RATIONALITY, THEORY ACCEPTANCEAND DECISION THEORY

J NICOLAS KAUF/vtANNUruversite du Quebec, Trozs Runeres

ABSTRACT

Following Kuhn's main thests according to which theory revisionand acceptance is always paradigm relative, 1 propose to outlinesome posable consequences of such a vtew First, asktng thequestion zn what sense Bayestan decision theory could serve asthe appropriate (normative) theory of rationality examined fromthe potnt of view of the eptstemology of theory acceptance, 1 argue that Bayestanism leads to a narrow eonception of theory acceptance Second, regarding the different types of theory revi-sion, t e expanszon, contraction, replacement and residuaisshifts, 1 extract from Kuhn's vzew a series of indtcations show-ing that theory replacement cannot be rationalized within theframework of Bayestan deciston theory, not even within a moresophisticated version of that model Third, and ftnally, I willpotnt to the need for a more comprehensive model of rationalitythan the Bayesian expected uttltty maximization model, theneed for a model whtch could better deal wtth the dtfferent as-pects of theory replacement 1 will sh,ow that Kuhn's citstinctionbetween normal and revoluttonary science gives us several hintsfor a more adequate theory of rationality zn sczence 1 will alsoshow that Kuhn is not in a position to fully artzculate his mainideas and that he well be confronted wtth a serious problemconcerning collective choice of a paradigm

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It seems dear that In the psycho-sociological and histoncal

© Principia, 2(1) (1998) pp 3-20 Published by Editora da UFSC, andNEL — Epistemology and Logic Research Group, Federal University ofSanta Catarina (UFSC), Brazil

4 J Nicolas Kaufmann

perspective of Thomas Kuhn's theory of science, revision ofa scientific theory, and if necessary of the prevailing para-digm, is a matter of choice, choice between cogrative op-tions which may be theories, hypotheses, principies, meth-odolowcal devices, etc or whole paradigms, a choice whichis always relative to cogmtive (and other sorts of) objec-tives Nobody dentes that scientific research should be arational enterprise, even though Kuhn's approach openedfor several of his readers the door to arationality, if notoutright irrationality 1

Contrary to Lakatos who saw in Kuhn's Structure ofScientific Revolution no rational cause nor reasons for acoming scientific crisis and the emergence of a new theoryor a new paracligm, no way to compare theories and para-digms by common standards of rationality, because eachparadigm contamed its own criteria of rationality, Baye-sians believe that theory choice must be rattonally justifted,and that it is so justified when the cholce is made in accor-dance with the principies and rules of the balnear model of(subjectively) expected utility maximaation In the contextof theory revision, the general aim for the defenders of theBayes approach is to furnish a representation of epistemicstates (the stattcs) and of state transitions (the dynamics)caused by epistemic inputs Epistemic states can be repre-sented by probability functions defmed over a language (ora set of possible worlds) A probability function provides ameasure of the individual's degree of belief m the sentencesor propositions As a first of several rationality constramts,these probability functions have to sansfy the probabilityaxioms2 guaranteemg coherence in a set of degrees of beliefBayesians of ali sorts accept Thomas Bayes' "Dutch book"argument exploaed by Frank Ramsey (1926) tf one doesnot subscribe to the axioms of the probability calculus, adever bookmaker will be In a position to exploit you while

Rationality, Theory Acceptance, and Decision Theory

you are forced to make bets in an incoherent manner, to beinconststent between the odds acceptable on diffetentpropositions, you will lose whatever the truth-value of thepropositions you believe in 3

The second component of Bayesianism concerns be-lief kinematics governed by the principie of Bayestan condi-tionalization for cases where epistemic inputs cause achange of behef according to a rule describable in prob-abihstic terms by learrung E, the agent shifts from Prold toPr„,, where the difference between Pr oid(A/E) and Prn,(A)must be greater than O and Prom (A/E) > O The principieof conditionalization states that tf you start with a probabi-lity function P, and then learn somethmg that is capturedby the sentence E, you should shift to a new probabilityfunction P' defmed by P'(A) = P(A/E), the conditional prob-alnlity of A given E, this new probability bemg just theratio P(A &E)/P(E) when P(A) > O There are a lot of ques-tions concerning the justification of the principie of inter-temporal credal conditionalization as normativeiy necessaryfor the rationality of belief change, but it remains a cor-nerstone of Bayesian behef kinematics (see Earman, 1992)

If scientific inquiry is controlied by considerattonsanalogous to those that are relevant in practical matters,the deusion maker must not only have i) a ftnite list ofcogrative options (theones, etc ) from whtch he can choose(0 1 „0„,), a firate hst of states of nature (S 1 , ,S) withprobability assignments relative to the total evidence p(S„e)such that the total available evidence entalis that only oneof these can be true, each option being consistent with thetotal evidence u) The decision maker must also be able todetermine and describe in ali relevant aspects relative to hisepistemic goals and deszderata the outcomes or results (r13)which are realized when a certam state of nature (S,) is thecase In) 'The rational decision maker must be in a position

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6 .1 Nwolas Kaufmann

to make a utility assignment (umque up to the choice of a Opoint and una) to each specified result, u(r,), in the light ofthe objectives, epistemic, practical, moral and aestheticgoals he may combine in the numencal measure of thisvalue or utility These utility assignments have to be madein accordance with the structural principies governing thecombination of preferences (desirabilities or intensities ofdesires concerning outcomes seen In the light of epistemicgoals) with degrees of belief (probabilities for the states ofnature) These coherence principies of preferences (andprobabilities) concern preference ordenngs, such as theprincipie of comparabilay (weak preference ordenngs haveto be reflexive, complete and transitive), continuity, mo-notony, substitution and reduction 4 iv) According to theBayes rule, a rational deasion maker has to choose thecognitive option which maximizes the expected utility(relative to the available evidence) maxEU(0„e) = maxili=ip(S,,e) u(r)

The outimed Bayesian programme offers a prob-abilistic epistemology where theory choice does not reallyconsist in accepting a theory as true but merely in prob-abilifying different versions of it over time Within theframework given by Bayes, scientists my decide to devotetime, treasure and trouble to one research programmerather than another But this is a deasion of instautionalinvestment which does not really amount to the adopnonof an epistemic attitude regardmg a theory (except whenthe probability of as truth approaches 1 which neariy neverhappens) In this case, one has to focus more on the utilitycomponent than on the probability component

Kuhn's conception of theory choice is remarkablefor its omission of any reference to the probability of theo-nes or degrees of belief and confirmation of hypothesesamong which one has to chose 5 But when the choice has

Rationality, Theory Acceptance, and Dectsion Theory

to be made given a system of utatty asszgnments, Bayes' pro-gramme rtself gives no mstructions as to the way utilityassignments have to be made in the first place The advan-tage of Kuhn's paradigm approach is to focus on this aspectof the decision problem (epistemic preferences, cognitivevalues, epistemic entrenchment, etc ) in order to broadenthe Bayesian perspective which is clearly too narrow tocover the whole complex of theory choice This appearsclearly from the writings of Thomas Kuhn smce his seminalStructure of Scientzfic Revolutzon

II

Traditionally, four types of epistemic changes and theoryrevisions were distinguished in matters of theory-choiceThese types have the following characteristics

Expansion. a change that happens when "a shift is madefrom Kl to 1K2 containing K1 obtamed by adding a sentencee to K1 and forming a deductive closure" (Levi, 1983, 25)

Contraction a change obtamed when a shift is made fromKl to K2 when some beliefs are retracted from Ki and nonew belief is added, the contracted state of belief beingclosed under logical consequences (Levi, 1983, 25, Garden-fors, 1988, 60)

Replacement: a sentence representing the epistemic inputto a consistent K (contaming h) causes a shift to a consis-tent K2 (contaming h), the input sentence leads to a con-tradiction of the beliefs already in K 1 Replacement takesplace when a saentist is "converted from a commitment toone theory to a commitment to another conflicting withthe first" (Levi6 (1983), 26)

Residual shift shifts that are not dassifiable by the otherthree categories (as mentioned by Levi for completeness)

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8 J Nicolas Kaufmann

According to Gardenfors and Levi, even though Kuhndoes not explicaly say so, epistemic changes which occur in"normal soence", are revisions that may be charactensed asforms of expansions and contractions Both authors tnedto explicate scientific progress in the context of "normalsoence" in a Bayesian framework showing that the only ex-pansion method is Bayesian conditionalization understoodas expansion of belief (see Gardenfors (1988), sections 5 2and 5 7) The epistemic desideratum for expansion is to addto a given corpus new error-free information, which meanssupplying a function that is an information-determining prob-ability, further cri-teria for the evaluation of the expansionstrategies may also be necessary When these critena andepistemic goals for expansion strategies are given (see Levi(1983), chapter 2), the Bayesian deasion rule of the maxi-mum expected utility can be applied In the context of"normal" expansion It may be possible that the epistemicgoals conflict, necessaating a trade-off between, for in-stance, nsk of commating an error and gain of informa-nonal value This trade-off depends naturally on the saen-uses evaluations of the informational value of potential an-swers, on his nsk-prone or risk-aversive attrtude, and on aseries of practical aims a scientist is after in a given context

On the other hand, contraction also may be de-scnbed and reconstructed as a contraction of probabilityfunctions (with the help of speafic postulates formulated byGardenfors (1988), section 5 7) in such a way that contrac-non can be regarded as “backward" conditionalization Theepisterruc aims and desiderata of contraction being theminimization of unnecessary loss of informational value(which seems counterproducnve in the light of the generalepistemic objective of scientific research which is to aug-ment pertinent information)

In spae of ali the relanve success of the Bayesian

9Rationality, Theory Acceptance, ctnd Dectston Theory

programme, Kuhn' thinks that for "revolutionary science"when theory replacement (and much more) takes place,"debate over theory-choice cannot be cast in a form thatresembles logical or mathematical choice (1970, 199) Morepessimistically, he maintams that in debates "over theory-choice there can be no recourse to good reasons insteadtheory must be chosen for reasons that are ultimately per-sonal and subjective, some sort of mystical appercepnon isresponsible for the decision actually reached" (199) It is thecontention of Kuhn that theory replacement cannot berationalized within the framework of Bayesian decisiontheory His main reason is to show that the kmd of changeIn "revolutionary science" involves a paradigm shift, whichis a change in value commuments not as being a matter ofdegrees of belief in the first place, but as a matter of epis-temic preferences, cognitive values and utilities The prob-ability strategy and the way of companng degrees of beliefrelative to an idenncal and comparable background nolonger works in this context because "revolunonary sci-ence" is marked by the replacement of the very same frame-work, it is marked by a paradigm shift in Kuhn's terms Inthis case, there no longer exists a common backgroundagainst which both alternatives (of theory-choice) could beepistemically evaluated "Sir Karl takes it for granted thatproponents of competing theones do share a neutral lan-guage adequate to the companson of such observation re-ports I am about to argue that they do not If I am right,says Kuhn, then `truth' may, like 'proof be a term withonly intra-theoretic application" (1970b, 265-66) Kuhn hasseveral reasons to reject Bayesianism, the strongest onebeing the following

In a penod of theory change when theory replace-ment and paradigm shift take place, there is no way toconditionalize on the information that a new and hereto-

10 I Nicolas Kctufmann

fore unarticulated theory 12 has been introduced Thiswould be nonsensical, because conditionalization can onlytake place when prior to the time of replacement there wasa well defined probability for this information, i e for thenew theory T2 But this possibility is clearly ruled out, ex-cept when one is willing to attnbute an arbarary probabil-ay value or inalai probabilities for as yet unborn theonesThis is not, as Kuhn showed convinangly by his detailedhistoncal investigations, what really happened dunng se-entific revolutions The transfer of allegiance from para-digm to paradigm does not obey Bayesian deesion algo-nthms (Kuhn (1970b), 260), the important factor in para-digm shift is persuasive argumentation, not logical proof byconditionalization (lindem, 261) lhe meaning of thisstatement is to say that theory choice is a shift in valuecommitments These commaments are normally changed,as a matter of sociological fact, by persuasion because thischange does not depend on degrees of belief, but on achange of preferences which constaute only a prelude tothe possibility of proof lhe statement does not mean thatparadigm shift is an intuinve or even mystical affair Kuhntotally rejects in the end On the contrary, there must begood reasons for any theory choice These reasons concernvalue commaments, the neglected part in the Bayesian ap-proach It is well understood that normally seentific re-search is supposed to be value free relatively to non-cogninve values, value freedom being aself an ideal re-questing impartictlity (stipulating that acceptance of a theoryshould depend solely on cognitive values), autonomy(seentific research programmes should be pursued withregard to the Implementation of the cognitive objectives ofa specific scientific community) and neutraltty (seentificresearch should be independent of any particular non-cogninve value perspective 8

11Rationality, Theory Acceptance, and Decision Theory

According to Gardenfors (1988, sections 4 6 and4 7), the value commitments relate essentially to what hecalls the epistemic entrenchment of some components of atheory "A change in paradigm typically involves a radicalchange in the ordenng of epistemic entrenchment, and,vice versa, a substantial change of the degrees of epistemicentrenchment of the theses In a scientific field is a stronginclication of what Kuhn calls a `scientific revolution"(ibidem, 88) It is important to notice that the degree of en-trenchment with the formal propernes of transitivity, con-junctiveness (connectivity), etc is not fixed by how prob-able a beliefis judged to be but rather by how important thebelief is to inquiry and deliberanon Within the paradigmapproach to the idea of epistemic entrenchment, whatinduded in the paradigm (according to Lakatos, whatinduded in the "core") is the most entrenched part, whichis given up only in paradigm shift A paradigm shift, de-scnbed by Kuhn, involves, then, a radical shift in the or-denng of epistemic entrenchment The ordenng of thisentrenchment depends typically on the epistemic valueswhich must be seen as essentially context dependant,where the context includes, as Kuhn has shown, muchmore than the degrees of belief of the scientific deasionmaker In relation to paradigm shift in chemistry, for in-stance, Kuhn noted that according to the phlogiston the-ory, qualitative facts such as colour and taste of substanceswere more important than quantitative information such asmeasured weights, after Lavoisier and Dalton these quanti-tative properties were considered as being more fundamen-tal For what reasons ? The reasons have to do with the listof epistemic desiderata Kuhn cites accuracy,fruitfulness (explanatory and predictive power), consistencyand scope These iterns function as cogrative values whichdetermine paradigm choice They are the common values

12 J Nicolas Kaufmann

members of the suentific communay are supposed to shareHowever, these common values do not guarantee, Kuhnreminds us, that each individual member of the communitymakes the same deasion in the "same" arcumstances thereis "no neutral algorahm for theory-choice, no systematicprocedure which, properly applied, must lead each individ-ual In the group to the same deasion" ("Postscript", 206)Individuais may apply these cntena differently to the sameproblem, and this diversity is maintained for very goodreasons As long as the most debberate and best consideredjudgments in suence may be wrong — which is the mark offaillibilism, "a is vaally important that different individuaisdecide in different ways" (1970b, 241) Furthermore, thecritena are =precise, and individuais may differ abouttheir applications in concrete cases In many arcumstancesthey may dearly prove to conflict with one another,"accuracy may, for example, dictate the choice of one the-ory, scope the choice of as competi:toe (1977, 322) For thisand other reasons, simple deasion theory is not useful insuch contexts These considerations indicate that theory-choice must be made in accordance with a more elaboratemodel of deasion making, a model which incorporatesmore details in as utility component

III

It is my contention that Kuhn has conclusively argued thattheory-choice needs a more comprehensive model of ra-nonalay than the one recommended by the Bayesian ap-proach He repeatedly explained that existing theones ofrational deasion are "not quite right, and that we mustreadjust or change them to expiam why suence works as rtdoes" (1970b, 264) They are not only descnptively inade-quate but also detective from the normative point of view

Rationality, Theory Acceptance, and Decision Theory

Kuhn did not only ask a (descnptive) quesnon concerningthe critena which saentists are observed to follow whenevaluatmg theones, but at the same time he asked a nor-mative question to know in what sense these critena arealso rattonal bases for their judgment (1983, 563) I wouldlike to point out in this final part two types of contnbu-tions one might expect from the paradigm approach ofKuhn The first, a positive one, concerns the way to ar-ticulate in more detail the utility or value component of theexpected utility maximization model lhe second, a nega-tive remark, concerns a senous difficulty which anses fromthe Kuhnian conception of the procedure for theory-choice(with paradigm change)

a) As Hempel said some years ago, an account ofscientific inquiry as a rational pursuit, "will have to speafycertain goals of scientific inquiry as well as some methodo-logical principies observed in their pursuit, finally, it willhave to exhibit the instrumental rationality of the princi-pies in relation to the goals" (1979, 58) In Kuhn's view, aparadigm mcorporates these elements A paradigm is con-caved as a constellation of group commitments not onlyconcerning shared beliefs in heunstics and symbolic gener-alizations, but also, and most importantly, epistemic (andother) value commitments Shifts are made as a funcnon ofprionnses among cogninve values and reiative importanceof epistemic critena discussed extensively by McMullin(1996) and expanded significantly by Lacey (1997)

In several of his papers following the "Postscript",Kuhn gives us his list of goals of scientific inquiry, the listof epistemic desiderata or values which serve as the cntenafor evaluation of the outcomes of the several cognitive op-tions to judge the adequacy of a theory (including itsmethodological principies) Kuhn knows that he does notyet possess a complete and eventually well articulated list of

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14 Nicolas Kaufmann

these goals and critena Such an enterpnse supposes thatcriteria for choice can be unambiguously stated As con-cerns this problem, Kuhn is justifiably pessimisticprogress has been made for this matter Sometimes he de-clares that a full articulation within a univocal decisionalgonthm is "not a quite attainable ideal" (1970b, 326) Hislist of cogninve values contains the following iteras accu-racy, intra- and inter-theoretic consistency, broad scope,simplicity and fruitfulness These shared values of a scien-tific community are said to be effecnve, but their effective-ness does not depend on their being sufficiently articulatedto dictate the choice of each individual who subscnbes tothem As Kuhn's case studies clearly illustrated, thesena admit vanation from individual to individual, vanationin interpretanon, application and relative weighting

Accuracy can be interpreted In the broad perspectiveof empincal adequacy, say as range of quantification anddevelopment of measunng techniques, exactness and num-ber of successful predictions, best approximation to truth,high degree of confirmation, corroboranon ortude, self-evidence, etc , some of which Kuhn explicitlyexcluded Conststency can be understood in terms of self-consistency of a theory, closure under logical consequencesand logical omniscience, conceptual coherence (homogene-rty), nomological entrenchment, idealized equilibnum ofsets of sentences, compatibility with other theories, andmany other meanings Optimality of scope could mean thata theory's consequences should extend beyond observa-nons, laws or subtheones it was initially designed to ex-

piam. But what counts as optimal may vary from time totime, from individual to individual Simplicity generallyunderstood as the law of least effort may cover actual com-putational labour requested to make predictions, complex-ity of the mathemancal apparatus of a theory, of proce-

Rattonaltty, Theory Acceptance, and Dectston Theory

dures to extrapolate from data, for example of curve-frtting,simplicityi when the criterion is used to select a hypothesisfor further test, simplicity2 as the final arbitration criterionwhen deasive evidence is lacking Simphaty is independentof truth because the question is not to know if nature itselfis simple The last criterion In the list is fruttfulness whichallows a large range of interpretations Contrary to Popperwho insists on fruitfulness in problem raising, 9 Kuhn insistson efficency In problem solving, on the hearings of theo-nes on subsequent results, on the many signs of progres-siveness of a research programme, beside overall usefulnessin practical technological control of natural processus

Not only does Kuhn admit vanation in interpreta-tion of the epistemic values, but also different judgments ofthese values in concrete situations of application wherevalues can be weighted differently by different individuaisEven though they look ambiguous in application and maythen be an insufficient haus for a shared algonthm ofchoice, they nevertheless specify what saentists must con-Reler in reachtng a deasion, what they may consider rele-vant, what they are required to justify as the basis forchoices they make (see Kuhn (1977), 331) A further prob-lem anses from the fact that the specified cognitive valuesrepeatedly prove to conflict with one another when youcannot satisfy both at the same time with the same theoryThen one has to teul how to make trade offs, how to com-bine them in a single multi-critenal deasion algonthm

The multiple vanations within the value componentof a hypothetical deasion procedure for theory-choice andparadigm change show that it is not only difficult to articu-late In due detail the different cntena and cognitive values,but that it is even more difficult to elaborate on such ba-sis a unique deasion algonthm forang each individual tomake the same deasion in an identical or similar context

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16 Nicolas Kaufmann

Kuhn comes to a sceptical conclusion concerrung such anenterpnse the identified vanations are too heavily contextdependant However, multi-critenal deasion analysisl°should recommend rtself as a general framework for the for-mulation of principies of combinanon, principies of domi-nation and principies of trade-off between the differentteria

b) The sceptidsrn nourtshed against a shared ded-sion algorithm dia not prevent Kuhn from maintainingthat in paradigm change and theory-choice, "it is the com-munity of specialists rather than its individual membersthat make the effective deasion" ("Postscript", 200) "As inpohtical revolutions, so in paradigm choice — there is nostandard higher than the assent of the relevant commu-nity " (1970, 94) Even more specifically, Kuhn asserts thatit is a "group licensed way of seeing" and solving a problem("Postscript", 189) Rational deasion for acceptance of sa-entific theones appears to be not individual choice, butcoliective or social choice This kind of choice must guar-antee, against individual and sub jective vanations, the ob-jectivity of the whoie enterpnse What is at stake is the foi-lowing Given the preferences of the individual members ofa scientific community concerning the interpretation, modeof application and weighting of the common values andepistemic critena, the problem is to fix a procedure ac-cording to which the community is in a position to specifywhat is collectively best or best overall for scence Theproblem for Kuhn is now to give a dear account of howthe group decision is to be effected Earman (1992, 199)finds "this idea puzzling", and he does not find in Structureof Scientific Revolution any hints as to the decision proce-dure which would end up in a rational consensus whenindividual members of the saentific community have di-vergent degrees of belief obtained from different value com-

17Rationality, Theory Acceptance, and Decuton Theory

maments It is a fact that we cannot learn from Kuhn'swritings what normative rationalay constraints have to beimposed on a hypothetical collective deasion procedure

In a period of revolutionary saence and paradigmchange, there is a real dash between the supporters of anew paradigm and the rest of the saentific community,there is a dear lack of intersubjective agreement Kuhnmust then show how intersubjective agreement or consen-sus is restored when individual soentists start from differ-ent value commaments He must show what can count asa rational process of convergence He must inclicate howrational agreement is to be reached on interpretation, ap-plication and relative weighting of common values for the-ory-choice In the first hand Do ali the members have toagree when the group "decides" on a theory or paradigrn ? Isit a mater of a majority vote? Or do we simply have to ex-clude from the group of specialists those who &sagre& Inthis case, we are back to the problem of circularay a seen-tific communay is defined in terms of a shared paradigm,and a paradigm is what members of the seentific commu-nity have in common, arcularay Kuhn invuted philoso-phers do avoid This is not the only problem when para-digm shift is to be reconstructed as a rational enterpriseWe have to ask Kuhn where the "good reasons [are] forbeing persuaded", and what reasons are "ultimately deasivefor the group" (1970a, 199) The main problem, acutelyformulated by Earman (1992) is that the collective cannotdecide, "it cannot rationally decide to agree if the individu-ais disagree" This is certainly true In matters of saence —probably different from politics

A further problem would be to indicate the relationbetween cognaive values and epistemic entrenchment, thatis to show how cognaive values determine degrees of en-trenchment of beliefs which influence the epistemic com-

18 J Nicolas Kaufmctnn

mitment function (a function that determines, as a rule,how an epistemic state would change as a result of vanousinputs), and to show how this function is related to condi-nonalization

Let us conclude I have indicated in what sense Bay-esianism offers a narrow account of ranonal deasion mak-ing in science, and that this account is inadequate for thecase of "revolutionary science" Kuhn, in focusing on thecognitive value component of decision theory, gives severalhints for a more elaborate model, but the paradigm ap-proach is also confronted with difficult problems in sofar asit gives no idea of the rationality constraints for rationalagreement and rational consensus in paradigm change

References

Earman, John 1992 Bayes or Bust ? A Crtitical Examinationof Bayesian Confirmation Theory Cambndge, MA 'TheMIT Press

Gardenfors, Peter 1988 Knowledge in Flux, Modeling theDynamics of Epistemic States Cambndge, MA The MITPress

Hempel, Cari G 1979 "Scientffic Rationality Analytic vsPragmatic Perspectives " In Geraets, Theodor (ed ), Ra-tionality Today/La rationalite aujourd'hut Ottawa Uni-versity of Ottawa Press, 46-58

Keeney, Ralph L & Raiffa, Howard 1993 Decisions withMultiple Objectives, Preferences and Value TradeoffsCambndge, MA Cambndge University Press

Kuhn, Thomas 1970a "Postscript " In The Structure of Sci-entific Revolutions Chicago University of Chicago Press

— 1970b "Reflections on my Cntics " In Lakatos, I &.Musgrave, A (eds ), Critiasm and the Growth of Know/-edge Cambndge Cambndge University Press, 231-79

— 1977 "Objectivity, Value Judgments, and TheoryChoice " In The Essential Tenston Chicago ChicagoUniversity Press, 320-39

19Rationallty, Theory Acceptance, and Dectsion Theory

— 1983 "Rationalay and Theory Choice " Journal ofPhdosophy 80 563-70

Lacey, Hugh 1997 "The Constitunve Valu.es of Science "Principia 1(1) 3-41

Lakatos, Imre 1970 "Falsification and the Methodology ofScentific Research Programmes " In Imre Lakatos &Alan Musgrave (eds ), Criticism and the Growth of Knowl-edge Cambndge Cambndge University Press, 91-197

Levi, Isaac 1983 The Entrepnse of Knowledge, An Essay onKnowledge, Credal Probability, and Chance Cambndge,MA The MIT Press

McMullin, E 1996 "Values in Science " In W Newton-Smith (ed ), A Companion to the Phdosophy of ScienceCambndge Blackwell

Popper, Karl R 1959 The Logic of Sczentific Discovery NewYork Harper & Row, 1965

Ramsey, Frank P 1926 "Truth and Probabilay " In Philo-sopiucal Papers, Edaed by D H Mellor CambndgeCambridge University Press, 1994, 52-95

Scluck, Frederick 1986 "Dutch Books and Money Pumps "Journal of Philosophy 83 112-8

KeywordsBayesianism, Kuhn, Theory Acceptance

I Nzcolas KaufmannDepartement de Phdosophie

Unzverszte du QuebecTrozs-Rivieres (Qc)G9A 5H7 Canada

Notes

'In Lakatos' eyes, theory choice is a matter of "mob psychology""Thus, in Kunh,'s vzew scientzfic revolution in irratzonal, a matter formob psychology" (Lakatos (1970), 178)2 Ax 1 02p(A)2 = 1 for ali sentences A in L (nonnegativity),

Ax 2 p(T) = 1 for the probability of truth (normalization),Ax 3 For ali sentences A, B logically distinct

(---.(A & B)), p(AuB) = p(A) + p(B) (addinvity)

20 J Nicolas Kaufmann

It is, however, not certam that the "Dutch Book" argument is aknock down argument (see Schick, 1986)4 Continuity with xa the best and x2 the worst option In X, thereexist for each alternative x in X a probability p such that a ra-no-nal person is mdifferent between x (for sure) and the lottery[pxa , (1—p)x2]

Monotony with two probability distributions between theoptions x and y, a rational person prefers the one which is betterand has a higher probability

Substrtunon if a rational person is indifferent between prob-ability distributions x* and x from X, x* and x can then be sub-strtuted in any context without modifying the preferences

Reducnon or complexity a ranonal person is indifferent be-tween a composed lottery (whose results are themselves lottenes)and the simple lottery obtamed by multiplication of the prob-abilmes accordance with the rules of the probability calculusThis was rightly observed by Earman (1992, ch 8 3)Replacement may be treated by Gardenfors (1988) under the

headmg of "revision" While Levi (1983, 26) makes reference toKunh's "revolutionary saence", Gardenfors does not

The main references for this position are Kuhn (1970a),"Postscript", Kuhn (1970b, 1977 and 1983)

An excellent discussion of theses matters can be found Lacey(1997)9 "Science never pursues the illusionary aim of making its answersfinal, or even probable Its advance is, rather, towards the infi-nue yet attainable aun of ever discovenng new, deeper and moregeneral problems, and of subjecting its ever tentative answers toever renewed and ever more ngorous tests " (Popper (1959), 281)How can fruitfulness in problem ming be a desideratum of scien-tific inquiry? How could a problem solved ever raise more deeperproblems? It is quite clear that when condusions advocated assolutions to a problem, are In conflict with previous views ordata, there is no problem solved and no virtuel

See especially Keeny and Raiffa (1993) analysing deasions withcompeting objectives illustrated by applications of mul-

ttattribute analysis addressmg value trade-offs, the structunng ofobjectives and the measurement of their achievements