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In Sidney Morgenbesser (Ed., Philosophy ofScience Today. New York: Bas ic Book;I n c . , 1 9 6 7 . P p . 5 5 - 6 7 .IVHAT IS ASCIENTIFIC THEORY?Patrick Suppes

Often when we ask what is a s ea nd -so , pie expect a d e a r anddefinite answer. If, for euample, someone asks me what is a ra-tional number , I may give the simple and precise armer that arational number is th e ratio of two integen. Ther e a r e o t he rkinds of simple questions for which a prese answer art begiven bu t for which in ordinary tak a rather vague a n m e r busually given and accepted. Someone reads a b u t nectarines in abook. b u t has never seen a nectarine, or pasibly has seen nectar-ines b u t is n o t familiar wth their English name. Ne may ask me, W h a t is a nectarine? and I would probably apIy, X smooth-skinne d sort of peach. &&y, this is not a very exact answer,b u t if my questioner k n o w wh at peaches are, i t may corne dosetobeing satisfactory.

T h e rind o question I want to discuss fits neither one of thesepatterns. Saentifc theories areno t like rational numbers ornectarines. Certainly they are n o t like nectarines, for they areno t sim pl e phj-sical objects. T h e y are like rational numben i nn o t being phjsical objects, but they are total ly unlilre rationalnumbers in tha t s c i e n ~ eheories m o t be defined in anyple or direct way in terms o other non-ghysical, a b m c tobjects.

Gaxl examples of the kind of question we shdl andj-ze iathis chapterare probided by th e familiar inquiries: ?\hat isphjsics?,*7\hat is psychology?, %hat is science? To none O Ethese questions d o we expect a simple and precise a.uwerOntheotherhand, here are m a n y interesting things eo be said

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WHAT IS A SCIESTIFIC THEORY?about the sort of thing physics or psychology is. I shall be tryingto show in this essay that this is also true of scientific theories.

mTHE ST A SD A R D SKETCHThe standard sketch of scientific theories-and I emphasizee word sk.et&-runs something like the following. A scien-tific theory consists of two parts. One part is an abstract logicalcalculus. In addition to the vocabulary of logic, this calculus in-cludes ehe primitive symbols of the theory, and the logical stpu~c-re of the theory is fixed by stating the axioms or postulates ofe theory in terns of its primitive symbols. For many theoriesthe primitive symbols will be thought of as theoretical t e m Ekeeelectron or particle that are not possible eo relaee in an ysimple way to observable phenomena.The second part of the theory is a set of mles that assign anmpirical content to the logical calculus by providing what areally called co-srdinating definitions or empirical inter-

tations for a t least some of ehe primitive and defined symbobthe calculus. It is always emphasized that the first part alone isnot sufficient to define a scientific theory, fo r without a systematics dfication of the intended empiricalnterpretation of thery, i t is not possible in any sense to evaluate the theory as a

of science, although it can be studied simply as a piece ofe mast striking thingabout this characterization is its

schematic nature.Concerning he first part of a theory,logical calculus, it is unheard of eo find a substantive exampletheory actually worked out as a logical calculus in the w r i t -of most philosophers of science. Much handwaving is in-ed in to demonstrate that ths working out of the logicalculm is simple in principleand onlya matter of tedious

T h e sketch of ehe second part of a theory, that is, the co-ordinating definitions or empirical interpretations of some of theterms, is also highly schematic. A common defense of the rela-dvely vague schema offered is that the variety of different em-

ure mathematics.

etail, but concrete evidence is seldom given.

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PATRICK SUPPESpirical interpretations, for exam ple, the many d ifferent methodsof measur ing mass-make a precise characterization difficult.M oreover, as we move from the precisely formulated theory o n tothe very loose and elliptica l sort of experim ental languag e usedby almost all scientists, i t is difficult to impose a definite p at te rnon the rulesof empirical interpretation.T h e view I want to suppor t in thi s essay is not tha t this s tand-ard sketch is wrong, but rather tha t i t is fa r too simple. Its verysketchiness makes i t possible to om t both importane prope rtiessf theories and significantdistinctions &a t may be in t roducedbetween different Iheories.

egin with, there has been a strong tendency o n ehe p a n ofanyphilosophers to speak of the first p a t of alogicalcalculuspure ly in syntactical t e m . %hecdefinitions provided in the second pa rt do n o t inIogic provide an ad eq ua te semantics for thui te a ar t from questions about direct empinen t and natural f rom a logical s tandpoint to UR

Is of the theory. Th ese m od ek a re hig hly abstract,mon-linguistic entities,oftenquite remote in theirconceptionfrom empirical obsepvations. ]It may well be asked what doesthe concept of a model have to ad d to the familiar discussiom ofempirical interpretation oI think i t is trueo say philosophersind it easier totalk ab ou t theories th an ab ou t models of theories.

for h i s are several, but perhaps the most impor tan tfollowing: In the first place, philosophers exam ples of theoriesare usually qu ite simple in character, arad therefore are easy todiscuss in a straightforward inguisticmanner. %nplace, the ntrodu ction of models of a eory inevitably i n a ~duces a strongermathematicalelement into e discussion. It isa natura l thing to talk a b u t theories as linguistic entities-thatt, o speak explicitly of the precisely defined set of Sentences sf

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WEIAT IS A SCIESTIFIC THEORY?the theory and the like-when the theories are given in what iscalled standard formalization.Theories are ordinarily said to have a standard formalizationwhen they are formulated within first-order logic. Roughiy speak-ing, first-order logic is just the logic of sentential connectives andpredicates holdjng for one type of object. Unfortunately, when atheory asumes more than first-order logic, it is neither naturalnor simple to formalize i t in this fashion. Forexample, if inaxiomatizing geometry, we want to define lines as certain se ls ofpoints, we must work within a framework that already includesthe ideas of set theory. To be sure, i t is theoretically possible toaxiomatize simultaneousliy geometry and the elevantof set theory, but this is awkward and unduly laborous.Theories of more complicated structure like quantum me-c h a n i c s , classical thermodynamics, or a modernquantitativeversion of learning theory, need to use not only general ideas ofset theory but also manyreFormalization of su& theopractical. Theories of this s

observations to the quantitative assertions needed for more elab-orate theoretical stages of science.h n d y s i s of howfrom the qualitative to thequantitative may be provided by axiomatizing appropriate algebras of experimentally=&able operations and relations. Given an axiomatized theoryof measurement of some empiricalquantity such as mass, &fance, or force, the mathematical tast is to prove a representationtheorem for models of the theory which establishes, roughly

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PAXUCK SUPPESspeaking, that anyempirical model is isomorphic to some nu-merical model of the theory. The existence of this isomorphismbetween models justifies th e application of numbers to things.

IVe cannot literally take a number in our hands and apply i tto a physical object. Tihat we can do is to show that the structureof a set of phenomena under certain empirical operations is thesame as the structure of some set of numbers under arithmeticaloperations and reiations. The definition of isomorphism o&models in the given context makes the intuitive dea of S Q ~structure precise. The great significance of finding such an is6morphism of models is that we may then use all our %amiliarknowledge of computational methods, as applied o the arith-metical model, to nfer facts about t he isomorphicempiricalmodel. A linpistic formulation of ths central notion of anempirical model of a theory of measurement being isomorphicto a numerical model s extremely awkward and tedious to formu-late. But in model-theoretic t e m the notion is sinn Ie and infact represents a direct application of the very geneisomorphism used throughout all do

The second example of the usecussion of reductionism in the phie problem formulated in connection with &e question of re-ducing one science to another may be f ~ ~ u ~ a ~ e ~s a series ofl e m using t.he notion of a tion theorem %or&eels of a theory. For instance, esis that psy&oIogy mayreduced to physiology would any peopleppropri-established if one could show that for a n y mode1 of a psy-ogical theory it was possible towithin physiological theory.e absence at the present time of

question of reductionyCh010,aY OP IphySiOlOgYical example from phpics isdynamics to statistical mechanics.usually not stated in absolutely satisfactory form from a bgicalstandpoint, there is no doubt that i t is substantially correct andrepresents one of the great triumphs of matbematicdl phyks.

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WHAT IS A SCIESTIFIC THEORY?

NTRI XSI C VERSUS E X T R I S S I C

uite apa r t f rom the two applications j u s t mentioned of theconcept of a model of a heory, we may br ing this concept toear direcely on the question of characterizing a scientific theory.e contrast I wish eo draw is betwee n ntrinsic and extrinsicraceerization. T h e f o r m u l a ~ o n of a theory asculus or, to p u t ie in terms that H prefer, as astandard ormalization, gives an intr insiccharacis is certainly not the Q+ approach. For instance, a n a t u r a l

ueseion to ask within ehe context of logic is if a certain theorynt-ord er logic . I n ordes to f o w u h t e such a quest ion ina precisea m e r , i t is necessary eo have some exerinsic way of characteriz-

cala be axiomatized with standard formalization,

ne of the simplest ways ofzation is simply to defineeory. T o ask if we can axiom atize ehe theoryif we can staee a set of U ~ O H ~ Such that therecisely the models in thedefinedof a theory formulated both e x t h -nsider ehe extr insic ormulat ion of

s isom orph ic o some frag-rea1 n u m b e n T h e xthinsiction of a theory usually ollows thesortgiven orte a partic ula r m od el of ehecal ess-thanrelation)and henmodels of ehe theory in re la t ion to

sic characterization is plow to fo rmula teof models \cithoutnly to the in tr insic

15th the present case the sol utio ngh even it is not easily formulatedintrinsic axioms are just those fo r a

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PATRICK SUPPE5simple ordering plus th e axiom that the ordering mu st containin its dom ain a c oun table subset, dense w i t h respect to the order-ing in quest ion.A casual inspection of scientific theories suggests that the usualform ulations are intrinsic rather than extrinsic in character, andthereforehat the qu estion of extrinsic orm ulations suallyarises only in pu re mathematics. T h is would also seem to be ahappy resul t ,forourphilosop hical ntuition ssurely ahat a nintrinsic characterization is in genera l to be p referred to an ex-

problem or" intrinsic axiomatization of a s d e n -orecomplicated an d consid erablymoresubtlewou ld indicate . Fortunately, i t is preckely bytion of the cliass of m d e I s of the heory thatroper perspective and formuIaEedIe consideration of its exact solu-ve one s imple examp le . The axiom for classicaln i a are ordinari lysta ted n such a way that aem, as a frame of reference, k tacitly assumed.

ne effect of this is that elationsh ipsdeducible romt necessarily invariant with respect eo Galileantransformat ions. $Ve can view the tacit assum ption of a frame ofnce as an extr insic aspect of the familiar characterizationstheoryy.From &e standpoint of the models of the theory,e d3cuI ty in &e standardaxiomatizations of mechanics ka t a l arge num ber of form ally distinct modeIs ma y be used toexpress the same mecha nical faces. Each of these different mo dels

resents th e tac it choice of a di f fe ren t L n m e of reference, butmo dels represen ting the sam e Ene chanid facts are related byd e a n transformations. It is thus fa i r to sa a t in th i s instancedifferenceetweenmodelselated by deanransforma-Gons does n o t have any heoretical significance, and i t may beded as adefect of the asio m s tha tels elrist. It is impor t an t to r e d i z eelsrelated by Galilean ransformacioInt usual ly made under the heading sf e m p i r i d in te rp re ta -Ia is a conceptual

tions of the theory.

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WHAT IS A SCIEhTEIC THEORY?theoretical side of physics. I have introduced this example herein order to provide a simple instance of how the explicit con-sideration of models can lead to a more subtle discussion of thenature of a scientific theory. It is certainly possible from a p h i bsophical standpoint to maintain hatparticle mechanics as ascientific theory should be expressed only in t e m of Galileaninvariant relationships, and that the customary f 0 ~ ~ l a t i o ~redefective in this respect.

I turn now to the second part of theories mentioned above.%t s m e hat in the foregoing discussion we have been using theword theory to refer only to the first part of theories-that is,to he axiomatization of the theory or the expression of thetheory as a logical calculus-but as I emphasized at the begin-ning, the necessity of providingempirical nterpretation of atheory is just as important as the development of the formal sideof the theory. My central point on this aspect of theories is that

story is much more complicated than the familiar remarksut cwrd ina ting definitions and empirical interpretations of

theories would indicate. The kind of coordinating definitionsoften described by philosophers have their place inpopularphilosophical expositions of theories, but in the actual practiceof testing scientific theories a more elaborate and more sophisti-cated fowal machinery for relating a theory to data is required.

The concrete experience that scientists label anexperimentcannot itselfbe connected to a theory in any complete sense.That experience must be put through a conceptual grinder thatin many cases is excessively coarse. Once the experience is passed

the inder,often in the form of thequitefragmentaryn canonical form and constitute a model of the experi-

ment. It is &is model of the experiment rather han a modelof the theory for which direct coordinating definitions areprovided. It is also characteristic that the model of the ex-62

of complete experiment,hexperimental data

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PATRICK SLTPESperiment is of a relatively different logical type from that sf themodel of the theory. It is common for the models of a theory tocontain continuous functions or nfinite sequences, but for themodel of the experiment to be highly discrete and finitistic incharacter.

The assessment of the reIation between the model ofehe ex-perimentand some designated model o theory is a character-istic fundamentalroblem of mode tistical methodology.

about this methor present purposest place, it is itse 1 and theoretical int has been a typical function of this method-

ology to develop an elaborate theory of experimentation thatintercedes between any fundamentalsaentific theory and rawexperimental experience.

I t is not possible inrather eIaborate hierard beween the fundamental scientific

ts presumed to support i t . My onlyexplicit the existence of this hierarchyere is no simple procedure for giving cor a theory. It is even a bowderization

coadinathg definitions are given to establish the proper COR-nections between models of the theory and models of the experi-ment in the sense of &e canonical f o w of the data justtioned. The elaborate ple, forstimatingtheoretical pammeeers theory bom modelsof the experiment are not adequately covered by a reference to

dinating definitions.someone a s k s , What is a scientific eoq? it seem to me

ere is no simple response to be given. Are we to indude asthe.theory the ~ ~ e ~ ~ ~ ~ ~ o r ~ e d ~ u tta ti stid methodology for

ia the theory? If we are eo take seriously thestandard daimse ccwrdinating definitions are part of the theory,seem inevitable that we must also include in a m

led description of theories a ~ e ~ ~ oor designingments, estimating parameters and testing goodness-of-fit

of the theory. It does not seem to me important to givedefinitions of the form: X is a scientific theory if, and

l

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WHAT PS A SCIESXIFIC THEORY?o n I r if, so-and-so.1t;hat is impor t an t is to recognize th at heexistence of a hierarchy of theories arising from the metho dologyof experimentat ion or est ing he undam ental heory is a nessential in gre die nt of an y sop histicated scientific discipline.

T h e r e is one view Qf scientific hleories which is undoubtedly ofconsiderable mportanceandwhich I have not yet mentioned.T h i s is the view that theories are to be looked at from an inst ru-entalviewpoint . The most im po rtant un ction of a heory,according to t h i s view, is no t to organize o r assert stateme nts th atare true or false b u t to furnish m aterial principles of inference&at may be used in inferr ing one se t of facts from mo t h e r . Thus,i n ehe familiar syllogism all me n are m ortal; Socsates is a m a n ;therefore,Socrates is mo rtal, hemajorpremise aE1 m enaremortal,according to th i s instruinentalviewpoint , is convertedineo a principle of inference. And the syllogism S OW plas only &e

m a logical sta nd po int i t is clear that th% is a fairly trivialove, and the question naturally arises if there is anything more1 to besaidabout he nst rumentalviewpoint .ore tha n a verba l difference between these two ways of lookingtheories or laws is ehe arg um ent hat wh en theoriesarere-ded as principles of inference rather than as major premises,ongerconcerned direcely to estab lish their truth or

to evaluate heir usefulness i n n fe r r ingnew state-ct. It is characteristic of discussions in this vein byhilosophers hat I-IQ genuinelyoriginal ormalnot ionshavef these discussions to displace the dassical semant icaloeions of tru th an d validity. T o talk, for instance, about lawshaving different jobs than statem ents of fact is trivial unless somesystematic sema ntical no tions are introduced to replace ehe seand-a d nalysis.From anoth er direct ion there has been one concerted seriouseffort to provide orm al ramework for t he vdua f ion of

mise Socrates is a man.

ose interestingargument orclaiming khat th

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PATRICK SUPPEStheories which replaces the classical concept of t ru th .F l 'ha t Ih a v e i n m i n d is m ode rn statistic al decision theory. It is typicalof statisticaldecision heory to talkaboutact ions ather hanstatem ents. On ce the focus is shifted from statements to actions,it seems quit e natur al to replace the concept of tmth by that ofexpected loss or risk. It is appropr ia te to ask if a s tatement ist rue, but i t does no t make much sense to ask if i t is risky. O ne o ther hand , i t is reasonable to ask how risky an action is, b u t

t to ask if i t is true. It is ap par en t hat s tatist icaldecisioneory.,when taken l itera lly , projec ts a more radica1 h u u r n e n t a lview of theories than does the view already sketched.Theor ies are not regarded even as principles of inference but

as methods of organizing evidence to dedde a\..hich one of severalact ions to take. $%en theo ries are regarded as principles of in-ference, it is a straightforavard matter to r e tu rn to the classicalview and to connect a theory as a principle of inference with theconce pt of a theory as a m e a jo r p re se in an a rgu m ent . Th econ nec tion betw een the classical view and the view of theories ashserumen ts leading eo the taking sf an action is certainly m oreremote and indirec t .gh many xamples of applications of the ideas of

t u e on ehe foundations of statistics, Lbese e x am p le s in n o caseea1 wit h c om plic ated scientific theories, an d P have seen no seri-ous discussion of the t rea tment of scientific heories from ehedpoine of statistical decision heory. Aga in, i t is fair to saywhen we wane to ealk ab ou t ehe eva luati on of a sophisticatedscientific heory,disciplines ike sta tist ic2 decision heory hav e

oe yet offered any genu ine alternative to the sema ntical notionsof t ru th an d validity. I n face, evena a u a l inspection of theof statistical decision theory shows th at in spiee of &etalorie nta tion of the un dam ent al ideas, formalde-velopment of the theory is wholly dependen ton hes tandardsemantical notions and inno sense replace them .

$ n a t I mean by this is tha t in concentra t ing on the taking ofan action as the term inal s tateof an inquiry the decision theoristshavefound it necessary to use seandardsemantical notions in

se decisionheoryave bee n worked ou tn recentitera-

escribing evidence, their OIM theory, and so fo r

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WHAT IS A SCIESTIFIC THEORY?I cannot recall a single discussion by decision theorists in whichparticdar observation statements are treated in terms of utilityrather than in ternls of their truth orfalsity.It seems apparent that statistical decision theory does not atthe present time offer agenuinelycoherent or deeply originalnew view of scientific theories. Perhaps future developments ofdecision theory will proceed in ths direction. Be that as it may,there is one still more radical nstrumental view that I wouldlike to discuss as the final point to be covered in this essay. As Ihave already noted; it is characteristic of many instrumentalanalyses to distinguish he s ta tu of theories from the s t a t u ofparticular assertions of fact. It is the point of a more radicalinstrumental, behavioristic view of the use of language to chal-lenge this distinction and to look at the entire use of language,induding the statement of theories as well as of particular mat-&ers of fact, from a behavioristic viewpoint.According to this view of the matter, all uses of language arewith strong emphasis on the language users. It ise semantical analysis of modern logic gives a veryinadequate account even of the cognitive uses of language, be-c a k e it does not explicitly consider the production and receptionof linguistic stimuli by speakers, writers, listeners, and readers.It is plain&atfor he behaviorist -an ultimatelymeaningfulanswer to the question What is a scientific theory? cannot begiven in t e m of the kinds of concepts considered earlier. Anadequate and complete answer can be given only in terms of anexplicit and detailedconsideration of both theproducers andconsumers of the theory. There is much that is attractive in thisbehaviorist way of looking at theories or language in general.What i t lacks at present, however, is sufficient scientific depth anddehiteness to serve as a genuine alternative to the precise no-tions of modern logic and semantics. Moreover, mu& of thelanguage of models and theories discussed earlier in his chapteris surely so approximately correct that any behaviorist revisionof our way of looking at theories must yield the ordinary talkabout models and theories as a first approximation. It is a matterfor the future to see whether or not the behaviorists approachwll deepen our understanding of the nature of scientific theories.66

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PATRICK SL'PPESIn current perspective, themethodsandconcepts of modernlog ic p rov ide a satisfactory a n d p o w ~ f u let of tools for analyzingthe de tai led str uc tu re of scientific theories. l\That wou ld seem to

be needed for the present s deeper and more detailed applicationof these tools t o t he job of analysis. I have tried to indicate w hatI th ink a re some of the more fru itfu l directions for future in-vestigation.