Galavotti_Suppes

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MARIA CARLA GALAVOTI'I

SOME OBSERVATIONS ON PATRICK SUPPES PHILOSOPHYOF SCIENCE

ABS TRA CT. Th e paper outlines the main traits of Patrick Suppes' 'probabilisticempiricism '. It com bines the conviction that probability should be assigned a centralrole within epistemology with a seriou s consideration of experimentation. First Suppes'empiricism and its close connection with pragmatism is described. Then, his views onprobability are discussed at length, together with his theory of probabilistic causality.Lastly, Suppes' notion of rationality is recalled. Th e main features of Suppes' position inthe whole are identified w ith its pluralism and its local character. It is argued that in placeof a general philosophical view Suppes works out a method allowing a representationof phenomena in which both theories and data, abstract mathematical construals andparticular experimental techniques, are all given attention and find their place.

If one were to review the literature on philosophy of science in recentyears, one would be faced with all sorts of claims to the effect thatempiricism is dead, or at least in mortal agony. Many have claimedthat the empiricist way of looking at things has proved incapable ofcapturing the complexity characterizing human knowledge in general,and the scientific enterprise in particular. At the same time, manyhave urged that empiricism has nothing to say, and should just giveway to some form of relativism, or even to methodological anarchism.Contextually, metaphysical tendencies have been resumed in order tosolve some of the numerous problems left open by the empiricist wayof looking at things.These attitudes have in most cases resulted from dissatisfaction withlogical positivism. A criticism of the strictures imposed on episte-mology by logical positivism, however, does not necessarily implyabandoning empiricism altogether. In addition to the voices pleadingthe cause of anarchism and/or a return to metaphysics, the revision oflogical positivism has opened alternative roads to empiricism, inspiredby a genuinely constructive attitude.One of them has been indicated by Patrick Suppes, who calls it'probabilistic empiricism'. In what follows I will try to elucidate the

P. Hum phreys (ed .), Patrick Suppe s: Scientific Philosophel; Vol. 3, 245-270.@ 1994 Kluwer Academ ic Publishers. Printed in the Netherlands.


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246 MARIA C ARLA GALAVOTTImain traits of this position, which is in many ways innovative. Assuggested by the label attached by Suppes to his own point of view,this combines an empiricist attitude to philosophy with a probabilisticcomponent. At its basis we find the conviction that the notion ofprobability should be assigned a central role within epistemology. Thisis clearly stated by Suppes, who says thatit is probabilistic rather than merely logical con cepts that provide a rich enough frame-work to justify both our ordinary ways of thinking about the world and our scientificmethods of investigation (1984a, p. 2. See also 19 80, p. 171).Probabilistic empiricism should then replace logical empiricism, andaccordingly probability, and not logic, should be the point of departureof our investigations into philosophy of science and epistemology.It is worth stressing how this fundamental conviction involves ashift in emphasis from the linguistic aspects of the language of scienceto its content. In other words, attention to the syntactical structure ofscientific discourse gives way to consideration of the complex proce-dures, like measurement and model building, which allow phenomenato be investigated and organized within scientific theories. This marks amajor difference between the form of empiricism advocated by logicalempiricism and that put forward by Suppes. As a matter of fact, a sim-ilar attitude has recently become quite widespread, and logical empiri-cism has often been criticized for having attached too much importanceto the linguistic aspects of science. Let us then turn to some of themore distinctive features of Suppes' position. To start with, it seemsappropriate to characterize his 'empiricism' and to illustrate its closeconnection with pragmatism. Suppes' views on probability will then bediscussed at length, together with the main philosophical implicationsof his approach.

EMPIRICISMIn his self-profile written in 1978, Suppes calls himself "the only gen-uinely empirical philosopher I know" (Suppes, 1979, p. 45), and by thishe is stressing the influence of scientific work on his own philosophy.No doubt it receives a peculiar flavour from his twofold activity, as aphilosopher and as an experimental scientist. This double militancy isat the basis of the importance Suppes ascribes to experimentation. It iscertainly experimentation with all the problems connected with it that


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ON PATRICK SUPPES ' PHILOSOPHY O F SCIEN CE 247occupy the central place within Sugpes9empiricism. Here the tradition-al distinction between the two contexts of 'discovery9and 'justification'introduced by Reichenbach, and widely accepted by philosophers of sci-ence, is superseded by an approach in which experimentation and relatedproblems pervade the whole 'reconstruction' of scientific investigation.The attention paid to such problems influences above all Suppes' viewof theories, while being at the root of the importance he ascribes tomeasurement, as well as probability.Suppes' view of theories is probably the most well-known aspectof his philosophy of science, and has been analysed in detail,' mainlyfocusing on the formalization of theories and on his dictum to the effectthat 'to formalize a theory is to define a set-theoretical predicate'.2 HereI will briefly recall the centrality in that perspective of the notion ofmodel, together with the pluralism this brings with it.For Suppes models are the entities in terms of which a theory is tobe defined. Models provide the connection between a theory and thephenomena under investigation, through the notion of structure. Thistask is fulfilled by showing that "the structure of a set of phenomenaunder certain empirical operations is the same as the structure of someset of numbers under arithmetical operations and relations", where theidea of 'sameness of structure' is to be taken in terms of a suitable notionof isomorphism (Suppes, 1967, p. 59). Isomorphism plays a crucial rolein representing a theory in terms of its models. For Suppesthe best and strongest characterization of the models of a theory is expressed in termsof a significant representation theorem,where this is a proof to the effect thata certain class of models of a theory distinguished for some intuitively clear conceptualreason is shown to exemp lify within isomorphism every model of the theory (Supp es,1988a, p. 259).Another crucial notion in this context is that of invariance, which givesa criterion of meaningfulness according to whichan empirical hypothesis, or any statement in fact, which uses numerical quantitiesis empirically meaningful only if its truth value is invariant under the appropriatetransformations of the numerical quantities involved (Suppes, 1988a, p. 265).

The representation of a theory in terms of its models here takes theplace of the 'received view' of theories delivered by logical empiricism,according to which a theory consists of a logical construction plus a set


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248 MARIA CARLA GALAVOIT1of rules ass igning an empirical meaning to its terms, o r at least to someof them.In a general way - Suppes says - he best insight into the structure of a complex theoryis by seeking representation theorems for its models, for the syntactic structure of acomplex theory ordinarily offers little insight into the nature of the theory (Suppes,1988a, p. 254).In other words, knowledge of the syn tactical structure of a theory is notenough; in order to understand what a theory is about we should insteadlook for its models.

PRAGMATISMThis move away from the 'received view' of theories goes in the direc-tion of a pragmatist philosophy of the kind upheld by authors like C.S. P eirce, W. James, J. Dewey and E. Nagel, who was Suppes' teacherat Colum bia from 1947 to 1950. According to a pragmatist approach,scientific activity is perpetual problem solving and theories typicallyqualify as local construals.Like our ow n lives and endeavors - Suppes says - scientific theories are local and aredesigned to meet a given set of problems (Suppes, 1981b, pp. 14-15).

Locality goes hand in hand w ith a peculiar pluralism, characterizingboth the notion of model and that of structure, neither of which isam enab le to a univocal definition. Th e point is extensively dealt withby Suppes in an article published in 1962 bearing the title 'Models ofData '. Since this does not seem to be among his best known papers, itis worth recalling its central ideas. The main thesis is summarized bythe claim that "the relation between em pirical theories and relevant datacalls fo r a hierarchy of models of different logical type" (Suppes, 1962,p. 253). When analysing the linkage between theory and experimentaldata one therefore has to distinguish m odels of the theory from m odelsof the performed experiments, and models of the data obtained. To ahierarchy of m odels there corresponds a hierarchy of the problems onetypically encounters at the different levels of analysis, in the course ofthe complex procedure aimed at comparing theories with experiments.This conclusion is suggested by a close inspection of the statisticalmethods employed at each level of such comparison, which includemeasurement, experimental design, estimation of parameters, tests ofgoodness of fit, identification of exogenous and endogenous variables,


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O N PATRICK SUPP ES' PH ILOSOPHY OF SCIENCE 249and the like. A detailed analysis of such methods not only points tothe need for a plurality of different models, it also clarifies the directionof the dependence between models. The dependence is such that in ahierarchy of models characterized by an increasing level of abstractionone does not move from top to bottom, but rather from bottom totop. In other words, given a model of the data, exhibiting a certainstatistical structure of the phenomenon under investigation, one looksfor a theoretical model that fits it.What I have attempted to argue - says Suppes - s that a whole hierarchy of modelsstands between th e model of the basic theory and the com plete experimental experience.Moreover, for each level of the hierarchy there is a theory in its own right. Theory atone level is given empirical meaning by making formal connections with theory at alower level (Su ppes, 1962, p. 260).

As a direct consequence of considering theories not in any abstractway, but rather in connection with experimentation, we then have, inaddition to a hierarchy of models, also a hierarchy of theories.If someo ne asks 'what is a scientific theory?' - Suppes says - t seems to m e there is nosimple response t o be given . . .What is important is to recognize that the existence ofa hierarchy of theories arising from the m ethodology of experimentation for testing thefundamental theory is an essential ingredient of any sophisticated scientific discipline(Supp es, 1967, pp. 63-64).This is a lesson to be learned from a careful analysis of the role playedby statistical methods in experimentation and theory making. This sortof analysis is precisely what, according to Suppes, is missing from thetraditional approach taken by philosophers of science,who write about the rep resentation of scientific theories as logical calculi [and] go on tosay that a theory is given empirical mean ing by providing interpretations of coordinatingdefinitions for some of the primitive or defined terms of the calculus (Ibidem).

As Suppes points out, this lesson emerges most explicitly from somebranches of the social sciences, like learning theory, to which he mostlyrefers. It is in fact a common feature of disciplines which have notreached a highly theoretical development to make extensive use ofsophisticated methods for evaluating evidence and testing hypotheses.It is noteworthy that recent econometric research points exactly in thesame direction indicated by Suppes, and propounds a pluralistic view ofmodel building that bears strong resemblance to the approach outlinedin 'Models of ~ a t a ' . ~One can see that within Suppes' philosophy of science data receiveat least the same importance ascribed to theories. The structure of data


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250 MARIA CARLA GALAVOTTIdelivered by observation is in itself the object of interest and investiga-tion, and calls again for pluralism. Detailed analysis of such structuresindicates that there is no univocal answer to the question 'what aredata?' sincethe 'data' represent an abstraction from the complex practical activity of producingthem. Steps of abstraction can be identified, but at no one point is there a clear anddistinct reason to exclaim, 'H ere are the data!' (Supp es, 1988b, p. 30).Depending on the desired level of abstraction different pieces of infor-mation will then count as 'data'. In addition, a multitude of context-dependent elemen ts will have a bearing on it.The refusal to search for a unique characterization of importantconcepts is a major feature of Suppes' philosophy. He has repeatedlystressed that the complexity of phenomena and the variety of practicalsituations in which phenomena a re investigated a re such that importantnotions in science as well as in philosophy canno t be cooped up in somedefinition given once and for all. Plurality then becomes for Suppesone of the tenets of the 'new metaphysics' by means of which he fightsthe chimeras of a traditional view of rationality also shared by logicale m p i r i ~ i s m . ~he ideal of the unity of science should then be abandonedin favour of the recognition thatthe sciences are characteristically pluralistic, rather than unified, in language, subjectmatter, and method (Supp es, 1984a, p. 10).This abandonment of the ideal of the unity of science goes hand inhand with the rejection of the neopositivistic ideal of reductionism.Suppes has convincingly and repeatedly argued that the diversity oflanguage, subject matter and m ethods both in different disciplines andin different branches of the same discipline is such that reduction iseither impossible, o r - when possible - uninteresting and barren.5Suppes' pragmatically oriented view of theories opposes anotherchim era of rationality, namely the idea that "scientific knowledge can inprinciple be m ade complete" (Suppes, 1984a, p. 2) and that the shift fromold to new theories brings with it a convergence to some finite value.On the contrary, one of the main tenets of Suppes' 'new metaphysics'am oun ts to the claim thatthe collection of past, present, and future scientific theories is not converging to somebounded fixed result that will in the limit give us complete knowledge of the universe(Supp es, 1984a, p. 10).


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ON PATRICK SUPPE S' PHILOSOPHY O F SCIENCEPROBABILISTIC APPROA CH

Suppes' 'new metaphysics', of which pluralism and incompleteness areessential ingredients, is illustrated in the volume Probabilistic Meta-physics which appeared in print in 1984. The main purpose of thiswork is to establish a probabilistic approach to philosophy of science,intended to supersede the 'neotraditional metaphysics' centred on deter-minism, namely the idea that the future is determined by the past andthat every event has a sufficient determinant cause. As a first step inthat direction one finds a claim to the effect thatcertainty of knowledg e - ither in the sen se of psychological im mediacy, in the sen se oflogical truth, or in the sen se of com plete precision of measurements - s unachievable(Supp es, 1984a, p. 10).Among the arguments put forward by Suppes to support this claim,one of the most convincing comes from imprecision of measurement,arising once again from his experimentalist attitude. Measurementitself has been extensively studied by Suppes, who has contributedimportant work to it. Without going into details, it is worth recallingthat imprecision of measurement does not come only in connectionwith human or instrumental errors, but arises in a more substantial wayfrom certain developments of our century's physics, like Heisenberg'suncertainty principle.6 Uncertainty then pervades not only the levelof experimentation, but is to be encountered at the level of physicaltheories as well. In view of this, Suppes holds that the ideal of certaintyshould be renounced together with the other 'chimeras of rationalism'discussed above, completeness of knowledge and unity of science.Recognition of uncertainty "at the most fundamental level of theoret-ical and methodological analysis" (Suppes, 1984a, p. 99) leads directlyto probability, because probabilistic methods provide 'a natural way'of working out the form of empiricism advocated by Suppes. In otherwords, probability is the tool that allows him to build the pars con-struens of his 'new metaphysics', once the way has been cleared fromthe 'chimeras of rationalism'. Its fundamental tenets are precisely thatthe basic laws of natural phenomena are essentially probabilistic, andthat causality, as well as the theories of meaning and rationality, areprobabilistic, not deterministic in character. Among other things, thisinvolves the conviction that "our conception of matter must contain anintrinsic probabilistic element" (Suppes, 1984a, p. lo), and leaves thedoor open to the admission of randomness in nature.


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MARIA CAR LA GALAVOTTI

BAY ESIANISM

As far as the interpretation of probability is concerned, Suppes hasalways called himself a Bayesian and a subjectivist. However, this con-ception of probability strays in many ways from that of an 'orthodax'Bayesian like Bruno de Finetti, to whom he often refers in his writings.With no intention of making a comparison between the two, let me tryto focus on what I regard as the most original traits of Suppes' position.A central feature is the strict connection between probability and mea-surement, inspired once again by Suppes' experimentalist attitude. Byconnecting probability with measurement he has come to the convic-tion that exact values should be substituted by probability intervals. Anumber of results on upper and lower probabilities due to Suppes andzanotti7 testify to the fruitfulness of this approach.Another important feature of Suppes' perspective is the convictionthat probability and utility are notions to be dealt with separately. In thisconnection he agrees with de Finetti, with whom he shares a Bayesianapproach to scientific inference. It is worth mentioning that the adop-tion of a Bayesian framework leads Suppes to an original treatment ofproblems like the paradoxes of confirmation8 and the problem of totale ~ i d e n c e . ~o the latter, he offers a solution essentially based on the ideathat under Bayesian conditionalization there is no additional problem oftotal evidence, once coherence is satisfied.Disagreement with de Finetti comes in connection with the fact thatfor Suppes the subjective theory of probability offers necessary butnot sufficient conditions for a theory of rationality. For one thing, thesubjective theory of probability offers no way of evaluating differentprobability assessments due to experts, nor for dealing with uncertainevidence. The main disagreement, however, regards de Finetti's rejec-tion of the ideas of 'unknown' and 'objective' probability. Moreover,Suppes ascribes great importance to the notion of randomness, regardedas meaningless by de Finetti. While interpreting de Finetti's attitudetowards the above mentioned topics as a result of his positivistic andreductionistic attitude, Suppes devotes a certain effort to working themout. Let me briefly recall his views in this connection.In interpreting probability, Suppes makes the point that the questionof the meaning of probability statements is not different from that ofthe meaning of statements about physical properties or magnitudes, likemass and weight. In all such cases


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ON PATRICK SUPPES' PHILOSOPHY OF SCIENCE 253there is not really an interesting and strong distinction between subjective and objective,or between belief and knowledge (Suppes, 1983, p. 399).

The important thing appears instead to be completeness of informa-tion, and the relevant distinction to be made is that between completeknowledge in principle or in practice and incomplete knowledge withthe possibility of learning more. When talking about the meaning ofa probability statement, one has in the first place to ask whether it isbased on complete information, in the sense that there is no additionalinformation we can conditionalize on that will bring about a change inthe probability value. This is an important feature to be considered,especially when completeness of information comes from physical the-ory.Another element that according to Suppes should be taken intoaccount is the point in time at which the utterance of the probabilitystatement is located. As he observes, "this is especially true for prop-erties of events as opposed to properties of objects" (Suppes, 1983,p. 400), because insofar as events are concerned, we have more infor-mation after their occurrence than before. Suppes concludes that "intalking about completeness of information it is important to stress atwhat point in time the matter is being discussed" (Ibidem).Suppes' claims in this connection raise some perplexity. One mightobject that the problem referred to by his remarks does not have muchto do with completeness of information, being related to the tensionbetween two different contexts in which probability statements mayoccur, corresponding to their predictive use, on the one hand, and theirdescriptive and explanatory use on the other. As widely stressed byrecent literature on probabilistic explanation, such contexts should notbe seen as overlapping, because they exhibit a fundamental asymme-try. This in turn reflects another important difference to be pointedout, between probability statements about single events and probabilitystatements about properties of objects. It is a matter of fact that whendealing with single events characterized by probabilistic behaviour wecan only (if ever) reconstruct the history behind their occurrence afterthey have taken place. This, however, does not have much to do withthe meaning of probability statements, but with explanation of singleevents. In this context, in fact, we do not just have a statement giving theprobability of an event prior to its happenings, but we have in additionthe information that the event itself has actually happened, no matterhow small a probability it was assigned beforehand. The preceding


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254 MARIA CARLA GALAVOTTIconsiderations also have some bearing on probabilistic causality, to bediscussed later.

OBJECTIVE PROBABILITYWhere completeness of information really matters is in connection withthe problem of 'objective probability'. It is no doubt an important fea-ture of Suppes' point of view to recognize that probability statementsacquire a special meaning when based on completeness of informationin the light of physical theories. In this case one tends to attach anobjective meaning to them. While de Finetti vigorously denied thatthere can be any sense in talking about 'objective probability', Suppesadmits such a notion. In a paper presented at a conference, on whichI had the chance to comment,1 he advocates a 'propensity' view ofobjective probability. Coherently with the general attitude character-izing Suppes' philosophy of science, he gives representation theoremsfor such phenomena as radioactive decay, response strengths and cointossing. In all such cases, plus a version of the three-body problem thatexhibits what he calls a 'propensity for randomness', in order to obtaina representation of the phenomena at hand one has to give structuralaxioms, that are built on information which is not purely probabilistic incharacter. Representation of decay, for example, is obtained by meansof a 'waiting-time axiom' whichis a structural axio m that would never be encountered in the standard theory of subjectiveprobability a s a funda men tal axiom. It is an axiom special to certain physical phenomena(Supp es, 1987a, p. 345).Suppes' conclusion is that such an axiom represents "a qualitativeexpression of a propensity". Still discussing the same case, he remarksthatthe probabilities we obtain from th e representation theorem are not unique but are onlyuniqu e up to fixing the decay parameter. Again, this is not a subjective concept but verymuch an objective on e (Suppes, 1987a, p. 346).And once again he concludes thatidentifyin g and locating the number of physical parameters to be determined is a way ofemp hasizing that propensities have entered and that a purely probabilistic theory with aunique measure has not been given (Ibidem).One can certainly agree that in the cases discussed by Suppes 'objective'considerations of some sort enter into the evaluation of probabilities.


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ON PATRICK SUPPES' PHILOSOPHYOF SCIENCE 255The question, however, is whether an appeal to the notion of propensityis a fruitful move in this connection.In my comments on Suppes' papers I raised some doubts, mainly dueto the fact that his treatment of the matter seemed to overlook the widedebate on propensities going on in the literature, and to underestimatethe implications, mainly with regard to indeterminism, that the notionof propensity brings with it. Instead of going back to such questions,I now wish to say that I am still dissatisfied with Suppes' treatmentof the matter, but on slightly different grounds. I emphasize that weagree that a purely subjective notion of probability cannot account forall evaluations of probability, and some notion of 'objective chance' isrequired. His theorems are very useful in order to clarify at what point,in the representation of phenomena exhibiting probabilistic behaviour,considerations which are not purely subjective are to be encountered.However, I doubt that the notion of propensity, especially if taken inthe vague meaning that Suppes attaches to it, can serve the purpose ofproviding a sound basis on which objective chance could be founded.In other words, Suppes' appeal to propensity does not seem to involvemuch more than the introduction of an extra term that adds nothing tothe structural axioms.In general, objective considerations in the evaluation of probabilitiesare essentially dictated by scientific theories. At least in this sense,then, the notion of 'objective chance' is linked to the view of scien-tific theories which is adopted. As Suppes pointed out - and I agreewith him - t is a lacuna of de Finetti's position to overlook the roleplayed by considerations which are not purely subjective in the eval-uation of probabilities. The main reason why de Finetti rejected thenotion of objective chance altogether comes from his general attitudeto philosophy, an attitude Suppes calls 'positivistic', and I have called'anti-realist'." In other words, de Finetti's main concern was to keepprobability free from metaphysics. However, in the light of a relativisticand pragmatist view of scientific theories like that upheld by Suppes,admitting that certain elements, in situations characterized by complete-ness of information, can guide probability evaluations, does not meanopening the door to metaphysical ontology. 'Objective chance' can sim-ply keep the pragmatist character pertaining to theories, and the onlything that matters is a clear distinction between 'objective' and subjec-tive elements entering in the evaluation of probabilities. Incidentally,one might recall that the other founder of subjectivism, F. P. Ramsey,


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256 MARIA CA RLA GALAVOTTIadmits of a notion of objective chance supported by a pragmatically ori-ented view of scientific theories which bears some analogy with Suppes'own position.

INDETERMINISMSuppes puts forward a most interesting view of indeterminism, basedon the notion of stability. Its starting point is instability in mechanics,which amounts to the consideration thatwide divergence in the behaviour of two systems identical except for initial conditionsis observed even when the initial conditions are extremely c lose (Suppes, 1991b, p. 9).Unstable systems reflect a fundamental feature of indeterminism, name-ly unpredictability, for their future behaviour is not predictable on thebasis of their present behaviour. According to this kind of analysisthe notion of randomness, which represents the extreme case of unpre-dictability, is not to be seen as incompatible with determinism. On thebasis of results taken from the theory of unstable dynamical systems, itcan therefore be shown thatthere is no opposition between completely deterministic systems and random systems- and that moreover - the same phenomena can be both deterministic and random(Suppes, 1988c, p. 400).In view of this, randomness can be seen as a "limiting case of unstabledeterminism" (Suppes, 1991b, p. 17). The bridge between randomnessand determinism is provided by instability, in the sense that randomsequences can be generated by deterministic but very unstable sys-tems of classical mechanics. Moreover, randomness is characterized bycomplexity, as random sequences "are the limiting case of increasinglycomplex deterministic sequences" (Ibidem). Suppes' conclusion is thattalk in terms of stable or unstable systems should supersede the oppo-sition between determinism and indeterminism, and that complexity, asreferred to results, should be preferred to randomness, as referred toprocedures.If the preceding remarks seem to suggest that the choice betweendeterminism and indeterminism is essentially a matter of taste, there is anadditional aspect of the question to which Suppes draws attention. Thisamounts to the fact that, for those who accept the standard formulationof quantum mechanics, indeterminism looks much more plausible thaninstability, for


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ON PATRICK SUPPES' PHILOSOPHY O F SCIENCE 257unstable deterministic mechanical systems cannot be construed to be consistent withstandard quantum mechanics. Th e conclusion of this line of argument is that standardquan tum mechanics is the most outstanding exam ple of an intrinsically indeterministictheory (Suppes, 1991b, p. 16).The question of the choice between indeterminism and instability, how-ever, remains open, insofar as there are alternative theories to the stan-dard formulation of quantum mechanics. In view of all this, Suppesmaintains that a responsible philosophy of science should leave thedoor open to indeterminism. This is indeed the starting point of Sup-pes' 'new metaphysics'.

CAUSALITYA further important feature of Suppes' perspective amounts to the con-viction that there is no opposition between indeterminism, or the admis-sion of the existence of randomness in nature, and causality. In hiswell-known monograph of 1970A Probabilistic Theory of CausalitySuppes advocates a probabilistic theory, that has become the object ofmuch attention and debate. Its peculiar feature, that distinguishes itfrom other theories of probabilistic causality, like those put forward byI. J. Good, H. Reichenbach andW.C. Salmon, is to be identified with itsgeneral formulation, which is intended to make it applicable to the vari-ous contexts where causal speech occurs. l2 Suppes' notion of causalitycan be formulated both in terms of events and of random variables, andis compatible with different interpretations of probability. Remarkably,no 'ultimate genuine causes' are contemplated within this theory. Onthe contrary, the notion of cause, genuine or spurious, is strictly linkedto the specification of the set of concepts on which the set of events thatcan serve as causes in a given context is to be defined. This is a pointstressed by Suppes not only in his monograph of 1970, but also in morerecent writings. For example, in his Self-projile he writes:I do think that the insistenc e on relativizing the analysis of cause to a particular concep-tual framew ork is a point on w hich to make a stand (Suppes, 1979, p. 24).His notion of probabilistic causality is then characterized as intrinsicallyrelativistic. Conceived in this way, it testifies to Suppes' relativistic andpluralistic attitude towards philosophy and epistemology.Much of the debate on Suppes' theory of causality revolves aroundthe problem of accounting for what can be called 'surprising events',


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258 MARIA CARLA GALAVOTI'Irelative to which causes behave as counteracting, or negatively relevantto the effect. The problem is strictly linked to that of the existence of twosorts of causal talk, one in terms of kinds of events, the other in termsof single events. In this respect, probabilistic causal talk simply reflectsthe distinction between different kinds of probability statements, thatwas recalled earlier. As previously observed, to such a distinction therecorresponds a tension between explanation and prediction, which is evenmore evident in connection with causal analysis. In fact, according toa widespread opinion causality is strictly related to explanation, and anadequate theory of probabilistic causality should be able to account forsingle events as well as classes of them, even when such events are in factunpredictable. While recognizing the relevance of this distinction, inhis 1970 monograph Suppes holds that "the natural setting for extendedscientific analysis of causal relations is provided by classes of eventsrather than individual events" (Suppes, 1970, p. 80). This convictionreflects an attitude that tends to give a privileged place to predictionover explanation, and does not take causal talk as necessarily connectedwith explanatory talk. This accounts for the fact that Suppes has neverattempted to trace a systematic distinction between the two kinds ofcausal analysis. Also in this connection - as with regard to genuinecauses-Suppes clarifies the kind of causal analysis adopted by referenceto a detailed specification of the context.The quest for a detailed causal analysis in terms of single eventsis strictly linked to the quest for a specification of ultimate genuinecauses. Both are rooted in the conviction that causality is an intrinsicallyexplanatory notion. This has inspired a number of attempts at providingthe probabilistic notion of causality with some concept of homogeneity,so devised as to make the specification of causes depend on maximalspecification of factors which are relevant to the effect. Proposals inthis direction have been made by N. Cartwright, E. Eells, W. Spohnand many others, and are the object for much debate. The positiontaken by Suppes is utterly skeptical: "the search for homogeneity - hesays- seems as quixotic and metaphysically mistaken as the search forultimate causes" (Suppes, 1984a, p. 56). Also in this connection hisanswer points in the direction of a contextualization of the notion ofcause, because it is only within a specific context that it can be decidedat what point one can stop scrutinizing the data and take as exhaustivethe information available at a certain time.


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ON PATRICK SUPPES' PHILOSOPHY O F SCIENCE 259In the light of the endless discussions raised by the problems men-tioned above, Suppes' relativism and pluralism with respect to the char-acterization of probabilistic causality, together with his general formu-lation of the notion of cause, reflect a very sensible position. Clearly,this should be taken more as a point of departure, than one of arrival.In other words, the distinction among different contexts where causaltalk occurs should open the way to a detailed analysis of the specif-ic features characterizing causality within such contexts. In his 1970monograph Suppes indicates three main conceptual frameworks wherecausal statements are to be found. They are the following:

On e conceptua l fram ewo rk is that provided by a particular scientific theory; the second isof the sort that arises in connection with a particular experiment or class of experiments;and the third is the most general framework expressing our beliefs with respect to allinformation availab le to us.I3This tripartition calls for a more articulated analysis, aiming at a detailedspecification of the various kinds of experiments performed, as well asthe statistical techniques adopted in order to detect causality and theprobability functions being used. Obviously, the degree of theoreticalabstraction and sophistication attained by particular sciences makinguse of causal talk is crucial with respect to a characterization of theconceptual framework in which causality occurs.As a final remark on causality, it might be observed that a view likeSuppes', according to which there is no strict linkage between causal-ity and explanation, could be fruitfully supplemented by a notion likemanipulability. A suggestion to this effect comes from econometrics,where probabilistic causality has been dealt with in a highly origi-nal fashion. It combines a functionalist approach with a manipulativenotion of causality, in the framework of a view of model building whichbears strong analogies with Suppes', as pointed out before. Withinsuch a perspective, causality is not seen as a property of explanatoryaccounts, being rather a sort of 'qualified predictability', pertaining tothose models that can serve as a basis for practical intervention on somevariables, which are precisely those taken as causal.14 The distinctivefeature of a causal model lies in the manipulative character of its vari-ables, as opposed to purely predictive models which forecast the futuretrend of some variable under study. A generalization of a view of thissort calls for a detailed analysis of the notion of experiment and itsimplications, with respect to various disciplines making use of causaltalk. In this connection the distinction enters between experimental and


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260 MARIA CARLA GALAVOITTInon-experimental sciences, together with specification of the techniquesadopted by specific disciplines. This looks like a promising direction inwhich Suppes' theory of probabilistic causality could be expanded.

RATIONALITY

The view of rationality emerging from Suppes' philosophy is according-ly local and pragmatic in character.'' In the first place he distinguishesbetween two aspects of rationality, to which there correspond two dif-ferent approaches. The first is a 'dynamical' approach, dating back toAristotle, according to which rational action is defined as performed inaccordance with good reasons, or reasons tending to the achievementof some purpose. The second approach, called 'kinematic', applies toaction choice. It is ruled by the overall principle of maximizing expect-ed utility, characterizing the utilitarian tradition of Bentham and Bayes.This has been given great impulse by our century's Bayesianism.The 'dynamical' approach is developed by Suppes in terms of justi-fied procedures, based on the idea that good reasons should be providedin support of the procedures to be adopted in order to attain a givenpurpose. Since the very concept of 'procedure' is always referred toexpected results, the model based on 'justified procedures' is to be seenas complementary with respect to the model of expected utility. Onceagain, instead of a contraposition we find in Suppes' thought a pluralisticattitude, aimed at combining different approaches within a compositeperspective.

A similar spirit pervades Suppes' attitude towards the model ofexpected utility. His main point in this connection is that the 'clas-sical ' Bayesian model should be implemented in such a way as togain applicability in many practical situations, both in everyday lifeand scientific practice. Suppes reaffirms the importance of allowing forestimates in terms of 'interval' probability values, and takes intuition,intention and individual judgment as crucial elements to be includedin a more elastic model of Bayesian rationality. Since such things asintuition and judgment also play a central role in view of the choiceof the procedures directed to a given end; they provide within Suppes'perspective a bridge between the two components of rationality. In theresulting view quantitative and qualitative elements, intuitive judgment


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ON PATRICK SUPPES' PHILOSOPHY OF SCIENCE 261and deliberation, individual beliefs and objective evaluations are alladmitted and complement each other.This kind of approach has the advantage of allowing for a probabilis-tic treatment of notions that are not to be dealt with in the framework ofthe 'classical' Bayesian model, like those of obligation and free wi11.16As a counterpart, Suppes asks for a renunciation of a general theory ofrationality, and for the acceptance in its place of a local view, resultingfrom theoretical as well as practical elements, within a mixture that isnot to be fixed once and for all.Th e use of modern quan titative methods of decision making - Suppes says - s neces-sarily limited but powe rful when properly applied. T he role of judgment and practicalwisd om in applying these meth ods will continue to be of central importance. Th etension between calculation, qualitative justified p rocedures, and judgment will notdisappear (Sup pes, 1984a, p. 221).

CONCLUDING REMARKSThe kind of philosophy Suppes offers us is not easy to locate withinthe framework of contemporary epistemology. Instead of the many'isms' - determinism, realism, individualism, and the like -which arethe object of so much debate, we find in Suppes' work an investigationinto science from inside. Such investigation, conducted in a pragmaticand empirical spirit, does not lead to a general philosophical view ofscience and reality. For Suppes philosophy reflects the local characterof science, its problems are dealt with in the framework of a specificcontext, and so are the proposed solutions.

This approach is not bound to give us a comprehensive theory of thekind logical positivists tried to work out. What it gives us is insteada method for dissecting notions and problems in a way that makes itpossible to distinguish between their various components, and allowsidentification of structure at different levels of abstraction. This opensthe way to a representation of phenomena in which both theories anddata, abstract mathematical construals and particular experimental tech-niques, are all given attention and find their place. The pluralistic andlocal character of Suppes' approach might look like a sign of weaknessto those who do not wish to abandon the neopositivistic ideals of sci-ence and rationality. However, the force of Suppes' position lies in itsconstructive attitude towards epistemological problems. This certainly


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262 MARIA CARLA GALAV07TIanswers that urge to understand human knowledge in general, and sci-ence in particular, that logical empiricist philosophers felt so strongly.Dipartimento d i Filosojia,via Zamboni, 38,40126 Bologna, Italy

NOTES' See for example Suppe (Ed.) (1977), and Moulines and Sneed (1979).

See his 'Self-profile' (Suppes, 1979, pp. 46-47), for some remarks on this 'slogan' asSuppes calls it.See for example Spanos (1986).See Suppes (1981a) and (1984a).See Suppes (1979).See Suppes (1984a, pp. 85ff.)

' See Suppes and Zanotti (1977) and (1989).See Suppes (1966a).see Suppes (1966b).

"' See Suppes (1987a, 1987b) and Galavotti (1987)." See Galavotti (1989).l 2 For a review of the debate on probabilistic causality, focusing on some of the topicsdiscussed in the following pages see Galavotti (1991).l 3 Suppes (1970, p. 13). This point is also discussed at length in Suppes (1984b).l 4 For a discussion of the epistemological relevance of the notion of causality developedby econometricians see Galavotti and Gambetta (1990) and Galavotti (1990).l 5 Suppes' views on rationality are outlined in (198 la, 198 c, 1984a).l 6 See Suppes (1973).

REFERENCESBogdan, R. J. (Ed.): 1979, Patrick Suppes, Dordrecht: Reidel.Galavotti, M. C.: 1987, 'Comments on Patrick Suppes "Propensity Representations of

Probability"', Erkenntnis, 26, 359-368.Galavotti, M. C.: 1989, 'Anti-Realism in the Philosophy of Probability: Bruno de

Finetti's Subjectivism', Erkenntnis,31, 239-261.Galavotti, M. C.: 1990, 'Explanation and Causality: Some Suggestions from Econo-

metrics', Topoi, 9, 161-1 69.Galavotti, M. C.: 1991, 'Probability and Causality', in: Atti del Congresso 'Nuoviproblemi della logica e della Jilosojia della scienza', Vol. I, Bologna: CLUEB,pp. 69-82.


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ON PATRICK SUPPES' PHILOSOPHY O F SCIENCE 263Galavotti, M. C . and Gambetta, G.: 1990, 'Causality and Exogeneity in Econom etricModels', in: R. Cooke and D. Costantini (Eds.), Statistics in Science, Dordrecht:Kluwer, pp. 27-40.Hintikka, J. and Suppes, P. (Eds.): 1966 , Aspects of Induc tive Logic, Am sterdam:North-Holland.Mou lines, C.-U . and Sneed , J.: 1979, 'Suppes' Philosophy of Physics', in: R . Bogdan(Ed.), pp. 59-9 1.Spanos, A.: 1986, Statistical Fou ndations of Econom etric Modelling, Cambridge:Cambridge University P ress.Suppe, F. (Ed.): 1979, The Structure of Scienti$c Theories, 2nd edition, Urbana: Uni-versity of Illinois Press.Suppes, P.: 1962 , 'Models of Da ta', in: E. Nagel, P. Suppes, and A. Tarski (Eds.),Logic, Methodology an d Philosophy of Science, Stanford: Stanford University

Press, pp. 252-261.Suppes, P.: 1966a, 'A Bayesian Approach to the Paradoxes of Confirmation', in: J.Hintikka and P. Suppes (Eds.), pp. 198-207.Suppes, P.: 1966b, 'Probabilistic Inference and the Concept of Total Evidence', in: J.Hintikka and P. Suppes (Eds.), pp. 49-65.Suppes, P.: 1967, 'What Is a Scientific Theory?', in: S. Morgenbesser (Ed.), Philosophyof Science Today, New York: Basic Books, pp. 55-67.Suppes, P.: 1970, Pro bab ilistic Theory of Causality, Amsterdam : North-Ho lland.Suppes, P.: 1973, 'The Concept of Obligation in the Context of Decision The ory', in:P. Suppes, L. Henkin, G. C. Moisil, and A. Joja (Eds.), Logic, Methodology andPhilosophy of Science IV, Amsterdam: North-Holland, pp. 5 15-529.Suppes, P.: 1979, 'Self-profile', in: R. Bogdan (Ed.), pp. 3-56.Suppes, P.: 1980 , 'Probabilistic Empiricism and Rationality', in: R. Hilpinen (Ed.),Rationality in Science, Dordrecht: Reidel, pp. 17 1-1 90.Suppes, P.: 1981a, La ogique du probable, Paris: Flamm arion.Suppes, P. : 198 1b, 'The Plurality of Science', in: P. D. Asquith and I. Hacking (Eds.),PSA 1978,Vol. 11, East Lansing: Philosophy of Science Association, pp. 3-16.Suppes, P.: 198 Ic, 'The Limits of Rationality', Graze rphilos oph ischen S tudien, 12/13,85-101.Suppes, P.: 1983, 'The M eaning of Probability Statem ents', Erkenntnis, 19, 397 -403 .

Suppes, P.: 1984a, Probabilistic Metaphysics, Oxford: B lackwell.Suppes, P.: 1984b, 'Conflicting Intu itions about Causality', in: P. Trench , T. Yueh ling,and H. Wettstein (Eds.), Midwest Studies in Philosophy, Causation and CausalTheories, Vol. IX, pp. 151-168.Suppes, P.: 1987a, 'Propensity Representations of Probability', Erkenntnis, 26, 335-358.Suppes, P.: 1987b, 'Som e Further Remarks on Propensity: Reply to Maria CarlaGalav otti', Erkenntnis, 26, 369-376.Suppes, P.: 1988a, 'Representation Theory and the Analysis of Structure', PhilosophiaNaturalis, 25, 254-268.Suppes, P.: 1988b, 'Empirical Structu res', in: E. Scheibe (Ed.), The Role of Experiencein Science, Berlin-New York: W alter de Gruyter, pp. 23-33.Suppes, P.: 1988c, 'Comment: Causality, Com plexity and Determinism', StatisticalScience, 3, 398-400 .


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264 MARIA CARLA GALAVOTTISupp es, P.: 199 1a, 'Indeterm inism or Instability, Does It Matter?', in: G. G. B rittan, Jr.(Ed.), Causality, Method an d Modality, Dordrecht: Kluwer, pp. 5-22.Supp es, P.: 1991 b, 'Can Psychological Softw are Be Reduced to Physiological H ard-

wa re?', in: E. Agazzi (Ed.), The Problem of Reduc tion in Science, Dordrecht:Kluw er, pp. 183-198.Suppes, P. and Zanotti, M.: 1977, 'On Using Random Relations to Generate Upper andLower Probabilities', Synthese, 36 , 4 2 7 4 4 0 .Suppes, P. and Zanotti, M.: 1989, 'Conditions on Upper and Lower Probabilities toImply Probabilities', Erkenntnis, 31 , 323-345.

COMMENTS BY PATRICK SUPPE SMaria Carla Galavotti gives a detailed and sympathetic overview of myphilosophy of science. Most of what she says I find myself in agreementwith. On a few points there is a divergence in our views but probablymore important are the questions she raises about positions I have notdeveloped in the detailed way that is needed. The two large topics raisedby Carla that I want to explore more carefully are, first, the relationshipbetween causality and experiments, and second, my nonfoundationalproblem-solving approach to science and the philosophy of science. Ifollow the discussion of these subjects with some more particular com-ments.Causality and Experiments. Carla remarks that already in my 1970monograph A Probabilistic Theory of Causality I indicated that therewere three main conceptual frameworks where causal statements wereto be found. These frameworks (i) were provided by a scientific theo-ry, (ii) arose in connection with particular experiments, and (iii) wereconcerned with our expression of beliefs. She rightly remarks that thetopic is not developed as thoroughly as it needs to be, for much moreneeds to be said about the various kinds of experiments and how theyrelate to causality. I emphasize of course it is possible to do experi-ments that do not directly bear on causality. Kinematical experimentsin physics are common and in other subjects as well, but still the greatbulk of experimentation is aimed at causal questions. This means thatthe theory of experimentation is itself an important part of the theoryof causality. The following classification is not meant to be definitiveor sufficiently detailed. I also amplify it in remarks on other papers inthese volumes, but it is 1 hink at least a beginning.


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ON PATRICK SUPPES' PHILOSOPHY OF SCIENCE 265

Experiments with Control Groups. In much of empirical science theimage of experimentation, at least in the social sciences and in medicine,is that of the experiment in which there are at least two groups, one theexperimental group and the other a control group. In a typical medicalexperiment, the experimental group will be given a certain treatmentand the control group either no treatment or a placebo. Often in suchexperimentation there is little if any underlying scientific theory, exceptfor the theory provided by the statistical theory of experimental designand the statistical theory of evaluation of the experimental results. Thisremark is not meant to denigrate the importance of such experiments.Major findings using this methodology can be found in many disci-plines. It is only in this century that the theory of experiments withcontrol groups has been put on a sound statistical basis. That statisticaltheory plays a very important role of offering a generalized theory ofexperimentation when there is little else in the way of scientific theoryto guide how the experiments are conducted. The pioneering work ofRonald Fisher on the design of experiments of this kind is one of thegreat landmarks of twentieth century intellectual thought.Experiments Testing a Theoretical Model. Most of the great exper-imental triumphs in science - experiments that are historical events tobe discussed for many years afterwards - are of this type. Here theexperimental setup is very different from that of the first type. There isordinarily no control group from a statistical or methodological stand-point. There is a completely different objective from that of the Fisheriancontrol-group experiment. The object is not to reject the null hypothe-sis, but to have data that enable a scientist to accept the null hypothesis,where the null hypothesis now is that the theory and the experimentyield the same predictions. Wonderful experimental examples of thiskind are easy to enumerate. A celebrated but less prominent one wasPoisson's realization that Fresnel's theory of diffraction implied that ifa small disk is held in a light emanating from essentially a point source,the center of the disks's shadow will be bright, in fact just about as brightas if no disk had been placed in the light's path. Poisson thought this wasa clear refutation of Fresnel's theory. An experiment was performedconfirming Poisson's prediction, contrary to his expectation.There is another point of interesting comparison with the first class.In the case of testing a theoretical model, from a general methodological


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266 MARIA CARLA GALAVOTI'Istandpoint it is felt to be most desirable to have a competing theory orcompeting theoretical model with which to compare the prediction of thesame experimental facts. In this case rather than an experimental groupand control group, there is, so to speak, a main theoretical model andan alternative theoretical model. The aim of refined statistical analysisis to compare the goodness of fit of these two models. It is a commonpiece of heuristic statistical advice that it is better to have almost anyalternative hypothesis or model rather than none. The insight we getfrom comparison of two theoretical models is almost without exceptionsuperior to simply looking at the comparison of a single theoreticalmodel and experimental data. In my own scientific experience one ofthe episodes I enjoyed the most was the concentration in the 1960s onthe comparison of all-or-none versus incremental learning. In this casethere were two very sharply defined theoretical ideas: whether the learn-ing occurs incrementally, as suggested by the description, or in a singlestep, as described by the phrase 'all or none'. The existence of thesetwo competing theoretical models spurred not only experimentation, butalso much more detailed examination of experimental data than wouldoften have been the case. My own contribution to this controversy,in the context of concept learning, is set forth in detail in Suppes andGinsberg (1963).

Measurement Experiments. A third class of experiments is concernedwith the accurate measurement of some important constant or physicalscale. Great examples are to be found in the long history of the mea-surement of the velocity of light. There is of course an overlap with thesecond class of experiments because in many tests of theoretical modelsa certain number of free parameters must be estimated from the data,but in these cases the real objective is the test of the theoretical model,not the estimation of the particular parameters whose exact values maynot be considered of fundamental importance. It is quite different in thecase of measurement experiments aimed at the value of an empiricalconstant that itself plays independently a role in theory. Volume I ofFoundations of Measurement (pp. 539-544) contains a six-page tablelisting various physical quantities and their dimensions which one wayor another we want to measure with detailed experiments when possible.The experiments devoted to the physical quantities listed in this tablefill hundreds of pages in experimental journals over the past century.


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ON PATRICK SUPPES' PHILOSOPHY OF SCIENCE 267The relation of the first two classes of experiments to causal ideasis clear enough. For the case of the first class, the rejection of thenull hypothesis leads to the conclusion that the treatment had a causaleffect. In the second class the notion of causality must be abstractedfrom the theoretical model but in most cases what is intuitively meantto be causal in the theory is fairly evident. In the third case, mattersare quite different. The experiments often are themselves not causalin character at all, but involve detailed measurement procedures whichmay themselves entail causal ideas but, more importantly, the exactmeasurement of various empirical quantities is the key to the detailedtesting of causal models, and so measurement experiments bear upon

causality in a significant even if indirect way.Observational Experiments. Contrary to some thinking about experi-ments, I want to classify as experiments those investigations which areobservational in nature, in the sense that the initial and boundary con-ditions of the system observed are disturbed as little as possible by theexperimenter and are not created artificially for the purpose of the exper-iment. Characteristic examples would be meteorological experimentsto measure thermal and turbulent conditions in clouds, astronomicalexperiments to observe particular features of the light from distant stars,or radio astronomy experiments aimed at similar observations aboutradio waves from distant objects.It is held by some stout-hearted statisticians that we can really notmake causal inferences when we cannot manipulate the experimentalconditions and thus we cannot really make good causal inferences inthe case of observational experiments. I believe in a more robust con-cept of causality. It is essential to our ordinary and deeply entrenchedmethods for dealing with the everyday world to be able to make suchcausal inferences as the following: 'The storm outside is now causingthe flood in my basement'. Certainly it can be the case that we have totake stronger precautions about the correctness of our causal inferencesin the case of observational experiments. It is also evident that there isa strong overlap between measurement experiments and observationalexperiments, and for that matter, observational experiments and exper-iments testing theoretical models, but in the second class of experimentI had especially in mind when controlled conditions of experimentationare deliberately created.


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268 MARIA CARLA GALAVOTI'IScience as Pluralistic Problem Solving. Galavotti catches very well inthe last part of her paper, as well as in the earlier remarks on pragmatism,the skepticism with which I greet overarching philosophical theories ofscience. Contrary to something I might have held to at the beginning ofmy career, physics or psychology, for example, are not to be organizedas one grand set of axiomatic systems whose interrelations are carefullydovetailed and extremely well developed. This may be possible formathematics but it is certainly, I now think, a mistaken ideal for physics.I have come to see that physics is a science of clever problem solving,and this is true of other areas of science as well. Good physicists are pastmasters at knowing just what particular physical assumptions are to bemade in analyzing a particular problem, something most mathematiciansare very bad at in spite of the great confidence some of them show attheir mastery of fundamental physical theory.There are of course individual foundational or philosophical ques-tions of great conceptual interest. What does not exist is an overarchingphilosophical foundation for the enterprise of science in the many dif-ferent forms it now takes. There is, as Carla emphasizes, in my view nounity of subject matter, method or language in science, and consequent-ly no philosophical view that will encompass in any nonsuperficial waythe great plurality of scientific activity.Now for some particular comments on Galavotti's analysis of myphilosophy of science.Probability of Single Events. In her discussion of Bayesianism, in myjudgment she makes too much of the special circumstances surroundingthe occurrence of single events. She says that "when dealing with sin-gle events characterized by probabilistic behavior we can only (if ever)reconstruct the history behind their occurrence after they have takenplace." But it seems to me there are obvious counterexamples to thisclaim. One of the best would be the modern intense observation of theformation and movement of hurricanes. Long before a hurricane hits theshore to create a disastrous single event, we know a great deal about thehistory of the hurricane. In no sense are meteorologists committed onlyto analysis after the event. They continually make predictions about thefuture behavior of the hurricane, including the prediction of the poten-tially disastrous single event of its moving onshore in a populated area.


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ON PATRICK SUPPES' PHILOSOPHY OF SCIENCE 269So I am less inclined than Galavotti to stress the difference betweenprobability statements about single events and probability statementsabout properties of objects.Propensities. This disagreement carries over to our running dialogueand intellectual differences about propensities. This is not the place toenter into that debate once again in full detail, but I think that Galavottiis correct that much of what I said in the past is still not sufficientlydetailed about the nature of propensities. More needs to be said. Oneway of saying more is to take the view of probabilities as fitting withindeterministic systems. In this case, we can look at properties of thedeterministic system that are not in themselves probabilistic properties,but that can be related, even causally if one desires, to the generationof probabilities. Example of such concepts would be the case of thegeneration of randomness in the motion of the three bodies. This isdiscussed in my paper on propensities, which Galavotti criticized andrefers to (Suppes, 1987a); in regions of unstable behavior randomnessis generated. It is a propensity of instability in this case to generaterandom behavior. In other cases, for example the classical coin tossingcases also discussed by me in the same paper, the propensity of thesystem that generates probability is slight variations in initial conditionstogether with the symmetry of the physical object, for example, the coinbeing tossed. Neither the variation in initial conditions nor the symme-try of the object is inherently probabilistic in character, but their jointpresence can cause the generation of probabilistic sequences. Almostcertainly Galavotti will not be satisfied with these further statements.It is a topic I hope we will be able to pursue in more detail on anotheroccasion.Determinism or Indeterminism. Concerning the discussion of insta-bility at the end of her section on objective probability, she quotes astatement of mine from Suppes 1991b on quantum mechanics as "themost outstanding example of an intrinsically indeterministic theory." Inthe spirit of Suppes 1991a and especially in view of a recent article ofmine emphasizing the transcendental character of determinism (1993) Iwould now want to say that quantum mechanics is equally congenial todeterminism or indeterminism, and the choice of an overarching viewof how to think about the world is transcendental in character. This


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270 MARIA CARLA GALAVOIT1point is not really a difference between Galavotti and me, but a pointof clarification as she puts it that "Suppes maintains that a responsiblephilosophy of science should leave the door open to indeterminism." Icertainly agree with this and now go on to say that necessarily that dooris open because of the transcendental character of determinism.It is a good thing that Carla and I continue to have rather strong dis-agreements about propensity, otherwise our philosophical conversationsmight become too irenic and congenial.

REFERENCESKran tz, D., Luce, D., Supp es, P., and Tversky, A.: 1971, Foun dations of Measurement,Volume I, New York: Academic Press .Supp es, P.: 1987a, 'Propensity Representations of Probability', Erkenntnis, 26, 335-358.Supp es, P.: 1991 a, 'Indeterm inism or Instability, Does It Matter?', in: G. G. Brittan, Jr.(Ed.), Causality, Method an d Modality, Dordrecht: Kluwer, pp. 5-22.Supp es, P.: 1991 b, 'Can Psychological So ftware Be Reduced to Physiological Hard-ware?', in: E. Agazzi (Ed.), The Problem of Reduction in Science, D ordrecht:Kluwer, pp. 183-198.Supp es, P.: 1993, 'The T ranscendental Character of Determinism ', Midwest Studies inPhilosophy, 18, 242-257.Suppes, P. and Ginsberg, R.: 1963, 'A Fundamental Property of All-or-None Models,Binomial Distribution of Responses Prior to Conditioning, with Application toConcept Formation in Children', Ps ~c ho log ica l eview, 70, 139-161.

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