Infinite Thought

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nfinite ThoughtTruth and the Return to hilosophy

L N DIOU

Translated and e ite byOliver eltham and ustin lemens


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ontinuumTh e Tower Building York RoadLondon, SE www.continuumbooks.com

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Editorial material and selection Oliver Feltharn a n d J u st i n ClemensPhilosophy andDesire Philosophy and Film, Philosophy nd thewar againstterrorism Alain BadiouPhilosophy andArt, and The Definition of Philosophy Seuil (from Conditions1992)Philosophy andthe Deathof Communism Editions de l Aube (from D undesastre obscur 1998English language translations: Philosophy an d Truth Pli; Philosophyand Politices RadicalPhilosophy; Philosophy and Psychoanalysis ( : )Ana{ysis; all other English language translations ContinuumReprinted 2003This paperback edition published 2004 by ContinuumAll rights reserved. No part of this publication may be reproduced ortransmitted in any form or by any means, electronic or mechanicalincluding photocopying, recording or any information storage or retrievalsystem, without prior permission in writing from the publishers.ritish Library Oatalcgufng-dn-Publicarlon DataA catalogue record for this book is available from the British LibraryISB:\ 0-8264-6724-5 Hardback)

0-8264-7320-2 (Paperback)

Typeset by BookEns Ltd, Royston, Herts.Printed and bound by in Great Britain by Th e Bath Press, Bath

ont nts

An introduction to Alain Badiou s philosophyI Phi losophy an d desire2 Philosophy a nd t ru th3 Philosophy an d politics Philosophy an d psychoanalysis5 Philosophy an d ar t6 Philosophy an d cinema7 Philosophy an d the death of communism8 Philosophy an d the w ar against

terrorism9 Th e definition of philosophy

10 Ontology an d politics: an interview withAlain Badiou

Index of names

v

395869799109 6465

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n introduction to l in adiou sphilosophyAlain Badiou is on e of France s foremost living philosophers.Ye t recognition of th e force an d originality of his work in th eEnglish-speaking world ha s been slow to come perhapsbecause it is difficult to assimilate his work within theestablished categories of contemporary French philosophy .However such recognition is now gathering mo men tu m. N ofewer than six translations of his major works tw ocollections of his essays an d on e monograph on his worka re c ur re nt ly in press. Th e first English-language conference devoted to his work was held in Ma y 2002 atCardiff a critical introduction to his w or k h as a pp ea re dan d three translations of his w or ks Ethics eleuze an dManifesto for Philosophy - a r e a l re a dy on th e shelves.f

Th e pre se nt volume aims to provide a brief accessibleintroduction to th e diversity an d power of Ba diou s thoughtc ol le ct in g a series of conference papers an d essays. Th eopening text sets the scene giving a polemical overview ofth e state of philosophy in relation to the contemporaryworld. Th e second chapter gives a general overview v ia t hecategories of ethics and truth of Badiou s model offundamental change in t he d om ai ns of art love politics


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Infinite Thoughtan d science - philosophy s four conditions . Th e followingchapters present specific applications of his central conception of philosophy as an exercise of thought conditioned bysuch changes in ar t Chapters 5 an d 6 on poetry an dcinema), love Chapter 4 on psychoana lysis) , politics Chapter 3) an d science. Since Badiou s work in relat ionto science is mainly found in the huge tome L Etre etI eoenement Being and Event) we chose to sketch the latter sargument in the introduction. Chapters 7 an d 8 exemplifya return to on e of philosophy s classical roles: the analyticaldenunciation of ideology, Badiou attacking first the w ar onterrorism an d then th e d eath of communism . Thepenultimate chapter sets ou t Badiou s doctrine on philosoph y in relation to its condi tions, an d th en the collectioncloses with an interview with Badiou in which he explainsan d reconsiders some of his positions.

In o u r in tr o du ction we identify on e of t he m an ne rs inw hic h B adi ou s philosophy differs from t he c ont e mpora ryFrench philosophy known as poststructuralism: its treatment of t he que st ion of th e subject . We t hen e ngage in along, at times difficult, bu t necessary exegesis of Ba diou s settheory ontology; nece ssary since it grounds his entiredoctrine, a nd n ot particularly long in relat ion to its matter;Being and Event comprises over 500 pages in t he F re nc hedit ion . At eve ry point we have attempted to render th etechnical detai ls in as clear a fashion as possible, yet withoutundue distortion. the prospective reader wishes to skip over the moreabstruse discussions offered in th e introduction, he or sheshould feel absolutely free to do so - for Badiou is still hisow n best exegete. He effectively tries to speak to those wh odo no t spend their lives in professional institutions, b ut a ctan d think in ways that usually exceed or ar e beneath notice.As Badiou himself puts it: Philosophy privi leges nol a nguage, not even t he o ne it is w r it t en i n.

An introduction to Alain Badiou s philosophyBadiou s question

Badiou is neither a po stst ru ct ur al ist n or a n a na lyt icphilosopher, an d for on e major reason: there is a quest ionwhich drives his thought, especially in his magnum opus,L Etre et l eoenement. T hi s q ue st io n is foreign to bothpoststructuralism an d analytic phi losophy - in fact no t onlyforeign, bu t unwelcome. is this question that governs thepeculiarity of B ad io u s t ra j ec t or y an d th e attendantdifficulties of his thought.

In th e introduction to L Etre et l ivenement Badiou seizesupon an e xc ha ng e b et we en Jacques-Alain Miller an dJ ac qu es L ac an d ur in g the famous Seminar XI.4 Miller,without blinking, asks L aca n, the grand theorist of thebarred subject, What is your ontology? 5 Fo r Badiou this isa crucial moment, for it reveals a fundamental difficulty one that many argue Lacan never solved, even with hisloopy 1970s recourses to knot theory. Th e difficulty is t ha t o freconciling a modern doctrine of th e subject (such as that ofpsychoanalysis) with an ontology. Hence Badiou s guidingquestion: How can a modern doctrine the subject be reconciledwith an ontology

Bu t what exactly does Badiou understand by a moderndoctrine of th e subject ? Badiou takes it as g iven that in th econtemporary w or ld t he subject ca n no longer be theorizedas the self-identical substance that underlies change, no r asth e product of reflection, no r as the correlate of an object.This set of negative definit ions is all very famil iar to a readerof poststructuralism. Surely one could object that posts t ruct ura li sm has developed a modern doctrine of th esubject?

Th e pr obl em w it h pos ts tr uc tura li sm is that exactly thesame set of negative definitions serves to delimit its implicitontology whether of desire or difference): t her e a r e no selfidentical substances, there are no stable products of

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Infinite Thou htreflection, an d since there are no s table objects there can beno correlates of such objects. Thus in poststrucruralism thereis no distinction between the general field of ontology and atheory of the subject; there is no tension between the beingof the subject and being in general.

Where Bad iou sees an essential question for modernphilosophy, then, poststructuralism sees nothing. For manythis lack of distinction between the being of the subject andthe being of everything else would appear to be a virtue; theprivilege of the rational animal is finally removed in favourof a less anthropocentric ontology. There is, however, aprice to be paid for lumping the subject together withwhatever else is usual ly recognized in an ontology.Poststructuralism typically encounters a number of problems in its theory of the subject. Funnily enough, theseproblems are quite clearly inherited From th e veryphilosophical tradition whose death poststructuralisrngleefully proclaims. There was enough lite left in the corpseto pass something on and wha t it passed on were the twofundamental problems in the thought of the subject.

The, first ;)roblem that of identity the second, problem,that o a g e ~ i Y the mind-body problem derIves or the mostpart from the former, an d the free will versus determinismdebate f rom the latter. Poststructuralists have concentratedalmost exclusively on a critique of the first problem, arguingthat there is no solution to the problem of the identity of thesubject because the subject has no substantial identity: theillusion of an underlying identity is produced by the veryrepresentational mechanism employed by the subject in itseffort to grasp its own identity. The same line of argument isalso applied to the identity ofany ent it y t hu s i nc ludi ng t hesubject within the domain of a general ontology. Fo rexample, in his introduction to a collection of PhilippeLacoue-Labarrh e s essays, Derrida identifies the subjectwith the self- de )constituting rnovemen t of th e text; the

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nintroduction to lain Badiou s philosopkvsubject is nothing o th er t ha n a perpetual movement oftranslation. This brings the subject within the ambit o f hismuch-maligned bu t fateful early ontological claim: There isno ou t sidc- text. The conseq uence of this move, of thismerger of the subject with a general ontology within thecontext of a general critique of identity an d representation,is the emergence of a pr ob lem with t he differentiation ofsubjects. How can one sub ject be differentiated fromanother without recourse to some sort of definable identity?

As for agency - philosophy s second fundamentalproblem in the thought of the subject - the consequenceof poststructuralisrri s almost exclusive concentration on thefirst problem has been that the critics of poststructuralismhave h ad an easy pitch: all they have ha d to do is to accusethe poststructuralists of robbi ng t he sub ject of agency: ifthere is no self-identical subject, then what is the ground forautonomous rational action? This is what lies behind theinfamous jibe that poststructuralism leads down a slipperyslope to apoliticism.

When poststructuralists do engage wi th the pr ob lem ofagency they again meet with difficulties, an d again preciselybecause they merge t he ir t heory of the subject with theirgeneral ontology. Fo r example, in his middl e per iodFoucaul t a rgued that networks of disciplinary power no tonl y r each i nt o th e mos t intimate spaces of the subject, bu tactually produce what we call subjects. However, Foucaultalso said that power produces resistance. His problem thenbecame t ha t o f accounting for the source of such resistance. the sub ject - r ight down to its most intimate desires,actions and thoughts - is constituted by power, then howcan it be the source of independent resistance? Fo r such apoint of agency to exist , Foucault needs some space whichhas no t been completely constituted by power, or a complexdoctrine on the relat ionship be tween resistance an dindependence. However, he has neither. his later work,

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Infinite Thoughthe deals with this problem by assigning agency to thosesubjects who resist power by means of an aesthetic project ofself-authoring. Again, the source of such privileged agency why do some subj ects shape themselves a ga in st t he grainan d no t others? - is not explained.

What does Badiou do when faced with these twofundamental problems of identity an d agency? First, Badiourecognizes a d is ti nct io n b et we en t he g en era l domain ofontology an d t he t he or y of th e subject. He does no t mergeth e one into th e other; rather the tension bet we en t he twodrives his investigations. Second, when it comes to the twoproblems, Badiou does the exact oppos ite to the posts trueturalists: he defers t he pr obl em of identity, leaving a directtreatment of it for t he unpubli s he d companion volume toBeing and Event, whi le he concentrates on t he p ro bl em ofagency.9

F or B ad io u t he q ue st io n of agencY is no t so much aquestion of ho w a subject ca n initiate an action in anautonomous manner but rather ho w a subject emergesthrough an autonomous chain of actions within a changing

\ s i t u a ~ i o n < I ~ ~ ~ U ~ i t ~ , p o t everyday actions or decisions thatprovIde eVIdence of agency for Badiou. It is rather thoseextraordinary decisions an d actions which isolate lan actorfrom their context , those act ions which show that a humanca n actually be a free agent that supports new chains ofactions an d reactions. .Q this reason, .not every human

. b ~ i n g is always a subject; yet some human beings ecomesubjects; those w ho a ct InjiJeHlj tQ a chance encounter withan evenilvhich disrupts the ;iluationAhey find themselves in.) -

A subject is born of a human being s decision thatsomething they have encountered which has happened intheir situation - however foreign a nd a bn or ma l - does infact belong to the situation an d thus cannot be overlooked.Badiou marks the disruptive abnormality of such an eventby stating that whether it belongs to a situation or no t is,

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An introduction to Alain Badiou s philosopkystrictly undecidable on the basis of.estahlished knowledge,Moreover the subject, as born of a decision.ds not limited toth e recognition of t h e \ ~ : c \ l h ~ n c e of an event, bu t extendsinto a prolonged investigation pC the consequences of such

a q e , v ~ n t ~ 0vestigation is no t a passive, scholarly affair;it entails no t o nl y t he active transformation of the situationi n ~ F l i c h t he e ve nt occurs bu t also the act ive transformationof the human being. Thus in Badiou s p h i l o s o p h y b c ; f , i ~ g ( )such thinK.as a s ll ? ject without such a p r ( l t ~ e s S ofsubjectivization. - .

For example when two people l l in love, their meeting- w hether th at meeting be their first hours together or thelength of their entire courtship - forms an event for them inrelation to which they change their lives. This certainly doesn ot m ea n that their lives are simply going to be the.,better,for it; on t he c ont ra ry love ma y involve d e b t , ~ l i e ~ a t e dfriends, an d r u ptu re with one s family. The: point is that lovechanges their relation to the world i ~ r ~ ~ o ~ ~ b l y : ' Th ed ur at io n o f the lovers relationship depends upon theirfidel ity to that event an d ho w they c hange a cc or di ng towhat they discover through their love. th e rea lm fscience the most obvious exal11ple of an event is theCopernican revolution, the e ~ l s ~ i I l g s u b j e c t ~ b e i n g thosescientists w ho w or ke d within its wake contributing to thefield we now n am e m o de rn physics .

Th e consequence of such a definit ion of the subject seemsto be that only brilliant scientists, modern masters, seasonedmilitants andcommitted lovers ar e adIriitte a into rhe fold. A

l i t t l e ~ n f a i ~ p e r h ; l p ~ ? Is Badiou s definition of th e subjectexclusive or elitist? On the on e side, you have human beings,nothing much distinguishing them from animals in theirpursuit of their interests, an d t hen , on th e other side, vou a ~ c C the n e ;- er i te o r fatttJful ~ ~ ~ t i shas a dangerous ring, an d on e could be forgiven forcomparing it at first g lance to Mormon doctrine. However -

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infinite Thoughtan d this is crucial - there is no predestination in Badiou saccount. There is nothing o th er t ha n c hanc e e nc ount er sbetween particular humans an d particular e ve nt s; a ridsubjects may be born ou t of such encounters. There is nohigher or de r w hi ch prescribes who will encounter an eventan d decide to ac t in relation to it. There is o nl y c ha nc e .Furthermore, there is no s im pl e distinction between subjectsan d humans. I I Some humans become subjects, bu t onlysome of the t im e, an d often t he y b re ak t he ir fidelity to anevent an d thus lose their subjecthood.

T hus , B adi ou displaces the problem of agency from thelevel of the human to the level of being. T hat is, his problemis no longer t ha t o f ho w an individual subject initiates a ne wchain of actions, since for h im th e subject only e I l e r g ~ s inthe course of such a chain of a ct ion s. His problem isaccounting for how an existing situation - given that beingfor B ad io u, is nothi ng ot he r than multiple situations - ca nbe disrupted an d transformed by such a chain of actions.This displacement of the problem of agency allows Badiouto avoid positing some mysterious a utonomous a gent w it hi neach human such as free will . H ow ev er , t he direct an dunavoidable consequence of t he di spl ac ement is that theproblem of agency becomes the ancient philosophicalproblem of h ow t he ne w o cc ur s in b ei ng .

tis no c oi nc id en ce that Badiou s q ue st io n - Wha; is thecompatibility of a s ub je ct with a general o nt ol og y? - l ea dsdirectly to this venerable philosophical problem, since it isthis very problem which also underlies Badiou s early work,Theorie du sujet.r? In that work, Badiou s so lut ion was todevelop a complex poststructuralist remodelling of theHegelian dialectic. L Etre et l eoenement Badiou s solutionis simply}o , ~ s ~ ~ ~ t d ; ~ t e ~ T e n t : happen , events withoutdirectly assignal:Sle causes which disrupt the order ofestablished situations. decisions ar e taken by subjects twork ou t the consequences of s uc h e ve nt s, new situations

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nintroduction to lain Badiou s philosophyemerge as a result of their work. Such events d 9 , ~ ? t ) ( ) r . I ,part o f w h at is , an d so they do no t fall under th e purview ofBadiou s general.ontology. Thus the r 1 1 , ; ~ ~ ) ~ ~ _ ~ ~ ~ t w e . s . r : r : . . , t ~ ebeing of subject an d th : g e n : q l ~ : d ~ m a l Q } . o , L B < l g l ~ ~ S .ontology IS a contingent relationship, wInch hmges oB._theoccurrence of an eventand the decision of a subject toactjnfidelitv to th a t e ve nt .WI;at, then, is this general domain of Ba diou s ontology?

A1adem ontology: being as multiple multiplicitiesAs a lr ea dy m en ti on ed , t he re a re tw o major traditions that

' ~ ~ i i o x a relation to ontology in l at e t we nt i et h-c ent ur yphilosophy: th e analytic tradition an d th e post-Heideggerea n tradition. Th e analvtic tradition either foreclosesontology in favour of epistem;lOgy r reduces ontology toa property of theories.P Th e post-Heideggerean traditionp er pe tu al ly a nn ou nc es t he e nd of fundamental ontology,while basing this pronouncement on its ow n f unda me nta lontology of desire or difference.Despite his rejection of their conclusions, Badiou does no tsimpfy dismiss the claims of these traditions. O n the contrary,Badiou t ak es his starting point from both traditions: th econcept of situation from vVittgenstein an d t he i de a of th eontological difference from Heidegger. He then forges an ew o nt ol og y within the furnace of their critiques ofontology.Heidegger formulates the o nt ol og ic al d if fe re nc e as thedifference between Being and.beings; ha t is, the differencebetween i f l d i ~ l d ~ - a l heings an d the fact of their Being, thatthey are. Fo r Badiou the term ' b e i n ~ s ) risks substantialization;it is too close to the t erm ' e n t i t y ~ existant or object .Instead, Badiou proposes the term situation which he definesas a presented multip)i ;it):::J.pr as the place of taking placeEE 32 Th e term i situatioif is prior to an y distinction

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Infinite Thoughtbetween substances and/or relations an d socovershoth.S itu ation s in clu de all those flows, properties aspects,concatenations of events, disparate collective phenomenabodies, monstrous an d virtual, that one might want toe xami ne w it hin an ontology. Th e concept of situation isalso designed to accommodate anything which is regardlessof its modality; that is, regardless of whether it is necessary, zcontingent possible, actual potential or virtual- a whim; .a (supermarket a work of art a dream a playground f ight, afleet of t rucks, a mine, a s tock prediction a game of chess, ora set of waves.

If Aristotle s fundamental ontological claim is There ar esubstances , t he n B ad io u s is There ar e s itua tions , or, inother words, There ar e multiple multiplicities . Th e keydifference between Badiou s claim and t ha t of Aristotle isthat for Aristotle each substance is a unity that belongs to atotality - the cosmos - which is itself a unit y. Fo r Badiouthere is no uni fied totality that encompasses these multiplemultiplicities. Furthermore there is no basic or primordialunity to these multiplicities.

It is these two aspects of his ontology which, according toBadiou, guarantee its modernity. fo r Badiou the task ofr.nodern. ontology is to b reak with classical ontology sfundamental u D i t y D f ~ i n g both in t he l at te r s i n g ~ i : /duaTitf\lIld irlirs totality-:f Leibniz expressed this bel ief ofclassical ontology in die formula: What is no t a being is no ta being. HHowever breaking with theclassical unity of being is nosimple task for ontology./fhe problem is that even if there isno pr imordi al e quival ence bet we en unity an d being, forB a di ou one must still recognize, following Lacan that there is

~ q m e oneness - I I y a de l un; T h a t is, although unity is no tprimordli.i), there is some kind of effect of unity-in th e R r ~ s e n t a t i o ~ o f l ~ e i n g . 1 5 Badiou s solut ion to this problem isto argue thatsituations --:_presented multiplicities - do have

An introduction to Alain Badiou s philosophyunity, ? , ~ t s\Jcb unity is the result of an operation termed the

c q Y E . L k - o ~ T h i s count is what Badiou terms the situation sstructurii A structure determines what belongs an d does no tbelOlig to the situation by counting various multiplicities aselements:\of th e situation. An element is a basic unit of asituation. A structure thereby generates unity at th e level ofeacli)element of th e s i i l l ~ t i o n : } r : l ~ ? g e n . : r a t e s unity at thelevel of the whole s i i u a t i ~ p y unifyiIlgJhe r n u l t i p l i 5 ~ i t y ( ) felements. This a statiC1 -definition of a situation: a

situation is a p r e s ~ n t e d _ : 1 l u l i l 1 1 i < ; i t y .. W h e r c ; ~ a : . ; we h :V e rio iCa::-ph ilosophers have oftenthought of unity as the fundamental property of Being, forB ad io u u ni ty is the ifject J gLj:ructuratiQu.. and not aground origin, or end. Th e consequence of th e u ni ty ofsituations b ei ng t he effect of an operation is that a multiplethat belongs to one situation ma y also belong to anothers it ua ti on : s it ua ti on s do not have mutually exclusiveiden tities.

Th e operation of th e count-for-oms is not pe rf orme d bysome agent separate to the multipl ic ity of the situation: inclassical or even relativist ontologies one ca n discern such anagent going under t he names of God History or Discourse.Th e distinction between a situation a n d j t s structuringcount-for-one only holds, strictly speaking,within ontology;t he s it ua ti on is nothing other than this o l ? ~ r : t i o n o fcounting-for-one .16 a situation is a counting-far-onethen Badiou also has a dynamic definition of a situation.Once he has both a dynami as welLis a ~ ~ . i l l . 1 i c . d a ~ ~ { t l o n ( ) f asituation - the operation of counting-for-one, an d unifiedpresented multiplicity - he is able to join his doctrine ofmultiplicity to a reworking of H ei degger s ontologi ca ldifference.

Badiou states that the ontological difference.stands betweena situation an d the being of that situation; as for Heideggerthis disjointing, in thought of situations from their being


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Infinite Thoughallows ontology to unfold. Unlike Heidegger, however, thebeing of a situation is not something that only a poeticsaying can approach: it is, quite simply and banal ly , thesituation before or rather, without the effect of the count for-one; it is the situation as a non-uni fied or inconsistentmultiplicity. After or with the effect of the count-for-one.sasituation is a unified or consistent multiplicity.. In order to understand this distinction) between an

i D r ~ ~ t i ~ t ~ i ; t iI(tiplicity . and a consistent rnultiplicjjy,consider the si tuation of a footbal l team. The par ticularteam we ~ a v e in.mind is a : ~ i r l s h a ~ } , ~ ; ~ , , ; e t of unruly playerseach havmg the ir own position, ~ r n g t h s and weaknesses;all of whom are united, however undisciplined and chaotictheir play, by their belonging to the team The Cats . ?Conside r then the same team from the point of view of itsbeing: it is a disparate multiplicity ofhuman bodies, each itsown multiplicity of bones, muscles, nerves, arteries, bile andtestosterone, each of these sub-e lements in turn a multiplicity of cells and so on, whi ch , at the b ~ r ~ level of theirbrute existence, have nothing to do with that unity termedThe Cats . That is, at the level of the being of each elementof the team there is nothing which inherently determinesthat it is an element of this football t eam. Thus. at theindifferent level of being, the si tuation termed h ~ Cats isan inconsistent and non-unified multiplicity. Granted, theproper name Cats does have a certain interpellative powerin the Althusscr ian sense, but it neither resides at norgenerates the level of being for Badiou the word neithermurders nor creates the thing, it merely assigns the thing a multiplicity - a certain identity.

In order to understand how Badiou might equat e theseinconsistent multiplicities with being, consider strippingsomething of all of its properties to the extent that even itsidentity and uni ty are removed. Fo r many philosophers,parading their commitment to desubstantialization, there

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nintroduction to lain Badiou s phdosopkvwould be nothing left after such an operation. However, forBadiou, what would be left would simply be the being ofthat something , and such being could only bl described as

a n l n c o n s i s . t ~ n t m u l t i p i i c i ~ ~ Not even - t ~ r m i e ~ s ~ ~ t t ~ rwould be a c e e p t a D r e , ~ - s i n c e matter would have been one ofthe general propert ies we stripped away from our something , Badiou s inconsistent multiplicity is therefore not to.be equated with Aristotelian p rime matter ; its actualstatus is, moreover, undecidable . Precisely because asituation provokes the question What was there before )allsituations? bu t provides no possible access to this beforethat is not irremediably compromised by post-situationalterminology and operations, it is impossible to speak oLinanYdixect way, With the thought of:inconsistent m ulh:phci tY. 1. it.l.lOUgh t t h e r e f o r e t o u c t ~ ~ . s ~ ~ ~ liIl1i s; wha-rBadiou calls, following Lacan, its real J-_ _. ~ , . ; . f . _

It is at this point that we turn to a discussion of Badiou suse of s e J J h e x ~ by means of which he gives all this ratherloose metaphysical t alk a solid and precise basis.f V J ~ y set theory?

Since Aristotle , ontology has been a privi leged subdiscipline of philosophy; otherwise known as the discourseon being. Badiou puts forward a radical thesis: if being isinconsistent multiplicity, then the only suitable discourse fortalking about it is no longer philosophy but mathematics.For Badiou, mathematics is ontology ,: Mathematicians, unbeknownst to themselves, do nothing other than continuallyspeak of or write being. This thesis enables Badiou toreformulate the classical language of ontology being,relations, qualities in mathematical terms: more specifically, those of set theory because it is one of the foundationaldisciplines of contemporary mathematics; any mathematicalproposition can be rewritten in the language of set theory.

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Infinite ThoughtIn 1 Eire el I'eoenement, Badiou sets forth two doctrines to

support his adoption of set theory. The first, the doctrine oninconsistent multiplicity, is explained in t he p revioussection. The second is the doctrine on the void. Together,these doctrines serve to bridge the gap between set theory,with its infinity of sets, and Badiou's multiplicities ofsituations.Take the first doctrine. If the being of situations isinconsistent multiplicity, what is required of the language of

such being? Simply that this language must present multiplicity as inconsistent, that is, as non-unified. To fulfil such arequirement a number of conditions must be me t. First, inorder to present multipl icity without unity, the multiplespresented in this language cannot be multiples of individualthings of any kind, since this wou ld be to smugg le back inprecisely what is in question the being of the One.Consequently, these multiples must also be composed ofmultiples themselves composed of multiples, and so OILSecond, ontology cannot present its multiples as belongingto a universe, to one all-inclusive total mult iple - for thatwould be to smuggle back the One a t a globallcvel. As such,ontology s multiples must be boundless; they cannot have anupper limit. The third condit ion is that ontology cannotdetermine a single concept of multiplicity, for that wouldalso unify its multiplicities and, by so doing , uni fy being .Set theory is the formal theory of non-unified multiplicities. It eets each of the three conditions outlinedabove . First, a set is a multiple of multiples called elements.However , t he re is no fundamental difference betweenelements and sets, since every element of a set is itself aset. Second, there is no set of sets; that is, there is no ultimateset which includes all the different types of set found in settheory. Such a set would have to thereby include itself,which is expressly forbidden, on pain of paradox, by one ofset theory's axioms, that of foundation. In set theory there

An introduction to Alain Badiou s ihilosophyis an infinity of infinite types of infinite sets. As for the thirdcondition, there is neither definition nor concept of a set inset theory. What there is in its p lace is a fundamental relation- 'belonging' as well as a series of variables and logicaloperators, and nine axioms stat ing how they may be usedtogether. Sets emerge from operations which follow theserules.The second doctrine, which Badiou uses to bridge the gap

between set theory's infinity of sets and particular nonontological situations, isNs doctrine on 'the void > Like thedoctrine of inconsistent multiplicity.x it is also a doctrineabout the nature of situations. Badiou argues that, in everysituation, there is a beirlg of the 'nothing'. He starts bystating that whatever is r ecognized as 'something', or asexisting, in a situation is counted-for-one n that situationan d vice versa. B y i ~ p l i c a t i o r i what is r/oilz'ing ,in a situationmust go uncounted. However, it is no t as though there issimply nothing in a situation which is uncounted - both the

~ o p e r a t i o n o f the count-lor-one and the inconsistent multiplewhich exists before the count are , by def in it ion, uncountable. Moreover, both a re necessary to the existence of asituation orprt;.se rtat on;fprecise y because they constitute a.situation as a situ;iTonthey-cannot be p ~ e s e ~ t e d within thesituation itself . _ A ~ ~ s o < ; . s s ~ r y b i i t ~ . ~ g p : i ~ ~ ~ n I ~ 1 2 1 e theyconstitute what Badiou terms the 'rultnlng'()r'fhe


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Infinite Thought An introduction to Alain Badiou s philosopf ySet theol)

A set is a unified multiplicity: its clements ar c n ot indefinitean d dispersed; one is able to speak of a single, unified set.B a di o u r e ad s l1 E as saying that multiple l1 is counted-forone as an element of th e set or th e set is th e count-farone of all those elements l1. E ac h o f those elements l1 could

the subset Xxhe set S

Sets ar e made up of elements. The elements of a set have nodistinguishing quality save t ha t o f belonging to it. This is wh yt he y a re referred to simply as variables Y- both w hent he y a re elements a nd w he n t he y a rc themselves consideredas sets. T he relation of belonging is th e basic relation of settheory; it is written l1 E l1 belongs to or, l1 is an elementof th e set There is another relation in set theory, termedinclusion, which is based entirely on belonging. Sets havesubsets , that ar e included in th e sets. A subset is a groupingo f some o f a set s elements. Each of a subset s elements mustbelong to th e initial set. Take for e xa m pl e t he set 8 whichconsists of th e elements l1, y. ca n be written {, ~ y }ha s various subsets like {o, an d y}. Each subset ca nitself be given a n a me , i n de x ed to a n a rb i tr ar y m ar k. F orexample, th e latter subset y}, m ig ht b e called th e subsetX. I t s i n cl u si on in 8 is written X 8.

elements

particularities of th e situation ar e removed or subtractedfrom it. So, for Badiou, every situation is ultimately foundedon a void. This is no t Heidegger s Ab-grund no r s it sometheological creation ex nihilo. The void of a situation issimply what is no t there, b ut what is necessary for anythingto be there.When we turn to set theory, it turns out it makes on einitial existential claim, that is, it begins by saying that juston e set ex is ts . This particular set is subtracted from th econditions of every other set in set theory: that of havingelements. This is th c null-set, a multiple of nothing o r o f th evoid. 20 O n th e sole basis of this s ~ t u s ~ n g operationsregulated by formal axioms, set t h e o r y \ : i I J f o l c l ~ an infinity offurther sets. S et t he or y t h us w ea ve s its sets ou t ofa void ,o ut o f what, in a ny o th er situation, is th e subtractive sutureto being o f t h at situation. In other words, we a l re a dy k no wthat ontology connects to other situations through being th etheory of inconsistent multiples. In each an d every nonontological situation, its inconsistent multiplicity is a void.Th e only possible presentation of a void in set theory is th enull-set. Thus, t h e s ec on d wa y in which set theory connectsto situations is that it constructs its inconsistent multiples ou tof its presentation of t h e v oi d, of t he s u tu r e to bcing o f everysituation.v

So much for th e general connection between situations an dset theory s infinite sets. There is al so a connection specific toeach situation: Badiou holds that t he s tr uc tu re of eachs it ua ti on c an b e w ri tt en as a type of set. That is, leaving allof a situation s properties aside an d considering o nly theb as ic r el at io ns w hi ch h ol d throughout its multiplicity, on eca n schematize a situation in ontology as a set.

What, t he n, a re sets an d ho w ar e they written?

16 17


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Infinite Thoughtbe counted and grouped an d subdivided in differentmanners, resulting in different sets: there is no restrictionon th e n um b er o f different sets they ca n belong to As notedabove, this is th e great flexibility of set theory once on estrips i denti t y a wa y f ro m m ul ti pl ic it y t he re is nothing toprevent a multiplicity from belonging to an y n um be r o fother multiplicities nothing, that is save its structure certain types of sets only admit mul ti pl es w it h certainstructures, bu t more on that later).

If on e compares set theory to classical ontologies indeedeven to that of Deleuze, its modernity is immediate. Itmakes no claims concerning th e nature of being, no rc on ce rn in g t he adequation of its categories to be ing Itmakes no attempt to anchor its dis co ur se in necessitythrough an appeal to some ground, w het her etymological,natural or historical It does no t place itself as on e linkagewithin a larger unified machinery such as evolution or complexity or chaos . there is a grand philosophicalclaim in Badiou s enterprise, it is not made within th ediscourse of set theory itself b ut rather holds in th eidentification of set theory as ontology. The basis of settheory is simply a set of axioms The necessity of theseax io ms h as b ee n tested r at he r t ha n declared i nsofar as alloperations mad e on their basis must h av e l og ic al lyconsistent results These results h av e b ee n tested through acentury of work within set t he or y. N i ne a xi oms r e gu l at e t heoperations an d th e existences w h ic h w ea v e the tissue of settheory s universe

Fo r Badiou these axioms constitute a decision in thought, astarting point. The axioms themselves of course are notpure historical beginnings since they ar e the result of a seriesof reformulations made over t he first few decades of settheory: these reformulations were designed to prevent th eoccurrence of logical inconsistency within th e domain of settheory. Rather, they mark t h e b e gi n ni n g of something ne w

In introduction to Alain Badiou s philosophyin scientific t hought i nas muc h as for example, it was no tpossible to conceive of two different types of infinity on elarger than th e other, before Cantor s pioneering work in settheory.

Se t theory itself comes in a number of varieties: fore xa mp le , t he re a re f ou nd at io na l an d anti-foundationaltypes with v ar yi ng n um b er s a n d types of axioms Badiou sow n choice is to plump for th e orthodox version of ZermeloFraenkel se t theory, with its nine axioms. These aregenerally called: Extensionality, Separation, Power-Set,Union, Empty Set Infinity, F o un d at io n , R ep la ce m en tan d Choice A n e xp la na ti on of all nine of these axiomswould exceed th e range of this presentation, bu t a quicksketch of five of t he n in e axioms s h ou ld s he d some light onho w t h e u ni ve rs e of set theory unfolds

The first concerns identity an d difference th e axiom ofextension: every element y of a set is also an element of aset an d th e inverse is true, then the sets an d ar eindistinguishable an d therefore identical. Consequently, inset theory ontology, th e regime of i dent it y a nd difference isfounded upon extension, no t quality. T hat is everydifference is localized in a point: for tw o sets to be differentat least on e element of on e of th e sets m us t n ot belong to th eother.

The ne xt t hre e constructive axioms allow the construction of a ne w set on th e basis of a n a lr ea dy existing set Theaxiom of separation states: I f there exists a set a then thereexists a subset of ll , all of whose elements y satisfy th eformula F. t enables a set defined bv a formula to bes e pa ra t ed out from an initial set If on e gives values to th evariables o ne could then, for example, sep ara te o ut t hesubset of a ll g r ee n a pp le s from th e set of apples greenapples being th e formula in this example).

The power-set axiom states that all of th e subsets o f aninitial set grouped together form another set termed th e

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Infinite Thoughtpower-set. Tak e for e xa mp le t he set { X}. It s threeelements can be g r ou p ed i n to th e following subsets: {} { ~ }{X} { {a X} an d X} to which must be added bothwhat is termed th e maximal subset { l ~ X} and by virtueof a rule explained later th e null-set {0} Th e power-set of{ X} is thus:{{o } { ~ } {X} { {ex X} X} {ex X} {0}}It is important to note that th e power-set of an y set is alwaysdemonstrably larger than th e initial set. T hi s m ea ns o ne ca nalways generate larger sets ou t o f a n y existing set.

Th e axiom of union states that all of th e elements 8 ofth e elements Y of an initial set o themselves form anotherset termed th e union-set. Th e ne w set is t hu s t he u ni on set of t he i ni ti al set o conventionally written ua. It showsthat sets ar e homogeneously multiple when decomposed.

All th e axioms listed so far presume the existence of at leaston e set bu t they do no t themselves establish the existence ofsets. The axiom of the null-set on th e other hand does. Itforms set theory s first ontological commitment. It states thatthere exi st s a n ul l- se t an em pty set to which no elementsbelong - 0 This null-set is th e initial point of existence fromwhich all t he o th er sets of set theory ar e unfolded using th econstructive axioms. Fo r example from 0 by th e operationsprescribed by th e axiom o f th e power-set on e ca ndemonstrate the existence of its power-set { } an d thenby repeating the operation further sets ca n be unfolded suchas {0 { } } an d {0 { } {0 {0}}} I t is just suchunfolding which constitutes the infinity of sets.

Each o f t hes e ax io ms ha s profound consequences forphilosophical problems once one allows that set theory isontology. In order to use set theory to address philosophicalp ro bl em s B ad io u makes a d is ti nc ti on b et we en o nt ol og yproper that is t he f or ma l language of set t he or y an d th ediscourse of meta-ontology that is a translation of set theory s

20

An introduction to Alain Badiou s philosophyaxioms an d theorems into philosophical terms. Thus for everyset-theoretical term there is an equivalent in the discourse ofphilosophy. Fo r example a set is s pok en of in meta-ontologyas a multiplicity a situation or a presentation .

One of th e traditional philosophical problems to whichset theory responds is t ha t o f t h e r e la ti on s hi p b e tw e en b ei ngan d l a ng ua g e. A c co r di n g to Badiou this relationship isconcentrated in t he w ay set theory ties th e existence of setst og et he r w it h t he ir definitions. In on e of th e first formulations of set theory that of Gottlieb Frege a set is defined ast he extension of a c on ce pt . T hi s m ea ns that for an y wellformed formula in a first order logic which defines aconcept a set of elements exists each of which satisfies th eforrnula.i? Th a t is t h er e c a n be no sets an d thus nothing inexistence for w hi ch t he re is no c on ce pt : e ve ry e xi st in g setcorresponds to a concept. Or whenever one has a definedconcept one ca n d irectly d ed uce the existence of acorresponding multiple. Thus the r el a ti on sh ip b e tw e enl a nguage a nd being is on e of exact correspondence.

However Frege s definition of sets - and by implicationhis articulation of th e relationship b e tw e en l a ng u ag e an dbeing - me t with a problem. In 1902 Bertrand Russelldiscovered a well-formed formula to which no existent setcould correspond without introducing contradiction into settheory.s The formula is t he set of al l sets w hi ch a re no tmembers of themselves . Th e contradiction ensues w he n o neasks whether the set o f elements which satisfies this formulabelongs to itself or not. I f it does belong to i ts el f then bydefinition it d oe s not an d if i t does no t belong to itself thenit does. This contradiction ruins th e consistency of th eformal language in which th e formula is made. Th econsequence of th e paradox is that it is no t true that forevery well-formed formula a corresponding multiple exists.

In order to avoid Russell s paradox the axiom ofseparation wa s developed. It proposes another relationship

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Infinite Thoughtb et we en t he existence of multiples an d well-formed formulas. Frege s definition of that relationship runs as follows:

Va) [F a a This proposition reads: There e xi st s a set such that everyterm a which satisfies t he f or mu la F is an element of thatset. Th e axiom of s e pa rat i on o n th e other hand looks likethis:

Va) Vy) [ y E a F y)) y E t reads: f there ex is ts a set a then there exists a subset ofa all of w ho se e le me n ts y satisfy t he f or mu la F. T heessential difference between F r eg e s d e fi ni ti on an d th eaxiom of separation is that th e f o rm e r d i re ct ly p ro p os es anexistence while th e latter is conditional upon there alreadybeing a set in e xi st en ce , a. Th e axiom of separation says that there is a set already in existence, then on e ca n separate outon e of its subsets, whose elements validate t h e f o rm u la F.Sa y for example that th e formula F is th e property rottenan d on e wants to make th e judgement Some apples arerotten. Via the axiom of separation, from th e supposedexistence of th e set of all a pp le s, o ne c o ul d s e pa rat e o u t th esubset of rotten apples.

T he relationship between being an d language implied byt he a xi om of separation is therefore no t on e of an exact fit,bu t rather on e in which language causes a split or divisionin e xi s te nc e EE, 53). T he conclusion Badiou t hu s d ra wsfrom set theory for th e traditional philosophical problem ofth e r elatio nshi p bet ween l an gu ag e an d being is that,a l th o u gh l an g u ag e bestows identity on being, being is inexcess of l a ng u a ge . T h is is quite clearly a materialist thesisas befits Badiou s Marxist heritage. In meta-ontologicalterms, th e axiom of separation states that an undefinedexistence must always be assumed in an y definition of a typeof multiple. In short, th e very conditions of the inscription of

22

An introduction to Alain Badiou s philosophexistence in language require that existence be in excess ofwhat the inscriptions define as existing.

So, what is t h e g e ne ra l result of Badiou s adoption of settheory as th e language of being? Quite simply that it ha snothing to sa y about beings themselves t hi s i s t h e p r ov in c eof other discourses such as p hys ics, anthropology an dl i terature. This is o ne r ea so n w hy B ad io u terms set theory asubtractive o nt ol og y: it s pe ak s of beings without reference totheir attributes or their identity; it is as if th e beings ontologyspeaks of have ha d all their qualities subtracted from them.As a result, unlike Plato an d Aristotle s ontologies, there isneither cosmos no r p h e no m en a , n e it h er c au se no r substance.S et t he or y o nt ol og y does n o t p ro po se a description of t hefurniture of the world , no r does it concern itselfwith carvingreality at the joints . Its ow n ontological c la im s im pl yamounts to s ay in g t he re is a multiplicity of multiplicities.Furthermore, set theory ontology is indifferent to th eexistence or non-existence of particular situations such ast he world or you, th e re ad er : B ad io u writes: w e ar eattempting to think multiple-presentation regardless o time which is founded hy intervention), an d s pa ce w hi ch is asingular construction, relative to certain types of presentation) EE, 293 . What set theory ontology does, in li eu ofpresenting what there is , is present th e ontological schemasof an y ontological claim; that is, it p re se nt s th e structure ofwhat an y situation says exists

ntological schemas o different situationsAlthough set theory ontology does no t recognize the infinitedifferentiations of concrete situations, it does recognize anu mbe r o f differences in th e structure of situations. Thisallows it to s c he rna t iz e d i ffe re n t concrete situations.According to Badiou s meta-ontology, t he re a re three.basics tr uc tu re s w hi ch ar e found underpinning e ve ry e x is te nt


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nfinite Thoughtsituation. To understand the dif fe rent ia tion of thesestructures it is necessary to return to the axiom of thepower-set and its meta-ontological equivalents.

The axiom of the power-set says that there is a set of allthe subsets ofan initial set, termed the power-set. In metaontological terms, the power-set is the state of a situation.Thi s means that every multiple already counted a s - ~ m e ~ i ;counted again at the level of its sub-multiples: the s ta te isthus a second count-for-one. Or , according to another ofBadiou s meta-ontological translations, if a set schematizes.a,presentation, then its power-set schematizes the representation of tha t presentation.v The state is made up of all thepossible regroupings of the elements of a situation; as such itis the structure which underlies any representational orgrouping mechanism in any situation. \ e should note thatas such the term s ta te includes bu t is i n no way reducible tothe position of a government and its administration in apolitical situation.

Badiou distinguishes three types of situation:(rtatural,historical and neutral. What makes them different at astructural level are the types of multiple which compose

t h e ~ There a re t hr ee types of multiple: normal multiples,:vhIch ar; both presented by the s i t u a ~ i o n ~ r : ? l e p r ~ s e n t e d byItS ~ t a t e (they are counted-for-one twice ; l,X crescentmultiples,

w h l ~ are o ~ l y represented by the state; and singularmultiples, which only oc cu r at the level of presentation,and which escape the effect of the second count-for-one. iNatural s itua tions are def ined as having no singularmultiples all of their multiples a re e ith er normal orexcrescent, and each normal element in turn has normalelem:nts E1 , 146 . Neutral situations ar e defined as havinga mIX of singular, normal and excrescent multiples.?Historical s ituations are defined by their having at leastone evental-sitc ; a sub-type of singular multiple. In settheory terms, a singular multiple is an element of a set, bu t

4

An introduction to Alain Badiou s philoso hYnot one of its subsets. Since each of a set s subsets is madeentirely of elements that already belong to the ini t ia l s et .the definition of a singular multiple is that, first, it is anelement of an initial set, and, second, some of its ownelements in turn do no t belong to the initial set. It is theseforeign elements which ar e responsible for the singulari tvof a singular multiple. An eoental-site is an extreme varietvof a singular multiple: none of an evental-site s e l e m e n t ~also belong to the initial set. Leaving l l ; ~ ~ a L s i t u a t i o n saside, le t us turn to examples of natural and historicalsituations.

Take, for an example of a natural situation, the ecosystemof a pond. Ths m ~ I I t i p k s which it presents include individualfish, tadpoles, reeds and stones. Each of these elements is alsorepresented at the level of the s ta te of the situation, which

~ a d i o u also q ua li fi es as the level of the knowledges of asituation - these elements are known elements of the situation.Each element o f an ecosystem is also one of the ecosystem ssubsets, because each of their clements also belong in turnto ecosystem; for example each fish s eating and breedinghabits belong to the e co sy st em as well as to each fish. Theseelements a re thus normal multiples. one examines such as i t ~ a t i ~ n it contains no singular terms: nothing is presentedwhich not also represented. The test of whether a situationis natural or not is whether there is any element of thesituation whose content is not also par t o f the situation - inecology, every element of a s ys te m, at whatever level of sizeor effect, is interconnected. Th e situation of the ecosystem ofa pond is thus a natural situation.

Take, by contrast, as an example of a historical situation,a c ol le c ti on of possible answers to the national is t concern ofwhat it is to beAustralian. Some of the multiples presented inthis situation would be individual stories about bronzedlifesavers, Anzac soldiers, larrikins, whinging poms, wowsers, convicts, explorers, bushrangers and squatters. One25


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Infinite Thoughtwould also find Don Bradman and the Eureka Stockadebelonging to such a collection. In the twenty-first century,this s itua tion s e lements would also comprise individualstories about the Italian-Australians, the Irish-Australians,the Chinese-Australians, the Greek-Australians, the Turkish-Australians, and so on. At the level of the state of thesituation one has submultiples such as hedonism, mateship,equality understood as samencss, the imperat ives fai r goand she ll be right mate , anti-British sentiment, distrust ofauthority, t he p rivi leging of know-how ov er th eory,Protestantism, and Catholicism, etc.

From both socio-economic and cultural perspectives,immigrant groups a re both p resen ted and re-presented.Their contribution to what it is to be Australian is bothknown an d knowable. For this reason we would argue thatnone of the presen ted immigrant multiples are singularmultiples. On the other hand, constitutively resistant toAnglo-Saxon dreams of assimilation, the mul tiple aboriginals forms an evcnral-site; its contents remain unknown.Of course, within other situations such as cultural, sociological and bureaucratic assessments of Australia, aboriginals a re re-presen ted. However, these spec ia lizeddiscourses are n ot in the position of furnishing answers tothe nationalist question What is it to be Australian? Th emultiple aboriginals forms an evental-sitc because thesovereignty of Australia, the immigrant nation , wzsfoundedupon the dispossession of indigenous peoples. Their relationto this particular piece of land was crucially no t recognizedat the very beginning of this entity termed Australia . Anyrepresentation of the con tent o f the multiple aboriginalswith reference to what it is to be Australian, would thuscau se t he uni ty of the si tuation to dissolve - in a sense, itwould entail the dissolution ustralia itself is thisconstitutive irrepresentability at the heart o f Australian nationalism that makes it a historical situation.

n introduction to lain Badiou s jJhilosoplyBadiou uses this division between natural and historical

situations to return to his basic quest ion: How does the newhappen in being? In our mythical, pollution-free pond,though there may be generation after generation of newbaby fish, nothing really changes: barr ing another naturalcatastrophe the ecosystem will remain in a state of homeostasis. In natura l situations Ecclesiastes proverb holdstrue: there is nothing new under the sun. In historicals ituations things are quite different. To return to ourexample of Australian nationalism, the inherent instabilityof the situation (it harbouring an unknowable evental-site inits mids t) r ende rs it susceptible to wholesale pol it icaltransforma tion.

However , the existence of an evental-site in a situationdoes no t guarantee that change will occur. Fo r thatsomething extra is required, a supplement as Badiou says,which is an v nt \ \ e are no t talking about any ordinaryevent here, like a birthday or Australia beating France inrugby, but r athe r of a totally disruptive occurrence whichhas no place in the scheme of things as they currently are.Who will say what this event has been or will be forAustralian nationalism was it the erection by Aboriginalactivists of a tent embassy opposite the National Parl iamentin 1972? The occurrence of an event is completelyunprcdictable.27 There is no meta-situation - History which would programme the occurrence ofevents in variousselected .situations, ;,

he precariousness of historical change extends further:no t only must an event occur at the evental-s ite of asituation, bu t someone must recognize and name that eventas a n event whose implications concern the nature o f theentire situation. Thus it is quite possible tha t an event occurin a situation but that nothing changes because nobodyrecognizes the event s importance for the situation. Thisinitial naming of the event as an event, this decision that it

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InJinite Thoughthas transformational consequences for t he e nt ir et y of asituation, is what Badiou terms an intervention . Th eintervention is the first moment of a process of fundamentalchange that Badiou terms a fidelity , or a generic truthprocedure . A gener ic truth procedure is bas ical ly a praxisconsisting of a series of enquiries i nto t he s i tua ti on made bymilitants w ho a ct in fidelity to th e event. Th e object of theseenqui ries is to work ou t ho w to t ra ns fo rm t he situation inline with what is revealed by the event s belonging to th esituation. Fo r e x amp le , w it hi n t he s i tua ti on of ar t in th eearly twentieth century, certain artists launched an enquiryinto the nature of sculpture once Picasso s cubist paintingsha d been recognized as art . Th e p ro ce du re m ad e ups uc h e nq ui ri es is termed a truth procedure because Itunfolds a ne w multiple: th e truth ofth e previous situation.Here B ad io u draws up on - an d displaces - Hcidegger sconception of truth as th e presentation of being. Th e ne wentitv is a truth inasmuch as it presents th e multiple being ofthe previous situation, stripped bare of an y predicates, ofan v identitv.

Fo r example, take an ar t cri ti c in th e e ar ly t w ent ie t hcentury wh o has just recognized that a cubist painting can,indeed, be called art . he was called upon to make apredicative definition of the contemporary situation of ar t that is, if someone asked hi m What is an? - he would havefound it impossible to respond - at tha t very moment, forh ir n, t he d is ru pt iv e e ve nt we no w call cubism was layingba re t he situation of ar t as a pure multiplicity of colours,forms, materials, proper n a m e s , , > ~ i t l e s sl?aces with nofixedcontours : In fact, th e common accusation that contemporaryar t is ~ r a { u i t l i ~ , indeterminate, an d as such could beanything whatsoever with a label slapped on it stuck in agallery; this v e ry a c cu sa ti on actually unknowingly strikesupon the very n at ur e o f a ne w mul ti pl e: it is anythingwhatsoever w it h r ega rd to established knowledge.

28

An introduction to Alain Badiou s jilli osOpkJiTo understand how a new multiple - such as mo der n ar t- ca n both exist, an d be stripped bare of any predicates (as

such being globally indescribable or anything whatsoeverwe must turn back to Badiou s use of set theory.Generic sets and processes transformation

In order to think about processes of f unda ment al c hangewithin his ontology Badiou ha d to work ou t how a multiple,a set, ca n be new. It is at this point that Badiou introducesthe c p \ t r , e ~ ~ i r \ c ~ ) 0 f h ~ s , , ; ~ v r k - what he calls t he gene:ic orindis c:ertllbrhtv . ThIS at once an extremely difficultconcept, bas;d on the most innovative mathematicalprocedures, ye t also intuitively graspable. Badiou takes. thisconcept from the work of Paul Cohen, an American. 1963 mathematician w ho i nve nte d th e genenc set

Th e first point to work ou t is what th e reference pointcould be within ontology for such n o ~ t J t y . Especially since settheory ontology appears to be a s ta tic , flat discourse, withno recpgnition of th e .supposed universality of the situationsof time .and history :) Th e reference p o in t t ur ns ou t to be

/ l ~ n g u a g ~ . In set theory, on e c an h av e models of set theorywhich are interpretations that flesh ou t th e bare bones of setsan d elements by giving values to the variables (such as y =green apples in t he e xa mp le used above . A model of settheory ha s its o wn l an gu ag e in which various formulasexpress certain properties such as green . Th e model itself,as a structured multiplicity, ca n be treated itse lf as a set.Cohen t akes as his s t ar t ing point what he terms a grollIl51model of set theory. Badiou takes this model as the schemaof a historical situa tion. Each subset of this model satisfies aproperty which ca n be expressed in the language used in themodel. That is, every multiple found in t he m od el ca n bediscerned using th e tools of language. A generic set, on theo ther h and , is a subset that is new insofar as it cannot be

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Infinite Thoughtdiscerned by that language. Fo r every property that oneformulates, even t he most general such as this apple andthis apple and this apple the generic set has at le st oneclement which does no t share that property. This makessense intuitively: when someone tries to tell you about a newexperience, whether it be meeting a person or s ee in g a workof ar t, t hey have a lot of trouble describing it accuratelyand, every time you try to help them by suggesting that itmight be a bi t like the person x or the filmy, they say Nono it s no t like that For every prope rty or concept youcome up with to describe this new thing, there is somethingin that new thing which does not qui te fit. This is all verywell bu t having a set which one can t quite describesounds a bit vague for set theory. The innovation of PaulCohen s work lay in his d is co ve ry of a method of describingsuch a multiple without betraying its indiscernibiluyt

But what about the process of this new mult iple cominginto being? How does a generic set provide the ontologicalschema of processes of radical change in political scientificartistic and amorous situations? Badiou holds that theground model schematizes an established historical situationbefore an event arrives. One can define a concept of ageneric subset within such a situation bu t one cannot knowthat it e xi st s - p re ci se ly because it is one of those excrescentmultiples noted above (which a re not presented at the levelof belonging to a situation). The generic subset is onlypresent at the level of inclusion and, unlike all the othersubsets it cannot be known via its properties. To show thata gcneric set actually exists Cohen d ev el op s a proccdurcwhereby one adds it to the existing ground model as a typeof supplement, thereby forming a new set. Within this newset the generic multiple will exist at the level of belonging,or in meta-ontological terms, presentation. The newsupplemented set p ro vi de s the ontological schema of ahistorical situation which has undergone wholesale change.

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nintrodu tion lain Badiou s philosopkyFur thermore , Cohen developed a method of making

finite descriptions of this new supplemented set u si ng onlythe resources of the initial set. Cohen termed this procedureforcing and Badiou adopts it as an ontological model of thenumerous practical enquiries that subjects who act inf id el it y to an event make whil e t hey arc attempting tobring about the change entailed by the event. That isalthough, say an activist working towards justice for theindigenous peoples in Australia will not know what overallshape justice will take they will be able to predict cer tain ofits features and some of their predictions may be v er if ie dearly on in the process of change. Fo r example, a particularexperiment in public health practices in indigenous communities may reveal i tsel f to be part of the movementtowards justice due to its sensitivity to issues of selfdetermination and cultural difference.

For Badiou, the actual work wh ich carries ou t thewholesale change of a histor ic al s it ua ti on - in his te rm s thef ide li ty p ra ct is ed by s ub je ct s to an event consists of suchexperiments; finite enquiries into the nature of the event usingan invented idiom to approximate what is discovered throughsuch enquiries. Historically one can understand this conceptof fidelity as a remodelling of the Marxis t concept of praxissubtracting the latter from the encompassing unities ofhistorical determinism revolutionary theory and the Partyline. What results from suchsubtractions is a p ra xi s made upof a hazardous series of bets bets on the nature of the situationto c om e. Many o f these bets will fall w id e of the mark, bu tthose that hi t the target will help construct the new situation.

Of course Badiou recognizes that the number of shapes afidelity can take especially in domains as d if fe re nt as art,politics science and love is infinite; and further, that anumber of different fidelities may be developed in the samesituation to the same event - for example, both PierreBoulez an d John Cage developed their music in f ide li ty to


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Infinite Thoughtthe event of Schoenberg s invention of the twelve-tone series,bu t in very different directions. Yet Badiou s general claim isthat in e h case of a fi del ity it is a matter of the new comingi nt o b ei ng , and in set theory onto logy the only way toschematizc that process is through Paul Cohen s concepts ofthe generic set and forcing. Thus, however particular - andi nd ee d, h ow ev er precarious a decolonization processwithin a c ol on ia li st p ol it ic al situation, at the level of thestructure of its m ul ti pl ic it y, it is a g en er ic set. The relationthis pr oc es s entertains with the established colonialistsituation is not one of pure exteriority romanticism) norof subsumption realism), bu t that of indiscernibiliiy That is,none of the categories employed by colonialist discoursess er ve to d is ce rn its nature.

Hence the indiscernibility of a g en er ic t ruth proceduregrounds both its singularity and i ts sovereignty, insofar as itis subtracted from and thus independent of any knownentity in the situation, s uc h as parliamentary democracy ,mining interests , the proletariat , or th e native .

But within the debates around post-colonialism, theromantics and the r ea li st s will always have one lasto bje ctio n to an argument such as ours: that there is anexception to the r ul e, s in ce the c at eg or ie s of one c ol on ia li stdiscourse in particular seem to serve quite well fordiscerning the nature of a decolonization process, the latestcategories of European philosophy, those of Alain Badiou sset theory ontology. However, this would be to miss thepoint entirely. Ontology does not discern the n ture of anysituation, much less th at o f a particular fidelity. Ontologyo nl y s pe ak s of the stru ture of m ul ti pl ic it y: it has nothing tosay about the qualities or identitv of anv concrete situation.For Badiou such would be the province of other discourses,practical or t he or et ic al . This is the first guard againstimperialism built into Badiou s philosophv - the indifferenceof ontology towards the concrete. .

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An introdu tion to Alain Badiou s p h i l o s o } ~ vThe second guard lies in Badious refusal of any

t rans it iv ity between ontology and politics. As a goodmaterialist, .Iie r ecognize s the autonomy of materialprocesses and argues that the names philosophy comes upwith to reflect particular political transformations arenot and nnot be identical to those names that are thrown up by theactual process of transformation within a political situation.The task of philosophy is no t to predict nor determine theshape of justice, or of modern art , or even the f or m a u ni fi edfield theory might take. Philosophy s ta sk is to reflect andlearn f ro m t ho se transformations happening in contempor-ary historical situations; to the point where it develops whatBadiou terms a of compossibility for all contemporaryfidelities. The relationship behveefiphilosophy and politics- as with art, science and love - is thus one of conditioningor dependence. Philosophy is no longer sovereign. t is as ifphi losophy has finally hea rd t ha t cry addressed to it ford ec ad es , a cry v oic ed by so many artists, scientists, activistsand lovers whose activities it has deafly appropriated fromon high, t he cry SHUT UP AND LISTEN

And even if Badiou s conception of philosophy maintainsa strict separation between the practice of philosophy andthe diverse practices of art, politics, science and love, it docshave one practical consequence. Quite simply, if you wantto do po li ti cs, go become an activist , go decide what eventhas happened in your political situation. you want to dophilosophy, try to think the compossibility of contemporarye ve nt s in each of the four domains of art, politics, scienceand love (and, of course, read all of Being and Event once it spublished). Just don t confuse the two.

note on notesFollowing Badiou s practice, we do no t r ef er en ce t ex ts hementions, trusting the readers own curiosity to guide them.

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Infinite ThoughtAdmittedly, it is a rather abrupt gesture. t does no t placethought under the sign of the demand for knowledge bu tsimply u nd er t ha t o f desire.

ot s

I. Th e follo wing tit les by Alain B ad i ou a re c u rr e nt l y in press orforthcoming: Being andEoent, trans. Oliver Feltham London:Continuum Books, forthcoming); Theoretical 11/ritings, trans.an d ed. A lb er to T os ca no and Ray Brassier London:Continuum Books, 2003); Handbook Inaesthetics, t ra ns . A.T os cano Stanford, CA: Stanford University Press, 2003); St.Paul: The Foundation Universalism, trans. R. Brassie r Stanford, CA: Stanford Univers ity Press, 20 3); On Beckett,ed. an d trans. Nina Power an d A. T os ca no w it h B ru noBosteels Manchester: CIinamen, 2 03); The Century/Le Sieclet ra ns . A. T o sc an o w it h r es po ns es by A. Toscano an d SlavojZizek Paris/London: Seuil/Verso, 2003). Badiou s bregdelvlitapolitique Paris: Seuil, 1998), translated by Jason Barker,is forthcoming from V er so . See also Peter Hallward, Subject toTru th : An Introduction to the Philosophy Alain Badiou Minneapolis: C niversity of Minnesota Press, forthcoming)an d P. Hallward ed.), Think Again: Alain Badiou and the Future PhilosojJlry London: Continuum Books, forthcoming).

2. See J Barker, Alain Badiou: A Critical Introduction London:Pluto Press, 2002); A. Badiou, Ethics: An Essay on theUnderstanding F.vil, trans. Peter Hallward London: Verso,2001); A. Badiou, Gilles Deleuze: The Clamor Being, trans.Louise Burchill Minneapolis: University of Minnesota Press,2 00); A. Badiou, AfaniJesto for P h i l o s o p ~ v trans. NormanMadarasz Albany, NY: SUNY Press, 1999).

3. A. Badiou, L Etr et l eoenement Pa ri s: E di ti on s elu Se ui l,1988). All further references will appear as page nu m bel S inbrackets in the body of th e text.

4. J ac qu es L ac an was a French psychoanalyst f am ou s for his

::

An introduction to Alain Badiou s j hilosopkvfusion of Freud, Sauss urean linguistics, structuralist anthropology, French psychiatry an d m a th e ma ti cs i nt o on econtinually evolving an d powerful theory of th e subject.Jacques-Aiain M il le r s ub se qu en tl y b ec am e Lacan s son-inlaw, executor of his esta te, head of one of the larges t Lacanianschools of psychoanalysis, an d on e of Lar a n s p re mie rcomrnentators.

5. Ontology is thc philosophical d iscou rse d efin ed b y Aristotle asthe science of being qu a b ein g . Histo rically it has treated s uchq uestio ns as What is b ein g ? an d Why is t he re somethingr a th e r t ha n nothing?

6. Fo r a particularly dens e a n d c o nc e nt ra te d elaboration ofBadiou s theory of the subject see A fin ally o bjectless subject ,in th e a n t h o l o ~ y Who Comes After the Subject? ed. E. Cadava L ondon: Routledge, 1991I

7. Jacques Derri da, Desistance , in Philippe Lacoue-Labarthe,~ v p o g r a p / ~ y , Mimesis, Politics, Philosophy, ed. Fynsk Cambridge,MA: Harvard University Press, 1989).

8. See, for instance, ]VI. Foucault, Power Knowledge: SelectedInterrinos and Other Writings 1 9 7 2 ~ 1 9 7 7 ed. Gordon, trans.C. Gordon et al. N e w Y or k: Pantheon, 1980).

9. A. Badiou, Logiques des mondes P a ~ i ~ : . S e ~ i ~ ~ o r t h c o m i n g ) .Insofar as B ad io u s c on ce pt of a , ~ e n e r i c m ul ti pl e, w h ic hm ak es up th e stuff of his faith fu l su bjects, d eliv ers a rigo rou sdefinition of s in gu la ri ty , o ne c ou ld argue that th e classicalproblem of th e id en ti ty o f subjects, or that of theirdifferentiation, is indirectly treated inasmuch as th e genericmultiple is strictly differentiated from e ve ry predicate, SeeGeneric scts an d processes of transformation , pp. 29 33.

10. Fidelity , ev en t , a nd s it ua ti on a re all technical terms ofBadiou;s .ontology an d their meaning will he explained inwhat follows; h owever, the reader s intuitive sense of thesewords ca n be trusted to provide an initial approximation.

11. At this point we s ho ul d n ot e an important complication ofBadiou s theory of th e su bject; Badio u also term s subject th e

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Infinite 7 houghtact ual i ndi vidual t heorems which make up modern physics.Similarly in th e domain of ar t he terms subject particularmusical works rather than their composers. This shift simplyreinforces his separat ion between t he human as an individuala n im a l, a n d the human acting as subject, thatis asapoint ofrisk, invention an d geclsion, . .

12. A. Badiou, Thiorie du suje P aris: S euil, 1981).13. Se e Willard V. O. Quine, O n t ol o gi c al r e la t iv i ty , l

Ontological Relatioity and Other SS lYf New York: ColumbiaUniversity Press, 1969).

14. G. W. Leibniz, Letter to Arnauld April 30 1687 , inPhilosophical Writings, trans. J T M o rr is L on do n: Dent Sons, 1934),72.

15. According to Badiou this was also Kant s problem in th e firstcritique insofar as th e l at te r d id no t grant i m me d ia t e u ni tyeither to the thing i ts el f or to th e sensuous m a ni fo ld , y etattempted to account for the apparent unity of experience.

16. See th e interview included in this volume.17. We would like to thank ou r colleague Amelia Smith for this

example.18. T hi s a x io m was introduced in order to d ea l w it h a paradox

t ha t a pp ea re d early in the development of set theory.Russell s paradox emerges on th e basis of sets being able tobe members of themselves. It is more fami l iar in th e paradoxof th e barber wh o shaves all t he m en in th e village who don tshave themselves: who shaves t he b ar be r? W e return to t hi sparadox below.19. Students of philosophy ma y be reminded of the status ofKant s Ding-an-sidi an d of transcendental apperception in th efirst Critique.

20. In French, l ensemble-uide. In Badiou s text this harmonizes ata terminological level w it h t he F re nc h for t he void of asituation : le vide de la situation.

21. Th e doctrine on inconsistent multiplicity is prior, in th e orderof argument, to t he d oc tr in e on the void of situations

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An introduction Alain Badiou sphilosophbecause to accept that set theory s null-set presents th enothing of s ituations , one must a l re a dy h a ve accepted thatsets present th e being of situations.

22. A first order l og ic c on si st s of a series of signs: existential an duniversal quantifiers, variables , p ro pe rt ie s a n d l og ic al c on nectors; disj uncti on, conj unct ion, i mpl i cat ion, negat i on an dequivalence. P ro pe rt ie s a re n ev er found in the position ofvariables, that is, first order logic does no t express propertiesof properties: that is th e province of second order logic.

23. See B. R us se ll , Letter to Frege , in J. Va n Heijenoort ed.},From Frege to Codel A Source Book in Mathematical Logic C a mb r id ge , M A: Harvard University Press, 1967), 124.

24. vVe s ho ul d n ot e that if this meta-ontological translation islegitima te, t he superior size an d complexity of the power-s et,with regard to its initial set, ha s fundamental consequencesfor the classical philosophical problem of th e relationshipbetween present at i on an d r ep re s en ta ti on a n d t hu s for an ypractice based on th e critique of representations), as it doesfo r th e classical political problem of t he r e la ti on b et we e n th estate an d th e people.

25. Du e to the excess of inclusion over belongi ng - t he superiorsize of a set s power-set compared to i ts el f - every situationhas excrescent multiples.

26. Evental-site is a neologism that ha s been coined in order tot ranslat e Badi ou s site euenementiel Event-site is n ot a pp ro p ri at e, b ec a us e it s ug ge st s that th e site is defim:d by th eoccurrence of an event, whereas in Badiou s conception, thereis no guarantee t ha t a n event will occur at a site ivinementiel,th e sole guarantcc being that if an event does occur in th esituation it will do so at that particular point of th e lattert er me d t he evental-site.

27. This is precisely h ow B ad io u b re ak s with historical dctcrrninIsms.28. Th e reference for th e mathematicians is P. Cohen, Set Theoryand theContinuum Hypothesis ]\\ew York: W.A. Benjamin, 1966).


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Infinite Thought29. See Meditations 34 an d 3 of L Etre et I eoenement for a full

explanation of Cohen s method.

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CH PTERhilosophy nd desireThis philosophical investigation begins under th e b an n er o fpoetry; thus recalling th e ancient tie between poetry an dphilosophy.

Rirnbaud employs a strange express ion: Ies revol teslogiques , logical revolts . Philosophy is something like a logical r evol t . P hil os ophy pits thought against injustice,a gai nst t he defective state of t he w or ld an d oflife. Ye t it pitsthought against injustice in a m o ve m en t w hi ch conservesan d defends argument an d reason an d w hi c h ul ti mat e lyproposes a ne w logic.

Mallarme states: All thought begets a throw of t he d ic e .I t seems to me that this enigmatic formula also designatesp hi lo so ph y b ec au se p h il os op h y p ro po se s to think th euniversal - that which is true for all thinking - yet it doesso on th e basis of a commitment in w hi ch c ha n ce alwaysplays a role, a commitment which is also a risk or a wager;

The four dimensional desire philosoph ;These t wo p oe ti c formulas capture th e desire of philosophyfor at base th e desire of philosophy implies a dimension ofrevolt: there is no philosophy without t he d is co nt en t of

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nfinite houghtthinking in its confrontation with the world as it is. Yet thedesire of philosophy also includes logic that is, a belief in thepower of argument and reason. Furthermore, the d e s i r ~ _ ( ) . f .\philosophy involves unioersality philosophy -addresses all

' h u r : t . 1 < . t r } ~ i . 5 - 1 h . i p ~ i n g b e i n g s since it supposes that all humansthink. Finally, ph11osophy'takesns,kj:-'ITii'iiKiilg'i's'a \vaysadCt:'lsl(lir which supports independent points of view. Thedesire of philosophy thus has { JUr dimensions: revolt, logic,universality and risk.I think that the contemporary world, our world, theworld that we strive to think and transform, exerts anintense pressure upon these { JUr dimensions of the desire ofphilosophy; such that all four dimensions, faced by thewor ld , find themselves in a diff icult and dark passage inwhich the destiny and even the very existence of philosophyis at stake.

To beg in with, as far as the dimension of r evolt isconcerned, this world, ou r world, the 'vVestern' world (withas many inverted commas as you wan t), docs not engage inthought as revol t, and for two reasons. First, this wor ldalready decrees itself free, it presents itselfas th e free world- this is the very name it gives itself; an 'isle' of liberty on aplanet otherwise reduced to s lave ry or devastation, Yet, att he same time - and this is the second reason this world,our world, standardizes and commercializes the stakes ofsuch freedom. It submits them to monetary uniformity, andwith such success t ha t our world no longer has to revolt tobe free s ince it guarantees us freedom. However, it does no tguaran tee us the free use of this freedom, since such use is inreality already coded, orientated and channelled by theinfinite glitter of merchandise. This is why this world exertsan intense pressure against the very idea that thinking canbe insubordination or revolt.

Our world also exert s a strong pressure on -the. dimension Iof logic; essentially because the world is submitted to the

h i l o s o p ~ v and desireprofoundly illogical regime of communic.ation. Comn,-lUnicat ion t ransmi ts a universe made up of disconnected Images,remarks, statemen ts and commentar ie s whose acceptedprinc ip le is incoherence . Day after day communicationundoe s all rel ations and all pr inciples, in an untenablejuxtaposition that dissolves every relation bet.ween theel ement s it sweeps a long in its flow. And wha t perhapseven more distressing is that J;I)}I;S,s,C\o,rrrnu;nication presentsthe wor ld to us as a spectacle devoid of memory, a spectaclein wh ich new images and new remarks cover, erase andconsign to oblivion the very images and remarks that havejust been shown and said. The logic which is specifically

undone t f ~ e r e is the logic of time. It is these processes ofcommunication which exert pressure on the resoluteness ofthinking's fidelity to logic; proposing to thought in the latter splace a type of imaginary dissemination.As for the universal dimension of the desire of philosophy,our world is no longer suited to it because the world isessentially a specialized and fragmentary world; fragmentedin response to the demands of the innumerable ramificationsof the technical configuration of things, of the apparatuses ofproduction, of the distribution of salaries, of the diversity offunctions and skills. And the requirements of this specialization and this fragmentation make it difficult to perce ivewhat might be transversal or universal ; that is, what mightbe valid for all thinking.

Finally we have the dimension of risk. Our world does notfavour riskv commitments or risky decisions, because it is aworld in w'hich nobody has the means any more to submittheir existence to the per il s of chance. Existence requiresmore and more elaborate calculation. Life is v o t ~calculating security, and this obsessiOii with calcul .. . a armean hv othcsi s th a

e t Irow e Ice, because in such a wQ lQ.LOu lIluch fISk a throw of the dice.


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nfinite houghtTh e desire for philosophy thus encounters four pr ncipalobstacles in the world These are: t he r ei gn of m e r ~ h a n d i s e ,

the reign of communication the need fo r technicalspecialization an d th e necessity for realistic calculations ofsecurity How can philosophy take on this challenge? Isphilosophy eapa ble of such a challenge? Th e answer must besought in th e state of contemporary philosophy.

hepresent state ~ f p h i l o s o p h . yWhat ar e t he p ri nc ip al g lo ba l tendencies in contemporaryphilosophy if we cons id er it f rom a bird s eye p oi nt o f view?I think it ca n be said that three principal orientations canbe dis tinguished in phi losophy today. Th es e o r ien tatio n scorrespond in some measure to three geographical loca-tions I will first name an d then describe them. Th e first ca nbe called the hermeneutic orientation which historicallygoes back to German romanticism. Th e best-known namesattached to this orientation ar e Heidegger an d Gadamcran d its historical site V s originally German. T hen there isthe analytic orientation originating with th e Vienna CircleTh e p rin cip al n ames co nn ected to it ar e those of Wittgcnstein an d Carnap. Despi te its Austrian origin it nowdominates English a nd A mer ica n a cade mi c philosophy.Finally we have w hat can be called the postmodernorientation which in fact borrows from th e other two Itis without doubt th e most ac tive in France an d includesthinkers as different as J ac qu es D cr ri da a nd Jean-Frans;oisLyotard. t is equally very act ive in Spain Italy an d LatinAmericaA hermeneutic orientation an analytic orientation and ap os tm od er n o ri en ta ti on : t he re a re of course innumerableintersections mixtures an d networks of circulation betweenthe three bu t t og et he r t he y form the most g lob al a nddescriptive geography possible of contemporary philosophy.

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hilosophy and desireWhat then interests us is h o w each o r ien tatio n designates oridentifies philosophy

T h e hermeneutic orientation assigns philosophy the ai mof deciphering th e meaning of Being th e meaning of Being-in-the-world an d its central concept is t ha t o f interpretationThere a re s ta te me nt s acts writings an d configurationswhose meaning is obscure latent hidden or forgottenPhilosophy must be p ro v id ed w ith a method of interpretation that will serve to clarify this obscurity a nd b ri ng forthfrom it an authentic meaning a meaning which would be afigure of ou r destiny in relation to the destiny of being itselfTh e fundamental opposition for hermeneutic philosophy isthat of th e closed an d the open In what is g iven in theimmediate world there is s o methin g d is simu lated an dclosed Th e aim of interpretation is to undo this closurean d open it up to meaning. From this point of view thevocation of philosophy is a vocation devoted to t he o pe n .This vocation marks a combat between th e world ofphilosophy a mIthe world of technique since the latter isthe accomplishment of closed nihilism

Th e analytic orientation holds t h f , , a j ? ~ f p h , i l ~ s ~ p h y tobe th e strict demarcation of those utteranc:es wh ic h h av emeaning an d those which do n ot Th e ai m is to demarcatewhat ca n be said an d what it is impossible or illegit imate tosay Th e essential instrument of analytic philosophy is thelogical an d grammatical analysis of utterances an dultimately of the entire lang u ag e. This time t he c en tr alconcept is n o t i n te rpre ta t io n bu t the rule Th e task ofphilosophy is to discover those rul es that ensure anagreement about meaning. Th e fundamental oppositionhere is between w ha t c an be regulated a nd w ha t c an no t beregulated or what conforms to a recognized law assuring anagreement about meaning a nd w h at eludes all explicit lawsthus falling into i llusion or discordance Fo r the analytico ri en ta ti on th e a im of philosophy is therapeutic an d

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nfinite houghtcritical. is a question of curing us of the illusions an d theaberrations oflanguage that divide us by isolating what ha sno meaning an d by returning to rules which aretransparent to all.

Finally the p o stmod ern o r ien tatio n holds th e ai m ofphilosophy to be the deconstruction of t he a cc e pt ed facts ofou r modernity. I n p ar ti cu la r p o str no d er n p h ilo so p hyproposes to dissolve th e great constructions of the nineteenthcentury to which we remain captive th e idea of thehistorical subject th e idea of progress t he i dea of revolutiont he i de a of h um an it y a nd t he ideal of science. It s ai m is toshow that these great constructions a r e : ; ; ~ t d t l t e d that welive in th e multiple that t he re a re no great epics of historyor of thought; that there is an irreducible plurality ofregisters an d languages in thought as in action; registers sodiverse an d heterogeneous that no great idea ca n totalize orreconcile them. At base th e objective of postmodernphilosophy is to deconstruct th e idea of totality to th eextent that philosophy itself finds itself d e s t a b i l i z ~ ~ d . Consequently the postmodern orientation activates what mightbe called mixed practices de-totalized practices or impurethinking practices. It situates thought on th e outskirts inareas that cannot be circumscribed. In particular it installsphilosophical thought at th e periphery of art an d proposesan untotaJizable mixture of t he c on ce pt ua l method ofphilosophy and the sense-orientated enterprise of art.

he common themesrif the three orientations ofphilosophyDo these three orientations so summarily described haveanything in common? Does anything allow us to sa y thatdespite this diversity features ca n be found which s ign al au ni ty o f c on t em p or ar y philosophy? I would suggest thatt he re a re two principal features that the three orientationshermeneutic analytic an d postmodern have in common.

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Philosophy and desireis these common fe at ur es w hi ch s ig na l that the threeorientations of philosophy ar e all contemporary an d thathowever different they ma y be their destiny is j oine d: t heydo not s imply provide on e possible division of thought bu trather pr ovi de t hre e expressions of th e same demands thatou r e poc h ma ke s on philosophy.

Th e first of these

Infinite Thought

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