagiorum Chiliades I 6, 69; in Ausgewahlte Werke, Vol. 7, ed. Theresia Payr (Darmstadt, 1972), p. 414 f.15 “ Quae supra nos, nihil ad nos. Dictum Socraticum deterrens a curiosa vestigatione rerum coelestium et arcanorum naturae. Refertur proverbii vice a Lactantio libro tertio, capite vigesimo: Ex his, inquit, unum eligam quod ab omnibus sit probatum. Celebre hoc proverbium Socrates habuit: Quod supra nos, nihil ad nos. Torqueri potest et in illos, qui de negociis principum aut theologiae mysteriis temere loquuntur. Vertere licebit et in contrarium; Quae infra nos, nihil ad nos, ubi significamus res leviusculas, quam ut nobis curae esse debeant.” Erasmus von Rotterdam, Ausgewàhlte Werke, Vol. 7, ed. cit., pp. 414,416 Cf. L. Caeli Firmiani Lactanti Divinae Institutiones, IIL 20; Corpus Scriptorum Ecclesiasticorum 19, p. 240,15. Though Lactantius seemingly rejects the Socratic warning as contrary to God-oriented piety, de facto he concurs as far as the campaign against vain curiosity is concerned. The Church father explicitly says that he prefers Socrates to those impii, who “ in secreta caelestis illius providentiae curiosos oculos voluerint immittere.” Ed. cit., p. 245,8 f.

In a learned and stimulating article Eberhard Jüngel pursues the function of the “ Socratic saying” in Luther’s theology: ‘Quae supra nos, nihil ad nos. Eine Kurzfor- mel der Lehre vom verborgenen Gott - im Anschluss an Luther interpretiert’, Evan- gelische Theologie 32 (1972), 197-240. A comparison e.g. with Gerson’s sermon “Contra vanam curiositatem” [particularly Oeuvres Complètes, ed. Mgr P. Glorieux, Vol. 3 (Paris, 1962), p. 233 f.] would have allowed for an equally solid grasp of Luther’s dependence on the preceding tradition as of his originality.1® “ Quoniam magnus es, domine, et humilia respicis, excelsa autem a longe agnoscis: nec propinquas nisi obtritis corde, nec inveniris a superbis, nec si illi curiosa peritia numerent

422 H. OBERMAN

stellas et harenam, et dimetiantur sidereas plagas, et vestigent vias astrorum.” Augustine Confessions, Lib. V. 3, 3. In the further context it becomes clear, however, that the charge of curiositas is not directed against the validity of the astronomical findings but against “border-crossing,” i.e. the vain effort to find beyond creation the creator: “non noverunt hanc viam, qua descendant ad ilium a se, et per eum ascendant ad eum. Non noverunt hanc viam, et putant se excelsos esse cum sideribus et lucidos, et ecce ruerunt in terram, et obscuratum est insipiens cor eorum. Et multa vera de creatura dicunt, et veritatem, creaturae artificem, non pie quaerunt, et ideo non inveniunt...” Cf. Lib. V. 3,5.

With great subtlety Hans Blumenberg presents the secondary argument of Augustine “mente sua enim quaerunt ista et ingenio, quod tu dedisti eis, et multa invenerunt” as the main thrust and sees in Augustine’s subtlety here the reason for its lack of influence; “ In dieser Subtilitat war der Gedankenicht traditionsfahig.” Die Legitimitât der Neuzeit, op. cit., p. 298.

“ III. 9. Cum ergo quaeritur, quid credendum sit, quod ad religionem pertineat, non rerum natura ita rimanda est, quemadmodum ab eis, quos physicos Graeci vocant; nec metuendum est, ne aliquid de vi et numero elementorum, de motu atque ordine et defectibus siderum, de figura caeli, de generibus et naturis animalium, fruticum, lapidum, fontium, fluminum, montium, de spatiis locorum et temporum, de signis imminentium tempestatiun, et alia sescenta de his rebus, quas illi vel invenerunt vel invenisse se existimant, Christianus ignoret, quia nec ipsi omnia reppererunt tanto excellentes ingenio, flagrantes studio, abundantes otio, et quaedam humana coniectura investigantes, quaedam vero historica experientia perscrutantes, et in eis, quae se invenisse gloriantur, plura opinantes potius quam scientes. Satis est Christiano rerum creatarum causam... non nisi bonitatem credere creatoris...” Enchiridion ad Laurentium de fide et spe et caritate. Corpus Christianorum 46, p. 52 f. (=ed. J. Barbel, Testimonia I, [Düsseldorf, 1960], p. 34) “V. 16. Quae cum ita sint, quando nobis Maronis ille versus placet: Felix, qui potuit rerum cognoscere causes, non nobis videatur ad felicitatem consequendam pertinere, si sciamus causas magnarum in mundo corporalium motionum, quae abditissimis naturae sinibus occuluntur: unde tremor terris, qua vi maria alta tumescant, [obicibus ruptis rursusque in se ipsa residant, et cetera huiusmodi. Sed bonarum et malarum rerum causas nosse debemus, et id hactenus, quatenus eas homini in hac vita erroribus aerumnisque plenissima, ad eosdem errores et aerumnas evadendas nosse conceditur. Ad illam quippe felicitatem tendendum est, ubi nulla quatiamur aerumna, nullo errore fallamur. Nam si causae corporalium motionum noscendae nobis essent, nullas magis nosse quam nostrae valetudinis, deberemus. Cum vero eis ignoratis medicos quaerimus, quis non videat, quod de secretis caeli et terrae nos latet, quanta sit patientia nesciendum?” Corpus Christianorum 46, p. 56 f. (=ed. cit., p. 39).

A restrictive interpretation of the Augustinian position we find with Hugo of St. Victor in his Expositio in Hierarchiam coelestem S. Dionysii Areopagitae, Migne, Patrologia latina 175, 925 A : “Praedicatus est Christus crucifixus, ut humilitate veritas quaereretur. Sed mundus medicum despexit, et non potuit verum agnoscere. Voluit enim contemplari opera Dei quae miranda fecerat, et quae proposuerat imitanda noluit venerari. Neque enim morbum suum attendit, ut pia devotione medicinam quaereret; sed de falsa sanitate praesumens dedit se ut vana curiositate aliena investigaret. Et videbatur extra se proficere, sed defecit in se et eum, qui erat supra se, non invenit.”

It is not, I believe, a significant difference over against Augustine to replace the realm “quae supra nos” with the personalized “qui supra nos,” also intended by Augustine. Much more telling is the “videbatur,” whereas Augustine would have conceded the


potential accuracy of secular research. Cf. note 16. This passage is referred to by Ger- son: “De errore philosophantium ex curiositate nimia loquitur Seneca in Epistola de liberalibus artibus (“quantum habent [philosophi] supervacui, quantum ab usu recedentis... diligentius loqui scirent quam vivere.” Ep. 88, 42); et Hugo melius in prooemio...” Oeuvres Complètes, ed. cit. Vol. 3, p. 231. Source identifications by S. E. Ozment, Jean Gerson, ed. cit., p. 82 f. N.B. the apparently necessary characterization of curiositas by nimia, parallel to vana.19 Ca/v/mPpera23, et/. ci7., col. 22; see footnote 12.20 “De motibus stellae Martis,” in Astronomia nova, Joannis Kepleri Astronomi Opera omnia, ed. Ch. Frisch (Frankofurti a. M. et Erlangae, 1858-1871), Vol. 3, pp. 153- 156.21 Cf. Thomas de Aquino, Contra Gentiles, III. Liber IV, ‘De unione hypostatica,’ cap. 55: “ ...virtus humilitatis in hac consistit ut aliquis infra suos terminos se contineat, ad ea quae supra se sunt non se extendens, sed superiori se subiiciat.” For a discussion of the Renaissance ideal of the “unlimited man,” the comprehensive “Uomo universale,” see note 62.22 Cf. J. Dillenberger: “Statistical evidence points to a predominant Puritan membership in the Royal Society,” op. cit., p. 130.2® See R. Hooykaas, op. cit., p. 148; cf. p. 945".; pp. 135-138.24 Nikolaus Kopernikus Gesamtausgabe, Vol. 2, De revolutionibus orbium caelestium (München, 1949), pp. 403, 29-404, 7: ... astronomus eam [hypothesim] potissimum arripiet, quae comprehensu sit quam facillima. Philosophus fortasse veri similitudinem magis requiret; neuter tamen quicquam certi comprehendet, aut tradet, nisi divinitus illi revelatum fuerit. Sinamus igitur et has novas hypotheses inter veteres nihilo verisimiliores innotescere, praesertim cum admirabiles simul et faciles sint, ingentemque thesaurum doctissimarum observationem [sic; lege: observationum] secum advehant. Neque quisquam, quod ad hypotheses attinet, quicquam certi ab astronomia expectet, cum ipsa nihil tale praestare queat, ne si in alium usum conficta pro veris arripiat, stultior ab hac disciplina discedat quam accesserit. Vale.” Ad lectorem de hypothesibus huius operis.

N.B.: The title page of the Nuremberg 1543 edition is enlarged by a publisher’s “blurb” : “Habes in hoc opere... motus stellarum... novis insuper ac admirabilibus hypothesibus ornatis.” For the bibliographical data see Gottfried Seebass, Bibliogra- phia Osiandrica (Nieuwkoop, 1971), p. 130 f.25 H. Bornkamm, op. cit., p. 182 f. ; K. Scholder, op. cit., p. 63.26 On the Cartesian dichotomy between the two experiences see J. Bots, Tussen Descartes en Darwin. Geloof en natuurwetenschap in de 18e eeuw in Nederland, (Assen, 1972), pp. 136-139 (German summary of this section, p. 186 f.).27 E. A. Burtt, The Metaphysical Foundations o f Modem Physical Science, 2nd. ed. (New York, 1951), p. 25; cited by J. Dillenberger, op. cit., p. 26 f. Franz Wolf, though more restrained, presents the same argument in his 1943 commemoration address: “Auch in den Einzelheiten war die Überlegenheit des kopemikanischen Systems über das des Ptolemaus so deutlich zunachst noch nicht zu erkennen.” ‘Von der Welt des Kopernikus bis in die Fernen der Spiralnebel - ein Blick in die Entwicklung der modemen Himmelskunde’, Karlsruher Akademische Reden 22 (1943), 5-23; 11. Cf. on ‘Die Schwache des Kopernikus’ Norbert Schiffers, Fragen der Physik an die Theologie. op. cit., p. 13 f.28 Karl Heinz Burmeister, Georg Joachim Rhetikus 1514-1574, Vol. 3, Briefwechsel (Wiesbaden, 1968), p. 55. It seems clear that Gisius refers to Osiander as responsible for

424 H. OBERMAN REFORMATION AND REVOLUTION 425

putting pressure on Petreius. Gisius’s interpretation of Osiander’s motives is - understandably - more malicious than convincing; dolens descendendum sibi esse a pristina professione, si hic liber famam sit consecutus.” In letters to Copernicus and his co-editor Rheticus Osiander had as early as April (20) 1541 developed his plan de campagne for winning over the two expected opposition parties. See K. H. Burmeister, op. cit.. Vol. 3, p. 25 : Peripathetici et theologi facile placabuntur [instead of : placa- bunter], si audierint, eiusdem apparentis motus varias esse posse hypotheses...” Cf. note 30.29 In early copies the name of Osiander is identified; as a matter of fact, this is the way in which Kepler could name Osiander as the author of the Preface. Yet even as late as Laplace the Preface was read as being written by Copernicus. See A. Koyré, op. cit., p. 99, note 14.3“ “Andreas Osiander an Rhetikus in Frauenburg, Nürnberg, den 20. April 1541. ‘...Peripathetici et theologi facile placabuntur, si audierint, eiusdem apparentis motus varias esse posse hypotheses, nec eas afferri, quod certo ita sint, sed quod calculum apparentis et compositi motus quam commodissime gubernet, et fieri posse, et alius quis alias hypotheses excogitet, et imagines hic aptas, ille aptiores, eandem tamen motus apparentiam causantes, ac esse unicuique liberum, immo gratificaturum, si Commodio res excogitet. Ita a vindicandi severitate ad exquirendi illecebras avocati ac provocati primum aequiores, tum frusta quaerentes pedibus in auctoris sententiam ibunt...’” K. H. Burmeister, op. cit.. Vol. 3, p. 25. For the parallel, partly identical letter of Osiander to Copernicus, dated on the same day, April 20,1541, see “Apologia Tychonis contra Ursum,” Kepleri opera omnia, ed. cit.. Vol. 1, p. 246.31 Kepleri opera omnia, ed. cit.. Vol. 3, p. 136.

Edward Rosen, Three Copernican Treatises, 2nd ed., 1959, pp. 28-33. The appendix of annotated bibliography (pp. 201-269) proved to be invaluaWe.33 E. Rosen, op. cit., p. 31. Cf. also Rheticus’s dedicatory letter to the Narratio Prima, quoted by Leopold Prowe, Nicolaus Copernicus, Vol. 2 (Berlin, 1884), p. 321,27.34 In contrast to assertio which means conviction, opinio means “view” in the sense of “assumption.”35 ... neuter tamen quicquid certi comprehendet aut tradet nisi divinitus illi revelatum fuerit.” For an accessible and emendated Latin text of Osiander’s Preface, see Emanuel Hirsch, Die Theologie des Andreas Osiander und ihre geschichtlichen Voraussetzungen (Gottingen, 1919), Anhang 1, p. 290.3« This universal vision as the essential advance beyond Ptolemaeus is highlighted by Matthias Schramm in his commemoration address in Tübingen, February 1, 1973, entitled “Die Leistungen des Copernicus.” The author kindly supplied me with his manuscript.37 “Der Mensch ist nicht, wie es die Stoiker bestimmen sollten, zur Betrachtung des Himmels disponiert, sondem seine theoretische Neugierde stellt ihn vor die Erschei- nung einer heterogenen und unerreichbaren Weltregion, für deren Erkenntnis ihm seine Natur keine Anhalte liefert. Die Erkenntnistheorie der astronomischen Resignation ist damit metaphysisch systematisiert,” Hans Blumenberg, Die kopernikanische Wende. (Frankfurt a. M., 1965), p. 64. Cf. Die Legitimitat der Neuzeit, op. cit., p. 346 flF.3* “Kopernikus hat nicht nur humanistische Formeln gebraucht, er hat mit seiner astronomischen Reform den genuinen Sinn der humanistischen Bewegung des aus- gehenden Mittelalters genauer getroffen und wesentlicher realisiert als viele von denen, die das Programm dieser Stromung ausdrUcklich formuliert hatten.” H. Blumenberg, Die kopernikanische Wende, op. cit., p. 77.

3® Nicole Oresme. Le Livre du ciel et du monde. Book II, 8. fol. 89 d; ed. Albert D. Menut and Alexander J. Denomy ,C.S.B. (Madison. 1968), p. 356,15 f.^ See Emst Zimmer, Entstehung und Ausbreitung der Coppernicanischen Lehre, Sitzungs- berichte der Phy.-Med. Sozietât Erlangen 74. (Erlangen, 1943), p. 406. These Quaestiones are part of a genre of composite volumes described by Pierre Duhem, Les Origi- gines de la statique. Vol. 2 (Paris, 1906), p. 59, note 1 ; p. 337 flf., note 1.

In another context - with respect to the significance of neostoicism as the “ setting” for Descartes, Spinoza, and Calvin - the French philosopher Eric Weil observes that such “authors are credited with an originality they themselves would not have admitted, simply because we do not study what every cultured man in their times had always present in mind.” See his article ‘Supporting the humanities’, in Daedalus 102,2 (1973), 27-38;33.42 On a broad (often manuscript) basis Lynn Thorndike presents Oresme’s views on astrology, magic, and miracles, A History o f Magic and Experimental Science, Vol. 3. (New York, 1934), pp. 398^71.43 Anneliese Maier herself has often been more ready to grant Oresme his subjective sense of exploring reality; see e.g. An der Grenze von Scholastik und Naturwissenschaft, Studien zur Naturphilosophie der Spatscholastik III, 2nd ed. (Roma, 1952), p. 354 f. In a characteristic formulation Anneliese Maier now ascribes to Oresme a view (earlier assigned by her to Albert of Sachsen) “ in der man eine erste Ahnung des Âquivalenz- satzes der modemen Mengenlehre sehen kann.” Die Vorlaufer Galileis im 14. Jahr- hundert, Studien zur Naturphilosophie der Spatscholastik I, 2nd ed. (Roma, 1966), p. 309.44 See Menut’s bibliography in Nicole Oresme. Le Livre du ciel et du monde, ed. cit., pp. 753-762.45 Anneliese Maier assigns to Jean Buridan the central role: “ ... Buridans Verdienst ist es, aus ail diesen Erkenntnissen die metaphysischen und methodologische Konse- quenzen gezogen zu haben: er ist der erste, der zu sehen glaubt, dass diese Prinzipien genügen, um das Naturgeschehen zu erklâren, und dass man auf die Annahme von Finalursachen und Finaltendenzen verzichten kann. Und damit hat er tatsàchlich den Gedanken vorweggenommen, der die Naturwissenschaft der folgenden Jahrhunderte beherrschen sollte.” Metaphysische Hintergründe der spàtscholastischen Naturphilosophie, Studien zur Naturphilosophie der Spatscholastik IV (Roma, 1955), p. 334 f.4« Book 1.2. fol. 7a ; ed. cit., p. 58,23. See also the synonyms used by d’Ailly, as quoted by Francis Oakley, ‘Christian Theology and the Newtonian Science: The Rise of the Concept of the Laws of Nature’, Church History 30 (1961), 433-457 ; 454 f., note 74.4’ Book II. 2. fol. 71a; ed. cit., p. 288, 236. Cf. Jean Gerson: “ Mundus est universitas rerum ab arte divina conditarum; quae res ab eius dominantissimo et liberrimo regimine suis legibus ordinantur...” “Lex est recta ratio practica secundum quam motus et operationes rerum in suos fines ordinate regulantur: vel est ipsa talis regulatio in quocumque....” “ Lex naturae est in rebus creatis regulatio motuum et operationum et tendentiarum in suos fines.” Opera omnia, vol. 3, ed. E. du Pin, “Definitiones terminorum ad theologiam moralem pertinentium,” coi. 107 A, coi. 108 A, coi. 108 C. GordonD. Kaufman’s effort to make Christian theology responsible for the modem ecological crisis, is - well-considered - a plea to return to a pre-nominalistic belief in a “divinized cosmos,” in which man is “embedded” : “The very ideas of God and man, as they have gradually been worked out over millennia, are so framed as to blur or even conceal man’s embeddedness in the natural order as we now are increasingly conceiving it. The great religious struggle between Israel and Canaan was over the question of the

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relative metaphysical importance of natural power and process on the one hand and personal moral will on the other. When Yahweh won that struggle it meant that the object of ultimate loyalty and devotion for men in the West would be conceived increasingly in terms of models rooted in man’s moral and personal experience, not in his sense of dependence upon and unity with the orders and processes of nature. Thus the very concept of God itself - as that concept has developed in the West - has built into it a depreciation of the metaphysical, and certainly the religious, significance of nature.” ‘A Problem for Theology; The Concept of Nature’, Harvard Theological Review 65 (1972), 337-336; 354 f. The confusion of historically heterogenous elements [e.g. depreciation of the metaphysical (!) and (!) certainly (!) the religious] is presented in an article which sets out to complain about too much historical research! “The great religious struggle between Israel and Canaan” is reflected both in Gen, 1:26 (man’s dominion over nature) and in Gen. 2:15 (man’s care and protection of nature). Francrs Bacon (fl626) perceptively points to vain curiosity as a threat to man’s proper use of nature: “Bacon feared that the new science would lead to a new hubris and a new fall, if it did not develop side by side with charity, for ‘knowledge puffs up, but charity edifies’ [I. Corinthians 8:1] ; to him the kingdom of man is closely tied up with the kingdom of God. The new science means the restoration of our dominion over nature which we have lost by our second fall ; it means a purification of the intellect from all its pride and misconceptions; it is a humble acceptance of what has been given in nature, ‘for the entering into the Kingdom of Man, founded on the Sciences, does not differ very much from the entering into the Kingdom of Heaven, where nobody can enter, except as a little child.’ Thus, Bacon’s divorce between science and theology was no divorce of science from religion. On the contrary, ths core of his prophetic message of the kingdom of man was his faith in the kingdom of God.” R. Hooykaas, op. cit., p. 69 f.

See, however, G. W. Coopland: “Of Oresme’s use of experience in the everyday sense little need be said; it is illustrated at every turn and furnishes the most attractive part of his work. It is evidently the result of wide interests and knowledge of his world, although in this connection, again, we discern that strange stopping short of closer and more searching enquiry demanded by modern standards. O f organised and controlled observation in the form of experiment we can find no trace.” Nicole Oresme and the Astrologers. A Study o f his Livre de divinacions (Cambridge, Mass., 1952), p. 35.

For the double function of imaginatio as “not fact” and as point of departure for inquiry, see Jean Buridan, as quoted by Pierre Duhem: “Et ideo sufficit eis accipere faciliorem imaginationem secundum quam, si esset vera, corpora caelestia moverentur tot motibus et talibus velocitatibus sicut nunc moventur, et non debent curare utrum sit ita in re sicut imaginantur. ... Sed de talis imaginationibus eorum et aliorum philosophus habet inquirere, quae sit vera et quae non. Le Système du monde. Vol. 4 (Paris, 1916), p. 138 f. For imaginatio as modus inveniendi loca planetarum, and therefore merely as calculatio à la Osiander see ibid., p. 146 f. Even the editors of Oresme’s Livre du ciel et du monde have not always differentiated between matter and method. “ Under these conditions, we may suppose that a ship could float on the surface of the sphere of air just as naturally as it would on the Seine River or on the surface of the sea (199d). This final ‘Ymagination’ in Oresme’s long critique of Aristotle’s De cae/o exhibits impressively the distance that separates the science of today from that of the 14th century.” Ed. cit., p. 30.

Jean Gerson uses for our ‘metacosm’ mundus archetypus: “Macrocosmus, est maior iste mundus exemplatus et productus a mundo archetypo Deo, continens in se universam creaturam, corporalem et spiritualem, ad ipsum Deum finaliter ordinatam. Micro-


cosmus, est minor quidem mundus, continens in se duplicem substantiam, corporalem scilicet et spiritualem Dei capacem, ad finem beatitudinis ordinatas.” Opera omnia. Vol. 3, ed. E. du Pin, “Definitiones terminorum ad theologiam moralem pertinentium,” coi. 107 B.81 See Anneliese Maier’s Addenda to the second edition of her Die Vorlaufer Galileis im l4 . Jahrhundert, Studien zur Naturphilosophie der Spatscholastik 1,2nd ed., (Roma, 1966), p. 315, and the comparison with Bradwardine’s view of the immensitas Dei, p. 315, note 1. Cf. John E. Murdoch: “U est remarquable qu’au Moyen Age, une telle spéculation sur l’infini se soit centrée sur le problème plus ancien, et en soi moins scientifique, de l’éternité du monde. Les raisonnements sur l’infini étaient initialement destinés à résoudre cette question plus traditionnelle. Au XlVe siècle, au contraire, dans beaucoup de cas, le problème de la possibilité d’un monde éternal était simplement devenu l’occasion de discuter des mystères de l’infini.” “ ‘Rationes Mathematice’, Un aspect du rapport des mathématiques et de la philosophie au Moyen Age.” = Conférence donnée au Palais de la Découverte de 4 Novembre 196L Histoire des Sciences (Université de Paris, 1962), p. 22.52 The significance of this “breakthrough of God” for Luther’s theology is described well by W. Elert, op. cit.. Vol. 1, p. 386 f.63 For Oresme’s fascination with the image of the clock see also Lynn Thorndike, op. cit.. Vol. 3, p. 441, note 1. For Jean Buridan - Oresme’s teacher also in this respect - see Quaestiones super libris quattuor de caelo et mundo; Liber II. qu. 22, ed. Ernest A. Moody (Cambridge, Mass., 1942), pp. 226-233.54 The wide spread of popular astrology is one of the many indications that the Arabian “myth screen” had not been sufficiently effective. See here Manfred Ullmann: “Die Deutungsmoglichkeiten der Planetenstellungen beruhen auf der Gleichsetzung der Planeten mit den Gottem, ein Vorgang, der sich seit dem 6. Jhdt. vor Chr., zunachst bei den Pythagoraern, dann im allgemeinen Sprachgebrauch, eingebürgert hatte. Alle Eigenschaften, Fâhigkeiten und Taten der Gotter, die in den Mythen ihren Niederschlag gefunden hatten, wurden nun mit den betreffenden Planeten assoziiert und ermoglichten es, die Konstellationen auszudeuten. Fiir die Araber und Muslime verloren die Namen der Planeten in der Übersetzung ihren Charakter als Gotternamen. Aber die Araber iibemahmen das komplizierte Gefiige der Deutungsmoglichkeiten, das ihnen ohne den antiken mythologischen Hintergrund ein rein mechanistisches, unerklarbares System bleiben musste.” Die Natur- und Geheimwissenschaften im Islam (Leiden, 1972), p. 348.55 Conversely, developments in the field of physics show effects on theology. After the Thomistic ontological relation between grace and movement, the new impetus-doctrine transforms “motion” and personalizes the concept of grace. We have pursued the history of theology and the history of the medieval sciences so long in separate departments that we stand only at the very beginning of seeing the interactions between shifts in these fields.5« “Et donques appert par ce que dit est que il ne s’ensuit pas se [= s i] Dieu est que le ciel soit et, par consequent, il ne s’ensuit pas que le mouvement du ciel soit, car selon vérité, tout ce depent de la volenté de Dieu franchement sanz ce que il soit aucune nécessité que II face ou produise telles choses ou ait faites et productes perpetuelment, si comme il fu plus a plain déclaré en la fin du XXXIVe chapitre du premier. Item, encore ne s’ensuit il pas se le ciel est que il soit meu, car si comme dit est. Dieu le meut ou fait mouver purement voluntairement. Et selon vérité, ce monstra II ou temps de Josué, quant le soleil se arresta par tant de temps comme dure un jour, car de ce dist l’Escripture: Et una dies facta est quasi due. Et est vraisemblable que lors cessa le

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mouvement journal de tout le ciel et des planetes et non pas le soleil seulement. Et pour ce disoit le Prophete en recitant ceste chose; Sol et luna steterunt in habitaculo suo, etc.” Nicole Oresme, Le Livre du ciel et du monde. Book II, 8. fol. 92 b; ed. cit., p. 364. Cf. Eccl. 46:5; Hab. 3:11.

“Or donques, posé que la terre fust meue avecques le ciel ou au contraire du mouvement du ciel, il ne s’ensuit pas que pour ce le / (92d) mouvement du ciel cessast. Et donques ce mouvement, quant est de soy, ne requiert pas de neccessité que la terre repose ou milieu. Item, ce n’est pas impossible que toute la terre soit meue d’autre mouvement ou d’autre maniéré : Job IXe : Qui commovet terram de loco suo,...” Nicole Oresme, Le Livre du ciel et du monde. Book II, 8. fol. 92 d; ed. cit., p. 366. Cf. Job 9:6.

Hardly more cautious is the explicit of a physics commentary. Quaestiones, assigned to Buridan: “Tu melius scribe, qui dixeris hoc fore vile / Si melius fuerit, plus tibi laudis erit!” Quoted by Pierre Duhem, Le Système du monde, op. cit.. Vol. 4, p. 132. The same desideratum from the inversed perspective is formulated by John Murdoch in his ‘Philosophy and the enterprise of science in the later Middle Ages’, The Interaction o f Science and Philosophy, ed. by Y. Elkana (Atlantic Highlands, N.J., 1974), pp. 51-74. 59 With all respect for my fellow country man, E. J. Dijksterhuis, who belongs to the pioneers in the history of science, I cannot share his view of Parisian nominalism. “Dat er in hunne werken van eenige verdere ontwikkeling der vruchtbare, maar nog geheel onontgonnen denkbeelden, die deze theorie bevatte, geen sprake is, typeert de deca- dentie, waarin de Scholastiek vervallen was ; toch waardeert men tenminste in de Parijsche philosophen van dezen tijd, dat ze althans het goede wisten te behouden, wanneer men in dezelfde periode de Italianen op mechanisch gebied ziet terugkeeren tot de te Parijs reeds lang overwonnen Aristotelisch-Averroistische dwalingen.” Fal en worp. Een Bijdrage tot de Geschiedenis der Mechanica van Aristoteles tot Newton (Groningen, 1924); Hoofdstuk II: Val en Worp in de Scholastiek, pp. 117-121 ; p. 118.

See, however, A. Koyré: “ ... personne, sauf Copernic, n’en a tiré une astronomie hélio-centrique. Pourquoi? Question oiseuse. Parce que personne, avant Copernic, n’a eu son génie. Et son courage. Ou peut-être, parce que, entre Ptolémée et Copernic, il n’y a eu personne qui fut à la fois astronome génial et pythagoricien convaincu.” Op. cit., p. 44.

“Quarto nunc primum accedam ad hoc opus, quod et tibi in mentem venit, ut hypothesibus artem astronomicam liberarem, solis contentus observationibus. Atque utinam haberemus omnium aetatum observationes idque iuxta nostras capiendi observationes rationes traditas, quas omnino iudico easdem esse, quibus primi artis indagatores usi sunt, et talem tablularum modum exquisiverimus, quod non perpetua opus haberent emendatione. ... Habeo etiam prae manibus novas de rerum natura philosophandi rationes, ex sola naturae contemplatione, onmibus antiquorum scriptis sepositis.” K. H. Burmeister, op. cit.. Vol. 3, p. 188. Cf.: “Gegen Ende seines Lebens versuchte Rheticus aus seinen reichen Erfahrungen als Astronom, Arzt und Chemiker ein neues philosophisches System aufzubauen, dessen Grundlage nur die Natur sein sollte: ‘ex sola naturae contemplatione’. Nur von daher, so schrieb er 1568 an Ramus, wolle er seine Naturphilosophie begründen. Er verzichte dabei auf aile Schriften der AUen. Diese Forderung hatte Rheticus, wie wir wissen, für Medizin, Astronomie und Astrologie ebenfalls aufgestellt.” K. H. Burmeister, op. cit.. Vol. 1, Humanist und Wegbereiter der modemen Naturwissenschaften (Wiesbaden, 1967), p. 173.

See the - in other respects - excellent study by Francis A. Yates, Giordano Bruno and the Hermetic Tradition, 2nd ed. (London, 1971), pp. 241-243. The Sun-analogies and Hermetic traditions - alluded to by Copernicus in his Preface - are certainly im-


portant characteristics of a movement we can trace from protohumanism (Richard de Bury’s library, used by Bradwardine and Holcot) to Pico and Reuchlin. See Eugenio Garin, Portraits from the Quattrocento, 2nd ed. (New York, 1972) pp. 145-149. Wayne Shumaker, The occult sciences in the Renaissance. A study in intellectual patterns. (Berkeley, 1972), pp. 201 flf; on the sun, ibid. p. 221. For a perspective on Copernicus’s discovery this tradition does not help us a step further. Here A. Koyré’s evaluation of the parallel case of Cusanus applies. See note 5. The ;?re-scientific and regressive impact of Renaissance “occultism” should be clearly seen. This should not be overlooked out of respect for the pre-modern ideal of comprehensive scholarship operative behind it. This perspective is particularly pertinent, since such claims continue to be advanced; “ Renaissance Hermeticism prepared the way emotionally for the acceptance of Copernicus’ revolutionized universal structure. In this case, then, scientific advance was spurred by the renewed interest in the magical Hermetic religion of the world.” Peter J. French, John Dee. The World o f an Elizabethan Magus (London, 1972), p. 103.

“ ...characteristic of all discoveries from which new sorts of phenomena emerge. Those characteristics include; the previous awareness of anomaly, the gradual and simultaneous emergence of both observational and conceptual recognition, and the consequent change of paradigm categories and procedures often accompanied by resistence.” Thomas S. Kuhn, The Structure o f Scientific Revolutions, 2nd ed. (Chicago- London, 1969), p. 63.64 And as Randall has shown, the Paduan Aristotelians a century later dominated the climate of thought with which Copernicus must have become familiar during his Italian study years. Cf. John Herman Randall, The School o f Padua and the Emergence o f Modem Science, Saggi e testi I (Padova, 1961), p. 24 f. ; p. 71 fF.«5 W . Jaeger, Paideia, op. cit., p. 220.6« There may not be much time left to adjust to the secular cosmos, since a postsecular cosmology is appearing on the intellectual horizon. Cf. Karl R. Popper; Thus we live in an open universe. We could not make this discovery before there was human knowledge. But once we have made the discovery there is no reason to think that the openness depends exclusively upon the existence of human knowledge. It is much more reasonable to reject all views of a closed universe - that of a causally as well as that of a probabilistically closed universe; thus rejecting the closed universe envisaged by Laplace, as well as the one envisaged by quantum mechanics. Our universe is partly causal, partly probabilistic, and partly open; it is emergent.” ‘Indeterminism is Not Enough’, Encounter 40 ( 1973), 20-26 ; 26.

D I S C U S S I O N

E. sylla : I am a little bit worried about the emphasis on the campaign apinst vain curiosity as something that may have led to Copernicus, and I tried to distinguish for myself various reasons why someone could be against intellectual endeavor or secular science. It seems to me that, for example, Lactantius, Augustine, the nominalists, and modem science represent four different reasons why one might criticize some kinds of intellectual activity. There is Lactantius, who really seems to be afraid of scientific discovery, believing that a person might hurt himself if he found out certain things. (“Curiosity killed the cat.”) There are some things that it is dangerous to know. I do not think he is very typical. Probably the most common position on vain curiosity is Augustme’s in the Confessions, the Enchiridion, and elsewhere where he says that

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science is perfectly good in itself, but it is not very important. The Christian doesn’t need to know how many stars there are, how many grains of sand there are, but it wouldn’t hurt him to know. If we had all the time in the world, all right. If you compare someone who, like Faustus, the Manichaean, is ignorant about astronomy, with someone who really knows astronomy, obviously it is better to know astronomy. Astronomy works, you can predict eclipses, and they happen as you say. But the Christian has more important things to do. So this view puts limits on science, but not because science has intrinsic limits, but just because it is not as important. And I think some of this is similar to the ideas of Bernard of Clairvaux, which Brian Stock talked about. Or Gerson. It is not really as anti-intellectual as Lactantius, but it is more pastoral, saying to people, “ let’s pay attention to the important things.”

H. OBERMAN : I don’t see the point of contention between us, because I brought in vana curiositas to try to interpret the immediate reaction of Luther in his Table Talk to Copernicus. Luther formulates his ideas in words that can only be understood once you have seen the whole medieval curiositas tradition. I think there is a consensus of scholarship that Lactantius is far more radical; he still thinks in terms of the apologetes. Augustine is already in a more relaxed situation. With Augustine there is a certain openness to scientia, although he warns of its spiritual dangers. There is an intensifica- cation of the warning in the Rule of Benedict, where curiositas is the first basis of superbia or pride. Then there is a warning that you should not look beyond the monastic walls or to science because it will lead you astray, scientia inflat, it will puff you up. We know that all too well : when you travel from campus to campus, you know that the words scientia inflat are very true! And then in the later Middle Ages, Gerson uses the expression in his famous sermon Contra vanam curiositatem to show that there are limits, and here he is completely right, there are limits for each faculty. The theologians should not feel that they can tell what physics should be, to do this they should become good physicists, and the logicians should not in their curiosity feel that they can plot the course of theology.

E. sylla : I think what bothered me was saying that being against vain curiosity is a typically nominalist position. Because the nominalists say let’s limit metaphysics, let’s limit theology, but at the same time they will be very committed to extending rational inquiry as far as it can go. If you take someone like Ockham or the more typical nominalists, they are not counselling a self-limitation upon rational inquiry; they are saying that each faculty should not trespass on the other faculties, but there isn’t a necessary limit within any faculty.

H. OBERMAN : I am in complete agreement with you. The nominalists are very keen on saying that you are curiosus when you try to penetrate the potentia absoluta Dei, and the theologians should stick to what God revealed about himself You should not go to Aristotle or to other sources, you should go to Scripture and the tradition of the Church So I think that the fight against curiosity is no longer anti-scientific, it is now used to show the limits of each faculty.

E. sylla : I don’t think that someone like Ockham would give a sermon against vain curiosity.

H. OBERMAN: I would love to find such a sermon by Ockham; I think that would be very revealing. But what Gerson did was to give a series of lectures in three weeks to the theological faculty warning against vain curiosity.

E. sylla : But I would claim that Gerson is not a typical nominalist, to the extent that he is doing that.

H. OBERMAN : There is quite a debate on Gerson’s nominalism. Combes shares your


view. I think that he has all the characteristics of a nominalist and the later nominalists always counted him in their list of “school saints.”

E. s y lla : In any case, I wanted to say that there are two things that are not necessarily always to be identified. Whereas I agree with you that the nominalists may be behind things like Copernicus, I am not so sure that sermons against vain curiosity ^ e of help; sometimes they are going to be allies, but they are not always going to be allies in producing something like what Copernicus is doing.

T. GREGORY: Sans doute il est vrai qu’il ne serait pas très justifié de considérer la polémique contra vanam curiositatem comme medieval obscurantism. Mais je ne voudrais pas qu’on aille à l’excès opposé, c’est-à-dire jusqu’à interpréter la polémique contra vanam curiositatem comme quelque chose qui peut préparer la méthode et les modèles fo r the coming era o f science. La polémique contra curiositatem dont tous soulignent les origines patristiques est toujours une polémique contre une science qui n’est pas finalisée vers la conversion spirituelle, n’est pas finalisée vers Dieu. Je me souviens d’un texte de S. Bonaventure, qui peut représenter un moment de cette tradition, lorsque, dans les Collationes in Hexaemeron, il dit: Salomon factus est curiosus et vanus, oblitus est sui. En d’autres mots, la curiosité c’est quelque chose qui porte à considérer les choses particulières et qui nous fait oublier Dieu, notre dernière et première pensée. Les textes que vous citez de Gerson et d’Erasme sont tout à fait dans la même tradition augustinienne, ils témoignent d’une polémique contre une science fin pour elle-même. Aussi, je ne vois pas comment on peut prendre cette polémique contre la curiosité comme un medieval obscurantism, pas plus que je ne puis considérer cette curiosité comme quelque chose qui va favoriser la naissance de la science moderne. Cette polémique que nous trouvons au XVIe siècle contra vanam curiositatem est tout à fait la même polémique augustinienne.

H. OBERMAN : As far as curiositas is concerned, there I tend to differ from you; vana curiositas becomes in the eleventh and twelfth centuries a single term; you no longer have to add the word ‘vana’ to characterize curiositas. For Gerson it is important to combat curiosity in the realm of theology, but its goal is to combat metaphysics. Its result, therefore, is to free physics from the claims of metaphysics.

You have for the first time with Brulifer, sometimes called “Scotellus,” and then with Luther - those are the two instances that I know of - texts where after centuries they speak again of the vana (or the mala) and bona curiositas. And at the moment when one can start to speak again about bona curiositas, then something very significant has happened. Because until that time you did not have to add the word vana. Curiositas was always to the detriment of yourself, implying, that is, that you are fragmented, you are going in all kinds of directions, and you lose yourself, and you therefore have to collect yourself, to get out of the disparateness of the outside world and find yourself and your strength. Curiositas was always that loss of internal substance. Now, what has happened, when for the first time one can talk again about bona curiositas, is that the investigation of this world is seen as useful. Thomas Aquinas solves the problem by distinguishing between curiositas and studiositas, but be leaves the word curiositas with the onus of being bad. Something has happened at the moment that you can talk about bona curiositas: the inner freedom to investigate the world.

B. stock : I would like to ask a question about Blumenberg’s Die Legitimitât der Neuzeit, which you quote and refute. One of the points Blumenberg goes into in detail is the question of curiositas in the Middle Ages. He makes a real contribution, I think Professor Oberman would agree. But do you realize that this paper was in part an answer to Blumenberg?

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H. OBERMAN : Accoiding to Blumenberg, the whole of the Middle Ages was engaged in a campaign contra curiositatem. He abbreviates it; and I point to the fact that it is a campaign contra vanam curiositatem, that you should take the qualification vanam seriously; that there were times when the two expressions were identical, but there were times when they were not. Blumenberg says that curiositas signifies the medieval scientific captivity (I put it now in my own terms), and that only with Copernicus are you freed from this. I wanted to show that akeady in the 15th century you see that there are other ways to deal with curiositas, that one is already seeing that though there is a dangerous curiositas, there is also a very productive curiositas, and that therefore the argument used by Blumenberg is not historically valid.

I think that the diflSculty of our discussion at the moment is that I have used the tradition concerning vain curiosity as a roimdabout way to help understand Luther’s first reaction. Another line of argument is that Osiander’s Preface is to be understood as nominalist, and that Copernicus is only to be understood on the basis of what I call the fertile crescent of new methods of inquiry into the world with experientia.

E. s ylla : All right, but then there is another reason why someone could be against excessive intellectual speculation which, I think, when you talk about experience and reality you seem to have in mind, and which I would identify as the viewpoint of Francis Bacon or of early modem science. It is the case in which you are against intellectual speculation because you want to have experience, to go to experiments, and be more empirical. And I don’t think that a nominalist, just because he is against over-extending theology into the natural realm, necessarily has experience as his alternative. The alternative may be giving demonstrable proofs, which would include reason, revelation, or experience, the three, but not so much concentration upon experience.

H. OBERMAN: After I had already worked for years with the distinction between potentia absoluta and potentia ordinata and had tried to pursue it in every new example, it appeared to me that there are different ways in which the dialectic of the two powers is applied in theology and in the area outside theology. In theology we know the truth because it is revealed. By the potentia absoluta we can imagine what other possibilities would have been available to God, which shows us the limits of our theological speculation about the given revelation. But in the rest of nature we do not really know what reality is. De potentia absoluta may there mean that whole realm that is not yet known to us, that we have still to penetrate. I am inclined to believe that there are a number of texts that one can only understand if one assumes that potentia ordinata refers to the course of the laws of nature as we already know them. Now we have to penetrate the potentia absoluta (as the not-yet-known) to enlarge that domain. Whereas in theology this would be impiety, it would be bona curiositas to want to enlarge the domain of the potentia ordinata and penetrate the unknown mysteries of God’s world; it is the task of the natural philosopher to do exactly this.

Now this leads also to a further preoccupation with the term imaginatio. Hitherto, John Murdoch has discussed if in papers of his. We can also refer to Curtis Wilson’s book on Heytesbury, w h e r e i s what we would translate as “sheer imagination” or “only imagination.” A quote from Wilson here: “ It is convenient to posit terms like ‘point’ and ‘instant’ - terms which the antiqui believed to stand for really existing indivisibles, but which actually refer to entities existing only secundum imaginationem - in order to avoid prolixity of speech.” Now, while Wilson shows the crucial role of imaginatio, he unfortunately restricts it to the realm of logic without pointing to its function as theoretical experiment on the bridge between logic and natural philosophy.So we can say that the importance of imaginatio in the scientific development of four


teenth century nominalists has perhaps not been sufficiently appreciated. There is a revealing definition by Pierre d’Ailly (who died in 1420, and it may be important for us to note that he belongs to the century after Ockham), which shows that Wilson’s interpretation of imaginatio can be right in some cases, but does not have to be right and is not appropriate if imaginatio is linked with apparentia. I shall read you this one text from his Sentence Commentary. “Dico quod imaginari multipliciter potest capi: Uno modo idem est quod mente concipere, et isto modo non solum vera sed etiam impossibilia et contradictoria possunt imaginari, quia non est aliud quam mente formare aliquam propositionem.” It seems to me that this is the interpretation that we have hitherto been dealing with. But now comes another interpretation: “Alio modo idem est quod mente formare aliquam propositionem cum apparentia quod ita sit.” (Petrus Alliacensis, Sent. I, q. 5 ad arg princip. 1 G G ; Strasbourg 1490, Reprint 1968, fol. k5r, col. 1.) And then he goes on to discuss the importance of apparentia and that, therefore, the imaginatio has to be oriented to apparentia. It seems to me that here we have another aspect of what one does per imaginationem; it is directed to some observations that one has made, but one tries now theoretically to devise and to forecast how experiments (now I am adding a lot of terms that do not occur in this immediate context) will work out. So, when related to the apparentia (that matters are as they are conceived), per imaginationem is not just sheer logical speculation but already stands on the borderline between the realms of logic and theoretical experiment.

In the realm of theology, the nominalists would want to insist that you have to base your arguments on revelation; in the realm of metaphysics they would say that people have been led astray, that there is no common opinion on matters of daily life, because they have been misled to become metaphysicians instead of physicists, to do metaphysics instead of physics, they have been dealing with general abstracts, and therefore they have not sufficiently analyzed the reality around them. So there are two ways in which the distinction between potentia absoluta and ordinata is used as a warning. In theology, one should stick to the business of interpreting Scripture and the tradition of the Church. On the other hand, those in other faculties should no longer read Aristotle, but should now actually analyze reality. They should start again cé ovo from the individual thing; that is the method W induction. On the basis of that, men develop or discover the natural laws that God put into this world. There, they are against intellectualism as speculation.

E. s ylla : But logic and mathematics are equally useful to them.J. MURDOCH: That is what bothers me, Heiko. Talking about fourteenth century

natural philosophy as such, I would think that experience or looking to nature, observation, plays very little role. Now what do we mean by an appeal to experience? It seems to me that there are about four or five things that can be meant and most of these are not really central (they may be permissible, they may occur from time to time in the fourteenth century in the central figures, but 1 do not think they are predominant). We can go back beyond the fourteenth century, we can worry about experimental procedure ; I think that this is just wrong, that it is not there. One confuses experimental procedure with a theory of experimental method and in their proper senses neither exists in the thirteenth century. So we can leave out experimental procedure and we can leave out theory of experimental method. But one might also maintain that what you mean by an appeal to experience is not an actual experiencing of anything, but rather simply a reference to the likes of “You know what such and such is, or you perfectly well know that experience gives this evidence or that evidence.” All right, that occurs. So does also the occasional implication that we should go out and observe something. But in

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most of the natural philosophy of the fourteenth century I don’t think that is important. What is significant (and here, I think, is where we meet) is the emphasis on cognitio intuitiva. Fine, all well and good; that is absolutely characteristic. But that is to develop an empiricist epistemology, which does not at all necessarily carry with it the necessity of basing science or building up science on observation, of appealing to experience. This being the case, I don’t think that we should be misled by the empiricist temper of the age, where the empiricist temper is specifically, or mostly, on the epistemological level.

E. sylla ; It is not only empiricism, but the desire for evidentness. “Show me, somehow.”

H. OBERMAN : May I try to answer John? In the field of theology it is a different kind of experience. There you have revelation, reason, and experience; there, “experience” has that other, more modern, connotation: something that you really have an inner feeling about. That is in the field of theology. Now outside the faculty of theology, for the astronomer, for example, it is quite clear that his field of experience is muchnarrower than in the other enterprises. Therefore, he has to work more with imaginatio, he has to conceive of theoretical solutions. He has to reach out for more experience.

In the field of theology experience helps lead to truth; in the field of natural philosophy, what it should do is to establish accuracy, to establish that what we observe in the world is understood by us. Assuming that this is a correct description of what takes place, Ockham is a reaction against a view of reality that talks about reality in abstractions and therefore separates us from reality. He wants to get back to it again. Therefore, the cognitio intuitiva. The way to marshall and discipline our minds is to apply logical propositions that we can check, on which we can really unite and after discussion come to the conclusion that they are true or not true. About the middle of the fourteenth century we get the next step in which the proposition is to be related to an outside truth. Only then have we marshalled and disciplined our minds, and brought back what Ockham wanted to reach, namely a clear conception of reality, to be sure by way of logic and the observation of the outside world together.

j. Mu r d o c h : I can bring you many examples of people - Swineshead, Bradwardine, all of these people - doing natural philosophy where observation or what “really is the case,” isn’t relevant to the issue. Where are these texts where what “really is the case” is relevant? I don’t want to say that there aren’t any, but it seems to me that they are very, very much in the minority. What works shall I look at and what examples will you point out to me? Most of the examples turn out to be secundum imaginationem examples where infinite this and infinitely small that are involved or some other circumstance that it would be impossible to observe.

H. OBERMAN : But where our discussion becomes most pertinent and sharp and revealing is at that point where secundum imaginationem thinking is no longer a theoretical, logical, mathematical device to train the mind; instead you want to relate it to the outside world on which it has to impinge and where it has to be verified, over and against apparentiae. Therefore, the d’Ailly quotation I cited is not so irrelevant. There is one kind of imaginatio that is sheerly theoretical. That seems to me to be the phase that you have been describing in the fourteenth century. With Bradwardine I am in precisely that climate of thought. But it seems to me there is something else that happens in the fourteenth century, and the next phase starts. The task that Oresme carries through is fantastic. He has already read in Buridan about the stick that you drop through the whole of the world and ask whether it would have different friction in the north than it would have in the south. We can laugh about it and ask how can you drop


a stick through the whole world? But the case is per imaginationem. It is a test that cannot be carried through, but it is already on its way to thinking how you could put different kinds of experience that you have had together and whether what you conclude would apply under all circumstances. It is not sheer imagination in the logical sense of the word.

j. MURDOCH: Oh, I think it is, because the most developed example of this is Swine- shead’s, isn’t it?

E. sylla : When you say in your paper that one use of imagination is to formulate hypotheses that will be confirmed by experiment, that does not apply here. They are not trying to formulate the case of dropping the stick through the center of the world in a way that could ever be realized experimentally.

J. MURDOCH: The secundum imaginationem element that is important in dropping the stick through the center of the world isn’t to imagine a hole in the world and dropping a stick at all. The secundum imaginationem element enters when it drops and one half passes the center and starts pushing it back the other way. How are you going to determine the relevant variations between the forces pushing it this way and the resistances pushing it back that way? To answer the question whether it ever gets to the center of the world, oscillates past it, and so on? Anyone can imagine dropping the stick through the world, but then to imagine how to apply Bradwardine’s law to the stick once I drop it - that requires more ingenuity.

H. OBERMAN: The diurnal rotation of the earth is discovered not because they already know it, but as a possibility, exactly by these tests per imaginationem. And only after we have conceived of this possibility, can we start to see whether it jibes with other elements. It is a theoretical reaching out for what cannot at the moment be verified, but it also makes very clear what is not yet verified. That is the point,

E, SYLLA : But they are not looking forward to checking their cases ; they are just trying to clarify their concepts,

s, victo r : There is no model of physical experiment that they could be planning these things for; it is only as an historian that you can see that the later development of experimental physics may have then proved the actual possibility of some of these things that were developed secundum imaginationem. But I don’t think even Copernicus looked for an empirical proof or suggested any things that might have served as empirical proofs of his theories.

H. OBERMAN: Oh yes, he felt that suddenly all the observations were falling into place and that he could explain them and that he actually had explained them.

GUY BEAUJOUAN

R É F L E X I O N S S U R LES

R A P P O R T S E N T R E T H É O R I E E T P R A T I Q U E

A U M O Y E N Â G E

Même s’ils ne sont pas marxistes, les historiens sont de plus en plus sensibles aux facteurs sociaux qui, dans toute civilisation, conditionnent les modalités de la vie culturelle. Pourtant, les travaux consacrés à l’histoire intellectuelle du Moyen Age semblent généralement peu enclins à cet engouement pour le social.

Certes, par vocation ou par une sorte de mimétisme, les spécialistes de la culture médiévale sont, encore aujourd’hui, plus volontiers “ conservateurs” que fascinés par les idéologies dites “ de gauche” . Mais, même s’il cessait d’en être ainsi, l ’histoire sociale de la pensée médiévale resterait extrêmement difficile au niveau même de la recherche érudite. ParticuUè- rement lancinante est, à cet égard, la question des rapports qui pouvaient exister, au Moyen Age, entre les connaissances théoriques et la vie réelle.

Ayant déjà pubUé, en 1957, une brochure intitulée Vinterdépendance entre la science scolastique et les techniques utilitaires^, je ne vais évidemment pas la resservir ici, mais, au contraire, essayer de réfléchir sur les orientations nouvelles qui semblent s’être dégagées, à ce sujet, depuis quinze ans. En un tel domaine, tout essai de bibliographie systématique est illusoire. Les pages qui vont suivre doivent donc beaucoup aux hasards de discussions avec des collègues, des élèves, des amis. Les principaux exemples ci-après retenus sont empruntés à mes propres recherches ou aux travaux qu’il m’a été donné de suivre dans le cadre du séminaire dont j ’ai la charge à la IVe section de l’Ecole pratique des Hautes Etudes.

QUELQUES REMARQUES GENERALES

On entrevoit désormais combien la société médiévale a profité des mutations techniques qu’ont amenées le brassage des ethnies, la résorption de l’esclavage, le déplacement vers le nord du centre de gravité du monde civiHsé, enfin, à partir du X le siècle, l’augmentation puis l’urbanisation croissante de la population. A la suite du hardi pionnier que fut Lefebvre des Noëttes, les synthèses de L. White^ et B. Gille^ présentent maintenant,

J. E. Murdoch and E. D. Sylla (eds.), The Cultural Context o f Medieval Learning, 437-484.All Rights Reserved.

438 G. BEAUJOUAN

aussi bien que possible, les grandes innovations médiévales antérieures au X lIIe siècle: étriers permettant la chevalerie de choc, attelage moderne, meilleure captation de l’énergie des rivières et du vent, adaptation des moulins à diverses activités industrielles, progrès dans la métallurgie du fer, labourages plus efficaces et rotation des cultures, transformation du métier à tisser et de la fabrication des draps, alourdissement des navires ronds du Nord et de l’Atlantique, passage du style roman au gothique, etc..., etc...

G. Duby'^ vient de fort brillamment caractériser le relatif dynamisme de cette période qui va de l’an mille à 1180: “ passage d’une économie fondée sur la guerre et le butin à une économie fondée sur l’agriculture” , avec par conséquent, en ce qui concerne notamment l’emploi des chevaux et des métaux, “ application retardée des outils de l’agression militaire aux travaux des champs” , avec aussi la magnificence pour la gloire de Dieu et le gaspillage des cours seigneuriales.

A de tels niveaux, il peut sembler vain de chercher des connexions symptomatiques entre pensée spéculative et travail manuel.

Un premier ordre de recherches consiste justement à préciser quelle fut, au Moyen Age, la place des techniques dans les diverses classifications des sciences et, plus généralement, quelle a été l’attitude de la scolastique à l’égard du travail et des arts mécaniques.

Bon nombre de textes sont commodément passés en revue dans Tassez récent ouvrage de P. Sternagel, Die '‘"artes mechanicae"' im Mittelalter: Begriffs- und Bedeutungsgeschichte bis zum Ende des 13. Jahrhmderts (Kallmünz, 1966). Faute cependant d’une bibliographie encore plus poussée, ce livre ne s’attarde guère aux controverses qu’ont pu susciter, parmi les érudits, certains des textes les plus importants,

Hugues de Saint-Victor occupe évidemment une place d’honneur pour avoir, dans son Didascalicon, fait de la “ mécanique” (c’est-à-dire de l’étude des techniques) l’une des quatre branches fondamentales de la philosophie. Bien que venant d’un mystique, une telle prise de position semble en rapport avec le développement économique et technique amorcé au X le siècle . Pourtant, contre M. Crombie et moi-même, le P* F. Alessio a fort brillamment contesté qu’il en fût ainsi®. Hugues de Saint-Victor a, en effet, une position moins personnelle qu’on ne croit: il s’inspire d’un passage du De civitate Dei de saint Augustin; or, ce dernier puisait dans le De natura deorum de Cicéron qui, lui-même, reflétait l’enseignement de

RAPPORTS ENTRE THÉORIE ET PRATIQUE 439

Posidonios et de Panetius. Pour Hugues de Saint-Victor, le travail des artisans tente d’imiter la Nature; la ratio des arts mécaniques est dès lors un moyen de comprendre la Création, donc une voie d’accès vers Dieu. Ceci paraît bien loin d’une conception de la science visant à augmenter l’emprise de l’homme sur le monde. L ’histoire des sciences est ainsi invitée à se méfier du risque d’anachronisme psychologique que, fatalement, pour les périodes anciennes, elle porte en elle.

Si, après bien des hésitations, l’on attribue à Hugues de Saint-Victor la Practica geometriae'^ connue sous son nom (vers 1125-1130), si même ce texte innove par la netteté de sa distinction entre théorie et pratique, il ne faut pas s’y tromper: les véritables préoccupations des Victorins n’allaient pas à l’arpentage, mais bien plutôt à la compréhension approfondie de divers passages de l’Ecriture^, tels ceux relatifs à l’arche de Noé (Hugues), au Tabernacle, au Temple de Salomon ou à la vision d’Ezechiel (Richard).

Encore faut-il se demander si, en prétendant découvrir là des relations numériques à valeur symbolique, les théologiens n’exerçaient pas une certaine influence encourageant des créations artistiques à structure mathématique.

Ceci conduit à un autre ordre de réflexions. Le problème de l’ interdépendance entre théorie et pratique s’est posé dès le haut Moyen Age, mais surtout dans un secteur assez particulier, celui des relations entre musicus et cantor.

Abstrait de la pratique musicale grecque, le traité de Boèce s’appUquait assez mal au plain chant grégorien; caractéristique est, à cet égard, le cas des “ tropes de hauteur” de la musique grecque abusivement assimilés aux huit “ modes” médiévaux des tonaires. Ainsi, pour les écoles du X le siècle, dans le domaine privilégié de la musique, la relation théorie-pratique n’était pas l’habituel rapport entre science et applications; elle se trouvait marquée par la volonté de concilier une théorie et une pratique qui, historiquement, n’étaient pas nées l’une pour l’autre. De là la foi, exceptionnelle pour l’époque, d’un Gui d’Arezzo quant au progrès: "'Usque in hunc diem ars paulatim crescendo convaluit...’’' . Pour Jean d’Afiligem (Cotto), au tout début du X lle siècle, le chantre sans formation musicale est comme un ivrogne qui parvient à rentrer chez lui, mais sans savoir par quelle rue il est passé: “ Cm/ ergo cantorem melius comparaverim quam ebrio qui domum quidem repetit, sed quo calle revertatur penitus ignorat)"^^. Et de citer Gui d’Arezzo:

440 G. BEAUJOUAN

“ iVûAw qui facit quod non sapit diffinitur bestia''^^.A la faveur d’un contexte philosophique imprégné de platonisme, la

musique a habitué les esprits au rôle éminent que doivent jouer les mathématiques dans le dialogue théorie-pratique. Les textes relatifs aux orgues et aux carillons sont, à cet égard, très intéressants^ .

La fonction du monocorde a, en cela, été capitale. Or, grâce justement aux instruments pédagogiques alors couramment employés (monocorde, rithmomachie, main, abaque, astrolabe, etc.), l’enseignement scientifique du X le siècle apparaît relativement concret^^, surtout si on le compare à la scolastique ultérieure.

Mieux aussi que plus tard les études universitaires, la vie monastique du haut moyen âge se prêtait à la conciliation de la culture intellectuelle avec le goût pour les techniques ou la création artistique: on pense, par exemple, au moine Oliva de Ripoll, à Eilmer de Mahnesburyi^ ou à Héze- lon de Clunyï®.

Une publication très récente permet de bien conndtre un cas analogue, celui du chroniqueur, canoniste et théologien Odorannus de Sens (mort peu après 1045). Non seulement il se consacre à la musique théorique et pratique (division du monocorde et tonaire), mais on le voit aussi s’intéresser à la géométrie et au symboUsme des nombres, travailler de ses propres mains pour construire un puits ou pour confectionner un crucifix et une châsse ®.

C ’est, peut-on dire, à la même lignée qu’appartiennent le moine Théophile, auteur du De diversis artibus, et même, au X lIIe siècle, le chroniqueur Matthew Paris dont les cartes et les dessins sont si passionnants à étudier!’.

Pour apprécier les liens existant au Moyen âge entre science et savoir- faire, il faut bien se garder de trop penser aux architectes et aux ingénieurs de la Renaissance. Envisagé dans un contexte authentiquement médiéval, le problème concerne au premier chef la musique, le symbolisme des nombres, l’alchimie, les cartes géographiques, l’illustration des manuscrits scientifiques, les instruments astronomiques et, bien sûr, la médecine. Pour ce qui est de cette dernière, theorica et practica sont nettement différenciées dans le Kitâb-al-mâlikî d’ ‘A lî ibn al-*Abbâs traduit en latin, dès avant 1085, par Constantin l’Africain (Pantegni) puis, en 1127, par Etienne d’Antioche (Regalis dispositio).

Le cas des premiers architectes et ingénieurs du Moyen Age latin est


assez difficile à appréhender. On connaît, dans l’Angleterre de la seconde moitié du X lle siècle un intéressant groupe d’architectes militaires appelés ingénieurs (par exemple, dès 1157-58, Ailnoth qui démantèlera, en 1174, les châteaux forts des rebelles; vers 1170, Richard l’ingénieur, “ v/> artificiosus et prudens architectus''; ou encore "''Mauricius ingeniator'' et "'Urricus ingeniator Regis''). En ce qui concerne la France, apparaît en 1182, dans une charte de l’abbaye poitevine de Nouaillé^^, un Petrus ingeniator". Comme l’ indique R. E. Latham^o, le mot ingeniator se trouve dans le Domesday Book^^ dès 1086, c’est-à-dire avant la grande époque des traductions arabo-latines. Uingeniator c’est celui qui, avec des machines de guerre généralement en bois {ingenia), prépare la défense ou l’attaque d’une place forte (il y a, pour dire cela, un verbe ingeniaré). Il reste à se demander si la mode de ce titre à'ingeniator est ou non en rapport avec la scientia ingeniorum ( ‘ilm al-hiyal) incluse dans la classification des sciences d’al-Fârâbï que vulgarisa, peu après 1150, Dominicus Gundi- salvi: ""Scientia vero ingeniorum docet modos excogitandi et adinveniendi qualiter, secundum numerum, corpora naturalia coaptentur per artificium aliquod, ad hoc ut usus quem querimus proveniat ex eis” ^ . Cette définition englobe à la fois l ’algèbre et la science des machines.

Dans son interprétation d’al-Fârâbï, Dominicus Gundisalvi trahit certes sa connaissance de Hugues de Saint-Victor; pourtant, selon ce courant nouveau d’origine arabe, le propos est tout différent. Il n’est plus question d’arts mécaniques plagiant la nature et servant donc à la comprendre; il s’agit bien de techniques appliquant des sciences théoriques en vue d’une certaine efficacité.

Avec sa subdivision de chaque branche en spéculative et active, la classification du savoir selon al-Fârâbi a surtout exercé une influence dans la mesure où, comme pour l’illustrer, les traducteurs ont révélé à l’Occi- dent chrétien de nouvelles sciences encore inconnues de lui au X le siècle (à commencer, pourrait-on dire, par la géométrie spéculative, naturellement aussi l’algèbre, l’optique, la statique etc.).

Mais c’est ici qu’intervient une sorte de paradoxe lié à la manière dont, aux X lle et X lIIe siècles, les moines ont renoncé à l’exercice de certaines activités en voie de professionnalisation comme la médecine^s et l’architecture^ . Bien sûr avec l’essor des universités à dominance théologique, juridique voire médicale, les connaissances d’origine livresque s’enrichirent et le parallélisme theorica-practica apparut cororne un lieu commun

442 G. BEAUJOUAN

au début de maints commentaires scolastiques. On peut se demander pourtant si, dans le cadre des Facultés universitaires, au Moyen Age comme plus récemment encore, les “ clercs” ne se coupaient pas un peu de la vie réelle. Ne devinrent-ils pas encore moins sensibles aux problèmes pratiques que ne l’étaient, fût-ce avec un bagage intellectuel plus limité, certaines fortes personnalités antérieures ou extérieures au système universitaire^s?

Au X lIIe siècle, la classification des arts mécaniques semble assez peu varier d’un texte à un autre, les différences de détail reflétant plus ou moins l ’environnement social de chaque auteur (importance, par exemple, de l ’architecture chez Vincent de Beauvais, du commerce et de la marine chez Raymond Lulle). Il serait bon que soient commodément regroupés et analysés de plus nombreux passages (même très courts) où des maîtres de la scolastique parlent incidemment des techniques. Sans un tel instrument de travail, les discussions risquent de rester assez académiques, celles notamment sur le rôle des franciscains.

Par leur sensibiUté à la Nature, par leurs voyages d’apostolat et de mission, par leur attention aux problèmes des gens du peuple, par aussi leur goût des mathématiques selon une certaine tradition augustinienne, les frères mineurs constituaient peut-être, dans la société des X lIIe, X lVe et XVe siècles, une sorte de levain favorable au progrès technique et aux découvertes. Il est loisible d’imaginer une trame continue entre l’enthousiasme de Roger Bacon pour Pierre de Maricourt et la protection dispensée à Christophe Colomb par le prieur de la Râbida^s.

Inutile de citer encore, tellement ils l’ont été souvent, les célèbres passages de Roger Bacon sur les possibilités attendues d’une ingénieuse ap- pUcation des sciences : ce sont là des professions de foi certes exceptionnelles pour l’époque, mais sans doute plus remarquables par leur ton que par leur contenu.

Comparées en effet à celles précédemment apparues au Moyen Age, les nouveautés techniques de la période 1190-1330 sont, peut-on dire, plus fines et donc plus immédiatement rattachables à la science de l’époque (boussole et magnétisme de Petrus Peregrinus; lunettes et optique; poudre à canon et alchimie pratique; horloges mécaniques et instruments astronomiques comme l’astrolabe ou l’équatoire). Mais plus encore que la question de leurs liens avec le savoir théorique, se pose le problème de la dépendance de ces nouveautés techniques vis-à-vis de leurs antécédents


chinois. Or, malgré les admirables travaux de Joseph Needham 7, l’historien ne parvient pas à bien reconnaître conunent s’est effectuée la transmission entre la Chine et la Chrétienté. On en est réduit à la notion de stimulus diffusion"' (des récits oraux de voyageurs poussant des bricoleurs occidentaux à réinventer ce qu’avaient déjà trouvé les Chinois).

Ceci est symptomatique d’un effarant contraste entre, d’une part, la richesse de nos sources d’information sur le moindre désaccord doctrinal au sein de la scolastique et, d’autre part, notre désarroi lorsqu’il faut situer dans leur véritable ambiance l’intérêt d’un Roger Bacon pour les techniques, les dessins d’ingénieur d’un Villard de Honnecourt ou l’arrivée des inventions chinoises en Occident. D ’un côté une foule de manuscrits soigneusement conservés; de l’autre, des conversations aussitôt envolées, des croquis généralement tracés sur la cire, le sablées ou le plâtre et, en tout cas, destinés à disparaître.

DES OBSCURITÉS LIÉES À LA TYPOLOGIE DES SOURCES

Pour ce qui est du Moyen Age, l ’historien des sciences travaille comme celui de la philosophie. L ’histoire des techniques est, au contraire, beaucoup plus proche de l’archéologie. On peut dès lors se demander si, avant de reprocher au Moyen Age un excessif cloisonnement social entre “ clercs” et praticiens, il ne faudrait pas d’abord constater un manque d’interdisciplinarité entre, d’une part, l ’histoire des idées et, d’autre part, celle de l’art, des découvertes maritimes voire de l’économie.

Lorsque des réseaux de tracés directeurs sophistiqués sont superposés à des photographies d’oeuvres d’art médiévales, lorsque sont attribués à des artistes du Moyen Age, y compris à Dante29, \q plus extravagant symbolisme des nombres, lorsque sont prêtées aux marins des X lVe et XVe siècles les méthodes nautiques du XVIe, lorsque l’alchimie donne heu aux plus journaUstiques divagations, l’érudit sérieux est irrité et tenté de condamner comme fantaisiste tout ce qui ne s’accorde pas avec les enseignements des manuscrits scientifiques de l’époque. Ce genre d’arguments, objecte-t-on, n’est pas décisif. En effet, à travers les oeuvres d’art et les performances techniques du Moyen Age, se manifesteraient des enseignements oraux et des savoir-faire transmis comme initiatiquement sous le sceau du secret, traditions et procédés dont il serait évidemment chimérique de chercher la divulgation dans des livres normaux.

444 G. BEAUJOUAN

Qu’il concerne la construction des cathédrales, les découvertes maritimes, l’art militaire, l’alchimie ou même certaines survivances du gnosticisme, le thème du “ secret” pourrait, à lui seul, faire l’objet d’un grand colloque. On y trouverait un complexe mélange de notions fort diverses: naturellement les secrets qu’exigent les affrontements militaires, diplomatiques ou économiques; les secrets corporatifs dont le contenu n’est pas obligatoirement d’ordre technique; la tradition hermétique propre à l’alchimie, mais aussi un cliché rhétorique lié à l’idée que la science est un trésor susceptible d’être caché et découver L ’historien risque, en tout cas, d’être inconsciemment influencé par une foule de notions non médiévales liées au mouvement rose-croix, à la franc-maçonnerie et même au romantisme.

Que cela soit ou non la conséquence de ce fameux secret, il est très difficile de correctement évaluer les connaissances théoriques qu’impliquent les capacités techniques du Moyen Age. Face à la grande abondance des textes scientifiques encore conservés, les documents vraiment techniques sont exceptiormels avant le XVe siècle et leur interprétation comporte souvent une considérable part de subjectivité.

Qu’il me soit permis de brièvement évoquer une petite recherche à laquelle je me suis naguère amusé^i.

La scène se passe en 1391 et la question se pose de savoir si la cathédrale de Milan doit être construite ad quadratum (c’est-à-dire aussi haute que large) ou ad triangulum. Dans cette seconde éventualité, quelle doit-être la hauteur d’un triangle équilatéral dont la base est de 16 unitates contenant chacune 8 quantitates^ soit un total de 96. Nous écririons

A = 96 X ^ = 83,136...

Telle n’était évidemment pas la façon d’opérer sur le chantier d’une cathédrale. Pour discuter donc avec les “ ingénieurs” , intervient un spécialiste, Gabriel Stornaloco "'expertus in arte geometriae... causa discutendi cum inzigneriis dictae fabricae...". Exemple presque unique d’un calcul médiéval appliqué à l’architecture, ce texte (dont l’original a malheureusement disparu) n’est plus aujourd’hui connu que grâce à sa publication par L. Beltrami en 1887.

X X V II'‘'‘radix de dcc mxx sesâra quia tregesime quod est aliquid minus de L X X X I I i r


A en croire le grand archéologue Erwin Panofsky, voici quel aurait été le sens de ce passage, h désignant la hauteur du triangle équilatéral de

base 96:

2 1010

~ 1 0 x - 2 7 [ = 4 0 5 ]

donc A < 84.

Il suffirait alors d’apporter une légère correctionD C DCC M X , X SESQUIALTERA X X V II...”

Sans entrer dans tous les arcanes de cette interprétation, retenons qu’elle revient à penser qu’on pouvait, au Moyen Age, calculer la hauteur d’un triangle équilatéral en prenant le double du dixième du huitième de la moitié de la base multiplié par 100 puis par 700 et divisé par 1010.

Il faut vraiment beaucoup croire à l ’ésotérisme de la tradition architecturale du Moyen Age pour imaginer que Stornaloco ait ainsi procédé et qu’il n’ait pas connu la formule alors très répandue selon laquelle, dans un triangle équilatéral, le rapport de la hauteur à la base est approximativement de 13/15, ahas 26/30.

Puisque Beltrami avait, pour ainsi dire, dessiné l’original sans le comprendre, point n’est besoin d’être grand paléographe pour restituer le

très mauvais latin:X X V I

"'‘de duccione in X X sesnarà’\ c’est-à-dire que la phrase entière peut se comprendre “ résultat provenant de la multiplication par 26; mais, en prenant le trentième, cela fait un

peu moins de 84” .

A = ?^[=83.2]<84

On voit à quel point les généralisations sont hasardeuses en ces matières: les documents sont trop peu nombreux et leur interprétation est trop différente selon la spécialité et les préjugés de l’interprétateur.

Le cas de Stornaloco n’est, du reste, pas caractéristique puisqu’il s’agit, non d’un “ ingénieur” ordinaire, mais d’un spécialiste, ""expertus in arte geometriae"^ intervenant à titre exceptionnel.

446 G. BEAUJOUAN

En ce qui concerne, à proprement parler, les architectes et maîtres maçons du Moyen Age, leur bagage scientifique vient d’être examiné dans deux publications raisonnables et bien documentées qu’on peut désormais retenir comme base de discussion: d’une part, un excellent article de L. R. Shelby, The Geometrical Knowledge o f Mediaeval Master Masons, dans Speculum, Al, n° 3 (juillet 1972), 395-421. D ’autre part, la toute nouvelle édition revue et augmentée du si stimulant ouvrage de Pierre du Colombier, Les chantiers des cathédrales (Paris, Picard, 1973). Sur l’essentiel, ces deux chercheurs arrivent, grosso modo, aux mêmes conclusions.

Si rares sont les documents vraiment révélateurs que, fatalement, on revient toujours aux mêmes. Pour le X lIIe siècle, le fameux recueil de Villard de Honnecourt; à l’aube de la Renaissance, Matthaus Roriczer32 avec sa Geometria deutsch (1487-88) et son petit livre sur la construction exacte des pinacles, Das Bûchlein von der Fialen Gerechtigkeit (1486). De même que, pour les dessins proprement techniques, B. Gille^^ admet une certaine continuité des carnets de Villard de Honnecourt au Bellifortis de Konrad Kyeser; de même peut-on voir en Roriczer l’enregistreur de la tradition gothique au moment oij elle va disparaître. Encore faut-il noter, avec L. R. Shelby, que la Geometria deutsch ne puise pas seulement dans l ’enseignement coutumier des maîtres-maçons, elle s’inspire aussi, non sans énormes contresens34, d’un texte latin analogue à l’anonyme De inquisicione capacitatis figurarum^^.

Il est tentant d’établir une distinction simpliste; parlerait latin la science tournée vers la philosophie; serait en langue vulgaire le savoir susceptible d’applications pratiques. Mais les choses sont, en réaUté, plus complexes. Il n’y a presque aucune parenté entre, d’une part, ce qui se trouve chez Villard de Honnecourt (magister 2), comme “ figures estraites de geometric” et, d’autre part, une géométrie pratique elle aussi en dialecte picard du X lIIe siècle (MS 2200 de la Bibliothèque Ste Geneviève). Cette dernière est, comme l’a découvert S. Victor^®, une adaptation du traité latin '‘‘‘Artis cuiuslibet consummatio..." et elle fait suite à une arithmétique en français qui, elle-même, démarque l’algorisme d’Alexandre de Villedieu. Les géométries pratiques en langue vulgaire se rattachent généralement aux traités de calcul, à l’héritage des agrimenseurs et souvent aussi à la pratique du quadrant. Tel, au contraire, qu’on peut l’entrevoir à travers Villard de Honnecourt et Roriczer, le bagage géométrique des maîtres- maçons exclut à la fois les démonstrations et les calculs; ses sortes de recet


tes se ramènent à des constructions de figures retenues davantage par l ’oeil que par l’esprit. Typique est (Figure 1) la façon dont se trouve visuaUsée, chez Roriczer, l’approximation de 7r = 3y

Un cas très curieux est, au fol. 20 de Villard de Honnecourt (magister 2), la spirale pour la taille des clefs de tiers et quint-point: la prudence s’impose cependant, car la très ingénieuse interprétation de Branner a été contestée®' .

Qu’englobait cette géométrie quasi artisanale et comportait-elle, en particulier, la connaissance de la “ proportion dorée” ? Si corporatif que fût ce savoir, n’a-t-il pas été enrichi grâce aux conversations de certains architectes médiévaux, comme Roriczer lui-même, avec des patrons cultivés détenant des livres de science?

Par la fascination à la fois mystique et artistique qu’il exerçait au Moyen Age38, par ses relations surtout avec le nombre d’or, le pentagone régulier fournit, à propos de ces deux questions, un exemplaire objet de recherche et de réflexion.

Que, pour un architecte médiéval, la construction d’un pentagone régulier constituât une sérieuse difficulté théorique et donc l’un des plus beaux fleurons de son savoir géométrique, cela apparaît bien à la manière dont procède Roriczer (Figure 2), d’une seule ouverture de compas, en partant de deux cercles égaux passant chacun par le centre de l’autre. Cette construction s’avère mathématiquement incorrecte, mais très approchée; elle est, du reste, bien connue pour avoir été reprise et vulgarisée par Albrecht Dürer^». Incontestablement le premier à publier cette astuce, Roriczer l’avait-il imaginée lui-même ou l’avait-il héritée de la tradition médiévale? Rien ne permet de dire, en tout cas, qu’il l’ait puisée à une source livresque.

Voici, à son propos, quelques observations d’une mathématicienne.

448 G. BEAUJOUAN

” •4 « ‘ ‘ÎS 5

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450 G. BEAUJOUAN

Mlle Debarnot, qui a bien voulu l’examiner pour nous. L ’étrange procédé de Roriczer dérive peut-être de la construction de l’hexagone régulier sur

trois cercles (Figure 3); si alors, pour réduire de 12° l’angle ABN, on pose/--S

le point K au cinquième de l’arc CN, les points F, E et K donnent l’illusion d’être alignés. Mais si, comme Roriczer, on obtient effectivement K en

prolongeant FE, l’angle AB K est supérieur d’environ 22 minutes aux 108 degrés que doit avoir l’angle du pentagone régulier^®. Le sommet du pentagone de Roriczer tombera dès lors à l’intérieur du cercle circonscrit, à une distance, il est vrai, inférieure au cinquantième du côté. Une si faible erreur était sans importance pour un artiste médiéval et, à supposer même qu’ il fût parvenu à la constater expérimentalement, il l’eût sans doute attribuée à une imprécision du tracé.

Comment par ailleurs imaginer que des artisans médiévaux n’aient jamais demandé à des clercs ce qu’enseignait Euclide à propos du pentagone?

Il semble, en tout cas, que certaines figures des Eléments étaient retenues pour elles-mêmes, à la manière de Villard de Honnecourt ou de Roriczer, c’est-à-dire comme des formules visualisées et débarrassées de toute démonstration. Les figures les plus frappantes pour l’oeil s’étaient, du reste, vu attribuer de pittoresques sobriquets comme, par exemple, le pont aux ânes (Elem. I, 5), la tunique de François {Elem. I, 47), la patte d’oie (Elem. III, 7) ou la queue de paon {Elem. III, 8) (Figure 4). Pour ce qui est de ces deux dernières dénominations (j>es anseris et cauda pavonis), on a autrefois cru qu’elles apparaissaient pour la première fois, en 1509, dans la révision des Eléments par Luca Pacioli, autrement dit chez un mathématicien de la Renaissance justement célèbre pour avoir vulgarisé la “ divine proportion” . En fait, ces noms de figures semblent issus d’une sorte d’argot scolaire médiéval. Le P* John Murdoch me signale, par exemple, la façon dont Bradwardine conclut, dans son De continuo, un raisonnement par l’absurde: “ circulus habet multa centra; pes anseris infirmatur, de cauda pavonis pulcherrime penne cadunt et tota geometria de speris et circuUs subvertetur” " !.

Dans le manuscrit 2085 de Salamanque, j ’ai découvert, il y a quelques années, une Mathematica due à un médecin toulousain du milieu du X lVe siècle, Philippus Elephantis Anglicus^^ Qq ^g te n’est pas encore publié, mais l’un de mes élèves, Paul Cattin, l’a transcrit et en a méticuleusement


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452 G. BEAUJOUAN

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retrouvé les sources^ . La partie géométrique s’inspire principalement des Eléments d’Euclide dans la version de Campanus. Philippe Eléphant indique les noms de diverses figures'* . Deux de ces appellations sont bien connues: la fameuse caudapavonis {Elem. III, 8) et aussi elefuga, “ la fuite des misérables” pour le pont aux ânes {Elem. I, 5). D ’autres dénominations semblent au contraire ne pas avoir été signalées jusqu’ici: Victoria (Elem. II, W), figura equatrix (Campanus VI, 9 = fig. Elem. VI, %), figura exemplaris (Campanus VI, 18=£’/ew. VI, 20), Faratra, c’est-à-dire pharetra (papéxpa le carquois {Elem. X III, 18) (Figures 5, 7, 8). Deux figures se rattachent à la quadrature du cercle : figura mediatrix [pour un cercle donné, aire de l’octogone régulier inscrit moyenne géométrique entre l’aire du carré inscrit et celle du carré circonscrit'^®] ou encore pax et concordia [quadrature du cercle proprement dite' ®] (Figure 6). Noter enfin la figura cotis [coj=pierre à aiguiser] pour diviser plus ou moins approximativement un angle dans une proportion donnée (Figure 5).

Mais revenons au pentagone régulier, car son tracé, chez Euclide, se trouve justement jalonné par deux des figures dont Philippe Eléphant révèle les surnoms et donc la célébrité au Moyen Age. Ainsi la construction du pentagone régulier {Elem. IV, 11) part, on le sait, du triangle isocèle “ qui a chacun des angles de la base double de l’angle restant” {Elem. IV, 10) (Figure 7). L ’ illustration de cette dernière proposition n’est pas très frappante pour l’oeil, elle se voit cependant attribuer un nom très remarquable: la figure de Démon ou de celui qui comprend, Demonis sive intelligentis. C ’est que, pour obtenir ce fameux triangle isocèle, il faut savoir diviser un segment de droite selon la section dorée, comme Euclide l ’a précédemment enseigné {Elem. II, 11): “ Couper une droite donnée de manière que le rectangle compris sous la droite entière et l’un des segments soit égal au carré du segment restant” . La figure donnant la solution de ce problème devait être populaire puisque, toujours d’après Philippe Eléphant, elle porte un nom triomphal: Victoria (Figure 7). La pharetra ou carquois fait également intervenir la section dorée pour déterminer l ’arète du dodécaèdre {Elem. X III, 18) (Figure 8). Commentateur du Timée de Platon, Philippe Eléphant était sans doute fasciné par la divine proportion, puisque plagiant avec quelques variantes Campanus X IV 10, il écrit: '‘Mirabilis itaque estpotencia linee secundum proporcionem habentem medium duoque extrema divise; cui cum plurima philosophantium admiracione digna conveniant, hoc precipuum ex suorum^’

454 G. BEAUJOUAN

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456 G.BEAUJOUAN

p partage be en moyenne et extrême raison

bp arête du dodécaèdre

Pharetra

Fig. 8.

principiorum invariabili natura producit ut tam diversa solida tum magnitudine, tum basium numero, tum etiam figura, irracionali quadam symphonia racionabiliter conciliet''.

Les considérations précédentes ne suffisent évidemment pas pour approuver ou condamner ceux qui croient retrouver dans l ’art médiéval le fameux partage “ en extrême et moyenne raison” . Largement répandue par les nombreuses copies des Eléments, la section dorée pouvait très bien s’être vulgarisée même chez des artistes ignorant le latin. Point n’est besoin d’avoir lu Euclide pour comprendre, si quelqu’un vous l’explique, le tracé d’un pentagone régulier. Il n’était pas nécessaire de posséder un coûteux manuscrit des Eléments pour retenir des constructions comme la Victoria ou la figura Demonis. Il n’est donc pas du tout invraisemblable que de telles figures aient eu une tradition propre^® analogue à celle qu’atteste, pour d’autres procédés, la géométrie allemande de Roriczer. On pourrait en dire autant de la figure par laquelle, au chap. 10 du livre I de VAlma- geste, Ptolémée donne très simplement les côtés du pentagone et du décagone réguliers inscrits (Figure 9); cette figure devait sembler remarquable puisque, par exemple, elle est reprise avec insistance par Abraham ibn Ezra^® et judicieusement utilisée dans la Practica geometric de Leonardo Fibonacci®®. On la trouve aussi interpolée après la figure illustrant la proposition II, 11 des Eléments d’Euclide^i.

RAPPORTS ENTRE THÉORIE ET PRATIQUE

b

457

d e = e g e b = e z

z d cote du décagone

b z côte du pentagone

Fig.9.

Il semble bien que cette figure se soit vulgarisée indépendamment du texte de Ptolémée, et ceci à un niveau si peu savant qu’on ait pu commettre l’erreur d’y prendre de triangle isocèle bez pour équilatéral. Une telle méprise est attestée, peu avant 1492, au fol. 13 de l’actuel manuscrit A de rinstitut52; “ Si un cercle a son centre placé sur le milieu de la base d’un triangle équilatéral et que sa circonférence passe par le sommet de l’angle supérieur, ce cercle contiendra nécessairement en lui cinq des bases du susdit triangle équilatéral” ®» (Figure 10).

458 G. BEAUJOUAN

De ce théorème assez grossièrement approximatif Léonard de Vinci tire, au fol. 17'" du même manuscrit, la construction suivante (Figure ll)^^;

Fig. 11.

cmn équilatéral tnr = rn nb==bc mb = ma

a, centre du cercle circonscrit au pentagone de côté mn

On trouve cependant ailleurs, dans ses notes, des formules assez dif- férentes^® jnais dont pareillement il conviendrait de déceler les antécédents médiévaux.

Les constructions d’Euclide et de Ptolémée partaient, en fin de compte, l’une et l’autre, de la section dorée: on objectera sans doute qu’un praticien comme Roriczer ne les connaissait pas puisqu’il préconisait un procédé tout différent et d’ailleurs erroné. Mais le problème, notons-le, n’était pas posé de la même façon puisque, chez Euclide et Ptolémée, c’est le cercle d’inscription qui était donné; c’est, en revanche, le côté du pentagone®® dans les exemples ci-dessus empruntés à Roriczer et à Léonard de Vinci.

Puisque les architectes et sculpteurs du Moyen Age n’assimilaient guère les formules numériques et les raisonnements de type euclidien, l’application de constructions géométriques apparemment savantes se réduisait souvent, semble-t-il, à la mise en oeuvre de quelques angles caractéristiques (par exemple 36° dans la construction du décagone ou du pentagone).

Cette importance de certains angles confère un tout spécial intérêt aux


recherches récemment consacrées à l’équerre. Principal instrument et presque emblème de l’architecture aux Xle, X lle et X lIIe siècles, l ’équerre est souvent représentée.

Or il faut bien faire, avec A. Sené, la constatation suivante: “ Les équerres romanes et du premier âge gothique se présentent comme de fausses équerres, c’est-à-dire qu’il leur manque le côté de l’hypoténuse, ce qui est parfaitement classique, mais les plus anciennes d’entre elles possèdent une particularité remarquable: leurs bras sont de largeurs inégales et, fait plus étrange encore, très souvent les bords n’en sont pas parallèles deux à deux: ils convergent et divergent créant un angle droit interne situé sur un axe différent de l’externe” . Il est bien possible en effet que, en plus naturellement de l’angle droit, ces équerres médiévales matérialisaient certains angles intéressants: 60 et 30° souvent; 54 et 36° parfois^?. B. G. Morgan et A. Sené ® croient que, par le non-parallélisme de leurs côtés internes, elles pouvaient aussi donner les angles d’or (58° 16' 51" et 31° 43' 03") c’est-à-dire les angles que forment avec la diagonale les côtés d’un rectangle obéissant à la divine proportion

y/5 + i = 1,618...

C’est en effet grosso modo le cas pour l’équerre de Liverpool dont les côtés rectangulaires intérieurs forment avec l’hypoténuse les fameux “ angles d’or” . Malheureusement ce remarquable instrument semble ne dater que du XVIIIe siècle. E. Maillard a pareillement lié à la mise en oeuvre du nombre d’or trois magnifiques instruments de la Renaissance (?) aujourd’hui conservés au Musée de Cluny à Paris^®: une équerre pliante, un niveau et une règle à fil à plomb. Mais tout ceci ne prouve rien en ce qui concerne le Moyen Age.

A Reims, en revanche, sur la tombe de l’architecte Hugues Libergier ( t après 1263), se trouve représentée une équerre dessinée, semble-t-il, en suivant les contours de celle effectivement possédée par le défunt maître. L ’hypoténuse forme avec les côtés intérieurs des angles de 31° 30' 10" et 58° 29' 50" (Figure 12), valeurs très proches, on le voit, de celles indiquées ci-dessus pour les angles d’or.

En fin de compte, et avec tous les aléas d’une telle méthode, c’est seulement en partant des proportions mesurées sur les monuments eux-mêmes qu’on peut discuter l’emploi, aux X lle et X lIIe siècles, de cette prétendue

460 G. BEAUJOUAN

Fig. 12. Tombe de Hugues Libergier. Reproduced by permission of the Liverpool University Press from B. G. Morgan, Canonic Design in English Medieval

Architecture, Liverpool, 1961.

équerre “ canonique” construite selon le nombre d’or*®. Personne n’a, du reste, encore montré comment matériellement, sur le terrain, de telles équerres auraient pu être utilisées à grande échelle. Détail étrange, l’une des cathètes est parfois représentée courbée, ce qui suggérerait l'emploi de tels instruments pour la taille des voussoirs et la construction des arcs


Fig. 13. Taille des voussoirs et construction d’un arc: utilisation des équerres à bords non parallèles d’après Shelby. Reproduced by permission of the Society for the History

of Technology and the author from Lon R. Shelby, ‘Medieval Masons’Tools II, Compass and Square’, Technology and Culture 6 (1965).

d’ogive (Figure 13). C’est alors le rayon de courbure et non plus le nombre d’or qui expliquerait la divergence des côtés interne et externe de certaines équerres«i.

Il semble que ces bizarres équerres tombèrent en désuétude au fur et à mesure que le compas s’imposa entre les mains d’artistes moins inexperts en géométrie. Mais ici encore que de pièges pour l’historien! Revenons un instant sur la tombe de Hugues Libergier (seconde moitié du X lIIe s.): près de l’équerre susmentionnée, se trouve représenté un compas. Selon O. von Simson®2 “ this proportion compass seems to be based on the golden section” . En réalité, ce compas n’est pas basé sur la section dorée pour cette excellente raison que, comme l’a montré Pierre Du Colombier®^, ce n’est pas un compas de réduction, mais un compas à branches croisées (Figure 14).

462 G. BEAUJOUAN

Dans une progression géométrique ayant pour raison le nombre d’Or, chacun des termes est égal à la somme des deux précédents: il y a donc là une série dite de Fibonacci. Le nom du célèbre mathématicien pisan se trouve ainsi fréquemment invoqué pour garantir l’intérêt prétendûment porté au nombre d’Or par les architectes du X lIIe siècle. Comment ne pas constater, à cette occasion, les dangers de l’à-peu-près et des rapprochements hâtifs?

Chacun sait que, dans son Liber abbaci (1202,1228), Leonardo Fibonacci calcule la progéniture d’un couple de lapins®* selon la célèbre série récurrente 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377... Dans son récent petit livre, par ailleurs excellent, sur le nombre d’or, M. Cleyet-Michaud®® ajoute comme une chose bien connue: “ Désireux d’en savoir davantage, Fibonacci eut l ’ingénieuse idée de comparer deux termes consécutifs de la série en question, c’est-à-dire, pour être plus précis, d’étudier comment se comporte le rapport M(„+d/w„. Cette idée devait le conduire au nombre d’or” . En effet, dès le rapport 89/55, apparaît le nombre d’or 1.618 avec trois décimales exactes.

Malheureusement, loin d’éclairer l’histoire de l’art, tout ceci ne fait que l ’égarer. Il suffit, pour s’en convaincre, de relire de Liber abbaci: Fibonacci n’y calcule les termes de sa série que par une succession d’additions. Il ne

RAPPORTS ENTRE THÉORIE ET PRATIQUE

donne nulle part l’équivalent de la formule

463

1Un = -7='

1 + V 5 \ " / 1 - V 5

■ - (

Il n’envisage pas, non plus, que le rapport de deux termes consécutifs tende vers le nombre d’or (1 +^5)/2. C ’est qu’on en est venu à donner comme de Fibonacci lui-même les considérations d’arithmétique supérieure exposées, à son propos, par E. Lucas®®. Ce dernier pourtant attribue expressément au XVIIe siècle, nommément à Albert Girard (1595- 1632), la découverte du lien entre le nombre d’or et la série de Fibonacci®'^,

Fibonacci a cependant parfaitement connu les propositions d’Euclide et de Ptolémée sur le pentagone et l’hexagone réguliers. Comme par exemple Abù Kâmil®®, il les a utilisées pour résoudre par l’algèbre divers problèmes de géométrie, et ceci en deux endroits de sa Practica geometrie^^ : aucun recoupement, du reste, avec la progéniture du couple de lapins.

Si, changeant complètement d’horizon, nous quittons les chantiers des cathédrales pour étudier les navigations annonciatrices des grandes découvertes maritimes, nous retrouvons les mêmes problèmes de méthode: la même difficulté à harmoniser sciences et techniques; les mêmes incertitudes de l’historien face au secret; la même difficulté à suivre des traditions orales (ou de métier) dont seuls d’exceptionnels affleurements apparaissent dans la documentation écrite; les mêmes efforts enfin de quelques érudits ingénieux pour imaginer, grâce aux instruments et aux cartes ou à l ’aide de manuels tardifs, des procédés restés curieusement absents du savoir livresque médiéval.

Plusieurs colloques et d’assez nombreux travaux ont, ces quinze dernières années, sensiblement éclairé les conditions dans lesquelles, malgré sa finalité essentiellement astrologique, l’astronomie médiévale fut mise au service de l’art nautique.

Certes, dès lors qu’ils utiUsaient des cartes nautiques à lignes de rhumb tracées en fonction de la boussole, les marins du X lVe siècle étaient susceptibles de recourir à certaines méthodes scientifiques (cf. Raymond Lulle à propos du nocturlabe ou des élémentaires tables trigonométriques bientôt dites de marteloioy^.

En simplifiant un peu, et sous réserve de deux ou trois textes controversés, on peut dire que l’astronomie nautique a vu le jour, au Portugal, durant la décennie 1480-1490. Elle n’est pas le fruit d’une plus grande

464 G. BEAUJOUAN

précision des tables astronomiques'^^, ni même d’un brusque rapprochement entre astronomie et marine. Elle fait partie d’un vaste effort d’organisation et même, pourrait-on dire, d’une véritable politique scientifique orchestrée par Jean II, le “ prince parfait” (relevés de latitudes, mise en service de grands astrolabes en bois, vulgarisation scientifico-technique annonçant les futurs manuels nautiques, missions terrestres par Aden pour préparer l ’aboutissement vers l’ Inde des navigations le long des côtes occidentales de l’Afrique, etc.).

Sans doute ne faut-il pas trop considérer comme une institution établie la fameuse de savants juifs et chrétiens à qui le roi confiait l ’examen des questions scientifiques touchant les découvertes maritimes. Il y a là cependant, sans doute pour la première fois dans l’histoire, un effort cohérent pour mettre la science au service d’une grande entreprise nationale, avec ses énormes c o n s é q u e n c e s ’ ^^

Pour la période antérieure à ce tournant décisif des années 1480-1490, les liens entre astronomie et navigation restent incertains, mais l’attitude actuelle des chercheurs, face à ce problème, est très symptomatique.

Les deux positions extrêmes sont simples. Beaucoup d’historiens des sciences constatent que, malgré le grand nombre des traités consacrés aux instruments astronomiques et malgré l’insistance quasi-publicitaire de ces textes sur les moindres usages des dits instruments, la littérature scientifique ne décrit pas l’utilisation nautique du quadrant ou de l’astrolabe avant la fin du XVe siècle. L ’emploi de tels instruments s’accorde, du reste, fort mal avec l’utilisation de la carte-portulan à rhumbs magnétiques. A l’inverse, divers marins-historiens (Portugais le plus souvent) soulignent avec raison la fréquence des voyages aux Açores à partir de 1427 et la quasi-impossibilité de repérer ces îles sans un rudiment d’astronomie nautique: le silence des textes s’expliquerait par la “ politique du secret” .

Entre ces deux positions radicalement opposées, d’intéressants efforts de conciliation ont été récemment tentés’ . Les érudits reconnaissent de plus en plus les limites de ce qu’ils peuvent attendre de la documentation écrite. D ’autre part, bien que les astronomes ou astrologues médiévaux fussent couramment capables de déterminer à terre la latitude géographique, les historiens de la marine commencent à admettre que, si une astronomie nautique a dû exister avant 1480, elle ne pouvait pas consister à prendre en mer la latitude avec un astrolabe ou un quadrant pour la reporter sur une carte.


On s’est dès lors demandé si, dans la Httérature nautique de la Renaissance, certains détails jusque là négUgés pour leur bizarrerie n’étaient pas, en réalité, des survivances de procédés archaïques.

En 1551, par exemple, Martin Cortés révèle que, sur les cartes-portulans sans parallèles ni indications de latitudes, la distance entre le cap de Sâo Vicente (Portugal) et la plus grande des îles Berlenga indique tacitement une différence de trois degrés. On ne trouve antérieurement aucune mention de cette convention. Pour vérifier cependant si elle était déjà admise à la fin du Moyen Age, R. Laguarda Trias a, sur diverses cartes nautiques des X lVe et XVe siècles, mesuré et, grâce à l’échelle, évalué en milles cette distance Sâo Vicente-Berlenga prétendument indicatrice de trois degrés. A en croire Laguarda Trias, les résultats obtenus ne sont pas quelconques: on verrait ainsi s’imposer implicitement dans les cartes nautiques, à partir de 1327, le degré de 56 milles 2/3 selon al-Farghânï ou Sacrobosco, et ensuite, à partir de 1424, le degré de 66 milles 2/3 commechez al-Çasan al-Marràkushi'^^,

Bien qu’essentiellement faites pour la navigation à l’estime, les cartes- portulans auraient donc permis un approximatif contrôle des distances grâce aux différences de latitude.

Tant que des tables de déclinaison solaire n’étaient pas vulgarisées parmi eux, les marins du XVe siècle ne pouvaient pas, de jour, utiliser profitablement le quadrant. De nuit, les choses étaient tout aussi compliquées puisque, à l’époque, l ’étoile polaire se trouvait à environ trois degrés et demi du pôle.

En combinant, d’une part, une difficile citation de Diogo Gomes se rapportant aux années 1456-1462 et, d’autre part, une note seulement publiée en 1565 mais reflétant sans doute une tradition ancienne, E. G. R. Taylor et A. Teixeira da Mota ont proposé une curieuse théorie.

Les navigateurs du XVe siècle n’auraient donc pas cherché à savoir la valeur absolue de leur latitude comme pour faire le point; ils se seraient contentés de demander au quadrant de leur fournir les différences de latitude entre divers Ueux d’observation, ce qui était évidenmient très facile à condition de viser la même étoile circumpolaire dans une position convenue de la Petite Ourse. En marquant sur le limbe de l’ instrument les positions successives du fil à plomb lors d’une série de telles observations le long de la côte occidentale de l’Afrique, on constituait un utile moyen de contrôler sa route lors d’une expédition ultérieure (Figure 15).

466 G. BEAUJOUAN

Tout ceci est bien différent de ce que professaient les traités de quadrant plus ou moins liés à l’enseignement des universités médiévales (celui de Robertus Anglicus, par exemple). En revanche, cette manière de se placer en latitude n’est pas sans rappeler les procédés employés par les navigateurs arabes dans l’Océan Indien'^s.

Il est, à première vue, bien difficile d’admettre une quelconque parenté entre l ’art nautique de l’Océan Indien et celui de l’Atlantique avant que les Portugais n’aient atteint le Cap de Bonne-Espérance. Cette bizarre suggestion réapparaît pourtant à propos d’une question fort délicate, celle des mesures linéaires employées pour caractériser des angles'^®.

Lorsque, en juin 1455, Alvise de Cadamosto se trouve à l’embouchure de la Gambie, à 13° 30' de latitude Nord, il trouve que la Tramontane s’élève au-dessus de la mer la hauteur d'une lance. Quand, en 1462, Pedro de Sintra est à l’île Shenge, à 7° 55' de latitude Nord, il note l’étoile polaire “ à la hauteur d'un homme sur la mer” . Ces textes ont fourni les arguments les plus contraires pour soutenir, soit l’existence d’une véritable astronomie nautique dès cette époque, soit à l’inverse la crasse ignorance des premiers découvreurs.

Or, dans son célèbre Conciliator (dif. LX V II) Pierre d’Abano fait état d’une conversation au cours de laquelle Marco Polo lui aurait dit s’être trouvé dans l’hémisphère sud là où le pôle antarctique s’élève à plus d’une alnce de soldat {polum antarcticum a terra elevatum quantitate lancee militis longe in apparentiay^. Dans le livre même de Marco Polo, la lance


n’est jamais employée comme mesure angulaire; c’est cependant en une autre unité linéaire (la goue=coudée) qu’y est évaluée la hauteur croissante de la Tramontane au fur et à mesure que le voyageur remonte de l ’équateur vers le nord. D ’une façon assez voisine, Jourdain de Sévérac, voyageant vers 1324-1327 également en Inde, indique la hauteur de la Tramontane en doigts (sans doute l’isba* arabe couramment utilisé, dans rOcéan Indien, pour la hauteur des étoiles, comme le montrent, par exemple, les instructions nautiques d’Ibn Mâdjid, le célèbre pilote arabe

de Vasco da Gama).Une telle manière d’apprécier les angles est, semble-t-il, complètement

étrangère à la, pourtant si abondante, littérature astronomique du Moyen Age latin. On la trouve, au contraire, dès le Xe siècle, dans le célèbre livre de ‘Abd al-Rahmân al-Sûfï sur les constellations’ ». Pour indiquer les distances angulaires entre étoiles y apparaissent la lance (rumh), la stature d’un homme (qâmat al-insân), la coudée (dhirâ*), l ’empan (shibr), le doigt

(isba‘).Distance entre a Andromedae et y Pegasi, la lance aurait valu 14° (six

coudées de 2° 20' chacune), ce qui s’accorde assez bien avec le texte de Cadamosto sur la Tramontane haute d’une lance à 13° 30' de latitude

Nord’ 9.Le Dr Paul Kunitzsch connaît mieux que personne les tables d’étoiles

du Moyen Age islamique. Je l’ai donc consulté sur ces curieuses mesures d’angles : sa réponse mérite ici réflexion. Qu’elles soient arabes ou occidentales, observe-t-il, les tables médiévales d’étoiles fixes fournissent les coordonnées, toujours en degrés et minutes, jamais en mesures linéaires. Le livre d’al-Süfï ne fait qu’apparemment exception. Pour chacune des 48 constellations ptoloméennes, il comporte en effet quatre sections.

1° discussion sur les étoiles de la constellation.2° excursus sur la nomenclature purement arabe de certaines étoiles.3° deux figures de la constellation vue comme au ciel et comme sur un

globe céleste.4° table des étoiles comprises dans la constellation.C ’est seulement dans la première de ces quatre sections qu’al-$ùfï

emploie des mesures angulaires du type lance, stature d’un homme, coudée, empan, doigt. Il semble en cela, ajoute P. Kunitzsch, se conformer à l’astronomie populaire arabe indigène, celle des Bédouins, telle qu’elle s’exprimait, par exemple, dans les livres d’al-anwâ*.

468 G. BEAUJOUAN

On assiste donc ici à la peu fréquente juxtaposition d’un savoir évidemment livresque et d’une science populaire normalement transmise de bouche à oreille. Cette tradition orale échappe presque complètement à l ’historien, mais c’est surtout à elle que se rattachent les instructions nautiques arabes en vers dont on conserve les mises par écrit au XVIe siècle. Ibn Mâjid ne déclare-t-il pas lui-même que “ la meilleure description de la mer se fait oralement” ?so.

En histoire des techniques, les secteurs où prévalent ainsi les traditions orales sont souvent ceux où se produisent d’intéressants échanges entre civilisations différentes: ceci sans que, naturellement, aucune traduction de texte n’intervienne. Dans de tels cas, l’étude de la métrologie pourrait beaucoup nous apprendre; malheureusement, il s’agit là d’un domaine aride, difficile et encore fort mal exploré.

A propos, par exemple, des mesures d’angles qui viennent d’être évoquées, bien des questions se prêteraient à de longues discussions. Les coudées médiévales ont-elles une parenté avec le coude astronomique grec généralement évalué à 2°? S’il faut attribuer une valuer de 1° 36' (360/ 224) à l’isba* (doigt) des navigateurs arabes de l’Océan Indien du XVe siècle, il y a là, selon J. Needham, une frappante ressemblance avec le chih des marins chinois qui fréquentaient les mêmes eaux® , du reste le chih se subdivisait en 8 chio, comme l ’içba* en 8 zam. Mais la valeur de l ’i|ba* n’est pas tout à fait la même selon les diverses données (mathématiques, astronomiques ou géographiques) qui peuvent servir à la fixer® : il n’est pas facile de discerner quelle était la définition originelle, à supposer qu’il y en eût une.

A ce casse-tête métrologique se rattachent des discussions, elles aussi fort délicates, sur les liens possibles entre la dioptre grecque, le kamal de rOcéan Indien et le bâton de Jacob ou arbalestrille. Ce dernier instrument fut révélé aux astronomes occidentaux par le grand savant juif Levi ben Gerson (1288-1344) qui, selon B. Goldstein®^, en serait bien l’inventeur. Mais Laguarda Trias se demande s’il n’y a pas là un écho des méthodes pratiquées dans les régions de faible latitude comme l’Océan Indien®"*. On ne pourra se faire une idée à ce sujet que lorsque le Goldstein aura publié l’important travail qu’il prépare actuellement sur Levi ben Gerson. Une fois de plus, la question des rapports entre théorie et pratique débouche sur celle des relations entre théorie et expérience ou observation.


ORIENTATIONS POUR LA RECHERCHE

On ne fait guère progresser l’étude de la pensée médiévale en y adjoignant de vagues considérations sociales. D ’autre part, l ’histoire des techniques est encore, pour le Moyen Age, une discipline si difficile et si incertaine qu’on ne saurait, sans risques, philosopher de seconde main sur ses résultats les plus récents: il faut préalablement vérifier comment, par qui et d’après quoi, ces prétendus résultats ont été obtenus. Il a été montré ci- dessus avec quelle circonspection il convient de manier, par exemple, les données relatives à l ’architecture et à la navigation.

Les rapports entre théorie et pratique se prêtent donc mal à des recherches systématiques où se puissent engager des médiévistes débutants: trop grande y est la part des polémiques, des rapprochements fortuits, des trouvailles faites par hasard sur des détails apparemment minimes.

Il est certes des secteurs dont l’exploration place l’érudit tout près de la frontière entre théorie et pratique®®: par exemple les arithmétiques conunerciales qui permettent de comparer l’enseignement des universités et celui destiné aux futurs marchands ; la géométrie pratique®® sous réserve de ce qui a été dit plus haut; bien sûr la chasse, l’hippiatrie, la chirurgie, les réceptaires, les carnets d’ingénieurs du XVe siècle; les instruments astronomiques et les horloges aussi.

A ce propos, certains historiens ont du mal à comprendre que les horloges mécaniques aient été des instruments astronomiques de prestige avant de devenir des machines à rythmer la vie sociale®’ . C ’est ainsi souvent par le biais de l’astrologie (donc des instruments astronomiques, y compris les horloges) que, aux X lVe et XVe siècles, des médecins en sont venus à valablement s’intéresser aux techniques®®.

Même si elle est moins révélatrice qu’on ne le pense généralement, la comparaison entre science latine et savoir en langue vulgaire a une certaine signification sociale. On peut en dire autant des raisons qui semblent avoir induit les premiers imprimeurs à publier (ou à négliger) tels ou tels traités scientifiques®®.

L ’histoire de certains mots témoigne excellemment des échanges entre la pensée spéculative et la vie réelle: nous l’avons vu à propos d'ingenium et de ses dérivés. Encore convient-il que la recherche ne s’enferme pas a priori dans le vocabulaire purement philosophique voire scientifique.

S’il reste beaucoup de documents à découvrir et de textes à publier, il

470 G. BEAUJOUAN

semble aussi souhaitable que, surmontant l’obsession d’une sorte de perfection formelle, les meilleurs médiévistes ne se cloisonnent pas dans des spécialités trop étroites. Bien des documents connus peuvent ainsi être réexaminés dans un esprit plus compréhensif. Que de connexions à établir, par exemple, entre l’alchimie et la numismatique, entre les recettes des manuscrits et les examens de vestiges archéologiques en laboratoire, entre les fascinantes cartes géographiques du Moyen Age et toutes sortes d’autres domaines.

Un gigantesque et déUcat travail reste à faire sur les recettes: on a trop tendance à les considérer comme “ populaires” voire “ folkloriques” , surtout lorsqu’elles sont en langue vulgaire. En réaUté, beaucoup d’entre elles proviennent d’ouvrages savants. Il est malaisé de vérifier si une recette, apparemment nouvelle, dérive de l’expérience ou si elle remanie, pour des raisons a priori, une recette antérieure (typique est le cas des ingrédients rares et coûteux remplacés par des produits faciles à trouver).

Il est un autre secteur insuffisamment exploré: c’est celui des illustrations de manuscrits scientifiques. N ’insistons pas ici sur les problèmes que peut poser la fiUation des enluminures par rapport à un stemma codicum naturellement établi d’après les accidents du texte: qu’on pense, par exemple, aux mappemondes dites de Beatus® ou encore aux herbiers français du XVe siècle actuellement étudiés par Mlle Opsomer. Mais une fois connue l’image originale, reste à retrouver si elle copie un modèle antique ou oriental, si elle s’inspire d’un autre ouvrage médiéval, si elle illustre littéralement le texte ou si elle apporte un témoignage visuel sur la réalité.

La réponse à ces questions est souvent fort délicate. Voici, par exemple, l ’éléphant que Matthew Paris prétend représenter d’après nature ^Hpso elephante exemplariter assistente'’ ; l ’animal est si raide qu’on le dirait en bois. La contradiction n’est qu’apparente, car l’auteur croyait, d’ailleurs à tort, que la patte d’un éléphant ne comportait aucune arti- culation®!.

Il y a même, chez Villard de Honnecourt, le dessin d’un lion dont on nous dit:” saciés bien qu’il fu contefais al v if” ... et pourtant il a une face humaine. Cependant, dans l’album de ce même Villard de Honnecourt, se trouve une recette fort valable pour conserver leurs couleurs naturelles aux fleurs d’un herbier. Des préoccupations de ce genre n’apparaîtront, semble-t-il, qu’au début du XVIIe siècle dans la littérature proprement


botanique®^. Donc, une fois de plus, Villard de Honnecourt témoigne d’un savoir pratique qu’on chercherait en vain dans les livres de l’époque, en l’occurrence ceux destinés aux médecins et aux apothicaires du Moyen Age.

Pratique, observation et expérience sont indissolublement Uées. C ’est pourquoi il est si passionnant de voir progressivement se réveiller, au Moyen Age, l’aptitude à traduire par un dessin une idée ou une réalité® . Les plans et cartes terrestres présentent, à cet égard, un particulier intérêt.Il y a beaucoup à trouver en ce domaine, comme l’a montré, dans un dernier article, le regretté P. François de Dainville®' .

Je n’insiste pas davantage sur cette question capitale des illustrations scientifiques médiévales. Le P ' John Murdoch prépare, à ce sujet, un volume important et impatiemment attendu® .

Lorsque le médiéviste veut réfléchir sur les rapports théorie-pratique, il consulte assez volontiers les traités théoriques, mais il ne refait guère, dans de semblables conditions d’environnement, les gestes mêmes des praticiens médiévaux. Notre compréhension du Moyen Âge s’en trouve fondamentalement déséquihbrée.

Ecole pratique des Hautes Etudes, Paris

N O T E S

1 Paris, 1957 (Conférences du Palais de la Découverte, série D, n° 46).2 L. White, Medieval Technology and Social Change (Oxford, 1962); trad, française (Paris, 1969). Idem, Machina ex Deo: Essays in the Dynamism o f Western Culture (Cambridge, Mass., 1968).3 B. G 'i\\Q,à3.m Histoire générale des techniques, dir. M.Daumas, t. 1 (1962), pp. 425- 601, et t. 2 (1965), pp.1-139. Cf. ci-dessous, note 33.4 G. Duby, Guerriers et paysans (V lIe -X IIe siècle): premier essor de l'économie européenne (Paris, 1973).® Voir, dans le présent volume, T. Gregory, La nouvelle idée de Nature et de savoir scientifique au X lle siècle.® F. Alessio, La filosofia e le “ artes mechanicae" nel secolo X II, dans Studi medievali, ser. 3a, anno 6 (1965), fasc. 1, pp. 71-161.’ R. Baron éd., Hugo de Sancto Victore, Opera propaedeutica: Practica geometrie (Notre Dame, 1966).* Dans quelle mesure, jusqu’à la fin du Xlle siècle, le quadrivium était-il effectivement mis à contribution pour la compréhension des Saintes Ecritures? C ’est là une importante question que se propose d’étudier M. Stephen K. Victor: voir déjà, dans sa thèse (citée ci-dessous n. 36), les considérations intitulées Practical Geometry in Education. ® Gui d’Arezzo, Micrologus, ed. J. Smits Van Waesberghe (Roma, 1955), p. 223.

472 G. BEAUJOUAN

Johannis Affligemensîs De musica cum Tomrîo, ed. J. Smits Van Waesberghe (Roma, 1950), p. 52.

Gui d’Arezzo en tête des Regulae rythmicae publiées dans M. Gterbert, Scriptores ecclesiastici de musica, t. 2, p. 25.

J. Smits Van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im M ittel- alter (Leipzig, 1969).13 G. Beaujouan, L ’enseignement du "quadrivium” , dans Settimane di studio..., 19, La Scuola neir Occidente latino deWalto medioevo (Spoleto, 1972), pp. 639-667.

L. White, Eilmer o f Malmesbury: An Eleventh Century Aviator. A Case Study o f Technological Innovation: Its Context and Tradition, dans Technology and Culture 2 (1961), 97-111.

J. Stiennon, Hézelon de Liège, architecte de Cluny I I I , dans Mélanges René Crozet (Poitiers, 1966), 1.1, pp. 345-358. K. J. Conant, Cluny: les églises et la maison du chef d ’Ordre (Mâcon, 1968). Le P‘‘ Conant croit à une savante structure mathématique du plan de Cluny III, mais ses thèses sont contestées par F. Salet et A. Erlande-Branden- burg, Cluny I I I , dans Bulletin nwnumental 126 (1968), 235-232.

Odorannus de Sens, Opera omnia, textes édités, traduits et annotés par R.-H. Bautier et M. Gilles, et, pour la partie musicologique, par M.-E. Duchez et M. Huglo (Paris,1972) [Sources d ’histoire médiévale publiées par l’institut de Recherche et d’Histoire des Textes, n° 4].

R. Vaughan, Matthew Paris (Cambridge, 1958).L. F. Salzman, Building in England Down to 1540 (Oxford, 1952), p. 11. J. H. Roimd,

The Staff o f a Castle in the Twelfth Century, dans English Historical Review 35 (1920), 90-97: sur ingeniator, pp. 93-95. Références dans Transactions o f the Archeological Society o f Birmingham 48 (1925), 43-44.

Archives historiques du Poitou 49 (1936), 345. Je dois cette référence à Mme Bautier (fichier du nouveau Du Cange).

R. E. Latham, Revised Medieval Latin Word List from British and Irish Sources (London, 1965). M. Latham m’a fourni de précieux renseignements sur les plus anciens emplois du mot ingeniator en Angleterre: je l’en remercie bien vivement.

“Waldivus ingeniator” sans autre précision, dans Domesday Book, t. 1, 365b. On trouve ensuite un “Gaufridus ingeniator” en 1130 (Pipe Roll, p. 143).22 Domingo Gundisalvo, De scientiis, ed. M. Alonso (Madrid, 1954), p. 109, Idem, De divisione philosophiae, ed. L. Baur, dans Beitr. z. Gesch. d. Phil. M . A. 4, 2-3 (1903), 122. Al-Fârâbï, Catàlogo de las ciencias, ed. trad. A. Gonzalez Palencia, 2a ed. (Madrid- Granada, 1953), pp. 51 et 104.23 V. L. Bullough, The Development o f Medicine as a Profession (New York, 1966).24 p. Du Colombier, Les chantiers des cathédrales (Paris, 1973), Chapitre IV.25 J’ai étudié le cas du monastère de Guadalupe où, encore au jh 'Ie siècle, une médecine restée conventuelle avait im tel prestige qu’elle attirait, comme stagiaires, des praticiens déjà pourvus de titres universitaires. Cf. G. ^u}o\jia.n. Médecine humaine et vétérinaire à la fin du Moyen Age (Paris, 1966), p. 380.2« Voir, par exemple, J. Cortesâo, Os ikscobrimentos portugueses (Lisboa, 1960), pp.70-78.2’ J. Needham, Clerks and Craftsmen in China and the West (Cambridge; 1970). Idem, Science and Civilisation in Chirm, en particulier le tome 4, Physics and Physical Technology, part 2, Mechanical Engineering (Cambridge, 1965), et part 3, Ci\il Engineering and Nautics (Cambridge, 1971).2* Le calcul algorismique médiéval est basé sur la possibilité de successivement effacer


divers chiffres pour les remplacer par d’autres: “Loco delete figure in pulvere...". En dehors même de l’imprimerie, l’abaissement du prix du papier a eu des conséquences très importantes.2» L.-P. May, Dante et la Mystique des nombres (Paris, 1968), par exemple p. 30 sur 3,1416!3° A. Cortesâo, “Descobrimento” e descobrimentos (Coimbra, 1972), sur la distinction entre première trouvaille et découverte officielle. J’ajouterai, pour ma part, que la version portugaise du Secretum secretorum montre bien la relation entre “descubrir” et “encubrir” un secret. J. Barradas de Carvalho termine un important travail sur l’emploi de ce mot “découverte”.31 G. Beaujouan, Calcul d ’expert, en 1391, sur le chantier du Dôme de Milan, dans Moyen Age 69 (1963), 555-563.32 Rééd. F. Geldner (Wiesbaden, 1965).33 B. Gille, Les ingénieurs de la Renaissance (Paris, 1964), p. 28.34 Par exemple la proposition selon laquelle un triangle ^uilatéral de côté 3 aurait même surface qu’un carré de côté 2.35 Edité par M. Curtze, dans Abhandlungen zur Geschichte der Mathematik 8 (1898), 30-68.3« S. K. Victor, Practical Geometry in the High Middle Ages: An Edition with Translation and Commentary o f the "Artis cuiuslibet consummatio” (Harvard University, May1973). S. Victor insiste sur les éléments communs à cette géométrie et aux carnets de Villard de Honnecourt. Mais, même sur ces points, l’esprit des deux documents est bien différent. Cf. ci-dessous, note 86.37 R. Branner, Villard de Honnecourt, Archimedes and Chartres, dans Journal o f the Society o f Architectural Historians 29 (1960), 91-96 et polémique ibid. 30 (1961), 143- 145. L. R. Shelby, Setting Out the Key Stones o f Pointed Arches, dans Technology and Culture 10 (1969), 537-548.38 Voir par exemple J. Schouten, The Pentagram as a Medical Symbol (Nieuwkoop,1968).39 A. Dürer, Underweysung der Messung mit dem Zirckel und Richtscheyt (Nürnberg, 1525), livre 2. Traduction latine: Institutionum geometricarum... (Paris, 1532), p. 55.40 S. Günther, Die geometrischen Naherungskonstruktionen Albrecht Diirers (Ansbach, 1886), pp. 5-7. Voir la bibliographie indiquée par M. Steck dans Dictionary o f Scientific Biography, Vol. 4, p. 261.41 Thorn, Gymnasialbibliothek, R 4° 2, p. 159. Erfurt, Ampl. Q° 385, fo. 20v.42 G. Beaujouan, Manuscrits scientifiques médiévaux de l ’Université de Salamanque (Bordeaux, 1962), p. 101. Idem, La science anglaise dans les bibliothèques de Salamanque au XVe siècle, dans Mediaeval and Renaissance Studies 5 (1961), spécialement pp. 263-269.43 P. Cattin, L ’oeuvre encyclopédique de Philippe Eléphant: mathématique, alchimie, éthique (milieu du X lV e siècle), dans Ecole nationale des chartes. Positions des thèses (1969), pp. 9-15.44 L’unique manuscrit, celui de Salamanque, est une assez mauvaise copie. Tracées dans les marges, les figures y apparaissent souvent défectueuses ou mutilées par le relieur. Du reste, les noms ici étudiés ne se trouvent pas sous les figures, mais dans le texte, à la fin de la proposition correspondante: “ Hec figura dicitur...” .45 Ce théorème se trouve, par exemple, dans le De triangulis de Jordanus Nemorarius, ed. M. Curtze (Thom, 1887), proposition IV, 15: ''Octogonus circulo inscriptus inter quadratum eidem inscriptum et quadratum circumscriptum proportionalis."

474 G. BEAUJOUAN

Chez Raymond Lulle, la figure de la quadrature du cercle porte un autre nom, celui de “figura magistralis". Il s’agit, notons-le, de quelque chose d’assez différent puisque, pour Lulle, la surface du cercle est égale à celle d’un carré dont les côtés se situent à mi-distance entre ceux du carré inscrit et ceux du carré circonscrit. Cf. J.-M. Millâs Vallicrosa, E l libro de la "Novageometria” de Ramôn Lu ll (Barcelona, 1953), pp. 16 et 84.

“ superiorum” dans les éditions de Campanus.Dans le MS Paris Bibl. Nat. lat. 7219 (XVe siècle) se trouvent rassemblées, sans le

texte, les diverses figures des Eléments d’Euclide selon Campanus, trois d’entre elles portant des noms caractéristiques: dulkarnon (I, ^6),pes anseris (III, 7) et caudapavonis (III, 8). Chaque figure porte l’indication chiffrée de la proposition qu’elle illustre. Ce recueil était donc sans doute destiné à rendre compréhensible un exemplaire des Eléments copié sans figures. Bien que ce ne soit pas ici le cas, il a évidemment pu exister une tradition orale liée à la mémorisation visuelle de certaines figures.

J.-M. Millâs Vallicrosa, E l libro de los fundamentos de las tablas astronômicas de R. Abraham ibn Ezra (Madrid-Barcelona, 1947), p. 127.5“ Edition B. Boncompagni (Roma, 1862), pp. 105 et 208.

Paris, Bibl. Nat., MS lat. 2719: voir, ci-dessus, note 48.62 Léonard de Vinci, Le manuscrit A de l'institut de France, transcr. N . de Toni, trad. A. Corbeau (Grenoble, 1972), pp. 58-59.

Traduction plus compréhensible, mais moins littérale que celle de l’édition Corbeau citée ci-dessus. Cf. éd. Ch. Ravaisson-Mollien, Vol. 1 (Paris, 1881), p. 23.

Ed. N . de Toni et A. Corbeau, pp. 72-73. Ed. Ravaisson-Mollien, p. 27.Par exemple aux fol. 13 " et 14 du MS B de l’institut (années 1485-1490). Ed. N . de

Toni, trad. F. Authier et A. Corbeau (Grenoble, 1960), n®* 150-153, pp. 38-41: “Je constate que les côtés du pentagone s’éloignent du cercle de 1/5 de ces côtés” . Pourtant, Léonard construit un triangle équilatéral sur le côté donné du pentagone et, aux 4/5 de la hauteur de ce triangle, il place le centre du cercle circonscrit au pentagone.

Bien que les Eléments n’enseignassent pas à construire un pentagone régulier sur un côté donné, il n’était pas très difiScile d’imaginer une solution euclidienne à ce problème. C ’est ce que fit, peu après 990, Abü’l-Wafà’ dans son “ Livre sur ce qui est nécessaire aux artisans en fait de constructions géométriques". Il y proposa deux constructions du pentagone régulier, l’une très simple, l’autre plus sophistiquée mais d'une seule ouverture de compas. Cf. F. Woepcke dans Journal asiatique, 5e série, 5 (1855), 327-328. Voir aussi la bibliographie donnée par A. P. Youschkevitch dans Dictionary o f Scientific Biography, Vol. 1, pp. 39-43, en particulier S. Krasnova dans Fiziko-matematicheskie nauki v stranakh vostoka, 1, 4, (Moscou, 1966), 42-140.57 Equerre de l’architecte des stalles de Saint-Pierre de Poitiers (après 1270). Equerre du cimetière de Niederhaslach dans le Bas-Rhin (1326). Voir A. Sené, Quelques instruments des architectes et des tailleurs de pierre au Moyen Age: hypothèses sur leur utilisation, dans Actes du Congrès de la Société des historiens médiévistes de l ’enseignement supérieur: Besançon, 2 -4 juin 1972 (publ., 1973), pp. 39-58.

B. G. Morgan, Canonic Design in English Mediaeval Architecture (Liverpool, 1961).A. Sené, Un instrument de précision au service des artistes du Moyen Age, dans Cahiers de civilisation médiévale 13, n° 4 (oct.-déc. 1970), 349-358. Id., Les équerres au Moyen Age, dans Actes du 95 Congr. Nat. des Soc. savantes: Reims 1970: archéologie (Paris,1974), pp. 525-548.6* E. Maillard, Les cahiers du Nombre d ’Or, fasc. 1 : Albert Dürer (Paris, 1961), pl. 7 et pp. 21-22. Voir aussi le fasc. 3 : Eglises du X lle au XVe siècle (Paris, 1964), notamment pp. 23-31 sur les équerres médiévales.


Nous ne pouvons fournir ici une bibliographie des innombrables publications - souvent très discutables - consacrées au nombre d’or. Aux références spécialement données dans les notes voisines ajouter, par exemple, M. Borissavlievitch, Le Nombre d ’Or et l ’esthétique scientifique de l'architecture (Paris, 1963). T. Brunes, The Secrets o f Ancient Geometry and its Use, 2 vols. (Copenhagen, 1967). Rappelons aussi P. H. Michel, De Pythagore à Euclide (Paris, 1950), pp. 523-630.81 L. R. Shelby, Research Notes. Mediaeval Mason’s Tools. 11. Compass and Square, dans Technology and Culture, 6 (1965), 236-248.82 O. von Simson, The Gothic Cathedral (London, 1956), p. 34.83 P. Du Colombier, Le compas du maître d ’oeuvre, dans Bulletin de la Société natioruile des Antiquaires de France (12 janvier 1966), pp. 17-26.84 Ed. de B. Boncompagni, Scrittid i Leonardo Pisano, Vol. 1 (Roma, 1867), pp. 283-284.85 M. Cleyet-Michaud, Le nombre d ’or (Paris, 1973), p. 72.88 E. Lucas, Recherches sur plusieurs ouvrages de Léonard de Pise et sur diverses questions d ’arithmétique supérieure, dans Bullettino di bibliografia e di storia dette scienze matematiche e fisiche 10 (1877), 131 sqq.87 soit faicte une telle progression 0, 1, 1, 2, 3, 5, 8, 13, 21, etc., dont chasque nombre soit égal aux deux précédens; alors deux nombres pris immédiatement dénot- teront la mesme raison, comme 5 et 8 ou 8 et 13 etc., et tant plus grands, tant plus près... tellement que 13,13,21 constituent assez précisément un triangle isocèles ayant l’angle du pentagone” . Albert Girard précise bien qu’il s’agit là d’une “particularité non encor par cy devant practiquée” . On trouve cependant, dès 1610, dans la Strena de Kepler, ce lien entre la série de Fibonacci et la “Divine proportion” . Cf. J. Kepler, Gesammelte Werke, B. 4 (München, 1941), p. 270: trad, anglaise par C. Hardie, The Six-Comered Snowflake (Oxford, 1966), pp. 20-21.8® Du pentagone et du décagone : trad, latine de Gérard de Crémone dans le MS Pans, Bibl. nat., lat. 7377A fol. 93e. Cf. H. Suter, Die Abhandlung des Abu Kâmil Shogà^ b. Aslam über das Fünfeck und Zehneck, dans Bibliotheca mathematica, 3. Folge, 11, 2 (1911), pp. 15-42. M. Yadegari et M. Levey, Abu Kâmil’s "On the Pentagon and Decagon” , dans Japanese Studies in the History o f Science, n° suppl. 2 (1971), 1-54.89 Distinctiones, 3 et 8 {de quibusdam subtilitatibus geometricis)', édition Boncompagni, pp. 105-107 et 207-216. J’ai vérifié les textes dans les trois manuscrits de la Bibliothèque nationale: lat. 7223, lat. 10258 et nouv. acq. lat. 1207.70 E. G. R. Taylor, Mathematics and the Navigation in the X lllth Century, dans Journal o f the Institute o f Navigation, 13 (I960), 1-12.71 II y a longtemps qu’a été abandonnée la thèse attribuant, en matière de découvertes maritimes, un certain rôle à Regiomontanus et à l’école astronomique allemande. Jusqu’ici, en revanche, l’almanach perpétuel d’Abraham Zacut passait pour la source des tables solaires du régime nautique d’Evora. Celles-ci semblent, en réalité, dériver tout simplement des tables alphonsines alors vieilles de deux siècles et demi. Cf. E. Poulie, Les conditions de la navigation astronomique au XVe siècle (Coimbra, 1969), pp. 13-16.72 L. Mendonça de Albuquerque, Introduçâo à historia dos Descobrimentos (Coimbra, 1962) et Curso de histôria da nàutica (Rio de Janeiro, 1971). A. Cortesâo, Historia da cartografia portuguesa (Coimbra, 1969-1971); trad, anglaise.73 G. Beaujouan, Science livresque et art nautique au XVe siècle, dans Aspects internationaux de la découverte océanique: 5e colloque int. d ’hist. maritime (Paris, 1966), pp. 61-85. Voir aussi ci-dessous, note 76.74 R, Laguarda Trias, La aportaciôn cientffica de Mallorquines y Portugueses a la

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cartografianàutica (Madrid, 1964), spécialement pp. 41-49. Voir également, ci-dessous, note 84.5 A. Teixeira da Mota, Méthodes de navigation et cartographie nautique dans l ’Océan

Indien avant le XVIe siècle (Lisboa, 1963). G. Ferrand, Introduction à l ’astronomie nautique arabe (Paris, 1928). Voir maintenant les importants travaux de G. R. Tibbetts (ci-dessous, note 82).

G. Beaujouan, L ’astronomie dans la Péninsule ibérique à la fin du Moyen Age (Coimbra, 1969), surtout pp. 17-20.

Le contexte relatif au Nuage de Magellan est emprunté par Pierre d’Abano à VAbumasar in Sadan. Cf. L. Thorndike, dans Isis 45 (1954), 22-32. R. Lemay: voir ci- dessous, à la note 80. L. Olschki, Marco Polo, Dante Alighierie la cosmografia medievale, dans Oriente poliano ( studi in occasione del V II centenario della noscita di Marco Polo) (Roma, 1952), pp. 45-65.

Description des étoiles fixes, trad. H. C. F. C. Schjellerup (St. Petersbourg, 1974), p.26 et sqq. Cf. Emmy Wellesz, An Islamic Book on Constellations (Oxford, 1965).

Peut-être la stature d’un homme est-elle la moitié d’une lance de 14°, soit 7°: ceci s’accorderait assez bien avec la latitude de 7°55’ (Pedro de Sintra).

Dans la littérature géographique arabe, maints renseignements sont donnés comme ayant été recueillis de la bouche même des marins; mais cette dernière formule n’est souvent qu’une sorte de cliché. Il est cependant certain que très tôt les navigateurs arabes de l’Océan Indien se transmirent oralement des instructions nautiques assez précises. En ce qui concerne, par exemple, les dangers du Chenal de Mozambique et la recommandation de contourner Madagascar, R. Lemay a attiré l’attention sur un très intéressant passage de VIntroductorium maius d’Abu M a‘shar (848 de notre ère). Voir X lle Congrès int. d ’hist. des sciences (Paris, 1968): Actes, 1.1 A, pp. 109-110 [=Revue de Synthèse (1968)] et t. IB, p. 100 (observations de J. Vemet) puis 103-104.

J. Needham (cf. ci-dessus note 27), Sc. and Civ. in Chirui, t. 4, part 3:... Nautics, p. 573.*2 G. R. Tibbetts, Arab Navigation in the Indian Ocean before the Coming o f the Portuguese (London, Luzac, 1972). L ’auteur a présenté les idées essentielles de ce livre dans The Navigational Theory o f the Arabs in the Fifteenth and Sixteenth Centuries (Coimbra,1969). Interprétations parfois un peu différentes chez H. Grosset-Grange, La navigation arabe de jadis: nouveaux aperçus sur les méthodes pratiquées en Océan Indien, dans Navigation 17 (1969), 227-237 et 437-448; autres études du même auteur sous presse. Importants travaux aussi du Dr Ibrahim Khoury: Afimad ibn Màgid, la "Hâwiya” , abrégé versifié des principes de ruiutique, dans Bulletin d ’études orientales 24 (1971), 249-386; I. Khoury a également publié, à Damas, des textes de Soleimân el-Mahrî.

B. R. Goldstein, Prelimirmry Remarks on Levi ben Gerson’s Contribution to Astronomy, dans The Israel Academy o f Sciences arui Humanities, Proceedings 3, n° 9 (Jerusalem, 1969), 239-254 (surtout pp. 244-246).

R. Laguarda Trias, Interpretaciôn de los vestigios del uso de un método de navegaciôn preastronômica en el Atldntico (Coimbra, 1970), surtout p. 25. Cf. du même auteur. Las màs antiguas determirmciones de latitud en el Atldntico y el Indico (Madrid, 1963).

On puisera utilement dans deux ouvrages collectifs à participations surtout allemandes; Fachliteratur des Mittelalters: Festschrift fü r G. Eis (Stuttgart, 1968) et A. Zimmermann, Methoden in Wissenschaft und Kunst des Mittelalters (Berlin, 1970).

Voir la thèse de S. K. Victor citée à la note 36. Un ouvrage compilé par un “clerc” peut vouloir être pratique, mais ne pas l’être pour autant. Symptomatique apparaît, dans r “ Artis cuiuslibet...” une amusante confusion: pour donner l’aire des polygones.


l’anonyme parisien de 1193 présente, en réalité, la formule des nombres polygonaux selon l’arithmétique de Boèce. On peut pareillement s’interroger sur l’utilité réelle d’im traité comme la Practica geometriae de Dominicus de Clavasio, ed. H. L. L. Busard,

Archive fo r History o f Exact Sciences, 2, n° 6 (1965), 520-575. L ’un de mes élèves,H. L ’Huillier étudie actuellement la géométrie inédite de Nicolas Chuquet dont, en liaison avec l’algèbre, la valeur semble, en fin de compte, plus pédagogique que pratique.

J. Le Goflf, Le temps du travail dans la “ crise” du X lV e siècle: du temps médiéval au temps moderne, dans Moyen âge 69 (1963), 597-613.

S. Bedini et F. Maddison, Mechanical Universe: the Astrarium o f Giovanni de Dondi (Philadelphia, 1966). E. Poulie, Un constructeur d ’instruments astronomiques au XVe siècle, Jean Fusoris (Paris, 1963); noter le cas du médecin Henri Amault de Zwolle.®9 Outre le répertoire de Klebs et les réflexions qu’il inspira à G. Sarton, voir aussi maintenant M. B. Stillwell, The Awakening Interest in Science During the First Century o f Printing (1450-1550) (New York, 1970).

F. de Dainville, La Gallia dans la mappemonde de Saint-Sever, dans Actes du 93e congrès national des sociétés savantes (1968), section de géographie (Paris, 1970), pp. 391-404. Voir notamment p. 392.

Voir, ci-dessus, note 17.92 J. E. Opsomer, Note sur l ’art des herbiers aux siècles passés, dans Annales du 51e congrès (Malines, 1970) de la Fédération archéologique et historique de Belgique. 9e section: Histoire des sciences, pp. 518-525.

Outre la bibliographie sur les carnets d’ingénieurs, voir notamment L. C. Mac- Kinney, Medical Illustration in Medieval Manuscripts (London, 1965); P. Huard et M.D. Grmek, M ille ans de chirurgie en Occident, Ve-XVe siècles (Paris, 1966). M. Destombes, Mappemondes A. D. 1200-1500 (Amsterdam, 1964).»4 F. de Dainville, Cartes et contestations au XVe siècle, dans Imago mundi 24 (1970),99-121.»5 A paraître aux éditions Ch. Scribner de New York, en supplément au Dictionary o f Scientific Biography.

D IS C U S S IO N

G. beaujouan : Plus progresse, d’un côté, l’histoire des sciences, et, de l’autre, l’histoire des techniques, plus grande est notre impatience de ne pas bien parvenir à concilier théorie et pratique au moyen âge. Il y a grand danger à introduire dans un tel débat des notions pensées de façon moderne, comme les concepts de science, de technique, voire de technologie.

L ’architecte et l’ingénieur du moyen âge méritent certes de retenir ici toute notre attention. Mais c’est dans un contexte psychologique authentiquement médiéval qu’il nous faut observer le couple theorica-practica du Xle au XVe siècle: je pense, par exemple, à la musique, aux instruments astronomiques, à la médecine et même au symbolisme des nombres ou à l’interprétation des songes.

Dans mon rapport, mes préoccupations ne sont pas tournées vers l’épistémologie. Très modeste ouvrier de l’histoire, je suis surtout préoccupé de faire consciencieusement mon travail d’historien. Je suis un homme qui s’interroge, à la base, sur ce métier d’historien, sans se préoccuper de l’utilisation idéologique des résultats qu’il peut offrir à des penseurs installés plus haut.

J’insiste donc sur la problématique. Nous en trouvons, je crois, une bonne illustra

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tion à propos des recherches récentes sur l’application de l’astronomie à la navigation au XVe siècle. Scrutons le cas de conscience de l’historien.

Il existe, au moyen âge, un très grand nombre de traités consacrés aux instruments astronomiques. Avec une sorte d’ostentation quasi publicitaire, ces textes multiplient les usages des quadrants et astrolabes, mais sans se référer à une éventuelle utilisation nautique. Tirant argument des silences de cette masse de manuscrits, les “rats de bibliothèques” sont portés à affirmer que l’astronomie médiévale ne s’est pas appliquée à la navigation, pas du moins avant 1480. Rappelant cependant que les voyages aux Açores se sont multipliés à partir de 1427, les historiens marins prétendent au contraire que le repérage de ces îles aurait été impossible sans une certaine détermination astronomique de la latitude en mer.

Face à cette contradiction, deux attitudes sont évidemment possibles. La première se cramponne à l’aphorisme; “Pas d’Histoire sans documents” . Elle est celle du policier à la frontière: “Vos papiers! Si vous n’avez pas de papiers, vous n’existez pas!” . Au contraire, la seconde attitude procède secundum imaginationem. Selon elle, les choses les plus importantes étaient secrètes et seuls se trouvaient divulgués des éléments relativement secondaires. L ’imagination de l’historien serait alors plus valable que les documents. A nous donc d’imaginer, en fonction des résultats qu’elles ont permis, les techniques mises en oeuvre par les architectes des cathédrales ou les navigateurs des Grandes Découvertes.

Entre deux positions de cet ordre, vous le voyez, il ne reste qu’un sentier très étroit pour l’historien scrupuleux, mais non borné par la manie du document. Il faut bien admettre, surtout pour le moyen âge, l’existence de traditions techniques artisanales et orales dont, fatalement, on ne trouve qu’exceptionnellement l’écho dans les documents.Il y a là une sorte à'underground de la science dont, seulement de façon très sporadique, on décèle la trace dans des témoignages fortuits, dans des représentations iconographiques, dans des cartes et plans, dans la manière même dont, sur un original, apparaissent les petits trous laissés par la pointe d’un compas.

Mon rapport est une réflexion sur la difficulté d’explorer cet underground de la science médiévale, sur les efforts qui restent à faire pour mieux coordonner le savoir livresque et le dynamisme technique du moyen âge. Dans cette délicate recherche, une part décisive revient à l’étude des instruments, qu’ils soient effectivement conservés ou seulement connus par des dessins.

Je voudrais insister sur un dernier point. L ’historien de la vie intellectuelle médiévale apprendrait beaucoup en essayant de refaire matériellement, si modestes soient-ils, les gestes mêmes de l’homme du moyen âge.

j. MURDOCH! The question that M. Beaujouan put us, the “question des rapports qui pouvaient exister au moyen âge entre la connaissance théorique et la vie réelle,” is in my eyes - and I do not think that it is due to the fact that I have not worked in practica - perhaps one of the most difficult questions of all to resolve or to get even partial answers to, and, as one reads through M. Beaujouan’s paper, it is evident why this is so. The only thing I can do is to ask other questions, in particular about the pair theorica and practica and about other points that to me indicate the difficulty of establishing in any proper sense the relations between theoria and praxis in the Middle Ages.

The fost and major thing that I would like to do is merely to address myself to the problem of the two domains themselves, theorica and practica, and ask, what should they be? O f course, there is no problem in deciding that the application of astronomy within navigation, the application of geometry within architecture, and many of the other case histories that M. Beaujouan cites, certainly are relevant to the two do


mains; but how far - let us look first at practice or practica - should we extend this domain? I think that what I am about to say is partly explicit and certainly implicit in M. Beaujouan’s paper, namely, that we must take it beyond the realm of the application of science, hard or soft, to the affairs of everyday life. We must move it, for instance, to exegetical use of the so-called theoretical sciences. Whenever there are handbooks or treatises of one sort or another in which the theoretical material is intended for external use, for example a handbook of natural philosophy and logic for pastoral theology or something of the sort, would this not move one from the realm of theory into praxis? The praxis in this case would be pastoral theology.

Related to this is the question of the didactic use of theorica in the Middle Ages. M. Beaujouan cites the instruments that we are told existed, chez Gerbert par exemple, for the purpose of teaching the new profane sciences. But in addition to this, visual materials of any sort, illustrations, diagrams, schemata: do these not also move us from theory into praxis! There are, of course, those diagrams and pictures that are necessary in order to carry out the science itself (what I refer to are such things as astronomical diagrams, geometrical diagrams, diagrams for optics). These do not take us into praxis. But there are diagrams that do, I have in mind, for example, diagrams that are representations of vie réelle in one fashion or another. Herbals are the most evident case, but there are also didactic treatises in medicine, where one finds illustrations of, for example, points of cautery or so-called blood-letting men; these things are necessary to cany out medicine on the practical level.

One of the problems in investigating these, it seems to me, is that although observation and new external material may have been used in these illustrations, for the most part it seems to me this is not the case. They seem to be derivative in the sense that you can put together filiations of manuscripts where one illustration clearly seems to be copied from another. So a great deal of investigation into the manuscript histories of illustrations must go together with the question whether an illustration is representing something in the outer world.

Yet another kind of illustration that moves in the direction of the practical is the attempt to gloss a text. There is, for instance, the supposed eleventh century graph of the motion of the planets in latitude that has come into the history of science in various guises. But what is being “graphed” is twelve lines of Pliny. No observations whatsoever are involved. So we should pay very close attention when we are looking at such diagrammatic material to whether there need be any outside input in order to give us a picture or whether it is part of what M. Beaujouan called science livresque.

Finally, and I think most important of all, are the so-called schemata which are not a gloss of a text, not a representation of something external, not a diagram that is necessary for the calculations being carried out in this or that mathematics, but representations of a world system. There are very elaborate and beautiful ones showing the four elements, the four seasons, the four ages of man, etc., appearing in the works of Isidore, Macrobius, Bede, William of Conches, and others, and borrowed from one work to another. I think that one should also consider these as moving in the direction of the practical. The schemata are clearly of tremendous importance for the teaching of these treatises, but have been ignored by historians of science and philosophy.

Let me say something much more briefly about theorica and then conclude with a few reflections on the problem of the relation between theorica and practica. It seems to me that one of the things we should do - and M. Beaujouan is certainly aware of this - is to divide theorica abstractly into that theorica which cannot possibly, or only by the greatest stretch of the imagination could possibly, have relations to the practical (there

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is certaiiüy a great deal of medieval science that could only under the most unusual circumstances be applied to anything having to do with la vie réelle) and those theories that look as if they could receive practical application. Now it turns out, it seems to me, that the sciences that can be applied are the most traditional. This is a curious fact: that which is newest in medieval Latin science is not that capable of application; that which is more traditional - astronomy, optics, traditional mathematics - is more capable of application. This is a first approximation; let us try this idea out, see how it works.

Concluding with a few reflections on how difficult it is to establish the possible chain between the practical, on the one hand, and the theoretical on the other, even in the more traditional sciences like mathematics, I shall choose geometry as an example. Begin from the most theoretical of all: Euclid’s geometry. As this develops, there is an excessive didacticism as I have argued on numerous occasions elsewhere. In the version of Euclid that is presented to the medieval thinker, there are numerical examples all over the place. This is indeed moving one in the direction of application, of practice. So a possible chain might go from there to practical geometries. Then one has to move somehow (and I cannot fill in the links) either from Euclid with his didacticism or from practical geometry to actual practice, architecture or what have you.

Let me offer a few reflections on these links. If you are asking about the link between Euclid and practical geometry, there are not just many versions of Euclid, but many of them with a great number of marginalia. There is almost no mention in these marginalia of anything to do with (a) external practical things or (b) even practical geometry. Why so? Are there references to practical geometry, the necessity of paying attention to it and studying it, in university materials? If so, when and where? Such references might enable us to bridge the gap between Euclid’s geometry on the one hand and practical geometry on the other hand. What about the link between practical geometries and actual practice? If you believe the article of Lon Shelby cited by M. Beaujouan, the problem probably should be decided negatively, or mostly negatively, because he says that what one finds within practical geometries, namely the uses of the astrolabe, the quadrant, is absent in Villard. His conclusion is that, if you ask about the so-called géometrîe pratique that is mentioned in Villard, its relation to masonry or architecture is no more solid, no closer, than the relation of geometry to portraiture within Villard.

G. beaujouan : Quelques mots justement à propos de la géométrie pratique. Depuis que j ’ai rédigé le texte provisoire de mon rapport, m’est parvenue la belle thèse de M. Stephen K. Victor, Practical Geometry in the High Middle Ages: An Edition o f the “Artis cuiuslibet consummatio” . La lecture de ce travail m’a beaucoup frappé et voici pourquoi.

V A rtis cuiuslibet est une géométrie pratique parisierme de 1193. Bien qu’elle cite Johaimes Hispalensis, elle continue la tradition de Gerbert et de la Geometria incerti auctoris publiée par Bubnov. La base théorique d’un tel savoir est donc déjà pratique puisqu’elle dérive des agrimensores et des usages de l’astrolabe. En ce qui concerne la finalité pratique de VArtis cuiuslibet^ya\ été frappé par un fait stupéfiant: l’anonyme de 1193 enseigne à calculer l’aire des polygones en donnant les formules des nombres polygonaux selon Boèce. Quelle que fût sa bonne volonté de servir à la pratique, un tel texte semble avoir été compilé sans aucun contact avec des practiciens.

s. victor : Of course that is the case. But, at one time I remember that M. Beaujouan had an objection to the consideration of astronomical instruments, and also treatises on these practical instruments and on practical geometry, as didactic. That is, M. Beau- jouan preferred to think that there was a more practical bent to them. Now it seems to me that the didactic is practical in a very real sense.


G. beaujouan : Ça dépend à qui on enseigne.s. victo r : Exactly. And that’s the point. Now, clearly, if we look at practical

arithmetic, an accountant or a banker had to know arithmetic. All right, he learned it somewhere and he applied it. Where would he have learned it? Would the treatises of theoretical arithmetic have been of much use to him? No, he wanted to know how to do calculations. So he would have turned to the treatises on practical arithmetic, or he would have been taught out of these treatises.

One needn’t find inunediate applications of a treatise in order to call it practical, in other words. I think that second-hand application, that is with didactic intervention, is perhaps the most fruitful place to look. And this ties in with the things that Professor Murdoch mentioned about exegesis, on some of which I have worked and continue to work. This again is a didactic tradition and the geometry that is talked about in describing Biblical architecture is practical in a voy real sense, but not in the sense of manually or physically practical.

Now another way in which practical geometry is practical is not in its intent, but in its historical origin. M. Beaujouan just mentioned the development of the tradition of practical geometry out of the tradition of the agrimensores. Now I think there is no doubt in anyone’s mind that the texts of the Roman agrimensores, the field measurers, were genuinely practical handbooks.

So this brings us to the links that John Murdoch wants to establish. The links, I think, are not going to be found, at least at first, between Euclid and practical geometry. Practical geometry is not an application of Euclid in any sense. It is rather a growth out of a tradition that was genuinely practical, and called practical for that reason. I try to show in my thesis that practical geometry is not called practical geometry until there is a model of theoretical geometry in the new translations of Euclid in the twelfth century in the West. I think this is an important point. It shows that these practical geometries are not attempts to apply Euclid. They do acquire much Euclid in the thirteenth and fourteenth centuries. But this is not why they are practical in the beginning. These are later incursions, additions, and improvements.

G. beaujouan : Je veux répondre à vous - et aussi à M. Murdoch - sur le plan de la

J’en prends pour exemple l’arithmétique dont des secteurs où le choses sont le plus claires grâce à la richesse de la documentation. Prenons les deux traités d’arithmétique les plus répandus dans l’Occident médiéval: l’algorisme d’Alexandre de Villedieu et celui de Sacrobosco. Ils se trouvent, l’un et l’autre, inclus dans une tradition universitaire et, s’ils débouchent sur quelque chose de pratique, c’est sur l’application du calcul à l’astronomie et à l’astrologie.

Si nous examinons, en revanche, les arithmétiques commerciales de la fin du moyen âge, nous y trouvons une tradition qui, par divers intermédiaires méridionaux, dérive du Liber abbaci de Fibonacci. La situation apparaît donc assez étrange. D ’un côté l’algorisme tourné vers l’astronomie et accroché au calcul sur le sable avec corrections successives en effaçant. En face, des arithmétiques commerciales enseignant le calcul écrit sur papier avec retenues. On le voit par cet exemple: l’utilisation effective d’un traité théorique n’est pas implicite dans le texte lui-même.

R. hashed: Mais, dans cet exemple, M. Beaujouan, il n’y a pas de théorie; il s’agit de l’application d’une pratique à une pratique. Voyez l’arithmétique de l’époque: qu’on ^ace ou qu’on suive la méthode de retenue, il s’agit essentiellement d’une pratique. Un traité d’arithmétique, c’est un traité pratique.

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G. BEAUJOUAN: Je suis d’accord. Mais il y a quand même deux choses: D ’une part la science consignée par un enseignement livresque et d’autre part la pratique. Peut-être y a-t’il équivoque sur l’emploi du mot théorie.

R. rashed : Je ne suis pas spécialiste, et j ’ai quelques difficultés à comprendre le mot pratique. Vous m’avez expliqué le mot théorie, je comprends mieux, disons, la science livresque. Mais, à suivre la discussion, il me semble qu’il y a déjà plusieurs notions de pratique qu’on utilise en même temps et en leur donnant la même signification. Ma question est de savoir comment différencier entre “théories appliquées” - s’il y a vraiment, dans la période que vous considérez, des théories appliquées - et la plupart des applications qui, en effet, sont simplement des recettes. A moins qu’il n’y ait une troisième catégorie d’application: ce que vous appelez “applications théoriques” . Ce qu’on vise dans cette troisième catégorie d’application n’est pas du tout l’utilité mais simplement l’exercice d’une théorie qu’on vient de découvrir.

G. BEAUJOUAN: Du point de vue philosophique, c’est une horreur de confondre ces notions, mais dans la vie réelle, pour quelqu’un qui a le malheur de n’être qu’historien et pas philosophe, les choses sont assez claires! Vous oubliez qu’au moyen âge le monde occidental est complètement sous-développé; il ne faut pas projeter des notions trop raffinées au milieu de problèmes qui se présentent, malgré tout, dans un certain état de sous-développement.

R. rashed : Je n’oublie pas la nature de ce développement. J’essaye simplement de distinguer, pour pouvoir suivre votre discussion, les différents sens de “pratique” .

G. BEAUJOUAN: Oui. Mais dans la réalité, il y a toute une série d’attitudes pouvant s’échelonner entre la théorie pure et la pratique la plus matérielle.

R. rashed: D ’accord, M. Beaujouan, mais j ’ai grand doute qu’il y ait des théories appliquées, aussi bien dans le moyen âge chrétien que dans l’Islam.

G. beaujouan: Je veux préciser mon problème en l’illustrant par un exemple évoqué dans mon rapport. Lorsque, travaillant sur le chantier d’une cathédrale, un artiste ou un artisan voulait correctement tracer un pentagone régulier, était-il susceptible d’avoir une conversation à ce sujet avec un chanoine de cette cathédrale? L ’artisan considérait, sans le connaître, qu’Euclide était le patron des maîtres maçons. Le chanoine était-il susceptible de consulter, pour la circonstance, une géométrie pratique ou un exemplaire des Eléments d’Euclide? Socialement et intellectuellement, un tel dialogue entre “clerc” et “praticien” était-il possible? C’est à ce niveau, purement historique, que je me pose des questions: elles n’ont rien de philosophique, même inconsciemment.

r . rashed : Le dialogue théorie-pratique peut être étudié à travers la pensée théorique des auteurs, et principalement chez les philosophes arabes, où se modifie la distinction traditionnelle entre science et art. Or l’intérêt de la subdivision de chaque branche en spéculative et active n’est pas seulement d’avoir permis aux traducteurs de révéler à rOccident chrétien de nouvelles sciences - la géométrie spéculative, l’algèbre, l’optique, la statique, etc. L’innovation porte sur le statut même de la notion d’art, telle qu’elle fut élaborée par les philosophes arabes, puis transmise à l’Occident par des philosophes latins comme Albert le Grand. Le renouvellement de cette notion va permettre le rapprochement du “penser” et de l’“agir”, de l’universel et du particulier, du théorique et du pratique.

Depuis al-Kindi, le couple Hlm-^aiml, science-action, ne se présente pas conmie un rassemblement de deux notions dont l’une est supérieure à l’autre et la domine (comme la distinction aristotélicienne), mais comme deux aspects complémentaires de la connaissance, qui remplissent cependant deux fonctions différentes. C ’est ce qu’exprime Ibn Sînâ dans son introduction à la logique d'al-Shifâ'. Il semble que ce soit à travers


des sciences comme la médecine pour Ibn Sînâ, la musique pour al-Fârâbi, que ces philosophes ont pu définir la double fonction théorique et pratique du savoir. La médecine fait partie pour Ibn Sînâ de ces disciplines qui, comme la rhétorique, le tir à l’arc, la lutte et la dialectique, sont toutes art.

Mais c’est sans doute à al-Fârâbi qu’il revient d’avoir précisé le statut de ces sciences intermédiaires qui utilisent des principes théoriques d’une part, des notions dégagées empiriquement d’un objet et au cours d’une pratique d’autre part. Telle est la fonction de Hlm al-hiyal, celle de l’art également, dans les productions artificielles de l’homme. Dans la Physique d’al-Fârâbi, en effet, la notion aristotélicienne de l’art comme imitation de la nature est remplacée par celle de l’art comme création, où l’homme dégage des notions de forme à partir des principes de la science d’une part, d’un savoir dégagé de la matière d’une chose particulière, d’autre part.

Parmi les sciences, la musique se distingue comme un exemple privilégié d’une discipline qui requiert à la fois des connaissances communes, des démonstrations apodic- tiques, et d’une pratique dont al-Fârâbi est sans doute le premier à avoir donné une définition aussi claire: l’expérience. Reprenant la notion aristotélicienne d’expérience proposée dans les Seconds analytiques, al-Fârâbi l’élabore, et, ce qui n’avait pas été fait par Aristote, la distingue de l’induction à laquelle on pourrait à première vue l’identifier, puisque les deux démarches portent sur des cas particuliers. L ’expérience est, selon al-Fârâbi, le renouvellement plusieurs fois d’une sensation concernant de nombreux objets jusqu’au point où l’intellect intervient pour effectuer son opération et introduire la certitude. C ’est dans cette opération de la raison que l’expérience se distingue de l’induction, car, dit al-Fârâbi, dans la démarche de l’induction l’intellect n’intervient à aucun moment. Si al-Fârâbi prend le soin d’affirmer qu’il ne fait ici qu’expliciter le point de vue d’Aristote, un retour au passage évoqué montre que les Seconds analytiques ne proposent pas de distinction nette entre induction et expérience, mais que ces deux démarches sont confondues et considérées comme deux moments d’une même étape dans le processus aristotélicien de formation des idées qui va de la sensation pure aux stades les plus élevés de l’intellection. On voit ainsi quels enseignements, pour la question des rapports entre théorie et pratique au moyen âge, pourraient être dégagés d’une étude approfondie d’oeuvres comme la Musique d’al-Fârâbî et la Médecine d’Ibn Sinâ, et que le retour à une oeuvre aussi connue que le Recensement des sciences s’avère également fructueux.

r . mckeon: M. Beaujouan’s communication clears up a difficulty that we have been having for the last four days, but now we are trying to force him into the way we have been talking about it. We always put the theoretic in a science that we can recognize as a product of thinking, and then we put the application out in the product of the artisan who is working. But let’s take the second example that M. Beaujouan puts in at the center of his paper, namely architecture. This has a tradition which even in the Middle Ages goes back to Vitruvius. Vitruvius begins by saying that architecture has two parts, ratiocinatio and fabrica. These two parts are in architecture, not in astronomy or any other recognized science. The ratiocinatio of architecture, he explains, is the solution of the theoretic problem, which can then be translated into the habits of the hand and the use of implements. Therefore the architect is the planner and the artisan, Vitruvius then goes on to say that there are technological disciplines that the architect should have. He should know philosophy, he should know mathematics, he should know history, he should know literature. But this doesn’t mean that he has to know Euclid: he has to know how to add, subtract, draw lines, and be able to perform operations of this kind. In literary criticism you find exactly the same situation.

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It seems to me, therefore - and I would deny that M. Beaujouan is merely an artisan in history, he is the philosopher among us - what M. Beaujouan has given us is a way by means of which we can, beginning with the eleventh and twelfth centuries, ask what it is that went into the Middle Ages as ratiocinatio, as modes of thinking. We dodged the question “ Is this science?” by saying “Let’s call it natural philosophy,” but that was a dodge. These are forms of ratiocinatio. Out of the twelfth and thirteenth centuries there then developed a form in which all the theory moved up into science. This is the evolution we are talking about. We should not answer the question “Which is theory and which is practice?” by saying that you find the theory in Euclid and the practice in the knack of chopping bricks or stones into particular forms. This I look upon as the great contribution made by M. Beaujouan’s paper.

P H IL O S O P H Y A N D S C IE N C E

IN S IX T E E N T H -C E N T U R Y U N I V E R S I T I E S :

SO M E P R E L I M I N A R Y C O M M E N T S *

I. IN T R O D UC T IO N

In Spite o f the enormous amount o f research which has been devoted to an understanding o f the history o f universities, much further work is required before we can begin to comprehend fully the place o f these institutions in the Western cultural life o f the past seven or eight centuries. i Not only is much basic work left to be done in the documents themselves o f even the most important and influential university centers, but we are sorely in need o f synthetic and comparative studies relating several universities to one another. Nevertheless, even on the basis o f the materials which have already been published, we are in a position to begin some sort o f synthesis.2 Though we know a great number o f individual facts from various universities concerning philosophy instruction in the sixteenth century, for example, no one has yet attempted an overall evaluation o f these materials with an eye towards an eventual synthesis.^ This certainly is not the only question to be faced by historians o f universities, but it is one to which little attention has previously been given, and, at the same time, one which is o f potential interest to scholars in a variety o f different fields.

In the present paper I should like to deal with several aspects o f university culture in the sixteenth century. Among the topics which I shall touch on are: (1) philosophy teaching in the universities; (2) changes wrought on the universities by humanism, the Reformation, and scientific change ; and (3) developments in the teaching o f medical and mathematical subjects. To this I shall add a brief comparison between two representative universities, viz., Pisa and Oxford, in which more specific elements o f change (or lack o f it) can be isolated. Finally, I hope to be able to present a provisional sketch o f the regional variations between universities during the sixteenth century. In venturing into this vast area, I realize the partial nature o f the evidence I am utilizing, for as yet I have not been able to explore systematically even all o f the relevant published information on

CHARLES B. SCHMITT

J. E. Murdoch and E. D. Sylla (eds.). The Cultural Context o f Medieval Learning, 4 8 5 - 5 3 7 . All Rights Reserved.

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this subject. Yet even the impressionistic picture which I paint might have the virtue o f encouraging others to think more deeply about this topic and to investigate it in greater detail. In the meantime I hope to be able to pursue further studies on this subject with the view o f extending and amplifying the views which I put forth here. In brief, what follows is to be considered merely a preliminary attempt at a general synthesis.

II. M ETHODO LOGICAL PREMISES

Before continuing it might be well to raise some o f the methodological problems which we encounter when attempting to deal with university history o f the sort with which we are here concerned. A t present I shall limit myself to four o f the major points.

First, when we propose to study universities in general over a period o f a century or two, we are faced with a vast number o f variations o f all sorts. Geographically universities range from Aberdeen and Uppsala in the north, to Catania and Évora in the south, and to Cracow and Budapest in the east. Some such as Bologna, Padua, Salamanca, and Paris were large and famous international centers, while others were miniscule by comparison and served only local needs. After the Reformation we find universities aligning themselves with one or another religious group and new universities being in one or another camp from the outset. Scottish universities which were originally Cathohc, became strongly Calvinist; in Germany, Freiburg and Cologne remained Catholic, while Tübingen and Wittemberg became Protestant; Leiden was founded as a Calvinist university, Jena as a Lutheran one, and Würzburg as a Catholic one. Some universities were very much influenced by new intellectual currents (e.g. humanism), while others continued on along traditional lines. As mathematical sciences developed some felt this influence quite deeply, while others seemingly ignored such novelties. Consequently, though there are some rather general patterns o f university organization and teaching during the Renaissance, there are perhaps more variations than is generally realized. In short, there are many individual facts to betaken account o f before we can hope for a synthetic overview which is anything but superficial.

Secondly, nearly all o f the scores o f universities (there were about 100 by 1650) have left behind their own documents. While some universities have been well served by historians, there are others in which the basic

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research into the documents has hardly begun. Only in a few cases have matriculation lists and graduation lists been published for the early modern period. Though the medieval period up to about 1400 is well covered in some instances (e.g. Paris and Oxford), the later period has often been hardly considered by modern historians using sound historical methods. While the Padua attended by Harvey and the Cambridge attended by Milton and later by Newton are reasonably well understood - though even here there are gaps - we know relatively little about the Pisa attended by Galileo or the Tübingen attended by Kepler. In a sense, a more general synthetic approach is not possible until the extant primary sources are brought to light.

This brings us to the third point. University history has, perhaps somewhat more than most other branches o f intellectual history, been prey to what the Italians call campanilismo^ which is not precisely nationalism, but what might be termed “ extreme regionalism.” This approach has resulted in the production o f many rather narrowly conceived histories o f a single university. These, however, should not be scorned, for they are often excellent ranging from Fabroni’s eighteenth-century one for Pisa to the recent one o f Jena. Some are even truly distinguished, e.g. Annerstedt’s work on Uppsala. On the other hand such works tend to take a narrow view and there is little or no use o f a comparative approach, at least once we get past the medieval centuries. The task before us now is to attempt a comparative study o f early modern university history without losing sight o f individual and local characteristics.

Finally, we must go beyond the apparent sources for the study o f university history and begin to dig deeper. For example, it is becoming increasingly apparent that statutory requirements for teaching tell only a part o f the story. When upon occasion one attempts to uncover what was actually taught in the classroom, it often turns out that the statutes were only followed in the loosest o f senses. To demonstrate this gulf between statutory theory and classroom practice in even one case for a single university, however, requires much painstaking research and many such instances must be carefully investigated before we can come to have a reliable general picture o f the overall situation.

in. MEDIEVAL BACKGROUND

It was in the twelfth and thirteenth centuries, when the oldest and most

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influential universities were talcing shape," that philosophy worked its way into a central position o f the curriculum. As the corpus Aristotelicum was gradually recovered by the West during the thirteenth century,® it became increasingly realized that here was a ready made structure around which to build an educational system to prepare trained individuals for a place in society, especially as physicians and theologians. The impact o f Aristotelian philosophy on the law faculties o f universities was not so dramatic perhaps, though further work is needed to reveal its precise role. It was in the arts faculties, however, that the new learning gradually became entrenched, supplanting the rhetorical tradition o f the twelfth century. By the late thirteenth and early fourteenth century,® the basic structure o f philosophy instruction was fixed and it was to remain a foundation stone o f education in arts, science, medicine, and theology until the end o f the seventeenth century and even later in certain localities. It was not so much that Aristotehanism was selected from several aspirant philosophical and scientific systems as it was that it alone presented itself to the men o f the Middle Ages as a comprehensive system o f natural truth upon which to erect a variety o f different structures. For them, as for the men o f the next several centuries, it represented philosophy (i.e. scientia) pure and simple.

As university arts faculties developed in the Middle Ages, it seems as though they took on a different coloration in different universities. Those institutions with strong theological orientations - e.g. Paris and Oxford - developed arts faculties with certain emphases, while those more directed toward the study o f medicine developed in another direction.® This seems to explain, in part at least, why Montpellier, Bologna, or Padua came to have different biases than did Paris or Oxford. On the other hand, other factors were operative, and the famous school o f natural philosophy and mathematics centered at Merton College, Oxford,® certainly rivaled the medical universities in its pursuit o f scientific studies. But, both that school and the contemporary one that developed at Paris under Buridan and Oresme were short lived,i® expiring before the end o f the fourteenth century, though having a continuity in Italy, Germany, and Eastern Europe for some time.^i

These two traditions - the theological and medico-scientific ones - continued on into the sixteenth-century universities. Though we are here concentrating on that century, it becomes increasingly apparent that ours


is part o f a larger question, viz., the fortuna o f university philosophy and science from roughly the time o f the Black Death until the revolution wrought by Galileo and Descartes.^^ This is the period during which, according to commonly received opinion, the Aristotelian philosophy, though still entrenched in the universities, had outlived its usefulness and served largely to hold back the progress o f mankind, which had been freed from the shackles o f darkness by the Renaissance, Reformation, and Scientific Revolution.i^

It must be stressed that there was a very marked continuity in university philosophy and science teaching during the period just mentioned, ca. 1350-1650. On the other hand, there were also remarkable developments and changes, though the latter become apparent to us only after an intensive scrutiny. One often reads about the breakdown o f scholastic- AristoteUanism because o f Humanism, Copernicanism, Ramism, etc., but traditional philosophy and science were alive, well, and flourishing throughout the sixteenth century.^^ In retrospect, we might be able to see some o f the roots o f their destruction in fifteenth- and sixteenth- century developments, but it was apparent to only a very few at the time. The criticisms o f Petrarca, Valla, More, Erasmus, Gianfrancesco Pico, Copernicus, Ramus, Telesio, and Bruno all had legitimate content, but were for the most part one-sided and lacked balance. I f these men were able to show a few Aristotelian doctrines to be in error, they could in no way produce a comprehensive alternative system to replace the established one. This is, I think, one o f the keys to understanding why Aristotehanism maintained its hold for so long. Despite flaws - which were evident to many from antiquity onwards - it still covered such a wide range that no other system could challenge its cultural hegemony. What did happen, however, was that a syncretic approach was developed by a number o f philosophers o f the Renaissance, and we find non-Aristotelian doctrine being absorbed increasingly into commentaries and textbooks. The precise way in which this happened was quite complicated and varied from one instance to another. It requires a much fuller treatment than can be given here.

IV. ARISTOTELIANISM IN THE SIXTEENTH CENTURY

The task o f attempting to understand the philosophy and science taught in the universities during the above mentioned three-century period is a

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daunting one. It is fraught with difficulties on all sides. Here we shall focus upon the sixteenth century and try to illustrate briefly what seem like the major strands o f the development o f Aristotelianism within the universities.

University philosophy in this century must be viewed in relation to various external factors which affected it. In addition to social, political, and economic forces - which, among other things, brought about changing functions for the universities and modifications o f various sorts in university populations and the social backgrounds o f incoming students^® - we must bear in mind the various new intellectual traditions which emerged. In my opinion, there are three o f these which should particularly be considered: the new scientific and philosophical developments, humanism, and the Reformation. Let us look at each o f these in turn more carefully.

Though important, one should not be tempted to overvalue the significance o f new philosophical and scientific ideas. During the sixteenth century we find not only the re-introduction o f previously lost ancient materials such as Plato,i® Stoic texts, ’ and a tomism,but also are published the writings o f men hke Copernicus, Vesalius, Telesio, Patrizi, and Bruno. On the whole, however, the influence o f this material was but relatively little felt in university education, though perhaps on specific points o f detail some o f this material was assimilated into the philosophy teaching to a greater extent than is normally realized.^® O f this we shall say more below. In my view the influence o f these newly introduced ideas had to be confined to relatively small issues since, all things considered, Aristotelianism still represented a more comprehensive and internally coherent system than any that was available to replace it. 20

The impact o f humanism was much more significant.^! First o f all, the newly developed techniques o f the humanists allowed the weeding out o f spuria from the corpus Aristotelicum. Medieval mainstays gradually disappeared from the editions. To take but one example the pseudo-Aristotelian work which passed under the title o f Secreta secretorum was widely read and used in the Middle Ages - more than 50 manuscripts o f it are still extant22 - and there were at least seventeen printed editions o f it in Latin or vernacular between 1501 and 1540, but only three printings during the last sixty years o f the century. 3 Confidence was gradually lost in those works that could no longer be claimed as legitimate. 4 Secondly,


new texts, which the humanists were able to uncover in their systematic search for ancient literary remains, were introduced and exerted significant influence, while filling in some o f the gaps in the system. Two such examples are the Poetica^^ and Mechanica, works which were all but unknown in the Middle Ages, but which came to be the focus o f enormous interest in the sixteenth century. Moreover, the greatly expanded knowledge o f the ancient world and o f the ancient languages, which the humanists were gradually able to obtain, made possible vastly superior editions o f the Greek texts and better Latin renderings.^’ These progressively replaced the medieval translations in the university teaching o f Aristotle.28 What is more, despite much variation from university to university, there seems to have been a general tendency to concentrate increasingly on a study o f the Greek text o f Aristotle as the sixteenth century wore on. About the turn o f the sixteenth century, we see for the first time an attempt on the part o f philosophers to begin teaching from the Greek text. 2» By the early seventeenth century specially prepared Greek editions o f various Aristotelian writings, accompanied by detailed conmientaries based on the Greek text, were in wide circulation. Particularly important were those prepared by the Jesuit Fathers at Coimbra^o and those o f the Italian ex-patriate, Giulio Pace.^i These editions were meant to be used by those who read Greek and who were prepared to study Aristotle in the original language. Even the handbooks and commentaries o f the later sixteenth century, while not usually including the Greek text, do explicate key Greek terms found in Aristotle and assume at least some knowledge o f Greek on the part o f the reader. In short, spurred by the humanist emphasis on the study o f original texts rather than translations, the university reading o f Aristotle took on a new cast in the courseo f the sixteenth c e n t u r y . ® ^

O f equal or perhaps even greater importance was the coming o f the Reformation. Though not exerting quite the same sort o f influence as did humanism, the emergence o f various religious factions in the course o f the century left a very definite and recognizable mark on the intellectual Ufe o f the universities. Even though Luther was himself quite anti-Aristotelian,33 his educational reformer Philip Melanchthon saw matters quite differently. 34 The net result was that, regardless o f religious persuasion, universities emerged from the years o f turmoil ensuing upon the events o f 1517 to remain staunchly Aristotelian regardless o f confessional af

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filiation. This is true o f Calvinist universities such as Edinburgh or Leiden, o f Lutheran universities such as Tübingen or Jena, as well as Catholic universities such as Padua, Salamanca, Coimbra, or Cologne. The way in which Aristotle was taught varied somewhat from place to place, though regional differences were often greater than those imposed by religious affiliation. At the end o f the sixteenth century and more markedly in the seventeenth century we see the development o f two different sets o f manuals and textbooks, one for use in Catholic universities and the second for use in Protestant ones.^s On the other hand, there continued to be more intellectual interchange between the two camps than is normally realized. Not only was Spanish scholasticism, particularly Suarez, most influential in Germany,®* both in Catholic and Protestant quarters, but equally influential was the important commentary tradition that developed in Italy in the sixteenth century.®' Or, to give another example, though the seventeenth-century textbook tradition that dominated philosophy teaching in England (e.g. Burgersdijk, Keckermann, and Magirus) was the Northern European Protestant one, a surprising interest was also shown in the writings o f Italian and Spanish Catholic commentators^^ during the late sixteenth and early seventeenth centuries.

The major point to keep in mind with regard to the influence o f the Reformation on university philosophy is that, despite the enormous changes which were wrought, in the final analysis the end product in all universities, regardless o f religious afiiliation, was fundamentally Aristotelian. As much as Luther or others wanted to get away from the rather rigid intellectual structure which had grown up during the “ Babylonian Captivity o f the Church,” when all was said and done the die had been cast centuries earlier and the appeal o f Aristotelian Scholasticism remained too strong to be thrown aside easily. Though sceptical and other notions may have invaded the theological debates o f the sixteenth century from time to time, the basic framework remained the Aristotelian one which had been forged in the medieval universities. In fact, the net result o f the coming o f the religious split was a more firmly entrenched Aristotelian scholasticism than we can find in the first third o f the sixteenth century. The precise way in which Protestant and Catholic scholasticism differed from one another has yet to be documented, though one’s initial impression is that there were definite variations and characteristic emphases.39


Bearing in mind this general picture o f a scholastic curriculum in Aristotelian philosophy continuing throughout the sixteenth century, even though impinged upon and partially transformed by various new intellectual tendencies, let us now look at the actual philosophy teaching in a bit more detail. As already mentioned, it largely retained the form that it had assumed in the fourteenth century. The grounding in logic was deeply rooted in a range o f Aristotelian texts, though there is variation. The Pisa statutes o f 15434« specify only Porphyry’s Isagoge and Aristotle’s Posterior Analytics, while those o f Coimbra o f 155941 ]ist the entire Organon in addition to the Dialectica o f Georgius Trapezuntius from the fifteenth century, and a Tübingen study plan for 1524 2 lists besides Aristotle also the thirteenth-century text book o f Peter o f Spain. Paul o f Venice’s Summulae logicae was officially named as a text at Padua in 1496 and remained in use for some years.43 Natural philosophy in all o f the universities seems to have been solidly based upon Aristotle and no extraneous texts introduced. In several institutions the newly discovered Mechanica served as a teaching text,44 until its spurious nature was discovered in the early seventeenth century, and its influence gradually waned. It was lectured on at Padua a number o f times between 1548 and 1600.45 At Uppsala, as the 1626 statutes tell us, it was read along with the commentaries o f Guido Ubaldo and Henri de Monantheuil.46 An interesting feature o f the teaching o f moral philosophy is that in Italy it was often not taught by philosophers, but came under the responsibilities o f the humanists or teachers o f Latin and Greek.4^ Though the Pisan statutes, for example, do not mention specifically any Aristotelian works o f moral philosophy, we know that the Rhetoric, Ethics, axid Politics were all taught from time to time by the “ Lettore d’Humanita” during the second half o f the sixteenth century.48 In the field o f metaphysics, the work o f Aristotle by that name seems to have been universally used.

This, then, in brief, is the sort o f thing which the statutes tell us. It would be worthwhile to go through the extant statutes for the period and determine precisely which works were officially required from university to university. In fact this would seem to be a starting point for a full investigation o f the question. Once we have determined what the philosophy requirements were de jure we can more confidently examine other materials to learn what they were de facto, in so far as this is possible on the basis o f extant sources. From our prehminary study o f selected

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statutes it appears that we can expect little change before the end o f the sixteenth century. The seventeenth century, however, will probably present us with a somewhat different picture, though one cannot be too certain o f this. The reformed Laudian statutes o f 1636 for Oxford, early seventeenth-century teaching practice in Italy, and the situation in the Dutch universities seem to indicate that changes were slow in coming.^»

What we do see even from this partial picture is that there was a strong emphasis on logic and natural philosophy as the foundation stones o f philosophical education. Only rarely did metaphysics have the place which it later attained in this area.^» The Metaphysica was printed and commented on much less frequently than works such as the Meteorology, Posterior Analytics, or De anima, for example, While the works o f moral philosophy were widely read - perhaps the Nicomachean Ethics was as influential as any o f Aristotle’s works during the sixteenth century® - in Italy at least it did not occupy a very central place in the philosophy curriculum. Works o f moral philosophy were, however, quite important in both the Jesuit and the Lutheran curricula which were oriented towards an educational ideal somewhat different from that obtaining in the older Itahan universities. The seventeenth-century philosophical handbooks indicate that, i f anything, Aristotelian moral philosophy came to have a more important place in the overall cursus than it had had in previous centuries.

In addition to a domination o f the curriculum by Aristotelian texts, there were occasionally a few other materials added. As we have seen this occurred especially in logic where the medieval work o f Peter o f Spain or the fifteenth-century texts o f Paul o f Venice or Georgius Trapezuntius sometimes supplemented, i f they did not replace, the Organon.

The place o f Plato requires particular comment. Although at least as early as Ficino an attempt was made to give Plato a more central role in philosophical and theological education, this met with little success. Ficino’s own Theologia Platonica, modeled in some ways on Thomas’s Summa contra g e n t i le s ,never was accepted in university circles as a teaching text, though it was widely read and influential in other spheres. Egidio da Viterbo’s commentary on the Sentences, ad mentem Platonis, was never printed or even finished and was apparently but a minor success.55 In the second half o f the sixteenth century, however, we see the beginnings o f a moderate attempt to insert some Platonic teaching into a few philosophy curricula. In Oxford documents o f both 1549 and o f 1564/


6556 see that moral philosophy lecturers are offered the possibiUty o f teaching Plato’s Republic as an alternative to Aristotle’s Politics or Ethics. Whether such an option was ever actually taken advantage o f I have thus far not been able to determine.^? We do know that during the last quarter o f the sixteenth century, the teaching o f specifically Platonic philosophy courses was introduced into the universities o f Pisa, Ferrara, and Romeos and that several platonically oriented individuals were teaching at Paris.^» Differently oriented was the Paduan mathematician Francesco Barozzi who introduced a consideration o f the mathematical sections o f the Republic into his lectures in addition to utilizing Proclus’s commentary on

Euclid.®®To go beyond the information contained in the statutes and in various

archival records is, however, most necessary, i f we are to have a more accurate picture o f the situation. To do this for even one university involves great difficulties, let alone attempting to get a general picture based on a number o f representative institutions. For this, i f for no other reason, an understanding and comprehensive synthesis lies far in the future.

V. T W O e x a m p l e s : PISA A N D OXFORD

Let us now look at the situation in a little more detail in two specific universities, which were medieval foundations, but continued to flourish during the sixteenth century. The two which I have chosen are Pisa and Oxford. O f the first I can claim to have a little specialized knowledge and the second presents an instructive example from another part o f Europe. Our findings here will only be indicative o f certain general tendencies, for one thing which is learned from the study o f university history during this period is how much variation there was and how difficult it is to generalize from only a few instances. Let us first look at Pisa.

Pisa was a university o f moderate importance, though it was the major university o f the Medici and did produce Galileo. For our purposes we can speak o f the university for the period after 1543, when it was re-opened with new statutes and a new impetus towards excellence after having been closed frequently by war and political disputes during the previous half century.® The new statutes o f 1543 remained in effect with few modifications until the eighteenth century.® The university had about 40 to 50 staff* members and 300 to 400 students during this period with a certain

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amount o f expansion towards the end o f the century. Two-thirds to three- quarters o f the students were in the law faculty; most o f the others studied arts with a mere handful in theology. Philosophy was, o f course, emphasized in the arts faculty and the curriculum was completely Aristotelian and traditional, at least until 1576 when the first (optional) Platonic course was introduced, and, indeed, this met with a good deal o f opposition. On the whole, humanism and new movements in philosophy had very little impact on philosophy teaching at Pisa and even at the end o f the century there were men lecturing on philosophy who showed no evidence o f ever having looked at the Greek text o f Aristotle. Their writings are largely on rather traditional lines, though we do find some surprises. One interesting feature, for which I have found no explanation - though Oxford here offers a similar and even more extreme example - is that there is no ready nearby source o f textbooks for the students.®^ Moreover, whereas professors in Padua and Bologna tended to publish their commentaries on Aristotle, those at Pisa left theirs mostly in manuscript.

Both by reading the works o f the professors and by looking into student correspondence we see the quite conservative nature o f the teaching there, which contrasts markedly with certain more progressive tendencies to be found at Padua.®^ On the other hand, Galileo’s unpublished Logical Questions which apparently took form during the early 1580’s, when he was a student, show a full acquaintance with the logical developments in other universities o f Northern Italy.®® We know very little about the way logic was taught at Pisa, largely because we have few books and manuscripts by those who taught it. We do know that logic teaching was a low paid position and that one normally taught it for a few years before being named to a chair o f natural philosophy or medicine. This was apparently the case in most Italian universities and even one such as Zabarella, whose logical works became famous, spent only a few years teaching the subject before moving on to natural philosophy. ® We also have evidence, in the form o f a manuscript, that an introductory and somewhat condensed and elementary logic course was put on for those in the law faculty.®» At Pisa there is no evidence whatever, to the best o f my knowledge, o f any influence or even concern with Ramus during this period. Indeed, except for Viotti,®® little note seems to have been taken o f Ramus in Italy and the situation contrasts with most all o f the countries o f northern Europe where the impact o f the Ramist reform was most evident for more than a century.’ ®


In short, Pisa represents a stronghold o f conservative Aristotelianism little affected by outside influences and still very much in the medieval mold.’ Little new came from the philosophy faculty, but more interesting developments came from elsewhere. In fact, i f Pisa showed little innovative spirit in the standard philosophy curriculum, in other ways it was quite progressive. Botany, anatomy, humanities, and mathematics all show elements o f advanced attitudes and, occasionally, as in the case o f having the first established university botanical garden, Pisa gained a Europeanwide r e p u t a t i o n . Moreover, the year by year list o f books taught by the lecturer in humanities indicates that in that subject a very wide range o f Greek and Latin literature was c o v e r e d . ’ 3

Andrea Cesalpino was a botanist and medical man, but wrote more penetratingly on Peripatetic natural philosophy and with greater subsequent influence, both in Italy and abroad, than did any o f his colleagues who were professionally tied to teaching philosophy per seJ^ Galileo came from mathematics with a strong aversion to Aristotelian natural philosophy, though significantly enough many o f the problems to which he addressed himself were those o f the natural philosopher. Both o f these instances indicate that despite the fact that Aristotelianism was primarily the province o f the professional philosopher it also spread over into other disciplines. For Cesalpino it provided a structure within which to discuss theoretical problems o f natural philosophy o f interest to the physician. For Galileo it provided a framework within which to discuss a central problem on which his later fame was based, i.e. motion. Galileo rejected many aspects o f the Aristotelian analysis, but his ability eventually to set forth answers to that problem stemmed in large measure from his training in natural philosophy, as well as in mathematics.

Oxford presents a different and, in some ways, a more confusing picture, as well as one which is more nebulous owing to a much leaner array

o f extant documentary evidence.With regard to Oxford and particularly with regard to the teaching o f

philosophy, we are on much firmer ground for the end o f the sixteenth century than for the beginning.’ ® The growing importance o f the colleges as teaching institutions has made it much more difficult to pin down precise details o f teaching practice and, indeed, to determine who was actually teaching at any given time.’ ® For Oxford we seem to lack the rotuli which form the starting point for the study o f most other univer-

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sities. On the other hand, the fact that the medieval tradition o f frequent disputations by both students and masters continued to play an important role in the educational practice o f English universities gives us other insights into the situation.' ’ One v onders whether the actual approach to the study o f philosophy was different elsewhere or whether the surface differences merely hide fundamental similarities. A number o f the questions disputed'^® and perhaps some o f the disputations themselves are still preserved’ ® and give a valuable insight into the intellectual life in the university in the sixteenth century. Before turning to a fuller analysis o f these, however, I should like to briefly discuss other matters.

By and large Kearney’s overview®» o f the Oxford situation in the sixteenth century seems accurate enough, though his analysis is not based on the fullest possible exploitation o f the evidence and seldom penetrates as deeply as one might have wished. On the whole, however, his characterization o f Oxford as being in the first generation o f the sixteenth century scholastic, in the second humanist, and in the third Ramist, with a return to scholasticism at the end o f the century, seems plausible, i f perhaps not detailed enough. One o f the problems which must be faced is that we have different sorts o f evidence for different periods. The titles o f disputations, the published Aristotelian treatises, and a few manuscripts and notebooks o f Aristotelian orientation are almost all from the last quarter o f the century. It may well be that the middle o f the century was equally Aristotelian, but that we have less extant evidence with which to substantiate this fact. I fear that a definitive answer to philosophy teaching at Oxford during the first three quarters o f the sixteenth century must await a scholar who can devote several years to a careful consideration o f all o f the extant evidence. Consequently, the bulk o f my remarks must be directed towards the last quarter o f the century.

For the first time we see the beginnings o f the printing o f Aristotelian philosophical works in Britian. I f one looks at the history o f book printing, he is met with a fact which is unassailable. Very little Aristotle - indeed few classical editions o f any sort - was printed in Britain before the seventeenth and eighteenth century. The evidence o f the Index Aureliensis shows that nine Aristotle editions appeared in London, one only at Oxford, and one at Edinburgh in the sixteenth century with no other British imprints appearing.®^ This contrasts with over 450 sixteenth-century editions in France, over 200 in German-speaking lands, over 150 in Italy


and about 20 in Poland and a similar number in the Low Countries. The Iberian peninsula produced relatively few editions o f Aristotle in this list, but a great abundance o f conmientaries, o f which we have practically none from Britain. Thus, in the sixteenth century, the British Isles are very much on the outer margin o f the European philosophical culture in which they played a central role in the thirteenth and fourteenth centuries and will again assume an important position in the seventeenth century. Though there were not many books printed in Britain, nor were there many philosophers o f note in the sixteenth century the teaching o f the subject went on, though largely derivative from Continental sources.

Among the philosophers in Oxford who did produce books which had a certain importance and influence were Griffith Powel o f Jesus College and John Case o f St. John’s, among others. Powel’s commentaries on the Posterior Analytics and Sophistical Refutations o f 1594 and 1598® are much more advanced than the low level introductory manuals o f John Seton®4 and Edward Brerewood.®® Though perhaps some years behind the Continent in these matters, his books do draw very heavily upon Italian and other sources for the explication o f Aristotle’s ideas. In the Preface o f his two works he states clearly that N ifo and Pace would be followed in the Sophistical Refutations^^ and Pace, Zabarella, and Crellius were primary sources for the Posterior Analytics. ' What is more, there is frequent recourse to the Greek text and, even more interestingly, mathematical examples are often discussed. Though I have not specifically made a comparison on this matter, it strikes me that mathematics was more central to his conception o f logic than it had been for the Italians. Zabarella, nevertheless, was his main recent authority and the Paduan’s influence is everywhere evident. In short, Powel’s volumes are respectable and up- to-date compendia o f Aristotelian logic and should be related to the European-wide context rather than remaining the province o f a few scholars who work on British intellectual history in a most insular way.

The same strong Italian orientation is to be found in the work on demonstration by John Flavel®® o f Wadham College published in 1619. Not only is a specifically “ Paduan” topic such as Be regressu discussed in detail,®® but once again Zabarella is the major source o f ideas and the writings o f Petrella, Tomitano, Balduino, Tommaso de Vio, and Giulio Pace are utilized, as well as Soto, Crellius, and others. Nor is such an orientation confined to logical writings. Crakanthorpe’s Metaphysical

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o f the same date draws upon various Catholics including Zabarella, Fonseca, Bellarmino, and Sixtus o f Siena; as well as the Protestants Timpler, Keckermann, Zanchius, and Luther; besides the occultists Giorgi and Postel.

John Case®i is obviously a major figure in the development o f the late sixteenth-century wave o f scholasticism. He wrote several very bulky works on various branches o f Aristotelian philosophy. As a dominant force at Oxford at the end o f the sixteenth century he certainly deserves careful monographic treatment. Rather than discussing his work at length, in the present paper, however, I should like to say something about the quaestiones from the last quarter o f the century, published by Andrew Clark nearly a century ago but still largely unstudied.

These quaestiones were the ones set twice each year for the incepturi for the M.A. in arts. These disputations were the culmination o f the whole educational process, which in addition to requiring the student to hear a prescribed number o f lectures also involved a long series o f disputations in parvisis, which seem to have served as preparation for the more advanced disputations for the M.A.®^ We know little about the preliminary stages, but the topics discussed must have been elementary ones such as the questions raised in the introductory logic textbooks o f Seton and Brerewood. To some extent even this might be reconstructed through proper attention to manuscript sources.

The more advanced disputations disclose some rather interesting aspects. In addition to the lists o f Clark, several manuscripts seem to have either a record o f some o f the actual disputes or practice sessions meant to prepare one for the ordeal. A careful study o f these - as well as the report o f the disputations held during the visit o f Queen Elizabeth in 1566 and again in 1592® - can give us an insight not only into how they were carried out, but some idea o f nature o f philosophical discussion at Oxford.

Though the quaestiones themselves are largely from Aristotle and the peripatetic tradition, they betray certain constantly recurring themes, which should be investigated further. For example, quite unexpectedly the theme o f women comes in quite frequently, perhaps because England was then ruled by a Queen, but perhaps for other reasons as well. Topics such as “ An foeminae sint literis instruendae” recur time and again.®^

We also find an unexpected concern with various problems o f occultism. To what extent this side o f Renaissance thought was firmly entrenched in


Oxford at the time is not wholly clear, but we know that when the Savilian professorships o f geometry and astronomy were established by statute in 1619 it was expressly forbidden for the incumbents to cultivate the occult side o f their profession.®® This would seem to indicate that there were occultists about and, indeed, we need look no further than John Dee to discover that this is true.®" The quaestiones, however, are constantly concerned with such themes, as a few examples will show.®® In 1581 there was set a question o f judicial astrology, three years later there was one dealing with the problem o f sympathy and antipathy, which was repeated in 1603, in 1586 the basic alchemical question o f whether gold can be produced from base metals found its way into the disputations, in 1590 “ An divinatio astrologica sit probanda” was posed, and in 1593 a question for debate was “ An chymicus sit philosophus.”

The contemporary revival o f atomism is also well represented. The 1581 questions contain one on whether a plurality o f worlds is possible, and a similar one is repeated in 1588. The next year “ An visus sit extramittendo” was posed and may reflect Democritus’s peculiar theory o f vision.

We also find a strikingly large number o f epistemological questions which seem to reflect a sceptical threat. Perhaps this is connected with an interest in Sextus Empiricus and scepticism at Oxford in the late sixteenth century as evidenced by a Latin translation o f John Wolley now contained in MS Sandcroft 17.®® Though I am particularly sensitive to this issue, the interest in the basic sceptical problems seems unmistakable. In 1586 we find the question “ An omnia constent opinione,” which is again repeated in the same form in 1604. “ An contradicere sit summa scientia” is asked in 1593 and two years later “ An sit certa rerum scientia.” Certainly these are answered in an antisceptical fashion whenever the expected answer is indicated, but such topics still seem to indicate a pressing concern with the sceptical question. This once again intimates that we still are in need o f a solid scholarly study on scepticism in Tudor and Stuart England and one based on sound scholarly methodology rather than the philo-vernacularism o f the literary historian.^®®

Much more is to be learned from a careful study o f all o f the material relating to these disputations, but I hope that even my brief survey indicates what we might find there. What it seems safe to say, even at this very beginning stage o f inquiry, is that a wide range o f topics was discussed in philosophy at Oxford in the sixteenth century. While the an

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swers given to the questions posed were probably by and large Aristotelian, we find other positions being given serious consideration.

As I have indicated much work is still required before we can begin to understand in any systematic and penetrating way what philosophical life was like in sixteenth-century Oxford. The medieval carry-over o f the disputation technique seems to have functioned as pedagogic tool in the sixteenth century, when it had been eliminated by most other universities. One feels that in practice it was perhaps not too different from the “ Academic” change advocated by Ramus and Talon at Paris in mid-century, loi From this emphasis on encouraging the student to express himself and to engage in philosophical debate grew the tutorial system which later became the envy o f universities throughout the world.

VI. MED ICAL A N D SCIENTIFIC CHANGES WÎTHIN THE UNIVERSITIES

OF THE SIXTEENTH CEN TU R Y

In a previous section the impact o f new philosophical and scientific ideas on the development o f the sixteenth-century universities was minimized. Our statement there, however, is in need o f qualification. While it would be a mistake to over-emphasize the significance o f new ideas in the overall educational context, we must not go to the other extreme and accept the widely received opinion that universities o f the Renaissance were static and resistant to change. We have already given some indications how novel materials and subjects such as Platonic philosophy, were sometimes introduced into university curricula. It remains, however, to indicate other instances where the teaching o f medical and scientific subjects was affected in an important way. For the present, I shall principally concentrate on two areas o f study where innovations o f lasting influence became accepted into university teaching.

The first lies in the field o f medical studies where the sixteenth century saw the development o f several important changes in the way in which students were trained. Three innovations which come immediately to mind are the introduction o f botanical studies, clinical medicine, and public anatomical demonstrations. Each o f these played a significant role in insuring that the medical training which a student received at Padua for example, was far better at the end o f the sixteenth century than it had been at the beginning. In short, the education received by Harvey about 1600


was much different from that gained by Linacre a century p r e v i o u s l y .

Though the study o f botany had been closely tied to medicine from antiquity, it was only in the course o f the sixteenth century that specific chairs in the subject were established in medical faculties throughout Europe. After botany had been separated off from practical medicine for the first time with the establishment o f a chair o f botany at Rome in 1513, ®3 many other universities followed suit in the sixteenth century, including Padua (1533), Bologna (1534), Ferrara (1543), Pisa (1544), and Montpellier (1598). The teaching o f the subject was soon followed by the foundation o f botanical gardens, the first being those o f Pisa and Padua, both dating from about 1544.1® The second half o f the century saw such gardens springing up frequently in connection with the establishment o f university chairs. The university interest in materia medica was, o f course, accompanied by a growing fascination with simples and an extensive worldwide exchange o f both botanical information and botanical specimens, which led to a vastly increased knowledge o f the richness o f the plant world.i®^ The institutional establishment o f botany also brought with it much more, however. Beginning with Luca Ghini’s teaching at Bologna in 1534 and later at Pisa, a broad approach to the study o f the natural world developed among university botanists.ô® In addition to theoretical instruction in the subject, students were familiarized with the plants themselves and with the range o f their uses. ®’ Benedetto Varchi, who was one o f Ghini’s students at Bologna, later recalled that the practical aspect o f his master’s teaching extended to several fields o f natural history other than botany.i®^ in fact, university lecturers on botany quite soon began lecturing upon minerals,i®^ and perhaps also poisons.ii® By the second half o f the sixteenth century the teacher o f botany could cover a wide range o f natural history subjects in his lectures and even a wider range in his own researches. This is perhaps best exemplified by Ulisse Aldrovandi, whose significance in this respect does not yet seem wholly appreciated, m In brief, the introduction o f botany into the medical curriculum had far reaching implications for the development o f a medical and scientific education more broadly based than previously, and this novel element was a contribution o f the sixteenth century.

Another important addition was the introduction o f a clinical element into university medical education.î^ Undoubtedly the roots o f this go far back into the Middle Ages and practical medicine had always been a

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part o f the education, sometimes, as at Montpellier, being the dominant part. W e also know that the Padua statutes o f 1496 spell out the requirement that the medical student spend at least a year working alongside “ a famous physician.” ii3 The precise meaning o f the stipulation is somewhat vague, but by the middle o f the sixteenth century, we can recognize the beginnings o f the institutionalization o f clinical practice in the training o f the physician. The individual usually credited with originating the practice o f taking students with him to the bedsides o f the ill is Giambattista da Monte. The practice was apparently already established at Padua somewhat earlier, for Vesalius tells us o f this requirement as early as 1537. In any case, before mid-century, students were used to visiting the ill o f the hospital o f S. Francesco with their professor and learning at first hand the practical aspects o f treating such patients. Thus, besides the renewal o f medical studies through reading o f Galenic texts that were not known to the Middle Ages, there was a parallel evolution o f the practical side o f the training o f students.

A third important contribution on the part o f university medical faculties was the development o f immensely improved anatomical teaching. The revolution o f Vesalius is well known, but in actuality his work is merely the high point o f the remarkable changes in the subject which span from the end o f the fifteenth century to the end o f the sixteenth. Though the origins o f pubUc anatomical demonstrations are masked in obscurity, it is evident that temporary anatomical theaters were already in use at Padua in the 1490s when Alessandro Benedetti was teaching the s u b j e c t ,

The role o f dissection became increasingly important during the sixteenth century with Vesalius, Falloppia, and others. By the end o f the century the first permanent theaters had been constructed and the teaching o f the subject was on a wholly new footing. This development is so well known, however, that there is no need to delay over a further discussion o f it other than saying that this important advance in medical science and medical education evolved wholly within university precincts.

A second area o f change, and perhaps o f significant advance, which I should like to discuss is that o f mathematics. Once again I shall confine the discussion to sixteenth century Italian universities, particularly two o f them, Padua and Pisa. Unfortunately, our understanding o f the position o f mathematics in sixteenth century universities is as yet in a very rudimentary state. While scholars have devoted some attention to the study


of sixteenth century mathematics, little attempt has been made to understand the teaching and research in the subject which went on within the universities. From the middle o f the century onward we find two different patterns o f mathematical teaching developing at Pisa and at Padua.

It must be kept in mind that mathematics, as the subject was understood in the sixteenth century, comprised various other disciplines including astronomy, astrology, optics, geography, mechanics, etc. University teaching reflects this. Euclid, Sacrobosco, and Ptolemy were the mainstays o f the mathematics curriculum, but other works, including those o f Georg Purbach and Oronce Fine, were also taught in some localities. As mentioned above we can see two different orientations at Pisa and at Padua. It so happens that Galileo taught at both places, therefore, to some extent, being heir o f both traditions. Let us first look at Pisa.ii^

The statutes o f that studio specifically state that Euclid, Sacrobosco, and Ptolemy were the texts to be taught by the lecturer o f mathematics in a three year cycle. We find, through reference to the archival records o f what was actually taught, that this pattern was in the main followed, though with certain modifications. For example, works o f Purbach and Finé were also taught upon occasion and the annual sequence o f text prescribed by the statutes was not followed ad litteram. The statutory requirement for Ptolemy is left quite vague, saying merely quaedam Ptolmaei. A study o f the extant manuscript materials shows that this allowed the lecturers quite a latitude in the selection o f teaching texts. The Quadri- partitium, a rather brief work o f Ptolemy dedicated to judicial astrology and having strongly occult overtones, was a favorite teaching text. Moreover, the Geography was apparently taught quite often. From the teaching activity o f Filippo Fantoni, GaUleo’s predecessor as a mathematics lecturer, emerged a long work synthesizing the fields o f geography and astronomy. Included in it are sections describing parts o f the New World which had recently been revealed by the Renaissance explorations. Thus the knowledge contained in Ptolemy’s Geography was supplemented by new materials and an attempt was made to synthesize the whole into a Compendiaria institutio cosmographiae et astronomiae. Though this work survives in several manuscripts and was being prepared for publication at the time o f Fantoni’s death in 1591, it was never printed. Other writings to emerge from the Pisan mathematicians are oriented in a strongly astrological way, though we also find among the manuscripts left behind

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treatises on motion and on mathematical certitude, which form direct links with the Padua tradition and with Galileo’s early Pisan work. Nevertheless, the astrological and pseudo-scientific side o f the mathematical arts seem to have been more cultivated at Pisa than were those aspects which modern historians o f science find more congenial.

The situation in Padua in the sixteenth century seems to have been somewhat different, though I must admit that I have not yet had the opportunity to look into the possible intrusions o f the occult tradition in the mathematical teaching there, From all indications Paduan mathematics instruction had a broader basis, a wider range o f mathematical and astronomical topics were taught, and there were fruitful interconnections between mathematics and other subjects contained in the university curriculum. What is more the Paduan lecturers published a larger number o f works, and we are consequently in possession o f more materials through which to understand what was being done there.

As at Pisa, Euclid, Sacrobosco, and Ptolemy dominated. Again, there is clear evidence that Ptolemy’s Geography was taught upon occasion and that Francesco Barozzi, one o f the key figures in Paduan mathematics o f the second half o f the sixteenth century, devoted a good deal o f his time in preparing a Cosmographia, based in part on Ptolemy. In addition, however, there was also a serious interest in Proclus’s mathematical works. After Alessandro Piccolomini first came into contact with the Commentary on Book I o f Euclid's Elements during his years at Padua, it remained for Barozzi to publish a Latin version o f this work for the first time in 1560.11® There was, in fact, a strong tendency among Paduan mathematicians, during the half century before Galileo came there, to go back to Greek sources. Thus, such an effort was not confined to humanist-mathematicians outside the universities.

Perhaps more significant, but even less studied, was the interest o f these Paduan mathematicians in certain key philosophical problems connected with methodology and natural philosophy. Though attention has been given to a possible influence o f methodological discussions by Paduan philosophers on Galileo, little has been done to investigate the methodological interests o f pre-Galileian Paduan mathematicians. Yet such an interest is manifest. Several o f the mathematicians wrote on Aristotle’s logical works, including the Posterior AnalyticsM^ A t Padua, we also find an interest in the Pseudo-Aristotelian Mechanica throughout


the second half o f the sixteenth century, thus establishing it as one o f the centers for study o f the work.i^o Three successive mathematics teachers, Catena (1548-1576), Moleto (1577-1588), and Galileo (1592-1610), all taught the book along with other mathematical works. Moleto, as we learn from Antonio Riccoboni,i2 i his contemporary and the first historian of the university, taught a wide range o f mathematical subjects, including, in addition to the more usual ones, optics, mechanics, cosmography, anemography, and hydrography. Barozzi, who was a contemporary o f Moleto, had an equally broad range o f interests, as his publications show.

One is compelled to conclude that mathematics teaching and research, as it developed in sixteenth century universities, was somewhat more broadly conceived than has usually been thought to be the case. This can also be verified through looking at the situation beyond Padua and Pisa. It has recently been shown that mathematics played quite an important role in the Jesuit Ratio Studiorum, in part at least through the efforts o f Christopher Clavius, who was responsible for impressing upon his colleagues in the Society the importance o f mathematical studies. At the end o f the sixteenth and beginning o f the seventeenth century, we also find the development o f practical mathematical skills within university contexts,

for example at Leiden.I have covered all o f this far too briefly, but from even the few examples

given in medical and mathematical studies, I hope I have been able to indicate to sonie degree that new and important fields o f study could enter into university curricula. The standard accounts perhaps focus unduly upon the failure o f universities to adopt the Copernican system and tend to lose sight o f the changes which were made. A more accurate assessment o f the situation must however be based on further research in the source materials, accompanied by an attempt to abandon the worn out clichés and slogans which plague most general interpretations o f the period.

VII. REGIONAL VARIATIO NS

While at this stage o f our knowledge it would be impossible to give a full panorama o f university philosophy in Europe in the sixteenth century, we can at least attempt to sketch in a brief picture region by region.

Let us start with Italy, where humanism emerged first and began to exert some influences on the u n i v e r s i t i e s . 122 it was there, presumably for

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the first time, that Aristotle was taught from the Greek text. In the beginning, this was done by the humanists who were teaching moral philosophy, but by 1497 a chair for the teaching o f the natural philosophy o f Aristotle in Greek was instituted at Padua.i^s in the course o f the sixteenth century, we find an increasing tendency to read and comment on the Greek text in university philosophy courses. Moreover, as the sixteenth century advanced, the Greek commentaries on Aristotle (Alexander, Themistius, Philoponus, Simplicius), some o f which were only recovered in the fifteenth and sixteenth centuries, attained an increasing importance in the interpretive framework.124 On the other hand, the medieval approach to Aristotle continued throughout the sixteenth century and the constant reprinting o f Averroes’s commentaries on the works (especially between 1550 and 1575) bear eloquent witness to this fact.i^s Consequently, in Italy, and this holds, as we shall see, for other areas as well, there was a mixture o f old and new, o f conservative as well as progressive tendencies. This admixture o f “ medieval” and “ humanistic” elements, often juxtaposed in a most unexpected way, was a constant feature o f sixteenth- century philosophical life.

In Italy, we find a strong continuity, it seems, with the medieval approach o f direct reading and commentary on the works o f Aristotle himself. In most places, students still read (or, at least, had read to them) the prescribed texts with commentaries, and, from what I have been able to gather, handbooks and compendia were significantly less used than in most other countries.126 jh e extensive and detailed commentary which was so common in thirteenth and fourteenth-century universities continued to dominate the Italian scene to the end o f the sixteenth and into the seventeenth century. Again there may be regional variations in this, and further study o f the matter is required. Extensive commentaries on one or more o f Aristotle’s works were published by Nifo, Boccadiferro, and Vimercato down to Pendasio, Zabarella, Cremonini and Liceto at the end o f the century and into the beginning o f the next one.

In Spain and Portugal we find in many ways a quite different picture. First o f all there was not the strong fourteenth and fifteenth century tradition o f Aristotelian Scholasticism which we find in most o f the remainder o f Europe. A strong emphasis on this philosophy seems to have come to Spain only with Francisco de Victoria’s return from his Paris studies.127 This tradition arrived roughly at the same time as did Eras-


mian h u m a n i s m ^ ^ s and both had enormous fortunae. On the whole the philosophy in sixteenth-century Spanish and Portuguese universities can be characterized as “ conservative” in the sense o f perhaps retaining more o f the medieval characteristics than what we find elsewhere. Medieval logic and natural philosophy seems to have held on longer on the Iberian peninsulai29 than in Italy, for example. Morover, humanistic influence, particularly by way o f emphasizing the Greek text and introducing an extended range o f ancient commentaries, was from all indications less prominent than in Italy. Towards the end o f the century in the wake o f the post-Tridentine Counter-Reformation, there was a very strong Thomistic revival, especially in the “ School o f Salamanca,” where the markedly theological orientation o f Francisco de Victoria was carried on by Cano, Soto, and Bânez.i3o Though there was a continuing interest in problems o f natural philosophy, such as motion, through the middle o f the century, the ultimate orientation became increasingly theological as the Counter-Reformation implemented by the Council o f Trent took hold. This led to a textbook tradition, which supplanted the careful reading o f Aristotelian writings, in the next century becoming formalized in the comprehensive handbooks o f John o f St. Thomas^®^ and the Alcalà Cursus. These were strongly theological in orientation, and the previous emphasis on natural philosophy and logic which had been a part o f medieval scholasticism is present only in a severely watered-down ver-sion.133

In Portugal the development was along somewhat different lines. In place o f a handbook approach, the Coimbra commentaries took form.i34 In these there is still a very strong focus on the text, the full humanistic apparatus which had been acquired in the past century being utilized to interpret the Greek Aristotle. The Coimbra editions also contain a comprehensive commentary, though theological elements, e.g. in the Physics, are emphasized and the more naturalistic aspects seem definitely to be played down.^®® Nevertheless, they are models o f what a real “ text” book should be, and they exerted an enormous influence not only in the Iberian peninsula but also in Catholic Germany, the Low Countries, and

France.^®®France presents particular problems. On the one hand we know that

far more sixteenth-century editions o f Aristotle were published on French soil than elsewhere; on the other hand, we have very little detailed modem

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secondary literature on university philosophy teaching there during the Renaissance and seventeenth century.^^v of the approximately 1100 sixteenth-century editions o f Aristotelica recently listed in the Index Aure- liensis we find that about 300 came from Paris and more than 150 from Lyon, the two most important centers (Venice produced only 134).i38 Who read these editions? O f course some were exported, but what happened to the many copies which remained in France? While Paris is perhaps the best studied o f the medieval universities, as we reach 1500 we are faced with a nearly complete blank when it comes to understanding what happened in the day to day teaching o f philosophy or in even the decade to decade development o f the subject. Ramus and Talon, o f course, caused an uproar, but while that was happening university life certainly continued as usual. 1 9 The other French universities, with perhaps the exception o f the medical faculty at M o n tp e l l i e r , a r e equally little studied. Early in the century we know that the fourteenth-century traditions o f natural philosophy continued in France, but this seems to have died out some time in the ISlOs. " ! Sixteenth-century France was torn by religious dispute giving rise to a vast polemical literature, and we also see the rise o f a rich new literary culture, but what was happening in the university philosophy teaching? Here is a vast field o f research yet to be tapped, and one is hesitant to hazard even the wildest o f guesses.

In Germany and the Low Countries the picture is a bit clearer. Both were strongholds o f Scholastic Aristotelianism o f a remarkable range o f varieties. With the coming o f Luther and the Reformation there was a strong reaction against the rationalistic approach o f scholastic philosophy and theology. Already in the Heidelberg Disputation o f 1518 this is abundantly c l e a r . 142 j n f^ct, Luther was very unfavorably disposed toward the university philosophy t r a d i t i o n . What apparently happened, however, was that even the new somewhat anti-rationalistic approach o f a Luther had to be adapted for didactic purposes and through Melanchthon the teaching method o f Reformed universities became thoroughly Aristote- lian.144 There was a strong dose o f humanism to be sure - one need only look at Melanchthon’s own commentaries on Aristotle to see this - but what emerged was still fundamentally Aristotelian, though Aristotelian with a difference. A t Tübingen, for instance, the teaching o f Jakob Schegki‘ 5 and Andreas Planer,i46 which spanned most o f the sixteenth century, indicates a clear knowledge o f tradition as well as novelty. The


moral training o f the individual seems, however, to have been the main objective o f university education. ' ' Toward the end o f the century and through most o f the seventeenth, we find the development o f a strong orientation toward text book philosophy which sets the foundation for the Wolflian tradition which emerged at the beginning o f the eighteenth

century.With the Reformation in Germany there was a split in the universities.

Some, e.g. Tübingen and Wittemberg, became Protestant, while others, e.g. Freiburg and Cologne, remained Catholic. New universities show the same split, some are Protestant (e.g. Jena) and others are Catholic (e.g. Würzburg). Toward the end o f the sixteenth century, the Jesuits became strong and dominated teaching in the latter group.^^s As elsewhere, Jesuit education became closely aligned with humanism and with Aristotelian philosophy. Perhaps more dependent on Iberian and Italian traditions than were the Protestants - though only slightly so -, the Catholics too continued to teach the traditional texts. A t the end o f the century, however, when the Protestants went more and more in the direction o f handbooks and compendia, the Jesuits adopted the Coimbra course.

German Protestants and Catholics alike were keenly alive to what was happening south o f the Alps. Zabarella in logic,i®® Cesalpino in natural philosophy,i5i and Suarez in metaphysics^^a were used by both groups, while the gradual invasion o f Ramus was more confined to the Protestants.

In Britain we see certain reflections o f the continental situation. Cambridge was not really significantly different from Oxford - at least when viewed in the perspective o f the European-wide situation. There were, o f course, variations in detail. The Scottish universities offer a somewhat different picture. Aberdeen, Edinburgh, Glasgow, and St. Andrews all seem to have adhered to a strong European commentary system o f exposition o f Aristotle,1 3 indicating a certain contrast with the English universities.

For England, the general picture o f philosophy teaching is as follows. After the early sixteenth century brought a wave o f enthusiasm for humanism,i54 not only with native born men such as Colet, More, and Linacre, but with great Continental figures such as Erasmus and Vives which was continued in mid-century by Pole, Hervet, and others, there seems to have been a growing tendency towards the end o f the century to return to an Aristotelian curriculum. Printed editions o f Aristotle and o f

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peripatetic commentaries proliferated, and we see more and more manuscript works o f similar orientation. The seventeenth century saw a continuation o f this, only partially stemmed by the strong personalities and intellectual perspicacity o f the Cambridge Platonists who built upon the Ficinian Platonic tradition introduced to England a century earlier by Colet and More. Like most other places, after a wavering induced by humanist reform in the first half o f the sixteenth century, there was a return to Aristotelian orthodoxy, which was supplanted only in the second half o f the seventeenth century, when Cartesianism, the New Science, Lockean empiricism, and other novel developments found theirway into universities.i^s

V I I I . C O N C L U S I O N S

The general picture we have then on the basis o f this preliminary analysis indicates once more that we must look at the whole situation in greater detail - locality by locality and decade by decade. Until this is done - at least for a substantial part o f the whole - we cannot hope to have more than a few vague and questionable generalizations at our disposal. Yet, even at this stage, we can be fairly sure o f certain matters.

First o f all, several fourteenth-century traditions - including nominalism, the logical traditions o f sophismata and insolubilia, and the Merton and Paris schools o f philosophy o f motion - continued on into the first few decades o f the sixteenth century and after that quickly lost ground to other approaches and sets o f problems. The printing history o f the medieval texts in question as well as new commentaries being written on Aristotle indicate this. Why this happened is not clear. Humanism had a strong impact, as did the réintroduction o f the writings o f the Greek commentators on Aristotle, but neither o f these facts explains why the calculatores and writers on sophismata lost out, while the commentaries o f Aver- roes did not. In brief, certain medieval aspects o f the tradition expired in the early sixteenth century, while other equally medieval aspects continued to play an important role.

Secondly, though I am unable yet to document this precisely it seems increasingly clear to me that it was during the first third o f the sixteenth century that humanism began to play an ever more important role in the philosophical teaching o f the universities. Erasmianism invaded Spain


and England, Aristotle was increasingly taught from the Greek text in Italy, and German universities such as H e i d e l b e r g ^ ^ e and Tiibingen^s’ came to absorb humanistic ideals in a steadily expanding way. This wave o f enthusiasm left a permanent mark, though during the second half o f the century there was, in certain quarters at least, a return to a more traditional sort o f Aristotelian orthodoxy.

This leads me to the third point. Even where there was some degree o f innovation in philosophy teaching - the use o f Valla and Trapezuntius in some logic courses in Spain, a strong development o f humanism at Paris and Oxford and Agricola’s increasing influence in dialectic - this gave way to a new burst o f emphasis on Aristotle towards the end o f the century. This seems to be evident nearly everywhere in Europe. What is more this new wave o f enthusiasm for the Stagirite carried on into the seventeenth century and was a dominant factor in university education for most, i f not all o f the century. The fact that there was a visible wave o f humanist anti- Aristotelian and anti-Scholastic thought in the first half o f the sixteenth century - Erasmus, More, Ramus - has led interpreters to assume that that was the death knell o f the movement. What they fail to realize is that it revived and was probably stronger (or at least as strong) in the first half o f the seventeenth century than in the first half o f the sixteenth.

Finally, I should like to propose what I feel might be a possible explanation for the Aristotelian “ revival.” As the new religiously divided Europe took shape during the middle years o f the century, a new line o f rational defense had to be found. Though scepticism had a certain degree o f novelty and charm for a few, it was not - as it never has been - the philosophical position o f the many and, certainly, was not a philosophy which could be institutionalized. Though mysticism and anti-rationalism were rife in the later Middle Ages and into the sixteenth century - we might recall the Imitatio Christi and the Rhineland mystics, Geiler von Kayserberg and Sebastian Brant, the Joachimites and Savonarola - Catholics and Protestants alike (at least the bulk o f them represented in intellectual circles) took refuge in an already well-known and easily accessible rational approach to the world: Aristotelianism. Lutheran anti-intellectualism was short-lived and Catholic devotionalism and mysticism proved to be but a splinter movement and Trent ruled that there was to be a tightening o f reigns, a return to discipline, and carefully structured intellectual life. Thus, after the initial smoke caused by the confessional fragmentation

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had blown away, all sides concentrated upon educational reforms whereby theologians and polemicists could be trained in a new orthodoxy. The basis o f all these was one or another variety o f Aristotelian-based philosophy. Thus, Aristotelianism continued as the foundation stone o f philosophical education. There were differences, however, between these new “ Aristotehanisms” i58 and the earlier ones, but the precise details o f this must be left for another occasion.

Consequently, in the final analysis, though Catholics and Protestants alike wanted to - and to a certain extent, did - reform their educational systems, the Aristotelian-Scholastic element still loomed large. As yet there was not a comprehensive and solid substitute to replace it. There were chinks in the armour to be sure, as there were internal flaws, which ultimately led to the tradition’s downfall. Perhaps these are more apparent to us in retrospect than to all but the most astute o f the system’s sixteenth- century critics. It was only the coming o f Cartesianism, the New Philosophy o f Galileo and others, and the seventeenth-century popularization and promulgation o f Copernicanism that led to the beginnings o f new philosophical traditions in universities. Thus, it was in the course o f the eighteenth century - the century in which the self-consciousness o f national characreristics, national vernacular literatures, and nationalism in general began to assume a dominating importance - that individualized national traditions in philosophy and science began developing. This is what ultimately replaced Aristotelianism in the universities. It must, nevertheless, always be remembered that even then many remnants o f the old system remained imbedded in the new and that one area o f Aristotelian philosophy, logic, was still retained for several more centuries with little change.

The Warburg Institute,University o f London

N O T E S

* This is a revised and expanded version of papers which have served as the basis of several seminars and lectures at the Warburg Institute, the University History Seminar at Oxford University, Summer Meeting of the British Society for the History of Science (Exeter, 1972), and elsewhere. I am indebted to Mr. T. H. Aston who first invited me to bring together some of my thoughts on this subject. I hope to be able to publish more detailed and more comprehensive studies on the same topic at some future date. In the


meantime I invite comments and suggestions of interested readers regarding the ideas put forth in the present paper, which has benefited from comments by Mrs. L. Jardine» C. H. Lohr, J. E. McGuire, I. W . F. Maclean, P. Machamer, and C. Webster.1 The best general survey remains S. d’Irsay, Histoire des universités françaises et étrangères des origines à nos jours (Paris, 1933-35), 2 vols. For a review of literature on the history of universities from the time of d’Irsay’s book until about 1960 see S. Stelling- Michaud, “L’histoire des universités au moyen âge et à la Renaissance au cours des vingt-cinq dernières années,” X le Congrès international des sciences historiques. Rapports I (I960), 97-143.2 Again d’Irsay (note 1) must remain the starting point. For the Middle Ages H. Rash- dall. The Universities o f Europe in the Middle Ages, ed. F. M. Powicke & A. B. Emden (Oxford, 1936), 3 vols, is the fundamental work. More limited in scope, but still useful are H. Denifle, Die Entstehung der Universitaten des Mittelalters bis 1400 (Berlin, 1885) ;G. Kaufmann, Geschichte der deutschen Universitaten (Stuttgart, 1888-96; reprint Graz, 1958); and C. M. Ajo G. y Sâinz de Zûfiiga, Historia de las universidades hispanicas (Madrid-Avila, 1957-66), 7 vols.3 Much valuable material is collected, however, in studies such as P. Dibon, La philosophie néerlandaise au siècle d‘or, I (Paris-Amsterdam, 1954) and B. Nardi, Saggi sull’- aristotelismo padovano dal secolo X IV al X V I (Firenze, 1958).4 The account of Rashdall (note 2) is still standard.5 R. Lemay, Abu Ma^shar and Latin Aristotelianism in the Twelfth Century (Beirut, 1962) and F. van Steenberghen, Aristotle in the West: The Origins o f Latin Aristotelianism, tr. L. Johnston (Louvain, 1955) tell the story. Further details are to be found in the Aristotles Latinus. Dr. C. H. Lohr is preparing a synthetic study on Aristotelianism in the West and when his work is complete a number of fundamental questions should be much clearer. See his ‘Aristotle in the West; Some Recent Books’, Traditio 25 (1969), 417-31 for some observations as well as his ‘Medieval Latin Aristotle Commentaries’, appearing serially in Traditio 23 (1967) sqq.« For Paris see C. Thurot, De l'organisation de l ’enseignement dans l ’université de Paris au moyen-âge (Paris, 1880; reprint Frankfurt, 1967) and for Oxford, J. A. Weisheipl, ‘Curriculum of the Faculty of Arts at Oxford in the Early Fourteenth Century’, Mediaeval Studies 26 (1964), 143-85. Much useful information is to be found in J. Koch (ed.), Artes liberales: Von der antiken Bilding zur Wissenschaft des Mittelalters (Koln-Leiden, 1959) and esp. Arts libéraux et philosophie au moyen âge [Actes du quatrième congrès international de philosophie médiévale] (Montréal-Paris, 1969).7 See especially Rashdall (note 2), Thurot (note 6), Weisheipl (note 6), and H. Denifle6 E. Chatelain (eds.). Chartularium Universitatis Parisiensis (Paris, 1889-97), 4 vols. A useful recent comparative study with further references is G. Leff", Paris and Oxford in the Thirteenth and Fourteenth Centuries (New York, 1968). It is worth remembering that theology developed later at many universities, especially those of Italy. On this see d’Irsay (note 1) 1,161 and the reference cited in the next note.8 For the documentation of this see P. O. Kristeller, ‘Renaissance Aristotelianism’, Greek, Roman and Byzantine Studies 6 (1965), 157-74, at 162-63 and the literature cited in his notes 14-16.9 There is now quite a substantial literature on the development of natural philosophy at Merton College. I shall limit myself to mentioning a few of the more important pieces. The starting point is now J. A. Weisheipl, ‘Repertorium Mertonense’, Mediaeval Studies 31 (1969), 174-224. See also Thomas o f Bradwardine, His Tractatus de Proportionibus: Its Significance fo r the Development o f Mathematical Physics, ed. H. L. Crosby

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(Madison, 1955); William Heytesbury, Medieval Logic and the Rise o f Mathematical Physics, ed. C. Wilson (Madison, 1956); M. Clagett, The Science o f Mechanics in the Middle Ages (Madison, \959), passim ', M. McVaugh, ‘Amald of Villanova and Brad- wardine’s Law’, Isis 58 (1967), 56-64; A. G. Molland, ‘TheGeometrical Background to the “Merton School’” , British Journal fo r the History o f Science 4 (1968-69), 105-25;E. Sylla, ‘Medieval Quantification of Qualities: The “ Merton School’” , Archive fo r History o f Exact Sciences 8 (1971), 9-39. Also important are two unpublished theses (thou^ Weisheipl’s has now mostly appeared in article form): J. A. Weisheipl, “Early Fourteenth-Century Physics and the Merton School” (Oxford, 1957) and A. G. Molland, '^Geometria speculativa of Thomas Bradwardine: Text with Critical Discussion” (Cambridge, 1967).

It is not entirely clear why these traditions died out relatively rapidly in the places where they originated, but continued on elsewhere. Their technical and specialized nature only in part explains this. It is now clear, however, that the fourteenth-century traditions continued on at Oxford only in abbreviated and watered-down versions. See J. M. Fletcher, “The Teaching and Study of Arts at Oxford c. 1400-c. 1520” (Oxford D. Phil. Thesis, 1961), 179-93.

In general it seems that rather derivative commentaries and compendia began to win the field. Important among these are the largely unstudied writings of Johannes Ver- soris, who perhaps as well as anyone represents the late medieval variety of Aristote- lianism which dominated universities of the late fifteenth century. A brief glance at the number of MSS and printed editions of his writings indicates their popularity. Ver- soris was a contemporary of Ficino and from all appearances was far better known to the literate public of Western Europe in the fifteenth century than was the famous Platonist. Modem scholarship has focused upon the Platonist rather than his Aristotelian contemporary, making him a famous “Renaissance” figure, while the Aristotelian lies lost in oblivion. For information on Versoris, with a listing of his works, MSS, and editions of them, and further bibliography, see the article by Lohr (note 5), in Traditio27 (1971), 290-9.

On this see esp. Clagett (note 9), 629-71. For further details see esp. M. Qagett, Giovanni Marliani and Late Medieval Physics (New York, 1941; reprint, 1967); P. Duhem, Système du monde (Paris, 1913-58), vol. X ; P. Duhem, Études sur Léonard de Vinci (Paris, 1906-13), 3 vols., passim’, T. E. James, “ De primo et ultimo instanti Petri Alboini Mantuani. Edited with an Introduction, Analysis, and Notes” (Columbia University Dissertation, 1967) ; A. Maier, Ander Grenze von Scholastik undNaturwissenschaft (Roma, 1952), 354-84 (“Die Nachwirkung der Oresme’schen Lehre”); M. Markowski, Burydanizm w Polsce w okresie przedkopernikanskim (Wroclaw et al., 1971), an important study with an English summary, pp. 531-39; C. Vasoli, ‘La cultura dei secoli XIV-XVr, in Atti del primo convegno internazioruile di ricognizione delle fonti per la storia della scienzaitaliana: i secoli X IV -X V I, ed. C. Maccagni (Firenze, 1967), 31-105. It should be noted that there was particularly at Paris some continuity of the fourteenth- century tradition, as Clagett (pp. 635-40) indicates. Further work is required on this topic, as well the related one of the extent of a revival at the end of the fifteenth and beginning of the sixteenth century at Paris as evidenced by the reprinting of the works of Buridan.12 For some information and further bibliography see my Critical Survey and Bibliography o f Studies on Renaissance Aristotelianism, 1958-1969 (Padova, 1971) and my ‘Towards a Reassessment of Renaissance Aristotelianism’, History o f Science 11 (1973), 159-93.


13 This opinion is so commonly portrayed in general histories of science and philosophy that there is no need to document it. Let us hope that we see in the next few decades a serious attempt to understand why things developed as they did in the early modern period in view of the actual primary evidence rather than beginning with a priori assumptions as to what was important and what was trivial.14 One clear indication of this is the extent to which Aristotle editions and commentaries continued to be printed throughout the sixteenth century. There were 1100 editions of one or more of Aristotle’s works during the century and probably nearly as many commentaries, compendia, paraphrases, etc. For a reasonably comprehensive list of Aristotle editions see F. E. Cranz (ed.), A Bibliography o f Aristotle Editions, 1501-1600 (Baden-Baden, 1971). Professor Cranz is preparing a more detailed bibliography of Aristotle editions before 1520 and his results will show quite clearly how many more Aristotle items there are than are listed under Aristotle’s name in the Index Aureliensis, which forms the basis of the volume mentioned above. O f other bibliographical works special mention should be made of L. W . Riley, Aristotle Texts and Commentaries to 1700 in the University o f Pennsylvania Library (Philadelphia, 1961). This collection should make the University of Pennsylvania a natural center for studies on later Aristotelianism.15 For Oxford, for example, see L. Stone ‘The Educational Revolution in England, 1560-l640',PastandPresentno. 28 (1964), and ‘Literacy and Education in England’, Past and Present no. 42 (1969), 6^139; Curtis (note 75). A recent interesting paper on Avignon is J. Verger, ‘Le rôle social de l’université d’Avignon au XVe siècle’. Bibliothèque d'humanisme et Renaissance 33 (1971), 489-504.1® On this see below pp. 494-5.1’ There was a strong Stoic element in Pomponazzi’s thought, for example. See L. Zanta, La renaissance du Stoïcisme au XVIe siècle (Paris, 1914) and Petri Pomponatii Mantuani libri quinque de fato, de libero arbitrio et de praedestinatione, ed. R. Lemay (Lugano, 1957), ad indicem (p. 482). It would be interesting to investigate sixteenth and seventeenth-century “Aristotelian” treatments of moral philosophy to determine the extent of Stoic influence there.18 Though there is some evidence of influence from Atomism in the sixteenth century, it seems to gain in importance in the next century in thinkers such as Sennert and Maig- nan. For the latter see Emmanuel Maignan, Cursus philosophicus, 2nd éd., enlarged (Lyon, 1673), 223-46 for a defense of the possibility of a void existing in nature, a quite un-Aristotelian position.19 Another equally important point is that even those thinkers who were avowedly anti-Aristotelian absorbed much more peripatetic doctrine then they themselves realized. See my comments on this in Schmitt, Survey (note 12), 129-32. A similar point is made by Kristeller (note 8), 157, 173.2® Though I am largely in agreement with the points made by N. W . Gilbert, ‘Renaissance Aristotelianism and Its Fate: Some Observations and Problems’, in Naturalism and Human Understanding. Essays on the Philosophy o f John Herman Randall, Jr. (Buffalo, 1967), 42-52,1 now feel that he has tended to underestimate the staying power of the Aristotelian tradition through most of the seventeenth century. Though many of the criticisms brought against it in the course of the sixteenth century were quite devastating on particular issues, few if any off’ered the same comprehensiveness. I am not certain that it is merely a question of “ inertia,” i.e. of the inability of new and better ideas to oust the older ones, but tend rather to feel that we see the whole matter somewhat out of perspective. While it may seem obvious to us that Copernicus is superior to Aristotle,

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it perhaps was not so obvious at the time and each side had supporters. The same is true of Ramism or Telesianism. This whole question deserves much fuller consideration.21 See esp. P. O. Kristeller, ‘Humanism and Scholasticism in the Italian Renaissance’, Studies in Renaissance Thought and Letters (Roma, 1956), 553-83 and E. Garin, ‘Le traduzioni umanistiche di Aristotele nel secolo X V ’, A tti e memorie dell’Accademia fiorentina di sdenze morali "La Colombaria,” n.s. 2 (1947-50), 55-104.22 See the Aristoteles latinus, ed. G. Lacombe et al. (Roma etc., 1939 sqq.) for details.23 See Cranz (note 14), 163-4. It should be noted, however, that the Secreta secretorum was never a university text and did not find its way into the university curriculum. Its widespread influence and diffusion is unquestionable, however. Of the extensive literature on the subject see the general remarks in L. Thorndike, History o f Magic and Experimental Science (New York, 1923-58) II, 267-lS and passim. O f more recent books see the two recent German theses W. Hirth, Studien zu den Gesundheitslehren des soge- nmnten Secreta secretorum (Heidelberg, 1969) and F. Wurms, Studien zu den deutschen und den lateinischen Prosafassung des pseudo-aristotelischen Secreta secretorum (Hamburg, 1970).24 A number of such spuria are not contained in the editions of the Opera by Isaac Casaubon (Lugduni, 1590) and by Guillaume DuVal (Lutetiae Parisiorum, 1619), though they do still contain quite a niunber of other works which modem scholarship generally holds not to be genuine.25 See esp. E. N. Tigerstedt, ‘Observations on the Reception of the Aristotelian Poetics in the Latin West’, Studies in the Renaissance 15 (1968), 7-24 and B. Weinberg, A History o f Literary Criticism in the Italian Renaissance (Chicago, 1961), 2 vols.2® See H. M. Nobis, ‘Über zwei Handschriften zur friihneuzeitlichen Mechanik in italienischen Bibliotheken’, Sudhoffs Archiv 53 ( 1969), 326-32; idem., ‘Die wissenschafts- historische Bedeutung der peripatetischen Quaestiones mechanicae ais Anlass für die Frage nach ihrem Verfasser’, Maia 18 (1966), 265-76; M. Schramm, ‘The Mechanical Problems of the Corpus Aristotelicum, the Elementa Iordani super Demonstrationem Ponderum^ and the Mechanics of the Sixteenth Century’, in Maccagni (note 11), 151-63 ; and P. L. Rose & S. Drake, ‘The Pseudo-Aristotelian Questions in Mechanics in Renaissance Culture’, Studies in the Renaissance 18 (1971), 65-104. It should be noted that the Mechanica is generally thought by most modem scholars (though Nobis, in the works cited above, is an exception) to be spurious. Nevertheless, it seems to be a relatively early work of the Peripatetic school and maintained an important position throughout the sixteenth century.27 This, however, has yet to be docimiented. For some indications see Garin (note 21) ; J. Glucker, ‘Casaubon’s Aristotle’, Classica et Mediaevalia 25 (1964), 274-96; L. Minio- Paluello, “Attività filosofico-editoriale aristotelica dell’Umanesimo veneziano,” in Umanesimo europeo e umanesimo veneziano (Firenze, 1964), 245-62; J. Soudek, ‘Leonardo Bruni and His Public: A Statistical and Interpretative Study of the Annotated Version of the (Pseudo-) Aristotelian Economics', Studies in Medieval and Renaissance History 5 (1968), 51-136; and E. F. Rice, ‘Humanist Aristotelianism in France: Jacques Lefèvre d’Étaples and His Circle’, in A. H. T. Levi (ed.). Humanism in France at the End o f the Middle Ages and in the Early Renaissance (Manchester, 1970), 132-49.28 One sees that translations by Quattrocento figures such as George of Trebizond, Theodoms Gaza, Bessarion, and Poliziano came gradually to replace the standard medieval ones. In the sixteenth century, the translations of Lefèvre, Vatable, Périon, and Grouchy, among others, became increasingly popular. Very little work indeed has been done on these sixteenth-century translators and their editions and it is difficult in


many cases even to find out the basic facts about their lives. It must also be noted, however, that new sixteenth-century translations of a “medieval” commentator such as Averroes were made in profusion. Of Averroes’s 38 extant commentaries on Aristotle, 15 were translated (from Arabic) into Latin in the thirteenth century, and 19 more were translated (from Hebrew) into Latin in the sixteenth century! See H. A. Wolfson, ‘Revised Plan for the Publication of a Corpus Commentariorum Averrois in Aristotelem' Speculum 38 (1963), 88-104, at 92-94. This startling fact should be kept constantly in mind when we are tempted to see Averroism as fading out about 1500 and a purified, humanistic approach to Aristotle carrying the day after that. Multi-volume editions of Aristotle with Averroes’s commentaries appeared at Venice in 1550-52,1560,1562, and 1575. For details see Cranz (note 14).29 See below note 123.

This edition with translations and commentary on the most important works of Aristotle appeared at Coimbra between 1592 and 1605 and was often reprinted elsewhere. See F. Stegmiiller, Filosofia e teologia nos universidades de Coimbra e Évora no século X V I (Coimbra, 1959), 95-99 (with further references). For a list of the many editions of the commentaries see C. Sommervogel, Bibliothèque de la Compagnie de

nouvelle éd. (Bmssels-Paris, 1890-1932) II, 1273-78; IX, 62-63, which is probably the fullest list now available. Also see below, note 136.

He produced editions with Latin translations and commentaries of the Organon (Geneva, 1584; Frankfurt, 1591; Frankfurt, 1592; Frankfurt, 1597; Frankfurt, 1598; Geneva, 1605; Hanau, 1606; Hanau, 1611; Hanau, 1617; Hanau, 1623; Helmstadt, 1682), the De anima (Frankfurt, 1596; Hanau, 1611 ; Frankfurt, 1621), and the Physica (Frankfurt, 1596; Hanau, 1608; Hanau, 1629).®2 This can be verified by the reader by looking at most any commentary (but not all) on Aristotle from the sixteenth century. An attentive reading of representative commentaries on Aristotle from different localities could give us some indication of the level of knowledge of the Greek text the writer assumed on the part of his readers. Though I have not studied this matter in detail, it seems clear to me that at Padua it was assumed that students had a better grasp of Greek than at Pisa (for the period 1550- 1600), for example. It also seems to the present writer, on the basis of his reading in printed and manuscript commentaries on Aristotle, that there was a general and substantial increase in literacy in the Greek language among university students throughout Europe during the first half of the sixteenth century.53 F. Nitzsch, Luther und Aristoteles (Kiel, 1883). Cf. d’Irsay (note 1), I, 308-9. For Luther’s anti-Aristotelian feelings see e.g. D. Martin Luthers Werke, Kritische Ausgabe (Weimar, 1883 sqq.) I, 221sqq.(99 conclusiones contra scholasticam theologiam [1517]), 355 {Disputatio Heidelbergae habita [1518], conclusio 36).34 On the shift from Luther’s view to the more sympathetic attitude of Melanchthon see P. Petersen, Geschichte der Aristolelischen Philosophie im Protestantischen Deutschland (Leipzig, 1921), esp. 19-108 and E. Lewalter, Spanisch-Jesuitische und Deutsch- Lutherische Metaphysik des 17. Jahrhunderts (Hamburg, 1935; repr. Darmstadt, 1967).35 See below pp. 509-11.3* For some indications see Petersen (note 34), 287-93 and passim', K. Eschweiler, ‘Die Philosophie der spanischen Spatscholastik auf den deutschen Universitaten des 17. Jahrhunderts,’ Spanische Forschungen der Gorres-Gesellschaft, I. Reihe, Band I (1928), 251-325; M. Wundt, Die deutsche Schulmetaphysik des 17. Jahrhunderts (Tübingen, 1939); and E. Lewalter, Spanisch-Jesuitische und Deutsch-Lutherische Metaphysik des 17. Jahrhunderts (Hamburg, 1935; repr. Darmstadt, 1967).

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See Petersen (note 34). For the specific case of Zabarella see W. F. Edwards, “The Logic of lacopo Zabarella” (Columbia University Dissertation, 1960). The reader can easily verify for himself the extent to which the thought of Italian writers on Aristote- lianism penetrated German scholasticism by looking at the writings of the figures mentioned in Petersen’s book.

See, for example, the Quaestiones of John Day of Oriel College, Oxford, written in 1589 found in MS Oxford, Bodleian, Rawl. D. 274,127-259. as well as the writings of Powel, Case, Flavel, and Crakanthorpe cited below, pp. 499-500. It is also interesting to note that there are a series of notes on Zabarella’s De natura logicae made, it seems, by a Scottish student about 1600 in Edinburgh University Library MS Dc.3.89, fols. 152sqq.3 A few students of the period have taken a comparative view, but the majority have been content to focus upon one or another locality, or, at best, upon one or another religious grouping. A beginning, however, has been made in studies such as- E. J. Ashworth, ‘Propositional Logic in the Sixteenth and Early Seventeenth Centuries’, Notre Dame Journal o f Formal Logic 9 fl968), 179-92; ‘The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries’, Archiv f i ir Geschichte der Philosophie 51 (1969), 260-85; ‘The Treatment of Semantic Paradoxes from 1400 to 1700’, Notre Dame Journal o f Formal Logic 13 (1972), 34-52; N .W . Gilbert, Renaissance Concepts o f Method (New York, 1960) ; P. Reif, ‘The Textbook Tradition in Natural Philosophy’, Journal o f the History o f Ideas 30 (1969), 17-32; W. Risse, Die Logik der Neuzeit. Band /.• 1500-1640 (Stuttgart-Bad Cannstatt, 1964).

F. Buonamici,‘Sull’antico statuto della UniversitàdiPisa:alcunipreliminarinotizie storiche’. Annali delle Università toscane 30 (1911), 46-47.

S. Leite (ed.), Estatutos da universidade de Coimbra (1559) (Coimbra, 1963), 315-17.J. Haller, Die Anfange der Universitat Tubingen, 1477-1537 (Stuttgart, 1927-29),

II, 39^0.“Deputati ad sophistariam teneantur legere Logicam Pauli Veneti et Quaestiones

Strodi cum Dubiis Pauli Pergulensis et pro tertia lectione Regulas seu Sophysmata tisberi [i.e. Heytesbury],” F. Facciolati, Fasti Gymnasii Patavini (Patavii, 1757) II, 118.

See Drake & Rose (note 26), 92-100.45 Ibid., 94-6.

C, Annerstedt, Upsala Universitets Historia (Upsala, 1877f.), Bihang I, 278.On this question in general see Kristeller, Studies (note 21), 337-53, 553-83 and

Renaissance Thought H (New York, 1965), 20-68; Garin (note 21); and Soudek (note 27). The sixteenth-century teaching of moral philosophy at Padua has recently been treated by A. Poppi in a paper to be published in the volume cited below in note 58. For the moment see the summary in J.-C. Margolin, ‘Platon et Aristote à la Renaissance’, Bibliothèque d ’Humanisme et Renaissance 36 (1974), 157-73, at 161.

See my ‘The Faculty of Arts at Pisa at the Time of Galileo’, Physis 14 (1972), 243-72, at 254.

Statutes continued to prescribe the same texts well into the seventeenth century, however, and change seems to have come relatively slowly. This question has yet to te studied in detail. To limit ourselves to one example here we might mention that the so- called “Laudian Statutes” of 1636 have remarkable similarities to those of previous centiyies. See Statutes o f the University o f Oxford Codified in the Year 1636 under the Authority o f Archbishop Laud Chancellor o f the University, ed. J. Griffiths (Oxford, 1888), 33-40. But see Schmitt, Reassessment (note 12), note 22.

Metaphysics was not wholly without importance in the philosophy curriculum.


What I mean to emphasize here is that vis-à-vis logic and natural philosophy metaphysics did not have the central importance which it was to attain in the eighteenth and nineteenth centuries. See A. Gabriel, ‘Metaphysics in the Curriculum of Studies of the Mediaeval Universities’, in Die Metaphysik im Mittelalters, ed. P. Wilpert [Miscellanea Mediaevalia, vol. 2] (Berlin, 1963), 92-102 and Lewalter (note 36).51 For some indications see Cranz (Note 14).52 There is little literature indeed on this subject, but for some indications see Petersen (note 34), 166-86, for Germany, and A. Levi, French Moralists: The Theory o f the Passions 1585-1649 (Oxford, 1965), 152-65, for France. A striking example of how important Aristotelian ideas on moral philosophy still were and how influential they were on the crucial problems of the century is to be found in L. Hanke, Aristotle and the American Indians. A Study o f Race Prejudice in the Modern World (Chicago, 1959).53 p. O. Kristeller, ‘Francesco da Diacceto and Florentine Platonism in the Sixteenth Century’, in Studies (note 21), 287-336.54 E. Gilson, ‘Marsile Ficin et le Contra Gentiles', Archives d ’histoire doctrinale et littéraire du Moyen Age 24 (1957), 101-13; P. O. Kristeller, Le thomisme et la pensée italienne de la Renaissance (Montréal-Paris, 1967), esp. 93-98.1 have not been able to see A. B. Collins, “The Doctrine of Being in the Theologia Platonica of Marsilio Ficino, with Special Reference to the Influence of Thomas Aquinas” (Dissertation University of Toronto, 1968).55 E. Massa, I fondamenti metafisici della "dignitas hominis” e testi inediti di Egidio da Viterbo (Torino, 1954) and J. W . O ’Malley, Giles o f Viterbo on Church and Reform (Leiden, 1968), 15-16 & passim.5« S. Gibson, Statuta antiqua universitatis Oxoniensis (Oxford, 1931), 344, 390.57 We do know that quaestiones dealing with Platonic philosophy appeared from time to time in the disputations which students engaged in before taking the M.A. For example in 1602 the following question was set: “An depravati Alcibiadis mores ad parentes magis quam ad praeceptores sint referendi.” A. Clark (ed.). Register o f the University o f Oxford, vol. I I (1571-1622) : Part I, Introductions (Oxford, 1887 = Oxford Historical Society, vol. 10), 175. For further information on these quaestiones see below, 500-1.58 I have dealt with this in greater detail in a paper entitled “L’introduction de la philosophie platonicienne dans l’enseignement des universités à la Renaissance,” to be published in the Actes of the Seizième Colloque international du centre d’études supérieures de la Renaissance (Tours). For the present see Kristeller (note 21), 291-94 and Schmitt (note 48), 263-4.59 Louis Le Roy had strong sympathies with Plato and translated several works into French (see W. Gundersheimer, The Life and Works o f Louis Le Roy [Geneva, 1967]). Though the proposed reforms of Petrus Ramus and Omer Talon were strongly criticized by Jacques Charpentier, all three drew some inspiration from the Platonic tradition, though in different ways. For the influence of one aspect of the Platonic tradition on Ramus and Talon see, inter alia my Cicero Scepticus: A Study o f the Influence o f the Academica in the Renaissance (The Hague, 1972), 78-91. For Charpentier see his Platonis cum Aristotele in universa philosophia comparatio (Paris, 1573), which is very sympathetic to the Platonic tradition, as the Preface (fol. Diii) shows. Plato was apparently also taken seriously by Vincent RaflTar, Professor of Greek and Latin Philosophy from 1589 to 1606, whose works amply show this fact (copies in Bibliothèque Nationale) and on whom there is very little secondary literature indeed. He published De Platonicae atque Aris totelicae philosophiae conjunctione oratio... (Paris, 1604) (see

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B N catalogue, vol. 145, page 740). For some information on Raffar see C. P. Goujet, Mémoire historique et littéraire sur le collège de France (Paris, 1758; reprint Geneva, 1971) II, 223-34.

Procli Diadochi Lycii philosophi platonici ac mathematici probatissimi in primum Euclidis Elementorum librum Commentariorum in universam mathematicam disciplinam principium eruditionis tradentium libri I U I a Francisco Barocio... opera cura... (Patavii, 1560) and Francisci Barocii... Commentarius in locum Platonis obscurissimum et hactenus a nemine recte expositum in principio Dialogi octavi de Rep. ubi sermo habetur de numero geometrico de quo proverbium est, quod numero Platonis nihil obscurius (Bononiae, 1566).

For the history of the university see esp. the standard work A. Fabroni, Historia academiae pisanae... (Pisis, 1791-95), 3 vols., esp. vol. 2 for the sixteenth century. A brief survey is to be found in G. B. Picotti, “Per la storia dell’università di Pisa,” in his Scritti vari d istoriapisana e toscana... (Pisa, 1968), 11-48. See also Schmitt (note 48), and the recently published A. Verde, Lo studio fiorentino, 1473-1503: ricerche e documenti, vols. I-II (Firenze, 1973), which also deals with Pisa in the period indicated and has an extensive bibliography of other studies relevant to the same subject.

See Buonamici (note 40) for details.Relatively few university textbooks were printed at Florence, the major printing

center closest to Pisa. See, for example, A. M. Bandini, De florentina luntarum typo- graphia (Lucae, 1791), which shows that the Florentine branch of the Giunta publishing empire produced a much smaller percentage of university texts than did the Venice or Lyons branches. I am indebted to my friend William Pettas for information on this and other points regarding book printing in sixteenth-century Tuscany. A mere handful of suitable books were printed at Lucca, principally by Busdraghi. The question of the book trade and provision of textbooks for students in sixteenth-century Pisa does not seem to have been studied in detail as yet. Though there are several incunables printed at Pisa, there were apparently no books whatever produced in the city during the sixteenth century, a press being re-established only in 1609. For some information see U. Morini, ‘La tipografia in Pisa dal secolo XV alia metà del secolo X IX ’ and A. Segré, ‘Un libraio ed un tipografo nel secolo XVI in Pisa’, in Miscellanea storico-let- teraria a Francesco M ariotti nel cinquantesimo armo della sua carriera tipografica (Pisa, 1907), 34-43, 67-69; and F. Vincentini, ‘Notizie sulle stampede pisane dalle origini al I860’, Bollettino storico pisano 8 (1939), 33-63.

Many examples of this could be given. Giulio Angeli da Barga (tl601), who taught logic at Pisa and later medicine for some years (1577-92), seems to have published nothing, but left behind many manuscripts. Most are to be found at Pisa, Biblioteca universitaria, 231-234, 332-346, 355.1 am preparing a repertorium of the works of Pisa professors of the Faculty of Arts for the period 1543-1609. When this has been completed we shall see clearly the extent of the unpublished writings.

By this I do not mean to endorse the thesis of Renan, Busson, Randall, and others [recently reiterated by Martin Pine, ‘Pomponazzi and the Problem of “Double Truth” Journal o f the History o f Ideas 29 (1968), 163-67)] that there was a unique secular quality about Padua which made it more progressive than other universities. It seems to me that the objections of P. O. Kristeller, ‘The Myth of Renaissance Atheism and the French Tradition of Free Thought’, Journal o f the History o f Philosophy 6 (1968), 233-43 [but first published in Spanish many years ago] have not been adequately met by Pine.

What does seem evident, however, is that Padua was a wealthy and prestigious university in a sense in which Pisa was not. In medicine and in mathematics, as well as


in natural philosophy and logic, there was a degree of innovation and originality at Padua not to be found at Pisa.«« See MS Firenze, Biblioteca nazionale, Galileo 27. Cf. Schmitt (note 12), 45.

A. Poppi, La dottrina della scienza in Giacomo Zabarella (Padova, 1972), 16.MS Firenze, Biblioteca nazionale, magi. VIII. 49, fois. 176-99 contains a short

treatise on syllogisms by Francesco Buonamici apparently used in his instruction of law students. Cf. Garin, Scienza e vita civile nel Rinascimento italiano (Bari, 1965), 141. The extent to which the Aristotelian logical texts were used in the instruction of law students has hardly been studied. When the research of Dr. H. Jaeger of Paris, which in part deals with the way in which logical texts were used to instruct law students, has been published we should be in a better position to evaluate the significance of this aspect of “Aristotelianism.”

See N . W . Gilbert, Renaissance Concepts o f Method (New York, 1960), 152-57 and C. Vasoli, La dialettica e la retorica dell’Umanesimo (Milano, 1968), 521-27.

Ramus’s influence seems to have been confined nearly completely to Protestant philosophers. The researches of Ong, Risse, and Vasoli seem to show this.

See the remarks by Garin (note 68), 109-46 and E. A. Moody, ‘Galileo and Avem- pace: the Dynamics of the Leaning Tower Experiment’, Journal o f the History o f Ideas12 (1951), 163-93, 375-422, as well as my paper referred to in note 48 and my forthcoming papers ‘The University of Pisa in the Renaissance’, History o f Education 2 (1973) and ‘Girolamo Borro’s Multae sunt rwstrorum ignorantium causae (Ms. Vat. Ross. 1009)’, Humanism and Philosophy: Renaissance Essays in Honor o f Paul Oskar Kristeller (scheduled for publication in 1973).

By ‘conservative’ here I mean that the philosophy teaching at Pisa was little influenced by the humanist movement, which perhaps more than anything else represented pro- gressivism and novelty at the time. That is to say, at Pisa little attempt was made to study the Greek text of Aristotle and little use was made of the newly recovered ancient Greek commentaries on Aristotle. This, I think, offers a significant contrast with Padua. ’2 See our discussion below, p. 503.■8 For some indications see Schmitt (note 48).

See esp. U. Viviani, Tre medici aretini (A . Cesalpino, F. Redi, e F. F olli) (Arezzo, 1936), 5-72; the introduction of M. Dorolle to Césalpino, Questions péripatéticiennes (Paris, 1929), 1-93; and W. Pagel, William Harvey’s Biological Ideas (Basel, 1967), 169-209. For his influence in Germany some information is to be found in P. Petersen, (note 34).

C. E. Mallett, A History o f the University o f Oxford (London, 1924-27), 3 vols, is of little use, though it does present to us a number of facts and anecdotes. More valuable are W. S. Howell, Logic and Rhetoric in England 1500-1700 (Princeton, 1956); M. H. Curtis, Oxford and Cambridge in Transition 1558-1642 (Oxford, 1959); Fletcher (note 10); J. K. McConica, English Humanists and Reformation Politics (Oxford, 1965); andH. Kearney, Scholars and Gentlemen: Universities arui Society in Pre-Industrial Britain, 1500-1700 (London, 1970). Further bibliography is to be found in the excellent volume E. H. Cordeaux & D. H. Merry, A Bibliography o f Printed Works Relating to the University o f Oxford (Oxford, 1968). A new general history of the university is now being prepared under the direction of T. H. Aston.7® For some information on the changing situation see Curtis (note 75), 36ff. See also A. B. Emden, An Oxford Hall in Medieval Times, 2nd. ed. (Oxford, 1968), 228-9, which discusses the reduction of the number of halls in the late fifteenth and early sixteenth centuries.

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77 Clark (note 57) is still the best source of information on this.’8 Clark (note 57), 170-9,189-94 lists the questions disputed in philosophy and medicine for the years 1576-1622.’9 Some sample disputations seem to be preserved in Oxford, Bodleian Library, Rawl.D.274, fols. 127-259. This is John Day’s notebook and it illustrates both the range of questions discussed and the authorities used. To cite but a few examples should suflBce to give an idea of its contents: “An corpus naturale sit subiectum physices?” (with a mention of Zabarella in the discussion) [132]; “An ratio insit brutis?” (with references to Galen, Toletus, and Fonseca) [141]; “An motus sit in mobile vel in movente?” (with reference to Toletus) [144]; “An mixta moveantur admotum elementi praedominantis?” [159]; “An amicitia sit virtus?” (with a quotation from Plato in Greek) [213]. Among the authorities most frequently cited in the disputations are the Collegium Conim- bricense, Fonseca, Javellus, Piccolomineus, Thomas Aquinas, Toletus, Zabarella, and Zanchius. Cf. Kearney (note 75), 82-8.

Op. cit. For a discussion of the situation and an incisive critique of Kearney’s methodological and factual shortcomings see the review by J. K. McConica in English Historical Review 87 (1972), 121-5.

There were, however, other books of Aristotelian orientation and the early seventeenth century brought an increase in Aristotle editions. For Oxford see F. Madan, Oxford Books (Oxford, 1895-1931) I, 317 {ad indicem).*2 See Cranz (note 14) for details.*3 Analysis Analyticorum Posteriorum sive librorum Aristotelis de demonstratione, in qua singula capita per quaestiones et responsiones perspicue exponuntur', adhibitis quibusdam scholiis ex optimis quibusque interpretibus desumptis, opera et studio G. P. Oxoniensis confecta et edita in usum iuniorum (Oxoniae, 1594; editio secunda, Oxoniae, 1631) and Analysis lib. Aristotelis de sophisticis elenchis, in qua singula capita per quaestiones et responsionespercipue et dilucide exponuntur... opera et studio G. P. Oxoniensis confecta et edita in usum iuniorum (Oxoniae, 1598). For additional information on Powel see Dictionary o f National Biography (hereafter D N B ) XVI, 243.

Dialectica loannis Setoni Cantabrigensis... I have used the London, 1577 ed. The work was first printed, it seems, in 1545 and was reprinted at least ten times between then and 1639. For further information on the work and its author see Howell (note 75), 50-6.

Elementa logicae in gratiam studiosae iuventutis in Academia Oxoniensi. Authore Edouardo Brerewood olim Aeneanasensis alumno dignissimo (Londini, 1614), which was reprinted at least ten times by 1684. On Brerewood see DNB II, 1181-82.86 . Qui primos in hac re obtinent, sunt Niphus et Pacius, quorum uterque mihi post bellum finitum in subsidium venit, utriusque tamen ope et opera in quibusdam locis explicandis usus sum.” Analysis... de sophisticis elenchis... (note 83), fol. 4*’.87 “Ego levem ac simplicem illam viam tyronibus ostendi, per quam, tamquam per ianuam ad diligentissimam et exactissimam aliorum interpretationem, praesertim Zabarellae et Crellii (quos solos in hac re consuli vellem) aditus patefiat.” Analysis Analyticorum Posteriorum... (note 83), fol. 5>.88 Tractatus de demonstratione methodicus et polemicus quatuor libris absolutus: ante haec in usum iuventutis in Collegio Wadhami apud Oxonienses privatis praelectionibus traditus, a loanne Flavel Art. Mag. et eiusdem Collegii Socio (Oxoniae, 1619). On Flavel see D N B VII, 253.8 Ibid., Xyi-AX, De regressu, ubi obiter de circulo, which is largely drawn from Zabarella.


Introductio in metaphysicam authore Ri[chardo] Crakanthorpe olim Collegii Reginae Oxon. Socio (Oxoniae, 1619). The same author also wrote Logicae libri quinque: de praedicabilibus, de praedicamentis, de syllogismo, de syllogismo demonstrativo, de syllogismo probabili... (Londini, 1622), a long comprehensive treatment of the subject. Zabarella again stands out as a major authority. On Crakenthorpe see DNB V, 2-3 and Kearney (note 75), 83.91 In the near future I plan to work on Case in greater depth. For the present some information is contained in D NB III, 1171-2; Howell (note 75), 190-3; and W. H. Stevenson & H. E. Salter, Early History o f St. John’s College Oxford (Oxford, 1939) 133,256, 337-8. Among his writings are Speculum quaestionum moralium in universam Aristotelis philosophi summi Ethicen... (Oxoniae, 1585) [the first book printed at Oxford]; Summa veterum interpretum in universam dialecticam Aristotelis... (Oxoniae, 1592); Ancilla philosophiae seu epitome in octo libros physicorum Aristotelis... (Oxoniae, 1599); and Lapis philosophicus seu commentarius in octo libros physicorum Aristotelis in quo arcana physiologiae examinantur (Oxford, ca. 1600).

Cited above in note 78.See Clark (note 57), 21-3 ; Curtis (note 75), 89. For further information on the teach

ing system at Oxford at the time see also the works of Weisheipl (note 6) and Fletcher (note 10).

For details of the visits see the reports printed in C. Plummer (ed.), Elizabethan Oxford. Reprints o f Rare Tracts (Oxford, 1887).

Clark (note 57), 170-9, under the year 1581. Other related questions include: “An natura intendat foeminam?” (1585); “An foeminarum ingenia sint acutiora quam virorum?” (1590); “An foeminae jucundius vivant quam viri” (1495); “Foeminae esse debent literatae?” (1596); “An reprehendendus sit Aristoteles quia inter bona felicis bonam uxorem non commemoravit?” (1606).

In the section entitled “De utriusque professoris munere et officio,” we read “Genethliacorum vero doctrinae et totius in universum divinatricis astrologiae sibi penitus noverit [scii, professor astronomiae] interdictam professionem.” S. Gibson (éd.), Statuta antiqua Universitatis Oxoniensis (Oxford, 1931), 529.

For this aspect of Dee see esp. P. J. French, John Dee: The World o f an Elizabethan Magus (London, 1972), which cites earlier literature. See also N. H. Clulee, ‘John Dee’s Mathematics and the Grading of Compound Qualities’, Ambix 18 (1971), 178- 211. Unfortunately, many recent students of Dee have overemphasized this “occult” side and have failed to recognize his more conventional scientific and mathematical achievements. See, however, E. Rosen, ‘John Dee and Commandino’, Scripta mathematica 28 (1970), 521-6; P. L. Rose, ‘Commandino, John Dee and the De superficierum divisionibus of Machometus Bagdedinus’, Isis 63 (1972), 88-93 and the further note by A. G. Watson in Isis 64 (1973), 382-3.98 The following examples are taken from Clark (note 57), 170-9. It is interesting to note that the anti-alchemical and perhaps generally anti-occult thrust of these questions parallels a similar attitude in John Case. See, for example, his Lapis philosophicus (note 91) 175-83 and passim. For example. Case discusses the question “Utrumarte chymica naturale aurum fiat” at some length (pp. 181-3), concluding that “artem posse rem vere naturalem fingere, aurumque verum et naturale efformare,” though he rejects the conventional alchemical solution to the question and is particularly critical of the Paracelsians. Case distinguishes sharply between the legitimate Aristotelian use of “art” and the illegitimate use of it characterized by the Paracelsians. I shall discuss this question further in my forthcoming study on Case.

526 C. SCHMITT

9® See F. Madan et a l. Summary Catalogue o f Western Manuscripts in the Bodleian Library at Oxford (Oxford, 1895-1953) III, 95 [no. 10, 318]. I plan to study this MS in greater detail on another occasion.100 This subject has been largely studied by historians of English vernacular literature who have nearly uniformly given undue emphasis to the so-called literary works written in the vernacular language and have paid little attention to the vast learned literature of the period written in Latin.101 On this see my Cicero Scepticus. A Study o f the Influence o f the Academica in the Renaissance (The Hague, 1972), 78-108.102 por a survey of the situation at Harvey’s time see G. Whitteridge, William Harvey and the Circulation o f the Blood (London-New York, 1971), 9^0. For the situation a hundred years earlier, i.e. in Linacre’s time, see my ‘Thomas Linacre and Italy’, to appear in Linacre Studies, ed. F. Maddison & M. Felling (Oxford, 1975).103 For some general information see P. A. Saccardo, La botanica in Italia (Venezia, 1895) [also published in Memorie del R. Istituto Veneto... 25, no. 4].104 There is now quite a large literature on this, but see esp. E. Chiovenda, “Nota sulla fondazione degli orti medici di Padova e di Pisa,” A tti dell’ V III congresso internazionale di storia della medicina (Roma, 1930; published Pisa, 1931), 488-509.105 An adequate history of botany during this period has yet to be written, though there is a large, widely dispersed secondary literature on the subject. For some information with additional bibliography see K. H. Dannenfeldt, Leonhard Rauwolf (Cambridge, Mass., 1968); H. Fischer, Conrad Gessner, 1516-1565 (Zürich, 1966); C. B. Schmitt, ‘Some Notes on Jacobus Dalechampius and His Translation of Theophrastus (Manuscript: BN, lat. 11, 857)’, Gesnerus 26 (1969), 36-53; J. Stannard, ‘Dioscorides and Renaissance Materia Medica’, Analecta Medico-Historica (London, 1966), 1-21 ; J. Stannard, ‘P. A. Mattioli; Sixteenth-Century Conunentator on Dioscorides’, Bibliographical Contributions. University o f Kansas Libraries I (1969), 59-81. A fundamental orientation is provided by C. E. Dubler, ‘La materia médica’ de Dioscorides: transmisiôn medieval y renacentista (Barcelona, 1953-59), 6 vols.106 See esp. L. Sabbatani, ‘La cattedra dei semplici fondata a Bologna da Luca Ghini’, Studi e memorie per la storia dell’Université di Bologna 9 (1926), 13-53. For further information and additional bibliography see the article by A. G. Keller in Dictionary o f Scientific Biography (hereafter DSB). 5 (1972), 383-84.107 For Ghini’s “simplicis medicinae tradendae et monstrandae munus” see Sabbatani (note 106) 20,32. For a similar example at Pisa see Schmitt (note 48), 254n.57.108 Sabbatani, 20-1.109 pof Ghini see the testimony of Benedetto Varchi, Questione sull’alchimia, codice inedito (Firenze, 1827), 34, which reads “ ...Mess. Luca Ghini Medico, e Semplicista singularissimo, oltra la grande non solamente cognizione, ma pratica dei Minerali tutti quanti, secondo che a me parve quando gli udii da lui pubblicamente nello Studio di Bologna...” Cf. Sabbatani (note 106), 20-1.110 See Schmitt (note 48), 254-55.111 For some information see Intorrw alia vita e alle opere di U. Aldrovandi (Bologna, 1907), an excellent volume which has unfortunately inspired little further research on the topic. See also the article of C. Castellani in DSB I (1970), 108-10.112 This subject does not seem to have been adequately treated in the literature, but see F. Pellegrini, La clinica medica padovana attraverso i secoli (Verona, 1939), 81 flF.;C. D. O ’Malley (ed.). The History o f Medical Education (Berkeley-Los Angeles, 1970), 95-96. This paragraph is based on these works.


113 Statuta Dominorum Artistarum Achademiae Patavinae (Venetiis, ca. 1496), 28'^. There is a microfilm of the Marciana copy [shelfmark; 12.C.141] of this rare work in the Wellcome Library [microfilm 89] which I use. The text is also printed in the 1589 ed. o f the Statuta and in A. Favaro, ‘Lo Studio di Padova al tempo di Niccolô Copernico’, A tti del Reale Istituto Veneto di Scienze, Lettere ed Arti, ser. 5, 6 (1880), 285-356. See also my paper cited above in note 10211 G. de Bertolis, ‘Alessandro Benedetti: il primo teatro anatomico padovano’, Acta medicae historiae Patavinae 3 (1956-57), 1-13; E. A . Underwood, ‘The Early Teaching of Anatomy at Padua with Special Reference to a Model of the Padua Anatomical Theatre’, Annals o f Science 19 (1963), 1-26, esp. 5-6; W. Heckscher, Rembrandt’s Anatomy o f Dr. Nicolaas Tulp (New York, 1958), 182-3. For the text in Benedetti describing his theatre see [Alexander Benedictus], Historia corporis humani sive anatomice [Venice, 1502]. For a discussion of the significance of this see my paper on Linacre cited

above in note 102.115 The next paragraphs are based on my paper cited above in note 48 and on my forthcoming ‘The University of Pisa in the Renaissance’, History o f Education 2 (1973).11« Here I base myself largely on A. Favaro, ‘I lettori di matematiche nella Université di Padova dal principio del secolo X IV alia fine del XVF, Memorie e documenti per la storia della Université di Padova 1 (1922), 1-70; G. Crapulli, Mathesis universalis: genesi di una idea nel X V I secolo (Roma, 1969), esp. 42-62. For possible occult tendencies see the paper of Galluzzi cited below in note 118, esp. 49 n. 24.117 Crapulli (note 116), 44.11® In primum Euclidis Elementorum librum commentariorum libri //// (Patavii, 1560). On Barozzi’s life and works see, in addition to the works cited in note 116, also B. Boncompagni, ‘Intorno alia vita ed ai lavori di Francesco Barozzi’, BuUettino di bibliografia e di storia delle scienze matematiche 17 (1884), 795-848; Dizionario Biografico degli Italiani V I (1964), 495-9; G. C. Giacobbe, ‘Francesco Barozzi e la Quaestio de certitudine mathematicarum', Physis 14 (1972), 162-93 ; and P. Galluzzi, ‘II “Platonismo” dei tardo Cinquecento e la filosofia di Galileo’, in P. Zambelli (ed.), Ricerche sulla cultura delVItalia moderna (Bari, 1973), 39-79, esp. 49-53.11® For some information see Crapulli (note 116), 44-50.120 p. L. Rose & S. Drake (note 26), esp. 92-96.121 A. Riccoboni, Orationes (Patavii, 1591), 41-46.122 On this see esp. Kristeller (note 21), 553-83 (‘Humanism and Scholasticism in the Italian Renaissance’), as well as the same author’s paper cited in note 8.123 The first incumbent was apparently Niccolô Leonico Tomeo (1456-1531). For the document telling of his appointment see J. L. Heiberg, Beitrage zur Geschichte Georg Valla’s und seiner Bibliothek (Leipzig, 1896), 19. See also I. Facciolati, Fasti Gymnasii Patavii (Patavii, 1757), vol. I, LV-LVI. On Leonico Tomeo in general the best study seems to be A. Serena, Appunti letterari (Roma, 1903), 3-32. According to another tradition going back to Francesco Patrizi da Cherso, Francesco Cavalli was the first to teach Aristotle from the Greek text at Padua. See Schmitt (note 102), note 91 and passim.124 For some general information see Kristeller (note 21), 341 n. 13. On specific points see B. Nardi (note 3), 365-442 (“ II commento di Simplicio al De anima nelle contro- versie della fine del secolo XV a del secolo XVI”) ; C. B. Schmitt, Gianfrancesco P ico della Mirandola (1469-1533) and His Critique o f Aristotle (The Hague, 1967) ad indicem [John Philoponus]; F. E. Cranz, ‘Alexander Aphrodisiensis’, in Catalogus translationum et commentariorum (Washington, 1960f.) I, 77-135; II, 411-22; and E. P. Ma-

528 C. SCHMITT

honey, ‘Nicoletto Vernia and Agostino Nifo on Alexander of Aphrodisias: an Unnoticed Dispute’, Rivista critica di storia della filosofia 23 (1968), 268-96. Dr. C. H. Lohr of the Raimundus-Lullus-Institut of the University of Freiburg is the general editor of a new project to reprint the Renaissance translations of the Greek commentaries on Aristotle [Commentaria in Aristotelem Graeca. Corpus versionum Latinarum sedecimo (sic) saeculo impressorum] with the Minerva Publishing Co. of Frankfurt. When these reprints are available further work on this material will become easier.125 See above note 28.128 This generalization must be subjected to careful study. At present I can offer no specific documentation for this view.127 See esp. R. G. Villoslada, La universidad de Paris durante las estudios de Francisco de Vitoria O.P. (1507-1522) (Romae, 1938).12® On this see esp. M. Bataillon, Erasme et l ’Espagne (Paris, 1937).129 For natural philosophy see esp. the studies of W. A. Wallace, including ‘The Enigma of Domingo de Soto: Uniformiter difformis and Falling Bodies in Late Medieval Physics’, Isis 59 (1968), 384-401; ‘The “Calculatores” in Early Sixteenth-Century Physics’, British Journal fo r the History o f Science 4 (1969), 221-32, where further references may be found. For logic see the many publications of V. Munoz Delgado, esp. La logica nominalista en la Universidad de Salamanca (1510-1530) (Madrid, 1964) and ‘Lôgica Hispano-Portuguesa hasta 1600 (Notas bibliografico-doctrinales)’ in Repertorio de historia de las ciendas eclesiasticas en EspanaW (1972), 9-122 (with a bibliographical foundation for other studies).130 A general orientation with additional bibliography on this vast subject is to be found in G. Fraile, Historia de la filosofia H L Del Humanismo a la Ilustracion (Madrid, 1966), 410-21,131 Cursus philosophicus thomisticus secundum exactam, veram, genuiruim Aristotelis et Doctoris Angelici mentem (Madrid, 1637-8), which went through various later editions. Cf. the useful article with further bibliography in Enciclopedia filosofica, 2nd. ed. (Firenze, 1967) III, 206-7 (by A. Munoz Alonso).132 The course began to be published in 1624 and was reprinted several times thereafter. A five volume version is Cursus philosophicus Collegii Complutensis ad clariorem fo r mam redactus (Lugduni, 1670f.). Florencio dei Nifio Jesus, Los complutenses (Madrid, 1961) is the best secondary work. Cf. Enciclopedia filosofica (note 131) I, 1506-7.133 This can be seen, for example, in the rather half-hearted way in which the problem of the void is treated in Collegii Complutensis... Disputationes in octo libros physicorum Aristotelis (Lugduni, 1667), 215-9. This might be contrasted with the vigorous and “ modern” approach to the subject found in a “progressive” and “experimental” Aristotelian such as Emmanuel Maignan. See his Cursus philosophicus (note 18), 228-46. The process of increasing simplification in logic in the scholastic manual tradition was called to attention some years ago by P. Boehner, Medieval Logic: An Outline o f Its Development from 1250 to ca. 1400 (Chicago, 1952).134 These were only in part “commentaries” [i.e. for the Physica, De coelo, Meteora, Parva naturalia. De anima, and De generatione et corruptione]. The Ethica Nicomachea volume is a relatively brief collection of disputations and the common Dialectica [under which title were published two quite different recensions] only covers a part of the Organon. There was no commentary on the Metaphysica [but that of Fonseca was commonly used to fill this lacuna], nor on the Poetica, Politica. Rhetorica, Oeconomica, etc.135 It is instructive to compare the Physics commentary, especially the sections on


projectile motion, with those of Buridan or Albert of Saxony or with the discussion of this problem by members of the “ Merton School.” The fourteenth-century treatments are far more detailed.136 I am preparing a study of the diffusion of the Commentaries throughout Europe. This will be accompanied by a bibliography of the various printings. In general, the individual commentaries were printed from ten to twenty times during the years 1590- 1635. For example, the De anima has the following editions: Coimbra, 1598; Cologne, 1600,1603, 1609,1617,1619,1629; Lyon, 1600,1604,1612,1616, 1627; Venice, 1602, 1606, 1608, 1616; Strasbourg, 1627.137 Some information is to be found in E. Gilson, Études sur le rôle de la pensée médiévale dans la formation du système cartésien (Paris, 1930) and Levi (note 52). Further bibliography can be found in the section by L. V. Rosenfield (‘Aristotelian and Scholastic Tradition’) in Critical Bibliography o f French Literature (Syracuse, 1947-68) III, 486-90.138 Cranz (note 14).139 For the early part of the century much valuable information is to be found in A. Renaudet, Préréforme et humanisme à Paris pendant les premières guerres d ’Italie (1494-1517) (Paris, 1916; 2nd, ed. Paris, 1953) and Villoslada (note 127). Though we lack a comprehensive and detailed study for the later period much valuable information is to be found in C. P. Goujet, Mémoire historique et littéraire sur le collège royal de France (Paris, 1758); A. Lefranc, Histoire du collège de France (Paris, 1893); W. J. Ong, Ramus: Method and Decay o f Dialogue (Cambridge, Mass., 1958); as well as the unwieldy, difficult to use, and often unreliable C. E. Bulaeus, Historia universitatis Parisiensis (Parisiis, 1665-73; repr. Frankfurt, 1966), esp. vol. 6. A useful guide, esp. for the extant manuscript and archival sources, is J. Bonnerot, ‘L ’ancienne Université de Paris, centre international d’études’. Bulletin o f the International Committee o f Historical Sciences 1 (1926-29), 661-82.140 See V. L. Saulnier, ‘Médicins de Montpellier au temps de Rabelais’, Bibliothèque d'humanisme et Renaissance 19 (1957), 425-79; Matricule de V Université de Médecine de Montpellier (1503-1599) (Genève, 1957).141 For some indications see Villoslada (note 127) and H. Elie, ‘Quelques maîtres de l’université de Paris vers l’an 1500’, Archives d ’histoire doctrinale et littéraire au moyen âge 18 (1950-1). 193-243 and M. Clagett, The Science o f Mechanics in the Middle Ages (Madison, 1959), 638-40, 653-59, as well as the older studies of Duhem.142 Text cited above in note 33.143 Nitzsch (note 33) has collected and analyzed the relevant information.144 See the literature cited above in notes 34 and 36 as well as the older works of H. E. Weber, Der Einfluss der protestantischen Schulphilosophie auf die orthodox-lutherische Dogmatik (Darmstadt, 1908; repr. 1968) and Die philosophische Scholastik des deutschen Protestantismus im Zeitalter der Orthodoxie (Leipzig, 1907) and P. Althaus, Die Principien der deutschen reformierten Dogmatik im Zeitalter der Aristotelischen Scholastik (Leipzig, 1914).145 On Schegk see esp. C. Sigwart, ‘Jakob Schegk, Professor der Philosophie und Medicin’, Kleine Schriften (Freiburg, 1889) I, 256-91 and W. Pagel, ‘William Harvey Revisited’, History o f Science 8 (1969), 1-81 & 9 (1970), 1-41, at 9, 26-30. James Hinz is preparing a Ph. D. thesis on Schegk at Stanford University, and I am indebted to him for allowing me to see his unpublished “Jacob Schegk (1511-1587), Aristotelian Polymath,” which contains much valuable information.146 There seems to be little readily accessible information on him, but see Allgemeine

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Deutsche Biographie 26 (1888), 231-2. Though he was one of Kepler’s teachers little attention seems to have been paid to this fact. See, however, the Exhibition Catalogue Kepler und Tübingen (Tübingen, 1971), items 24, 32, 37, 38.

Sturm and Melanchthon were the key figures here. Of the large literature devoted to them and their educational ideas see esp. C. Schmidt, La vie et les travaux de Jean Sturm (Strasbourg, 1855: repr. Nieuwkoop, 1970); K. Hartfelder, Philipp Melanchthon als Praeceptor Germaniae Œerlin, 1889) and Petersen (note 34).

The studies of Petersen and Wundt amply show this. See also F, Ruello, ‘Christian Wolff et la scolastique’. Traditio 19 (1963), 411-25; A. Bissinger, Die Struktur der Gotteserkenntnis: Studien zur Philosophie Christian Wolffs (Bonn, 1970) and the review of the latter by C. A. Corrin in Journal o f the History o f Philosophy 11 (1973),270-4.149 This is too vast a topic to treat here. For a general orientation see d’Irsay (note 1)I, 342-61. The case of Freiburg has been dealt with in T. Kurrus, Die Jesuiten an der Universitat Freiburg i. Br. 1620-1773 (Freiburg, 1963).15“ See Edwards (note 37) and Petersen (note 34), esp. 196-9 for some indications. According to Petersen it was Fortunatus Crellius who first introduced Zabarella’s work in Germany. The Strasbourg professor Johannes Hawenreuter was one of Zabarella’s champions in Germany and was responsible for several of the German editions of his works. The Paduan’s writings had a remarkable in Germany as illustrated bythe numerous German editions of the Opera logica [Basel, 1594; Cologne, 1597, 1602, 1603; Frankfurt, 1608, 1623] and De rebus rmturalibus [Cologne, 1590, 1594, 1597, 1601; Frankfurt, 1606, 1617, 1654].

Some information is in Petersen (note 34) ad indicem. Cesalpino’s Quaestiones peripateticae were printed at Cologne in 1646; the De metallicis at Nuremberg in 1602; and the Speculum artis medicae Hippocraticum at Frankfurt in 1605 and at Strasbourg in 1670.152 See esp. the studies of Eschweiler and Lewalter cited in note 36.153 This is a general impression which is difficult to document briefly. Among other things there are a number of extant manuscript commentaries on Aristotle from Scottish universities including the following: Aberdeen, University Library, MS 116 [commentary on Ethica, dated 1602-3]; MS 150 [annotations on the Organon, dated 1623]; MS 186 [commentary on Logic and Physics, dated 1605-7]; Edinburgh, University Library, MS Dc. 5.55 [annotations on Physica, De coelo, etc., dated 1661-62]; MS La. in. 721 [annotations on the Physica, De coelo, etc., dated 1647, from St. Andrews].154 Of the large literature on this see R. Kelso, The Doctrine o f the English Gentleman in the Sixteenth Century (Urbana, 1929); S. R. Jayne, John Colet and Marsilio Ficino (Oxford, 1963); McConica (note 75): and H. C. Porter, Erasmus and Cambridge (Toronto, 1970).155 Thus the really radical change in university philosophy teaching (i.e. esp. natural philosophy) seems to have come, at least in Northern Europe, at the end of the seventeenth and beginning of the eighteenth centuries. The detailed analysis of this phenomenon must wait for another occasion.15* See the material cited by L. Bertalot, ‘Humanistische Vorlesungsankündigungen in Deutschland im 15. Jahrhundert’, Zeitschrift f iir Geschichte der Erziehung und des Un- terrichts 5 (1915), 1-24.157 H. Hermelink, ‘Die Anfânge des Humanismus in Tübingen’, Wiirttembergische Vierteljahrschrift f iir Landesgeschichte, new series, 15 (1906), 319-36.158 On this term see my book cited above in note 12.


D I S C U S S I O N

c. SCHMITT : I have tried to give a general interpretation of the significance of philosophy and science in sixteenth century universities and to focus on something that perhaps doesn’t fall directly within the scope of this meeting. It does, I think, relate to it insofar as we see the continuity of certain traditions discussed here. On the basis of research as it now stands, I have tried to summarize what I think the situation is, but it must be emphasized that despite all of the work that has been done on the Renaissance per se, very little has been done on the universities and on the continuity of earlier traditions during this period.

In a way I think we are victims of a confused periodization of history. I do not deny that the term ‘Renaissance’ has some meaning, but its significance is more limited than normally realized. It means something quite precise in the development of the arts or in the recovery of classical literature, but I think the term is confusing when applied to science.

One of the great problems of history of science is that we now have quite detailed studies on fourteenth century science and on seventeenth century science, but, except for a few major figures like Vesalius and Copernicus, we really know very little indeed about the scientific thought of the intervening centuries. And we know particularly little about that type of thought which continued in the universities through to the end of the seventeenth century, viz., the medieval philosophical and scientific traditions initiated with the introduction of Aristotelian doctrine in the twelfth century. This formed the foundations of the universities and continued to dominate until the end of the seventeenth century. This unity of the Aristotelian tradition in the West as a dominant pedagogical instrument is largely lost sight of by virtue of our division of chronology into the Middle Ages and the Renaissance. Our particular historiographical approach to the Renaissance has emphasized novelty. It has stressed the formation of academies, the introduction of Platonic philosophy and so forth, but has done very little to try to illuminate the continuity of earlier traditions, Aristotelianism, for example, in the Renaissance. The universities are considered to be typically medieval institutions and are therefore not studied by Renaissance scholars with the care that they deserve.

I must say that I find many traditional interpretations of the Renaissance very unacceptable; for example, the normal view one gets from various writings on the Renaissance is that Aristotelianism died out and that Platonism took over. It seems to me that no matter how you look at it this is not the case. If you look at it in a purely statistical way, you see something like ten to twenty times as many editions of Aristotle were published during the sixteenth century as were editions of Plato, that Aristotelianism continued to dominate the universities and was also important in the academies along with Platonism. Even in something like literary theory and practice, where most histories tell us Platonism took over, Aristotelianism again dominated.

The other view we often find is that humanism, a creation of the Renaissance, destroyed the scientific spirit of the Middle Ages. It seems to me that this is equally false, and that there is no direct connection between the rise of humanism and the decline of science in the universities. In fact, in the places where we have the best documentation, that is Paris and Oxford, we know that science had already declined fifty years before humanism was introduced into these institutions. Now the humanists were very critical of the medieval scholastic tradition, but as an institutional factor it

532 C. SCHMITT

does not seem that humanism was responsible for the decHne of science in the universities. Furthermore, I think that humanism contributed in a number of ways to the development of scientific ideas during the period. Most of all, I think by introducing new texts and by fostering a new critical spirit toward the interpretation of texts. The mathematical works, which I think prove to be a decisive factor in the development of early modern science, were introduced by humanists and largely translated and edited by humanist mathematicians.

G. beaujouan : On a dit que la guerre est une chose trop sérieuse pour être confiée aux militaires! On pourrait dire de la même manière que l’histoire du XVIe siècle est une chose trop importante pour être confiée aux historiens de la Renaissance! C ’est donc fort à propos que nous sommes invités à discuter le très intéressant rapport de M. Schmitt, même si apparemment il déborde les limites chronologiques de notre colloque.

Les questions que je voudrais poser touchent à deux domaines. Le premier se rattache à la méthodologie de l’histoire des universités au XVIe siècle comparées à celles du moyen âge. Le second, c’est évidemment la diflférence qu’il y a entre l’aristotélisme proprement médiéval et cet aristotélisme qui reprend vigueur à l’époque du Galilée.

Sur les grandes lignes, probablement parce que je suis médiéviste, je suis totalement d’accord avec M. Schmitt. Je suis d’accord avec lui sur l’impact relativement faible des innovations scientifiques dans l’enseignement universitaire; sur l’influence relativement limitée - en dehors de la purification des textes - des tendances humanistiques, sur la persistance et même la renaissance de l’aristotélisme dans la seconde moitié du XVIe siècle; sur l’impact assez faible de la Réforme protestante.

Il y a cependant un autre point qui différencie fondamentalement le XVIe siècle du moyen âge, sans que M. Schmitt y ait insisté: c’est l’existence des livres imprimés. La question que je voudrais poser est la suivante; dans quelle mesure pensez-vous que l’emploi des livres imprimés a modifié la pédagogie universitaire? Lorsque l’on catalogue des fonds de manuscrits, on sent bien que les manuscrits du XVIe siècle n’ont plus la même fonction que ceux du XVe. Si, comme le remarque M. Schmitt, les universités du XVIe siècle ont assumé les progrès de l’anatomie, de la botanique, voire de la géographie, ceci est évidemment en rapport avec l’histoire du livre et de la gravure.

c. SCHMITT : The impact of printing upon university education is not a subject that I know a great deal about, but one that should be investigated more fully. I think there is no doubt that printing had a very strong influence on university teaching if for no other reason than that by the second or third decade of the sixteenth century books were relatively cheap and students could have their own copies, whereas in the Middle Ages only wealthy students could aff'ord to own manuscripts. We have a great deal of evidence of this sort of thing. In the middle of the sixteenth century Plato was taught particularly in the Greek courses at Paris and we see a number of very small economical issues of works of Plato, the dialogues, the Greek texts of which are only twenty or thirty pages long. A number of these which exist in various libraries are covered with notes in the margin by a student, which shows that students in the sixteenth century could own their own text books. And this example could be multiplied many times. I think that this is one of the great changes.

Furthermore, and this is something that Brian Stock has emphasized several times at the Colloquium, there is greater communication given this situation of printed books. There were fairs in Frankfort and Lyon, for example, where people came from all over Europe to buy books. There was shipping of books from Venice to Northern Europe through the Straits of Gibraltar, and so forth. We know all of these facts. Books really did change the situation.


G. beaujouan : Et au niveau de la pédagogie même?c. SCHMITT : I am not certain whether it really changed the level of instruction in any

way that is completely independent from the fact that humanists developed new methods of giving good critical texts. Modern editors and the medievalists tend to emphasize how bad these humanist texts are and that there are better manuscripts from earlier periods, but I think that on the whole the general quality control, if we can use such a term, of the printed text did change the situation quite significantly.

G. beaujouan : Ma seconde observation relative à la méthodologie de l’histoire universitaire était la suivante: j ’ai été frappé dans votre rapport par l’observation tout à fait juste que les facultés des arts sont beaucoup plus importantes par exemple à Paris et à Oxford que dans les universités italiennes. Et vous donnez comme explication de l’importance de la faculté des arts à Paris et à Oxford le voisinage d’une faculté de théologie puissante. Je me demande si une autre raison de la débilité relative des facultés des arts italiennes n’était pas qu’il existait en Italie une certaine forme d’enseignement primaire et secondaire, je pense par exemple aux écoles d’abaque ou à d’autres enseignements destinés aux enfants de la classe marchande et commerciale. Et d’une manière generale, ma question est la suivante: peut-on vraiment comprendre de l’intérieur le problème des universités du XVI siècle si on ne le juge pas en fonction des autres formes d’enseignement, qu’il s’agisse d’enseignement secondaire ou d’enseignement technique plus spécialisé dehors des universités?

c. SCHMITT : Yes, this is a very important point and a good criticism of what I have done in this paper. I must admit that I have not looked into the secondary education to the extent that I should have, but in several cases - for instance at Pisa and also at Oxford and Cambridge in the sixteenth century - we find people in universities complaining that the incoming students are not well prepared, that they do not know Latin, and consequently can’t follow the lectures, and so forth. So, there seems to be some question whether the secondary education was adequate for those going into the universities during this period.

I did not mean to give the impression that the Arts Faculties were weaker in Italy than in the North. I think that there is a difference in orientation. At Padua, for example (and in general in Italian universities, although there are variations), medicine is considered an Arts Faculty subject. At Pisa there was also a very close relation between medical and arts subjects. Theology was quite different and a very small faculty. There was a very large faculty of Law - and this is the general pattern, that Law was by and large perhaps twice as large or more than the Arts Faculty. The important aspect of Italian universities during this period is the Law Faculty about which I have said nothing.

G. beaujouan : Pour ne pas allonger mon commentaire, je pose tout de suite ma question finale, elle concerne la continuité de l’aristotélisme et même sa restauration lors de la tentative de remise en ordre des esprits qui marque la seconde moitié du XVIe siècle. Cette survie d’Aristote ne s’explique pas seulement par la routine. La Renaissance n’a trouvé aucun système philosophique capable de remplacer celui d’Aristote. M. Schmitt se demande pourquoi Averroès a bien survécu dans les universités du XVIe siècle, alors que la littérature des Calculationes et Sophismata a complètement sombré à partir de 1520-1530. C ’est, je pense, parce que l’oeuvre d’Averroès illustre cette cohérence du système aristotélicien alors que, au contraire, la littérature des Sophismata apparaît comme une dégénérescence perverse de la logique d’Aristote. Malheureusement M. Schmitt refuse dans son rapport de caractériser ces nouveaux aristotélismes de la Contre-Réforme par rapport à ceux du moyen âge. Il y a pourtant

534 C. SCHMITT

là un point qui me semble pour nous, ici, d’une extrême importance. Peut-être M. Schmitt pourrait-il nous caractériser ici ce que sont, selon lui, les différences importantes entre l’aristotélisme de la fin du XVIe siècle et l’aristotélisme médiéval. Voilà: c’est un peu lui demander d’ajouter trois pages à son rapport, mais ce sont, je crois, trois pages utiles.

c. schmitt: This is very diflScult and, if I might just make a sort of parenthetical statement of how I came to study this subject at all, I think this might illuminate the problem to some degree. I began by studying the university of Pisa at the end of the sixteenth century because I thought it might shed some light on Galileo. Most scholars working on Galileo have emphasized his connection to Padua and his relation to nonuniversity traditions of the sixteenth century or perhaps to traditions of the fourteenth century. But it seemed to me that it would be more useful, if there were a scholastic influence on Galileo, to look at what was going on at Pisa when he was a student there. It became apparent to me after a year or two that this method of approach had numerous difficulties, the main one of which is that you can’t really study Pisa in isolation from other universities; you must study what is going on in general throughout Europe.

When I looked at other universities, mostly focusing upon six or ten characteristic universities, some Protestant, some Catholic, some German, some Spanish, some Italian, and so on, it became apparent that there was tremendous diversity. I have almost come to the conclusion that you can’t make any general statement about sixteenth century universities. To distinguish between, say, universités in 1500 and universities in 1350 would, I think, involve great problems. I think that you could do it for individual universities. One can say, for example, that Oxford in 1550 as compared to Oxford in 1350 or 1400 had certain very different characteristics. In 1350, of course, the Merton School was still very strong. In 1400 it is less strong and the impression I get is that Scotist philosophy and theology were the dominant factors. The very technical and high level intellectual activities of the Merton School were almost lost sight of and the logic text books were sort of watered-down versions of what they had been fifty years earlier. In 1550 we see this tradition that spanned the fifteenth century dying out. We see the advent of humanism, Ramus was beginning to hit Oxford (in the 1550’s and 1560’s this happened), we see a new emphasis on learning Greek, and so on. There is, in short, a strong humanistic influence. At the end of the century we find a revival of Aristotelianism, but it is not the Aristotelianism of the fourteenth century; it is an Aristotelianism that comes largely by way of Italy, an Aristotelianism that has certain humanist aspects, but also one that gives due emphasis to Italian commentators on Aristotle, such as Nifo, Boccadiferro, and Zabarella. So this is the case with Oxford. I think that one can do the same for other universities, but to give a characteristic view of universities in, say, 1550, is, I think, very, very diflficult. There are so many regional variations that it is almost impossible to generalize.

G. beaujouan : Et même on peut se demander si la caractéristique à un moment n’est pas propre à tel collège plutôt qu’à l’ensemble de l’université.

c. schmitt: Yes, this is another thing that is very important: the college system became dominant in the English imiversities and continued in some degree also in Salamanca and Paris. The Italian universities had residential colleges but as there was no instruction in the colleges there was greater unity. In fact, the Continental system with a few exceptions, Paris probably the most important one, was a single university with general lectures being given by the professors, with unified statutes, whereas the English universities had great variations from college to college. This is a characteristic which has remained to the present day.


T. GREGORY: Je crois, en ce qui concerne le problème posé pour l’histoire des universités, qu’il serait très important d’utiliser aussi les reportationes des étudiants: elles sont tout à fait nécessaires, je crois, pour connaître la vie réelle des universités. C’est dommage qu’on n’ait pas un répertoire des reportationes de la Renaissance et du XVIIe siècle. Il y en a un grand nombre dans les bibliothèques européennes et je crois qu’elles sont parmi les sources les plus importantes pour connaître la variation des perspectives dans la culture des universités à la Renaissance. Dans les reportationes, les étudiants saisissent souvent des nuances, des mots d’fôprit qui témoignent la vivacité de l’enseignement du professeur, ses polémiques contre certaines thèses traditionnelles, ou contre certains collègues ; et tout ce-là est parfois très important pour suivre le mouvement réel des idées.

Pour le XVIIe siècle - je m’excuse, je déborde un peu les limites chronologiques - il y a une autre source que je crois très importante, plus importante aussi que les manuels - la variation dans la culture réelle est toujours en avance en égard aux manuels - : les positions des thèses, qu’il faudrait étudier. On voit s’annoncer des problèmes et des intérêts nouveaux qui étaient en train d’animer et modifier la culture universitaire.

En ce qui concerne les manuels, il faut encore pousser la recherche parce que les manuels constituent sans doute un moyen d’unification des écoles différentes. Si on considère les manuels de Colmbre, on peut voir qu’il y a une structure de pensée qui est toujours aristotélicienne, mais on développera par exemple les doxographies. Là nous voyons l’influence de l’humanisme. Il y a des perspectives sur l’histoire des doctrines qui ne changent pas tout de suite la pensée aristotélicienne, mais qui donnent des matériaux pour changer les perspectives.

En ce qui concerne les problèmes justement posés par M. Beaujouan sur la différence entre l’aristotélisme à la fin du XVIe siècle et au moyen âge, il faut avant tout souligner la diversité substantielle des universités, mais aussi des milieux intellectuels. Par exemple, il y a une tradition averroïste qui est presque toujours la même. Au XlIIe siècle elle représentait une position avancée, au XVIe siècle il est évidemment une position arriérée, très conservatrice. Il y a une continuité des écoles qui, selon la période, va changer en réalité; le cas de l’averroïsme est typique. On doit aussi distinguer, dans les traditions de l’université, les branches différentes de la recherche philosophique: quelqu’unes restent presque telles quelles dans leur thématique traditionnelle (c’est le cas de la métaphysique, par exemple), d’autres changent profondément, comme par exemple la logique va f.hanger de façon très profonde, sous l’influence de l’école d’Oxford surtout. L’influence de la logique nominaliste surtout est très large jusqu’à la fin du XVIIe siècle. A l’intérieur de l’aristotélisme il faut donc distinguer entre une discipline et l’autre. La logique, par exemple, a une histoire tout à fait particulière.

G. beaujouan: M. Schmitt a raison de marquer que, si la logique nominaliste eut une certaine importance au XVIe siècle, son influence déclina tout de même à partir des années, disons, 1530. Son recul semble dès lors rapide.

M.-Th. d alv e r n y : Je pense qu’il faudrait ajouter un petit mot pour une autre tradition qui est à la fois philosophique et scientifique et dure pendant tout le moyen âge, mais est tout de même très développée encore au XVIe siècle, c’est la tradition galénique. Parce que la médecine est tout de même basée non seulement sur l’enseignement médical mais aussi sur la philosophie de Galien. Et ce qui est assez curieux, c’est que des auteurs qui dans le reste de leur enseignement suivent les classements d’Aristote, dès qu’ils en viennent a la médecine - je pense à Ibn Sinâ dont le premier livre du Canon est plein d’exposés philosophiques - suivent la philosphie de Galien.

c. schmitt: Yes, that is a very important point and an omission from my paper.

536 C. SCHMITT

Particularly in the methodological discussions of the universities of the fourteenth, fifteenth, and sixteenth centuries this plays a very important role.

M. GILMORE; Charles, you speak toward the end of your paper about the revival of Aristotelian studies and commentaries in the second part of the sixteenth century. I know that you have not intended to deal with the lawyers, but I am struck with the fact that you have in that same period in the law faculties a kind of revolt against earlier humanist criticism. There comes a conviction that texts like the Digest cannot really be understood by what were called mere grammarians or mere philologists. I wonder if you see a parallel kind of resurrection of the importance of medieval commentaries occurring in theology, philosophy, and the law.

c. SCHMITT: This is a very interesting point. One of the great shortcomings of all my work in this field is my complete ignorance of the history of law. The one point that I do mention, and this has always been a puzzling point to me, is the editions of Aver- roes’s commentaries on Aristotle at Venice between 1550 and 1575. This is a fourteen volume work which was reprinted, I think, five times within twenty-five years. Now they don’t print books like this unless people are reading them, but, at this stage I can’t really make any generalization on a genuine revival of these medieval traditions. There was, of course, in the post-Tridentine period a revival of Thomism. This is very evident in Spain and in Italy and leads to the revival of certain medieval traditions. It would be interesting to trace commentaries on the Physics, for example, to see what the range of authorities mentioned are, say in twenty-five commentaries dating from 1450 to 1650 or something like this, just to get a general idea. But other than this I can’t really say very much.

H. oberm an : Charles, you may want to be careful about concluding from reprints to the popularity of the books. In the first place, in the beginning of the sixteenth century there are a remarkable number of printers that go bankrupt. And, secondly, very often books are published because particular politicians provide the initial sum and encourage publication. And then we get the complaint that one can’t sell the books. Just because we have the books in our libraries does not then automatically allow us to say that the book was read. It is not like a medieval manuscript.

G. beaujouan : Ceci pose un problème qui se rattache à la question des sources, que soulevait M. Gregory. Dans la plupart de nos bibliothèques, les livres imprimés sont catalogués même quand ils le sont très minutieusement, sans tenir absolument aucun compte des gloses et des notes qu’ils renferment. Je pense à l’experience actuellement tentée par M. Gingerich, qui à cherché à voir personellement tous les exemplaires imprimés de Copernic: elle montre l’intérêt qu’il y a à examiner tous les exemplaires d’une livre en identifiant la main des annotateurs et en remarquant les pages qui sont salies ou les pages qui n’ont jamais été lues par les propriétaires. Ceci constitue une source absolument essentielle de l’histoire universitaire du XVIe siècle: une source qui est pratiquement inaccessible du fait de la manière dont sont catalogués les livres imprimés dans toutes les bibliothèques.

c. SCHMITT : Yes, this is a very important point. I have looked at many, many editions and copies of, for example, Aristotle’s logic in the sixteenth century in which every vacant space is covered with notes, even interlinear annotations. Very often the annotator becomes tired and by the time he gets through the De interpretatione and the Categories he has given up, but the first few pages of the books are very often covered and this is characteristic of all sixteenth century textbooks.

H. oberm an : Just one comment on the fact that you often find that only the first pages have been very heavily annotated. It seems to me that in this early printing-uni-


versity marriage the matter is not very different from what happens today, when students complain, at least against German academic traditions, that you announce a course on the Middle Ages from Charlemagne until the end of the Middle Ages, but then you never get further than the school of Chartres. You find comments where the student says finis lecture, - and they never went further. The professor used all his time to deal with the first books.

c. SCHMITT : Yes, this is a very important point. The statutes say that you should read Aristotle’s Physics and what you very often find is that the manuscript commentaries are only Books I, II, and VIII, for example.

I N D E X

The following index includes names, concepts, and selected Arabic, Greek, and Latin terms. Under the entry ‘manuscripts’ are listed the manuscripts cited. An attempt was made to alphabetize medieval Latin authors by their first names in Anglicized form. Renaissance authors, on the other hand, are generally alphabetized by their last names left in vernacular form. Arabic authors are alphabetized according to the name by which they are most often called. Particles have been ignored in alphabetization unless strong previous tradition emphasizes them. Since to cross-reference every medieval and Renaissance (and, indeed, more modern) author by each of the names he has ever been called by would have unduly lengthened the index, the wise reader should check under each of the various parts of a name sought before concluding that its possessor is not referred to in the book.

Abailard, Peter see: Peter Abelard ‘Abbasid empire 53, 87, 91, 106, 110 ‘Abd al-Jabbâr 107 ‘Abd al-Rahmân al-§üfi 467 ‘Abdallah ibn al-Zubayr 96, 99 ‘Abdalmalik 89, 92, 93, 96, 97, 98, 100,

101, 104, 105 ‘Abdalqadir Badran 103 ‘Abdalqâhir al-Baghdâdî 102 ‘Abdalwâhid ibn Ayman 94 ‘Abdassalàm Muhammad Hârün 101 Abelard, Peter see: Peter Abelard ‘Abid ibn Sharya 98 Abraham 157Abraham ibn Ezra 456, 474 Abü Bakr 94, 95, 97 Abû Bishr Mattâ 79 Abû Hanifa 73 Abû Hâshim 91, 95, 103, 108 Abü Hurayra 92Abu’l-Çusayn al-Baçri 69, 76, 77, 80 Abu’l-Jüd ibn al-Layth 45 Abü Kâmil 34, 50, 58, 59, 60, 463 Abü M'shar 194, 202, 203, 206, 212, 215,

216, 476, 515 Abü Rida, M. A. 79 Abu’l-Çaq'ab Jakhdab ibn Jar'ab 94 Abu’I Wafâ’ 53, 55, 59, 474 accidents, definition of 370

Adam of Balsham 209 Adam Wodeham 279, 321, 324, 325,

327-28, 330, 331, 332, 333, 334, 335 additivity 295, 330, 334 Adelard of Bath (Adelhard of Bath) 159,

188, 194, 197-98, 210 administration

(mathematical needs of) 53-57 administrative bureaus

(development of) in Islam 53-55 Aegidius Romanus see: Giles of Rome affectus 226, 245, 247, 248, 264 Agricola, Rudolph 513 agrimensores 480, 481 Ahnaf ibn Qays 90 d’Ailly, Peter see: Peter d’Ailly Ailnoth 441Ajo G. y Sainz de Zùniga, C. M. 515 al-Akhtal 100^alama (sign) 69, 70, 77, 79, 82 Alan of Lille 165, 198, 200, 202 Albert of Saxony 303, 337, 425, 529 Albertus Magnus 165, 168, 178, 338,

482Albumasar see: Abu Ma'shar alchemy 194, 206, 208, 213-14, 440

contrasted with astrology 214 scientia de alkimia 205

Aldrovandi, U. 503

540 INDEX

Alessio, F. 212, 438 Alexander of Aphrodisias 177, 508 Alexander Neckham 160 Alexander of Villedieu 446, 481 Alfarabi see: al-Fârâbï Alfarghani see: al-Farghani Alfonsus Vargus Toletanus 314 Algazel, see: al-Ghazali algebra, Islamic 4, 6, 33-60, 147

(arithmetization of) 34-40 (autonomy of) 51, 57-58 (development of symbolism in) 33 (historiography of) 33-34, 50-52 (philosophy of) 40-42, 51 (social history of) 50-59 (systematization o f) 43-50

Alger of Liège 166 Alhazen see: Ibn al-Haytham ‘All 91, 95‘Ali ibn al-‘Abbas 158, 211, 440 ‘Alids 95, 96 Alkindi see: al-Kindi allegory see: nature, allegorical interpre

tation of Alonso Alonso, M, 145, 211, 472 Alpago, Andrea 146 Althaus, P. 529 Alvarus Thomas 343 Alvise de Cadamosto 466 *amal (action) 482amâra (sign) 69, 70, 76, 77, 79, 82, 83Ambrose 163, 179, 394Amine, Osman 145‘âmm (general) 72, 73, 75, 76, 77Ammonius 146amr (imperative) 72, 75, 76‘Amr ibn Sa'id al-Ashdaq 97‘Amr ibn ‘Ubayd 88analogy see: qiyasanalysis

(languages of) in fourteenth century learning 25, 280-87 origins 287-89 application of 289-307 compared to thirteenth century

synthesis 307-9 and their social base 309-12

see also: measure languages ancilla (handmaid) 380

Andronicus of Rhodes 176 Angeli da Bargo, Guilio 522 angelic motion 289 angles, measures of 468 anima mundi 199, 201 animal intelligens 199 Annerstedt, C. 487, 520 al-Ançâri, Çafwàn 88 Anselm 109, 325 anthropocentric 396£inti-intellectualism 429-30, 510, 513 see

also: contra vanam curiositatem àvTiXÆtuPàvû) (apprehend) 64, 65, 77 Antoni, Carlo 260 Antonius Andrea 168 apologetics 88 àjiôSeiÇiç apparentia 433, 434 al-*aql (intellect) 73Aquinas, Thomas see: Thomas Aquinas Arabic language

(structure of) 51 Arabic science see: science, Arabic Archimedes 43, 44, 473 architecture, medieval

and practical mathematics 444-63,482, 483-84

Aristotle (his works, Aristotelianism) 23, 42, 60, 75, 79,107,122,123,124,130, 131,132,133,134,135,146,147,152, 153, 157, 159, 161, 162, 167, 168-83, 185,186,187,194,199,210,215,216, 275,276,278,281,284,298, 308,309, 313,318,320,322,323, 328,332,337, 338, 340, 351, 352, 353, 355-57, 360, 361, 363, 366, 367, 369, 370,373, 393, 397, 398,401,408,413,417,423,426, 430,433, 487-537 passim

(study of Greek text of) 491 of Middle Ages and 16th century com

pared 533-34, 535 printing of his works 498-99, 509-10,

517arithmetic 33-60 passim, 124, 125, 4SI Arius 164Arnald of Villanova 267, 318, 516 Arnaldez, M. 51 Arnault de Zwolle, Henri 477 Amobius 163

INDEX 541

arts (jechne) 118ff, 120-21, 122, 483 see also: liberal arts

Arts Facuhies 23,275, 336, 349, 378,488, 533

al-Ash‘ari 66 Ash'arites 87, 110 Asclepius 201, 207 Ashworth, E. J. 520 Aspall, Geoffrey of 389 Aston, T. H. 514, 523 astrolabe 217-18, 440, 464, 478, 480 astrology 9, 124, 194 203, 208, 215, 278

(natural vs superstitious) 214-15 and astronomy 213-14, 215 and magic 214 and science 207-8, 213-14 as expression of a new concept of

nature 203-6 in 16th century universities 505-6

astronomical tables 463-64, 467 astronomy

Copernican contemporary religious reaction to

398^104 hypothetical? 404-7, 415-16

mathematical 44, 54, 414-15 as intermediary between algebra and

practice 51, 52-53, 57 in al-Fàrâbi 124, 125 in medicine 202-3, 215 in navigation 463-68, 478 in Sentence commentaries 278-79 in 16th century universities 505-6 see also: instruments, astronomical

Athanasius 164 atheism 522 Athenagoras 162 atomism 490, 501 auctoritas 196, 197, 198, 325 augmentation 296, 328 Augustine (Augustinian) 109, 153, 163,

166,179,199,212,213,230,231,237, 257,267, 316, 338, 344,353,272, 394, 401, 417, 422, 429, 430, 431, 438

Aulus Gellius 163 Aurifaber, J. 420 Authier, F. 474 authority

(ecclesiastical) 374

authoritarian 221 autonomy

of man 359, 407of secondary causes 212, 213, 216 of science 5, 349, 352-53, 354, 359, 363,

372, 373, 377 vs a “sublimated science” 363, 367

Avempace see: Ibn Bâjja Averroes see: Ibn Rushd Averroists, Latin 183, 395, 408 see also:

Ibn Rushd; truth, doctrine of double Avicenna see: Ibn Sina âyn (thing) 65, 75, 78 Ayyüb al-Sakhtiyâni 102

Bâbai 99Bacon, Francis 214, 230, 268, 426, 432 Bacon, Roger see: Roger Bacon Badawi, A. 79al-Baghdadi, Muhammad ibn ‘Abd

al-Bàqî 40, 525 Bagdedinus, Machometus see: al-Bag-

dàdi, Muhammad ibn ‘Abd al-Baqi Balduino, Girolamo 499 Bandini, A. M. 522 Bafiez, Domingo 509 Banü Hâshïm 96 Banû Müsâ 49 Banü Quraysh 96, 97 al-Bâqillâni, Abü Bakr 69-70, 76, 77 al-Bâqir, Muljammad 89, 90 Barach, C. and J. Wrobel 211 Barbarus, Hermolaus 168 Barbel, J. 422Barbier de Maynard, C. 103 Baron, R. 471Barozzi, Francesco 495, 507, 522 Barradas de Carvalho, J. 473 al-Barràdî 98Bartholomew the Englishman 160,190 base, in number systems 56 Basil 179 Basileus 106al-Ba§ri see: Abu’l ûsayn al-BaçriBataillon, M. 528Baudry, L. 389Baur, L. 472Bautier, R.-H. 472bayâ 96

542 INDEX

bayân (explanation) 61, 64, 65, 66, 68-69, 70, 71, 75-6, 78, 81, 82, 83

Beaujouan, G. 5, 6, 321, 472, 473, 475, 476

Beck, H.-G. 103 Becker, C. H. 99Bede (the Venerable) 153, 158, 197, 479 Bedini, S. 477 belief see: faith Bellarmino, Roberto 500 Beltrami, L. 444-45 Ben-David, J. 339, 349, 379 Benedetti, Alessandro 504 Benedict 231

(Rule of) 219, 430 Berengar of Tours 393, 394 Bernard of Chartres 162 Bernard of Clairvaux 7, 221-268, 430

and consideration 246-54 and the corporeal 226-28 and experience 223-29 and knowledge 229-39 his mysticism 226, 235-39, 264-65 and reform 239-46

Bernard of Morlas 165 Bernard Sylvester 165,198,200,203, 204,

206, 210, 211 Bertalot, L. 530 Berthold of Constance 166 Bertolis, G. de 527 Bessarion (Cardinal) 518 bestiaries 193 Biel, G, see: Gabriel Biel Birch, T. B. 383, 389 al-Bîrûni 44, 45, 47 Bissinger, A. 530 Blachère, R. 98 Blasius of Parma 345 Blumenberg, H. 406-7, 418, 422, 431-32 Boccadiferro, Ludovico 508, 534 Bodard, C. 260Boehner, P. 317, 319, 321, 323, 339, 381,

384, 387-88, 391, 528 Boethius 153,159,166,168,169,170,171,

172,176,177,179,189,195,197,211, 379, 393, 439, 477, 480

Boethius of Dacia 378, 380, 387, 389, 390 Bongratia of Acoli 168 Bonaventura 165, 183, 186, 402, 431

Boncompagni, B. 474, 475, 527 Bonnerot, J. 529 bookkeeping 341 Borelli, A. 419 Borissavlievitch, M. 475 Bomkamm, H. 420, 423 Borro, Girolamo 523 Bots, J. 423 Bourbaki, Nicholas 50 Bradwardine, T. see: Thomas Bradwar-

dineBrahe, Tycho 424 Branner, R. 447 Brant, Sebastian 513 Bravmann, M. 99 Brecht, B. 398, 399, 400 Brerewood, Edward 499, 500 Brethren of Purity see: Ikhwan al-Safa’ Brini Savorelli, M. 212 Brulifer (“Scotellus”) 431 Brunes, T. 475 Brunetto Latini 161 Bruni, Leonardo 518 Bruno, Giordano 419, 489, 490 Bubnov, N. M. 480 Buescher, G. 386 Bulaeus, C. E. 529 Bullough, V. 472 Buonamici, F. 520, 522, 523 bureaucracy see: administrative bureaus Burgersdijk, Franco Petri 492 Buridan, John see: John Buridan Burleigh (Burley), Walter see: Walter

BurleyBurmeister, K. 423, 424, 428 Burtt, E. A. 423 Bury, R. G. 67, 77, 79, 80 Busard, H. L. L. 337, 477 Busdraghi, Vincenzo 522 Busson, H. 522 al-Bustânî, Butrus 78 Buttimer, C. B. 211 Buytaert, E. 381 al-Bûzjâni see: Abu’l-Wafâ’

Cahen, C. 55, 100calculation, art of 34 see also: arithmetic calculatores^ Oxford 306, 318, 341, 342,

512, 533

INDEX 543

Callus, D. 378, 389Calvin, J. (Calvinism) 220, 222, 400, 402,

403, 425, 492 and revelation vs experience 400,

420-21Campanus see: John Campanus Cano, Melchor 509 cantor 439 Cantor, Moritz 60 capitalism 220 Cardan, Jerome 33caritas, and intension and remission of

forms 288-89, 294, 301, 324, 325, 328, 333

carpenter’s square see: square, carpenter’sCasaubon, Isaac 518Case, John 499, 500, 520Cassiodorus 153,189Cassirer, E. 418Castellani, C. 526categorematic 285Catena, Pietro 507cathedrals see: architectureCattin, P. 450cauda pavonis 450-51, 453, 474 causarum series 195, 196, 198, 212, 213 cause (causality)

(efficient) 406, 409, 412 (final) 406, 409, 416 (prime or divine) 212, 360, 370 (secondary or natural) 195, 203-5, 212,

213, 281, 370 see also: legitima causa et ratio

Cavalli, Francesco 527 Centiloquium (pj.-Ptolemy) 203, 206 Centiloquium theologicum (;j^.-Ockham)

323certitude 25, 287, 288, 340, 341, 373 Cesalpino, Andrea 497, 511 Chalcidius 199, 210 charity

(effective vs affective) 247-49 see also: caritas

Charpentier, Jacques 521 Chartres

(school of) 198, 213, 245 charts, geographical and nautical 440,

463, 464, 465 Chatelain, A. 386

Cheiko, Louis 146 Chenu, M.-D. 351-52, 354 chih (angular measure) 468 Chinese origins of Western technology

(question of) 443 Chiovenda, E. 526 Christians

(possible influences of) on early Islam,100-1,107

Chuquet, Nicholas 35, 477 Cicero 113, 159, 161, 162, 169, 111, 175,

177,178,179,200,201,208,249,415, 438

Citeaux (Cistercians) 219, 228, 243, 255- 56, 263, 265

their technology 254-55, 265 Clagett, M. 318, 392, 407, 516, 529 Clark, A. 500, 521, 524, 525 classifications of the sciences 113-47

passim, 392, 438-42 (Alexandrian) 146, 147, 189 (Aristotelian) 116 in Dominic Gundisalvo 159, 441 in al-Fârâbi 117, 146,147, 441 in Hugh of Saint Victor 438-39 in Ibn Sina 146, 156 (Islamic) 116

Clavius, Christopher 507 Clement of Alexandria 163

-Clement of Rome 163,164 Cleyet-Michaud, M. 462 clock

analogy 410 (mechanical) 469

Clulee, N . H. 525 Cluny (Cluniac) 219, 265

(church o f) 472 codicology 275cognitio intuitiva 266, 357-59, 374, 394,

409, 434 of non-existents 358-59

Coimbra, College of (manuals of) 491,509, 511, 535

Colet, John 511, 512 Colson, F. H. 80 Columbus, Christopher 442 Columella 159 Combes, A. 323, 430 Commandino, F. 525

544 INDEX

Commandments, Ten 396 Communication, techniques of 262, 532 communities, intellectual 12, 22-28 Companus of Novara 453, 474 compass (magnetic) 463 compasses (mathematical) 418, 461-62,

474 complexio 202 Conant, J. B. 373-74, 376 Conant, K. J. 472 concomitance 362, 365, 382 condemnations (censure) 272, 276, 296-

97, 364of 1277 313, 338, 360, 371, 408

configuration of quality 282, 283 conscientia 230, 231, 232 consideratio 247, 249, 250, 251, 252, 253,

254, 258contemplatio 225, 247, 249, 252, 253, 254 Constantine (I) 164Constantine the African 158, 186, 202,

211,440context, cultural see: cultural context continuity (mathematical) 276, 289, 294,

313medieval language of continuity-infin-

ity 284-85, 286, 295, 298-303 contra vanam curiositatem 5, 212, 397,

401,402,403,404,406,408,411,414, 417-18,426,429, 430,431,432

Coopland, G. W. 426 Copernican Revolution

modem popular views of 397-99 Copernicus, N. (Copernican) 5, 397-407,

410-17, 429, 431-32, 435, 489, 490, 514, 517, 527, 531, 536

Corbeau, A. 474 Cordeaux, E. H. 523 Corrin, C. A. 530 Cortés, Martin 465 Cortesao, J. 472, 473, 475 councils, church 164-65, 361, 389, 408 Counter-Reformation 509 Courcelle, P. 211 Courtenay, W. J. 323 Cousin, Victor 170,175 Crakanthorpe, Richard 499-500,520,525 Cranz, F. E. 517, 518, 521, 527 Crapulli, G. 527

Crathorn 321creation 278, 353, 418, 439

ex nihilo 370 see also: Hexaemeron

Crellius, Fortunatus 499, 530 Cremonini, Cesare 508 Creutz, R. 211Crombie, A. C. 321, 380, 438 Crosby, H. L. 318, 515 cross-cultural factors 2, 8-9, 64 see also:

intercultural cubit (astronomical measure) 467 cultural context 14-16, 20 cultures, medieval

as expressed in the organization of sciences 151-92 passim

cultures, relations between see: cross-cultural factors

curiositas campaign against vain curiosity see:

contra vanam curiositatem curiosity

scientific 218 Curtis, M. H. 523, 525 Curtze, M. 473

dactylonomy see: al-üqad Dainville, F. de 471, 477 dalàla 69Dalechampius, Jacobus 526 dalü (indicant, logical proof) 69, 70, 71-

72, 76, 77, 82, 83 dalil al-khifab 81

Daniel of Morley 189,194,202,204,205,207, 215

Dannenfeldt, K. H. 526 Dante 241, 443, 476 4arürl (necessary) 108 Darwin, C. (Darwinism) 403 Daumas, M. 471 Day, John 520, 524 Debamot (Mile) 450 decagon, construction of 458 decision-making

(rules for) 7, 225-26 (man’s capacity for) 246, 254

Dee, John 429, 501, 525 De Goeje, M. J. 78 Deichgraber, K. 211

INDEX 545

Democritus 84, 501 demonstration

in mathematics 125 in metaphysics, 128, 129-30

Denifle, H. 386, 515 denominatio 282, 283, 288 Denomy, A. 425 Denziger, H. 394derivatives (in Islamic mathematics) 49,

50Descartes, René (Cartesian) 15, 33, 184,

185, 403, 425, 489, 514 Destombes, M. 477 devotio moderna 401 Dhahabi 93,103 dhirâ (cubit) 467 Diacetto, Francesco da 521 dialectical form 89, 91-93, 99, 105, 107

see also: kalam Dibon, P. 515 didacticism 480, 481 digit (astronomical measure) 467 dignitas hominis 207, 209, 264 dilectio D ei 323-24, 325, 326, 329 Dillenberger, J. 420, 423 dimensions, indeterminate 365 Diogenes of Babylon 74 Diogenes Laertius 64, 74, 75, 76, 77, 79 Dionysius {pseudo-) 199, 422 Diophantus of Alexandria 34, 50 Dioscorides 526 Pirar ibn *Amr 88, 92 disciplines (need for delineation o f) 10 discovery

(concept of) 444, 473 discriminant

in cubic equations 46-47, 48 disputations

at 16th century Oxford 498, 500-2 ‘divine’ proportion 450 divine science see: metaphysics Diwald-Wilzer, S. 101 diwan (administrative bureau) 53-55 Domesday Book 441 Domingo de Soto 499, 509 Dominic (Dominicans) 266, 391 Dominic of Clavasio 477 Dominic Gundisalvo 145, 147, 156, 158,

159, 186, 205, 441

Donatus 159 Dorelle, M. 523 Doucet, V. 322, 328 Dozy, R. 78Drake, S. 419, 518, 520, 522 Dubler, C. E. 526 Duby, Georges 254-55 Duchez, M.-E, 472 Du Colombier, P. 446, 461, 472 Dürer, Albrecht 447, 474 Duhem, Pierre 15,16, 272, 319, 376,407,

408, 426, 428, 516, 529 dulkarnon 474Duns Scotus, John see: John Duns Scotus duplication of a cube 44 Durkheim, E. (Durkheimian) 52 DuVal, Guillaume 518

earth(motion of) 411, 415, 419, 435

eccentrics (astronomical) 416 eclipses 280 Ecphantus 415 education

(Arabic) 87,159 (Latin) 159-60 (primary and secondary) 533 see also: universities

Edwards, W. F. 520, 530 Effler, R. 338 Egidius de Campis 279 Eilmer of Malmesbury 440 Eis, G. 476Eisenstadt, S. N, 259, 260 elefuga 451, 453 elementans 203 elephant, picture of 470 Elert, W. 420, 427 Elie, H. 319, 529 Elizabeth I (England) 500 Elkana, Y . 312, 388, 428 Ellies-Dupin, Louis 425, 427 Emden, A. B. 323, 515, 523 empeiria 268empiricism 314, 417, 434 see also:

experience encyclopedias 8,151-192 passim

(Greek) 153-54, 187 their impact on the Latin

546 INDEX

encyclopedia 161-67 (Latin) 152-53, 158, 185-87, 190 (Hebrew) 154-55(Muslim) 155-57, 187, 188, 190-91

their impact on the Latin encyclopedia 152,157,167,182-84,186

(Roman) 152-53, 187 engineers, medieval 440-41,444ffsee also:

ingeniator Ennami 103 Epicurus 68, 84 epicycles 416epistemological closure 51,57,58 see also:

sciences, diffuse vs exact equations 40

(quadratic) 33 (theory of) 44, 45

(cubic) 33, 43 (theory of) 43-48, 50

equinoxes, precession of 278-79 Erasmus, Desiderius 401, 408, 431, 489,

508-9, 511, 512, 513 Erfurt, University of 316 Eriugena see: John Scotus Erigena Erlande-Brandenburg, A. 472 eschatology 264, 266 Eschweiler, K. 519, 530 eternity 289, 302, 314, 338, 353, 427 ethics 132 see also: moral concerns,

political science Etienne of Antioch 440 Etienne Tempier 276, 338, 390, 395 Eucharist 5, 360-72, 393-94, 410

(physics of) problems concerning Christ’s

presence 362-68 problems of transubstantiation

368-70problems of the species of bread

370-72and Aristotelian physics of change and

place 363Euclid {Elements) 37, 38, 39, 52, 60, 118,

126,159,185,187, 318, 328,450,453, 456,458,463,480,481,482,483,484,505, 506

Eudemus 172 Eudoxus 154Eugene III (pope) 249, 256

Eunapius 154 Eutocius 44evidence 25, 287, 340, 341, 434 evident and non-evident things 67-68 evil 91Evrard the German 162 excessus mentis 264 excessus (mathematical) 329, 330

secundum proportionem vj secundum quantitatem 318

exegesis 439, 479, 481 experience (experiment, observation) 5,

11, 16, 108, 120, 127, 132-33, 134,189, 207, 216, 223-29, 230, 245, 265, 357, 360, 368, 400, 402, 406, 409-11, 412,413,416,426,432,433,434,435,483 see also: experientia, experimentum, experiri, expertus

experientia 224, 225, 265, 266, 267, 396, 409, 432

patet 268 experiment see: experience experimentum 223, 224, 225, 265, 266,

267 see also: i'tibâr experiri 223, 224, 226, 405 expertus 223, 224, 226

novit 266 explanation see: bayân extension (mathematical) 365, 367, 410 Ezechiel

his vision 439

fabrica 483 Fabroni, A. 487, 522 Facciolati, F. 520, 527 fffida (significance) 61 faith 5, 373

and reason 109, 110, 311, 419 falâsifa (philosophers) 110 Falloppia, Gabriella 504 Fantoni, Filippo 505 al-Fârâbi 4, 6, 107, 156, 158, 159, 168,

194, 205, 441, 483 Enumeration o f the Sciences 113-47,

188, 189, 191, 192 Short Commentary on Aristotle’s Prior

Analytics 181-82 al-Farazdaq 97 al-Farghânî 194, 465

INDEX 547

al-Fayrüzabâdi 78fatwâ (legal) opinion) 97Favaro, A. 527Fermat, Pierre de 185Ferrand, G. 476Festugière, A. J. 211Fibonacci see: Leonardo FibonacciFicino, M. 494, 516, 521, 530figura cotis 452, 453figura demonis sive intelligentis 453, 455,

456figura equatrix 452, 453 figura exemplaris 452, 453 figura magistralis 474 figura mediatrix 453-54 Finé, Oronce 505 fiqh Oaw) 69, 131, 146

Usül al-fiqh, 61-85 Firmicus Maternus 204, 212 Fischer, H. 526 fifra (inborn) 92, 109 Flavel, John 499, 520 Fletcher, J. M. 516, 523, 525 Florencio dei Nino Jésus (Fr.) 528 fiorilegia 189 Folli, F. 523Fonseca, Pedro da 500, 524 fontes 402, 408 foreknowledge, divine 91, 395 forma mundi 405 Fraile, G. 528Francis of Assisi (Franciscans) 216, 264,

391, 442 Francisco de Victoria 508, 509 Franciscus of Marchia 313 Franciscus Mayronis 314 free will 91, 92, 105, 106, 174, 251, 295,

301, 305, 325, 326-27, 395 French, P. 429, 525 Frisch, C. 423 Frontinus 159 fuqahff (jurists) 110 future contingents 174, 274, 278, 395

Gabriel Biel 344, 381 Gabriel Stomaloco 444-45 Gabriel, A. 521Galen (-ic) 79, 153, 155, 158, 194, 202,

218, 267, 504, 524, 535

Galileo Galilei (Galilean) 13,15,18, 266, 347,348,390,399,400,404,413,417,487, 489, 495-97, 505, 506, 507, 514, 523, 534

Galluzzi, P. 527 Gardet, Louis 101 Garin, E. 212, 518, 520, 523 Garland the Computist 178 Gaufridus ingeniator A l l Gaza, Theodorus 518 Geldner, F. 473 generation and corruption 293 geocentric 398-99 Geoffrey of Aspall 389 Geoffrey of Vinsaud 162 geomancy 206Geometria incerti auctoris 480 geometric figures, practical use of 450-58 geometric series 462-63 geometry

(algebraic) 34, 42-50 in al-Fârâbi 115, 117-18, 124,125 as a subalternating science 355, 356 (practical) 439, 444-63 (theoretical vs practical) 480-84

Georgias 154 Gerard of Cremona 145 Gerard of Odo 276, 313, 314, 380 Gerbert of Aurillac 159, 166, 217, 218,

480Gerbert, M. 472 Gessner, Conrad 526 gesticulation see: ishâra ghâlib al-zann (most-likely opinion) 66,

69, 77Ghaylân al-Dimashqi 92, 102al-Ghazali 82, 109, 110Ghini, Luca 503Giacobbe, G. C. 527Gibson, S. 521, 525Gilbert de la Porrée 168-69, 171, 222Gübert, N. W. 517, 520, 523Giles of Rome 364, 365, 373Giles of Viterbo 494Gille, B. 437, 446Gilles, M. 472Gilson, E. 260, 261, 378, 380, 381, 387,

390, 391, 521, 529 Gingerich, O. 417, 536

548 INDEX

Giorgi, Francisco 500 Girard, Albert 463 Gisius, T. 404Glorieux, P. 313, 314, 378, 421 Glucker, J. 518 God 61-75 passim, 91, 92, 97

(anti-anthropomorphic view of) 66-67 (infinity of) 289, 300, 314 (proof of existence of) 108-9, 129-30,

131, 143, 355 (relation to man of) 245, 301 see also: omnipotence, onmiscience,

potentia Dei absoluta, potentia D ei ordinata

Godfrey of Saint-Victor 264 “golden” proportion, section, mean, etc.

447,450,453,456,458,459,460,461,462, 463

Goldstein, B. 468 Gomes, Diogo 465 Gonzalez Palencia, Angel 145, 472 Goujet, C. P.Grabmaim, M. 147, 336 grace 242^5 passim, 291, 293-94, 334,

335, 427 gradus 282, 326, 328, 331, 337

non gradus 299, 324 grammar 84

(Islande) 81, 83,146 (Stoic) 82 in sophisms 304its application to theology 351-52

Grant, E. 332 Gratian 166, 185 gravia et levia 278 Gregory the Great (I) 164 Gregory IX (Pope) 378 Gregory of Nazianzus 164 Gregory of Nyssa 240 Gregory of Rimini 340 Gregory, T. 4, 6, 7, 9, 211, 471 Griffiths, J. 520 Grmek, M. D. 477 Grosset-Grange, H. 476 Grouchy, Nicholas de 518 Guelluy, R. 314, 381, 387, 388 Giinther, S. 473 Gundersheimer, W. 521 Gundissalinus see: Dominic Gundisalvo

Guy of Arezzo 439-40

Habiba 102al-Hâdi ila’I-ljaqq Yahyâ ibn al-^jtusayn

see: Yahyâ ibn al-IJusayn hadith (tradition) 82, 87

hxidith al fifra 92 Haring, N. M. 211 al-yajjâj 89 al-Ifâl (state) 78, 79 Haller, J. 520 Hamidullah, M. 79 iianaf! 62, 63, 73hand-span (unit of astronomical measure)

467 Hanke, L. 521 Hardie, C. 475 al-Uariri 78 Hartfelder, K. 530 Hârün ibn ‘Abd al-yamid 54 Hârûn al-Rashîd 106 Harvey, William 487, 502, 523, 529 tiasan al-Baçrî 89, 92, 93,105 ^asan ibn ‘Ali 96IJasan ibn Muhammad ibn a1-ïJanafiyya

91, 92, 93, 94,95, 96, 97-98, 99,104, 106

al-Uasan al-Marrakushi 465 Haskins, C. H. 210, 211,212 Haspyl see: Geoffrey of Aspall Haverel Norvici 328-29 Hawenreuter, Joharmes 530 Heckscher, W . 527 Heiberg, J. L. 527 heliocentric 411, 412-13, 414 Hell 91, 92 Hélot, L. and H. 78 Çenànâ 99 Henry of Hassia 314 Henry of Oyta 316, 325, 327 Heracleides of Pontus 415 Heraclius 106Herman the Dalmatian see: Hermaim of

CarinthiaHerman Lurtz de Nuremberg 279, 337 Hermann of Carinthia 159, 200-1, 203,

204Hermelink, H. 530hermeneutics 81, 82, 154, 161, 163, 403

INDEX 549

Hermes Trismepistus (hermetic) 207, 444 see also: De Sex principiis (pseudo- hermetic)

Herrad of Landsberg 203 Hervet, Gentian 511 Hesychias of Miletus 154 Heytesbury, W . see: William Heytesbury Hexaemeron

(exegesis of) 196, 197, 315 hexagon, regular

(construction of) 450, 463 Hézelon of Cluny 440 Hicks, R. D. 77 Hildebert of Lavardin 165 Hincmar 166 Hinz, J. 529 Hippias 154 Hippocrates (-ic) 202 Hippolytus of Rome 163 Hirsch, E. 424 Hirth, W . 518 al-Hishâm 92, 97, 104 Hispanus, P. see: Peter of Spain historiography of medieval learning

11-28, 151-52, 220-21, 262, 265, 271-73, 344-48, 485-87, 531

and practice 437, 443, 469-71, 477-78 history

(stages of) in Bernard of Clairvaux 242

Hoffmann, F. 315, 391 homo

faber 209, 398 viator 209

Honorius of Autun 158 Honorius Inclusus 158 Hooykaas, R. 417, 420-21, 423, 426 Horace 162 horn angle 332, 335 Horten, M. 78 Hosea 236Howell, W. S. 523, 524, 525 Hrabanus Maurus 153, 158, 188 Huard, P. 477 Hugh Libergier 459-61 Hugh of Saint Victor 197, 200, 201, 208,

209, 215, 264,422,423,438, 439, 441 Hugh of Santalla 203, 204, 215

Huglo, M. 472

hukm (judgment) 61, 76 human/-ism, -ist 8,151,238,343,402,408

in 16th century universities 489,490-91,493, 496, 498, 507-12, 533, 534

humanities 163, 412 yusamaddin al-Qudsi 102 yusayn 95, 96 Huygens, Christiaan 185 Hyginus 159 hypotheses 415, 416

in astronomy see: astronomy, Copernican, hypothetical?

iatrosophists 154Ibadites 89, 90, 98Ibn Abi ‘Umar al-‘Adani 93Ibn ‘Asakir 103Ibn Bàjja 523Ibn Batta 103Ibn Sajar 93, 103Ibn al-Haytham 38, 44, 49, 267, 345 Ibn Uazm 40 Ibn Hisham 101 Ibn Kathir 102 Ibn Khaldün 54,107 Ibn Labbân 54, 56 Ibn Mâdjid, Ahmad 467, 476 Ibn Man?ûr 78 Ibn al-Murtada 101,102 Ibn Rushd 156-57, 338, 365, 508, 512,

519,533,535,536 see also: Averroists Ibn Sa‘d 90, 103Ibn Sina 70, 75, 80, 130, 146, 156, 158,

159,167, 181, 188,189, 194, 202, 216 338, 482, 483, 535

Ibn Taymiyya 40,109, 110 Ibn Wahb, Isljâq 79 Ibn al-Zubayr see: ‘Abdallah ibn al-

Zubayr Ibrâhâm ibn Sinân 49 igneus vigor 199 ignis

aethereus 200 artifex 195, 200, 201

al-Iji, ‘Adudaddin 102 ijtihâd (judgment) 66, 68-69, 70, 77 see

also: mujtahid Ikhwan al-Çafâ’ 155, 189 ‘ilia (cause) 74, 82

550 INDEX

illuminatio in Bernard of Clairvaux 235-39

illustration 440, 470-71 ‘«7m (knowledge) 69Him al-hiyal 147,441,483 see also: scientia

de ingeniis imaginatio 413, 426, 432-33, 434, 345

secundum imaginationem arguments 281, 292, 294, 297, 300, 301, 305, 307, 312, 331, 337,409-11

impetus theory 313, 411, 427 impossible propositions in algebra 42 de incipit et desinit 284, 306, 323 indicant see: dalil indicant of a discourse 61, 63 indivisibles 301, 313, 326, 332, 432 induction

vs experience in al-Fârâbi 483 mathematical 39

infinitum as a logical term 319, 337 infinitesimals/infinitesimalists 34, 48, 49 infinity 278, 289, 313, 427

(mathematics of) 285 (medieval language of) 284-85,298-303 (unacceptable and admitted) 301-2 of sets and sub-sets 302, 319, 338

ingenia 441, 469 see also: scientia de ingeniis

ingeniator (inzignerius) 441, 444, 472 Innocent III (Pope) 361, 369 Inquisition 375, 419 de insolubilibus 280, 335, 512 instants 322, 323, 324, 325, 326, 327, 332,

368, 432 see also: de primo et ultimo instanti

institutional factors see: social factors instruments 459

(pedagogical) 440, 479 (astronomical) 440, 464-68, 478 see also: names of individual instru

ments instrumentum 227

(corporis) 228, 263 integrity, intellectual 375 intelligences 129 intelligibles 128intension and remission of forms 184-85,

282-83, 285, 286, 287, 289, 293, 294, 296, 299, 300, 301, 323, 343 jee also:

measure languages intention

(first and second) related to the Trinity 278,314

use of second intentional point of view in the fourteenth century 282,286, 287, 288, 312, 338, 343

intercultural influences, as rearrangements of

schemata 157-58 relations 151-92 passim see also: cross-cultural factors

interdisciplinary relations 2, 4-6, 12, 15, 17, 18, 19, 24, 64

of algebra and arithmetic 4 intuitive cognition see: cognitio intuitiva irjâ ' (postponement) 73, 95

K.al-Irja^ 93, 96, 97, 98 irrational quantities 38 d’Irsay, S. 515, 530 Isaac 258Isaac Israeli 159, 160 ifba' (unit of astronomical measure) 467,

468Ishaq ibn tJunayn 79 ishara (gesture) 65, 66, 67, 69, 70, 78 Isidore of Seville 153, 158, 159, 187, 188,

190, 215, 479 Islam 31-147 passim

(law in) 4, 8, 87,147 Islamic sciences see: sciences, rational vs

traditional Islamic iteration 48iUibâr ( experimentum) 268 Ivo of Chartres 166,185

Jâbir ibn Zayd al-Azdi 98 Jaeger, H. 523 Jaeger, W. 417, 429 Ja‘far al-$âdiq 90al-Jàhi?, Abü ‘Uthmân ‘Amr ibn B a ^ 78,

79, 82, 83, 101 Jaki, Stanley 390 James, T. E. 516al-Jaççâç, Abü Bakr al-Râa 61-85 al-Jahshayàrî 54 Javellus, Crisostomus 524 Jayne, S. R. 530 Jean see: John

INDEX 551

Jerome 164Jesuits 219, 491, 494, 507, 511 Jews see: Judaism jihâd (religious war) 73 Joachim of Fiore (Joachimites) 165, 256,

513Johannis see: John John II (Portugal) 464 John XXIII (pope) 315 John of Affligem 439 John Bode 337John Buridan 321, 334,350,372,375, 376,

379,391, 393,407,425,426,428,434,488, 516, 529

John of Damascus 99, 100, 103 John of Dondi 477 John Dumbleton 320, 337 John Duns Scotus 178,274,287,321,338,

341, 344,364,382,386,387,393,395, 396, 534 see also: (pseudo-) Scotus

John of Falisca 276 John Fusoris 477John Gerson 343, 396,401, 402,407,417,

421, 423, 425, 426, 430, 431 John Hispalensis 480 John Lutterell 364, 391 John Major (Jean Mair) 319 John Mirecourt 296, 325, 333, 334 John Pecham 345 John of Ripa 293, 313, 335 John of Sacrobosco 465, 481, 505, 506 John of St. Thomas 509 John of Salisbury 161-62, 165, 170, 171,

208, 215John Scotus Erigena 197-98,199, 240 John of Seville 203, 212 John Versoris 516 Jordanus Nemorarius 473, 518 Joshua 400, 410, 427 Jourdain de Sévérac 467 Judaism 107

(theology in) 88 judgment see: ijtihàd Jüngel, Eberhard 421 Julia Domna (Empress) 153 Julian the Apostate 154 jurisprudence see: legal theory justification 291 see also: merit Justin Martyr 162,163

Ka^ba 97kalâm 4, 6, 8, 66, 75, 83, 89, 90, 93, 98,

99, 101, 131, 146, 156 (definition of) 105, 107-9 and theology 89, 108, 109 see also: theology, Islamic

Kalbfieisch, Carl 79al-Karaji, Abü Bakr Muhammad ibn al-

Hasan 33, 34, 35-39, 40, 45, 53, 54, 56, 57, 59, 60

al-Karkhi, Abü Bakr Muhammad ibn al- yasan see: al-Karaji

al-Karkhi, ‘Ubayd Allah ibn al-Çasan 62 Karpp, H. 421 al-Kâshi 33, 60 Kaufman, G. D. 425-26 Kaufmann, G. 515 Kaysaniyya 95 see: Saba'iyya Kayserberg, Geiler von 513 Kearney, H. 498, 523, 524 Keckermann, Bartholomaous 492, 500 TÔ K E T Ô G a i 77, 78, 79 Keller, A. G. 526 Kelso, R. 530 Kennedy, E. S. 59Kepler, Johannes 400,403, 404,413,417,

419, 421, 424, 475, 487, 530 khabar (statement) 72, 75, 76 Khadduri, Majid 79 Khârijites 88, 89, 90, 98, 105 khâss (particular) 72, 73, 75, 76 khaft (writing) 65, 66, 67, 70, 78 al-Iüiayyâmi 33, 34, 43-45, 47, 48 al-Khàzin, Abü Ja‘far 43 khitâb (discourse) 61,64,65,76,77,81,82 Khoury, A.-T. 104 Khoury, I. 476 Khoury, P. 104 Khoury, R. G. 103al-Khwariznu, Muhammad ibn Ahmad

ibn 55, 56al-Khwarizmi, Muhammad ibn Müsâ 33,

34, 48, 50, 58, 59, 60 Kieffer, J. S. 79 al-Kindi, Abü ‘Umar 54 al-Kindi, Ya‘qûb ibn Ishaq 79, 80, 155,

158, 482kingship, virtuous 132-33, 134, 143 Klebs, A. 477

552 INDEX

Klibansky, R. 418 Kneale, W. and M. 78, 319 knowledge 109, 110

in Bernard of Clairvaux 229-39 puffs up see: scientia inflat

Knowles, D. 321, 339, 394 knuckles see: *uqad Koch,J. 391,515 Koestler, A. 400 Koran see: Qur'an Koyré, A. 418, 424, 428, 429 Krasnova, S. 474Kristeller, P. O. 515, 517, 518, 520, 521,

522, 523, 527 Kürzinger, J. 314 Kuhn, T. S. 420, 429 al-Kulini 89 Kunitzsch, P. 467 Kurrus, T, 530kuttâb (scribes) 53, 54, 55, 58, 59 Kyeser, Konrad 446

Lacombe, G. 518 Lactantius 401, 406, 429 laf? (utterance) 61, 66, 76, 77, 78, 82 Laguarda Trias, R. 465, 468, 476 Lambert of Saint-Omer 158 Lammens, H. 104 lance {rumb), unit of astronomical

measure)Lanfranc (of Canterbury) 394 language

(science of) in al-Fârâbî 113, 115, 116, 118-19, 146

Laoust, H. 103 lapidaries 193 Laplace, P. 424, 429 Last Judgment 92 Latham, R. E. 441 latitude (geographical)

(determination of) 464-65 latitudo 282, 293, 299, 318, 320, 328, 332,

337 motus 320 proportionis 320

Laudian statutes, Oxford 494, 520 Lauterbach, A. 420law 2, 8, 147, 157, 159-60, 313, 391-92,

409, 533, 536

its importance in Islam 87, 147 see also: fiqh\ lawgiver, divine; legal

theorylawgiver, divine 131, 138, 139, 140, 141,

142, 144,146 learning

(unitary character of medieval) 5, 271-348

Lebensfûhrung see: plan of living Leclerq, J. 210, 260 Lefèvre d’Étaples, J. 518 Lefebvre des Noëttes 437 Leff, G. 332, 394, 515 Lefranc, A. 529legal theory, in Islam 61-85 passim, 113,

114, 115, 137^5 (influence of theology on) 72-73

legitima causa et ratio 193, 196, 210 see also: cause; causarum series; ratio

Le Goff, J. 477 Leite, S. 520Aækxôv (meaning) 64, 76, 84, 85 Lemay, R. 476, 515, 517 Xé^iç (speech) 64, 66, 77, 81, 82 Leonardo Fibonacci (of Pisa) 456, 462,

463, 481 Leonardo da Vinci 458, 516 Leonico Tomeo, Niccolô 527 Le Roy, Louis 521 Levey, M. 475 Levi ben Gerson 468 Levi, A. H. T. 518, 521 Lewalter, E. 519, 530 Lewis, B, 78 lex 425lex naturae 425 L ’Huillier, H. 477(anon.) Liber Mamonis in astronomia 194 Liber Sententiarum see: Peter Lombard liberal arts 147, 153, 158, 159, 162, 163,

165, 166, 183, 230, 231, 237, 415 their use in theology 274-312 their status in medieval universities

349-54 Liceto, Fortunio 508 limits

(upper and lower) 49 “limit setting” languages 285, 286,299,

300, 318

INDEX 553

see also: de incipit et desinit; de maximo et minimo; de primo et ultimo instanti

Linacre, Thomas 503, 511, 527 literacy

in early Islam 105-6 logic

(Aristotelian) 84, 120, 167, 176, 177, 188

the Organon 79, 122, 123, 124, 159, 168-83 passim, 355-57, 493, 499, 519

(atomistic or Epicurean) 84, 156, 167 in the Hebrew tradition 179-82 (Neoplatonic) 156, 167, 168 (sophistic) 84(Stoic) 4,8,63-65,67-68,70-72,74-77,

84-85, 156, 167 (applications of) in Islamic law 4, 8,

61-85(applications of) 11,155 (history of) in the West 167-79 in al-Fârâbi 113,115,117,119,120-24,

128, 138-39 in medieval universities 351 in Sentence Commentaries 279-80 in sophismata 304in sixteenth century universities 493,

494, 496 and nominalism 433

XÔYOÇ 64, 66, 76, 81, 82, 84 Lohr, C. H. 515, 516, 528 Lombard, Peter see: Peter Lombard Lucas, E. 463 Luckey, P. 33, 60 Lull, Raymond 442, 463, 474 Luther, M. (Lutheranism) 220, 376, 399,

400,401,408,415,421,427,430,431, 432, 491, 492, 494, 500, 510, 513

Maccagni, C. 516, 518 McCarthy, R. J. 79 McConica, J. K. 523, 524, 530 machina mundi 405, 410, 411 McKeon, Richard 4, 6, 8 Mac Kinney, L. C. 477 McMullin, E. 386 Macrobius 158, 199, 201, 479 McVaugh, M. 318, 515

Madan, F. 524, 526 Maddison, F. 477, 526 Madelung, W . 93, 95, 96, 102, 103 Madkour, I. 146madlül (that which is indicated) 71-72,76 madrasa 87, 101 Magellan, F. de 476 magic 194, 206, 208, 213, 214 Magirus, Johannes 492 al-Mâhânï, Muhammad ibn ‘Isa 43, 44,

45Mahdi, Mushin 4, 6 Mahoney, E. P. 527-28 Maier, Anneliese 15, 272, 319, 320-21,

364,375,378,381, 383,387,389, 392,407, 408, 425, 516

Maignan, E. 517, 528 Maillard, E. 459Maimonides 107, 155, 179, 183, 189

O f Logical Terminology, 180-82 Makdisi, George 101 makh$ü? bi* l-dhikr (that which is partic

ularly mentioned) 61-63, 76, 81 Mallet, C. E. 523 malikism 147 al-Ma’mûn 107 man

(inner and outer) 229, 239-41 see also: homo

ma^nâ (meaning) 61, 64, 76, 82 Manichaeans 88, 101, 107 al-Mançûr 100 Mançür ibn Sarjûn 104 manuscripts

as evidence of intellectual communities 27-28

citedAberdeen, University Library 116

530Aberdeen, University Library 150

530Aberdeen, University Library 186

530Bruges 192: 322, 323, 324, 325, 327,

328, 333 Bruges 503: 324, 326, 331, 335 Cairo, Dâr al-Kutub 191 ; 77 Cairo, Dâr al-Kutub 26: 77 Cambridge, Peterhouse 272: 320,337

554 INDEX

Edinburgh University Library Dc.3.89: 520

Edinburgh, University Library Dc.5.55: 530

Edinburgh, University Library La.m. 721: 530

Erfurt, Ampl. Q° 107: 314 Erfurt, Ampl. Q° 385: 473 Florence, Biblioteca nazionale,

Galileo 27: 523 Florence, Biblioteca nazionale magi.

VIIL49: 523 Istanbul, Damad Ibrahim Pasa 877 :

103London, BM Harley 3243: 334 Napoli, BN VII. C. 28: 329 Oxford, Balliol 93: 313 Oxford, Bodleian, Can. misc. 177:

314Oxford, Bodleian, Rawl. D. 274:

520, 524Oxford, Bodleian, Sandcroft 17: 501 Oxford, Oriel 15: 325, 327 Paris, Bibl. de I’lnstitut (Leonardo

Codex) A .: 457-58 Paris, Bibl. de I’lnstitut (Leonardo

Codex) B.: 474 Paris, BN lat. 7219: 474 Paris, BN lat. 7223:475 Paris, BN lat. 7377A: 475 Paris, BN lat. 10258: 475 Paris, BN lat. 11857: 526 Paris, BN lat. 14576: 313 Paris, BN lat. 15883: 330, 331 Paris, BN lat. 15894: 316 Paris, BN lat. 16401: 337 Paris, BN lat. 16408: 313, 314 Paris, BN lat. 16409: 313, 314 Paris, BN lat. 16621: 313 Paris, BN lat. 16535: 313 Paris, BN nouv. acq. lat. 1207 : 475 Paris, Bibliothèque Ste Geneviève

2200: 446 Pisa, Biblioteca universitaria MSS

231-234, 332-46, 355: 522 Prague, Univ. III.B. 10: 330 Salamanca 2085 : 450 Sevilla, Colomb. 7-7-29: 314 Thorn, Gymnasialbibliothek, R 4° 2 :

318, 473 Troyes 62: 316, 317, 330 Valencia, Cated, 139: 314 Valencia, Cated. 200: 314 Vatican lat. 955: 327 Vatican lat. 986: 324, 380 Vatican lat. 1108: 327 Vatican lat. 1111: 322, 324, 326, 335 Vatican lat. 3088: 315-16 Vatican lat. 4353: 324 Vatican, Chigi B. V. 66: 322, 327,

328, 329 Vatican, Ross. 1009: 523 Vienna National-Bibliothek 4668 :

316Worcester Cath. F. 35: 313-14 Worcester Cathed. F. 118: 338

maps see: charts, geographical ma‘qûl (intelligized) 61 Marco Polo 466-67 Marcus Aurelius 153 marginalia 27, 480, 536 Margolin, J.-C. 520 Mariotti, Francesco 522 Markowski, M. 516 Marliani, Giovanni 516 Maronites 106 Marsilius of Inghen 334 Martianus Capella 158, 159, 188, 194 Marwân 96Marx, Karl (marxist) 52, 262, 437 masons, medieval master 446, 482 massa 207 Massa, E. 521 Massignon, L. 51 al-Mas‘üdi 54, 103 materia medica 503 material culture 262 material world

in Bernard of Clairvaux 222-28 Mates, B. 74, 79 mathematics 33, 59-60, 433

(applications of) 11, 53, 341^2, 344, 346-47, 444-46

(historiography of) 33-34, 50-52, 60 in al-Fârâbi 113-15, 124-26, 128 in 16th century universities 504-7

Matlub, A. 79 Matthaes, C. 211

INDEX 555

Matthew Paris 440, 470 Matthew of Vendôme 162 Mattioli, P. A. 526 Mauricius ingeniator 441 maxima

(mathematical) 49, 50 de maximo et minimo 276, 284, 287

May, L.-P. 473 mean degree theorem 283 mean speed theorem 318 measure languages 282, 284-85, 288,292,

294,295,296,299, 305, 306,311, 336, 340, 344, 346-47

origins of “frenzy to measure” 287-89, 340-43

see also: analysis, languages of; intension and remission of forms; lim its; proportiones language

Mechanica (ps.-Aristotle) 491,493, 506-7 mechanical arts 230,231,438,439,440-42

(new appreciation o f) 208-9, 264 see also: scientia de ingeniis; Hlm al-biyal

Medici 495medic/ine, -al 132-33,147, 155,157, 158,

159-60,202-3, 313, 391-92,440,441 scientia de medicina 205 (use of astro/-logy, -nomy in) 202-3,

215in 16th century universities 502-4, 533

anatomical demonstrations 502, 504 botanical studies 502-3 clinical medicine 502, 503-4

Meier, L. 316Melanchthon, P. 403, 420, 491, 510, 530 Mendonça de Albuquerque, L. 475 Menut, A. 425merit 293, 324, 325, 327, 328, 330, 331,

333Merry, D. H. 523 Merton, R. K. 263, 349 Merton College (Mertonians) 342, 488,

512, 515-16, 529, 534 metacosm 410 metaphysics 314, 493,494

in al-Fàrâbî 115,128-31 (rejection of or freedom from) 5, 340,

367,394,402,406,408-9,412,413, 430,431,433

metrology 468

Metz, A. 54 Michalski, K. 337 Michel, P. H. 475microcosm and macrocosm 202, 209, 410,

426-27 Migne, J. P. 422 mifina (inquisition) 87, 106-7 milla (religion) 138, 139, 141 Millâs VaUicrosa, J.-M. 474 Milton, John 487 minimum parts 324 Minio-Paluello, L. 518 mirabilia 213 miracles 360, 369

(elimination of) 198 missionary activities

their possible importance in Islam 88, 101, 111

modernization 222 (Weber’s theory of) 220-21

Moleto, Giuseppe 507 Molland, A. G. 516 Molteni, P. 335 Monantheuil, Henry de 493 monastic (-ism) 220, 232, 242, 246, 255

plan of living 219 and theory and practice 440, 441

monocord 4 ^ monomials 39 monothelitism 106 Monroux, J. 260 Monte, Giambattista da 504 Monte, Guidoubaldo del 493 Moody, E. 314, 317, 319, 321, 338, 427,

523moral concerns 198, 219-68 passim, 277,

344, 494, 495, 511 More, Thomas 489, 511, 512, 513 Morgan, B. G. 459 Morini, A. U. 522 Moses 155, 157, 402, 421 mosque 87motion 184,186, 226, 320, 338, 427, 497,

512, 529 of the earth 411, 415, 419, 435 see also: scientia de motu

motus vs mutatio 322 Mu'âwiya 90, 96,100, 104 Mueller, Johannes 475

556 INDEX

Müller, M. 211Muhammad (the Prophet) 61-85 passim,

90, 94, 96, 97 Muhammad ibn al-yanafiyya 96 mujmal (indefinite discourse) 72, 77 mujtahid, 73 see also: ijtihâd Mukhtâr 91, 94, 95, 96 mulk (kingship, possession) 97 multiplication of species 278, 345 De mundi constitutione (anon) 197 mundus 425 see also: machina mundi Mufloz Alonso, A. 528 Mufioz Delgado, V. 528 al-murad (what is intended) 61, 82 Murdoch, John 4, 7, 312, 316, 317, 319,

320,321,330, 333, 335, 380, 388,427, 428, 450, 471

Murji’ites 88, 93, 95 music, science of

in al-Fârâbi 115, 124, 125 and theory and practice 439-40, 483

musicus 439mutakallim, mutakallimün 75, 85, 92,104,

106, 107, 108, 109, 110, 111,213 (definition of) 108-110

MuUazilites, mu^tazila 66-67, 73, 88, 89,92, 101, 106, 108

mysticism 146, 226, 235-39, 264-65, 402, 513

Nader, A. N. 88 Nagel, T. 102 Nallino, C. A. 78names, common and proper, in the Stoics

74-75 Nardi, B. 515, 527 nafaba (to erect) 69 al-Nasawi 54, 56 nafba see: nu^ba tiaskh (abrogation) 65, 76, 77 Nasrallah 104na$$ (definite discourse) 72, 75, 76 natura 199, 200, 201, 203, 211

as qualitas planetarum 203 natural philosophy/science

in al-Fârâbî 113,115, 126-28 (twelfth century) 4, 7, 9, 158, 215-16 (changes in) between the thirteenth and

fourteenth centuries 280, 307-9,

317, 339-40 in 16th century universities 494, 497,

506(lack of certainty in) 375-76

natureallegorical interpretation of 9,193, 213

campaign against 195-97 (new idea of) and astrology, magic,

alchemy 206-7, 213-14 (symbolical vs physical approaches to)

188,193-210 passim, 426 (man’s new relation to)

post-Copernicus 398 navigation, astronomical

theory and practice in 463-68, 478 al-Na??âm, Ibrahim ibn Sayyâr 66, 90 necessary see: darûrî necessary propositions in algebra 41 necromancy 266 Needham, J. 443, 468, 472 Nelson, Benjamin 259 Ne0“Plat0n/-ic, -ism 146, 154, 167, 199 neostoicism 425Newton, Isaac (Newtonian) 15,184, 274,

343, 404, 413, 487 Nicetas 415Nicholas of Autrecourt 358-59, 391 Nicholas of Cusa 418, 419, 429 Nicole Oresme 273,290,318,332,407-12,

427, 434-35, 488 Nietzsche, F. 390Nifo, Augustino 499, 508, 528, 534ni§ba see: nu^baNitzsch, F. 519Ni?âmalmulk 87Ni?âmiyya 87Noah’s arc 439Nobis, H. M. 518Nock, A. D. 211nominal/-ism, -ists 5, 266, 321, 341, 357,

358,359,372, 373, 375,377, 394, 396, 406-11, 412, 413, 430-31, 433, 512, 535

and science 407-14 numbers

(negative) 36 (real) 35, 39(symbolism of) 439, 440, 443 (theory of) 34, 38, 39

INDEX 557

see also: arithmetic numerals

(Arabic) 56, 161 (Indian) 56 (Roman) 56

nusba (signal) 68. 70, 71, 76, 77, 83 al-nu^ba al-dalla (indicative signal) 65,

66, 67, 68, 69, 77, 81, 82

Oakley, F. 425Oberman, H. 5, 321, 359, 381, 387 Obermann, J. 102 obligationes 317 observation see: experience occasionalism 213 occultism 500-1, 505-6 Ockham, William of see: William of

OckhamOckham’s “razor” 281, 360 see also:

William of Ockham O’Donnell, J. R. 319 Odorannus of Sens 440 Oehler, K. 419 ogive arches 460-61 Oliva of Ripoll 440 Olschki, L. 476 Olympiodorus 146 O’Malley, C. D. 526 onmipotence of God 278 omniscience of God 278 Ong, W. J. 523, 529 operation, mathematical

(concept of) 56-57 opinion, most likely see: ghâlib al-?ann Opsomer, J. E. 470, A ll optics 125,146,216,278,344-46,355,356 oral traditions 91,105, 443,463,468,478

see also: transmission Oresme, Nicole see: Nicole Oresme Origen 164, 240, 344 originality

in mathematics 33 vs transmission 59-60

originsof mathematical developments 33,

59-60Osiander, A. 400,403,404,406,407,412,

426, 432 Oxford University

in the 16th century 343, 494-95, 497- 502, 533, 534

Ozment, S. 417, 423

Pace, Giulio 491, 499 Pacioli, L. 450 pactum cum ecclesia 394-95 Padua, University of 496, 499, 502, 503,

504, 505, 506, 507 Pagel, W. 523, 529 paideia

in Aristotle 153 Panetius 439 Panofsky, E. 445 paper 93, 98, 99 Pappus 38, 40 papyrus 93, 98, 99 Paqué, R. 391Paracelsus (Paracelsian) 525 parchment 93Paris, University of 162, 343, 350, 391,

510, 533 statutes of 1366: 276, 279, 296

partes proportionales 285, 300, 327, 333 particular vs general

in Islamic legal theory 72-74 in the Stoics 74-75 see also: ‘dmm and khàff

particularism (vs abstractions) 340, 341 see also: nominalism; Ockhamism

particularization see: takh^if particularly mentioned, legal theory con

cerning the 61-63 see also: al-makh$ü$ bVl-dhikr

Pascal, Blaise 185 Paschasius Radbertus 393 Patrizi (da Cherso), Francesco 490, 527 Paul (Pauline) 223, 111, 229, 230, 231,

237, 239, 240, 245, 247, 250, 253, 259 Paul III (pope)

(dedicatory letter of Copernicus to) 400, 405, 406, 411, 414-15, 419

Paul of Pergula 520 Paul of Venice 493, 494 Pavet de Courteille, A. 103 pax et concordia 453-54 Payr, Theresia 421 Pedro de Sintra 466, 476 peira 267

558 INDEX

Pellegrini, F. 526 Felling, M. 526 Pelzer, A. 383, 391 Pendasio, Federico 508 pentagon, regular

(construction of) 450, 453, 456, 458,463, 482

perfection of species 274, 301, 321 Périon, J. 518perspectives 411 see also: optics pes anseris 450-51, 474 Peter 163Peter of Abano 466, 476 Peter Abelard 85,165,166,167,168,178,

181,182,185,189,197, 222,368, 385 Dialectica 170-77, 188 Sic et Non 166, 185, 189

Peter d’Ailly 396, 407, 425, 433, 434 Peter of Candia 276 Peter Cantor 393Peter CeflFons 279,280,314,330,335,339,

380Peter Damian 189, 193, 240 Peter Helias 162 Peter John Olivi 313, 364, 375 Peter Lombard {Sentences and commen

taries on the Sentences) 23,165, 166, 185, 275, 277-80, 316, 340, 343, 350, 352, 361, 362, 368, 370, 393

Peter of Mantua 516 Peter of Maricourt (Peter Peregrinus) 442 Peter of Pulka 279Peter of Spain 179, 267, 303, 319, 337,

493, 494Petersen, P. 519, 520, 521, 523, 530 Petrarca, Francesco 489 Petreius 424Petrella, Bernardino 499 Pettas, W. 522 pharetra 453, 456 Philip Elephantis Anglicus 450-56 Philo Judaeus 74-75, 76, 155, 179 Philolaus 415 Philoponus 508 philosopher’s stone 207 philosophia mundi 198, 210 philosophy

(the theological context of the advanced or best medieval) 274,277,353-54,

393in al-Fâràbi 123-24 of mathematics 40-42 teaching in sixteenth century 493

Philostratus 153, 154 qxBvfi (utterance) 64, 76, 81, 82, 84 Photius 154, 165, 187, 189 physica 158Physiologus 188, 212, 213 Piccolomini, Alessandro 506, 524 Pico, Gianfrancesco 489, 527 Pico, Giovanni 429 Picotti, G. B. 522 Pierre see: PeterPin, E. du see: Ellies-Dupin, Louis Pine, M. 522 Pines, S. 104,106Pisa, University of 495-97, 503, 504, 505,

506, 507 place

of Christ in the Eucharist 362,363,366, 382

plan of living (ideal, rational) 219, 246, 255, 263

Planer, Andreas 510 Pliny the Elder 153, 190, 479 Plotinus 176, 177Plato (Platonism) 9, 113, 131, 132, 134,

157,166,176,177,180,198,199,201, 203,210,215,216,261,338,390,398, 411, 417, 440, 453, 490, 494-95, 496, 502, 512, 516, 521, 524, 531, 532

Plummer, C. 525 Plutarch 76, 80, 415 Pohlenz, Max 80 Pole, Reginald 511 political context

of early Islamic theology, 93-99, 106-7 political science

its importance in Islam 113 in al-Fàrâbi 114, 115, 131-37, 143^5 see also: kingship, virtuous

Poliziano, Angelo 518 polygons and polygonal numbers, con

fusion of 476-77, 480 polynomials, arithmetic operations on

3 5 ^Pomponazzi, P. 517, 522 pons asinorum 451, 453

INDEX 559

Popper, K. 429 Poppi, A, 520, 523Porphyry 156, 159, 166, 167, 168, 169,

170,171,172,176,179,180,181,188, 493

“Porphyry’s tree” 167, 188, 340 Porter, H. C. 530 Posidonius 439possible propositions in algebra 42 Postel, Guillaume 500 potentia

activa 284 passiva 284

potentia Dei absoluta 281, 292, 297, 300, 312, 357-59, 360, 361, 372, 394, 396, 408, 409, 411, 430, 432, 433

potentia Dei ordinata 357-59, 361, 394, 396, 408, 409, 432, 433

Poulie, E. 475 Powel, GriflBth 499, 520 power

(concept of) in algebra 35 Powicke, F. M. 515 ‘practice’

its definition 482 practice see: theory, and practice predestin/-ation, -arian 90, 92, 93, 97, 98,

106Preserved Tablet 66de primo et ultimo instanti 284, 287, 294,

296, 320 printed books

their influence on university teaching 532-33

Priscian 159Proclus 40, 495, 506, 522 Prodicus 154professionalization 392-93, 441 proofs, rational 66, 68, 77 Prophet, see: Muhammad proportion 453 see also: “golden” pro

portion; “divine” proportion; proportiones languages

proportiones languages 283,286,287, 294, 296, 299, 316, 320, 323

propositions as the bearers of certitude 287-88 as the focus of Stoic logic 85

propter quid demonstration 355

Protagoras 154 Prowe, L. 424 Psellos (Michael) 154, 179 Ptolemy (Ptolemaic) 153, 159, 194, 203,

208,216,267,274, 397,413,423,424,428, 456, 457, 458, 463, 505, 506 jce also: Centiloquium (ascribed to Ptolemy)

Purbach, Georg 505 Puritanism and science 403

Qadarites, Qadariyya 88, 89, 90, 91, 92,93, 97, 98, 99, 106

al-Qà(Ji, Abû Yûsuf 62 qâmat al-insàn (height of a man, unit of

astronomical measure) 467 Qasim ibn Ibrahim 91, 102, 103 Qatâda 97qawl (speech) 61,64,65,66,67,70,76,77,

81,82Qazwini, Zakariyya Ibn Muhammad

188qiyas (analogy, reasoning) 68, 69, 70,

73-74, 76, 77, 82, 120 quadrant 464, 465, 466, 478, 480 quadrivium 153, 157, 161, 184, 352, 354,

471, 472 qualitas planetarum 195, 203 qualities

of Christ in the Eucharist 362 acc. to St. Thomas 362 acc. to Ockham 366-67

quantitasres quanta 340, 341

quantity (irrational) 38(Ockham’s view of) 363-65, 375 in Aegidius Romanus 364, 365 of Christ in the Eucharist 362, 363

acc. to St. Thomas 365 acc. to Aegidius Romanus 365 acc. to Ockham 365-66

of the bread in the Eucharist 362 quies media 330 Qudama ibn Ja'far 55 al-Qûhi 49 Quintilian 153, 162Qur^ân 61-77 passim, 82, 83, 91, 92, 94,

96, 100, 146

560 INDEX

Raby, F. J. E. 317 RaflFar, Vincent 521-22 rainbow 278, 344, 345, 346 Ralph Strode 520Ramus, Peter (Ramism) 412, 489, 496,

502, 510, 511, 513, 518, 521, 529, 534 Randall, J. H. 429, 517, 522 Rashdall, H. 515 Rashed, Roshdi 4, 6 ratio 193, 196, 197, 198, 210, 211, 217,

234, 251 physica 212 naturalis 195opposed to auctoritas 196-98 see also: legitima causa et ratio

ratiocinatio 483, 484 rationality, scientific 221 Ratramnus 393 Rauwolf, Leonhard 526 Ravaisson-Mollien, C. 474 Raymond Lull 442, 463, 474 Raymond of Marseilles 215 al-Râzi, Fakhr al-Din 78, 158 reason 108, 116, 358, 360, 367, 374, 397,

432, 434 Rebecca 258recipes (for compound medicines) 470 Redi, F. 523 reform (renewal)

of the individual (theory of) in Bernard of Clairvaux

237-46, 264 Reformation (Protestant) 5, 8, 399, 400,

408, 491-92 Regiomontanus see: Mueller, Johannes regression, mathematical 40 regula mundi 195 Reif, P. 520 religion

relation to economic or social change 263

see also: milla Renaissance

Twelfth Century 193 Italian 412, 531

Renan, E. 51, 522 Renaudet, A. 529 reportationes 535 res

permanentes 284, 287 successive 284

Reuchlin, Johann 429 revelation 5,109,116,129,131, 357, 367,

374, 400, 408, 432, 433, 434 resolution of its conflicts with natural

science 360fF Rhabanus see: Hrabanus Maurus Rheticus, J. 404, 405, 411, 412, 423, 424 Riccoboni, Antonio 507 Rice, E. F. 518 Richard de Bury 429 Richard Fitzraph 332 Richard ingeniator 441 Richard Killington 313, 317, 323, 324,

325, 329, 331, 334, 335 Richard of Mediavilla 364 Richard of Saint-Victor 208, 439 Richard Swineshead 273, 290, 305, 318,

321, 335, 337, 346, 353, 434, 435 Rijk, Lambertus de 175, 319, 321 Riley, L. W. 517 Risse, W. 520, 523 Rist, J. M. 80 Ritter, H. 79, 89, 102 Robert Anglicus 466 Robert of Chester 159 Robert Grosseteste 342, 344, 345 Robert Halifax 322-23, 324, 326, 331,

333, 334, 335 Robert Holcot 274, 315, 321, 325, 326,

327, 335, 340, 341, 429 Robert Kilwardby 168 Robertson, H. M. 221 Rochais, H. M. 260 Roehl, R. 261Roger Bacon 183,186, 341, 342,345,442,

443Roger Rosetus 276, 321-22, 324, 325,

326-27, 328, 333, 334, 335, 336, 341, 380

Roger Swineshead 317 roots, extraction of, in algebra 35-37 Roriczer, M. 446,447,448,449,450,456,

458Rosato, P. 418Rose, P. L. 518, 520, 525, 527 Rosen, E. 405, 525 Rosenfield, L. V. 529

INDEX 561

Ross, W. D. 79 Roth, Guenther 259 Round, J. H. 472 Rubinacci, R. 102,103 Ruello, F. 323, 530 Rufinus 164 “rule”

definitions of 118 rumb (lance, unit of astronomical mea

sure) 466-67 Ruska, J. 212

Saadia Gaon 88,155 Saba’ites, Saba’iyya 94, 95 Sabbatani, L. 526 Saccardo, P. A. 526 Sachau, E. 102sacramentum salutaris allegoriae 193, 195,

209Sacrobosco see: John of SacroboscoSahas, D. J. 103,104§a‘id al-Andalusi 146,147Salet, F. 472Salim ibn tJutay’a 98Salter, H. E. 525Salzman, L. F. 472al-Samaw’al 34-42, 57, 59, 60Sandaeus, Maximilianus 418Sandubi, H. 78Saijûn 104Sarton, G. 477Saulnier, V. L. 529Savonarola, Girolamo 513Schacht, Joseph 79,102Schaeffler, R. 419Schegk, Jakob 510schemata 479Schepers, H. 321Schiffers, N. 418, 423Schjellerup, H. C. F. C. 476Schmidt, C. 530Schmidt, R. W. 379Schmitt, Charles 7, 516, 517, 520, 521,

522, 526, 527 Scholarios, Georgios 179 scholasticism (scholastic method) 23,166,

508, 513 Scholder, K. 420, 421, 423 Schouten, J. 473

Schramm, M. 424, 518 Schwarz, M. 102 sciences, medieval

(Arabic)(Latin praise of) 194, 304

(autonomous vs handmaiden) 5,349-96 (diffuse vs exact) 6, 51-52, 57-58 (rational vs traditional Islamic) 116-17 (subaltemating and subalternate)

355-57(theoretical vs practical) 4, 5, 11, 116,

124, 127-28, 132-37, 143-45 (definition of) 216

(Aristotelian) 352 distinguished from arts 118ff (historiography o f) 15 see also:

historiography of medieval learning

(organization of) 4,8,151,156 see also: classification of the sciences

a part of philosophy 271, 273-74 and other intellectual endeavor 10

theology 155-56, 352-77 their methodological unity with

theology 274-75, 280-303 their use in theology 353

according to St. Thomas 354-57 according to Ockham 357-60

see also: arithmetic, astronomy, geometry, granunar, language, legal theory, logic, mathematics, metaphysics, music, natural philosophy /science, optics, political science, theology, and scientia

scientia 245, 250 inflat 229-31, 234, 244, 426, 430 vs conscientia 230, 231, 232 medieval investigations of its nature

211, 287 scientia de agricultura 205 scientia de ingeniis 125,126,146,147, 441 scientia de iudiciis 205 scientia de motu 305, 306, 313, 336 see

also: motion, motus scientia de nigromantia secundum physicam

205scientia de ponderibus 125, 145 scientia de prestigiis 205 scientia de speculis 205

562 INDEX

scientia de ymaginibus 205 scientific method 107 scientific rationality see: rationality,

scientific; reason de scire et dubitare 280 (pseudo-) Scotus 178 Scott, T. K. 321, 379 scribes, in Islam see: kuttâb Secreta secretorum 490 “secrets” (technological) 444, 464 secularization 359, 413-14 Seebass, G. 423 Segré, A. 522CTT]âivôêvov (that which is signified) 64,

65, 71-72, 76 ormaîvov (that which signifies) 64, 65,

71-72, 76, 82 oîijaavTiKôç 64 CTT1U8ÎOV 67-68, 77, 79, 82, 84

commemorative 67, 70 èvSeiKxiKôç (indicative) 67, 81

Sené, A. 459 Seneca 201, 317, 423 Sennert, Daniel 517 Sentences see: Peter Lombard Sergius (father of John of Damascus) 100 Serlo ofWylton317 Seton, John 499, 500 Severianus 159De Sex principiis 203, 204, 205, 207, 215 Sextus Emphicus 64, 65, 67, 68, 70, 75,

76, 77, 80, 81, 82, 501 Sezgin, F. 102al-Shafi‘i 68-69, 70, 76, 79, 82 al-Shahrazûri 57, 59 shakh? (individual) 65, 75, 77 Shakir, A. M. 78, 79, 103 Shakir, M. M. 103 al-Shammâkhï 90 Shapiro, H. 317 shariâ (religious law) 66, 138 shay (thing) 75, 77, 78 Shehaby, Nabil 4, 8 Shelby, L. R. 446, 461, 473, 480 shibr (hand, unit of astronomical measure)

467Shi‘ites 89, 90, 93, 95, 106 Shumaker, W. 429 Sibawayh 81

Siger of Brabant 393 Siger of Courtrai 336 signal see: CTTi|j,eîov nufba significant discourse 61, 63, 64 Silverstein, T. 211 Silvestre De Sacy, A. I. 78 Simonin, H. D. 339 Simplicius 508 Simson, O. von 461 find *at al-kitaba (scribal art) 53 sine tables 44 Sixtus of Sienna 500 skepticism

falsely ascribed to Ockham 373-75,394 in the 16th century 501, 513

Smits Van Waesberê, J. 471, 472 social factors 2, 6-8, 12, 19-28, 437

vs intellectual 21-22, 26 vs individual 22-28 and Islamic algebra 50-59 and early Islamic theology 93-99, 101,

106-7, 110-11 and al-Fâràbi’s classification of religion

and political science 140-43, 144^5

and the thought of Bernard of Clair- vaux 222, 254-59

and fourteenth century learning 309-12 and the autonomy of medieval science

349-54, 377, 391-93 see also: universities

social science in Bernard of Clairvaux 253

sociology of science V, 1, 20, 50-52, 57, 262, 263, 310 see also: social factors

Socrates (Socratic) 401 Soleiman el-Mahri 476 Sombart, W. 221 Sommervogel, C. 519 sophismata 186,303-7, 335, 336, 337, 379,

512, 533 physicalia 306

sophists 154 Soto, Domingo 499, 509 Soudek, J. 518, 520 specialization 349-50, 392-93 speech see: qawl Spinoza, Benedictus de 185, 425 spiritus vitalis 201

INDEX 563

square, carpenter’s 418, 459-61 Stannard, J. 526 stars

action of 195 Steck, M. 473Steenberghen, F. Van 376, 378, 380, 390,

515Stegmüller, F. 325, 331, 519 Stelling-Michaud, S. 515 Steneck, N. 314 Stemagel, P. 438 Stevenson, W. H. 525 Stiennon, J. 472 Stifel, Michael 35 Stillwell, M. B. 477 Stock, B. 7, 211 Stoic (s) 174, 490

logic see: logic. Stoic physics 200, 201

Stone, L. 517 Strode, Ralph 520subalternating and subalternate sciences

in Aristotle 355, 356 in St. Thomas 355-57

substance-accident terminology 394 sufism 146 Sumaniyya 106Summulus de motu incerti auctoris 318 sun

(hegemony of) 200 symbolism 412

sunna (traditions) 61, 63, 73, 75, 76, 77 Sunnites 95suppositio 279, 284, 285-86, 287-88, 304,

332, 333, 520 (determinate vs merely confused) 320

Sturm, John 530 Suarez, Francisco 492, 511 Sudhoff, K. 210 Çuhâr al-‘Abdi 90, 91, 98 Suidas 154, 187 al-$üli 54 Suter, H. 475Swineshead, R. see: Richard Swineshead Sylla, E. 5, 7, 318, 320, 321, 332, 387, 516 syllogistic arts

in al-Fàràbi 121-22 symbol see: nature, allegorical interpreta

tion of, symbolical vs physical ap

proaches; numbers, symbolism of Synan, E. 321, 339 syncategorematic 285, 306 synthesis, medieval

disintegration of 373

al-Tabari 54, 96, 97 Tabernacle 439 Tabula smaragdirui 207 Tadhâri 79 tahlil (analysis) 125takhî? (particularization) 65, 72, 75, 76 Talbot, C. H. 260 Talon, Omer 502, 510, 521 al-Tamimi, Abu ‘Ubayda Muslim ibn Abi

Karima 90 Tannery, P. 50 tarkib (synthesis) 125, 126 Tartaglia, Niccolô 33 Tatian 162 Tawney, R. H. 221 Taylor, E. G. R. 465, 475 teacher-student relations 27-28 techne see: arts technology

positive evaluation of 7 (changes in medieval) 437-38 Chinese influences? 442-43

Teixeira da Mota, A. 465 Telesio, Bernardino 489, 490, 518 Tempier, E. see: Etienne Tempier Templars 255-56, 264 Temple of Soloman 439 Tertullian 163textbooks in 16th century universities

496, 509, 511, 520 Thâbit ibn Qurra 49 Thales 411, 417 Themistius 163, 169, 175, 508 Theodoric of Freiberg 345, 346 Theodorus Abû Qurra 103 theologians

in Islam see: Mutakallim theology

Islamic 87 beginnings of 4, 87-111 political context of 93-99, 106-7,

110-11 and Christianity 99-101

564 INDEX

and political philosophy 113 in encyclopedias 155 see also: kalam

(natural vs revealed) 129-31, 141, 183 in education 159-60 in al-Fârâbi 114, 115, 137-45 (application of analytical languages in)

289-307, 311 and science 155-56, 272, 274

is theology a science? 277-78, 342 the sources of theological knowledge

108-110 Theophilus 440 Theophrastus 172, 526 theory and practice 4, 5,11,158,229,230,

238, 245, 397, 437-84 jee also: sciences, theoretical vs practical

in astronomical navigation 463-68,478 in music 439-40

Thierry of Chartres 159, 198, 200, 203, 213, 217

Thomas Aquinas (Thomistic) 5, 7, 110, 161,167,178,183,186,213,220,313, 338, 342, 344, 352, 353, 354-57, 359, 360, 361-73, 376-77, 379, 391, 393-94, 395, 396, 423, 427, 431, 494, 509,521, 524, 536

Thomas Bradwardine 290, 318, 332, 392, 407, 429, 434, 435, 450, 515

his law 283, 287, 318, 427, 516 Thomas Buckingham 324 Thomas of Cantimpré 160 Thorndike, L. 313, 407, 427, 476, 518 Thurot, C. 515 Tibbets, G. R. 476 Tigerstedt, E. N. 518 Tillich, Paul 414 time 325

(continuity of) 300, 326, 332 Timpler, Clemens 500 Toletus, Franciscus 524 Tomitano, Bernardino 499 Tommasco de Vio 499 Toni, N. de 474 Toulouse University 162 Tractatus de principiis theologiae

(ps.-Ockham) 317 traditional sciences see: sciences, rational

vs traditional Islamic

transformations (affine) 48-49

translation 8-10, 16, 80, 158, 183, 194,195, 218

transmission in mathematics 59 in early Islam 90-91 see also: oral transmission, printed

books, written literature transubstantiation 361, 362, 368-70, 394 Trapezuntius, Georgius 493,494,513,518 Trapp,D. 314, 339 trigonometry 51 Trinity 278, 279 trisection of an angle 44 Tritton, A. S. 104 trivium 153, 157, 161, 352, 354 Troeltsch, E. 221 Tropfke, Johannes 60 truth 412, 416

(doctrine of double) 183, 373, 403, 522 (self-evident) 358, 368

Tschimhaus, Ehrenfried W. von 185 TuyKàvov (object) 64, 65, 75 Tulp, Nicolaas 527 al-Tûsi, Sharaf al-Din 34, 45^9, 60

Ubaldo, Guido see: Monte, Guidoubaldo del

Ulam, A. 418 Ulhnann, M. 427 ‘Umar I 94, 95, 97, 100 'Umar II 89, 90Umayyad empire 54, 88, 90, 91, 94, 95,

97,99 ‘ummâl (governors) 53 Underwood, E, A. 527 unity of late medieval learning 5, 7,

271-348 (external evidence of) 275-77 (social base of) 309 fî

universe (infinity of) 419

imiversities (medieval) 7, 162, 272-73, 275, 339,

391, 441(faculties of) 159-60, 349-50, 403(religious goals of) 349(and theory and practice 440,441-42,

INDEX 565

466, 481 (sixteenth century) 7-8, 485-537

(historiography of) 485-87, 531 (Aristotelianism in) 487-537 passim (astronomy in) 505-6 (mathematics in) 504-7 (medicine in) 502-4 (influence of humanism on) 490-91,

531 see also: humanism (influence of Reformation on) 491-92

see also: Reformation regional variations among 486,

507-12, 534 Italy 507-8Spain & Portugal 508-9 France 509-10 Germany 510-11 Britain 511-12

see also: names of individual universities

al-uqad (knuckles) 65, 67, 78 al-Uqlidisi 55-56 Urricus ingeniator Regis 441 Urso of Calabria 202, 215 ususfructus 227, 233utens hoc mundo tanquam non utens 111,

257, 263 ‘Uthman 95, 99

Valla, George 513, 527 Valla, Lorenzo 489 Van Ess, Joseph 4, 6, 8 Varchi, Benedetto 503, 526 Varro 109, 153 Vasco da Gama 467 Vasoli, C. 516, 523 Vatable, Franciscus 518 Vaughn, R. 472 velocity of alteration 329 verbal indicants 66, 68 see also: indicant

of a discourse, lafy Verde, A. 522 Verger, J. 517 Vemet, J. 476 Vernia, Nicoletto 528 Vesalius, Andreas 490, 504, 531 via moderna 401 Victor, S. 446, 471, 476, 480 victoria 453, 455, 456

Viète, François (Franciscus Vieta) 33, 47 Vignaux, P. 317, 321, 323, 339 Villard of Honnecourt 443,446,447,450,

470-71 Vmoslada, R. G. 528, 529 Vimercato, Francesco 508 Vincent of Beauvais 160,190, 442 Vincentini, F. 522 Viotti, Bartolomeo 496 Virgil 165, 201 virtus agitativa 200 vis

genitiva 195, 196 naturae 197

Vitruvius 153, 483 Vives, Juan Luis 511 Viviani, U. 523 Voobus, A. 104 void space 274, 313 voluntarism 292, 295 voluntas Dei 195, 196, 197, 198, 212, 213,

217Von Grunebaum, G. E, 78, 101,102 voyages of discovery 463, 464

Wadding, L. 391Wahb ibn Munabbih 98,103Waldivus ingeniator A l lal-Walid 100Wallace, W. A. 528Wallerand, G. 336Walter Burley (Burleigh) 168, 318, 320,

332, 373 Walter Chatton 321 Walzer, R. 146

(suspended) 72-73, 75war

Oust) 255 Wasil ibn ‘Atâ’ 88 Waszink, J. H. 210 waters above the heavens 197, 217 Watson, A. G. 525 Watt, W. M. 103 Webb, C. 212 Weber, H. E. 529Weber, Max (Weberian) 7, 52, 219-21,

255, 263 Weil, E. 425 Weinberg, B. 518

566 INDEX

Weisheipl, J. A, 335, 336, 378, 386, 515, 525

Weizsacker, F. von 400 Wellesz, Emmy 476 Wendelin Steinbach 344 Whewell, William 15 White, H. 260White, Lynn, Jr. 259, 418, 437, 472 Whitteridge, G. 526 will 291, 293, 333 see also: free will

divine 396 see also: voluntas Dei', voluntarism

William of Conches 158, 188, 195-97, 198, 213, 215, 217, 218, 222, 479

William Heytesbury 290, 305, 318, 337, 351,432, 516, 520

William of Hirschau 158 William of Ockham (Ockhamism) 5, 7,

178,274,281,287, 314, 317,338,341,344, 354, 357-77, 391, 394-96, 407, 430, 434 see also: nominalism

William of Saint-Thierry 198, 213, 264 William of Sherwood 179, 319, 337 Willner, H. 211Wilpert, P. 378, 380, 387, 389, 390, 521 Wilson, Curtis 318, 320, 321, 334, 432,

433, 516 Winckelmann, J. 259 wisdom {sapientia)

vs science 199 Witelo 345, 346 Wittich, Claus 259 Woepcke, F. 33, 50, 474 Wolf, F. 423Wolff, Christian (Wolffian) 511 Wolfson, H. A. 519 Wolley, John 501

women 500work, attitudes toward

in Bernard of Clairvaux 7 work ethic 220 writing see: khaff written literature

in early Islam 90-91, 98, 105 vs oral culture 247, 262

Wulf, M. de 339 Wundt, M. 519, 530 Wurms, F. 518

Yadegari, M. 475Yahyà ibn al-yusayn 91, 93, 98Yates, F. 428Yazid III 97, 103Yazid al-Azdi, Abû Zaharyyâ’ 102 Youschkevitch, A. P. 474 yufid (to signify) 61

Zabarella, Jacopo 496,499,500, 508, 511, 520, 524, 534

Zacut, Abraham 475 al-?ahiri, Dâwüd ibn Khalaf 83 Zambelli, P. 527 Zanchius 500, 524 Zayd 94Zayd ibn ‘Ali 95 Zaydiyya (Zaidites) 91, 98 Zayed, S. 79 Zaynal-'Abidin 96, 97 Zeller, F. and C. 415 zero 56Zeuthen, H. G. 50 Zimmer, E. 425 Zimmermann, A. 476 Zoroastrians 100

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