CARNAP, RUDOLF - University of Toronto · 2018. 12. 22. · CARNAP, RUDOLF (18 May 1891–14 September 1970) Rudolf Carnap (1891–1970), preeminent member of the Vienna Circle, was

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CCARNAP, RUDOLF

(18 May 1891–14 September 1970)

Rudolf Carnap (1891–1970), preeminent memberof the Vienna Circle, was one of the most influen-tial figures of twentieth-century philosophy ofscience and analytic philosophy (including the phi-losophies of language, logic, and mathematics).The Vienna Circle was responsible for promulgat-ing a set of doctrines (initially in the 1920s) thatcame to be known as logical positivism or logicalempiricism (see Logical Empiricism; Vienna Cir-cle). This set of doctrines has provided the pointof departure for most subsequent developments inthe philosophy of science. Consequently Carnapmust be regarded as one of the most importantphilosophers of science of the twentieth century.Nevertheless, his most lasting positive contribu-tions were in the philosophy of logic and mathe-matics and the philosophy of language. Meanwhile,his systematic but ultimately unsuccessful attemptto construct an inductive logic has been equallyinfluential, since its failure has convinced most phi-losophers that such a project must fail.

Carnap was born in 1891 in Ronsdorf, near Bar-men, now incorporated into the city of Wuppertal,

in Germany (Carnap 1963a). In early childhood hewas educated at home by his mother, Anna Carnap(nee Dorpfeld), who had been a schoolteacher.From 1898, he attended the Gymnasium at Bar-men, where the family moved after his father’sdeath that year. In school, Carnap’s chief interestswere in mathematics and Latin. From 1910 to 1914Carnap studied at the Universities of Jena andFreiburg, concentrating first on philosophy andmathematics and, later, on philosophy and physics.Among his teachers in Jena were Bruno Bauch, aprominent neo-Kantian, and Gottlob Frege, afounder of the modern theory of quantification inlogic. Bauch impressed upon him the power ofKant’s conception that the geometrical structureof space was determined by the form of pure intui-tion. Though Carnap was impressed by Frege’songoing philosophical projects, Frege’s real (andlasting) influence came only later through a studyof his writings. Carnap’s formal intellectual workwas interrupted between 1914 and 1918 while he didmilitary service during World War I. His politicalviews had already been of a mildly socialist/pacifist

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nature. The horrors of the war served to make themmore explicit and more conscious, and to codifythem somewhat more rigorously.

Space

After the war, Carnap returned to Jena to beginresearch. His contacts with Hans Reichenbach andothers pursuing philosophy informed by currentscience began during this period (see Reichenbach,Hans). In 1919 he read Whitehead and Russell’sPrincipia Mathematica and was deeply influencedby the clarity of thought that could apparentlybe achieved through symbolization (see Russell,Bertrand). He began the construction of a putativeaxiom system for a physical theory of space-time.The physicists—represented by Max Wien, head ofthe Institute of Physics at the University of Jena—were convinced that the project did not belong inphysics. Meanwhile, Bauch was equally certain thatit did not belong in philosophy. This incident wasinstrumental in convincing Carnap of the institu-tional difficulties faced in Germany of doing inter-disciplinary work that bridged the chasm betweenphilosophy and the natural sciences. It also probablyhelped generate the attitude that later led the logicalempiricists to dismiss much of traditional philoso-phy, especiallymetaphysics. By this point in his intel-lectual development (the early 1920s) Carnap wasalready a committed empiricist who, nevertheless,accepted both the analyticity of logic and mathemat-ics and the Frege-Russell thesis of logicism, whichrequired that mathematics be formally constructedand derived from logic (see Analyticity).Faced with this lack of enthusiasm for his original

project in Jena, Carnap (1922) abandoned it to writea dissertation on the philosophical foundations ofgeometry, which was subsequently published asDer Raum. Most traditional commentators haveregarded the dissertation as a fundamentally neo-Kantian work because it included a discussion of‘‘intuitive space,’’ determined by pure intuition, in-dependent of all contingent experience, and distinctfrom both mathematical (or formal) space andphysical space (see Friedman 1999). However, re-cent reinterpretations argue for a decisive influenceof Husserl (Sarkar 2003). In contrast to Kant,Carnap restricted what could be grasped by pureintuition to some topological and metric propertiesof finite local regions of space. He identifies thisintuitive space with an infinitesimal space and goeson to postulate that a global space may be con-structed from it by iterative extension. In agreementwith Helmholtz and Moritz Schlick (a physicist-turned-philosopher, and founder of the Vienna

Circle) (see Schlick, Moritz), the geometry of physi-cal space was regarded as an empirical matter. Car-nap included a discussion of the role of non-Euclidean geometry in Einstein’s theory of generalrelativity. By distinguishing among intuitive, math-ematical, and physical spaces, Carnap attempted toresolve the apparent differences among philoso-phers, mathematicians, and physicists by assigningthe disputing camps to different discursive domains.In retrospect, this move heralded what later becamethe most salient features of Carnap’s philosophicalwork: tolerance for diverse points of view (so long asthey met stringent criteria of clarity and rigor) andan assignment of these viewpoints to differentrealms, the choice between which is to be resolvednot by philosophically substantive (e.g., epistemo-logical) criteria but by pragmatic ones (see Conven-tionalism).

The Constructionist Phase

During the winter of 1921, Carnap read Russell’sOur Knowledge of the External World. Between1922 and 1925, this work led him (Carnap 1963a)to begin the analysis that culminated inDer logischeAufbau der Welt ([1928] 1967), which is usuallyregarded as Carnap’s first major work. The purposeof the Aufbau was to construct the everyday worldfrom a phenomenalist basis (see Phenomenalism).The phenomenalist basis is an epistemologicalchoice (§§54, 58). Carnap distinguished betweenfour domains of objects: autopsychological, physi-cal, heteropsychological, and cultural (§58). Thefirst of these consists of objects of an individual’sown psychology; the second, of physical entities(Carnap does not distinguish between everyday ma-terial objects and the abstract entities of theoreticalphysics); the third consists of the objects of someother individual’s psychology; and the fourth,of cultural objects (geistige Gegenstande), whichinclude historical and sociological phenomena.

From Carnap’s ([1928] 1967) point of view, ‘‘[a]nobject . . . is called epistemically primary relative toanother one . . . if the second one is recognizedthrough the mediation of the first and thus presup-poses, for its recognition, the recognition of thefirst’’ (§54). Autopsychological objects are episte-mically primary relative to the others in this sense.Moreover, physical objects are epistemically pri-mary to heteropsychological ones because the lattercan be recognized only through the mediation ofthe former—an expression on a face, a reading inan instrument, etc. Finally, heteropsychologicalobjects are epistemically primary relative to cultur-al ones for the same reason.

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The main task of the Aufbau is construction,which Carnap ([1928] 1967) conceives of as theconverse of what he regarded as reduction (whichis far from what was then—or is now—conceivedof as ‘‘reduction’’ in Anglophone philosophy) (seeReductionism):

[A]n object is ‘reducible’ to others . . . if all statementsabout it can be translated into statements which speakonly about these other objects . . . . By constructing aconcept from other concepts, we shall mean the indica-tion of its ‘‘constructional definition’’ on the basis ofother concepts. By a constructional definition of theconcept a on the basis of the concepts b and c, wemean a rule of translation which gives a general indica-tion how any propositional function in which a occursmay be transformed into a coextensive propositionalfunction in which a no longer occurs, but only b and c.If a concept is reducible to others, then it must indeed bepossible to construct it from them (§35).

However, construction and reduction presentdifferent formal problems because, except in somedegenerate cases (such as explicit definition), thetransformations in the two directions may nothave any simple explicit relation to each other.The question of reducibility/constructibility is dis-tinct from that of epistemic primacy. In an impor-tant innovation in an empiricist context, Carnapargues that both the autopsychological and physi-cal domains can be reduced to each other (in hissense). Thus, at the formal level, either could serveas the basis of the construction. It is epistemicprimacy that dictates the choice of the former.

Carnap’s task, ultimately, is to set up a construc-tional system that will allow the construction ofthe cultural domain from the autopsychologicalthrough the two intermediate domains. In the Auf-bau, there are only informal discussions of how thelast two stages of such a construction are to beexecuted; only the construction of the physicalfrom the autopsychological is fully treated formal-ly. As the basic units of the constructional system,Carnap chose what he calls ‘‘elementary experi-ences’’ (Elementarerlebnisse, or elex) (an extendeddiscussion of Carnap’s construction is to be foundin Goodman 1951, chapter 5). These are supposedto be instantaneous cross-sections of the stream ofexperience—or at least bits of that stream in thesmallest perceivable unit of time—that are incapableof further analysis. The only primitive relationthat Carnap introduces is ‘‘recollection of similarity’’(Rs). (In the formal development of the system,Rs is introduced first and the elex are definedas the field of Rs.) The asymmetry of Rs is eventu-ally exploited by Carnap to introduce temporalordering.

Since the elex are elementary, they cannot befurther analyzed to define what would be regardedas constituent qualities of them such as partialsensations or intensity components of a sensation.Had the elex not been elementary, Carnap couldhave used ‘‘proper analysis’’ to define such quali-ties by isolating the individuals into classes on thebasis of having a certain (symmetric) relationshipwith each other. Carnap defines the process of‘‘quasi-analysis’’ to be formally analogous to prop-er analysis but only defining ‘‘quasi-characteristics’’or ‘‘quasi-constituents’’ because the elex are unana-lyzable. Thus, if an elex is both c in color and t intemperature, c or t can be defined as classes of everyelex having c or t, respectively. However, to saythat c or t is a quality would imply that an elex isanalyzable into simpler constituents. Quasi-analysisproceeds formally in this way (as if it is properanalysis) but defines only quasi-characteristics,thus allowing each elex to remain technically unan-alyzable Quasi-analysis based on the relation ‘‘partsimilarity’’ (Ps), itself defined from Rs, is the cen-tral technique of the Aufbau. It is used eventuallyto define sense classes and, then, the visual sense,visual field places, the spatial order of the visualfield, the order of colors and, eventually, sensa-tions. Thus the physical domain is constructedout of the autopsychological. Carnap’s accountsof the construction between the other two domainsremain promissory sketches.Carnap was aware that there were unresolved

technical problems with his construction of thephysical from the autopsychological, though heprobably underestimated the seriousness of theseproblems. The systematic problems are that whena quality is defined as a class selected by quasi-analysis on the basis of a relation: (i) two (different)qualities that happen always to occur together(say, red and hot) will never be separated, and(ii) quality classes may emerge in which any twomembers bear some required relation to eachother, but there may yet be no relation that holdsbetween all members of the class. Carnap’s re-sponse to these problems was extrasystematic: Inthe complicated construction of the world from theelex, he hoped that such examples would never oronly very rarely arise. Nevertheless, because ofthese problems, and because the other construc-tions are not carried out, the attitude of the Aufbauis tentative and exploratory: The constructionalsystem is presented as essentially unfinished. (Good-man 1951 also provides a lucid discussion of theseproblems.)Some recent scholarship has questioned whether

Carnap had any traditional epistemological

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concerns in the Aufbau. In particular, Friedman(e.g., 1992) has championed the view that Carnap’sconcerns in that work are purely ontological:The Aufbau is not concerned with the question ofthe source or status of knowledge of the externalworld (see Empiricism); rather, it investigates thebases on which such a world may be constructed(see Richardson 1998). Both Friedman andRichardson—as well as Sauer (1985) and Haack(1977) long before them—emphasize the Kantianroots of the Aufbau. If this reinterpretation is cor-rect, then what exactly the Aufbau owes to Russell(and traditional empiricism) becomes uncertain.However, as Putnam (1994, 281) also points out,this reinterpretation goes too far: Though the proj-ect of the Aufbau is not identical to that of Russell’sexternal world program, there is sufficient con-gruence between the two projects for Carnap tohave correctly believed that he was carrying outRussell’s program. In particular, the formal con-structions of the Aufbau are a necessary prerequi-site for the development of the epistemology thatRussell had in mind: One must be able to constructthe world formally from a phenomenalist basisbefore one can suggest that this constructionshows that the phenomena are the source of knowl-edge of the world. Moreover, this reinterpretationignores the epistemological remarks scatteredthroughout the Aufbau itself, including Carnap’sconcern for the epistemic primacy of the basis hebegins with. Savage (2003) has recently pointed outthat the salient difference between Russell’s andCarnap’s project is that whereas the former chosesense data as his point of departure, the latter choseelementary experiences. But this difference is simplya result of Carnap’s having accepted the results ofGestalt psychology as having definitively shownwhat may be taken as individual experiential bases;other than that, that is, with respect to the issue ofempiricism, it has no philosophical significance.In any case, by this time of his intellectual devel-

opment, Carnap had fully endorsed not only thelogicism of the Principia, but also the form thatWhitehead and Russell had given to logic (that is,the ramified theory of types including the axioms ofinfinity and reducibility) in that work. However,Poincare also emerges as a major influence duringthis period. Carnap did considerable work on theconceptual foundations of physics in the 1920s, andsome of this work—in particular, his analysis of therelationship between causal determination and thestructure of space—shows strong conventionalistattitudes (Carnap 1924; see also 1923 and 1926)(see Conventionalism; Poincare, Henri).

Viennese Positivism

In 1926, at Schlick’s invitation, Carnap moved toVienna to become a Privatdozent (instructor) inphilosophy at the University of Vienna for thenext five years (see Vienna Circle). An early versionof the Aufbau served as his Habilitationsschrift. Hewas welcomed into the Vienna Circle, a scientificphilosophy discussion group organized by (andcentered around) Schlick, who had occupied thechair for philosophy of the inductive sciences since1922. In the meetings of the Vienna Circle, the type-script of the Aufbau was read and discussed. WhatCarnap seems to have found most congenial in theCircle—besides its members’ concern for scienceand competence in modern logic—was their rejec-tion of traditional metaphysics. Over the years,besides Carnap and Schlick, the Circle includedHerbert Feigl, Kurt Godel, Hans Hahn, KarlMenger, Otto Neurath, and Friedrich Waismann,though Godel would later claim that he had littlesympathy for the antimetaphysical position of theother members. The meetings of the Circle werecharacterized by open, intensely critical, discussionwith no tolerance for ambiguity of formulation orlack of rigor in demonstration. The members of theCircle believed that philosophy was a collectiveenterprise in which progress could be made. Theseattitudes, even more than any canonical set of posi-tions, characterized the philosophical movement—initially known as logical positivism and later aslogical empiricism—that emerged from the work ofthe members of the Circle and a few others, espe-cially Reichenbach. However, besides rejecting tra-ditional metaphysics, most members of the Circleaccepted logicism and a sharp distinction betweenanalytic and synthetic truths. The analytic wasidentified with the a priori; the synthetic with thea posteriori (see Analyticity). A. J. Ayer, who at-tended some meetings of the Circle in 1933 (afterCarnap had left—see below), returned to Britainand published Language, Truth and Logic (Ayer1936) (see Ayer, Alfred Jules). This short bookdid much to popularize the views of the ViennaCircle among Anglophone philosophers, though itlacks the sophistication that is found in the writingsof the members of the Circle, particularly Carnap.

Under Neurath’s influence, during his Viennayears, Carnap abandoned the phenomenalist lan-guage he had preferred in the Aufbau and came toaccept physicalism (see Neurath, Otto; Physical-ism). The epistemically privileged language is onein which sentences reporting empirical knowledgeof the world (‘‘protocol sentences’’) employ terms

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referring to material bodies and their observableproperties (see Protocol Sentences). From Carnap’spoint of view, the chief advantage of a physicalistlanguage is its intersubjectivity. Physicalism, more-over, came hand-in-hand with the thesis of the‘‘unity of science,’’ that is, that the different empir-ical sciences (including the social sciences) weremerely different branches of a single unified science(see Unity of Science Movement). To defend thisthesis, it had to be demonstrated that psychologycould be based on a physicalist language In animportant paper only published somewhat later,Carnap ([1932] 1934) attempted that demonstration(see Unity andDisunity of Science). Carnap’s adop-tion of physicalism was final; he never went backto a phenomenalist language. However, what hemeant by ‘‘physicalism’’ underwent radical trans-formations over the years. By the end of his life, itmeant nomore than the adoption of a nonsolipsisticlanguage, that is, one in which intersubjective ispossible (Carnap 1963b).

In theViennaCircle,Wittgenstein’sTractatuswasdiscussed in detail. Carnap found Wittgenstein’srejection of metaphysics concordant with the viewshe had developed independently. Partly because ofWittgenstein’s influence on some members of theCircle (though not Carnap), the rejection of meta-physics took the form of an assertion that the sen-tences ofmetaphysics aremeaningless in the sense ofbeing devoid of cognitive content. Moreover, thedecision whether a sentence is meaningful was tobe made on the basis of the principle of verifiability,which claims that the meaning of a sentence is givenby the conditions of its (potential) verification (seeVerifiability). Observation terms are directly mean-ingful on this account (see Observation). Theoreti-cal terms acquire meaning only through explicitdefinition from observation terms. Carnap’s majorinnovation in these discussions within theCircle wasto suggest that even the thesis of realism—assertingthe ‘‘reality’’ of the external world—is meaningless,a position not shared by Schlick, Neurath, or Reich-enbach. Problems generated by meaningless ques-tions became the celebrated ‘‘pseudo-problems’’ ofphilosophy (Carnap [1928] 1967).

Wittgenstein’s principle of verifiability posedfairly obvious problems in any scientific context.No universal generalization can ever be verified.Perhaps independently, Karl Popper perceived thesame problem (see Popper, Karl Raimund). Thisled him to replace the requirement of verifiabilitywith that of falsifiability, though only as a criterionto demarcate science from metaphysics, and notas one to be also used to demarcate meaningfulfrom meaningless claims. It is also unclear what

the status of the principle itself is, that is, whetherit is meaningful by its own criterion of meaningful-ness. Carnap, as well as other members of theVienna Circle including Hahn and Neurath, rea-lized that a weaker criterion of meaningfulness wasnecessary. Thus began the program of the ‘‘liberal-ization of empiricism.’’ There was no unanimitywithin the Vienna Circle on this point. The differ-ences between the members are sometimes de-scribed as those between a conservative ‘‘right’’wing, led by Schlick and Waismann, which rejectedboth the liberalization of empiricism and the epis-temological antifoundationalism of the move tophysicalism, and a radical ‘‘left’’ wing, led by Neur-ath and Carnap, which endorsed the oppositeviews. The ‘‘left’’ wing also emphasized fallibilismand pragmatics; Carnap went far enough along thisline to suggest that empiricism itself was a proposalto be accepted on pragmatic grounds. This differ-ence also reflected political attitudes insofar asNeurath and, to a lesser extent, Carnap viewedscience as a tool for social reform.The precise formulation of what came to be

called the criterion of cognitive significance tookthree decades (see Hempel 1950; Carnap 1956 and1961) (see Cognitive Significance). In an importantpair of papers, Testability and Meaning, Carnap(1936–1937) replaced the requirement of verifica-tion with that of confirmation; at this stage, hemade no attempt to quantify the latter. Individualterms replace sentences as the units of meaning.Universal generalizations are no longer problemat-ic; though they cannot be conclusively verified,they can yet be confirmed. Moreover, in Testabilityand Meaning, theoretical terms no longer requireexplicit definition from observational ones in orderto acquire meaning; the connection between thetwo may be indirect through a system of implicitdefinitions. Carnap also provides an importantpioneering discussion of disposition predicates.

The Syntactic Phase

Meanwhile, in 1931, Carnap had moved to Prague,where he held the chair for natural philosophy atthe German University until 1935, when, under theshadow of Hitler, he emigrated to the United States.Toward the end of his Vienna years, a subtle butimportant shift in Carnap’s philosophical interestshad taken place. This shift was from a predominantconcern for the foundations of physics to that forthe foundations of mathematics and logic, eventhough he remained emphatic that the latter wereimportant only insofar as they were used in theempirical sciences, especially physics.

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In Vienna and before, following Frege andRussell, Carnap espoused logicism in its convention-al sense, that is, as the doctrine that held that theconcepts of mathematics were definable from thoseof logic, and the theorems of mathematics were de-rivable from the principles of logic. In the aftermathof Godel’s (1931) incompleteness theorems, how-ever, Carnap abandoned this type of logicism andopted instead for the requirement that the conceptsof mathematics and logic always have their custom-ary (that is, everyday) interpretation in all contexts.He also began to advocate a strong conventionalismregarding what constituted ‘‘logic.’’Besides the philosophical significance of Godel’s

results, what impressed Carnap most about thatwork wasGodel’s arithmetization of syntax. Down-playing the distinction between an object languageand its metalanguage, Carnap interpreted this pro-cedure as enabling the representation of the syntaxof a language within the language itself. At thispoint Carnap had not yet accepted the possibilityof semantics, even though he was aware of some ofTarski’s work and had had some contact with thePolish school of logic. In this context, the represen-tation of the syntax of a language within itself sug-gested to Carnap that all properties of a languagecould be studied within itself through a study ofsyntax.These positions were codified in Carnap’s major

work from this period, The Logical Syntax of Lan-guage (Carnap 1934b and 1937). The English trans-lation includes material that had to be omittedfrom the German original due to a shortage ofpaper; the omitted material was separately publishedin German as papers (Carnap 1934a and 1935).Conventionalism about logic was incorporatedinto the well-known principle of tolerance:

It is not our business to set up prohibitions but to arrive atconventions [about what constitutes a logic] . . . . Inlogic, there are no morals. Every one is at liberty tobuild up his own logic, i.e., his own form of language,as he wishes. All that is required is that, if he wishes todiscuss it, he must state his method clearly, and givesyntactic rules instead of philosophical arguments.

(Carnap 1937, 51–52; emphasis in the original)

Logic, therefore, is nothing but the syntax oflanguage.In Syntax, the principle of tolerance allows

Carnap to navigate the ongoing disputes betweenlogicism, formalism, and intuitionism/constructiv-ism in the foundations of mathematics withoutabandoning any insight of interest from theseschools. Carnap begins with a detailed study ofthe construction of two languages, I and II. The

last few sections of Syntax also present a fewresults regarding the syntax of any language andalso discuss the philosophical ramifications of thesyntactic point of view. (Sarkar 1992 attempts acomprehensible reconstruction of the notoriouslydifficult formalism of Syntax.)

Language I, which Carnap calls ‘‘definite,’’ isintended as a neutral core of all logically interestinglanguages, neutral enough to satisfy the stricturesof almost any intuitionist or constructivist. It per-mits the definition of primitive recursive arithmeticand has bounded quantification (for all x up tosome upper bound) but not much more. Its syntaxis fully constructed formally. Language II, whichis ‘‘indefinite’’ for Carnap, is richer. It includesLanguage I and has sufficient resources for theformulation of all of classical mathematics, and istherefore nonconstructive. Moreover, Carnap per-mits descriptive predicates in each language. Thus,the resources of Language II are strong enough topermit, in principle, the formulation of classicalphysics. The important point is that because ofthe principle of tolerance, the choice between Lan-guages I and II or, for that matter, any othersyntactically specified language, is not based onfactual considerations. If one wants to use mathe-matics to study physics in the customary way, Lan-guage II is preferable, since as yet, nonconstructivemathematics remains necessary for physics. But theadoption of Language II, dictated by the pragmaticconcern for doing physics, does not make LanguageI incorrect. This was Carnap’s response to the foun-dational disputes of mathematics: By tolerance theyare defined out of existence.

The price paid if one adopts the principle oftolerance is a radical conventionalism about whatconstitutes logic. Conventionalism, already appar-ent in Carnap’s admission of both a phenomenalistand a physicalist possible basis for construction inthe Aufbau, and strongly present in the works onthe foundations of physics in the 1920s, had nowbeen extended in Syntax to logic. As a conse-quence, what might be considered to be the mostimportant question in anymathematical or empiricalcontext—the choice of language—became prag-matic. This trend of relegating troublesome ques-tions to the realm of pragmatics almost by fiat,thereby excusing them from systematic philosophi-cal exploration, became increasingly prevalent inCarnap’s views as the years went on.

Syntax contained four technical innovations inlogic that are of significance: (i) a definition ofanalyticity that, as was later shown by S. C. Kleene,mimicked Tarski’s definition of truth for a forma-lized language; (ii) a proof, constructed by Carnap

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independently of Tarski, that truth cannot be de-fined as a syntactic predicate in any consistent for-malized language; (iii) a rule for infinite induction(in Language I) that later came to be called theomega rule; and (iv), most importantly, a generali-zation of Godel’s first incompleteness theorem thathas come to be called the fixed-point lemma. Withrespect to (iv), what Carnap proved is that in alanguage strong enough to permit arithmetization,for any syntactic predicate, one can construct asentence that would be interpreted as saying thatit satisfies that predicate. If the chosen predicate isunprovability, one gets Godel’s result.

Besides the principle of tolerance, the main phil-osophical contribution of Syntax was the thesisthat philosophy consisted of the study of logicalsyntax. Giving a new twist to the Vienna Circle’sclaim that metaphysical claims were meaningless,Carnap argues and tries to show by example thatsentences making metaphysical claims are all syn-tactically ill-formed. Moreover, since the arithme-tization procedure shows that all the syntactic rulesof a language can be formulated within the lan-guage, even the rules that determine what sentencesare meaningless can be constructed within the lan-guage. All that is left for philosophy is a study ofthe logic of science. But, as Carnap (1937) puts it:‘‘The logic of science (logical methodology) is noth-ing else than the syntax of the language of science. . . .To share this view is to substitute logical syntaxfor philosophy’’ (7–8; emphasis in original). Theclaims of Syntax are far more grandiose—andmore flamboyant—than anything in the Aufbau.

Semantics

In the late 1930s Carnap abandoned the narrowsyntacticism of Syntax and, under the influence ofTarski and the Polish school of logic, came to acceptsemantics. With this move, Carnap’s work enters itsfinal mature phase. For the first time, he acceptedthat the concept of truth can be given more thanpragmatic content. Thereupon, he turned to thesystematization of semantics with characteristicvigor, especially after his immigration to the UnitedStates, where he taught at the University of Chicagofrom 1936 to 1952. In his contribution to the Inter-national Encyclopedia of Unified Science (Carnap1939), on the foundations of logic andmathematics,the distinctions among syntactic, semantic, andpragmatic considerations regarding any languageare first presented in their mature form.

Introduction to Semantics, which followed in1942, develops semantics systematically. In SyntaxCarnap had distinguished between two types of

transformations on sentences: those involving‘‘the method of derivation’’ or ‘‘d-method,’’ andthose involving the ‘‘method of consequence’’ or‘‘c-method.’’ Both of these were supposed to besyntactic, but there is a critical distinction betweenthem. The former allows only a finite number ofelementary steps. The latter places no such restric-tion and is, therefore, more ‘‘indefinite.’’ Termsdefined using the d-method (‘‘d-terms’’) include‘‘derivable,’’ ‘‘demonstrable,’’ ‘‘refutable,’’ ‘‘resolu-ble,’’ and ‘‘irresoluble’’; the corresponding c-termsare ‘‘consequence,’’ ‘‘analytic,’’ ‘‘contradictory,’’‘‘L-determinate,’’ and ‘‘synthetic.’’ After the con-version to semantics, Carnap proposed that thec-method essentially captured what semanticsallowed; the c-terms referred to semantic concepts.Thus semantics involves a kind of formalization,

though one that is dependent on stronger inferencerules than the syntactical ones. In this sense, asChurch (1956, 65) has perceptively pointed out,Carnap—and Tarski—reduce semantics to formalrules, that is, syntax. Thus emerges the interpreta-tion of deductive logic that has since become thetextbook version, so commonly accepted that is hasbecome unnecessary to refer to Carnap when oneuses it. For Carnap, the semantic move has animportant philosophical consequence: Philosophyis no longer to be replaced just by the syntax of thelanguage of science; rather, it is to be replaced by thesyntax and the semantics of the language of science.Carnap’s (1947) most original—and influential—

work in semantics is Meaning and Necessity, wherethe basis for an intensional semantics was laid down.Largely following Frege, intensional concepts aredistinguished from extensional ones. Semanticalrules are introduced and the analytic/synthetic dis-tinction is clarified by requiring that any definitionof analyticity must satisfy the (meta-) criterion thatanalytic sentences follow from the semantical rulesalone. By now Carnap had fully accepted thatsemantic concepts and methods are more funda-mental than syntactic ones: The retreat from theflamboyance of Syntax was complete. The mostimportant contribution of Meaning and Necessitywas the reintroduction into logic, in the new inten-sional framework, of modal concepts that had beenignored since the pioneering work of Lewis (1918).In the concluding chapter of his book, Carnap intro-duced an operator for necessity, gave semantic rulesfor its use, and showed how other modal conceptssuch as possibility, impossibility, necessary implica-tion, and necessary equivalence can be defined fromthis basis.By this point, Carnap had begun to restrict his

analyses to exactly constructed languages, implicitly

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abandoning even a distant hope that they wouldhave any direct bearing on natural languages. Theproblem with the latter is that their ambiguitiesmade them unsuited for the analysis of science,which, ultimately, remained the motivation of allof Carnap’s work. Nevertheless, Carnap’s distinc-tion between the analytic and the synthetic cameunder considerable criticism from many, includingQuine (1951), primarily on the basis of considera-tions about natural languages (see Analyticity;Quine, Willard Van Orman). Though philosophicalfashion has largely followed Quine on this point, atleast until recently, Carnap was never overly im-pressed by this criticism (Stein 1992). The analytic/synthetic distinction continued to be fundamentalto his views, and, in a rejoinder to Quine, Carnapargued that nothing prevented empirical linguisticsfrom exploring intensions and thereby discoveringcases of synonymy and analyticity (Carnap 1955).Carnap’s (1950a) most systematic exposition of

his final views on ontology is also from this period.A clear distinction is maintained between questionsthat are internal to a linguistic framework andquestions that are external to it. The choice of alinguistic framework is to be based not on cognitivebut on pragmatic considerations. The externalquestion of ‘‘realism,’’ which ostensibly refers tothe ‘‘reality’’ of entities of a framework in somesense independent of it, rather than to their ‘‘reali-ty’’ within it after the framework has been accept-ed, is rejected as noncognitive (see ScientificRealism). This appears to be an anti-‘‘realist’’ posi-tion, but it is not in the sense that within a frame-work, Carnap is tolerant of the abstract entitiesthat bother nominalists. The interesting questionbecomes the pragmatic one, that is, what frame-works are fruitful in which contexts, and Carnap’sattitude toward the investigation of various alter-native frameworks remains characteristically andconsistently tolerant.Carnap continued to explore questions about the

nature of theoretical concepts and to search for acriterion of cognitive significance, preoccupationsof the logical empiricists that date back to theVienna Circle. Carnap (1956) published a detailedexposition of his final views regarding the relationbetween the theoretical and observational parts ofa scientific language. This paper emphasizes themethodological and pragmatic aspects of theoreti-cal concepts. It also contains his most subtle,though not his last, attempt to explicate the notionof the cognitive significance of a term and thusestablish clearly the boundary between scientificand nonscientific discourse. However, the criterionhe formulates makes theoretical terms significant

only with respect to a class of terms, a theoreticallanguage, an observation language, correspondencerules between them, and a theory. Relativization toa theory is critical to avoiding the problems thatbeset earlier attempts to find such a criterion. Car-nap proves several theorems that are designed toshow that the criterion does capture the distinctionbetween scientific and nonscientific discourse. Thiscriterion was criticized by Roozeboom (1960) andKaplan (1975), but these criticisms depend onmodifying Carnap’s original proposal in impor-tant ways. According to Kaplan, Carnap acceptedhis criticism, though there is apparently no in-dependent confirmation of that fact. However,Carnap (1961) did turn to a different formalism(Hilbert’s e-operator) in what has been interpretedas his last attempt to formulate such a criterion(Kaplan 1975), and this may indicate dissatisfac-tion with the 1956 attempt. If so, it remains unclearwhy: That attempt did manage to avoid the techni-cal problems associated with the earlier attempts ofthe logical empiricists (see Cognitive Significance).

Probability and Inductive Logic

From 1941 onward Carnap also began a systematicattempt to analyze the concepts of probability andto formulate an adequate inductive logic (a logic ofconfirmation), a project that would occupy him forthe rest of his life. Carnap viewed this work as anextension of the semantical methods that he hadbeen developing for the last decade. This under-scores an interesting pattern in Carnap’s intellectu-al development. Until the late 1930s Carnap viewedsyntactic categories only as nonpragmatically spec-ifiable; questions of truth and confirmation wereviewed as pragmatic. His conversion to semanticssaw the recovery of truth from the pragmatic to thesemantic realm. Now, confirmation followed truthdown the same pathway.

In Logical Foundations of Probability (1950b),his first systematic analysis of probability, Carnapdistinguished between two concepts of probability:‘‘statistical probability,’’ which was the relevantconcept to be used in empirical contexts and gener-ally estimated from the relative frequencies ofevents, and ‘‘logical probability,’’ which was to beused in contexts such as the confirmation of scien-tific hypotheses by empirical data. Though the latterconcept, usually called the ‘‘logical interpreta-tion’’ of probability, went back to Keynes (1921),Carnap provides its first systematic explication (seeProbability).

Logical probability is explicated from threedifferent points of view (1950b, 164–8): (i) as a

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conditional probability c(h,e), which measures thedegree of confirmation of a hypothesis h on thebasis of evidence e (if c(h,e) ¼ r, then r is deter-mined by logical relations between h and e); (ii) as arational degree of belief or fair betting quotient (ifc(h,e) ¼ r, then r is a fair bet on h if e correctlydescribes the total knowledge available to a bettor);and (iii) as the limit of relative frequencies in somecases. According to Carnap, the first of these, whichspecifies a confirmation function (‘‘c-function’’), isthe concept that is most relevant to the problemof induction. In the formal development of thetheory, probabilities are associated with sentencesof a formalized language.

In Foundations, Carnap (1950b) believed that aunique measure c(h,e) of the degree of confirmationcan be found, and he even proposed one (viz.,Laplace’s rule of succession), though he could notprove its uniqueness satisfactorily. His generalstrategy was to augment the standard axioms ofthe probability calculus by a set of ‘‘conventionson adequacy’’ (285), which turned out to be equiv-alent to assumptions about the rationality ofdegrees of belief that had independently been pro-posed by both Ramsey and de Finetti (Shimony1992). In a later work, The Continuum of InductiveMethods, using the conventions on adequacy andsome plausible symmetry principles, Carnap (1952)managed to show that all acceptable c-functionscould be parameterized by a single parameter, areal number, l 2 [0,1]. The trouble remainedthat there is no intuitively appealing a priori strate-gy to restrict l to some preferably very small subsetof [0,1]. At one point, Carnap even speculatedthat it would have to be fixed empirically. Unfor-tunately, some higher-order induction would thenbe required to justify the procedure for its estima-tion, and potentially, this leads to infinite regress(see Confirmation Theory; Inductive Logic).

Carnap spent 1952–54 at the Institute for Ad-vanced Study at Princeton, New Jersey, where hecontinued to work on inductive logic, often in col-laboration with John Kemeny. He also returned tothe foundations of physics, apparently motivatedby a desire to trace and explicate the relationsbetween the physical concept of entropy and anabstract concept of entropy appropriate for induc-tive logic. His discussion with physicists provedto be disappointing and he did not publish hisresults. (These were edited and published by AbnerShimony [Carnap 1977] after Carnap’s death.)

In 1954 Carnap moved to the University of Cali-fornia at Los Angeles to assume the chair that hadbecome vacant with Reichenbach’s death in 1953.There he continued to work primarily on inductive

logic, often with several collaborators, over thenext decade. There were significant modificationsof his earlier attempts to formulate a systematicinductive logic (see Carnap and Jeffrey 1971 andJeffrey 1980. An excellent introduction to this partof Carnap’s work on inductive logic is Hilpinen1975). Obviously impressed by the earlier work ofRamsey and de Finetti, Carnap (1971a) returned tothe second of his three 1950 explications of logicalprobability and emphasized the use of inductivelogic in decision problems.More importantly, Carnap, in A Basic System of

Inductive Logic (1971b and 1980), finally recog-nized that attributing probabilities to sentenceswas too restrictive. If a conceptual system usesreal numbers and real-valued functions, no lan-guage can express all possible cases using onlysentences or classes of sentences. Because of this,he now began to attribute probabilities to events orpropositions (which are taken to be synonymous).This finally brought some concordance betweenhis formal methods and those of mathematical sta-tisticians interested in epistemological questions.Propositions are identified with sets of models;however, the fields of the sets are defined usingthe atomic propositions of a formalized language.Thus, though probabilities are defined as measuresof sets, they still remain relativized to a particularformalized language. Because of this, and becausethe languages considered remain relatively simple(mostly monadic predicate languages), much of thiswork remains similar to the earlier attempts.By this point Carnap had abandoned the hope

of finding a unique c-function. Instead, he distin-guished between subjective and objective app-roaches in inductive logic. The former emphasizesindividual freedom in the choice of necessary con-ventions; the latter emphasizes the existence of lim-itations. Though Carnap characteristically claimedto keep an open mind about these two approaches,his emphasis was on finding rational a priori prin-ciples that would systematically limit the choice ofc-functions. Carnap was still working on this proj-ect when he died on September 14, 1970. He hadnot finished revising the last sections of the secondpart of the Basic System, both parts of which werepublished only posthumously.Toward the end of his life, Carnap’s concern for

political and social justice had led him to become anactive supporter of an African American civil rightsorganization in LosAngeles. According to Stegmul-ler (1972, lxvi), the ‘‘last photograph we have ofCarnap shows him in the office of this organization,in conversation with various members. He was theonly white in the discussion group.’’

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The Legacy

Thirty-five years after Carnap’s death it is easier toassess Carnap’s legacy, and that of logical empiri-cism, than it was in the 1960s and 1970s, when anew generation of analytic philosophers and philo-sophers of science apparently felt that they had toreject that work altogether in order to be able todefine their own philosophical agendas. This reac-tion can itself be taken as evidence of Carnap’sseminal influence, but, nevertheless, it is fair tosay that Carnap and logical empiricism fell into aperiod of neglect in the 1970s from which it beganto emerge only in the late 1980s and early 1990s.Meanwhile it became commonplace among philo-sophers to assume that Carnap’s projects hadfailed.Diagnoses of this failure have varied. For some it

was a result of the logical empiricists’ alleged in-ability to produce a technically acceptable criterionfor cognitive significance. For others, it was be-cause of Quine’s dicta against the concept of ana-lyticity and the analytic/synthetic distinction (seeAnalyticity; Quine, Willard Van Orman). Sometook Popper’s work to have superseded that ofCarnap and the logical empiricists (see Popper,Karl Raimund). Many viewed Kuhn’s seminalwork on scientific change to have shown that theproject of inductive logic was misplaced; they, andothers, generally regarded Carnap’s attempt to ex-plicate inductive logic to have been a failure (seeKuhn, Thomas; Scientific Change). Finally, a newschool of ‘‘scientific realists’’ attempted to escapeCarnap’s arguments against external realism (seeScientific Realism).There can be little doubt that Carnap’s project of

founding inductive logic has faltered. He neverclaimed that he had gone beyond preliminaryexplorations of possibilities, and, though there hasbeen some work since, by and large, epistemolo-gists of science have abandoned that project infavor of less restrictive formalisms, for instance,those associated with Bayesian or Neyman-Pearson statistics (see Bayesianism; Statistics, Phi-losophy of). But, with respect to every other casementioned in the last paragraph, the situation is farless clear. It has already been noted that Carnap’sfinal criterion for cognitive significance does notsuffer from any technical difficulty no matterwhat its other demerits may be. Quine’s dictaagainst analyticity no longer appear as persuasiveas they once did (Stein 1992); Quine’s preferencefor using natural—rather than formalized—language in the analysis of science has proved to

be counterproductive; and his program of natura-lizing epistemology has yet to live up to its initialpromise. Putnam’s ‘‘internal realism’’ is based onand revives Carnap’s views on ontology, and Kuhnis perhaps now better regarded as having contribu-ted significantly to the sociology rather than to theepistemology of science.

However, to note that some of the traditionallyfashionable objections to Carnap and logical em-piricism cannot be sustained does not show thatthat work deserves a positive assessment on itsown. There still remains the question: What, exact-ly, did Carnap contribute? The answer turns out tobe straightforward: The textbook picture of deduc-tive logic that is in use today is the one that Carnapproduced in the early 1940s after he came to ac-knowledge the possibility of semantics. The fixed-point lemma has turned out to be an importantminor contribution to logic. The reintroduction ofmodal logic into philosophy opened up new vistasfor Kripke and others in the 1950s and 1960s.Carnap’s views on ontology continue to influencephilosophers today. Moreover, even though theproject of inductive logic seems unsalvageable tomost philosophers, it is hard to deny that Carnapmanaged to clarify significantly the ways in whichconcepts of probability must be deployed in theempirical sciences and why the problem of in-ductive logic is so difficult. But, most of all, Carnaptook philosophy to a new level of rigor andclarity, accompanied by an open-mindedness (codi-fied in the principle of tolerance) that, unfortunate-ly, is not widely shared in contemporary analyticphilosophy.

SAHOTRA SARKAR

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——— (1934a), ‘‘Die Antinomien und die Unvollstandig-keit der Mathematik,’’ Monatshefte fur Mathematik undPhysik 41: 42–48.

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——— (1939), Foundations of Logic and Mathematics. Chi-cago: University of Chicago Press.

——— (1947),Meaning and Necessity: A Study in Semanticsand Modal Logic. Chicago: University of Chicago Press.

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——— (1950b), Logical Foundations of Probability. Chi-cago: University of Chicago Press.

——— (1952), The Continuum of Inductive Methods. Chi-cago: University of Chicago Press.

——— (1955), ‘‘Meaning and Synonymy in Natural Lan-guages,’’ Philosophical Studies 7: 33–47.

——— (1956), ‘‘The Methodological Character of Theoret-ical Concepts,’’ in H. Feigl and M. Scriven (eds.), TheFoundations of Science and the Concepts of Psychologyand Psychoanalysis. Minneapolis: University of Minne-sota Press, 38–76.

——— (1961), ‘‘On the Use of Hilbert’s e-Operator in Scien-tific Theories,’’ in Y. Bar-Hillel, E. I. J. Poznanski, M. O.Rabin, and A. Robinson (eds.), Essays on the Founda-tions of Mathematics. Jerusalem: Magnes Press, 156–164.

——— (1963a), ‘‘Intellectual Autobiography,’’ in P. A.Schilpp (ed.), The Philosophy of Rudolf Carnap. LaSalle, IL: Open Court, 3–84.

——— (1963b), ‘‘Replies and Systematic Expositions,’’ inP. A. Schilpp (ed.), The Philosophy of Rudolf Carnap. LaSalle, IL: Open Court, 859–1013.

——— (1971a), ‘‘Inductive Logic and Rational Decisions,’’in R. Carnap and R. C. Jeffrey (eds.), Studies in InductiveLogic and Probability (Vol. 1). Berkeley and LosAngeles: University of California Press, 5–31.

——— (1971b), ‘‘ABasic System of Inductive Logic, Part I,’’in R. Carnap and R. C. Jeffrey (eds.), Studies in InductiveLogic and Probability (Vol. 1). Berkeley and Los Angeles:University of California Press, 33–165.

——— (1977), Two Essays on Entropy. Berkeley and LosAngeles: University of California Press.

——— (1980), ‘‘A Basic System of Inductive Logic, PartII,’’ in R. C. Jeffrey (ed.), Studies in Inductive Logic andProbability (Vol. 2). Berkeley and Los Angeles: Univer-sity of California Press, 8–155.

Carnap, R., and R. C. Jeffrey (eds.) (1971), Studies inInductive Logic and Probability (Vol. 1). Berkeley andLos Angeles: University of California Press.

Friedman, M. (1992), ‘‘Epistemology in the Aufbau,’’Synthese 93: 191–237.

——— (1999), Reconsidering Logical Empiricism. NewYork: Cambridge University Press.

Godel, K. (1931), ‘‘Uber formal unentscheidbare Satze derPrincipia Mathematica und verwandter Systeme 1,’’Monatshefte fur Mathematik und Physik 38: 173–198.

Goodman, N. (1951), The Structure of Experience. Cam-bridge, MA: Harvard University Press.

Haack, S. (1977), ‘‘Carnap’s Aufbau: Some Kantian Reflec-tions,’’ Ratio 19: 170–175.

Hempel, C. G. (1950), ‘‘Problems and Changes in the Em-piricist Criterion of Meaning,’’ Revue Internationale dePhilosophie 11: 41–63.

Hilpinen, R. (1975), ‘‘Carnap’s New System of InductiveLogic,’’ in J. Hintikka (ed.), Rudolf Carnap, LogicalEmpiricist: Materials and Perspectives. Dordrecht, Neth-erlands: Reidel, 333–359.

Jeffrey, R. C. (ed.) (1980), Studies in Inductive Logic andProbability (Vol. 2). Berkeley and Los Angeles: Univer-sity of California Press.

Kaplan, D. (1975), ‘‘Significance and Analyticity: AComment on Some Recent Proposals of Carnap,’’ inJ. Hintikka (ed.), Rudolf Carnap, Logical Empiricist:Materials and Perspectives. Dordrecht, Netherlands:Reidel, 87–94.

Keynes, J. M. (1921), A Treatise on Probability. London:Macmillan & Co.

Lewis, C. I. (1918), A Survey of Symbolic Logic. Berkeleyand Los Angeles: University of California Press.

Putnam, H. (1994), ‘‘Comments and Replies,’’ in P. Clarkand B. Hale (eds.), Reading Putnam. Oxford: Blackwell,242–295.

Quine, W. V. O. (1951), ‘‘Two Dogmas of Empiricism,’’Philosophical Review 60: 20–43.

Richardson, A. (1998), Carnap’s Construction of the World.Cambridge: Cambridge University Press.

Roozeboom, W. (1960), ‘‘A Note on Carnap’s MeaningCriterion,’’ Philosophical Studies 11: 33–38.

Sarkar, S. (1992), ‘‘‘The Boundless Ocean of UnlimitedPossibilities’: Logic in Carnap’s Logical Syntax of Lan-guage,’’ Synthese 93: 191–237.

——— (2003), ‘‘Husserl’s Role in Carnap’s Der Raum,’’ inT. Bonk (ed.), Language, Truth and Knowledge: Contri-butions to the Philosophy of Rudolf Carnap. Dordrecht,Netherlands: Kluwer, 179–190.

Sauer, W. (1985), ‘‘Carnap’s ’Aufbau’ in KantianishcerSicht,’’ Grazer Philosophische Studien 23: 19–35.

Savage, C. W. (2003), ‘‘Carnap’s Aufbau Rehabilitated,’’ inT. Bonk (ed.), Language, Truth and Knowledge: Contri-butions to the Philosophy of Rudolf Carnap. Dordrecht,Netherlands: Kluwer, 79–86.

Shimony, A. (1992), ‘‘On Carnap: Reflections of a Meta-physical Student,’’ Synthese 93: 261–274.

Stegmuller, W. (1972), ‘‘Homage to Rudolf Carnap,’’ inR. C. Buck andR. S. Cohen (eds.),PSA 1970. Dordrecht,Netherlands: Reidel, lii–lxvi.

Stein, H. (1992), ‘‘Was Carnap Entirely Wrong, After All?’’Synthese 93: 275–295.

See also Analyticity; Confirmation Theory; Cogni-tive Significance; Conventionalism; Hahn, Hans;Hempel, Carl Gustav; Induction, Problem of; Induc-tive Logic; Instrumentalism; Logical Empiricism;Neurath, Otto; Phenomenalism; Protocol sen-tences; Quine, Willard Van Orman; Reichenbach,Hans; Scientific Realism; Schlick, Moritz; Space-Time; Verifiability; Vienna Circle

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CAUSALITY

Arguably no concept ismore fundamental to sciencethan that of causality, for investigations into cases ofexistence, persistence, and change in the naturalworld are largely investigations into the causes ofthese phenomena. Yet the metaphysics and episte-mology of causality remain unclear. For example,the ontological categories of the causal relata havebeen taken to be objects (Hume [1739] 1978), events(Davidson 1967), properties (Armstrong 1978), pro-cesses (Salmon 1984), variables (Hitchcock 1993),and facts (Mellor 1995). (For convenience, causesand effects will usually be understood as events inwhat follows.) Complicating matters, causal rela-tions may be singular (‘‘Socrates’ drinking hemlockcaused his death’’) or general (‘‘Drinking hem-lock causes death’’); hence the relatamight be tokens(e.g., instances of properties) or types (e.g., types ofevents) of the category in question. Other questionsup for grabs are: Are singular causes metaphysicallyand/or epistemologically prior to general causes orvice versa (or neither)? What grounds the intuitiveasymmetry of the causal relation? Are macrocausalrelations reducible to microcausal relations? Andperhaps most importantly: Are causal facts (e.g.,the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotem-poral relations)?

Some Issues in Philosophy of Causality:The Varieties of Causation

Causes can apparently contribute to effects in avariety of ways: by being background or standingconditions, ‘‘triggering events,’’ omissions, factorsthat enhance or inhibit effects, factors that remove acommon preventative of an effect, etc. Traditionallyaccounts of causation have focussed on triggeringevents, but contemporary accounts are increasinglyexpected to handle a greater range of this diversity.There may also be different notions of cause char-

acteristic of the domains of different sciences (seeHumphreys 1986; Suppes 1986): The seemingly in-deterministic phenomena of quantum physics mayrequire treatment different from either the seeming-ly deterministic processes of certain natural sciencesor the ‘‘quasi-deterministic’’ processes characteris-tic of the social sciences, which are presumed to be

objectively deterministic but subjectively uncertain.Another difference lies in the distinction betweenteleological (intentional, goal-oriented) and nonte-leological causality: While the broadly physicalsciences tend not to cite motives and purposes, theplant, animal, human, and social sciences often ex-plicitly do. Contemporary treatments of teleologicalcausality generally aim at avoiding the positing ofanything like entelechies or ‘‘vital forces’’ (of thesort associated with nineteenth-century accountsof biology), and also at avoiding taking teleologicalgoals to be causes that occur after their effects (seeSalmon 1989, sec. 3.8, for a discussion). In Wright’s(1976) account of ‘‘consequence etiology,’’ teleolog-ical behaviors (e.g., stalking a prey) are not causedby future catchings (which, after all, might notoccur), but rather by the fact that the behavior inquestion has been often enough successful in thepast that it has been evolutionarily selected for.Experience or inferences may also be operative inguiding behavior. While teleological causes raiseinteresting questions for the causal underpinningsof behavior (especially concerning whether anaturalistically acceptable account of intentionalitycan be given), the focus in what follows will be onnonteleological causality, reflecting the primaryconcern of contemporary philosophers of causation.

Singular vs. General CausationIs all singular causation ultimately general?

Different answers reflect different understandingsof the notion of ‘production’ at issue in the platitude‘‘Causes produce their effects.’’ In generalist (orcovering-law) accounts (see the sections on ‘‘Humeand Pearson: Correlation, Not Causation’’ and‘‘Contemporary Philosophical Accounts of Causal-ity: Generalist Accounts’’ below), causal productionis a matter of law: Roughly, event C causes event Ejust in case C and E are instances of terms in a lawconnecting events of C ’s type with events of E ’stype. The generalist interpretation is in part moti-vated by the need to ground inductive reasoning:Unless causal relations are subsumed by causallaws, one will be unjustified in inferring that eventsof C ’s type will, in the future, cause events of E ’stype. Another motivation stems from thinking that

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identifying a sequence of events as causal requiresidentifying the sequence as falling under a (possiblyunknown) law.

Alternatively, singularists (see ‘‘Singularist Ac-counts’’ below) interpret causal production as invol-ving a singular causal process (variously construed)that is metaphysically prior to laws. Singularistsalso argue for the epistemological priority of sin-gular causes, maintaining that one can identify asequence as causal without assuming that the se-quence falls under a law, even when the sequenceviolates modal presuppositions (as in Fair’s [1979]case: Intuitively, one could recognize a glass’sbreaking as causal, even if one antecedently thoughtglasses of that type were unbreakable).

Counterfactualaccounts (see ‘‘CounterfactualAc-counts’’ below) analyze singular causes in terms ofcounterfactual conditionals (as a first pass, event Ccauses event E just in case if C had not occurred,then E would not have occurred). Whether a coun-terfactual account should be considered singularist,however, depends on whether the truth of the coun-terfactuals is grounded in laws connecting types ofevents or in, e.g., propensities (objective single-casechances) understood as irreducible to laws. Yetanother option is to deny that either singular orgeneral causes are reducible to the other, and go onto give independent treatments of each type (as inSober 1984).

Reduction vs. NonreductionThere are at least three questions of reducibility

at issue in philosophical accounts of causation,which largely cut across the generalist/singularistdistinction. The first concerns whether causalfacts (e.g., the holding of causal relations) are re-ducible to noncausal facts (e.g., the holding ofcertain spatiotemporal relations). Hume’s general-ist reduction of causality (see ‘‘Hume and Pearson:Correlation, Not Causation’’ below) has a projec-tivist or antirealist flavor: According to Hume, theseeming ‘‘necessary connexion’’ between cause andeffect is a projection of a psychological habit ofassociation between ideas, which habit is formedby regular experience of events of the cause typebeing spatially contiguous and temporally prior toevents of the effect type. Contemporary neoHumeans (see ‘‘Hempel: Explanation, Not Causa-tion’’ and ‘‘Probabilistic Relevance Accounts’’below) dispense with Hume’s psychologism, focus-ing instead on the possibility of reducing causalrelations and laws to objectively and noncausallycharacterized associations between events. (Whe-ther such accounts are appropriately deemed

antirealist is a matter of dispute, one philosopher’sreductive elimination being another’s reductive in-troduction.) By way of contrast, nonreductive gen-eralists (often called realists—see ‘‘Causal Powers,Capacities, Universals, Forces’’ below) take themodally robust causal connection between eventtypes to be an irreducible feature of reality (seeRealism). Singularists also come in reductive orrealist varieties (see ‘‘Singularist Accounts’’ below).A second question of reducibility concerns

whether a given account of causation aims to pro-vide a conceptual analysis of the concept (hence toaccount for causation in bizarre worlds, containingmagic, causal action at a distance, etc.) or aims toaccount for the causal relation in the actual world,in terms of physically or metaphysically more fun-damental entities or processes. These different aimsmake a difference in what sort of cases and coun-terexamples philosophers of causation take toheart when developing or assessing theories. Acommon intermediate methodology focuses oncentral cases, leaving the verdict on far-fetchedcases as ‘‘spoils for the victor.’’A third question of reducibility concerns whether

macrocausal relations (holding between entities, orexpressed by laws, in the special sciences) are re-ducible to microcausal relations (holding betweenentities, or expressed by laws, in fundamental phys-ics). This question arises from a general desire tounderstand the ontological and causal underpin-nings of the structured hierarchy of the sciences,and from a need to address, as a special case, the‘‘problem of mental causation,’’ of whether andhow mental events (e.g., a feeling of pain) can becausally efficacious vis-a-vis certain effects (e.g.,grimacing) that appear also to be caused by thebrain events (and ultimately, fundamental physicalevents) upon which the mental events depend.Causal reductionists (Davidson 1970; Kim 1984)

suggest that mental events (more generally, macro-level events) are efficacious in virtue of superven-ing on (or being identical with) efficacious physicalevents. Many worry, however, that these appro-aches render macro-level events causally irrelevant(or ‘‘epiphenomenal’’). Nonreductive approaches tomacro-level causation come in both physicalist andnonphysicalist varieties (Wilson 1999 provides anoverview; see Physicalism). Some physicalists posita relation (e.g., the determinable/determination re-lation or proper parthood) between macro- andmicro-level events that entails that the set of causalpowers of a given macrolevel eventM (roughly, theset of causal interactions that the event, in appropri-ate circumstances, could enter into) is a proper sub-set of those of themicro-level eventP uponwhichM

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depends. In this ‘‘proper subset’’ strategy, the factthat the sets of causal powers are different providessome grounds for claiming that M is efficacious inits own right, but since each individual causal powerof M is identical with a causal power of P, the twoevents are not in causal competition. In anothernonreductive strategy—emergentism—the causalefficacy of at least some macro-level events (nota-bly, mental events) is due to their having genuinelynew causal powers not possessed by the physicalevents on which the mental events depend (seeEmergence). When the effect in question is physi-cal, such powers violate the causal closure ofthe physical (the claim that every physical effecthas a fully sufficient physical cause); but such aviolation arguably is not at odds with any cher-ished scientific principles, such as conversationlaws (see McLaughlin 1992).

Features of Causality: Asymmetry, TemporalDirection, Transitivity

Intuitively, causality is asymmetric: If event Ccauses event E, then E does not cause C. Causalityalso generally proceeds from the past to the future.How to account for these data remains unclear.The problem of explaining asymmetry is particu-larly pressing for accounts that reductively analyzecausality in terms of laws of association, for it iseasy to construct cases in which the laws are revers-ible but the causation is not (see, for example,Bromberger’s [1962] case in which the height h ofa flagpole is correlated with the length l of theshadow it casts, and vice versa, and intuitivelyh causes l but l does not cause h). Both the asym-metry and the temporal direction of causality canbe accommodated (as in Hume) by stipulativelyidentifying causal with temporal asymmetry:Causes differ from their effects in being prior totheir effects. But this approach rules out simulta-neous and backward causation, which are generallytaken to be live possibilities; and it also rules outreducing the direction of time to the (general) di-rection of causation, which some (e.g., Reichenbach1956) have wanted to do. The approach is alsomethodologically unsatisfactory, insofar as it failsto provide a basis for a unified resolution of pro-blems facing associationist accounts (e.g., the pro-blems of joint effects and of preemption discussed in‘‘Hume and Pearson: Correlation, Not Causation’’below).Other strategies use physical processes to explain

the temporal direction of causation. Reichenbachappealed to the direction of ‘‘conjunctive forks’’:processes in which a common cause produces joint

effects and, in accordance with what Reichenbachcalled ‘‘the principle of the common cause,’’ theprobabilistic dependence of the effects on eachother is ‘‘screened off ’’—goes away—when thecommon cause is taken into account. Such forksare, he claimed, always (or nearly always) open tothe future and closed to the past. Others havesuggested that the direction of causation is fixedby the direction of increasing entropy, or (morespeculatively) by the direction of quantum collapseof the wave packet. Alternatively, Price (1992) sug-gests that human experience of manipulatingcauses provides a basis for the (projected) beliefthat causality is forward directed in time (see‘‘Counterfactuals and Manipulability’’ below). Allthese accounts nonstipulatively explain the usualtemporal direction of causal processes. But neitherstipulative nor nonstipulative appeals to temporaldirection seem to explain the asymmetry of causa-tion, which intuitively has more to do with causesproducing their effects (in some robust sense of‘production’) than with causes being prior to theireffects. Nonreductive accounts in which causalityinvolves manifestations of powers or transfers ofenergy (or other conserved quantities) may be bet-ter situated to provide the required explanation, ifsuch manifestations or transfers can be understoodas directed (which remains controversial).

Another feature commonly associated with cau-sality is transitivity: If C causes D, and D causes E,then C causes E. This assumption has come intoquestion of late, largely due to the following sort ofcase (see Kvart 1991): A man’s finger is severed in afactory accident; a surgeon reattaches the finger,which afterward becomes perfectly functional. Theaccident caused the surgery, and the surgery causedthe finger’s functionality; but it seemsodd to say thatthe accident caused the finger’s functionality. Theprecise bearing of such cases on the transitivity claimremains unclear (see Hall 2000 for a discussion).

Challenges to Causality: Galileo, Newton, andMaxwell—How, Not Why

From the ancient through modern periods, ac-counts of natural phenomena proceeded by citingthe powers and capacities of agents, bodies, andmechanisms to bring about effects (see Hankinson1998; Clatterbaugh 1999). Galileo’s account of thephysics of falling bodies initiated a different ap-proach to scientific understanding, which becamea matter of determining how certain measurablequantities were functionally correlated (the ‘‘how’’of things, or the kinematics), as opposed to deter-mining the causal mechanisms responsible for these

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correlations (the ‘‘why’’ of things, or the dynam-ics). This descriptive approach enabled scientifictheories to be formulated with relatively high pre-cision, which in turn facilitated predictive and ret-rodictive success; by way of contrast, explanationsin terms of (often unobservable) causal mechan-isms came to be seen as explanatorily otiose atbest and unscientific at worst.

Newton’s famous claim in the Principia ([1687]1999), ‘‘Hypotheses non fingo’’ (‘‘I frame nohypotheses’’), regarding gravitation’s ‘‘physicalcauses and seats’’ is often taken as evidence that headvocated a descriptivist approach (though hespeculated at length on the causes of gravitationalforces in the Optics). And while Maxwell drewheavily upon Faraday’s qualitative account ofcausally efficacious electromagnetic fields (andassociated lines of force) in the course of develop-ing his theories of electricity and magnetism, helater saw such appeals to underlying causes as heu-ristic aids that could be dropped from the finalquantitative theory.

Such descriptivist tendencies have been encour-aged by perennial worries about the metaphysicaland epistemological presuppositions of explicitlycausal explanations (see ‘‘Causal Powers, Capaci-ties, Universals, Forces’’ below) and the concomi-tant seeming availability of eliminativist orreductivist treatments of causal notions in scientificlaws. For example, Russell (1912) influentially ar-gued that since the equations of physics do notcontain any terms explicitly referring to causes orcausal relations and moreover (in conflict with thepresumed asymmetry of causality) appear to befunctionally symmetric (one can write a ¼ f /m aswell as f ¼ ma), causality should be eliminated as‘‘a relic of a bygone age.’’ Jammer (1957) endorseda view in which forcebased dynamics is a sophisti-cated form of kinematics, with force terms beingmere ‘‘methodological intermediaries’’ enabling theconvenient calculation of quantities (e.g., accelera-tions) entering into descriptions. And more recent-ly, van Fraassen (1980) has suggested that whileexplanations going beyond descriptions may servevarious pragmatic purposes, these have no onto-logical or causal weight beyond their ability to‘‘save the phenomena.’’

Whether science really does, or should, focus onthe (noncausally) descriptive is, however, deeplycontroversial. Galileo himself sought for explana-tory principles going beyond description (seeJammer 1957 for a discussion), and notwithstand-ing Newton’s professed neutrality about theirphysical seats, he took forces to be the ‘‘causalprinciple[s] of motion and rest.’’ More generally,

notwithstanding the availability of interpretationsof scientific theories as purely descriptive, there arecompelling reasons (say, the need to avoid a sus-pect action at a distance) for taking the causallyexplanatory posits of scientific theories (e.g., fieldsand forces) ontologically seriously. The deeperquestions here, of course, concern how to assessthe ontological and causal commitments of scien-tific theories; and at present there is no philosophi-cal consensus on these important matters. In anycase it is not enough, in assessing whether causesare implicated by physical theories, to note thatterms like ‘‘cause’’ don’t explicitly appear in theequations of the theory, insofar as the commitmentsof a given theory may transcend the referents of theterms appearing in the theory, and given that manyterms—force, charge, valence—that do appear aremost naturally defined in causal terms (‘force,’ forexample, is usually defined as that which causesacceleration). It is also worth noting that the appar-ent symmetry of many equations, as well as the factthat cause terms do not explicitly appear in scien-tific equations, may be artifacts of scientists’ usingthe identity symbol as an all-purpose connectivebetween functional quantities, which enables thequantities to be manipulated using mathematicaltechniques but is nonetheless implicitly understoodas causally directed, as in f ¼ ma.Nor does scientific practice offer decisive illumi-

nation of whether scientific theorizing is or is notcommitted to causal notions: As with Maxwell, itremains common for scientists to draw upon ap-parently robustly causal notions when formulatingor explaining a theory, even while maintaining thatthe theory expresses nothing beyond descriptivefunctional correlations of measurable quantities.Perhaps it is better to attend to what scientists dorather than what they say. That they rarely leavematters at the level of descriptive laws linkingobservables is some indication that they are notconcerned with just the ‘‘how’’ question—though,to be sure, the tension between descriptive andcausal/explanatory questions may recur at levelsbelow the surface of observation.

Hume and Pearson: Correlation, Not Causation

The Galilean view of scientific understanding asinvolving correlations among measurable quanti-ties was philosophically mirrored in the empiricistview that all knowledge (and meaning) is ultimatelygrounded in sensory experience (see Empiricism).The greatest philosophical challenge to causalitycame from Hume, who argued that there is no

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experience of causes being efficacious, productive,or powerful vis-a-vis their effects; hence ‘‘we onlylearn by experience the frequent conjunction ofobjects, without being ever able to comprehendany thing like connexion between them’’ ([1748]1993, 46). In place of realistically interpreted ‘‘pro-ducing’’ theories of causation (see Strawson 1987for a taxonomy), Hume offered the first regularitytheory of causation, according to which event Ccauses event E just in case C and E occur, andevents of C ’s type have (in one’s experience) beenuniversally followed by, and spatially contiguousto, events of E ’s type. (As discussed, such constantconjunctions were the source of the psychologicalimprinting that was, for Hume, the ultimate locusof causal connection.) Hume’s requirement of con-tiguity may be straightforwardly extended to allowfor causes to produce distant effects, via chains ofspatially contiguous causes and effects.Hume’s requirement of universal association is

not sufficient for causation (night always followsday but night does not cause day). Nor is Hume’srequirement necessary, for even putting asidethe requirement that one experience the associationin question, there are many causal events that hap-pen only once (e.g., the big bang). The immediatemove of neo-Humeans (e.g., Hempel and Oppen-heim 1948; Mackie 1965) is to understand the gen-eralist component of the account in terms of lawsof nature, which express the lawful sufficiency ofthe cause for the effect, and where (reflectingHume’s reductive approach) the sufficiency is notto be understood as grounded in robust causalproduction. One wonders, though, what is ground-ing the laws in question if associations are neithernecessary nor sufficient for their holding and ro-bust production is not allowed to play a role. If thelaws are grounded in brute fact, it is not clear thatthe reductive aim has been served (but see thediscussion of Lewis’s account of laws, below).In any case, neo-Humean accounts face several

problems concerning events that are inappropriate-ly deemed causes (‘‘spurious causes’’). One is theproblem of joint effects, as when a virus causes firsta fever, and then independently causes a rash: Herethe fever is lawfully sufficient for, hence incorrectlydeemed a cause of, the rash. Another involvesviolations of causal asymmetry: Where events ofthe cause’s type are lawfully necessary for eventsof the effect’s type, the effect will be lawfully suffi-cient for (hence inappropriately deemed a cause of )the cause. Cases of preemption also give rise tospurious causes: Suzy’s and Billy’s rockthrowingsare each lawfully sufficient for breaking the bottle;but given that Suzy’s rock broke the bottle (thereby

preempting Billy’s rock from doing so), how is oneto rule out Billy’s rockthrowing as a cause?

The above cases indicate that lawful sufficiencyalone does not satisfy causality. One response is toadopt an account of events in which these are finelyindividuated, so that, for example, the bottlebreak-ing resulting from Suzy’s rockthrowing turns out tobe of a different event type than a bottlebreakingresulting from Billy’s rockthrowing (in which caseBilly’s rockthrowing does not instantiate a rock-throwing–bottlebreaking law, and so does notcount as a cause). Another response incorporatesa proviso that the lawful sufficiency at issue is thatof the circumstances (as in Mackie’s ‘‘INUS’’ con-dition account, in which a cause is an insufficientbut necessary part of a condition that is, in thecircumstances, unnecessary but sufficient for theeffect).

Nor is lawful sufficiency alone necessary for cau-sality, as the live possibility of irreducibly probabi-listic causality indicates. This worry is usuallysidestepped by a reconception of laws accordingto which these need express only some lawlike pat-tern of dependence; but this reconception makes ityet more difficult for regularity theorists to distin-guish spurious from genuine causes and laws (see‘‘Probabilistic Relevance Accounts’’ below fordevelopments). One neo-Humean response is toallow certain a priori constraints to enter into de-termining what laws there are in a world (as in the‘‘best system’’ theory of laws of Lewis 1994) inwhich the laws are those that systematize the phe-nomena with the best combination of (predictive)strength and (formal) simplicity, so as to accom-modate probabilistic (and even uninstantiated)laws (see also ‘‘Hempel: Explanation, Not Causa-tion’’ below).

The view that causation is nothing above (appro-priately complex) correlations was widespread fol-lowing the emergence of social statistics in thenineteenth century and was advanced by KarlPearson, one of the founders of modern statistics,in 1890 in The Grammar of Science. Pearson’s en-dorsement of this view was, like Hume’s, inspiredby a rejection of causality as involving mysteriousproductive powers, and contributed to causes (asopposed to associations) being to a large extentexpunged from statistics and from the manysciences relying upon statistics. An intermediateposition between these extremes, according towhich causes are understood to go beyond correla-tions but are not given any particular metaphysicalinterpretation (in particular, as involving pro-ductive powers), was advanced by the evolutio-nary biologist Sewall Wright, the inventor of path

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analysis. Wright (1921) claimed that path analysisnot only enabled previously known causal relationsto be weighted, but moreover enabled the testing ofcausal hypotheses in cases where the causal rela-tions were (as yet) unknown. Developed descen-dants and variants of Wright’s approach havefound increasing favor of late (see ‘‘Bayesian Net-works and Causal Models’’ below), contributing tosome rehabilitation of the notion of causality in thesocial sciences.

Hempel: Explanation, Not Causation

Logical empiricists were suspicious of causationunderstood as a metaphysical connection in nature;instead they located causality in language, in-terpreting causal talk as talk of explanation (seeSalmon 1989 for a discussion). On Hempel andOppenheim’s (1948) influential D-N (deductive-nomological) model of scientific explanation,event C explains event E just in case a statementexpressing the occurrence of E is the conclusion ofan argument with premises, one of which expressesthe holding of a universal generalization to theeffect that events of C ’s type are associated withevents of E ’s type and another of which expressesthe fact that C occurred (see Explanation).Imposing certain requirements on universal gen-eralizations (e.g., projectibility) enabled the D-Naccount to avoid cases of spurious causation dueto accidental regularities (S ’s being a screw inSmith’s car does not explain why S is rusty, evenif all the screws in Smith’s car are rusty). Hempelsuggested various strategies for how the D-N ac-count might avoid admitting spurious causes(explanations) associated with cases of asymmetryand preemption. For example, if one is willing tolet causal asymmetry depend on temporal asymme-try, one can avoid admitting the length of the shad-ow as explaining the height of the flagpole bynoting that the length of the shadow at T dependson the height of the flagpole at T �e, while no suchrelationship holds between the height of the flag-pole at T and the length of the shadow at T �e.

To accommodate the possibility of irreduciblyprobabilistic associations, as well as explanations(characteristic of the social sciences) proceedingunder conditions of partial uncertainty, Hempel(1965) proposed an inductive-statistical (I-S)model, in which event C explains event E if Coccurs and it is an inductively grounded law thatthe probability of an event of type E given an eventof type C is high (see Explanation; InductiveLogic). This account is subject to counterexamplesin which a cause produces an effect but with a

low probability, as in Scriven’s case (discussed byhim prior to Hempel’s extension, and developed inScriven 1975), where the probability of paresisgiven syphilis is low, but when paresis occurs, syph-ilis is the reason. A similar point applies to manyquantum processes. Such cases gave rise to twodifferent approaches to handling probabilistic ex-planation (or causation, by those inclined to acceptthis notion). One approach (see Railton 1978)locates probabilistic causality in propensities; theother (see ‘‘Probabilistic Relevance Accounts’’ be-low) in more sophisticated probabilistic relations.At this point the line between accounts that are

reductive (in the sense of reducing causal to non-causal goings-on) and nonreductive, as well as theline between singularist and generalist accounts,begins to blur. For while a propensity-based ac-count of causality initially looks nonreductive andsingularist, some think that propensities can beaccommodated in a sophisticated associationist ac-count of laws; and while an account based on rela-tions of probabilistic relevance initially looksreductive and generalist, whether it is so dependson how the probabilities are interpreted (as givenby frequencies, irreducible propensities, etc.).

Contemporary Philosophical Accounts ofCausality: Generalist Accounts

Probabilistic Relevance AccountsA natural response to Scriven-type cases is to

understand positive causal relevance in terms ofprobability raising (Suppes 1970): Event C causesevent E just in case the probability of events of E ’stype is higher given events of C ’s type than with-out. (Other relevance relations, such as being anegative causal factor, can be defined accordingly.)A common objection to such accounts (see Rosen1978) proceeds by constructing cases ‘‘the hardway,’’ in which it seems that causes lower the prob-ability of their effects (e.g., where a mishit golf ballricochets off a tree, resulting in a hole-in-one; orwhere a box contains a radioactive substance S thatproduces decay particles but the presence of Sexcludes the more effective radioactive substanceS0). Such cases can often be handled, however, bylocating a neutral context (where the golf ball is nothit at all, or where no radioactive substance is inthe box) relative to which events of the given typedo raise the probability of events of the effect type.A more serious problem for probability-raising

accounts is indicated by Simpson’s paradox,according to which any statistical relationship be-tween two variables may be reversed by includingadditional factors in the analysis. The ‘‘paradox’’

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reflects the possibility that a variable C can bepositively correlated with a variable E in a popula-tion and yet C be negatively correlated with E inevery partition of the population induced by a thirdvariable X. Just this occurred in the Berkeley sexdiscrimination case. Relative to the population ofall men and women applying to graduate school atthe University of California, Berkeley, being male(C ) was positively correlated with being admitted(E ). But relative to every partition of the popula-tion containing the men and women applying to aparticular department (X ), this correlation was re-versed. In this case the difference between the gen-eral and specific population statistics reflected thefact that while in every department it was easier forwomen to be admitted than men, women weremore likely to apply to departments that wereharder (for everyone) to get into. The general pop-ulation statistic was thus confounded: Being amale, simpliciter, was not in fact causally relevantto getting into graduate school at UC Berkeley;rather (assuming no other confounding was atissue), applying to certain departments ratherthan others was what was relevant.To use probabilistic accounts as a basis for test-

ing hypotheses and making predictions—and espe-cially in order to identify effective strategies(courses of action) in the social sciences and, in-deed, in everyday life—statistical confoundingneeds to be avoided. Cartwright (1979) suggestedthat avoiding confounding requires that the rele-vant probabilities be assessed relative to back-ground contexts within which all other causalfactors (besides the variable C, whose causal rele-vance is at issue) are held fixed. (Of course, reduc-tionists need to be able to specify these backgroundcontexts without appealing to distinctly causal fac-tors; see below.) Opinions differ regarding whetherevents of type C must raise the probability ofevents of type E in at least one such context, in amajority of contexts, or in every such context. Soone might take C to be a positive causal factor forE just in case p(E |C ^Xi) � p(E |C ^Xi) for allbackground contexts Xi, with strict inequality forat least one Xi. In this approach, smoking would bea positive causal factor for having lung cancer justin case smoking increases the chance of lung cancerin at least one background context and does notlower it in any background context.Practically, Cartwright’s suggestion has the dis-

advantage that one is frequently not in a positionto control for all alternative causal factors (thoughin some circumstances one can avoid having to dothis; see ‘‘Bayesian Networks and Causal Models’’below). Philosophically, the requirement threatens

reductive versions of probabilistic accounts withcircularity. Attempts have been made to provide anoncircular means of specifying the relevant back-ground contexts (e.g., Salmon 1984), but it is ques-tionable whether these attempts succeed, and manyare presently prepared to agree with Cartwright:‘‘No causes in, no causes out.’’

As mentioned, probabilistic accounts may ormay not be reductive, depending on whether theprobabilities at issue are understood as grounded inassociations (as in Suppes 1970) or else in powers,capacities, or propensities (as in Humphreys 1989and Cartwright 1989). In the latter interpretation,further divisions are introduced: If the propensitiesare taken to be irreducible to laws (as in Cart-wright’s account), then the associated probabilisticrelevance account is more appropriately deemedsingularist. Complicating the taxonomy here is thefact that most proponents of probabilistic accountsare not explicit as regards what analysis should begiven of the probabilities at issue.

Bayesian Networks and Causal ModelsPhilosophical worries concerning whether statis-

tical information adequately tracks causal influenceare echoed in current debates over the interpreta-tion of the statistical techniques used in the socialsciences. As noted above (‘‘Hume and Pearson:Correlation, Not Causation’’), these techniqueshave frequently been interpreted as relating exclu-sively to correlations, but increasingly researchersin computer science, artificial intelligence, and sta-tistics (see Spirtes, Glymour, and Scheines 1993;Pearl 2000) have developed nonreductive interpre-tations of these approaches as encoding explicitlycausal information and that appear to lead to im-proved hypothesis testing and prediction of effectsunder observation and intervention.

Another advantage claimed for such accounts isthat they provide a means of avoiding confoundingwithout imposing the often impracticable require-ment that the relevant probabilities be assessedagainst background contexts taking into accountall causal factors, it rather being sufficient to takeinto account all common causal factors. As a simpleillustration, suppose that A and B are known tocausally influence C, as in Figure 1.

To judge whether D influences C, Cartwrightgenerally recommends holding fixed both A andB, while Spirtes et al. (1993) instead recommendholding fixed only A. Cartwright allows, however,that attention to just common causal factors ispossible when the causal Markov condition (dis-cussed below) holds. As will be seen shortly, this

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condition must hold in order to implement thecausal modeling approach. So, the restriction tocommon causal factors is not really an advantageover Cartwright’s account.

In the causal modeling approach, one startswith a set of variables (representing properties)and a probability distribution over the variables.This probability distribution, partially interpretedwith prior causal knowledge, is assumed to reflect acausal structure (a set of laws expressing the causalrelations between the variables, which laws may beexpressed either graphically or as a set of structur-ally related functional equations). Given that cer-tain conditions (discussed below) hold between theprobabilities and the causal structure, algorithmictechniques are used to generate the set of all causalstructures consistent with the probabilities and theprior causal knowledge. Techniques also exist forextracting information regarding the results ofinterventions (corresponding to manipulations ofvariables).

While causal modeling approaches may lead toimproved causal inference concerning complex sys-tems (in which case they are of some epistemologi-cal interest), it is unclear what bearing they have onthe metaphysics of causality. Spirtes et al. (1993)present their account not so much as an analysis ofcausality as a guide to causal inference. Pearl(2000), however, takes the appeal to prior causalintuitions to indicate that causal modelingapproaches are nonreductive (and moreover basedon facts about humans’ cognitive capacities tomake effective causal inferences in simple cases).In any case, the potential of causal models to pro-vide a basis for a general theory of causality islimited by the fact that certain strong conditionsneed to be in place in order for the algorithms to becorrectly applied.

One of these is the causal Markov condition (ofwhich Reichenbach’s [1956] ‘‘principle of the com-mon cause’’ was a special case), which says thatonce one conditions on the complete set Pn

of ‘‘causal parents’’ (direct causes) of a variableV, V will be probabilistically independent of allother variables except V ’s descendants; that is, for

all variables X, where X is not one of V ’s des-cendants, P(V | Pn^X ) ¼ P(V | Pn). (In particular,where V is a joint effect, conditioning on the causalparents of V screens off the probabilistic influenceof the other joint effects on V.) Here again there isthe practical problem that in the social sciences,where the approaches are supposed to be applica-ble, one is often not in a position to specify stateswith sufficient precision to guarantee that thecondition is met. A metaphysical problem is that(contrary to Reichenbach’s apparent assumptionthat the condition holds in all cases involving acommon cause of joint effects) the causal Markovcondition need not hold in cases of probabilisticcausation: When a particle may probabilisticallydecay either by emitting a high-energy electronand falling into a lowenergy state or by emittinga low-energy electron and falling into a differentenergy state, the joint effects in either case willnot be probabilistically independent of each other,even conditioning on the cause; and certain casesof macrocausation appear also to violate thecondition.A second assumption of the causal modeling

technique is what Spirtes et al. (1993) call ‘‘faith-fulness’’ (also known as ‘‘stability’’ in Pearl 2000),according to which probabilistic dependenciesfaithfully reveal causal connections. In particular,if Y is probabilistically independent of X, given X ’sparents, then X is assumed not to cause Y. Again,this condition cannot be assumed to hold in allcases, since some variables (properties) may some-times prevent and sometimes produce an effect (aswhen birth control pills are a cause of thrombosisyet also prevent thrombosis, insofar as pregnancycauses thrombosis and the pills prevent pregnancy).In circumstances where the positive and negativecontributions of X to Y are equally effective, theprobabilistic dependence of effect on cause maycancel out, and thus X may inappropriately betaken not to be causally relevant to Y.

Causal Powers, Capacities, Universals, ForcesAs mentioned, some proponents of probabilistic

relevance accounts endorse metaphysical interpre-tations of the probabilities at issue. Such positionsfall under the broader category of nonreductive(‘‘realist’’) covering-law theories, in which laws ex-press (or are grounded in) more than mere associa-tions. The job such accounts face is to provide analternative basis for causal laws. Among other pos-sibilities, these bases are taken to be relations ofnecessitation or ‘‘probabilification’’ among univer-sals (Dretske 1977; Tooley 1977; Armstrong 1978),

Fig. 1.

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(law-based) capacities or powers associated withobjects or properties (Shoemaker 1980; Martin1993), or fundamental forces or interactions(Bohm 1957; Strawson 1987).Such accounts sidestep many of the problems

associated with reductive coveringlaw accounts.Since laws are not just a matter of association, arealist has the means to deny, in the virus–fever–rash case, that there is a law connecting fevers withrashes; similarly, in cases of preemption a realistmay claim that, for example, Billy’s rockthrowingand the bottle’s breaking did not instance the law inquestion (even without endorsing a fine-grainedaccount of event individuation). Of course, muchdepends here on the details of the proposed ac-count of laws. In the Dretske-Tooley-Armstrongaccount, causal laws are contingent, brute relationsbetween universals. Some find this less than satisfy-ing from a realist point of view, insofar as it iscompatible with, for example, the property of hav-ing spin 1 bestowing completely different causalpowers (say, all those actually bestowed by havingspin 1

2) on its possessing particulars. Other realists

are more inclined to see the nature of propertiesand particulars as essentially dependent on thecausal laws that actually govern them, a viewthat is quite plausible for scientific entities: ‘‘[C]ausal laws are not like externally imposed legalrestrictions that, so to speak, merely limit thecourse of events to certain prescribed paths . . . .[T]he causal laws satisfied by a thing . . . are inex-tricably bound up with the basic properties of thething which helps to define what it is’’ (Bohm1957, 14).The primary problem facing realist accounts is

that they require accepting entities and relations(universals, causal powers, forces) that many phi-losophers and scientists find metaphysically ob-scure and/or epistemologically inaccessible. Howone evaluates these assessments often depends onone’s other commitments. For example, many tra-ditional arguments against realist accounts (e.g.,Hume’s arguments) are aimed at showing thatthese do not satisfy a strict epistemological stan-dard, according to which the warranted posit of acontingent entity requires that the entity be directlyaccessible to experience (or a construction fromentities that are so accessible). But if inference tothe existence of an unexperienced entity (as the bestexplanation of some phenomena) is at least some-times an acceptable mode of inference, such astrict epistemological standard (and associatedarguments) will be rejected; and indeed, positivearguments for contemporary realist accounts ofcausality generally proceed via such inferences to

the best explanation—often of the patterns of asso-ciation appealed to by reductivist accounts.

Singularist Accounts

Singularists reject the claim that causes follow lawsin the order of explanation, but beyond this thereis considerable variety in their accounts. ContraHume, Anscombe (1971) takes causation to be a(primitive) relation that may be observed in cut-tings, pushings, fallings, etc. It is worth noting thata primitivist approach to causality is compatiblewith even a strict empiricism (compare Hume’sprimitivist account of the resemblance relation).The empiricist Ducasse (1926) also locates causa-tion in singular observation, but nonprimitively:A cause is the change event observed to be im-mediately prior and spatiotemporally contiguousto an effect event. While interesting in allowingfor a nonassociative, nonprimitivist, empiricist cau-sality, Ducasse’s account is unsatisfactory in allow-ing only the coarse-grained identification of causes(as some backward temporal segment of the entireobserved change); hence it fails to account for mostordinary causal judgments. Note that singularistsbasing causation on observation need not assertthat one’s knowledge of causality proceeds onlyvia observations of the preferred sort; they rathergenerally maintain that such experiences are suffi-cient to account for one’s acquiring the concept ofcausation, then allow that causation need not beobserved and that confirming singular causalclaims may require attention to associations.

Another singularist approach takes causation tobe theoretically inferred, as that relation satisfying(something like) the Ramsey sentence consisting ofthe platitudes about causality involving asymme-try, transitivity, and so on (see Tooley 1987). Oneproblem here is that, as may be clear by now, suchplatitudes do not seem to uniformly apply to allcases. Relatedly, one may wonder whether they areconsistent; given the competing causal intuitionsdriving various accounts of causality, it would besurprising if they were.

Finally, a wide variety of singularist accountsunderstand causality in terms of singular processes.Such accounts are strongly motivated by the intui-tion that in a case of preemption such as that ofSuzy and Billy, what distinguishes Suzy’s throw as acause is that it initiates a process ending in the bottlebreaking, while the process initiated by Billy’s thrownever reaches completion (see Menzies 1996 for adiscussion). Commonly, process singularists at-tempt (like Ducasse) to provide a nonprimitivistcausality that is both broadly empiricist, in not

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appealing to any properly metaphysical elements,and nonassociationist, in recognition of the diffcul-ties that associationist accounts have (both withpreemption and with distinguishing genuine causal-ity from accidental regularity). Hence they typicallyfill in the ‘‘process’’ intuition by identifying causal-ity with fundamental physical processes, includingtransfers or interactions, as in Fair’s (1979) accountof causation as identical with the transfer of energymomentum, Salmon’s (1984) ‘‘mark transmission’’account, and Dowe’s (1992) account in which thetransfer of any conserved quantity will suffice.

An objection to the claim that physical proce-sses are sufficient for causality is illustrated byCartwright’s (1979) case of a plant sprayed withherbicide that improbably survives and goes on toflourish (compare also Kvart’s 1991 finger-severingcase, discussed previously). While transfers andinteractions of the requisite sort can be tracedfrom spraying to flourishing, intuitively the formerdid not cause the latter; however, accepting thatthe spraying did cause the flourishing may not bean overly high price to pay.Adeeperworry concernsthe epistemological question of how accountsof physical process link causation understood asinvolving theoretical relations or processes offundamental physics with causation as ordinarilyexperienced. Fair suggests that ordinary experienceinvolvesmacroprocesses,which are in turn reducibleto the relevant physical processes; but even sup-posing that such reductions are in place, ordinarycausal judgments do not seem to presuppose them.

Counterfactual Accounts

Counterfactual accounts of causality take as theirstarting point the intuition that a singular causemakes an important difference in what happens.As a first pass, C causes E (where C and E areactually occurring events) only if, were C not tooccur, then E would not occur. As a second pass, Ccauses E only if C and E are connected by a chainof such dependencies (see Lewis 1973), so as toensure that causation is transitive (that is, causa-tion is the ‘‘ancestral,’’ or transitive closure, ofcounterfactual dependence). In addition to the re-quirement of counterfactual necessity of causes foreffects, counterfactual accounts also commonlyimpose a requirement of counterfactual sufficiencyof causes for effects: If C were to occur, thenE would occur. Insofar as counterfactual accountsare standardly aimed at reducing causal to non-causal relations, and given plausible assumptionsconcerning evaluation of counterfactuals, thelatter requirement is satisfied just by C and E ’s

actually occurring (which occurrences, as above,are assumed); hence standard counterfactual acc-ounts do not have a nontrivial notion of coun-terfactual sufficiency. A nontrivial notion ofcounterfactual sufficiency can be obtained by ap-peal to nested counterfactuals (see Vihvelin 1995):C causes E only if, if neither C nor E had occu-rred, then (if C had occurred, then E would haveoccurred).

Problems, Events, and BacktrackersWhile counterfactual accounts are often moti-

vated by a desire to give a reductive account ofcausality that avoids problems with reductive cov-ering-law accounts (especially those of joint effectsand of preemption), it is unclear whether counter-factual accounts do any better by these problems.First, consider the problem of joint effects. Sup-pose a virus causes first a fever, then a rash, andthat the fever and rash could only have been causedby the virus. It seems correct to reason in thefollowing ‘‘backtracking’’ fashion: If the fever hadnot occurred, then the viral infection would nothave occurred, in which case the rash wouldnot have occurred. But then the counterfactual‘‘If the fever had not occurred, the rash would nothave occurred’’ turns out true, which here meansthat the fever causes the rash, which is incorrect.Proponents of counterfactual accounts haveresponses to these objections, which require accept-ing controversial accounts of the truth conditionsfor counterfactuals (see Lewis 1979). Even so, theresponses appear not to succeed (see Bennett 1984for a discussion).Second, consider the problem of preemption. In

the Suzy-Billy case, it seems correct to reason thatif Suzy had not thrown her rock, then Billy’s rockwould have gotten through and broken the bottle.Hence the counterfactual ‘‘If Suzy’s throw had notoccurred, the bottlebreaking would not have oc-curred’’ turns out false; so Suzy’s rockthrowingturns out not to be a cause, which is incorrect. Incases (as here) of so-called ‘‘early preemption,’’where it makes sense to suppose that there was anintermediate event D between the effect and thecause on which the effect depended, this resultcan be avoided: Although the breaking does notcounterfactually depend on Suzy’s rockthrowing,there is a chain of counterfactual dependence link-ing the breaking to Suzy’s rockthrowing (and nosuch chain linking the breaking to Billy’s), and soher throw does end up being a cause (and Billy’sdoes not). But the appeal to an intermediate eventseems ad hoc and in any case cannot resolve cases

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of ‘‘late preemption.’’ Lewis (developing an ideabroached in Paul 1998) eventually responded tosuch cases by allowing that an event may becounted as a cause if it counterfactually influencesthe mode of occurrence of the effect (e.g., how orwhen it occurs), as well as if it counterfactuallyinfluences the occurrence of the effect, simpliciter.

Counterfactuals and ManipulabilityWhere counterfactual accounts may be most use-

ful is in providing a basis for understanding orformalizing the role that manipulability plays inthe concept of causation. One such approach seescounterfactuals as providing the basis for an epis-temological, rather than a metaphysical, account ofcausation (see Pearl 2000 for a discussion). Theidea here is that counterfactuals nicely model therole manipulability (actual or imagined) plays incausal inference, for a natural way to determinewhether a counterfactual is true is to manipulateconditions so as to actualize the antecedent. An-other approach takes counterfactuals to provide abasis for a generalist account of causal explanation(see Woodward 1997), according to which suchexplanations track stable or invariant connectionsand the notion of invariance is understood none-pistemologically in terms of a connection’s con-tinuing to hold through certain counterfactual (notnecessarily human) ‘‘interventions.’’ Whether thenotion of manipulability is itself a causal notion,and so bars the reduction of causal to noncausalfacts, is still an open question.

JESSICA WILSON

References

Anscombe, G. E. M. (1971), Causality and Determination.Cambridge: Cambridge University Press.

Armstrong, David M. (1978), Universals and Scientific Re-alism, vol. 2: A Theory of Universals. Cambridge: Cam-bridge University Press.

Bennett, Jonathan (1984), ‘‘Counterfactuals and TemporalDirection,’’ Philosophical Review 93: 57–91.

Bohm, David (1957), Causality and Chance in Modern Phys-ics. London: Kegan Paul.

Bromberger, Sylvain (1962), ‘‘What Are Effects?’’ inRonald J. Butler (ed.), Analytical Philosophy, vol. 1.Oxford: Oxford University Press.

Cartwright, Nancy (1979), ‘‘Causal Laws and EffectiveStrategies,’’ Nous 13: 419–438.

——— (1989), Nature’s Capacities and Their Measurement.Oxford: Clarendon Press.

Clatterbaugh, Kenneth (1999), The Causation Debate inModern Philosophy, 1637–1739. New York: Routledge.

Davidson, Donald (1967), ‘‘Causal Relations,’’ Journal ofPhilosophy 64: 691–703. Reprinted in Davidson (2001),Essays on Actions and Events. Oxford: Oxford UniversityPress, 149–162.

——— (1970), ‘‘Mental Events,’’ in L. Foster and J. Swan-son (eds.), Experience and Theory. Amherst: Mass-achusetts University Press. Reprinted in Davidson(2001), Essays on Actions and Events. Oxford: OxfordUniversity Press, 207–224.

Dowe, Phil (1992), ‘‘Wesley Salmon’s Process Theory ofCausality and the Conserved Quantity Theory,’’ Philos-ophy of Science 59: 195–216.

Dretske, Fred (1977), ‘‘Laws of Nature,’’ Philosophy ofScience 44: 248–268.

Ducasse, C. J. (1926), ‘‘On the Nature and Observability ofthe Causal Relation,’’ Journal of Philosophy 23: 57–68.

Fair, David (1979), ‘‘Causation and the Flow of Energy,’’Erkenntnis 14: 219–250.

Hall, Ned (2000), ‘‘Causation and the Price of Transitivity,’’Journal of Philosophy 97: 198–222.

Hankinson, R. J. (1998), Cause and Explanation in AncientGreek Thought. Oxford: Oxford University Press.

Hempel, Carl (1965), In Aspects of Scientific Explanationand Other Essays in the Philosophy of Science. NewYork: Free Press.

Hempel, Carl, and Paul Oppenheim (1948), ‘‘Studies in theLogic ofExplanation,’’Philosophy ofScience15: 135–175.

Hitchcock, Christopher (1993), ‘‘A Generalized Probabilis-tic Theory of Causal Relevance,’’ Synthese 97: 335–364.

Hume, David ([1739] 1978), A Treatise of Human Nature.Edited by L. A. Selby-Bigge. Oxford: Oxford UniversityPress.

——— ([1748] 1993), An Enquiry Concerning Human Un-derstanding. Edited by Eric Steinberg. Indianapolis:Hackett Publishing.

Humphreys, Paul (1986), ‘‘Causation in the Social Sciences:An Overview,’’ Synthese 68: 1–12.

——— (1989), The Chances of Explanation. Princeton, NJ:Princeton University Press.

Jammer, Max (1957), Concepts of Force. Cambridge, MA:Harvard University Press.

Kim, Jaegwon (1984), ‘‘Epiphenomenal and SupervenientCausation,’’ Midwest Studies in Philosophy IX: Causa-tion and Causal Theories, 257–270.

——— (1993), Supervenience and Mind: Selected Philosoph-ical Essays. Cambridge: Cambridge University Press.

Kvart, Igal (1991), ‘‘Transitivity and Preemption of CausalRelevance,’’ Philosophical Studies LXIV: 125–160.

Lewis, David (1973), ‘‘Causation,’’ Journal of Philosophy70: 556 –567.

——— (1979), ‘‘Counterfactual Dependence and Time’sArrow,’’ Nous 13:455– 476.

——— (1983), Philosophical Papers, vol. 1. Oxford: OxfordUniversity Press.

——— (1994), ‘‘Humean Supervenience Debugged,’’ Mind1: 473– 490.

Mackie, John L. (1965), ‘‘Causes and Conditions,’’ Ameri-can Philosophical Quarterly 2: 245–264.

Martin, C. B. (1993), ‘‘Power for Realists,’’ in Keith Cam-bell, John Bacon, and Lloyd Reinhardt (eds.), Ontology,Causality, and Mind: Essays on the Philosophy of D. M.Armstrong. Cambridge: Cambridge University Press.

McLaughlin, Brian (1992), ‘‘The Rise and Fall of BritishEmergentism,’’ in Ansgar Beckerman, Hans Flohr, andJaegwon Kim (eds.), Emergence or Reduction? Essays onthe Prospects of Nonreductive Physicalism. Berlin: DeGruyter, 49–93.

Mellor, D. H. (1995), The Facts of Causation. Oxford:Oxford University Press.

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Menzies, Peter (1996), ‘‘Probabilistic Causation and thePre-Emption Problem,’’ Mind 105: 85–117.

Newton, Isaac ([1687] 1999), The Principia: MathematicalPrinciples of Natural Philosophy. Translated by I.Bernard Cohen and Anne Whitman. Berkeley and LosAngeles: University of California Press.

Paul, Laurie (1998), ‘‘Keeping Track of the Time: Emend-ing the Counterfactual Analysis of Causation,’’ AnalysisLVIII: 191–198.

Pearl, Judea (2000), Causality. Cambridge: Cambridge Uni-versity Press.

Price, Huw (1992), ‘‘Agency and Causal Asymmetry,’’Mind101: 501–520.

Railton, Peter (1978), ‘‘A Deductive-Nomological Model ofProbabilistic Explanation,’’ Philosophy of Science 45:206–226.

Reichenbach, Hans (1956), The Direction of Time. Berkeleyand Los Angeles: University of California Press.

Rosen, Deborah (1978), ‘‘In Defense of a ProbabilisticTheory of Causality,’’ Philosophy of Science 45: 604–613.

Russell, Bertrand (1912), ‘‘On the Notion of Cause,’’ Pro-ceedings of the Aristotelian Society 13: 1–26.

Salmon, Wesley (1984), Scientific Explanation and theCausal Structure of the World. Princeton, NJ: PrincetonUniversity Press.

——— (1989), ‘‘Four Decades of Scientific Explanation,’’in Philip Kitcher and Wesley Salmon (eds.), ScientificExplanation, 3–219.

Scriven, Michael (1975), ‘‘Causation as Explanation,’’ Nous9: 238–264.

Shoemaker, Sydney (1980), ‘‘Causality and Properties,’’ inPeter van Inwagen (ed.), Time and Cause. Dordrecht,Netherlands: D. Reidel, 109–135.

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Sosa, Ernest, and Michael Tooley (eds.) (1993), Causation.Oxford: Oxford University Press..

Spirtes, P., C. Glymour, and R. Scheines (1993), Causation,Prediction, and Search. New York: Springer-Verlag.

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Suppes, Patrick (1970), A Probabilistic Theory of Causality.Amsterdam: North-Holland.

——— (1986), ‘‘Non-Markovian Causality in the SocialSciences with Some Theorems on Transitivity,’’ Synthese68: 129–140.

Tooley, Michael (1977), ‘‘The Nature of Laws,’’ CanadianJournal of Philosophy 7: 667–698.

——— (1987), Causation: A Realist Approach. Oxford:Oxford University Press.

van Fraassen, Bas (1980), The Scientific Image. Oxford:Oxford University Press.

Vihvelin, Kadhri (1995), ‘‘Causes, Effects, and Counterfac-tual Dependence,’’ Australasian Journal of Philosophy73: 560–583.

Wilson, Jessica (1999), ‘‘How Superduper Does a Physical-ist Supervenience Need to Be?’’ Philosophical Quarterly49: 33–52.

Woodward, James (1997), ‘‘Explanation, Invariance, andIntervention,’’ Philosophy of Science 64 (Proceedings):S26–S41.

Wright, Larry (1976), Teleological Explanation. Berkeleyand Los Angeles: University of California Press.

Wright, Sewall (1921), ‘‘Correlation and Causation,’’ Jour-nal of Agricultural Research 20: 557–585.

CHAOS THEORY

See Prediction

CHEMISTRY, PHILOSOPHY OF

Although many influential late-nineteenth- andearly-twentieth-century philosophers of sciencewere educated wholly or in part as chemists

(Gaston Bachelard, Pierre Duhem, Emile Myerson,Wilhelm Ostwald, Michael Polanyi), they sel-dom reflected directly on the epistemological,

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methodological, or metaphysical commitments oftheir science. Subsequent philosophers of sciencefollowed suit, directing little attention to chemistryin comparison with physics and biology despite theindustrial, economic, and academic success of thechemical sciences. Scattered examples of philo-sophical reflection on chemistry by chemists doexist; however, philosophically sensitive historicalanalysis and sustained conceptual analysis are rela-tively recent phenomena. Taken together, these twodevelopments demonstrate that chemistry addres-ses general issues in the philosophy of science and,in addition, raises important questions in the in-terpretation of chemical theories, concepts, andexperiments.Historians of chemistry have also raised a num-

ber of general philosophical questions about chem-istry. These include issues of explanation, ontology,reduction, and the relative roles of theories, experi-ments, and instruments in the advancement of thescience.Worries about the explanatory nature of the al-

chemical, corpuscularian, and phlogiston theoriesare well documented (cf. Bensaude-Vincent andStengers 1996; Brock 1993). Lavoisier and—to alesser extent historically—Dalton initiated shifts inthe explanatory tasks and presuppositions of thescience. For instance, prior to Lavoisier many che-mists ‘‘explained’’ a chemical by assigning it to atype associated with its experimental dispositions(e.g., flammability, acidity, etc.). After Lavoisierand Dalton, ‘‘explanation’’ most often meant theisolation and identification of a chemical’s constitu-ents. Eventually, the goal of explanation changed tothe identification of the transformation processes inthe reactants that gave rise to the observed propertiesof the intermediaries and the products. It is at thattime that chemists began to write the now familiarreaction equations, which encapsulate this change.These transformations cannot be described simply asthe coming of new theories; they also involvedchanges in explanatory presuppositions and lan-guages, as well as new experimental techniques(Bensaude-Vincent and Stengers 1996; Nye 1993).Thinking in terms of transformation processes

led chemists to postulate atoms as the agents ofthe transformation process. But atoms were notobservable in the nineteenth century. How is theexplanatory power of these unobservable entitiesaccounted for? Also, do chemical elements retaintheir identity in compounds (Paneth 1962)? Some-thing remains the same, yet the properties thatidentify elements (e.g., the green color of chlo-rine gas) do not exist in compounds (e.g., sodiumchloride, or common table salt).

The history of chemistry also raises a number ofinteresting questions about the character of knowl-edge and understanding in the science. Whereasphilosophers have historically identified theoreticalknowledge with laws or sets of propositions, thehistory of chemistry shows that there are differentkinds of knowledge that function as a base forunderstanding. Much of chemistry is experimental,and much of what is known to be true arises inexperimental practice independently of or only in-directly informed by theoretical knowledge. Whenchemists have theorized, they have done so freely,using and combining phenomenological, construc-tive (in which the values of certain variables aregiven by experiment or other theory), and deduc-tive methods. Chemists have rarely been able toachieve anything like a strict set of axioms or firstprinciples that order the phenomena and serve astheir explanatory base (Bensaude-Vincent andStengers 1996; Gavroglu 1997; Nye 1993).

Historical research has also raised the issue ofwhether theory has contributed most to the prog-ress of chemistry. While philosophers often point tothe conceptual ‘‘revolution’’ wrought by Lavoisieras an example of progress, historians more oftenpoint to the ways in which laboratory techniqueshave been an important motor of change in chemis-try, by themselves or in tandem with theoreticalshifts (Bensaude-Vincent and Stengers 1996; Nye1993). For example, during the nineteenth century,substitution studies, in which one element is re-placed by another in a compound, were drivenlargely by experimental practices. Theoretical con-cepts did not, in the first instance, organize theinvestigation (Klein 1999). Similar remarks can bemade regarding the coming of modern experimentaltechniques such as various types of chromatogra-phy and spectroscopy (Baird 2000; Slater 2002).Chemists often characterize a molecule using suchtechniques, and while the techniques are groundedin physical theory, the results must often be inter-preted in chemical language. These examples leadback to questions about the nature of chemicalknowledge. Arguably, the knowledge appears tobe a mix of ‘‘knowing how’’ and ‘‘knowing that’’which is not based solely in the theory (chemical orphysical) available at the time.

A number of the philosophical themes raised inthe history of chemistry continue to reverberate incurrent chemistry. For instance, what is the properontological base for chemical theory, explanation,and practice? While many chemists would unfail-ingly resort to molecular structure as the explana-tion of what is seen while a reaction is takingplace, this conception can be challenged from two


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directions. From one side, echoing the eighteenth-century conception of the science, chemistry beginsin the first instance with conceptions and analysesof the qualitative properties of material stuff(Schummer 1996; van Brakel 2001). One mightcall the ontology associated with this conception ametaphysically nonreductive dispositional realism,since it focuses on properties and how they appearunder certain conditions and does not attempt tointerpret them in any simpler terms. In this concep-tion, reference to the underlying molecular struc-ture is subsidiary or even otiose, since the focus ison the observable properties of the materials.Given that molecular structure is difficult to justifywithin quantum mechanics (see below), one canargue that it is justifiable to remain with the ob-servable properties. If this view is adopted, howev-er, the justification of the ontology of material stuffbecomes a pressing matter. Quantum mechanicswill not supply the justification, since it does notdeliver the qualitative properties of materials. Fur-ther, it still seems necessary to account for thephenomenal success that molecular explanati-ons afford in planning and interpreting chemicalstructures and reactions.

From the other side, pure quantum mechanicsmakes it difficult to speak of the traditional atoms-within-a-molecule approach referred to in the reac-tion equations and structural diagrams (Primas1983; Weininger 1984). Quantum mechanics tellsus that the interior parts of molecules should notbe distinguishable; there exists only a distributionof nuclear and electronic charges. Yet chemists relyon the existence and persistence of atoms and mole-cules in a number of ways. To justify these prac-tices, some have argued that one can forgo thenotion of an atom based on the orbital model andinstead identify spatial regions within a moleculebounded by surfaces that have a zero flux of energyacross the surfaces (Bader 1990). Currently, it is anopen question whether this representation falls nat-urally out of quantum mechanics, and so allowsone to recover atoms as naturally occurring sub-stituents of molecules, or whether the notion of‘atom’ must be presupposed in order for the identi-fication to be made. Here again there is a questionof the character of the theory that will give thedesired explanation.

A number of examples supporting the claim thatquantum mechanics and chemistry are uneasy bed-fellows will be discussed below as they relate to theissue of reductionism, but their relationship alsoraises forcefully the long-standing issue of how the-ory guides chemical practice. Even in this era ofsupercomputers, only the energy states of systems

with relatively few electrons or with high degreesof symmetry can be calculated with a high degree offaithfulness to the complete theoretical description.For most chemical systems, various semi-empiricalmethods must be used to get theoretically guidedresults. More often than not, it is the experimentalpractice independent of any theoretical calculationthat gets the result. Strictly theoretical predictionsof novel properties are rather rare, and whetherthey are strictly theoretical is a matter that can bedisputed. A case in point is the structure of the CH2

molecule. Theoretical chemists claimed to havepredicted novel properties of the molecule, viz., itsnonlinear geometry, prior to any spectroscopicevidence (Foster and Boys 1960). While it is truethat the spectroscopic evidence was not yet avail-able, it may have been the case that reference toanalogous molecules allowed the researchers to setthe values for some of the parameters in the equa-tions. So the derivation may not have been as apriori as it seemed.Like the other special sciences, chemistry raises

the issue of reductionism quite forcefully. Howev-er, perhaps because most philosophers have accept-ed at face value Dirac’s famous dictum thatchemistry has become nothing more than the appli-cation of quantum mechanics to chemical problems(cf. Nye 1993, 248), few seem to be aware of thedifficulties of making good on that claim using thetools and concepts available in traditional philo-sophical analyses of the sciences. No one doubtsthat chemical forces are physical in nature, butconnecting the chemical and physical mathematicalstructures and/or concepts proves to be quite achallenge. Although problems involving the rela-tion between the physical and the chemical sur-round a wide variety of chemical concepts, suchas aromaticity, acidity (and basicity), functionalgroups, and substituent effects (Hoffmann 1995),three examples will be discussed here to illustratethe difficulties: the periodic table, the use of orbi-tals to explain bonding, and the concept of molec-ular shape. Each also raises issues of explanation,representation, and realism.Philosophers and scientists commonly believe

that the periodic table has been explained by—and thus reduced to—quantum mechanics. This istaken to be an explanation of the configuration ofthe electrons in the atom, and, as a result of this, anexplanation of the periodicity of the table. In thefirst case, however, configurations of electrons inatoms and molecules are the result of a particularapproximation, in which the many-electron quan-tum wavefunction is rewritten as a series of one-electron functions. In practice, these one-electron


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functions are derived from the hydrogen wavefunc-tion and, upon integration, lead to the familiarspherical s orbital, the dumbbell-shaped p orbitals,and the more complicated d and f orbitals. Via thePauli exclusion principle, which states that the spinsare to be paired if two electrons are to occupy oneorbital and no more than two electrons may occupyan orbital, electrons are assigned to these orbitals.If the approximation is not made (and quantummechanics tells us it should not be, since the ap-proximation relies on the distinguishability of elec-trons), the notion of individual quantumnumbers—and thus configurations—is no longer meaningful(Richman 1999). In addition, configurations them-selves are not observable; absorption and emissionspectra are observed and interpreted as energytransitions between orbitals of different energies.In the second case, quantum mechanics explains

only part of the periodic table, and often it does notexplain the features of the table that are of mostinterest to chemists (Scerri 1998). Pauli’s introduc-tion of the fourth quantum number, ‘‘spin’’ or‘‘spin angular momentum,’’ leads directly to theAufbau principle, which states that the periodictable is constructed by placing electrons in lowerenergy levels first and then demonstrating thatatoms with similar configurations have similarchemical properties. In this way, one can say thatsince chlorine and fluorine need one more electronto achieve a closed shell, they will behave similarly.However, this simple, unqualified explanation suf-fers from a number of anomalies. First, the fillingsequence is not always strictly obeyed. Cobalt,nickel, and copper fill their shells in the sequence3d74s2, 3d84s2, 3d104s1. The superscripts denote thenumber of electrons in the subshell; the s shell canhold a maximum of two electrons and the five dorbitals ten. The observed order of filling is curiousfrom the perspective of the unmodified Aufbauprinciple for a number of reasons. The 4s shell,which is supposed to be higher in energy than the3d shell, has been occupied and closed first. Then,there is the ‘‘demotion’’ of one 4s electron in nickelto a 3d electron in copper. Second, configurationsare supposed to explain why elements falling intothe same group behave similarly, as in the exampleof chlorine and fluorine. Yet nickel, palladium, andplatinum are grouped together because of theirmarked chemical similarities despite the fact thattheir outer shells have different configurations (4s2,5s0 and 6s1, respectively). These and other anoma-lies can be resolved using alternative derivationsmore closely tied to fundamental quantum me-chanics, but the derivations require that theorbital approximation be dropped, and it was that

approximation that was the basis for the assign-ment into the s, p, and d orbitals in the first place. Itthus becomes an open question whether quantummechanics, via the Aufbau principle, has explainedthe chemical periodicities encapsulated in the table.

Similar questions about the tenuous relation be-tween physics and chemistry surround the conceptof bonding. At a broad level, chemists employ twoseemingly inconsistent representations, the valencebond (VB) and molecular orbital (MO) theories, toexplain why atoms and molecules react. Both arecalculational approximations inherited from atom-ic physics. The relations between the two theoriesand respective relations to the underlying quantummechanics raise many issues of theory interpreta-tion and realism about the chemical concepts (seebelow). Subsidiary concepts such as resonance arealso invoked to explain the finer points of bonding.Chemists have offered competing realist interpreta-tions of this concept, and philosophers have offeredvarious realist and instrumentalist interpretationsof it as well (Mosini 2000).

More specifically, a host of philosophical issuesare raised within the molecular orbital theory.Here, bonding is pictured as due to the interactionof electrons in various orbitals. As noted earlier,the familiar spherical and dumbbell shapes ariseonly because of the orbital approximation. Howev-er, there is no reason to expect that the hydrogenicwavefunctions will look anything like the molecu-lar ones (Bader 1990; Woody 2000). After thehydrogenic wavefunctions have been chosen asthe basis for the calculation, they must be pro-cessed mathematically to arrive at a value for theenergy of the orbital that is at all close to theexperimentally observed value. The molecularwave equation is solved by taking linear combina-tions of the hydrogenic wavefunctions, forming theproduct of these combinations (the ‘‘configurationinteraction’’ approach), and using the variationalmethod to produce a minimal energy solution tothe equation. The familiar orbitals appear onlywhen these three steps in the complete solutionhave been omitted (Woody 2000). Thus, the ideathat the familiar orbitals are responsible for thebonding is thrown into question. Yet the orbitalsclassify and explain how atoms and molecules bondextremely well. That they do provide deep, unified,and fertile representations and explanations seemscurious from the perspective of fundamental quan-tum mechanics. Clearly, more analysis is requiredto understand the relation clearly. If one insists ona philosophical account of reduction that requiresthe mathematical or logical derivability of one the-ory from another, how orbitals achieve their power

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remains obscure. Even when one abandons thatphilosophical account, it is not clear how the repre-sentations have the organizing and explanatorypower they do (see Reductionism).

As a final illustration of the difficulty of connect-ing physics and chemistry in any sort of strict fash-ion, consider the concept of molecular shape.Partly through the tradition of orbitals describedabove and partly through a historical tradition oforiented bonding that arose well before the conceptof orbitals was introduced, chemists commonly ex-plain many behaviors of molecules as due to theirthree-dimensional orientiation in space. Moleculesclearly react as if they are oriented in three-dimen-sional space. For example, the reaction I�þ CH3Br! ICH3 þ Br� is readily explained by invoking thenotion that the iodine ion (I�) attacks the carbon(C) on the side away from the bromine (Br) atom.(This can be detected by substituting deuteriumatoms for one of the hydrogens [H] and measuringsubsequent changes in spectroscopic properties.)As noted before, however, such explanations aresuspect within quantum mechanics, since talk oforiented bonds and quasi-independent substituentsin the reaction is questionable. Orientations mustbe ‘‘built into’’ the theory by parameterizing someof the theoretical variables. Unfortunately, there isno strict quantum mechanical justification for themethod by which orientation in space is derived.Orientation relies on a notion of a nuclear framesurrounded by electrons. This notion is constructedvia the Born-Oppenheimer approximation, whichprovides a physical rationale for why the nuclearpositions should be slowly varying with respect tothe electronic motions. In some measurementregimes, the approximation is invalid, and correctpredictions are achieved only by resorting to amore general molecular Hamiltonian. In morecommon measurement regimes, the approximationis clearly valid. But, as with the issues involved inthe case of the periodic table and orbitals, thephysics alone do not tell us why it is valid. Thereis a physical justification for the procedure, but thisjustification has no natural representation with theavailable physical theory (Weininger 1984). Shouldjustification based on past experience be trusted, orshould the theory correct the interpretive practice?In any case, the chemistry is consistent with, butnot yet derivable from, the physics.

All three examples are connected with a method-ological issue mentioned earlier, viz., the type oftheory that chemists find useful. As previouslynoted, chemists often must parameterize the physi-cal theories at their disposal to make them useful.All three of the cases described above involve such

parameterization, albeit in different ways. How is itthat such parameterizations uncover useful patternsin the data? Are they explanatory? When are theyacceptable and when not (Ramsey 1997)? These anda host of similar questions remain to be answered.Other epistemological and ontological issues

raised in the practice of chemistry remain virtuallyunexplored. For instance, the question of whetherone molecule is identical to another is answered byreferring to some set of properties shared by thetwo samples. Yet the classification of two mole-cules as of the ‘‘same’’ type will vary, since differenttheoretical representations and experimental tech-niques detect quite different properties (Hoffmann1995). For instance, reference can be made to thespace-filling property of molecules, their three-dimensional structure, or the way they respond toan electric field. Additionally, the determination ofsameness must be made in light of the question, Forwhat function or purpose? For instance, two mole-cules of hemoglobin, which are large biologicalmolecules, might have different isotopes of oxygenat one position.While this differencemight be usefulin order to discover the detailed structure of thehemoglobin molecule, it is usually irrelevant whentalking about the molecule’s biological function.How the explanatory practices of chemistry stand

in relation to the available philosophical accountsand to the practices of other sciences remains animportant question. Chemical explanations arevery specific, often lacking the generality invokedinphilosophical accounts of explanation.Moreover,chemists invoke a wide variety of models, laws, the-ories, and mechanisms to explain the behavior andstructure of molecules. Finally, most explanationsrequire analogically based and/or experimentallyderived adjustments to the theoretical laws and reg-ularities in order for the account to be explanatory.As mentioned earlier, chemistry is an extremely

experimental science. In addition to unifying andfragmenting research programs in chemistry, newlaboratory techniques have dramatically changedthe epistemology of detection and observation inchemistry (e.g., from tapping manometers to read-ingNMR [nuclearmagnetic resonance] outputs). Asyet, however, there is no overarching, completestudy of the changes in the epistemology of experi-mention in chemistry: for example, what chemistscount as observable (and how this is connected towhat they consider to be real), what they assumecounts as a complete explanation, what they assumecounts as a successful end to an experiment, etc.Additionally, what are the relations between

academic and industrial chemistry? What are therelative roles of skill, theory, and experiment in


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these two arenas of inquiry? Last but not least, thereare pressing ethical questions. The world has beentransformed by chemical products. Chemistry hasblurred the distinction between the natural and theartificial in confusing ways (Hoffmann 1995). Forinstance, catalytically produced ethanol is chemical-ly identical with the ethanol produced in fermenta-tion. So is the carbon dioxide produced in a forestfire and in a car’s exhaust. Why are there worriesabout the exhaust fumes but not the industriallyproduced ethanol? Is this the appropriate attitude?Last but not least, chemicals have often replacedearlier dangerous substances and practices; witnessthe great number of herbicides and insecticidesavailable at the local garden center and the prescrip-tion medicines available at the pharmacy. Yet thesereplacements are often associated with a cost. Oneneed think only of DDT or thalidomide to be flungheadlong into ethical questions regarding the harm-fulness and use of human-made products.Many of the above topics have not been ana-

lyzed in any great depth. Much remains to done toexplore the methodology and philosophy of thechemical sciences.

JEFFRY L. RAMSEY

References

Bader, R. (1990), Atoms in Molecules: a Quantum Theory.New York: Oxford University Press.

Baird, D. (2000), ‘‘Encapsulating Knowledge: The DirectReading Spectrometer,’’ Foundations of Chemistry 2:5–46.

Bensaude-Vincent, B., and I. Stengers (1996), A History ofChemistry. Translated by D. van Dam. Cambridge, MA:Harvard University Press.

Bhushan, N., and S. Rosenfeld (2000), Of Minds and Mole-cules: New Philosophical Perspectives on Chemistry. NewYork: Oxford University Press.

Brock, W. (1993), The Norton History of Chemistry. NewYork: W. W. Norton.

Foster, J. M., and S. F. Boys (1960), ‘‘Quantum VariationalCalculations for a Range of CH2 Configurations,’’Reviews of Modern Physics 32: 305–307.

Gavroglu, K. (1997), ‘‘Philosophical Issues in the History ofChemistry,’’ Synthese 111: 283–304.

Hoffmann, R. (1995), The Same and Not the Same. NewYork: Columbia University Press.

Klein, U. (1999), ‘‘Techniques of Modeling and Paper-Tools in Classical Chemistry,’’ in M. Morgan andM. Morrison (eds.), Models as Mediators. New York:Cambridge University Press, 146–167.

Mosini, V. (2000), ‘‘A Brief History of the Theory of Reso-nance and of Its Interpretation,’’ Studies in History andPhilosophy of Modern Physics 31B: 569–581.

Nye, M. J. (1993), From Chemical Philosophy to TheoreticalChemistry. Berkeley and Los Angeles: University ofCalifornia Press.

Paneth, F. (1962), ‘‘The Epistemological Status of the Con-cept of Element,’’ British Journal for the Philosophy ofScience 13: 1–14, 144–160.

Primas, H. (1983), Chemistry, Quantum Mechanics and Re-ductionism. New York: Springer Verlag.

Ramsey, J. (1997), ‘‘Between the Fundamental and thePhenomenological: The Challenge of ‘Semi-Empirical’Methods,’’ Philosophy of Science 64: 627–653.

Scerri, E. (1998), ‘‘How Good Is the Quantum MechanicalExplanation of the Periodic System?’’ Journal of Chemi-cal Education 75: 1384–1385.

Schummer, J. (1996), Realismus und Chemie. Wuerzburg:Koenigshausen and Neumann.

Slater, L. (2002), ‘‘Instruments and Rules: R. B. Woodwardand the Tools of Twentieth-century Organic Chemis-try,’’ Studies in History and Philosophy of Science 33:1–32.

van Brakel, J. (2001), Philosophy of Chemistry: Between theManifest and the Scientific Image. Leuven, Belgium:Leuven University Press.

Weininger, S. (1984), ‘‘TheMolecular StructureConundrum:Can Classical Chemistry Be Reduced to QuantumChemistry?’’ Journal of Chemical Education 61: 939–944.

Woody, A. (2000), ‘‘Putting Quantum Mechanics to Workin Chemistry: The Power of Diagrammatic Representa-tion,’’ Philosophy of Science 67(suppl): S612–S627.

See also Explanation; Laws of Nature; QuantumMechanics; Reductionism

CHOMSKY, NOAM

(7 December 1928–)

Avram Noam Chomsky received his Ph.D in lin-guistics from the University of Pennsylvania andhas been teaching at Massachusetts Institute of

Technology since 1955, where he is currently Insti-tute Professor. Philosophers are often familiar withthe early work of Chomsky (1956, 1957, 1959a,

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and 1965), which applied the methods of formallanguage theory to empirical linguistics, but hiswork has also incorporated a number of philo-sophical assumptions about the nature of scien-tific practice—many of which are defended in hiswritings.

This essay will first describe the development andevolution of Chomsky’s theory of generative lin-guistics, highlighting some of the philosophicalassumptions that have been in play. It will thenturn to some of the methodological debates in gen-erative linguistics (and scientific practice moregenerally), focusing on Chomsky’s role in thesedebates.

The Development and Evolution ofGenerative Grammar

A number of commentators have suggested thatChomsky’s early work in generative linguisticsinitiated a kind of Kuhnian paradigm shift in lin-guistic theory. While Chomsky himself would re-ject this characterization (at least for his initialwork in generative grammar), it is instructive toexamine the development of generative linguistics,for it provides an excellent laboratory for thestudy of the development of a young science, andin particular it illuminates some of the philosophi-cal prejudice that a young science is bound toencounter.

Chomsky’s role in the development of linguistictheory and cognitive science generally can best beappreciated if his work is placed in the context ofthe prevailing intellectual climate in the 1950s—onein which behaviorism held sway in psycho-logy departments and a doctrine known as Ameri-can Structuralism was prevalent in linguisticsdepartments.

American Structuralism, in particular as articu-lated by Bloomfield (1933 and 1939), adopted anumber of key assumptions that were in turnadopted from logical empiricism (see Logical Em-piricism). Newmeyer (1986, ch. 1) notes that thefollowing assumptions were in play:

. All useful generalizations are inductive gener-alizations.

. Meanings are to be eschewed because they areoccult entities—that is, because they are notdirectly empirically observable.

. Discovery procedures like those advocated inlogical empiricism should be developed for theproper conduct of linguistic inquiry.

. There should be no unobserved processes.

One of the ways in which these assumptionstranslated into theory was in the order that vari-ous levels of linguistic description were to betackled. The American Structuralists identifiedfour levels: phonemics (intuitively the study ofsound patterns), morphemics (the study of words,their prefixes and suffixes), syntax (the study ofsentence-level structure), and discourse (the studyof cross-sentential phenomena). The idea was thatproper methodology would dictate that one beginat the level of phonemics, presumably because itis closer to the data; then proceed to constructa theory of morphemics on the foundations ofphonemics; then proceed to construct a theory ofsyntax, etc.Notice the role that the concepts of logical em-

piricism played in this proposed methodology. Onefinds radical reductionism in the idea that everylevel must be reducible to the more basic phonemiclevel; verificationism in the contention that thephonemic level is closely tied to sense experience;and discovery procedures in the suggestion thatthis overall order of inquiry should be adopted(see Reductionism; Verificationism).Chomsky rejected most if not all of these

assumptions early on (see Chomsky [1955] 1975,introduction, for a detailed discussion). As regardsdiscovery procedures, for example, he rejectedthem while still a matriculating graduate student,then holding a position in the Harvard Society ofFellows:

By 1953, I came to the same conclusion [as MorrisHalle]if the discovery procedures did not work, it wasnot because I had failed to formulate them correctly, butbecause the entire approach was wrong. . . . [S]everalyears of intense effort devoted to improving discoveryprocedures had come to naught, while work I had beendoing during the same period on generative grammarsand explanatory theory, in almost complete isolation,seemed to be consistently yielding interesting results.(1979: 131)

Chomsky also rejected the assumption that allprocesses should be ‘‘observable’’— early theoriesof transformational grammar offered key examplesof unobservable processes. For example, in his‘‘aspects theory’’ of generative grammar (Chomsky1965), the grammar is divided into two different‘‘levels of representation,’’ termed initially deepstructure and surface structure. The deep-structurerepresentations were generated by a context-freephase structure grammar—that is, by rules (of de-composition, ‘‘!’’) of the following form, where Sstands for sentence, NP for noun phrase, VP forverb phrase, etc.

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S ! NP VP

VP ! V NP

NP ! John

NP ! Bill

V ! saw

These rewriting rules then generated linguisticrepresentations of the following form:

t ð1Þ

Crucially for Chomsky, the objects of analysis inlinguistic theory were not the terminal strings ofwords, but rather phrase markers—structuredobjects like (1). Transformational rules then oper-ated on these deep-structure representations toyield surface-structure representations. So, for ex-ample, the operation of passivization would take adeep-structure representation like (1) and yield thesurface-structure representation (abstracting fromdetail) in (2):

ð2Þ

The sentence in (3) is therefore a complex objectconsisting of (at a minimum) an ordered pair of thetwo representations corresponding to (1) and (2):

Bill was seen by John: ð3ÞClearly, Chomsky was committed not only to

‘‘unobserved’’ processes in the guise of transforma-tions, but also to unobserved levels of representa-tion. No less significant was the nature of the datathat Chomsky admitted—not utterances or writtenstrings, but rather speakers’ judgments of accept-ability and meaning. Thus, (3) is not a datum be-cause it has been written or spoken, but ratherbecause speakers have intuitions that it is (wouldbe) an acceptable utterance. Here again, Chomsky

broke with prevailing methodology in structuralistlinguistics and, indeed, behaviorist psychology, byallowing intuitions rather than publicly availablebehaviors as data.

Generative grammar subsequently evolved in re-sponse to a number of internal pressures. Crucially,the number of transformations began to proliferatein a way that Chomsky found unacceptable. Whyunacceptable? Early on in the development of gen-erative grammar, Chomsky had made a distinctionbetween the descriptive adequacy and the explana-tory adaquacy of an empirical linguistic theory(Chomsky 1965 and 1986b). In particular, if a lin-guistic theory is to be explanatorially adequate, itmust not merely describe the facts, but must do soin a way that explains how humans are able tolearn languages. Thus, linguistics was supposed tobe embeddable into cognitive science more broad-ly. But if this is the case, then there is a concernabout the unchecked proliferation of rules—suchrule systems might be descriptively adequate, butthey would fail to account for how we learn lan-guages (perhaps due to the burden of having tolearn all those language-specific rules).

Chomsky’s initial (1964 and 1965) solution to thisproblem involved the introduction of conditions ontransformations (or constraints onmovement), withthe goal of reducing the complexity of the descrip-tive grammar. In Chomsky (1965), for example, therecursive power of the grammar is shifted from thetransformations to the phrase structure rules alone.In the ‘‘extended standard theory’’ of the 1970s,there was a reduction of the phrase structure com-ponent with the introduction of ‘‘X-bar theory,’’and a simplification of the constraints on move-ment. This was followed by a number of proposalsto reduce the number and types of movement rulesthemselves. This came to a head (Chomsky 1977 and1981a) with the abandonment of specific transfor-mations altogether for a single rule (‘‘move-a’’),which stated, in effect, that one could move any-thing anywhere. This one rule was then supplemen-ted with a number of constraints on movement. AsChomsky and a number of other generative linguistswere able to show, it was possible to reduce a greatnumber of transformations to a single-rule move-aand to a handful of constraints on movement.

Chomsky (1981b, 1982, and 1986a) synthesizedsubsequent work undertaken by linguists workingin a number of languages, ranging from the romancelanguages to Chinese and Japanese, showing thatother natural languages had similar but not identicalconstraints, and it was hypothesized that the varia-tion was due to some limited parametric variationamong human languages. This work established the

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‘‘principles and parameters’’ framework of genera-tive grammar. To get an idea of this framework,consider the following analogy: Think of the lan-guage faculty as a prewired box containing a num-ber of switches. When exposed to environmentaldata, new switch settings are established. Applyingthis metaphor, the task of the linguist is to studythe initial state of the language faculty, determinethe possible parametric variations (switch settings),and account for language variation in terms of alimited range of variation in parameter settings. InChomsky’s view (2000, 8), the principles-and-para-meters framework ‘‘gives at least an outline of agenuine theory of language, really for the firsttime.’’ Commentators (e.g., Smith 2000, p. xi)have gone so far as to say that it is ‘‘the first reallynovel approach to language of the last two and ahalf thousand years.’’ In what sense is it a radicaldeparture? For the first time it allowed linguists toget away from simply constructing rule systems forindividual languages and to begin exploring in adeep way the underlying similarities of human lan-guages (even across different language families), toilluminate the principles that account for thosesimilarities, and ultimately to show how those prin-ciples are grounded in the mind/brain.In Chomsky’s view, the principles-and-parametersframework has yielded a number of promisingresults, ranging from the discovery of importantsimilarities between prima facie radically differentlanguages like Chinese and English to insights intothe related studies of language acquisition, lan-guage processing, and acquired linguistic deficits(e.g., aphasia). Perhaps most importantly, theprinciples-and-parameters framework offered away to resolve the tension between the two goalsof descriptive adequacy and explanatory adequacy.

Still working within the general principles-and-parameters framework, Chomsky (1995 and 2000,ch. 1) has recently articulated a research programthat has come to be known as the ‘‘minimalistprogram,’’ the main idea behind which is the work-ing hypothesis that the language faculty is not theproduct of messy evolutionary tinkering—for ex-ample, there is no redundancy, and the onlyresources at work are those that are driven by ‘‘con-ceptual necessity.’’ Chomsky (1995, ch. 1) initiallyseemed to hold that in this respect the languagefaculty would be unlike other biological functions,but more recently (2001) he seems to be drawn toD’Arcy Thompson’s theory that the core of evolu-tionary theory consists of physical/mathematical/chemical principles that sharply constrain the possi-ble range of organisms. In this case, the idea wouldbe not only that those principles constrain low-level

biological processes (like sphere packing in cell divi-sion) but also that such factors might be involvedacross the board—even including the human brainand its language faculty.In broadest outline, the minimalist program

works as follows: There are two levels of linguisticrepresentation, phonetic form (PF) and logicalform (LF), and a well-formed sentence (or linguis-tic structure) must be an ordered pair <p, l> ofthese representations (where p is a phonetic formand l is the logical form). PF is taken to be thelevel of representation that is the input to theperformance system (e.g., speech generation), andLF is, in Chomsky’s terminology, the input to theconceptual/intensional system. Since language is, ifnothing else, involved with the pairing of soundsand meanings, these two levels of representationare conceptually necessary. A minimal theorywould posit no other levels of representation.It is assumed that each sentence (or better, struc-

ture, S) is constructed out of an array or numera-tion, N, of lexical items. Some of the items in thenumeration will be part of the pronounced (writ-ten) sentence, and others will be part of a universalinventory of lexical items freely inserted into allnumerations. Given the numeration N, the compu-tational system (CHL) attempts to derive (compute)well-formed PF and LF representations, con-verging on the pair <p, l>. The derivation issaid to converge at a certain level if it yields arepresentation that is interpretable at that level. Ifit fails to yield an interpretable representation, thederivation crashes. Not all converging derivationsyield structures that belong to a given languageL. Derivations must also meet certain economyconditions.Chomsky (2000, 9) notes that the import of the

minimalist program is not yet clear. As matterscurrently stand, it is a subresearch program withinthe principles-and-parameters framework that isshowing some signs of progress—at least enoughto encourage those working within the program.As always, the concerns are to keep the numberof principles constrained, not just to satisfy eco-nomy constraints, but to better facilitate theembedding of linguistics into theories of languageacquisition, cognitive psychology, and, perhapsmost importantly, general biology.

Some Conceptual Issues in GenerativeGrammar

While Chomsky would argue that he does nothave a philosophy of science per se and that his

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philosophical observations largely amount to com-mon sense, a number of interesting debates havearisen in the wake of his work. The remainder ofthis essay will review some of those debates.

On the Object of StudyChomsky (1986) draws the distinction between

the notions of I-language and E-language, where I-language is the language faculty discussed above,construed as a chapter in cognitive psychology andultimately human biology. E-language, on theother hand, comprises a loose collection of theoriesthat take language to be a shared social object,established by convention and developed for pur-poses of communication; or an abstract mathemat-ical object of some sort.In Chomsky’s view (widely shared by linguists),

the notion of a ‘language’ as it is ordinarily con-strued by philosophers of language is fundamental-ly incoherent. We may talk about ‘‘the Englishlanguage’’ or ‘‘the French language’’ but these areloose ways of talking. Typically, the question ofwho counts as speaking a particular language isdetermined more by political boundaries than ac-tual linguistic variation. For example, there aredialects of German that, from a linguistic pointof view, are closer to Dutch than to standardGerman. Likewise, in the Italian linguistic situa-tion, there are a number of so-called dialects onlysome of which are recognized as ‘‘official’’ lan-guages by the Italian government. Are the officiallanguages intrinsically different from the ‘‘mere’’dialects? Not in any linguistic sense. The decisionto recognize the former as official is entirely apolitical decision. In the words attributed to MaxWeinreich: A language is a dialect with an armyand a navy. In this case, a language is a dialect withsubstantial political clout and maybe a threat ofseparatism.Chomsky (1994 and 2000, ch. 2) compares talk

of languages (i.e., E-languages) to saying that twocities are ‘‘near’’ each other; whether two cities arenear depends on our interests and our mode oftransportation and very little on brute facts ofgeography. In the study of language, the notionof ‘sameness’ is no more respectable than that of‘nearness’in geography. Informally we might grouptogether ways of speaking that seem to be similar(relative to our interests), but such groupings haveno real scientific merit. As a subject of naturalinquiry, the key object of study has to be the lan-guage faculty and its set of possible parametricvariations.

Not only is the notion of an E-language prob-lematic, but it will not help to retreat to talk aboutE-dialects. The problem is that what counts as aseparate E-dialect is also incoherent from a scien-tific point of view. For example, Chomsky (2000,27) reports that in his idiolect, the word ‘‘ladder’’rhymes with ‘‘matter’’ but not with ‘‘madder.’’ Forothers, the facts do not cut in this way. Do theyspeak the same dialect as Chomsky or not? Thereis no empirical fact of the matter here; it alldepends on individuals’ desires to identify linguis-tically with each other. Even appeals to mutualintelligibility will not do, since what we count asintelligible will depend much more on our patience,our ambition, and our familiarity with the practicesof our interlocutors than it will on brute linguisticfacts.

If the notion of E-language and E-dialect areincoherent, is it possible to construct a notion ofE-idiolect?—that is, to identify idiolects by externalcriteria like an individual’s spoken or written lan-guage? Apparently not. Included in what a personsays or writes are numerous slips of the tongue,performance errors, etc. How are we to rule thoseout of the individual’s E-idiolect? Appeal to theagent’s linguistic community will not do, sincethat would in turn require appeal to an E-language,and for the reasons outlined above, there is nomeaningful way to individuate E-languages. Inthe I-language approach, however, the problem ofindividuating I-idiolects takes the form of a coher-ent empirical research project. The idiolect (I-idiolect) is determined by the parametric stateof A’s language faculty, and the language facultythus determines A’s linguistic competence. Speechproduction that diverges from this competencecan be attributed to performance errors. Thus, thecompetence/performance distinction is introducedto illuminate the distinction between sounds andinterpretations that are part of A’s grammar andthose that are simply mistakes. The E-languageperspective has no similar recourse.

The Underdetermination of Theory by EvidenceOne of the first philosophical issues to fall out

from the development of generative grammar hasbeen the dispute between Quine (1972) andChomsky (1969 and 2000, ch. 3) on the indetermi-nacy of grammar. Similar to his argument forthe indeterminacy of meaning, Quine held thatthere is no way to adjudicate between two descrip-tively adequate sets of grammatical rules. So, forexample, imagine two rule sets, one envisioning

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structures like (1) above, and another positing thefollowing:

ð4Þ

Chomsky maintained that Quine’s argument issimply a recapitulation of the standard scientificproblem of the underdetermination of theory byevidence. And in any case it is not clear that thereare no linguistic tests that would allow us to choosebetween (1) and (4)—there are, after all, ‘‘constitu-ency tests’’ (e.g., involving movement possibilities)that would allow us to determine whether the XPor the VP is the more plausible constituent.

Even if there are several grammars that are con-sistent with the available linguistic facts (the factsare not linguistic behavior, for Chomsky, but intui-tions about acceptability and possible interpreta-tion), we still have the additional constraint ofwhich theory best accounts for the problem oflanguage acquisition, acquired linguistic deficits(e.g., from brain damage), linguistic processing,etc. In other words, since grammatical theory isembedded within cognitive psychology, the choicebetween candidate theories can, in principle, beradically constrained. But further, even if therewere two descriptively adequate grammars, eachof which could be naturally embedded within cog-nitive psychology, there remain standard best-theory criteria (simplicity, etc.) that can help us toadjudicate between the theories.

Intrinsic Versus Relational Properties inLinguistics

In the philosophy of science, it is routine to makethe distinction between ‘‘intrinsic’’ and ‘‘relational’’properties. So, for example, the rest mass of anobject would be an intrinsic property and its weightwould be a relational property (since it dependsupon the mass of the body that the object is stand-ing on). Similarly, in the philosophy of psychologythere is a common distinction between ‘‘individual-istic’’ and ‘‘externalist’’ properties. So, for example,there is the question of whether psychologicalstates supervene on individualistic properties (in-trinsic properties that hold of the individual inisolation) or whether they supervene on ‘‘extern-alist’’ properties (in effect, on relations between the

agent and its environment) (see Supervenience).Chomsky has argued that all scientifically inter-esting psychological and linguistic propertiessupervene upon individualist (intrinsic) properties.In particular, there is a brute fact about the state ofan individual’s language faculty, and that fact isdetermined in turn by facts about the individual inisolation—not by the environment in which theindividual is embedded. Because the language fac-ulty is part of our biological endowment, the natureof the representations utilized by the language fac-ulty are fixed by biology and are not sensitive toenvironmental issues such as whether one ismoving about on Earth or a phenomenologicallyidentical planet with a different microstructure(e.g., Putnam’s ‘‘Twin Earth’’).Thus Chomsky takes issue with philosophers like

Burge (1986), who argues in Individualism and Psy-chology that the content of the representations pos-ited in psychology are determined at least in part byenvironmental factors. Chomsky holds that if thenotion of content involves externalist or environ-mental notions, then it is not clear that it can playan interesting role in naturalistic inquiry in cognitivepsychology (see Psychology, Philosophy of ).If environmentalism is to be rejected in psychol-

ogy, then it naturally must be rejected in the se-mantics of natural language as well. That is: if thetask of the linguist is to investigate the nature of I-language; if the nature of I-language is a chapter ofcognitive psychology; and if cognitive psychologyis an individualistic rather than a relational science,semantics will want to eschew relational propertieslike reference (where ‘reference’ is construed as arelation between a linguistic form and some objectin the external environment). Thus Chomsky (1975and 2000) rejects the notion of reference that hasbeen central to the philosophy of language for thepast three decades, characterizing it as an ill-definedtechnical notion (certainly one with no empiricalapplications), and, following Strawson, suggeststhat in the informal usage, individuals ‘refer’ butlinguisticobjectsdonot (seeReference,Theoriesof ).This conclusion has immediate results for the

notion of theory change in science. If the notion ofreference is suspect or incoherent, then it can hardlybe employed in an account of theory change (as inPutnam 1988). How then to make sense of theorychange? Chomsky (2000) suggests the following:

Some of the motivation for externalist approachesderives from the concern to make sense of the historyof science. Thus, Putnam argues that we should take theearly Niels Bohr to have been referring to electrons inthe quantum-theoretic sense, or we would have to ‘‘dis-miss all of his 1900 beliefs as totally wrong’’ (Putnam

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1988), perhaps on a par with someone’s beliefs aboutangels, a conclusion that is plainly absurd . . . .

Agreeing . . . that an interest in intelligibility inscientific discourse across time is a fair enoughconcern, still it cannot serve as the basis for ageneral theory of meaning; it is, after all, only oneconcern among many, and not a central one for thestudy of human psychology. Furthermore, thereare internalist paraphrases. Thus we might saythat in Bohr’s earlier usage, he expressed beliefsthat were literally false, because there was nothingof the sort he had in mind in referring to electrons;but his picture of the world and articulation of itwas structurally similar enough to later con-ceptions so that we can distinguish his beliefsabout electrons from beliefs about angels. (43)(see Putnam, Hilary).

Against Teleological Explanation in LinguisticsA number of philosophers and linguists have

thought that some progress can be made in theunderstanding of language by thinking of it asprincipally being a medium of communication.Chomsky rejects this conception of the nature oflanguage, arguing that the language faculty is notfor communication in any interesting sense. Ofcourse, by rejecting the contention that languageis a social object established for purposes of com-munication, Chomsky has not left much room forthinking of language in this way. But he also rejectsstandard claims that I-language must have evolvedfor the selectional value of communication; heregards such claims as without basis in fact. Onthis score, Chomsky sides with Gould (1980),Lewontin (1990), and many evolutionary biologistsin supposing that many of our features (cognitiveor anatomical) did not necessarily evolve for selec-tional reasons, but may have been the result ofarbitrary hereditary changes that have perhapsbeen co-opted (see Evolution). Thus the langu-age faculty may not have evolved for purposes ofcommunication but may have been co-opted forthat purpose, despite its nonoptimal design forcommunicative purposes.In any case, Chomsky cautions that even if there

was selectional pressure for the language faculty toserve as a means of communication, selection is butone of many factors in the emerging system. Cru-cially (2000, 163), ‘‘physical law provides narrowchannels within which complex organisms mayvary,’’ and natural selection is only one factorthat determines how creatures may vary withinthese constraints. Other factors (as Darwin himselfnoted) will include nonadaptive modifications and

unselected functions that are determined fromstructure (see Function).

Inductive Versus Abductive LearningA number of debates have turned on whether

language acquisition requires a dedicated languagefaculty or whether ‘‘general intelligence’’ is enoughto account for our linguistic competence. Chomskyconsiders the general-intelligence thesis hopelesslyvague, and argues that generalized inductivelearning mechanisms make the wrong predictionsabout which hypotheses children would select in anumber of cases. Consider the following two exam-ples from Chomsky (1975 and [1980] 1992a):

The man is tall ð5Þ

Is the man tall? ð6ÞChomsky observes that confronted with evi-

dence of question formation like that (5)–(6) andgiven a choice between hypothesis (H1) and (H2),the generalized inductive learning mechanism willselect (H1):

Move the first ‘‘is’’ to the front of the sentence:

ðH1Þ

Move the first ‘‘is’’ following the first NP

to the front of the sentence:ðH2Þ

But children apparently select (H2), since informing a question from (7), they never make theerror of producing (8), but always opt for (9):

The man who is here is tall: ð7Þ�Is the man who here is tall? ð8Þ

Is the man who is here tall? ð9ÞNote that this is true despite the fact that the

only data they have been confronted with previousto encountering (7) is simple data like (5)–(6).Chomsky’s conclusion is that whatever accountsfor children’s acquisition of language, it cannot begeneralized inductive learning mechanisms, butrather must be a system with structure-dependentprinciples/rules. Chomsky (1975, ch.1; 2000, 80)compares such learning to Peircian abduction. Inother contexts this has been cast as a thesis aboutthe ‘‘modularity’’ of language—that is, that there isa dedicated language acquisition device, and it,rather than some vague notion of general intelli-gence, accounts for our acquisition of language (seeEvolutionary Psychology).

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Putnam (1992) once characterized Chomsky’snotion of a mental organ like the language facultyas being ‘‘biologically inexplicable,’’ but Chomsky([1980] 1992b) has held that it is merely ‘‘unex-plained’’ and not inexplicable; in his view thelanguage faculty is thus on the same footing asmany other features of our biology (see Abduction;Inductive Logic).

The Science-Forming FacultyOn a more general and perhaps more abstract

level, Chomsky has often spoken of a ‘‘science-forming faculty,’’ parallel to our language faculty.The idea is that science could not have formed inresponse to mere inductive generalizations, but thathuman beings have an innate capacity to developscientific theories (Chomsky credits C. S. Peircewith this basic idea). Despite Star Trekkianassumptions to the contrary, extraterrestrials pre-sumably do not have a science-forming faculty likewe do, and may go about theorizing in entirelydifferent ways, which would not be recognized as‘‘scientific’’ by humans.

While the science-forming faculty may be limit-ed, Chomsky would not concede that its limits arenecessarily imposed by the selectional pressures ofour prehistoric past. Just as the language facultymay not have evolved principally in response toselectional pressures, so too the science-formingfaculty may have emerged quite independently ofselectional considerations. As Chomsky (2000,ch. 6) notes (citing Lewontin 1990), insects mayseem marvelously well adapted to flowering plants,but in fact insects evolved to almost their currentdiversity and structure millions of years beforeflowering plants existed. Perhaps it is a similarsituation with the science-forming faculty. That is,perhaps it is simply a matter of good fortune forus that the science-forming faculty is reliable anduseful, since it could not have evolved to help uswith quantum physics, for example.

The Limits of ScienceThe notion of a science-forming faculty also

raises some interesting questions about the limitsof our ability to understand the world. Since whatwe can know through naturalistic endeavors isbounded by our science-forming faculty, which inturn is part of our biological endowment, it standsto reason that there are questions that will remainmysteries to us—or at least outside the scope ofnaturalistic inquiry:

Like other biological systems, SFF [the science-formingfaculty] has its potential scope and limits; we may

distinguish between problems that in principle fall with-in its range, and mysteries that do not. The distinction isrelative to humans; rats and Martians have differentproblems and mysteries and, in the case of rats, weeven know a fair amount about them. The distinctionalso need not be sharp, though we certainly expect it toexist, for any organism and any cognitive faculty. Thesuccessful natural sciences, then, fall within the inter-section of the scope of SFF and the nature of the world;they treat the (scattered and limited) aspects of the worldthat we can grasp and comprehend by naturalistic inqui-ry, in principle. The intersection is a chance product ofhuman nature. Contrary to speculations since Peirce,there is nothing in the theory of evolution, or any otherintelligible source, that suggests that it should includeanswers to serious questions we raise, or even that weshould be able to formulate questions properly in areasof puzzlement. (2000, ch. 4)

The question of what the ‘‘natural’’ sciences are,then, might be answered, narrowly, by asking whatthey have achieved; or more generally, by inquiryinto a particular faculty of (the human) mind, withits specific properties.

The Mind/Body Problem and the Question ofPhysicalismChomsky has consistently defended a form of

methodological monism (he is certainly no dualist);but for all that, he is likewise no materialist. InChomsky’s view the entire mind/body question isill-formed, since there is no coherent notion ofphysical body. This latter claim is not in itselfunique; Crane and Mellor (1990) have made asimilar point. There is a difference, however; forCrane and Mellor, developments in twentieth-century science have undermined physicalism, butfor Chomsky the notion of physical body wasalready undermined by the time of Newton:

Just as the mechanical philosophy appeared to be trium-phant, it was demolished by Newton, who reintroduceda kind of ‘‘occult’’ cause and quality, much to the dis-may of leading scientists of the day, and of Newtonhimself. The Cartesian theory of mind (such as it was)was unaffected by his discoveries, but the theory of bodywas demonstrated to be untenable. To put it differently,Newton eliminated the problem of ‘‘the ghost in themachine’’ by exorcising the machine; the ghost wasunaffected. (2000, 84)

In Chomsky’s view, then, investigations into themind (in the guise of cognitive science generally orlinguistics in particular) can currently proceedwithout worrying about whether they hook upwith what we know about the brain, or even fun-damental particles. The unification of scienceremains a goal, but in Chomsky’s view it is not

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the study of mind that must be revised so as toconform to physical theory, but rather physicaltheory may eventually have to incorporate whatwe learn in our study of the mind. According toChomsky this is parallel to the situation that heldprior to the unification of chemistry and physics; itwas not chemistry that needed to be modified toaccount for what we know about physics, but infact just the opposite:

Large-scale reduction is not the usual pattern; oneshould not be misled by such dramatic examples as thereduction of much of biology to biochemistry in themiddle of the twentieth century. Repeatedly, the more‘‘fundamental’’ science has had to be revised, some-times radically, for unification to proceed. (2000, 82)

Conclusion

The influence of Chomsky’s work has been felt in anumber of sciences, but perhaps the greatest in-fluence has been within the various branches ofcognitive science. Indeed, Gardner (1987) hasremarked that Chomsky has been the single mostimportant figure in the development of cognitivescience. Some of Chomsky’s impact is due to hisrole in arguing against behaviorist philosopherssuch as Quine; some of it is due to work that ledto the integration of linguistic theory with othersciences; some of it is due to the development offormal tools that were later employed in disciplinesranging from formal language theory (cf. the‘‘Chomsky Hierarchy’’) to natural language proces-sing; and some of it is due to his directly engagingpsychologists on their own turf. (One classic exam-ple of this was Chomsky’s [1959b] devastating re-view of Skinner’s [1957] Verbal Behavior. See alsohis contributions to Piatelli-Palmerini 1980) (SeeBehaviorism).With respect to his debates with various philoso-

phers, Chomsky has sought to expose what he hastaken to be double standards in the philosophicalliterature. In particular he has held that while othersciences are allowed to proceed where inquiry takesthem without criticism by armchair philosophers,matters change when the domain of inquiry shiftsto mind and language:

The idea is by now a commonplace with regard tophysics; it is a rare philosopher who would scoff at itsweird and counterintuitive principles as contrary to rightthinking and therefore untenable. But this standpointis commonly regarded as inapplicable to cognitive sci-ence, linguistics in particular. Somewhere in-between,there is a boundary. Within that boundary, science isself-justifying; the critical analyst seeks to learn about

the criteria for rationality and justification from the studyof scientific success. Beyond that boundary, everythingchanges; the critic applies independent criteria to sit injudgment over the theories advanced and the entititiesthey postulate. This seems to be nothing more than akind of ‘‘methodological dualism,’’ far more perniciousthan the tradtional metaphysical dualism, which was ascientific hypothesis, naturalistic in spirit. Abandoningthis dualist stance, we pursue inquiry where it leads.(2000, 112)

PETER LUDLOW

References

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——— (1939), Linguistic Aspects of Science: InternationalEncyclopedia of Unified Science (Vol. 1, No. 4). Chicago:University of Chicago Press.

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——— (1988), Language and Problems of Knowledge: TheManagua Lectures. Cambridge, MA: MIT Press.

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——— ([1988] 1992c), ‘‘From Language and Problems ofKnowledge,’’ in B. Beakley and P. Ludlow (eds.), ThePhilosophy of Mind: Classical Problems/ContemporaryIssues. Cambridge, MA: MIT Press, 47–50.

——— (1994), ‘‘Noam Chomsky,’’ in S. Guttenplan (ed.),A Companion to the Philosophy of Mind. Oxford: Black-well, 153–167.

——— (1995), The Minimalist Program. Cambridge, MA:MIT Press.

——— (2000), New Horizons in the Study of Language andMind. Cambridge: Cambridge University Press.

——— (2001), ‘‘Beyond Explanatory Adequacy,’’ MIT Oc-casional Papers in Linguistics, no. 20. MIT Departmentof Linguistics.

Crane, T., and D. H. Mellor (1990), ‘‘There Is No Questionof Physicalism,’’ Mind 99: 185–206.

Gardner, H. (1987), The Mind’s New Science: A History ofthe Cognitive Revolution. New York: Basic Books.

Gould, S. J. (1980), The Panda’s Thumb: More Reflectionsin Natural History. New York: W. W. Norton.

Lewontin, R. (1990), ‘‘The Evolution of Cognition,’’ inD. N. Osherson and E. E. Smith (eds.), An Invitation toCognitive Science (Vol. 3). Cambridge, MA: MIT Press,229–246.

Newmeyer, Frederick (1986), Linguistic Theory in America(2nd ed.). San Diego: Academic Press.

Piatelli-Palmerini, M. (ed.) (1980), Language and Learning:The Debate between Jean Piaget and Noam Chomsky.Cambridge, MA: Harvard University Press.

Putnam, H. (1988), Representation and Reality. Cambridge,MA: MIT Press.

——— ([1980] 1992), ‘‘What Is Innate and Why: Commentson the Debate,’’ in B. Beakley and P. Ludlow (eds.), ThePhilosophy of Mind: Classical Problems/ContemporaryIssues. Cambridge, MA: MIT Press.

Skinner, B. F. (1957),Verbal Behavior. NewYork:Appleton-Century-Crofts.

Smith, N. (2000), Foreword, in Chomsky, New Horizons inthe Study of Language and Mind. Cambridge: CambridgeUniversity Press.

See also Behaviorism; Cognitive Science; Innate-Acquired Distinction; Linguistics, Philosophy of;Psychology, Philosophy of; Physicalism

CLASSICAL MECHANICS

Over the centuries classical mechanics has been asteady companion of the philosophy of science. Ithas played different parts, ranging (i) from positingits principles as a priori truths to the insight—pivotal for the formation of a modern philosophyof science—that modern physics requires a farewellto the explanatory ideal erected upon mechanics;(ii) from the physiological analyses of mechanicalexperiences to axiomatizations according to thestrictest logical standards; and (iii) from the me-chanistic philosophy to conventionalism (see Con-ventionalism; Determinism; Space-Time). Corestructures of modern science, among them differen-tial equations and conservation laws, as well as corethemes of philosophy, among themdeterminismandthe ontological status of theoretical terms, haveemerged from this context. Two of the founders ofclassicalmechanics,Galileo andNewton, have oftenbeen identified with the idea of modern science asa whole. Owing to its increasing conceptual and

mathematical refinement during the nineteenthcentury, classical mechanics gave birth to the com-bination of formal analysis and philosophicalinterpretation that distinguished the modern phi-losophy of science from the earlier Naturphiloso-phie. The works of Helmholtz, Mach, and Poincaremolded the historical character of the scientist-phi-losopher that would fully bloom during the emer-gence of relativity theory and quantum mechanics(see Mach; Quantum Mechanics; Poincare; Space-Time).Mechanicsbecame ‘‘classical’’at the latestwith the

advent of quantum mechanics. Already relativisticfield theory had challenged mechanics as the lead-ing scientific paradigm. Consequently, present-dayphilosophers of science usually treat classical me-chanics within historical case studies or as the firsttouchstone for new proposals of a general kind.Nonetheless, there are at least two lines on whichclassical mechanics in itself remains a worthy topic

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for philosophers. On the one hand, ensuing fromsubstantial mathematical progress during the twen-tieth century, classical mechanics has developedinto the theory of classical dynamical systems.Among the problems of interest to formally mind-ed philosophers of science are the relationshipsbetween the different conceptualizations, issues ofstability and chaotic behavior, and whether classi-cal mechanics is a special case of the conceptualstructures characteristic of other physical theories.On the other hand, classical mechanics or semiclas-sical approaches continue to be applied widely byworking scientists and engineers. Those real-worldapplications involve a variety of features that sub-stantially differ from the highly idealized textbookmodels to which physicists and philosophers aretypically accustomed, and they require solutionstrategies whose epistemological status is far fromobvious.Often classical mechanics is used synonymously

with Newtonian mechanics, intending that its con-tent is circumscribed by Newton’s famous threelaws. The terms analytical mechanics and rationalmechanics stress the mathematical basis and theo-retical side of mechanics as opposed to practicalmechanics, which originally centered around thetraditional simple machines: lever, wedge, wheeland axle, tackle block, and screw. But the domainof mechanics was being constantly enlarged by theinvention of new mechanical machines and tech-nologies. Most expositions of mechanics also in-clude the theory of elasticity and the mechanics ofcontinua. The traditional distinction between me-chanics and physics was surprisingly long-lived.One reason was that well into the nineteenth centu-ry, no part of physics could live up to the level offormal sophistication that mechanics had achieved.Although of little importance from a theoreticalpoint of view, it is still common to distinguish statics(mechanical systems in equilibrium) and dynamicsthat are subdivided into a merely geometrical part,kinematics, and kinetics.

Ancient Greek and Early Modern Mechanics

In Greek antiquity, mechanics originally denotedthe art of voluntarily causing motions against thenature of the objects moved. Other than physics, itwas tractable by the methods of Euclidean geome-try. Archimedes used mechanical methods to deter-mine the center of mass of complex geometricalshapes but did not recognize them as valid geomet-rical proofs. His Euclidean derivation of the lawof the lever, on the other hand, sparked severecriticism from Mach ([1883] 1960), who held that

no mathematical derivation whatsoever couldreplace experience.

Pivotal for bringing about modern experimentalscience was Galileo’s successful criticism of Aristo-telian mechanics. Aristotle had divided all naturalmotions into celestial motions, which were circularand eternal, and terrestrial motions, which wererectilinear and finite. Each of the four elements(earth, water, fire, air) moved toward its naturalplace. Aristotle held that heavy bodies fell fasterthan light ones because velocity was determined bythe relation of motive force (weight) and resistance.All forces were contact forces, such that a bodymoving with constant velocity was continuouslyacted upon by a force from the medium. Resistanceguaranteed that motion remained finite in extent.Thus there was no void, nor motion in the void.Galileo’s main achievement was the idealization ofa constantly accelerated motion in the void that isslowed down by the resistance of the medium. Thismade free fall amenable to geometry. For today’sreader, the geometrical derivation of the law isclumsy; the ratio of different physical quantitiesv ¼ s/t (where s stands for a distance, t for a timeinterval, and v for a velocity) was not yet meaning-ful. Galileo expressly put aside what caused bodiesto fall and referred to experimentation. Historiansand philosophers have broadly discussed what andhow Galileo reasoned from empirical evidence.Interpreters wondered, in particular, whether thethought experiment establishing the absurdity ofthe Aristotelian position was conclusive by itselfor whether Galileo had simply repackaged empiri-cal induction in the deductive fashion of geometry.

Huygens’ most important contribution to me-chanics was the derivation of the laws of impactby invoking the principle of energy conservation.His solution stood at the crossroads of two tradi-tions. On the one hand, it solved the foundationalproblem of Cartesian physics, the program ofwhich was to reduce all mechanical phenomena tocontact forces exchanged in collision processes. Onthe other hand, it gave birth to an approach basedupon the concept of energy, which became an al-ternative to the Newtonian framework narrowlyunderstood.

The work of Kepler has repeatedly intriguedphilosophers of diverging orientations. Utilizingthe mass of observational data collected by Brahe,Kepler showed that the planetary orbits were ellip-ses. Kepler’s second law states that the line joiningthe sun to the planet sweeps through equal areas inequal times, and the third law states that the squareof the periods of revolution of any two planetsare in the same proportion as the cubes of their

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semi-major axes. All three laws were merely kine-matical. In his Mysterium cosmographicum, Kepler([1596] 1981) identified the spacings of the thenknown six planets with the five platonic solids. Itwill be shown below that the peculiar shape ofthe solar system given Newton’s laws of univer-sal gravitation can be explained without refer-ence to Kepler’s metaphysical belief in numericalharmony.

On the Status of Newton’s Laws

The most important personality in the history ofclassical mechanics was Newton. Owing to theactivities of his popularizers, he became regardedas the model scientist; this admiration included adevotion to the methodology of his Philosophiaenaturalis principia mathematica (Newton [1687,1713] 1969), outlined in a set of rules precedingbook III. But interpreters disagree whether Newtonreally pursued the Baconian ideal of science andlicensed induction from phenomena or must be sub-sumed under the later descriptivist tradition thatemerged with Mach ([1883] 1960) and Kirchhoff(1874). At any rate, the famous declaration notto feign hypothesis targeted the Cartesian andLeibnizian quest for a metaphysical basis of theprinciples of mechanics.

After the model of Euclid, the Principia beganwith eight definitions and three axioms or laws.Given Newton’s empiricist methodology, interpre-ters have wondered about their epistemologicalstatus and the logical relations among them. Cer-tainly, the axioms were neither self-evident truthsnor mutually independent:

1. Every body continues in its state of rest oruniform motion in a right (i.e., straight) line,unless it is compelled to change that state byforces impressed upon it.

2. The change of motion is proportional to themotive force impressed and is made in thedirection of the right line in which that forceis impressed.

3. To every action there is always opposed anequal reaction; or the mutual actions of twobodies upon each other are always equal, anddirected to contrary parts.

The proper philosophical interpretation of thesethree laws remained contentious until the end ofthe nineteenth century. Kant claimed to havededuced the first and third laws from the synthetica priori categories of causality and reciprocity, re-spectively. The absolute distinction between restand motion in the first law was based on absolute

space and time. Within Kant’s transcendental phi-losophy, Euclidean space-time emerged from pureintuition a priori. This was the stand againstwhich twentieth-centuryphilosophyof science rebel-led, having relativity theory in its support (seeSpace-Time).Admitting that the laws were suggested by pre-

vious experiences, some interpreters, includingPoincare, considered them as mere conventions(see Conventionalism). Positing absolute Euclideanspace, the first law states how inertial matter movesin it. But it is impossible to obtain knowledge aboutspace independent of everything else. Thus, the firstlaw represents merely a criterion for choosing asuitable geometry. Mach ([1883] 1960) rejectedabsolute space and time as metaphysical. All ob-servable motion was relative, and thus, at least inprinciple, all material objects in the universe weremutually linked. Mach’s principle, as it becamecalled, influenced the early development of generalrelativity but is still controversial among philoso-phers (see Barbour and Pfister 1995; Pooley andBrown 2002). To Mach’s mind, the three laws werehighly redundant and followed from a proper em-piricist explication of Newton’s definitions of massand force. Defining force, with Newton, as an ac-tion exerted upon a body to change its state, that is,as an acceleration, the first and second laws can bestraightforwardly derived. Mach rejected Newton’sdefinition of mass as quantity ofmatter as a pseudo-definition and replaced it with the empirical insightthat mass is the property of bodies determin-ing acceleration. This was equivalent to the thirdlaw. Mach’s criticism became an important moti-vation for Einstein’s special theory of relativity.Yet, even the members of the Vienna Circle dis-agreed whether this influence was formative orMach merely revealed the internal contradictionsof the Newtonian framework (see Vienna Circle).As to the second law, one may wonder whether

the forces are inferred from the observed phenom-ena of motion or the motions are calculated fromgiven specific forces. Textbooks often interpret thesecond law as providing a connection from forcesto motion, but this is nontrivial and requires aproper superposition of the different forces and adue account of the constraints. The opposite inter-pretation has the advantage of not facing the noto-rious problem of characterizing force as an entityin its own right, which requires a distinction be-tween fundamental forces from fictitious or inertialforces.Book III of Newton’s Principia introduced the

law of universal gravitation, which finally unifiedthe dynamics of the celestial and terrestrial spheres.

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But, as it stood, it involved an action at a distancethrough the vacuum, which Newton regardedas the greatest absurdity. To Bentley he wrote:‘‘Gravity must be caused by an Agent actingaccording to certain Laws; but whether this Agentbe material or immaterial, I have left to the Consid-eration ofmy readers’’ (Cohen 1958, 303). Given thelaw of universal gravity, the peculiar shape of thesolar system was a matter of initial conditions, afact that Newton ascribed to the contrivance of avoluntary agent.The invention of the calculus was no less impor-

tant for the development of mechanics than was thelaw of gravitation. But its use in the Principia wasnot consistent and intertwined with geometricalarguments, and it quickly turned out that Leibniz’sversion of the calculus was far more elegant. ThatBritish scientists remained loyal to Newton’s flux-ions until the days of Hamilton proved to be asubstantial impediment to the use of calculus inscience.

Celestial Mechanics and the ApparentTriumph of Determinism

No other field of mechanics witnessed greater tri-umphs of prediction than celestial mechanics: thereturn of Halley’s comet in 1758; the oblateness ofthe Earth in the 1740s; and finally the discovery ofNeptune in 1846 (cf. Grosser 1962). However,while Neptune was found at the location that theanomalies in the motion of Uranus had suggested,Le Verrier’s prediction of a planet Vulcan to ac-count for the anomalous perihelion motion ofMercury failed. Only general relativity would pro-vide a satisfactory explanation of this anomaly (seeSpace-Time).But in actual fact little follows from Newton’s

axioms and the inverse square law of gravitationalone. Only the two-body problem can be solvedanalytically by reducing it to a one-body problemfor relative distance. The three-body problem re-quires approximation techniques, even if the massof one body can be neglected. To ensure the conver-gence of the respective perturbation series becamea major mathematical task. In his lunar theory,Clairaut could derive most of the motion of thelunar apsides from the inverse-square law, providedthe approximation was carried far enough. Butd’Alembert warned that further iterations mightfail to converge; hence subsequent analysts cal-culated to higher and higher orders. D’Alembert’sderivation of the precession and nutation of theEarth completed a series of breakthroughs around1750 that won Newton’s law a wide acceptance. In

1785, Laplace explained the remaining chief anoma-lies in the solar system and provided a (flawed)indirect proof for the stability of the solar systemfrom the conservation of angular momentum(cf. Wilson 1995).

One might draw an inductivist lesson from thishistory and conceive the increased precision in thecore parameters of the solar system, above all theplanetary masses, as a measure of explanatory suc-cess for the theory containing them (cf. Harper andSmith 1995). Yet, the historically more influentiallesson for philosophers consisted in the ideal ofLaplace’s Demon, the intellect that became theexecutive officer of strict determinism:

Given for one instant an intelligence which could com-prehend all the forces by which nature is animated andthe respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data toanalysis—it would embrace in the same formula thegreatest bodies of the universe and those of the lightestatom; for it, nothing would be uncertain, and the future,as the past, would be present to its eyes.

(Laplace [1795] 1952, 4)

But the Demon is threatened by idleness in manyways. If the force laws are too complex, determin-ism becomes tautologous; if Newton’s equationscannot be integrated, perturbative and statisticalstrategies are mandatory; calculations could stillbe too complex; exact knowledge of the initialstate of a system presupposes that the precision ofmeasurement could be increased at will.

A further idealization necessary to make theLaplacian ideal thrive was the point mass approachof Boscovich ([1763] 1966). But some problemscannot be solved in this way—for instance, whethera point particle moving in a head-on orbit directedat the origin of a central force is reflected by thesingularity or goes right through it. In many cases,celestial mechanics treats planets as extended bod-ies or gyroscopes rather than point masses. Non-rigid bodies or motion in resisting media requireeven further departures from the Laplacian ideal.As Mark Wilson put it, ‘‘applied mathematiciansare often forced to pursue roundabout and shakilyrationalized expedients if any progress is to bemade’’ (2000, 296).

Only some of these expedients can be mathemat-ically justified. This poses problems for the rela-tionship of mathematical and physical ontology.Often unsolvable equations are divided into tracta-ble satellite equations. Continuum mechanics is acase in point. The Navier-Stokes equations arevirtually intractable by analytic methods; Prandtl’sboundary layer theory splits a flow in a pipe into

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one equation for the fluid’s boundary and one forthe middle of the flow. Prandtl’s theory failed in thecase of turbulence, while statistical investigationsbrought useful results. Accordingly, in this casepredictability required abandoning determinismaltogether years before the advent of quantummechanics (cf. von Mises 1922).

From Conserved Quantities to Invariances:Force and Energy

The framework of Newton’s laws was not the onlyconception of mechanics used by 1800 (cf. Grattan-Guinness 1990). There were purely algebraic ver-sions of the calculus based on variational problemsdeveloped by Euler and perfected in Lagrange’sAnalytical Mechanics ([1788] 1997). Engineers de-veloped a kind of energy mechanics that emergedfrom Coulomb’s friction studies. Lazare Carnot de-veloped it into an alternative to Lagrange’s reduc-tion of dynamics to equilibrium, that is, to statics.Dynamics should come first, and engineers had todeal with many forces that did not admit a potentialfunction.

The nature of energy—primary entity or justinferred quantity—was no less in dispute thanthat of force. Both were intermingled in contentand terminology. The eighteenth century wasstrongly influenced by the vis viva controversylaunched by Leibniz. What was the proper quantityin the description of mechanical processes: mv ormv2 (where m ¼ mass and v ¼ velocity)? After theLeibniz-Clarke correspondence, the issue becameassociated with atomism and the metaphysicalcharacter of conserved quantities. In the nineteenthcentury, ‘energy,’ or work, became a universalprinciple after the discovery of the mechanicalequivalent of heat. Helmholtz gave the principle amore general form based upon the mechanicalconception of nature. For many scientists this sug-gested a reduction of the other domains of physicalscience to mechanics. But this program failed inelectrodynamics.

Through the works of Ostwald and Helm, theconcept of energy became the center of a movementthat spellbound German-speaking academia fromthe 1880s until the 1900s. But, as Boltzmann untir-ingly stressed, energeticists obtained the equationsof motion only by assuming energy conservation ineach spatial direction. But why should Cartesiancoordinates have a special meaning?

Two historico-critical studies of the energy con-cept set the stage for the influential controversybetween Planck and Mach (1908–1910). WhileMach ([1872] 1911) considered the conservation

of work as an empirical specification of the instinc-tive experience that perpetual motion is impossible,Planck (1887) stressed the independence and uni-versality of the principle of energy conservation.Planck later lauded Mach’s positivism as a usefulantidote against exaggerated mechanical reduc-tionism but called for a stable world view erectedupon unifying variational principles and invariantquantities.Group theory permitted mathematical physicists

to ultimately drop any substantivalist connotationof conserved quantities, such as energy. The mainachievement was a theorem of Emmy Noether thatidentified conserved quantities, or constants of mo-tion, with invariances under one-parameter grouptransformations (cf. Arnold 1989, 88–90).

Variational Principles and HamiltonianMechanics

In 1696–7 Johann Bernoulli posed the problem offinding the curve of quickest descent between twopoints in a homogeneous gravitational field. Whilehis own solution used an analogy between geomet-rical optics and mechanics, the solutions of Leibnizand Jacob Bernoulli assumed that the property ofminimality was present in the small as in the large,arriving thus at a differential equation. The title ofEuler’s classic treatise describes the scope of thevariational calculus: The Method of Finding CurvedLines That Show Some Property of Maximum orMinimum (1744). The issue of minimality sparkedphilosophical confusion. In 1746 Pierre Moreau deMaupertuis announced that in all natural processesthe quantity

Rvds ¼ R

v2dt attains its minimum; heinterpreted this as a formal teleological principlethat avoided the outgrowths of the earlier physi-cotheology of Boyle and Bentley. Due to his defec-tive examples and a priority struggle, the principlelost much of its credit. Lagrange conceived of itsimply as an effective problem-solving machinery.There was considerable mathematical progressduring the nineteenth century, most notably byHamilton, Gauss, and Jacobi. Only Weierstrassfound the first sufficient condition for the varia-tional integral to actually attain its minimum value.In 1900, Hilbert urged mathematicians to sys-tematically develop the variational calculus (seeHilbert, David). He made action principles a coreelement of his axiomatizations of physics. Hilbertand Planck cherished the principles’ applicability,after appropriate specification, to all fields of re-versible physics; thus they promised a formal uni-fication instead of the discredited mechanicalreductionism.

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There exist differential principles, among themd’Alembert’s principle and Lagrange’s principle ofvirtual work, that reduce dynamics to statics, andintegral action principles that characterize the ac-tual dynamical evolution over a finite time by thestationarity of an integral as compared with otherpossible evolutions. Taking Mq as the space of allpossible motions q(t) between two points in config-uration space, the action principle states that theactual motion q extremizes the value of the integralW ½q� ¼ R b

aFðt; qðtÞ; _qðtÞÞdt in comparison with all

possible motions, the varied curves (q þ dq)2Mq

(the endpoints of the interval [a, b] remain fixed).If one views the philosophical core of action

principles in a temporal teleology, insofar as aparticle’s motion between a and b is also deter-mined by the fixed state, this contradicts the factthat almost all motions that can be treated by wayof action principles are reversible. Yet, already themathematical conditions for an action principle tobe well defined suggest that the gist of the matterlies in its global and modal features. Among thenecessary conditions is the absence of conjugatepoints between a and b through which all variedcurves have to pass. Sufficient conditions typicallyinvolve a specific field embedding of the variedcurves; also the continuity properties of the q 2Mq play a role. Thus initial and final conditionshave to be understood in the same vein as bound-ary conditions for partial differential equationsthat have to be specified beforehand so that thesolution cannot be grown stepwise from initialdata.There are also different ways of associating the

possible motions. In Hamilton’s principle, F is theLagrangian L ¼ T – V, where T is the kinetic and Vthe potential energy; time is not varied such that allpossible motions take equal time but correspond tohigher energies than the actual motion. For theoriginal principle of least action, F equals T, andone obtains the equations of motion only by as-suming energy conservation, such that at equaltotal energy the varied motions take a longer timethan the actual ones.Butterfield (2004) spots three types of modality

in the sense of David Lewis (1986) here. While allaction principles involve a modality of changed ini-tial conditions and changed problems, Hamilton’sprinciple also involves changed laws because thevaried curves violate energy conservation. Energe-ticists and Mach ([1883] 1960) held that u is unique-ly determined within Mu as compared with theother motions that appear pairwise or with higherdegeneracy, but they disagreed whether one could

draw conclusions about modal characteristics.Albeit well versed in their mathematical intri-cacies, logical empiricists treated action principleswith neglect in order to prevent an intrusion ofmetaphysics (Stoltzner 2003).

The second-order Euler-Lagrange equations,which typically correspond to the equations estab-lished by way of Newton’s laws, can be reformu-lated as a pair of first-order equations, Hamilton’sequations, or a single partial differential equation,viz., the Hamilton-Jacobi equation. Hamilton’sequations emerge from the so-called Legendretransformation, which maps configuration spaceðq; _qÞ into phase space ðq; pÞ, thus transformingthe derivative of position _q into momentum p. Ifthis transformation fails, constraints may be pres-ent. The core property of Hamilton’s equations istheir invariance under the so-called canonical trans-formations. The canonical transformation ðq; pÞ !ðQ;PÞ that renders the Hamiltonian H(Q,P) ¼T þ V equal to zero leads to the Hamilton-Jacobiequation. Its generator W ¼ S – Et (where Et is thetotal energy) can be interpreted as an action func-tional corresponding to moving wave fronts in or-dinary space that are orthogonal to the extremalsof the variational problem (cf. Lanczos 1986).

The analogy between mechanics and geometricoptics is generic and played an important role inSchrodinger’s justification of his wave equation.Hamilton-Jacobi theory was also a motivation forBohm’s reformulation of the de Broglie pilot wavetheory (see Quantum Mechanics). For periodicalmotions one can use S to generate a canonicaltransformation that arrives at action and anglevariables ðJ;oÞ, where J ¼ rpdq. This integralwas quantized in the older Bohr-Sommerfeldquantum theory. The space of all possible motionsassociated with a variational problem Mq can beconsidered as an ensemble of trajectories. Arguingthat in quantum theory all possible motions arerealized with a certain possibility provides someintuitive motivation for the Feynman path integralapproach (see Quantum Field Theory).

Variational principles played a central role inseveral philosophically influential treatises of me-chanics in the late nineteenth century. Most radicalwas that of Heinrich Hertz ([1894] 1956), who usedGauss’s (differential) principle of least constraintsto dispense with the notion of force altogether.There were no single mass points but only a systemof mass points connected by constraints. Hertz’sproblem was to obtain a geometry of straight linefor this system ofmass points. This task was compli-cated by Hertz’s Kantian preference for Euclidean

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geometry as a basis for the non-Euclidean geometryof mass points. Contemporaries deemed Hertz’sgeometrization of mechanics a ‘‘God’s eye view.’’Boltzmann (1897 and 1904) praised its coherencebut judged Hertz’s picture as inapplicable to pro-blems easily tractable by means of forces.

Hertz held that theoretical pictures had to belogically permissible, empirically correct, and ap-propriate (that is, sufficiently complete and sim-ple). Boltzmann criticized permissibility as anunwarranted reliance upon a priori laws of thoughtand held instead that pictures were historically ac-quired and corroborated by success. Around 1900,treating theories (e.g., atomism) as pictures repre-sented an alternative to mechanical reductionismand positivist descriptivism, until the idea of co-ordinative definitions between symbolic theoryand empirical observations won favor (see ViennaCircle).

Mathematical Mechanics and ClassicalDynamical Systems

After classical mechanics was finally dethroned asthe governing paradigm of physics, its coursebecame largely mathematical in kind and wasstrongly influenced by concepts and techniques de-veloped by the new-frontier theories of physics:relativity theory and quantum physics. There wassubstantial progress in the variational calculus,but the main inspirations came from differentialgeometry, group theory, and topology, on theone hand, and probability theory and measure the-ory, on the other. This has led to some rigorousresults on the n-body problem. The advent of themodern computer not only opened a new era ofcelestial mechanics, it also revealed that chaoticbehavior, ignored by physicists in spite of its earlydiscovery by Poincare, occurred in a variety ofsimple mechanical systems.

Geometrization has drastically changed theappearance of classical mechanics. Configurationspace and phase space have become the tangentand cotangent bundles on which tensors, vectorfields, and differential forms are defined. Coordi-nates have turned into charts, and the theory ofdifferentiable manifolds studies the relationshipsbetween the local level, where everything looksEuclidean, and the global level, where topologicalobstructions may arise. The dynamics acting onthese bundles are expressed in terms of flows de-fined by vector fields, which gives a precise mean-ing to variations. The picture of flows continuesHamilton-Jacobi theory. This elucidates that the

intricacies of variational calculus do not evaporate;they transform into obstructions of and conditionsfor the application of the whole geometricalmachinery, e.g., how far a local flow can be extend-ed. The constants of the motion define invariantsubmanifolds that restrict the flow to a manifold oflower dimension; they act like constraints. If aHamiltonian system has, apart from total energy,enough linearly independent constants of motionand if their Poisson brackets fF ;Gg ¼ Pm

i¼1ð@F=@qi@G=@pi � @G=@qi@F=@piÞ mutually vanish, thesystem is integrable (the equations of motion canbe solved) and the invariant submanifold can beidentified with a higher-dimensional torus.The geometrical structure of Hamiltonian me-

chanics is kept together by the symplectic formo ¼ dqi6dpi that is left invariant by canonicaltransformations. It plays a role analogous to themetric in relativity theory. The skew-symmetricproduct 6 of forms and the exterior derivative dare the main tools of the Cartan calculus and per-mit an entirely coordinate-free formulation of dy-namics. Many equations thus drastically simplify,but quantitative results still require the choice of aspecific chart.Mathematical progress went hand in hand with a

shift of emphasis from quantitative to qualitativeresults that started with Poincare’s work on then-body problem. Some deep theorems of Hamilto-nian mechanics become trivialities in this new lan-guage, among them the invariance of phase spacevolume (Liouville’s theorem) and the fact that al-most all points in a phase space volume eventually—in fact, infinitely often—return arbitrarily close totheir original position (Poincare recurrence) (seealso Statistical Mechanics).For the small number of mass points character-

istic of celestial mechanics, there has been majorprogress along the lines of the questions asked byThirring (1992, 6): ‘‘Which configurations are sta-ble? Will collisions ever occur? Will particles everescape to infinity? Will the trajectory always remainin a bounded region of phase space?’’ In the two-body problem, periodic elliptic motions, head-oncollisions, and the hyperbolic and parabolic trajec-tories leading to infinity are neatly separated byinitial data.For the three-body problem the situation is

already complex; there do not exist sufficient con-stants of motion. Two types of exact solutions werequickly found: The particles remain collinear(Euler) or they remain on the vertices of an equilat-eral triangle (Lagrange). The equilateral configura-tion is realized by the Trojan asteroids, Jupiter and

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the sun. In general, however, even for a negativetotal energy, two bodies can come close enough toexpel the third to infinity. In the four-body pro-blem, there exist even collinear trajectories onwhich a particle might reach spatial infinity in afinite time (Mather and McGehee 1975). Five bod-ies, one of them lighter than the others, can even bearranged in such a manner that this happens with-out any previous collisions because the fifth parti-cle oscillates faster and faster between the twoescaping planes, in each of which two particlesrotate around one another (Xia 1992; Saari 2005).Both examples blatantly violate special relativity.But rather than hastily resort to arguments ofwhat is ‘physical,’ the philosopher should followthe mathematical physicist in analyzing the logicalstructure of classical mechanics, including collisionsand other singularities.Can an integrable system remain stable under

perturbation? In the 1960s Kolmogorov, Arnold,and Moser (KAM) gave a very general answer thatavails itself of the identification of integrable sys-tems and invariant tori. The KAM theorem showsthat sufficiently small perturbations deform onlythe invariant tori. If the perturbation increases,the tori in resonance with it break first; or moreprecisely, the more irrational the ratio of the fre-quency of an invariant torus (in action and anglevariables) and the frequency of the perturbation,the more stable is the respective torus. If all invari-ant tori are broken, the system becomes chaotic (cf.Arnold 1989; Thirring 1992). The KAM theoremalso provides the rigorous basis of Kepler’s associ-ation of planetary orbits and platonic solids. Theratios of the radii of platonic solids to the radii ofinscribed platonic solids are irrational numbers of akind that is badly approximated by rational num-bers. And, indeed, among the asteroids betweenMars and Jupiter, one finds significant gaps forsmall ratios of an asteroid’s revolution time tothat of the perturbing Jupiter.If all invariant tori have broken up, the only

remaining constant of motion is energy, such thatthe system begins to densely cover the energy shelland becomes ergodic. No wonder that concepts ofstatistical physics, among them ergodicity, entropy,and mixing, have been used to classify chaotic be-havior, even though chaotic behavior does not suc-cumb to statistical laws. They are supplemented bytopological concepts, such as the Hausdorff dimen-sion, and concepts of dynamical systems theory,such as bifurcations (nonuniqueness of the timeevolution) and attractors (in the case of dissipativesystems where energy is no longer conserved).

MICHAEL STOLTZNER

References

Arnold, Vladimir I (1989), Mathematical Methods of Clas-sical Mechanics, 2nd ed. New York and Berlin: Springer.

Barbour, Julian B., and Herbert Pfister (eds.) (1995),Mach’s Principle: From Newton’s Bucket to QuantumGravity. Boston and Basel: Birkhauser.

Boltzmann, Ludwig (1897 and 1904), Vorlesungen uber diePrincipe der Mechanik. 2 vols. Leipzig: Barth.

Boscovich, Ruder J. ([1763] 1966), A Theory of NaturalPhilosophy. Cambridge, MA: MIT Press.

Butterfield, Jeremy (2004), ‘‘Some Aspects of Modality inAnalytical Mechanics,’’ in Michael Stoltzner and PaulWeingartner (eds.), Formale Teleologie und Kausalitat.Paderborn, Germany: Mentis.

Cohen, I. Bernhard (ed.) (1958), Isaac Newton’s Papers andLetters on Natural Philosophy. Cambridge, MA: HarvardUniversity Press.

Euler, Leonhard (1744), Methodus Inveniendi Lineas CurvasMaximi Minimive Proprietate Gaudentes sive SolutioProblematis Isoperimetrici Latissimo Sensu Accepti.Lausanne: Bousquet.

Grattan-Guinness, Ivor (1990), ‘‘The Varieties ofMechanicsby 1800,’’ Historia Mathematica 17: 313–338.

Grosser, Morton (1962), The Discovery of Neptune. Cam-bridge, MA: Harvard University Press.

Harper, William, and George E. Smith (1995), ‘‘Newton’sNew Way of Inquiry,’’ in J. Leplin (ed.), The Creationof Ideas in Physics: Studies for a Methodology ofTheory Construction. Dordrecht, Netherlands: Kluwer,113–166.

Hertz, Heinrich ([1894] 1956), The Principles of Mechanics:Presented in a New Form. New York: Dover Publica-tions.

Kepler, Johannes ([1596] 1981), Mysterium cosmographi-cum. New York: Abaris.

Kirchhoff, Gustav Robert (1874), Vorlesungen uber analy-tische Mechanik. Leipzig: Teubner.

Lagrange, Joseph Louis ([1788] 1997), Analytical Mechan-ics. Dordrecht, Netherlands: Kluwer.

Lanczos, Cornelius (1986), The Variational Principles ofMechanics. New York: Dover.

Laplace, Pierre Simon de ([1795] 1952), A PhilosophicalEssay on Probabilities. New York: Dover.

Lewis, David (1986), On the Plurality of Worlds. Oxford:Blackwell.

Mach, Ernst ([1872] 1911),History and Root of the Principleof the Conservation of Energy. Chicago: Open Court.

——— ([1883] 1960), The Science of Mechanics: A Criticaland Historical Account of Its Development. La Salle, IL:Open Court. German first edition published by Broc-khaus, Leipzig, 1883.

Mather, John, and Richard McGehee, ‘‘Solutions of theCollinear Four-Body ProblemWhich Become Unbound-ed in Finite Time,’’ in Jurgen Moser (ed.), DynamicalSystems Theory and Applications. New York: Springer,573–587.

Newton, Isaac ([1687, 1713] 1969), Mathematical Principlesof Natural Philosophy. Translated by Andrew Motte(1729) and revised by Florian Cajori. 2 vols. NewYork: Greenwood.

Planck, Max (1887), Das Princip der Erhaltung der Energie,2nd ed. Leipzig: B. G. Teubner.

Pooley, Oliver, and Harvey Brown (2002), ‘‘RelationalismRehabilitated? I: Classical Mechanics,’’ British Journalfor the Philosophy of Science 53: 183–204.

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Saari, Donald G. (2005), Collisions, Rings, and Other New-tonian N-Body Problems. Providence, RI: AmericanMathematical Society.

Stoltzner, Michael (2003), ‘‘The Principle of Least Actionas the Logical Empiricists’ Shibboleth,’’ Studies inHistory and Philosophy of Modern Physics 34: 285–318.

Thirring,Walter (1992),ACourse inMathematical Physics 1:Classical Dynamical Systems, 2nd ed. Translated byEvans M. Harrell. New York and Vienna: Springer.

von Mises, Richard (1922), ‘‘Uber die gegenwartige Kriseder Mechanik,’’ Die Naturwissenschaften 10: 25–29.

Wilson, Curtis (1995), ‘‘The Dynamics of the Solar System,’’in Ivor Grattan-Guinness (ed.), Companion Encyclopediaof the History and Philosophy of the MathematicalSciences. London: Routledge.

Wilson, Mark (2000), ‘‘The Unreasonable Uncooperative-ness of Mathematics in the Natural Sciences,’’ TheMonist 83 (2000): 296–314. See also his very instructiveentry ‘‘Classical Mechanics’’ in the Routledge Encyclope-dia of Philosophy.

Xia, Zhihong (1992), ‘‘The Existence of Noncollision Sin-gularities in Newtonian Systems,’’ Annals of Mathemat-ics 135: 411–468.

COGNITIVE SCIENCE

Cognitive science is a multidisciplinary approach tothe study of cognition and intelligence that emerg-ed in the late 1950s and 1960s. ‘‘Core’’ cognitivescience holds that the mind/brain is a kind of com-puter that processes information in the form ofmental representations. The major disciplinary par-ticipants in the cognitive science enterprise arepsychology, linguistics, neuroscience, computerscience, and philosophy. Other fields that are some-times included are anthropology, education, math-ematics, biology, and sociology.

There has been considerable philosophical dis-cussion in recent years that relates, in one way oranother, to cognitive science. Arguably, not all ofthis discussion falls within the tradition of philoso-phy of science. There are two fundamentally differ-ent kinds of question that philosophers of sciencetypically raise about a specific scientific field: ‘‘ex-ternal’’ questions and ‘‘internal’’ questions. If oneassumes that a scientific field provides a frameworkof inquiry, external questions will be about thatframework as a whole, from some external pointof view, or about its relation to other scientificframeworks. In contrast, an internal question willbe one that is asked within the framework, eitherwith respect to some entity or process that constitu-tes part of the framework’s foundations or withrespect to some specific theoretical/empirical issuethat scientists committed to that framework areaddressing. Philosophers have dealt extensivelywith both external and internal questions associatedwith cognitive science.

Key External Questions

There are three basic groups of external questions:those concerning the nature of a scientific field X,those concerning the relations ofX to other scientif-ic fields, and those concerning the scientific meritsof X. An interesting feature of such discussionsis that they often draw on, and sometimes evencontribute to, the literature on a relevant priormeta-question. For example, discussions concer-ning the scientific nature of a particular X (e.g.,cognitive science) may require prior conside-ration of the question, What is the best way tocharacterize X (in general) scientifically (e.g., interms of its theories, explanations, paradigm,research program)?

What Is Cognitive Science?There are many informal descriptions of cogni-

tive science in the literature, not based on anyserious consideration of the relevant meta-question(e.g., Simon 1981; Gardner 1985). The only system-atic formal treatment of cognitive science is thatof von Eckardt (1993), although there have beenattempts to describe aspects of cognitive psychologyin terms of Kuhn’s notion of a paradigm. RejectingKuhn’s notion of a paradigm as unsuitable for thecharacterization of an immature field, von Eckardt(1993) proposes, as an alternative, the notion of aresearch framework. A research framework consistsof four sets of elements D, Q, SA,MA, where D is aset of assumptions that provide a pretheoretical

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specification of the domain under study; Q is a setof basic empirical research questions, formulatedpretheoretically; SA is a set of substantive assump-tions that embody the approach being taken inanswering the basic questions and that constrainpossible answers to those questions; and MA is aset of methodological assumptions.One can think of what Kuhn (1970) calls ‘‘normal

science’’ as problem-solving activity. The funda-mental problem facing the community of research-ers committed to a research framework is to answereach of the basic empirical questions of that frame-work, subject to the following constraints:

1. Each answer is scientifically acceptable inlight of the scientific standards set down bythe shared and specific methodological as-sumptions of the research framework.

2. Each answer is consistent with the substan-tive assumptions of the research framework.

3. Each answer to a theoretical question makessignificant reference to the entities and pro-cesses posited by the substantive assumptionsof the research framework.

According to von Eckardt (1993), cognitive sci-ence consists of a set of overlapping research fra-meworks, each concerned with one or anotheraspect of human cognitive capacities. Arguably,the central research framework concerns the studyof adult, normal, typical cognition, with subsidiaryframeworks focused on individual differences,group differences (e.g., expert vs. novice, male vs.female), cultural variation, development, patholo-gy, and neural realization. The description offeredin von Eckardt (1993), summarized in Table 1, isintended to be of only the central research frame-work. In addition, it is claimed to be a rationalreconstruction as well as transdisciplinary, that is,common to cognitive scientists of all disciplines.Von Eckardt claims that research frameworks canevolve and that the description in question reflectscommitments of the cognitive science communityat only one period of its history (specifically, thelate 1980s/early 1990s).Cognitive science is a very complex and rapidly

changing field. In light of this complexity and ch-ange, von Eckardt’s original reconstruction should,perhaps, be modified as follows. First, it needs tobe acknowledged that there exists a fundamentaldisagreement within the field as to its domain. Thenarrow conception, embraced by most psycholo-gists and linguists, is that the domain is humancognition; the broad conception, embraced by arti-ficial intelligence researchers, is that the domain isintelligence in general. (Philosophers seem to be

about evenly split.) A further area of disagreementconcerns whether cognitive science encompassesonly cognition/intelligence or includes all aspects ofmind, including touch, taste, smell, emotion, mood,motivation, personality, andmotor skills. One pointon which there now seems to be unanimity is thatcognitive science must address the phenomenon ofconsciousness.

Second, a modified characterization of cognitivescience must describe it as evolving not only withrespect to the computational assumption (from anexclusive focus on symbol systems to the inclusionof connectionist devices) but also with respect tothe role of neuroscience. Because cognitive scienceoriginally emerged from cognitive psychology, arti-ficial intelligence research, and generative lin-guistics, in the early years neuroscience was oftenrelegated to a secondary role. Currently, most non-neural cognitive scientists believe that research onthe mind/brain should proceed in an interactiveway—simultaneously both top-down and bottom-up. Ironically, a dominant emerging view of co-gnitive neuroscience seems to be that it, ratherthan cognitive science, will be the locus of an inter-disciplinary effort to develop, from the bottom up,a computational or information-processing theoryof the mind/brain.

There are also research programs currently at theperiphery of cognitive science—whatmight be calledalternative cognitive science. These are researchprograms that investigate some aspect of cognitionor intelligence but whose proponents reject one ormore of the major guiding or methodological as-sumptions of mainstream cognitive science. Threesuch programs are research on situated cognition,artificial life, and the dynamical approach to cog-nition.

Interfield Relations Within Cognitive ScienceThe second group of external questions typically

asked by philosophers of some particular scientificfield concerns the relation of that field to otherscientific fields. Because cognitive science is itselfmultidisciplinary, the most pressing interfield ques-tions arise about the relationship of the varioussubdisciplines within cognitive science. Of the tenpossible two-place relations among the five coredisciplines of cognitive science, two have receivedthe most attention from philosophers: relationsbetween linguistics and psychology (particularlypsycholinguistics) and relations between cognitivepsychology and neuroscience.

Discussion of the relation between linguistics andpsychology has addressed primarily Chomsky’s

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Table 1. The central research framework of cognitive science

Domain-specifying assumptions

D1 (Identification assumption): The domain consists of the human cognitive capacities.

D2 (Property assumption): Pretheoretically conceived, the human cognitive capacities have a number of basic general

properties:

. Each capacity is intentional; that is, it involves states that have content or are ‘‘about’’ something.

. Virtually all of the capacities are pragmatically evaluable; that is, they can be exercised with varying degrees of success.

. When successfully exercised, each of the evaluable capacities has a certain coherence or cogency.

. Most of the evaluable capacities are reliable; that is, typically, they are exercised successfully (at least to some degree)

rather than unsuccessfully.. Most of the capacities are productive; that is, once a person has the capacity in question, he or she is typically in a position

to manifest it in a practically unlimited number of novel ways. Each capacity involves one or more conscious states.a

D3 (Grouping assumption): The cognitive capacities of the normal, typical adult make up a theoretically coherent

set of phenomena, or a system. This means that with sufficient research, it will be possible to arrive at a set of

answers to the basic questions of the research framework that constitute a unified theory and are empirically and

conceptually acceptable.

Basic questions

Q1: For the normal, typical adult, what precisely is the human capacity to ________?

Q2: In virtue of what does a normal, typical adult have the capacity to _______ (such that this capacity is

intentional, pragmatically evaluable, coherent, reliable, and productive and involves consciousness?a)

Q3: How does a normal, typical adult exercise his or her capacity to _________?

Q4: How does the capacity to __________ of the normal, typical adult interact with the rest of his or her cognitive

capacities?

Substantive assumptions

SA1: The computational assumption

C1: (Linking assumption): The human, cognitive mind/brain is a computational device (computer); hence, the

human cognitive capacities consist, to a large extent, of a system of computational capacities.

C2: (System assumption): A computer is a device capable of automatically inputting, storing, manipulating,

and outputting information in virtue of inputting, storing, manipulating, and outputting representations of that

information. These information processes occur in accordance with a finite set of rules that are effective and that are,

in some sense, in the machine itself.

SA2: The representational assumption

R1 (Linking assumption): The human, cognitive mind/brain is a representational device; hence, the human

cognitive capacities consist of a system of representational capacities.

R2 (System assumption): A representational device is a device that has states or that contains within it entities

that are representations. Any representation will have four aspects essential to its being a representation: (1) It will be

realized by a representation bearer, (2) it will represent one or more representational objects, (3) its representation

relations will be grounded somehow, and (4) it will be interpretable by (will function as a representation for) some

currently existing interpreter. In the mind/brain representational system, the nature of these four aspects is constrained

as follows:. R2.1 (The representation bearer): The representation bearer of a mental representation is a computational structure

or process, considered purely formally.

(a) This structure or process has constituent structure.b

. R2.2 (The representational content): Mental representations have a number of semantic properties.c

(a) They are semantically selective.

(b) They are semantically diverse.

(c) They are semantically complex.

(d) They are semantically evaluable.

(e) They have compositional semantics.b

(Continued )

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claim that the aims of linguistics are, first, to devel-op hypotheses (in the form of generative grammars)about what the native speaker of a language knows(tacitly) or that capture the native speaker’s linguis-tic competence and, second, to develop a theory ofthe innate constraints on language (‘‘universalgrammar’’) that the child brings to bear in learningany given language. Philosophers have focused onthe relation of competence models to so-called per-formance models, that is, models developed bypsychologists to describe the information processes

involved in understanding and producing lan-guage. Earlier discussion focused on syntax; morerecent debates have looked at semantics.

There are several views. One, favored byChomsky himself, is that a representation of thegrammar of a language L constitutes a part of themental apparatus involved in the psychologicalprocesses underlying language performance and,hence, is causally implicated in the production ofthat performance (Chomsky and Katz 1974). A sec-ond, suggested by Marr (1982) and others, is that

. R2.3 (The ground): The ground of a mental representation is a property or relation that determines the fact that

the representation has the object (or content) it has.a) This ground is naturalistic (that is, nonsemantic and nonintentional).

b) This ground may consist of either internal or external factors. However, any such factor must satisfy the

following restriction: If two token representations have different grounds, and this ground difference deter-

mines a difference in content, then they must also differ in theircausal powers to produce relevant effects across

nomologically possible contexts.b

. R2.4 (The interpretant): Mental representations are significant for the person in whose mind they ‘‘reside.’’ The

interpretant of a mental representation R for some subject S consists of the set of all possible determinate

computational processes contingent upon entertaining R in S.

Methodological assumptions

M1: Human cognition can be successfully studied by focusing exclusively on the individual cognizer and his or her place

in the natural environment. The influence of society or culture on individual cognition can always be explained by

appealing to the fact that this influence is mediated through individual perception and representation.

M2: The human cognitive capacities are sufficiently autonomous from other aspects of mind such as affect and

personality that, to a large extent, they can be successfully studied in isolation.

M3: There exists a partitioning of cognition in general into individual cognitive capacities such that each of these

individual capacities can, to a large extent, be successfully studied in isolation from each of the others.

M4: Although there is considerable variation in how adult human beings exercise their cognitive capacities, it is

meaningful to distinguish, at least roughly, between ‘‘normal’’ and ‘‘abnormal’’ cognition.

M5: Although there is considerable variation in how adult human beings exercise their cognitive capacities, adults are

sufficiently alike when they cognize that it is meaningful to talk about a ‘‘typical’’ adult cognizer and it is possible to

arrive at generalizations about cognition that hold (at least approximately) for all normal adults.

M6: The explanatory strategy of cognitive science is sound. In particular, answers to the original basic questions can, to a

large extent, be obtained by answering their narrow information-processing counterparts (that is, those involving

processes purely ‘‘in the head’’).

M7: In choosing among alternative hypothesized answers to the basic questions of the research framework, one should

invoke the usual canons of scientific methodolology. That is, ultimately, answers to the basic questions should be

justified on empirical grounds.

M8: A complete theory of human cognition will not be possible without a substantial contribution from each of the

subdisciplines of cognitive science.

M9: Information-processing answers to the basic questions of cognitive science are constrained by the findings of

neuroscience.c

M10: The optimal research strategy for developing an adequate theory of the cognitive mind/brain is to adopt a

coevolutionary approach—that is, to develop information-processing answers to the basic questions of cognitive

science on the basis of empirical findings from both the nonneural cognitive sciences and the neurosciences.c

M11: Information-processing theories of the cognitive mind/brain can explain certain features of cognition that cannot be

explained by means of lower-level neuroscientific accounts. Such theories are thus, in principle, explanatorily

ineliminable.c

Key: aNot in von Eckardt (1993); bControversial; cIncluded on normative grounds (given the commitment of cognitive science

to X, they should be committed to Y)

Table 1. (Continued )

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competence theories describe a native speaker’s lin-guistic input-output capacity (Marr’s ‘‘computa-tional’’ level) without describing the processesunderlying that capacity (Marr’s ‘‘algorithmic’’level). For example, the capacity to understand asentence S can be viewed as the capacity that mapsa phonological representation of S onto a semanticrepresentation S. Both views have been criticized.Against the first, it has been argued that because ofthe linguist’s concern with simplicity and generali-ty, it is unlikely that the formal structures utilizedby optimal linguistic theories will be isomorphic tothe internal representations posited by psycholin-guists (Soames 1984). A complementary point isthat because processing models are sensitive toarchitectural and resource constraints, the ways inwhich they implement syntactic knowledge haveturned out to be much less transparent than fol-lowers of Chomsky had hoped (Mathews 1991). Atbest, they permit a psycholinguistic explanation ofwhy a particular set of syntactic rules and princi-ples correctly characterize linguistic competence.Against the second capacity view, it has been ar-gued that grammars constitute idealizations (forexample, there are no limitations on the length ofpermissible sentences or on their degree of internalcomplexity) and so do not describe actual speakers’linguistic capacities (Franks 1995; see Philosophyof Psychology; Neurobiology).

Internal questions have been raised about bothfoundational assumptions and concepts and parti-cular theories and findings within cognitive science.Foundational discussions have focused on the coresubstantive assumptions: (1) The cognitive mind/brain is a computational system and (2) it is arepresentational system.

The Computational Assumption

Cognitive science assumes that the mind/brain is akind of computer. But what is a computer? Todate, two kinds of computer have been importantto cognitive science modeling—classical machines(‘‘conventional,’’ ‘‘von Neumann,’’ or ‘‘symbol sys-tem’’), and connectionist machines (‘‘paralleldistributed processing’’). Classical machines havean architecture similar to ordinary personal com-puters (PCs). There are separate components forprocessing and memory, and processing occurs bythe manipulation of data structures. In contrast,connectionist computers are more like brains, con-sisting of interconnected networks of neuron-likeelements. Philosophers interested in the computa-tional assumption have focused on two questions:What is a computer in general (such that both

classical and connectionist machines count as com-puters), and is there any reason to believe, at thecurrent stage of research, that human mind/brainsare one sort of computer rather than another? Theview that the human mind/brain is, or is important-ly like, a classical computer is called classicism; theview that it is, or is importantly like, a connection-ist computer is called connectionism.The theory of computation in mathematics de-

fines a number of different kinds of abstract ma-chines in terms of the sets of functions they cancompute. Of these, the most relevant to cognitivescience is the universal Turing machine, which,according to the Church-Turing thesis, can com-pute any function that can be computed by aneffective method, that is, a method specified by afinite number of exact instructions, in a finite num-ber of steps, carried out by a human unaided by anymachinery except paper and pencil and demandingno insight or ingenuity. Many philosophers andcognitive scientists think that the notion of a com-puter relevant to cognitive science can be adequatelycaptured by the notion of a Turing machine. Infact, that is not the case. To say that a computer(and hence the mind/brain) is simply a device equiv-alent to a universal Turing machine says nothingabout the device’s internal structure, and to saythat a computer (and hence the mind/brain) isan implementation of a Turing machine seems flat-out false. There are many dissimilarities. A Turingmachine is in only one state at a time, while hum-ans are, typically, in many mental or brain statessimultaneously. Further, the memory of a Turingmachine is a ‘‘tape’’ with only a simple linear stru-cture, while human memory appears to have acomplex multidimensional structure.An alternative approach is to provide an archi-

tectural characterization, but at a fairly high level ofabstraction. For example, von Eckardt (1993, 114)claims that cognitive science’s computational as-sumption takes a computer to be ‘‘a device capableof automatically inputting, storing, manipulating,and outputting information in virtue of inputting,storing, manipulating, and outputting representa-tions of that information,’’ where ‘‘[t]hese informa-tion processes occur in accordance with a finite setof rules that are effective and that are, in somesense, in the machine itself.’’ Another proposal,due to Copeland (1996) and specifically intendedto include functions that a Turing machine cannotcompute, is that a computer is a device capable ofsolving a class of problems, that can represent boththe problems and their solution, contains somenumber of primitive operations (some of whichmay not be Turing computable), can sequence

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these operations in some predetermined way, andhas a provision for feedback (see Turing, Alan).To the question of whether the mind/brain is a

connectionist versus a classical computer, discus-sion has centered around Fodor and Pylyshyn’s(1988) argument in favor of classicism. In theirview, the claim that the mind/brain is a connection-ist computer should be rejected on the grounds ofthe premises that

1. cognitive capacities exhibit systematicity(where ‘systematicity’ is the fact that some ca-pacities are intrinsically connected to others—e.g., if a native speaker of English knows howto say ‘‘John loves the girl,’’ the speaker willknow how to say ‘‘The girl loves John’’) and

2. this feature of systematicity cannot be ex-plained by reference to connectionist models(unless they are implementations of classicalmodels), whereas

3. it can be explained by reference to classicalmodels.

Fodor and Pylyshyn’s reasoning is that it is‘‘characteristic’’ of classical systems but not of con-nectionist systems to be ‘‘symbol processors,’’ thatis, systems that posit mental representations withconstituent structure and then process these re-presentations in a way that is sensitive to thatstructure. Given such features, classical modelscan explain systematicity; but without such fea-tures, as in connectionist machines, it is a mystery.Fodor and Pylyshyn’s challenge has generated ahost of responses, from both philosophers and com-puter scientists. In addition, the argument itselfhas evolved in two significant ways. First, it hasbeen emphasized that to be a counterexample topremise 2, a connectionist model must not onlyexhibit systematicity, it must also explain it. Second,it has been claimed that what needs explaining is notjust that human cognitive capacities are systematic;it is that they are necessarily so (on the basis ofscientific law).The critical points regarding premise 3 are espe-

cially important. The force of Fodor and Pylyshyn’sargument rests on classical systems being able to dosomething that connectionist systems (at a cogni-tive, nonimplementational level) cannot. However,it has been pointed out that the mere fact that asystem is a symbol processer (and hence classical)does not by itself explain systematicity, much lessthe lawful necessity of it; additional assumptionsmust be made about the system’s computationalresources. Thus, if the critics are right that connec-tionist systems of specific sorts can also explainsystematicity, then the explanatory asymmetry

between classicism and connectionism will no lon-ger hold (that is, neither the fact that a system isclassical nor the fact that it is connectionist can,taken by itself, explain systematicity, while eitherfact can explain systematicity when appropriatelysupplemented), and Fodor and Pylyshyn’s argu-ment will be unsound.

The Representational Assumption

Following Peirce (Hartshorne, Weiss, and Burks1931–58), one can say that any representation hasfour aspects essential to its being a representation:(i) It is realized by a representation bearer; (ii) it hassemantic content of some sort; (iii) its semantic con-tent is grounded somehow; and (iv) it has significancefor (that is, it can function as a representation for)the person who has it. (Peirce’s terminology wassomewhat different. He spoke of a representation’sbearer as the ‘‘material qualities’’ of the repre-sentation and the content as the representation’s‘‘object.’’)

In Peirce, a representation has significance fora person insofar as it produces a certain effect or‘‘interpretant.’’ This conception of representationis extremely useful for exploring the view of cogni-tive science vis-a-vis mental representation, for itleads one to ask: What is the representation bearer,semantic content, and ground of mental represen-tation, and how do mental representations havesignificance for the people in whose mind/brainsthey reside?

A representation bearer is an entity or state thathas semantic properties considered with respect toits nonrepresentational properties. The representa-tion bearers for mental representations, accordingto cognitive science, are computational structuresor states. If the mind/brain is a classical computer,its representation bearers are data structures; if it isa connectionist computer, its explicit representa-tion bearers are patterns of activation of nodes ina network. It is also claimed that connectionistcomputers implicitly represent by means of theirconnection weights.

Much of the theoretical work of cognitive psy-chologists consists of claims regarding the contentof the representations used in exercising one oranother cognitive capacity. For example, psycho-linguists posit that in understanding a sentence,people unconsciously form representations of thesentence’s phonological structure, words, syntacticstructure, and meaning. Although psychologistsdo not know enough about mental representationas a system to theorize about its semantics in thesense in which linguistics provides the formal

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semantics of natural language, if one reflects onwhat it is that mental representations are hypothe-sized to explain—certain features of cognitivecapacities—one can plausibly infer that the seman-tics of human mental representation systems musthave certain characteristics. In particular, a casecan be made that people must be able to represent(i) specific objects; (ii) many different kinds ofobjects including concrete objects, sets, properties,events and states of affairs in the world, in possibleworlds, and in fictional worlds, as well as abstractobjects such as universals and numbers; (iii) bothobjects (tout court) and aspects of those objects(or something like extension and intension); and(iv) both correctly and incorrectly.

Although cognitive psychologists have concern-ed themselves primarily with the representationbearers and semantic content of mental representa-tions, the hope is that eventually there will be anaccount of how the computational states and struc-tures that function as representation bearers comeby their content. In virtue of what, for example, dolexical representations represent specific words?What makes an edge detector represent edges?Such theories are sometimes described as one oranother form of ‘‘semantics’’ (e.g., informationalsemantics, functional role semantics), but this fa-cilitates a confusion between theories of contentand theories of what determines that content. Apreferable term is theory of content determination.Philosophers have been concerned both (a) to de-lineate the basic relation between a representation’shaving a certain content and its having a certainground and (b) to sketch alternative theories ofcontent determination, that is, theories of whatthat ground might be. A common view is that thebasic relation is strong supervenience, as definedby Kim (1984). Others, such as Poland (1994),believe that a stronger relation of realization isrequired.

How is the content of mental representationsdetermined? Proposals appeal either exclusively orin some combination to the structure of the repre-sentation bearer (Palmer 1978); actual historical(Devitt 1981) or counterfactual causal relations(Fodor 1987) between the representation bearerand phenomena in the world; actual and counter-factual (causal, computational, inferential) rela-tions between the representation-bearer state andother states in the mind/brain (Harman 1987;Block 1987); or the information-carrying or otherfunctions of the representation-bearer state andassociated components (based on what they wereselected for in evolution or learning) (Millikan1984; Papineau 1987).

Arguably, any adequate theory of content deter-mination will be able to account for the full rangeof semantic properties of mental representationalsystems. On this criterion, all current theories ofcontent determination are inadequate. For exam-ple, theories that ground representational contentin an isomorphism between some aspect of a rep-resentation (usually, either its formal structure orits functional role) and what it represents do notseem to be able to explain how one can representspecific objects, such as a favorite coffee mug. Incontrast, theories that rely on actual, historicalcausal relations can easily explain the representa-tion of specific objects but do not seem to be ableto explain the representation of sets or kinds ofobjects (e.g., all coffee mugs). It is precisely becausesingle-factor theories of content determination donot seem to have the resources to explain all as-pects of people’s representational capacities thatmany philosophers have turned to two-factor the-ories, such as theories that combine causal relationswith function (so-called teleofunctional theories)and theories that combine causal relations withfunctional role (so-called two-factor theories).The fourth aspect of a mental representation, in

the Peircian view, is that the content of a repre-sentation must have significance for the represent-er. In the information-processing paradigm, thisamounts to the fact that for each representation,there will be a set of computational consequencesof that representation being ‘‘entertained’’ or ‘‘acti-vated,’’ and in particular a set of computationalconsequences that are appropriate given the contentof the representation (von Eckardt 1993, chap. 8).

The Viability of Cognitive Science

Cognitive science has been criticized on severalgrounds. It has been claimed that there are phe-nomena within its domain that it does not have theconceptual resources to explain; that one or moreof its foundational assumptions are problematicand, hence, that the research program groundedin those assumptions can never succeed; and thatit can, in principle, be eliminated in favor of pureneuroscience.The list of mental phenomena that, according to

critics, cognitive science will never be able to ex-plain include that of people ‘‘making sense’’ in theiractions and speech, of their having sensations,emotions, and moods, a self and a sense of self,consciousness, and the capabilities of insight andcreativity and of interacting closely and directlywiththeir physical and social environments. Althoughno impossibility proofs have been offered, when

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cognitive science consisted simply of a top-down,‘‘symbolic’’ computational approach, this explana-tory challenge had a fair amount of intuitive plau-sibility. However, given the increasing importanceof neuroscience within cognitive science and thecontinuing evolution of the field, it is much lessclear today that no cognitive science explanationof such phenomena will be forthcoming. The big-gest challenge seems to be the ‘‘explanatory gap’’posed by phenomenal consciousness (Levine 1983)(see Consciousness).The major challenge against the computational

assumption is the claim that the notion of a com-puter employed within cognitive science is vacuous.Specifically, Putnam (1988) has offered a proofthat every ordinary open system realizes every ab-stract finite automaton, and Searle (1990) hasclaimed that implementation is not an objectiverelation and, hence, that any given system can beseen to implement any computation if interpretedappropriately. Both claims have been disputed. Forexample, it has been pointed out that Putnam’sresult relies on employing both an inappropriatecomputational formalism (the formalism of finitestate automata, which have only monadic states),an inappropriately weak notion of implementation(one that does not require the mapping fromcomputational to physical states to satisfy counter-factual or lawful state–state transitions), and aninappropriately permissive notion of a physicalstate (one that allows for rigged disjunctions).When these parameters of the problem are mademore restrictive, implementations are much harderto come by (Chalmers 1996). However, in defenseof Putnam, it has been suggested that this responsedoes not get to the heart of Putnam’s challenge,which is to develop a theory that provides neces-sary and sufficient criteria to determine whether aclass of computations is implemented by a class ofphysical systems (described at a given level). Analternative approach to implementation might bebased on the notion of realization of a (mathemati-cal) function by a ‘‘digital system’’ (Scheutz 1999).The major challenge to the representational as-

sumption is the claim that the project of finding anadequate theory of content determination is doom-ed to failure. One view is that the attempt by co-gnitive science to explain the intentionality ofcognition by positing mental representations isfundamentally confused (Horst 1996). The argu-ment is basically this: According to cognitive sci-ence, a mental state, as ordinarily construed, hassome content property in virtue of the fact that it isidentical to (supervenes on) a representational statethat has some associated semantic property. There

are four ways of making sense of this posited se-mantic property. The semantic property in ques-tion is identical to one of the following options:

1. the original content property,2. an interpreter-dependent semiotic-semantic

property,3. a pure semiotic-semantic property of the sort

posited in linguistics, or4. some new theoretical ‘‘naturalized’’ property.

However, according to Horst (1996), none ofthese options will work. Options 1 and 2 are circu-lar and hence uninformative. Option 3 is ruled outon the grounds that there is no reason to believe thatthere are such properties. And option 4 is ruled outon the grounds that naturalized theories of contentdetermination do not have the conceptual resourcesto deliver the kind of explanation required.

In response, it has been argued that Horst’s caseagainst option 3 is inadequate and that his argu-ment against option 4 shows a misunderstandingof what theories of content determination aretrying to achieve (von Eckardt 2001). Horst’s re-ason for ruling out option 3 is that he thinks thatpeople who believe in the existence of pure seman-tic properties or relations do so because there areformal semantic theories that posit such propertiesand such theories have met with a certain degree ofsuccess. But (he argues) when scientists developmodels (theories) in science, they do so by a processof abstraction from the phenomena in vivo thatthey wish to characterize. Such abstractions canbe viewed either as models of the real-world phe-nomena they were abstracted from or as descrip-tions of the mathematical properties of thosephenomena. Neither view provides a license fornew ontological claims. Thus, Horst’s argumentrests on a nonstandard conception of both theoryconstruction (as nothing but abstraction) and mod-els or theories (as purely mathematical). If, contraHorst, a more standard conception is substituted,then linguists have as much right to posit puresemantic properties as physicists have to positstrange subatomic particles. Furthermore, the exis-tence of the posited entities will depend completelyon how successful they are epistemically.

Horst’s case against option 4, again, exhibits amisunderstanding of the cognitive science project.He assumes that the naturalistic ground N of thecontent of a mental representation C will be suchthat the truth of the statement ‘‘X is N ’’ conjoinedwith the necessary truths of logic and mathematicswill be logically sufficient for the truth of the state-ment ‘‘X has C ’’ and that, further, this entailmentwill be epistemically transparent. He then argues

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against there being good prospects for a naturalistictheory of content on the grounds that natural-istic discourse does not have the conceptual resourc-es to build a naturalistic theory that will entail, in anepistemically transparent way, the truths about in-tentionality. However, as von Eckardt (2001) pointsout, Horst’s conception of naturalization is muchstronger than what most current theory of contentdetermination theorists have in mind, viz., strongsupervenience or realization (see Supervenience).As a consequence, his arguments that naturalizationis implausible given the conceptual resources ofnaturalistic discourse are seriously misguided.

BARBARA VON ECKARDT

References

Block, N. (1987), ‘‘Functional Role and Truth Conditions,’’Proceedings of the Aristotelian Society 61: 157–181.

Chalmers, D. (1996), ‘‘Does a Rock Implement EveryFinite-State Automaton?’’ Synthese 108: 309–333.

Chomsky, N., and J. Katz (1974), ‘‘What the Linguist IsTalking About,’’ Journal of Philosophy 71: 347–367.

Copeland, B. (1996), ‘‘What Is Computation?’’ Synthese108: 336–359.

Devitt, M. (1981), Designation. New York: ColumbiaUniversity Press.

Fodor, J. (1987), Psychosemantics. Cambridge, MA: MITPress.

Fodor, J., and Z. W. Pylyshyn (1988), ‘‘Connectionismand Cognitive Architecture: A Critical Analysis,’’ inS. Pinker and J. Miller (eds.), Connections and Symbols.Cambridge, MA: MIT Press, 1–71.

Franks, B. (1995), ‘‘On Explanation in the CognitiveSciences: Competence, Idealization and the Failure ofthe Classical Cascade,’’ British Journal for the Philosophyof Science 46: 475–502.

Gardner, H. (1985), The Mind’s New Science: A History ofthe Cognitive Revolution. New York: Basic Books.

Harman, G. (1987), ‘‘(Non–Solipsistic) Conceptual RoleSemantics,’’ in E. Lepore (ed.), New Directions in Seman-tics. London: Academic Press.

Hartshorne, C., P. Weiss, and A. Burks (eds.) (1931–58),Collected Papers of Charles Sanders Peirce. Cambridge,MA: Harvard University Press.

Horst, S. W. (1996), Symbols, Computation, and Intention-ality. Berkeley and Los Angeles: University of CaliforniaPress.

Kim, J. (1984), ‘‘Concepts of Supervenience,’’ Philosophicaland Phenomenological Research 45: 153–176.

Kuhn, T. (1970), The Structure of Scientific Revolutions.Chicago: University of Chicago Press.

Levine, J. (1983), ‘‘Materialism and Qualia: The Ex-planatory Gap,’’ Pacific Philosophical Quarterly 64:354–361.

Marr, D. (1982), Vision: A Computational Investigation intothe Human Representation and Processing of Visual In-formation. San Francisco: W. H. Freeman.

Mathews, R. (1991), ‘‘Psychological Reality of Grammars,’’in A. Kasher (ed.), The Chomskyan Turn. Oxford andCambridge, MA: Basil Blackwell.

Millikan, R. (1984), Language, Thought, and OtherBiological Categories. Cambridge, MA: MIT Press.

Palmer, S. (1978), ‘‘Fundamental Aspects of Cognitive Rep-resentation,’’ in E. Rosch and B. Lloyd (eds.), Cognitionand Categorization. Hillsdale, NJ: Erlbaum.

Papineau, D. (1987), Reality and Representation. Oxford:Blackwell.

Poland, J. (1994), Physicalism: The Philosophical Founda-tions. Oxford: Oxford University Press.

Putnam, H. (1988), Representation and Reality. Cambridge,MA: MIT Press.

Scheutz, M. (1999), ‘‘When Physical Systems Realize Func-tions,’’ Minds and Machines 9: 161–196.

Searle, J. (1990), ‘‘Is the Brain a Digital Computer?’’ Pro-ceedings and Addresses of the American PhilosophicalAssociation 64: 21–37.

Simon, H. (1981), ‘‘Cognitive Science: The Newest Scienceof the Artificial,’’ in D. A. Norman (ed.), Perspectiveson Cognitive Science. Norwood, NJ: Ablex Publishing,13–26.

Soames, S. (1984), ‘‘Linguistics and Psychology,’’ Linguis-tics and Philosophy 7: 155–179.

von Eckardt, B. (2001), ‘‘In Defense of Mental Representa-tion,’’ in P. Gardenfors, K. Kijania–Placek, and J.Wolenski (eds.), Proceedings of the 11th InternationalCongress of Logic, Methodology and Philosophy of Sci-ence. Dordrecht, Netherlands: Kluwer.

——— (1993), What Is Cognitive Science? Cambridge, MA:MIT Press.

See also Consciousness; Physicalism; Psychology,Philosophy of; Supervenience

COGNITIVE SIGNIFICANCE

One of the main objectives of logical empiricismwas to develop a formal criterion by which cogni-tively significant statements, which are true orfalse, could be delineated from meaningless ones,

which are neither. The desired criterion wouldspecify, and in some way justify, the logical empiri-cists’ conviction that scientific statements wereexemplars of significance and metaphysical ones


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were decidedly not (see Logical Empiricism).Finding such a criterion was crucial to logical em-piricism. Without it there seemed to be no defensi-ble way to distinguish metaphysics from scienceand, consequently, no defensible way to excludemetaphysics from subjects that deserved seriousphilosophical attention (see Demarcation, Problemof ). Accordingly, several logical empiricists devotedattention to developing a criterion of cognitive sig-nificance, including Carnap, Schlick, Ayer, Hempel,and, to a lesser degree, Reichenbach.Scientific developments also motivated the

project in two related ways. First, physics andbiology were demonstrating that a priorimetaphys-ical speculations about empirical matters wereusually erroneous and methodologically misguid-ed. Hans Driesch’s idea of an essential entelechywas no longer considered scientifically respectable,and the intuitive appeal of the concept of abso-lute simultaneity was shown to be misleading byEinstein (Feigl 1969). Scientific results demon-strated both the necessity and the fruitfulness ofreplacing intuitive convictions with precise, empiri-cally testable hypotheses, and logical empiriciststhought the same methodology should be appliedto philosophy. Formulating a defensible criter-ion that ensured the privileged epistemologicalstatus of science, and revealed the vacuity of meta-physics, was thought crucial to the progress andrespectability of philosophy.Second, many scientific discoveries and emerg-

ing research programs, especially in theoreticalphysics, were considerably removed from everydayobservable experience and involved abstract, math-ematically sophisticated theories. The logicalempiricists felt there was a need for a formal system-atization of science that could clarify theoreticalconcepts, their interrelations, and their connectionwith observation. The emerging tools of modernmathematical logic made this task seem imminentlyattainable. With the desire for clarity came thepursuit of a criterion that could sharply distinguishthese scientific developments, which provided in-sights about the world and constituted advances inknowledge, from the obfuscations of metaphysics.Formulation of a cognitive significance criterion

requires an empirical significance criterion to de-lineate empirical from nonempirical statements anda criterion of analyticity to delineate analyticfrom synthetic statements (see Analyticity). Mostlogical empiricists thought analytically true andfalse statements were meaningful, and most meta-physicians thought their claims were true but notanalytically so. In their search for a cognitivesignificance criterion, as the principal weapon of

their antimetaphysical agenda, the logical empiri-cists focused on empirical significance.

The Verifiability Requirement

The first attempts to develop the antimetaphysicalideas of the logical empiricists into a more rigorouscriterion of meaningfulness were based on theverifiability theory of meaning (see Verifiability).Though of auxiliary importance to the rational re-construction in the Aufbau, Carnap (1928a)claimed that a statement was verifiable and therebymeaningful if and only if it could be translatedinto a constructional system; for instance, by re-ducing it (at least in principle) to a system aboutbasic physical objects or elementary experiences(§179) (see Carnap, Rudolf ). Meaningful questionshave verifiable answers; questions that fail this re-quirement are pseudo-questions devoid of cogni-tive content (§180).

The first explicit, semiformal criterion originatedwith Carnap in 1928. With the intention of demon-strating that the realism/idealism debate, and manyother philosophical controversies, were devoid ofcognitive significance, Carnap (1928b) presented acriterion of factual content:

If a statement p expresses the content of an experience E,and if the statement q is either the same as p or can bederived from p and prior experiences, either throughdeductive or inductive arguments, then we say that q is‘supported by’ the experience E . . . . A statement p is saidto have ‘factual content’ if experiences which wouldsupport p or the contradictory of p are at least conceiv-able, and if their characteristics can be indicated.

(Carnap 1967, 327)

Only statements with factual content are em-

pirically meaningful. Notice that a fairly precise infer-

ential method is specified and that a statement has

factual content if there are conceivable experiments

that could support it. Thus, the earliest formal signif-

icance criterion already emphasized that possible, not

necessarily actual, connection to experience made

statements meaningful.

Carnap ([1932] 1959) made three significantchanges to his proposal. First, building on an earli-er example (1928b, §7), he developed in more detailthe role of syntax in determining the meaningful-ness of words and statements in natural languages.The ‘‘elementary’’ sentence form for a word is thesimplest in which it can occur. For Carnap, a wordhad to have a fixed mode of occurrence in itselementary sentence form to be significant. Besidesfailing to connect with experience in some way,statements could also be meaningless because they


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contained sequences of words that violated thelanguage’s syntactic rules, or its ‘‘logical syntax.’’According to Carnap, ‘‘Dog boat in of ’’ is mean-ingless because it violates grammatical syntax, and‘‘Our president is definitely a finite ordinal,’’ ismeaningless because it violates logical syntax,‘president’ and ‘finite ordinal’ being members ofdifferent logical categories. The focus on syntaxled Carnap to contextualize claims of significanceto specific languages. Two languages that differ insyntax differ in whether words and word sequencesare meaningful.

Second, Carnap ([1932] 1959) no longer requiredstatements to be meaningful by expressing con-ceivable states of affairs. Rather, statements aremeaningful because they exhibit appropriate dedu-cibility relations with protocol statements whosesignificance was taken as primitive and incorrigibleby Carnap at that time (see Protocol Sentences).Third, Carnap did not specify exactly how signifi-cant statements must connect to protocol state-ments, as he had earlier (1928b). In 1932, Carnapwould ascertain a word’s meaning by consideringthe elementary sentence in which it occurred anddetermining what statements entailed and wereentailed by it, the truth conditions of the statement,or how it was verified—considerations Carnapthen thought were equivalent. The relations wereprobably left unspecified because Carnap came toappreciate how difficult it was to formalize thesignificance criterion, and realized that his earliercriterion was seriously flawed, as was shown ofAyer’s first formal criterion (see below).

In contrast to antimetaphysical positions thatevaluated metaphysical statements as false, Carnapbelieved his criterion justified a radical eliminationof metaphysics as a vacuous enterprise. The defen-sibility of this claim depended upon the status of thecriterion—whether it was an empirical hypothesisthat had to be supported by evidence or a definitionthat had to be justified on other grounds. Carnap([1932] 1959) did not address this issue, though helabels the criterion as a stipulation. Whether thisstipulation was defensible in relation to other pos-sible criteria or whether the statement of the crite-rion satisfied the criterion itself were questions leftunanswered.

In his popularization of the work of Carnap([1932] 1959) and Schlick ([1932] 1979), Ayer(1934) addressed these questions and stated that asignificance criterion should not be taken as anempirical claim about the linguistic habits of theclass of people who use the ‘meaning’ of a word(see Ayer, Alfred Jules; Schlick, Moritz). Rather, itis a different kind of empirical proposition, which,

though conventional, has to satisfy an adequacycondition. The criterion is empirical because, tobe adequate, it must classify ‘‘propositions whichby universal agreement are given as significant’’ assignificant, and propositions that are universallyagreed to be nonsignificant as nonsignificant(Ayer 1934, 345).Ayer developed two formalizations of the criteri-

on. The first edition of Language, Truth, and Logiccontained the proposal that ‘‘a statement is verifi-able . . . if some observation-statement can be de-duced from it in conjunction with certain otherpremises, without being deducible from thoseother premises alone,’’ where an observation state-ment is one that records any actual or possibleobservation (Ayer 1946, 11).Following criticisms (see the following section)

of his earlier work, a decade later Ayer (1946)proposed a more sophisticated criterion by distin-guishing between directly verifiable statements andindirectly verifiable ones. In conjunction with a setof observation statements, directly verifiable state-ments entail at least one observation statementthat does not follow from the set alone. Indirectlyverifiable statements satisfy two requirements: (1)In conjunction with a set of premises, they entail atleast one directly verifiable statement that does notfollow from the set alone; and (2) the premises caninclude only statements that are either analytic ordirectly verifiable or can be indirectly verified onindependent grounds. Nonanalytic statements thatare directly or indirectly verifiable are meaningful,whereas analytic statements are meaningful but donot assert anything about the world.

Early Criticisms of the Verifiability Criterion

The verifiability criterion faced several criticisms,which took twogeneral forms.The first, alreadymen-tioned in the last section, questioned its status—specifically, whether the statement of the criterionsatisfies the criterion. The second questioned itsadequacy: Does the criterion ensure that obviouslymeaningful statements, especially scientific ones,are labeled as meaningful and that obviously mean-ingless statements are labeled as meaningless?Criticisms of the first form often mistook the

point of the criterion, construing it as a simple em-pirical hypothesis about how the concept of mean-ing is understood or a dogmatic stipulation abouthow it should be understood (Stace 1935). As men-tioned earlier, Ayer (1934, 1946) clearly recognizedthat it was not this type of empirical claim, nor wasit an arbitrary definition. Rather, as Hempel (1950)latermade clear, the criterionwas intended to clarify

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and explicate the idea of a meaningful statement. Asan explication it must accord with intuitions aboutthe meaningfulness of common statements and sug-gest a framework for understanding how theoreticalterms of science are significant (see Explication).The metaphysician can deny the adequacy of thisexplication but must then develop a more liberalcriterion that classifies metaphysical claims assignificant while evaluating clearly meaninglessassertions as meaningless (Ayer 1934).Criticisms of the second form often involved

misinterpretations of the details of the criterion,due partially to the ambiguity of what was meantby ‘verifiability.’ For example, in a criticism ofAyer (1934), Stace (1935) argued that the verifiabil-ity criterion made all statements about the pastmeaningless, since it was in principle impossibleto access the past and therefore verify them. Hisargument involved twomisconceptions. First, Staceconstrued the criterion to require the possibility ofconclusive verification, for instance a complete re-duction of any statement to (possible) observationsthat could be directly verified. Ayer (1934) didnot address this issue, but Schlick ([1932] 1979),from whose work Ayer drew substantially, empha-sized that many meaningful propositions, such asthose concerning physical objects, could never beverified conclusively. Accepting Neurath’s criti-cisms in the early 1930s, Carnap accepted that nostatement, including no protocol statement, wasconclusively verified (see Neurath, Otto). Recallalso that Carnap (1928b) classified statements thatwere ‘‘supported by’’ conceivable experiences—notconclusively verified—as meaningful.Second, Stace’s argument depended on the am-

biguity of ‘‘possible verification,’’ which madeearly formulations of the criterion misleadingly un-clear (Lewis 1934). The possibility of verificationcan have three senses: practical possibility, empiri-cal possibility, and logical possibility. Practicalpossibility was not the intended sense: ‘‘There are10,000-foot mountains on the moon’s far side’’ wasmeaningful in the 1930s, though its verification waspractically impossible (Schlick [1932] 1979).However, Carnap (1928a, 1928b, [1932] 1959),

Schlick ([1932] 1979), and Ayer (1934) were silenton whether empirical or logical possibility dividedthe verifiable from the unverifiable. Stace thoughttime travel was empirically impossible. The questionwas therefore whether statements about past eventswere meaningful for which no present evidence wasavailable, and no future evidence would be.In the first detailed analysis of the verifiability

criterion, Schlick ([1936] 1979) stated that the logicalimpossibility of verification renders a statement

nonsignificant. Empirical impossibility, whichSchlick understood as contradictng the ‘‘laws ofnature,’’ does not entail nonverifiability. If it did,Schlick argued, the meaningfulness of a putativestatement could be established only by empiricalinquiry about the laws of nature. For Schlick, thisconflated a statement’s meaning with its truth. Themeaning of a statement is determined (‘‘bestowed’’)by logical syntax, and only with meaning fixed apriori can its truth or falsity be assessed. Further-more, since some lawlike generalizations are yet tobe identified and lawlike generalizations are neverestablished with absolute certainty, it seems that asharp boundary between the empirically impossibleand possible could never be determined.Hence, therewould be no sharp distinction between the verifiableand unverifiable, which Schlick foundunacceptable.

For Schlick ([1936] 1979), questions formulatedaccording to the rules of logical grammar aremeaningful if and only if it is logically possible toverify their answers. A state of affairs is logicallypossible for Schlick if the statement that describesit conforms to the logical grammar of language.Hence, meaningful questions may concern statesof affairs that contradict well-supported lawlikegeneralizations. Schlick’s position implies that theset of meaningful questions is an extension of the setof questions for which verifiable answers can beimagined. Questions about velocities greater thanlight are meaningful according to Schlick, butimagining how they could be verified surpassesour mental capabilities.

Schlick’s emphasis on logical possibility wasproblematic because it was unclear that the verifi-cation conditions of most metaphysical statementsare, or entail, logical impossibilities. In contrast,Carnap ([1936–7] 1965) and Reichenbach (1938)claimed that metaphysical statements were nonsig-nificant because no empirically possible process ofconfirmation could be specified for them (seeReichenbach, Hans). Furthermore, if only the logi-cal possibility of verification were required for sig-nificance, then the nonsignificance of metaphysicalstatements could no longer be demonstrated bydemanding an elucidation of the circumstances inwhich they could be verified. Metaphysicians canlegitimately respond that such circumstances maybe difficult or impossible to conceive because theyare not empirically possible. Nevertheless, the cir-cumstances may be logically possible, and hencethe metaphysical statements may be significantaccording to Schlick’s position.

Faced with the problematic vagueness of theearly criteria, a formal specification of the criterionwas thought to be crucial. Berlin (1939) pointed out


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that the early verifiability criteria were open toobjections from metaphysicians because the detailsof the experiential relevance required of meaningfulstatements were left unclear: ‘‘Relevance is not aprecise logical category, and fantastic metaphysicalsystems may choose to claim that observation dataare ‘relevant’ to their truth’’ (233).

With formalizations of the criterion, however,came more definitive criticisms. Ayer’s (1946, 39)first proposal was seriously flawed because itseemed to make almost all statements verifiable.For any grammatical statement S—for instance‘‘The Absolute is peevish’’—any observation state-ment O, and the conditional S ! O, S and S ! Ojointly entail O, though neither of them alone usu-ally does. According to Ayer’s criterion, therefore,S and S! O are meaningful except in the rare casethat S ! O entails O (Berlin 1939).

Church (1949) presented a decisive criticism ofAyer’s (1946, 13) second proposal. Consider threelogically independent observation statements O1,O2, O3 and any statement S. The disjunction(øO16O2)V(øS6O3) is directly verifiable, sincein conjunction with O1 it entails O3. Also,(øO16O2)V(øS6O3) and S together entail O2.Hence, by Ayer’s criterion, S is indirectly verifiable,unless (øO16O2)V(øS6O3) alone entails O2,which implies øS and O3 entail O2 so that øSis directly verifiable. Thus, according to Ayer’scriterion, any statement is indirectly verifiable,and therefore significant, or its negation is directlyverifiable, and thereby meaningful.

Nidditch (1961) pointed out that Ayer’s (1946)proposal could be amended to avoid Church’s(1949) criticism by specifying that the premisescould only be analytic, directly verifiable, or indi-rectly verifiable on independent grounds and couldonly be composed of such statements. Thus that(øO16O2)V(øS6O3) and S together entail O2

does not show that S is indirectly verifiable because(øO16O2)V(øS6O3) contains a statement (S) thathas notbeen shown tobe analytic, directly verifiable,or independently verifiable on independent grounds.Unfortunately, Scheffler (1963) pointed out thataccording to Nidditch’s (1961) revised criterion, anargument similar to Church’s (1949) with the dis-junction øO2V(S6O1) shows that any statement Sis significant, unless it is a logical consequence ofan observation statement. Scheffler (1963) alsopointed out that Ayer’s second proposal makesany statement of the form S6(O1 ! O2) signifi-cant, where O1, O2 are logically independent obser-vation sentences and S is any statement. S6(O1 !O2) entails O2when conjoined with O1 and neitherthe conjunction nor O1 entails O2 alone.

Beyond Verifiability: Carnap and Hempel

While Ayer first attempted to formalize the verifi-ability criterion, Carnap ([1936–7] 1965) recognizedthe obvious weaknesses of verifiability-based signif-icance criteria. At roughly the same time, in the lightof Tarski’s rigorous semantic account of truth,Carnap was coming to accept that a systematic(that is, nonpragmatic) account might be possiblefor other concepts, such as ‘confirmation.’ He sub-sequently refocused the question of cognitive signif-icance away from verifiability, which seemed toconnote the possibility of definitive establishmentof truth, to confirmability—the possibility of ob-taining evidence, however partial, for a statement.In particular, Carnap thought a justifiable signifi-cance criterion could be formulated if an adequateaccount of the confirmation of theory by observa-tion were available. A better understanding of thelatter would provide a clearer grasp of how scientificterms are significant due to their connection to ob-servation and prediction and how metaphysicalconcepts are not, because they lack this connection.Yet, insights into the nature of confirmation oftheory by observation do not alone determine theform of an adequate significance criterion. Rather,these insights were important because Carnap([1936–7] 1965) radically changed the nature of thedebate over cognitive significance.Carnap reemphasized (from his work in 1932)

that what expressions are cognitively significantdepends upon the structure of language, and hencea criterion could be proposed relative to only aspecific language. He distinguished two kinds ofquestions about cognitive significance: those con-cerning ‘‘historically given language system[s]’’ andthose concerning constructible ones (Carnap [1932]1959, 237). Answers to the two kinds of questionsare evaluated by different standards. To be mean-ingful in the first case, an expression E must be asentence ofL, which is determined by the language’ssyntax, and it must ‘‘fulfill the empiricist criterion ofmeaning’’ (167) for L. Carnap does not disclose theexact form of the criterion—verifiability, testability,or confirmability—for a particular language, suchas English.The reason for Carnap’s silence, however, was

his belief that the second type of question posed amore fruitful direction for the debate. The secondtype of question is practical, and the answers areproposals, not assertions. Carnap ([1936–7] 1965)remarked that he was no longer concerned toargue directly that metaphysical statements arenot cognitively significant (236). Rather, his strat-egy was to construct a language L in which every


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nonanalytic statement was confirmable by someexperimental procedure. Given its designed struc-ture, L will clearly indicate how theoretical state-ments can be confirmed by observational ones, andit will not permit the construction of metaphysicalstatements. If a language such as L can be con-structed that accords with intuitions about the sig-nificance of common statements and is sufficient forthe purposes of science, then the onus is on themetaphysician to show why metaphysical state-ments are significant in anything but an emotiveor attitude-expressing way.In a review paper more than a decade later, Hem-

pel (1950) construed Carnap’s ([1936–7] 1965) posi-tion as proposing a translatability criterion—a sentence is cognitively significant if and only if itis translatable into an empiricist language (seeHempel, Carl). The vocabulary of an empiricistlanguage L contains observational predicates, thecustomary logical constants, and any expressionconstructible from these; the sentence formationrules of L are those of Principia Mathematica. Theproblem Carnap ([1936–7] 1965) attempted to rec-tify was that many theoretical terms of sciencecannot be defined in L.Hempel’s interpretation, however, slightly mis-

construed Carnap’s intention. Carnap ([1936–7]1965) did not try to demonstrate how theoreticalterms could be connected to observational ones inorder to assert translatability as a criterion ofcognitive significance. Rather, in accord with theprinciple of tolerance (Carnap 1934) Carnap’s proj-ect in 1936–7 was to construct an alternative tometaphysically infused language. The features ofthe language are then evaluated with respect tothe purposes of the language user on pragmaticgrounds. Although it seems to conflict with hisposition in 1932, Carnap (1963) clarified that a‘‘neutral attitude toward various forms of languagebased on the principle that everyone is free to usethe language most suited to his purposes, hasremained the same throughout my life’’ (18–19).Carnap ([1936–7] 1965) tried to formulate areplacement for metaphysics, rather than directlyrepudiate it on empiricist grounds.Three definitions were important in this regard.

The forms presented here are slightly modifiedfrom those given by Carnap ([1936–7] 1965):

1. The confirmation of a sentence S is complete-ly reducible to the confirmation of a class ofsentences C if S is a consequence of a finitesubclass of C.

2. The confirmation of S directly incompletelyreduces to the confirmation of C if (a) the

confirmation of S is not completely reducibleto C and (b) there is an infinite subclass C 0 ofmutually independent sentences of C suchthat S entails, by substitution alone, eachmember of C 0.

3. The confirmation of a predicate P reduces tothe confirmation of a class of predicates Q ifthe confirmation of every full sentence of Pwith a particular argument (e.g., P(a), inwhich a is a constant of the language) isreducible to the confirmation of a consistentset of predicates of Q with the same argu-ment, together with their negations.

With these definitions Carnap ([1936–7] 1965)showed how dispositional predicates (for instance,‘‘is soluble in water’’) S could be introduced into anempiricist language by means of reduction postu-lates or finite chains of them. These postulatescould take the simple form of a reduction pair:

ð8xÞðWx ! ðDx ! SxÞÞ;ð8xÞðFx ! ðRx ! ØSxÞÞ;

in which W, D, F, and R designate observationalterms and S is a dispositional predicate. (In thesolubility example, Sx ¼ ‘‘x is soluble in water’’;Dx ¼ ‘‘x dissolves in water’’; Wx ¼ ‘‘x is placed inwater’’; and R and F are other observationalterms.) If Dx $ øRx and Wx $ Fx, then thereduction pair is a bilateral reduction sentence:

ð8xÞðWx ! ðDx $ SxÞÞ:The reduction postulates introduce, but do not

explicitly define, terms by specifying their logicalrelations with observational terms. They also pro-vide confirmation relations between the two typesof terms. For instance, the above reduction pairentails that the confirmation of S reduces to thatof the confirmation of the set {W,D, F, R}. Carnap([1936–7] 1965) defined a sentence or a predicate tobe confirmable (following definitions 1–3 above) ifits confirmation reduces to that of a class of ob-servable predicates (156–7). Reduction postulatesprovide such a reduction for disposition terms suchas S. The reduction pair does not define S in termsof observational terms. If øWx and øFx, then Sx isundetermined. However, the conditions in which Sor its negation hold can be extended by addingother reduction postulates to the language. Carnapthought that supplementing an empiricist languageto include terms that could be introduced by meansof reduction postulates or chains of them (for ex-ample, if Wx is introduced by a reduction pair)would adequately translate all theoretical terms ofscientific theories.

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Although it set a more rigorous standard for thedebate, Carnap’s ([1936–7] 1965) proposal encoun-tered difficulties. Carnap believed that bilateral re-duction sentences were analytic, since all theconsequences of individual reduction sentencesthat contained only observation terms were tautol-ogies. Yet, Hempel (1951) pointed out that twobilateral reduction sentences together sometimesentailed synthetic statements that contained onlyobservation terms. Since the idea that the conjunc-tion of two analytic sentences could entail syntheticstatements was counterintuitive, Hempel madethe important suggestion that analyticity and cog-nitive significance must be relativized to a specificlanguage and a particular theoretical context. Abilateral reduction sentence could be analytic inone context but synthetic in a different contextthat contained other reduction postulates.

Hempel (1950) also argued that many theoreticalterms, for instance ‘‘gravitational potential’’ or‘‘electric field,’’ could not be translated into anempiricist language with reduction postulates orchains of them. Introducing a term with reductionpostulates provides some sufficient and necessaryobservation conditions for the term, but Hempelclaimed that this was possible only in simple cases,such as electric fields of a simple kind. Introducinga theoretical term with reduction sentences alsounduly restricted theoretical concepts to observa-tion conditions. The concept of length could notbe constructed to describe unobservable intervals,for instance 1 � 10�100 m, and the principles ofcalculus would not be constructible in such a lan-guage (Hempel 1951). Carnap’s ([1936–7] 1965) pro-posal could not accommodate most of scientifictheorizing.

Although ultimately untenable, adequacy condi-tions for a significance criterion were included inCarnap’s ([1936–7] 1965) papers, generalized byHempel (1951) as: If N is a nonsignificant sentence,then all truth-functional compound sentences thatnonvacuously contain N must be nonsignificant. Itfollows that the denial of a nonsignificant sentenceis nonsignificant and that a disjunction, conjunct-ion, or conditional containing a nonsignificant com-ponent sentence is also nonsignificant. Yet Hempel(1951) was pessimistic that any adequate criterionsatisfying this condition and yielding a sharp di-chotomy between significance and nonsignificancecould be found. Instead, he thought that cognitivesignificance was a matter of degree:

Significant systems range from those whose entire extra-logical vocabulary consists of observational terms,through theories whose formulation relies heavily on

theoretical constructs, on to systems with hardly anybearing on potential empirical findings. (74).

Hempel suggested that it may be more fruitful tocompare theoretical systems according to othercharacteristics, such as clarity, predictive and ex-planatory power, and simplicity. On these bases,the failings of metaphysical systems would be moreclearly manifested.Of all the logical empiricists’ criteria, Carnap’s

(1956) criterion was the most sophisticated. Itattempted to rectify the deficiencies of his 1936–7work and thereby avoid Hempel’s pessimistic con-clusions. Scientific languages were divided into twoparts, a theoretical language LT and an observationlanguage LO. Let VO be the class of descriptiveconstants of LO, and VT be the class of primitivedescriptive constants of LT. Members of VO desig-nate observable properties and relations such as‘hard,’ ‘white,’ and ‘in physical contact with.’ Thelogical structure of LO contains only an elementarylogic, such as a simple first-order predicate calculus.The descriptive constants of LT, called theoreti-

cal terms, designate unobservable properties andrelations such as ‘electron’ or ‘magnetic field.’ LT

contains the mathematics required by science alongwith the ‘‘entities’’ referred to in scientific physical,psychological, and social theories, though Carnapstressed that this way of speaking does not entailany ontological theses. A theory was construed as afinite set of postulates within LT and represented bythe conjunction of its members T. A finite set ofcorrespondence rules, represented by the conjunc-tion of its membersC, connects terms ofVT andVO.Within this framework Carnap (1956) presented

three definitions, reformulated as:

D1. A theoretical term M is significant relativeto a class K with respect to LT, LO, T, andC ¼df if (i) K � VT, (ii) M =2 K, and (iii)there are three sentences SM, SK 2 LT, andSO 2 LO such that:(a) SM contains M as the only descriptive

term.(b) The descriptive terms in SK belong toK.(c) (SM6SK6T6C ) is consistent.(d) (SM6SK6T6C ) logically implies SO.(e) ø[(SK6T6C ) logically implies SO].

D2. A theoretical term Mn is significant withrespect to LT, LO, T, and C ¼df if there isa sequence of theoretical constants <M1, ...Mn> (Mi 2 VT) such that everyMi is signif-icant relative to {M1, ... Mi�1} with respectto LT, LO, T, and C.

D3. An expression A of LT is a significant sen-tence of LT ¼ df if (i) A satisfies the rules of


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formation of LT and (ii) every descriptiveterm in A is significant, as in D2.

These definitions, especially D1 (d) and (e), areintended to explicate the idea that a significant termmust make a predictive difference. Carnap wasaware that observation statements can often be de-duced only from theoretical statements containingseveral theoretical terms. With D2 Carnap implicitlydistinguishes between theoretical terms whose signif-icance depends on other theoretical terms and thosethat acquire significance independently of others. Incontrast to his work in 1936–7, and in accord withHempel’s (1951) relativization of analyticity andcognitive significance, Carnap (1956) specified thatthe significance of theoretical terms is relativized toa particular language and a particular theory T.With the adequacy of his proposal in mind,

Carnap (1956, 54–6) proved an interesting result.Consider a language in which VT is divided intoempirically meaningful terms V1 and empiricallymeaningless terms V2. Assume that C does notpermit any implication relation between those sen-tences that contain only V1 or VO terms and thosesentences that contain only V2 terms. For a giventheory T that can be resolved into a class of state-ments T1 that contain only terms from V1, and T2

that contain only terms of V2, then a simple butadequate significance criterion can be given. Anytheoretical term that occurs only in isolated sen-tences, which can be omitted from T withoutaffecting the class of sentences of LO that it entailsin conjunction with C, is meaningless.The problem is that this criterion cannot be uti-

lized for a theory T 0 equivalent to T that cannot besimilarly divided. Carnap (1956), however, showedby indirect proof that his criterion led to the desiredconclusion that the terms of V2 were not significantrelative to T 0 (LO, LT, and C ) and that thereforethe criterion was not too liberal.

The Supposed Failure of Carnap

Kaplan (1975) raised two objections to Carnap’s(1956) criterion that were designed to show that itwas too liberal and too restrictive. Kaplan’s firstobjection utilized the ‘‘deoccamization’’ of T6C.The label is appropriate, since the transformationof T6C into its deoccamization T 06C 0 involvesreplacing all instances of some theoretical termswith disjunctions or conjunctions of new terms ofthe same type: an Occam-unfriendly multiplicationof theoretical terms. Kaplan proved that any de-ductive systematization ofLO byT6C is also estab-lished by any of its deoccamizations. This motivates

his intuition that deoccamization should preservethe empirical content of a theory and, therefore,not change the significance of its theoretical terms.

The objection is as follows: If any members of VT

are significant with respect to T, C, LT, and LO,then there must be at least one M1 that is signifi-cant relative to an empty K (D2). Yet, if T6C isdeoccamized such that M1 is resolved into two newterms M11 and M12 that are never found apart,then the original argument that satisfied D1 canno longer be used, since T 06C 0 do not providesimilar logical relationships for M11 and M12 indi-vidually. Hence, the sequence of theoretical termsrequired by D2 will have no first member. Subse-quently, no chain of implications that establishesthe significance of successive theoretical termsexists. Although deoccamization preserves thedeductive systematization of LO, according toCarnap’s criterion it may render every theoreticalterm of T 06C 0 meaningless and therefore renderT 06C 0 devoid of empirical content.

Creath (1976) vindicated the core of Carnap’s(1956) criterion by generalizing it to accommodatesets of terms, reformulated as:

D10. A theoretical term M is significant relativeto a class K with respect to LT, LO, T, andC =df if (i) K� VT, (ii)M =2 K, (iii) there is aclass J such that J � VT, M 2 J, but J andK do not share any members, and (iv) thereare sentences SJ, SK 2 LT, and SO 2 LO

such that:(a) SJ contains members of J as the only

descriptive terms.(b) The descriptive terms in SK belong toK.(c) (SJ6SK6T6C ) is consistent.(d) (SJ6SK6T6C ) logically implies SO.(e) ø[(SK6T6C ) logically implies SO].(f ) It is not the case that (9J 0)(J 0 � J ) and

sentences SJ 0, SK 02 LT, and SO 0 2 LO

such that:(f1) SJ 0 contains only terms of J 0 as its

descriptive terms.(f2) The descriptive terms of SK 0 be-

long to K.(f3) (SJ 0 6SK 0 6T6C ) is consistent.(f4) (SJ 0 6SK 0 6T6C ) logically im-

plies SO 0.(f5) ø[(SK 0 6T6C ) logically implies

SO 0].

D20. A theoretical term Mn is significant withrespect to LT, LO, T and C ¼ df if there isa sequence of sets <J1, ... Jn> (Mn 2 Jn andJi � VT) such that every member of everyset Ji is significant relative to the union of


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J1 through Ji�1 with respect to LT, LO, Tand C.

Condition (f ) ensures that each member of J isrequired for the significance of the entire set.Creath (1976) points out that any term made sig-nificant by D1 and D2 of Carnap (1956) is madesignificant by D10 and D20 and that according tothe generalized criterion, Kaplan’s (1975) deocca-mization criticism no longer holds.

Kaplan (1975) and Rozeboom (1960) revealed anapparent second flaw in Carnap’s (1956) proposal:As postulates (definitions for Kaplan’s criticism)are added to T6C, the theoretical terms it containsmay change from cognitively significant to nonsig-nificant or vice versa. Consider an example fromKaplan (1975) in which VO ¼ {JO, PO, RO}; LO isthe class of all sentences of first-order logic withidentity that contain no descriptive constants oronly those from VO; VT ¼ {BT, FT, GT, HT, MT,NT}; and LT is the class of all sentences of first-order logic with identity that contain theoreticalterms from VT. Let T be:

ðTÞ½ð8xÞðHTx ! FTxÞ�6½ð8xÞðHTx !ðBTxVØGTxÞÞ�6½ð8xÞðMTx $ NTxÞ];

and let C be:

ðCÞ½ð8xÞðROx ! HTxÞ�6½ð8xÞðFTx ! JOxÞ�6½ð8xÞðGTx ! POxÞ�:

GT, FT, and HT are significant with respect toT6C relative to the empty set (see Carnap [1956]D1) and, hence, significant with respect to LO, LT,T, and C (see Carnap [1956] D2). RO is significantrelative toK¼ {GT};MT andNT are not significant.

Consider a definitional extension T 0 of T in anextended vocabulary V 0

T and language L0T. After

adding two definitions to T:

ðDEF1Þð8xÞðD1Tx $ ðMTx6ð9xÞFTxÞÞand

ðDEF2Þð8xÞðD2Tx $ ðMTx ! ð9xÞGTxÞÞ;D1T is significant relative to the empty set and

therefore significant with respect to T 0, C, LO, andL0T (D2). D2T is significant relative to K ¼ {D1T},

and therefore significant with respect to T 0, C, LO,and L0

T (D2). MT, which failed to be significantwith respect to T, C, LO, and LT, is now signifi-cant with respect to T 0, C, LO, and L0

T. A similarprocedure makes NT significant. Kaplan thoughtthis showed that Carnap’s (1956) criterion was tooliberal. The procedure seems able to make anytheoretical term significant with respect to someextended language and definition-extended theory,

but ‘‘definitional extensions are ordinarily thoughtof as having no more empirical content than theoriginal theory’’ (Kaplan 1975, 90).Using the same basic strategy, Rozeboom (1960)

demonstrated that extending T6C can transforman empirically significant term into an insignificantone. Consider a term M that is significant withrespect to T, C, LT, and LO. Rozeboom showedthat if postulates (not necessarily definitions) areadded to T or to C to form T 0 or C 0, in some casesD1(e) will no longer be satisfied, and no othersentences S 0

M, S 0K, S

0O exist by which M could be

independently shown to be significant. Further-more, if T6C is maximally LO consistent, no theo-retical term of LT is significant, since D1(e) is neversatisfied; for any SO, if T6C is maximally LO

consistent then it alone implies SO. Rozeboom(1960) took the strength of his criticism to dependupon the claim that for a criterion to be ‘‘intuitivelyacceptable,’’ theoretical terms must retain signifi-cance if T or C is extended.Carnap (1956) can be defended in at least two

ways. First, as Kaplan (1975) notes, the criterionwas restricted to primitive, nondefined theoreticalterms. It was explicitly formulated to avoid criti-cisms derived from definitional extensions. Definedterms often play an important role in scientifictheories, and it could be objected that any adequatecriterion should apply directly to theories that con-tain them. Yet the amendment that any theoreticalterm within the definiens of a significant definedterm must be antecedently shown significant quellsthese worries (Creath 1976).Second, Carnap (1956) insisted that terms are

significant only within a particular language andfor a particular T and C. He did not intend toformulate a criterion of cognitive significance thatheld under theory or language change. If Carnap’s(1956) work on a significance criterion was an ex-plication of the idea of meaningfulness (Hempel1950), the explicandum was the idea of a meani-ngful statement of a particular language in a par-ticular theoretical context, not meaningfulnessper se. Hence, Kaplan and Rozeboom’s objections,which rely on questionable intuitions about theinvariance of significance as T6C changes, arenot appropriately directed at Carnap (1956). Thefact that Carnap did not attempt such an account isnot merely the result of a realization that so manyproblems would thwart the project. Rather, it is aconsequence of the external/internal frameworkthat he believed was the most fruitful approach tothe philosophical questions (Carnap 1947).Furthermore, Rozeboom’s acceptability condi-

tion is especially counterintuitive, since changes in


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T or C designate changes in the connections be-tween theoretical terms themselves or theoreticalterms and observation terms. Additional postulatesthat specify new connections, or changes in theconnections, between these terms can obviouslychange the significance of a theoretical term. Scien-tific advances are sometimes made when empiricalor theoretical discoveries render a theoretical termnonsignificant.

JAMES JUSTUS

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Feigl, H. (1969), ‘‘The Origin and Spirit of Logical Positiv-ism,’’ in P. Achinstein and S. F. Barker (eds.), TheLegacy of Logical Positivism. Baltimore, MD: JohnsHopkins Press, 3–24.

Hempel, C. (1950), ‘‘Problems and Changes in the Empiri-cist Criterion of Meaning,’’ Revue Internationale de Phi-losophie 11: 41–63.

——— (1951), ‘‘The Concept of Cognitive Significance: AReconsideration,’’ Proceedings of the American Academyof Arts and Sciences 80: 61–77.

Kaplan, D. (1975), ‘‘Significance and Analyticity,’’ inJ. Hintikka (ed.), Rudolf Carnap, Logical Empiricist.Dordrecht, Netherlands: D. Reidel Publishing Co.,87–94.

Lewis, C. I. (1934), ‘‘Experience and Meaning,’’ Philosophi-cal Review 43: 125–146.

Nidditch, P. (1961), ‘‘A Defense of Ayer’s VerifiabilityPrinciple Against Church’s Criticism,’’ Mind 70: 88–89.

Reichenbach, H. (1938), Experience and Prediction. Chi-cago: University of Chicago Press.

Rozeboom, W. W. (1960), ‘‘A Note on Carnap’s MeaningCriterion,’’ Philosophical Studies 11: 33–38.

Scheffler, I. (1963), Anatomy of Inquiry. New York: AlfredA. Knopf.

Schlick, M. ([1932] 1979), ‘‘Positivism and Realism,’’ in H.L. Mulder and B. F. B. van de Velde-Schlick (eds.),Moritz Schlick: Philosophical Papers (1926–1936), vol.2. Dordrecht, Netherlands: D. Reidel Publishing Co.,259–284.

———([1936] 1979), ‘‘Meaning and Verification,’’ in H. L.Mulder and B. F. B. van de Velde-Schlick (eds.), MoritzSchlick: Philosophical Papers (1926–1936), vol. 2.Dordrecht, Netherlands: D. Reidel Publishing Co.,456–481.

Stace, W. T. (1935), ‘‘Metaphysics and Meaning,’’ Mind 44:417–438.

See also Analyticity; Ayer, Alfred Jules; Carnap,Rudolf; Corroboration; Demarcation, Problem of;Explication; Feigel, Herbert; Hempel, Carl; LogicalEmpiricism; Neurath, Otto; Popper, Karl; RationalReconstruction; Reichenbach, Hans; Schlick, Mor-itz; Tarski, Alfred; Verifiability; Vienna Circle

COMPLEMENTARITY

The existence of indivisible interaction quanta is acrucial point that implies the impossibility of anysharp separation between the behavior of atomic

objects and the interaction with the measuring instru-ments that serve to define the conditions under whichthe phenomena appear. In fact, the individuality


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of the typical quantum effects finds its proper ex-pression in the circumstance that any attempt atsubdividing the phenomena will demand a changein the experimental arrangement, introducing newpossibilities of interaction between objects andmeasuring instruments, which in principle cannotbe controlled. Consequently, evidence obtainedunder different experimental conditions cannotbe comprehended within a single picture but mustbe regarded as complementary in the sense thatonly the totality of the phenomena exhausts thepossible information about the objects (Bohr2000, 209–10).

Complementarity is distinctively associated withthe Danish physicist Niels Bohr and his attempt tounderstand the new quantum mechanics (QM) dur-ing the heyday of its invention, 1920–1935. Physi-cists know in practice how to extract very preciseand accurate predictions and explanations fromQM. Yet, remarkably, even today no one is con-fident about how to interpret it metaphysically(‘‘M-interpret’’ it). That is, there is no compellinglysatisfactory account of what sort of objects andrelations make up the QM realm, and so, ultimate-ly, no one knows why the precise answers are asthey are. In classical mechanics (CM), physiciststhought they had a lucidly M-interpretable theory:There was a collection of clearly specified entities,particles, or waves that interacted continuouslyaccording to simple laws of force so that the systemstate was completely specified everywhere and at alltimes—indeed, specification of just instantaneousposition and momenta sufficed. Here the dynamicprocess specified by the laws of force, expressed interms of energy and momentum (Bohr’s ‘‘causalpicture’’), generated a uniquely unfolding systemconfiguration expressed in terms of position andtime (Bohr’s ‘‘space-time picture’’). To repeat thisfor QM, what is needed is a collection of equivalentquantum objects whose interactions and move-ments in space-time generate the peculiar QM sta-tistical results in ways that are as intuitively clear asthey are for CM. (However, even this appealing con-cept of CMproves too simplistic; there is continuingmetaphysical perplexity underlying physics; seee.g., Earman 1986; Hooker 1991, note 13.)

That M-interpreting QM is not easy is nicelyillustrated by the status of the only agreed-ongeneral ‘‘interpretation’’ to which physicists refer,Born’s rule. It specifies how to extract proba-bilities from the QM wave function (c [‘‘psi’’]-function). These are normally associated withparticle-like events. But without further M-interpretive support, Born’s rule becomes merelypart of the recipe for extracting numbers from

the QM mathematics. That it does not M-interpretthe QM mathematics is made painfully clear by thefact that the obvious conception of the QM state itsuggests—a statistical ensemble of particles, each ina definite classical state—is provably not a possibleM-interpretation of QM. (For example, no consis-tent sense can then be made of a superposition ofc-states, since it is a mathematical theorem that theQM statistics of a superposed state cannot all bededuced from any single product of classical statis-tical states.)Bohr does not offer an M-interpretation of QM.

He came to think the very idea of such an inter-pretation incoherent. (In that sense, the term‘‘Copenhagen interpretation’’ is a misnomer; Bohrdoes not use this label.) Equally, however, Bohrdoes not eschew all interpretive discussion of QM,as many others do on the (pragmatic or positivist-inspired) basis that confining the use of QM strictlyto deriving statistics will avoid error while allowingscience to continue. Bohr’s position is that thistoo is profoundly wrong, and ultimately harmfulto physics. Instead he offers the doctrine of comple-mentarity as a ‘‘framework’’ for understanding the‘‘epistemological lesson’’ of QM (not its ontologicallesson) and for applying QM consistently and asmeaningfully as possible. (see Folse 1985 for a gen-eral introduction. For extensive, more technicalanalyses, see Faye and Folse 1994; Honner 1987;Murdoch 1987. For one of many critiques, and theopposing Bohrian M-interpretation, see Cushing1994.)Although Bohr considered it necessary (‘‘un-

avoidable’’) to continue using the key descriptiveconcepts of CM, the epistemological lesson of QMwas that the basic conditions for their well-defineduse were altered by the quantization of QM in-teractions into discrete unanalyzable units. This,he argued, divided the CM state in two, the con-ditions for the well-defined use of (1) causal (ener-gy-momentum) concepts and (2) configurational(space-time) concepts being now mutually ex-clusive, so that only one kind of description couldbe coherently provided at a time. Both kinds ofdescription were necessary to capture all theaspects of a QM system, but they could not besimply conjoined as in CM. They were nowcomplementary.Heisenberg’s uncertainty relations of QM, such

as DxDp�. h=2p; where Dx is the uncertainly in theposition, Dp is the uncertainty in the momentum,and h is Planck’s constant (or more generally thecommutation relations, such as ½x; px� ¼ ih=2

_p

where h is again Planck’s constant, the magnitudeof quantization), are not themselves statements

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of complementarity. Rather, they specify thecorresponding quantitative relationships betweencomplementary quantities.These complementary exclusions are implicit in

QM ontologies. For instance, single-frequency(‘‘pure’’) waves must, mathematically, occupy allspace, whereas restricting their extent involvessuperposing waves of different frequencies, with apoint-size wave packet requiring use of all frequen-cies; thus, frequency and position are not uniquelycospecifiable. And since the wavelength l is thewave velocity V (a constant) divided by the fre-quency vðl ¼ V=nÞ, uniquely specifying wave-length and uniquely specifying position equallyare mutually exclusive. QM associates wavelengthwith momentum ð p ¼ h=lÞ and energy with fre-quency (E ¼ hn) in all cases with discrete valuesand for both radiation (waves) and matter ( parti-cles), yielding the QM exclusions. (Note, however,that wave/particle complementarity is but one as-pect of causal/configurational complementarity,the aspect concerned with physical conditions thatframe coherent superposition versus those thatframe localization.)Precisely why these particular associations (and

similar QM associations) should follow fromquantization of interaction is not physically obvi-ous, despite Bohr’s confident assertion. Of coursesuch associations follow from the QM mathe-matics, but that presupposes rather than explainscomplementarity, and Bohr intended comple-mentarity to elucidate QM. The physical andmathematical roots of quantization are still onlypartially understood. However, it is clear thatdiscontinuity leads to a constraint, in principle,on joint precise specification. Consider initiallyany quantity that varies with time (t), e.g., energy(E ), so that E ¼ f ðtÞ.Then across some time in-terval, t1 ! t2, E will change accordingly:E1ðt1Þ ! E2ðt2Þ.If E varies continuously, then both E and t are

everywhere jointly precisely specifiable becausefor every intermediate value of t between t1 and t2(say, t1þn) there will be a corresponding value forE: E1þn ¼ f ðt1þnÞ. Suppose, however, that E (butnot t) is quantized, with no allowed value betweenE1 and E2. Then no intermediate E value is avail-able, and energy must remain undefined during atleast some part of the transition period. This con-clusion can be generalized to any two or morerelated quantities. The problem is resolved if bothquantities are quantized, but there is as yetno satisfactory quantization of space and time(Hooker 1991).

Such inherent mutual exclusions should not bemistaken for merely practical epistemic exclusions(some of Heisenberg’s pronouncements not-withstanding). Suppose that the position of aninvestigated particle i is determined by bouncing(‘‘scattering’’) another probe particle p off of it,determining the position of i from the intersectionof the initial and final momenta of p. However, iwill have received an altered momentum in theinteraction, and it is tempting to conclude that weare thus excluded from knowing both the positionand the momentum of i immediately after the in-teraction. But in CM the interaction may be retro-spectively analyzed to calculate the precise changein momentum introduced by p to i, using conserva-tion of momentum, and so establish both the posi-tion and the momentum of i simultaneously. Moregenerally, it is in this manner possible to correct forall measurement interactions and arrive at a com-plete classical state specified independently of itsmethod of measurement. This cannot, in principle,be done in QM, because of quantization.

Faye (1991) provides a persuasive account of theorigins of Bohr’s ideas about the applicability ofphysical concepts in the thought of the Danishphilosopher Harald Høffding (a family friend andearly mentor of Bohr’s) and sets out Bohr’s conse-quent approach. According to Høffding, objectivedescription in principle required a separation be-tween describing a subject and describing a knownobject (Bohr’s ‘‘cut’’ between them) in a way thatalways permitted the object to be ascribed a unique(Bohr’s ‘‘unambiguous’’) spatiotemporal location,state, and causal interaction. These ideas in turnoriginated in the Kantian doctrine that an objectivedescription of nature requires a well-defined dis-tinction between the knower and the object ofknowledge, permitting the unique construction ofa well-defined object state, specified in applicationsof concepts from the synthetic a priori (essentiallyNewtonian) construction of the external world (seeFriedman 1992). We have just noted how CMsatisfies this requirement.

Contrarily, Bohr insisted, the quantum of actioncreates an ‘‘indissoluble bond’’ between the mea-surement apparatus (m-apparatus, including thesentient observer) and the measured (observed)system, preventing the construction of a well-defined system state separate from observing in-teractions. This vitiates any well-defined, globalcut between m-apparatus and system. Creating aset of complementary partial cuts is the best thatcan now be done. In fact, these circumstances aregeneralized to all interactions between QM

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systems; the lack of a global separation is expressedin their superposition, which defies reduction toany combination of objectively separate states.Consequently, Bohr regarded CM as an idealizedphysics (achieved, imperfectly, only in the limith !: 0) and QM as a ‘‘rational generalization’’ ofit, in the sense of the principle of affinity, theKantian methodological requirement of continuity.

Bohr’s conception of what is required of a physi-cally intelligible theory T can thus be summarizedas follows (Hooker 1991, 1994):

BI1. Each descriptive concept A of T has a setof well-defined, epistemically accessibleconditions CA under which it is unambigu-ously applicable.

BI2. The set of such concepts collectivelyexhausts, in a complementary way, the epi-stemically accessible features of the phe-nomena in the domain of T.

BI3. There is a well-defined, unified, and essen-tially unique formal structure S(T) thatstructures and coordinates descriptions ofphenomena so that each description is welldefined (the various conditions CA are con-sistently combined), S(T ) is formally com-plete (Bub 1974), and BI2 is met.

BI4. Bohr objectivity (BO) satisfies BI1–3 in themost empirically precise and accurate wayavailable across the widest domain of phe-nomena while accurately specifying the in-teractive conditions under which suchphenomena are accessible to us.

An objective representation of nature thus reflectsthe interactive access (‘‘point of view’’) of the know-ing subject, which cannot be eliminated. In coming toknow nature, we also come to know ourselves asknowers—not fundamentally by being modeled inthe theory as objects (although this too happens,in part), but by the way the very form of rationalgeneralization reflects our being as knowing subjects.

A very different ideal of scientific intelligibilityoperates in classical physics, and in many proposedM-interpretations of QM. Contrary to BI1, descrip-tive concepts are taken as straightforwardly charac-terizing external reality (describing anM, even if it isa strange one). Hence, contrary to BI2, these con-cepts apply conjointly to describe reality complete-ly. Contrary to BI3 and BI4, an objective theorycompletely and accurately describes the physicalstate at each moment in time and provides a uniqueinteractive dynamic history of states for all systemsin its domain. Accordingly, measurements areanalyzed similarly as the same kinds of dynamic

interactions, and statistical descriptions reflect(only) limited information about states and arenot fundamental (contrary to common readingsof QM). Here the objective representation of na-ture through invariances eliminates any inherentreference to any subject’s point of view. Rather,in coming to know nature we also come to knowourselves as knowers by being modeled in the the-ory as some objects among others so as to removeourselves from the form of the theory, disappear-ing as subjects. This shift in ideals of intelligibilityand objectivity locates the full depth of Bohr’sdoctrine of complementarity.

References

Bohr, N. (2000), ‘‘Discussion with Einstein on Epistemo-logical Problems in Atomic Physics,’’ in P. A. Schilpp(ed.), Albert Einstein: Philosopher-Scientist, 3rd ed. LaSalle, IL: Open Court, 199–242.

——— (1961), Atomic Theory and the Description of Nature.Cambridge: Cambridge University Press.

Bub, J. (1974), The Interpretation of Quantum Mechanics.Dordrecht, Netherlands: Reidel.

Cushing, J. T. (1994), ‘‘A Bohmian Response to Bohr’sComplementarity,’’ in J. Faye and H. J. Folse (eds.),Niels Bohr and Contemporary Philosophy. Dordrecht,Netherlands: Kluwer.

Earman, J. (1986), A Primer on Determinism. Dordrecht,Netherlands: Reidel.

Faye, J. (1991), Niels Bohr: His Heritage and Legacy. Dor-drecht, Netherlands: Kluwer.

Faye, J., and H. J. Folse (eds.) (1994), Niels Bohr andContemporary Philosophy. Dordrecht, Netherlands:Kluwer.

Folse, H. J. (1985), The Philosophy of Niels Bohr. Amster-dam: North-Holland.

Friedman, M. (1992), Kant and the Exact Sciences. Cam-bridge, MA: Harvard University Press.

Honner, J. (1987), The Description of Nature. Oxford: Clar-endon.

Hooker, C. A. (1972), ‘‘The Nature of Quantum Mechani-cal Reality: Einstein versus Bohr,’’ in R. G. Colodny(ed.), Pittsburgh Studies in the Philosophy of Science,vol. 5. Pittsburgh, PA: University of Pittsburgh Press.

——— (1991), ‘‘Physical Intelligibility, Projection, andObjectivity: The Divergent Ideals of Einstein andBohr,’’ British Journal for the Philosophy of Science 42,491–511.

——— (1994), ‘‘Bohr and the Crisis of Empirical Intelligi-bility: An Essay on the Depth of Bohr’s Thought andOur Philosophical Ignorance,’’ in J. Faye and H. J. Folse(eds.), Niels Bohr and Contemporary Philosophy. Dor-drecht, Netherlands: Kluwer.

Murdoch, D. (1987), Niels Bohr’s Philosophy of Physics.Cambridge: Cambridge University Press.

C. A. HOOKER

See also Classical Mechanics; Quantum Measure-ment Problem; Quantum Mechanics

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COMPLEXITY

See Unity and Disunity of Science

CONFIRMATION THEORY

When evidence does not conclusively establish (orrefute) a hypothesis or theory, it may neverthelessprovide some support for (or against) the hypothe-sis or theory. Confirmation theory is concernedalmost exclusively with the latter, where conclusivesupport (or ‘‘countersupport’’) are limiting cases ofconfirmation (or disconfirmation). (Included also,of course, is concern for the case in which theevidence is confirmationally irrelevant.) Typically,confirmation theory concerns potential support,the impact that evidence would have on a hypothe-sis or theory if learned, where whether the evidenceis actually learned or not is not the point; for thisreason, confirmation theory is sometimes called thelogic of confirmation. (For simplicity of expositionfor now, theories will be considered separatelybelow and not explicitly mentioned until then.)It is relevant here to point out the distinction

between deductive logic (or deductive evaluationof arguments) and inductive logic (or inductiveevaluation of arguments). In deductive logic, thequestion is just whether or not the supposed truthof all the premises of an argument gives an absoluteguarantee of truth to the conclusion of the argu-ment. In inductive logic, the question is whether thesupposed truth of all the premises of an argumentgives significant support for the truth of the conclu-sion, where, ideally, some measure of to what de-gree the premises support the conclusion (which issometimes called the inductive probability of anargument) would be provided (see InductiveLogic; Induction, Problem of; and Verisimilitude.As in each of these topics also, the question is oneof either qualitative or quantitative support that

premises or evidence provides to a conclusion orthat a hypothesis has. See Carnap, Rudolf, for anidea of degree of confirmation based on his pro-posed ‘‘logical’’ interpretation of probability anddegree of support.) In the theory of the logic ofsupport, confirmation theory is concerned primari-ly with inductive support, where the theory of de-ductive support is supposed to be more fullyunderstood.

The concept of confirmation can be divided intoa number of subconcepts, corresponding to threedistinctions. First, absolute confirmation and incre-mental confirmation may be distinguished. In theabsolute sense, a hypothesis is confirmed by evi-dence if the evidence makes (or would make) thehypothesis highly supported; absolute confirmationis about how the evidence ‘‘leaves’’ the hypothesis.In the incremental sense, evidence confirms a hy-pothesis if the evidence makes the hypothesis morehighly confirmed (in the absolute sense) than it is(in the absolute sense) without the evidence; incre-mental confirmation involves a comparison. Sec-ond, confirmation can be thought of eitherqualitatively or quantitatively. So, in the absolutesense of confirmation, a hypothesis can be, qualita-tively, left more or less confirmed by evidence,where quantitative confirmation theory attemptsto make sense of assigning numerical degrees ofconfirmational support (‘‘inductive probabilities’’)to hypotheses in light of the evidence. In the incre-mental sense of confirmation, evidence E may,qualitatively, either confirm, disconfirm, or be evi-dentially irrelevant to a hypothesis H, where in thequantitative sense, a numerical magnitude (which

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can be measured, ‘‘inductive probabilistically,’’ indifferent ways; see below) is assigned to the‘‘boost’’ (positive or negative, if any) that E givesH. Finally, confirmation can be considered to beeither comparative or noncomparative. Noncom-parative confirmation concerns just one hypothe-sis/evidence pair. In comparative confirmation, onecan compare how well an E supports an H withhow well an E 0 supports the same H; or one maycompare how well an E supports an H with howwell the same E supports an H 0; or one may com-pare how well an E supports anH with how well anE 0 supports an H 0.

The exposition below will be divided into twomain parts. The first part, ‘‘NonprobabilisticApproaches,’’will concern different aspects of qual-itative confirmation; and the second part, ‘‘Pro-babilistic Approaches,’’ will consider some majorquantitative approaches. Almost exclusively, as inthe literature, the issue will be incremental confir-mation rather than absolute confirmation. Bothnoncomparative and various kinds of comparativeapproaches will be described.

Nonprobabilistic Approaches

A simple and natural idea about the confirmationof a general hypothesis of the form ‘‘All Fs are Gs’’is that an object confirms the hypothesis if and onlyif it is both an F and a G (a ‘‘positive instance’’ ofthe hypothesis), disconfirms the hypothesis if andonly if it is an F but not a G (a ‘‘negative instance’’),and is evidentially irrelevant if and only if it is noteven an F (no kind of instance). Hempel ([1945]1965) calls this Nicod’s criterion (Nicod 1930). An-other natural idea about the confirmation ofhypotheses is that if hypotheses H and H 0 arelogically equivalent, then evidence E confirms, dis-confirms, or is irrelevant to H if and only if Econfirms, disconfirms, or is irrelevant to H 0, re-spectively. Hempel calls this the equivalence condi-tion, and distinguishes between criteria (definitionsor partial definitions) of confirmation and the con-ditions of adequacy that the criteria should satisfy.Hempel points out that Nicod’s criterion does notsatisfy the equivalence condition (as long as confir-mation, disconfirmation, and evidential irrelevanceare mutually exclusive). For example, a hypothesis‘‘All Fs are Gs’’ is logically equivalent to ‘‘All non-Gs are non-Fs,’’ but Nicod’s criterion implies thatan object that is an F and a G would confirm theformer but be irrelevant to the latter, thus violatingthe equivalence condition. Also, ‘‘All Fs are Gs’’ islogically equivalent to ‘‘Anything that is both an F

and a non-G is both an F and a non-F,’’ whichNicod’s criterion implies that nothing can confirm(a positive instance would have to be both an F anda non-F ).Thus, Hempel suggests weakening Nicod’s crite-

rion. The idea that negative instances disconfirm(i.e., are sufficient to disconfirm) is retained. Fur-ther, Hempel endorses the positive-instance criteri-on, according to which positive instances aresufficient for confirmation. Nicod’s criterion canbe thought of as containing six parts: necessaryand sufficient conditions for all three of confirma-tion, disconfirmation, and irrelevance. The positive-instance criterion is said to be one-sixth of Nicod’scriterion, and it does not lead to the kind of con-tradiction that Nicod’s full criterion does whenconjoined with the equivalence condition.However, the combination of the positive-

instance criterion and the equivalence condition(i.e., the proposition that the positive-instance cri-terion satisfies the equivalence condition) does leadto what Hempel called paradoxes of confirmation,also known as the Ravens paradox and Hempel’sparadox. Hempel’s famous example is the hypoth-esis H: ‘‘All ravens are black.’’ Hypothesis H islogically equivalent to hypothesis H 0: ‘‘All non-black things are nonravens.’’ According to theequivalence condition, anything that confirms H 0confirms H. According to the positive-instancecriterion, nonblack nonravens (positive instancesof H 0) confirm H 0. Examples of nonblack nonra-vens (positive instances of H 0) include white shoes,yellow pencils, transparent tumblers, etc. So it fol-lows from the positive-instance criterion plus theequivalence condition that objects of the kinds justlisted confirm the hypothesis H that all ravensare black. These conclusions seem incorrect orcounterintuitive, and the paradox is that the twoseemingly plausible principles, the positive-instancecriterion and the equivalence condition, lead, byvalid reasoning, to these seemingly implausibleconclusions. Further paradoxical consequencescan be obtained by noting that the hypothesis His logically equivalent also to H 00, ‘‘All things thatare either a raven or not a raven (i.e., all things) areeither black or not a raven,’’ which has as positiveinstances any objects that are black and any objectsthat are not ravens.Since the equivalence condition is so plausible

(if H and H 0 are logically equivalent, they canbe thought of as simply different formulations ofthe same hypothesis), attention has focused on thepositive-instance criterion. Hempel defended thecriterion, arguing that the seeming paradoxicalnessof the consequences of the criterion is more of a

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psychological illusion than a mark of a logical flawin the criterion:

In the seemingly paradoxical cases of confirmation, weare often not actually judging the relation of the givenevidence E alone to the hypothesis H . . . . [I]nstead, wetacitly introduce a comparison of H with a body of evi-dence which consists of E in conjunction with additionalinformation that we happen to have at our disposal.

(Hempel [1945] 1965, 19)

So, for example, if one is just given the informa-tion that an object is nonblack and a nonraven(where it may happen to be a white shoe or a yellowpencil, but this is not included in the evidence),then the idea is that one should intuitively judgethe evidence as confirmatory, ‘‘and the paradoxesvanish’’ (20). To assess properly the seemingly par-adoxical cases for their significance for the logic ofconfirmation, one must observe the ‘‘methodologi-cal fiction’’ (as Hempel calls it) that one is in aposition to judge the relation between the givenevidence alone (e.g., that an object is a positiveinstance of the contrapositive of a universalizedconditional) and the hypothesis in question andthat there is no other information. This approachhas been challenged by some who have argued thatconfirmation should be thought of as a relationamong three things: evidence, hypothesis, andbackground knowledge (see the section below onProbabilistic Approaches).Given the equivalence condition, the Ravens

paradox considers the question of which of severalkinds of evidence confirm(s) what one can considerto be a single hypothesis. There is another kindof paradox, or puzzle, that arises in a case of asingle body of evidence and multiple hypotheses.In Nelson Goodman’s (1965) well-known Grueparadox or puzzle, a ‘new’ predicate is defined asfollows. Let’s say that an object A is ‘‘grue’’ if andonly if either (i) A has been observed before acertain time t (which could be now or some timein the future) and A is green or (ii) A has not beenobserved before that time t and A is blue. Considerthe hypothesis H that all emeralds are greenand the hypothesis H 0 that all emeralds aregrue. And consider the evidence E to be the obser-vation of a vast number of emeralds, all of whichhave been green. Given that t is now or some timein the future, E is equivalent to E 0, that the vastnumber of emeralds observed have all been grue.It is taken that E (the ‘‘same’’ as E 0) confirms H(this is natural enough) but not H 0—for in orderfor H 0 to be true, exactly all of the unobserved(by t) emeralds would have to be blue, whichwould seem to be disconfirmed by the evidence.

Yet, the evidence E 0 (or E) consists of positiveinstances of H 0.

Since the positive-instance criterion can be for-mulated purely syntactically—in terms of simplythe logical forms of evidence sentences and hypoth-eses and the logical relation between their forms—a natural lesson of the Grue example is thatconfirmation cannot be characterized purelysyntactically. (It should be noted that an importantfeature of Hempel’s ([1945] 1965) project was theattempt to characterize confirmation purely syn-tactically, so that evidence E should, strictlyspeaking, be construed as evidence statements orsentences, or ‘‘observation reports,’’ as he put it,rather than as observations or the objects of ob-servation.) And a natural response to this hasbeen to try to find nonsyntactical features of evi-dence and hypothesis that differentiate cases inwhich positive instances confirm and cases inwhich they do not. And a natural idea here is todistinguish between predicates that are ‘‘projec-tible’’ (in Goodman’s terminology) and those thatare not. Goodman suggested ‘‘entrenchment’’ ofpredicates as the mark of projectibility—where apredicate is entrenched to the extent to which it hasbeen used in the past in hypotheses that have beensuccessfully confirmed. Quine (1969) suggesteddrawing the distinction in terms of the idea ofnatural kinds. A completely different approachwould be to point out that the reason why onethinks the observation of grue emeralds (E 0 or E)disconfirms the grue hypothesis (H 0) is because ofbackground knowledge about constancy of color(in our usual concept of color) of many kinds ofobjects, and to argue that the evidence in this caseshould be taken as actually confirming the hypoth-esis H, given the Hempelian methodological fic-tion. It should be pointed out that the positive-instance criterion applies to a limited, though veryimportant, kind of hypothesis and evidence: uni-versalized conditionals for the hypothesis and pos-itive instances for the evidence. And it suppliesonly a sufficient condition for confirmation. Hem-pel ([1945] 1965) generalized, in a natural way, thiscriterion to his satisfaction criterion, which appliesto different and more complex logical structures forevidence and hypothesis and provides explicit defi-nitions of confirmation, disconfirmation, and evi-dential irrelevance. Without going into any detailabout this more general criterion, it is worth point-ing out what Hempel took to be evidence for itsadequacy. It is the satisfaction, by the satisfactioncriterion, of what Hempel took to be some intui-tively obvious conditions of adequacy for defini-tions, or criteria, of confirmation. Besides the

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equivalence condition, two others are the en-tailment condition and the special-consequencecondition. The entailment condition says that evi-dence that logically entails a hypothesis should bedeemed as confirming the hypothesis. The special-consequence condition says that if evidence E con-firms hypothesisH and ifH logically entails hypoth-esisH 0, then E confirmsH 0. This last condition willbe considered further in the section below onprobabilistic approaches.

The criteria for confirmation discussed aboveapply in cases in which evidence reports and hypo-theses are stated in the ‘‘same language,’’ whichHempel took tobe anobservational language. State-ments of evidence, for example, are usually referredto as observational reports in Hempel ([1945] 1965).What about confirmation of theories, though,which are often thought of as containing two kindsof vocabulary, observational and theoretical?Hypothetico-deductivism (HD) is the idea that the-ories and hypotheses are confirmed by their obser-vational deductive consequences. This is differentfrom the positive-instance criterion and the satis-faction criterion. For example, ‘‘A is an F and A isa G,’’ which is a report of a positive instance of thehypothesis that all Fs are Gs, is not a deductiveconsequence of the hypothesis. The positive-instance and satisfaction criteria are formulationsof the idea, roughly, that observations that arelogically consistent with a hypothesis confirm thehypothesis, while HD says that deductive conse-quences of a hypothesis or theory confirm thehypothesis or theory.

As an example, Edmund Halley in 1705 pub-lished his prediction that a comet, now known asHalley’s comet, would be visible from Earth some-time in December of 1758; he deduced this usingNewtonian theory. The prediction was successful,and the December 1758 observation of the cometwas taken by scientists to provide (further) verysignificant confirmation of Newtonian theory. Ofcourse, the prediction was not deduced from New-tonian theory alone. In general, other needed pre-mises include statements of initial conditions (in thecase of the example, reports of similar or relatedobservations at approximately 75-year intervals)and auxiliary assumptions (that the comet wouldnot explode before December 1758; that other bod-ies in the solar system would have only an insignif-icant effect on the path of the comet; and so on). Inaddition, when the theory and the observation re-port share no nonlogical vocabulary (say, the theo-ry is highly theoretical, containing no observationalterms), then so-called bridge principles are neededto establish a deductive connection between theory

and observation. An example of such a principlewould be, ‘‘If there is an excess of electrons [theo-retical] on the surface of a balloon [observational],then a sheet of paper [observational] will cling [ob-servational] to it, in normal circumstances [auxilia-ry assumption].’’ Of course, if the prediction fails(an observational deductive consequence of a theo-ry turns out to be false), then this is supposed toprovide disconfirmation of the theory.Two of the main issues or difficulties that have

been discussed in connection with the HD ideahave to do with what might be called distributionof credit and distribution of blame. The first hasalso been called the problem of irrelevant conjunc-tion. If a hypothesis H logically implies an observa-tion report E, then so does the conjunction, H6G,where G can be any sentence whatsoever. So thebasic idea of HD has the consequence that when-ever an E confirms an H, the E confirms alsoH6G, where G can be any (even irrelevant) hy-pothesis whatsoever. This problem concerns thedistribution of credit. A natural response wouldbe to refine the basic HD idea in a way to make itsensitive to the possibility that logically weakerparts of a hypothesis may suffice to deductivelyimply the observation report. The second issuehas to do with the possibility of the failure of theprediction, of the observational deductive conse-quence of the hypothesis turning out to be false.This is also known as Duhem’s problem (Duhem1914) (see Duhem Thesis). If a hypothesis H plusstatements of initial conditions I plus auxiliaryassumptions A plus bridge principles B logicallyimply an observation report E (ðH6I6A6BÞ) EÞ,and E turns out to be false, then what onecan conclude is that the four-part conjunctionH6I6A6B is false. And the problem is how ingeneral to decide whether the evidence should becounted as telling against the hypothesis H, thestatements of initial conditions I, the auxiliaryassumptions A, or the bridge principles B.Glymour (1980) catalogues a number of issues

relevant to the assessment of HD (and accountsof confirmation in general) and proposes an al-ternative deductivist approach to confirmationcalled ‘‘the bootstrap strategy,’’ which attemptsto clarify the idea of different parts of a theoryand how evidence can bear differently on them. InGlymour’s bootstrap account, confirmation is arelation among a theory T, a hypothesis H, andevidence expressed as a sentence E, and Glymourgives an intricate explication of the idea that ‘‘Econfirms H with respect to T,’’ an explication thatis supposed to be sensitive especially to the ideathat evidence can be differently confirmationally

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relevant to different hypotheses that are parts of acomplex theory.

Probabilistic Approaches

One influential probabilistic approach to variousissues in confirmation theory is called Bayesianconfirmation theory (see Bayesianism). The basicidea, on which several refinements may be based,is that evidence E confirms hypothesis H if andonly if the conditional probability PðH jEÞ (de-fined as PðH6EÞ j pðEÞ) is greater than the un-conditional probability P(H ) and where P(S ) isthe probability that the statement, or proposition,or claim, or assertion, or sentence S is true (thestatus of what kind of entity S might be is a con-cern in metaphysics or the philosophy of language,as well as in the philosophy of science). Disconfir-mation is defined by reversing the inequality, andevidential irrelevance is defined by changing theinequality to an equality.Typically in Bayesian confirmation theory, the

function P is taken to be a measure of an agent’ssubjective probabilities—also called degrees of be-lief, partial beliefs, or degrees of confidence. Muchphilosophical work has been done in the area offoundations of subjective probability, the intentbeing to clarify or operationalize the idea thatagents (e.g., scientists) have (or should have only)more or less strong or weak beliefs in propositions,rather than simply adopting the attitudes of accep-tance or rejection of them. One approach, calledthe Dutch book argument, attempts to clarify theidea of subjective probability in terms of odds thatone is willing to accept when betting for or againstthe truth or falsity of propositions (see Dutch BookArgument). Another approach, characterized as adecision theoretical approach, assumes variousaxioms regarding rational preference (transitivity,asymmetry, etc.) and some structural conditions(involving the richness of the set of propositions,or acts, states, and outcomes, considered by anagent) and derives, from preference data, via repre-sentation theorems, a probability assignment P anda desirability (or utility) assignment DES such thatan agent prefers an item A to an item B if and onlyif some kind of expected utility of A is numericallygreater than the expected utility of B, when theexpected utilities are calculated in terms of thederived P and DES functions (see Decision Theo-ry). Various formulas for expected utility have beenproposed. (Important work in foundations of sub-jective probability include Ramsey 1931; de Finetti1937; Savage [1954] 1972; Jeffrey [1965] 1983; andJoyce 1999.)

Where P measures an agent’s subjective degreesof belief, P(H jE ) is supposed to be the agent’sdegree of belief in H on the assumption that E istrue, or the degree of belief that the agent wouldhave inH were the agent to learn that E is true. If aperson’s degree of belief in H would increase if Ewere learned, then it is natural to say that for thisagent, E is positively evidentially relevant to H,even when E is not in fact learned. Of course,different people will have different subjective prob-abilities, or degrees of belief, even if the differentpeople are equally rational, this being due to dif-ferent bodies of background knowledge or beliefspossessed (albeit possibly equally justifiable or ex-cusable, depending on one’s experience), so that inthis approach to confirmation theory, confirma-tion is a relation among three things: evidence,hypothesis, and background knowledge. The rea-son this approach is called Bayesian is because ofthe use that is sometimes made of a mathematicaltheorem discovered by Thomas Bayes (Bayes1764), a simple version of which is PðH jEÞ ¼PðE jHÞPðHÞ=PðEÞ. This is significant because itis sometimes easier to figure out the probability ofan evidence statement conditional on a hypothesisthan it is to figure out the probability of a hypoth-esis on the assumption that the evidence statementis true (for example, when the hypothesis is statisti-cal and the evidence statement reports the outcomeof an experiment to which the hypothesis applies).Bayes’s theorem can be used to link these twoconverse conditional probabilities when the priors,P(H ) and P(E ), are known (see Bayesianism).

Bayesian confirmation theory not only providesa qualitative definition of confirmation, discon-firmation, and evidential irrelevance, but alsosuggests measures of degree of evidential support.The most common is the difference measure:dðH;EÞ¼PðH jEÞ�PðHÞ, where confirmation,disconfirmation, and evidential irrelevance corre-spond to whether this measure is greater than, lessthan, or equal to 0, and the degree is measured bythe magnitude of the difference. Another common-ly used measure is the ratio measure: rðH;EÞ ¼PðH jEÞ=PðHÞ where confirmation, disconfirma-tion, and evidential irrelevance correspond towhether this measure is greater than, less than, orequal to 1, and the degree is measured by themagnitude of the ratio. Other measures have beendefined as functions of likelihoods, or converseconditional probabilities, P(E jH). One applicationof the idea of degree of evidential support hasbeen in the Ravens paradox, discussed above.Such definitions of degree of evidential supportprovide a framework within which one can clarify

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intuitions that under certain conditions (contrapos-itive instances of the hypothesis that all ravensare black [i.e., nonblack nonravens]) confirm thehypothesis that all ravens are black, but to a mi-nuscule degree compared with positive instances(black ravens).

What follows is a little more detail about theapplication of Bayesian confirmation theory to thepositive-instance criterion and the Ravens para-dox. (see Eells 1982 for a discussion and refer-ences.) Let H be the hypothesis that all ravensare black; let RA symbolize the statement thatobject A is a raven; and let BA symbolize thestatement that object A is black. It can be shownthat if H is probabilistically independent of RA,(i.e., P(H jRA) ¼ P(H )), then a positive instance(or report of one), RA 6 BA, of H confirms H inthe Bayesian sense (i.e., P(H jRA6BA) > P(H )) ifand only if P(BA jRA) < 1 (which latter inequalitycan naturally be interpreted as saying that itwas not already certain that A would be black ifa raven). Further, on the same independence as-sumption, it can be shown that a positive instance,RA6BA, confirms H more than a contrapositiveinstance, ø BA6øRA if and only if P(BA jRA) < P(øRA jøBA).

What about the assumption of probabilistic in-dependence of H from RA? I. J. Good (1967) hasproposed counterexamples to the positive-instancecriterion like the following. Suppose it is believedthat either (1) there are just a few ravens in theworld and they are all black or (2) there are lotsand lots of ravens in the world, a very, very few ofwhich are nonblack. Observation of a raven, even ablack one (hence a positive instance of H ), wouldtend to support supposition 2 against supposition 1and thus undermine H, so that a positive instancewould disconfirm H. But in this case the indepen-dence assumption does not hold, so that Bayesianconfirmation theory can help to isolate the kinds ofsituations in which the positive-instance criterionholds and the kinds in which it may not.

Bayesian confirmation theory can also be used toassess Hempel’s proposed conditions of adequacyfor criteria of confirmation. Recall, for example,his special-consequence condition, discussedabove: If E confirms H and H logically entails H 0,then E must also confirm H 0. It is a theorem ofprobability theory that if H logically entails H 0,then P(H 0) is at least as great as P(H ). If theinequality is strict, then an E can increase the prob-ability of H while decreasing the probability ofH 0, consistent with H logically entailing H 0. Thisfact can be used to construct intuitively compel-ling examples of an H entailing an H 0 and an E

confirming the H while disconfirming the H 0,telling against the special-consequence conditionand also in favor of Bayesian confirmation theory(e.g., Eells 1982).Some standard objections to Bayesian confirma-

tion theory are characterized as the problem of thepriors and the problem of old evidence. As to thefirst, while it is sometimes admitted that it makessense to assign probabilities to evidence statementsE conditional on some hypothesis H (even in theabsence of much background knowledge), it isobjected that it often does not make sense to assignunconditional, or ‘‘prior,’’ probabilities to hypoth-esis H or to evidence statements (reports of obser-vation) E. If H is a newly formulated physicalhypothesis, for example, it is hard to imaginewhat would justify an assignment of probabilityto it prior to evidence—but that is just what thesuggested criterion of confirmation, Bayes’s theo-rem, and the measures of confirmation describedabove require. Such issues make some favor a like-lihood approach to the evaluation of evidence—Edwards (1972) and Royall (1997), for instance,who represent a different approach and traditionin the area of statistical inference. According to oneformulation of the likelihood account, an E con-firms an H more than the E confirms an H 0 if andonly if P(E jH ) is greater than P(E jH 0). This is acomparative principle, an approach that separatesthe question of which hypothesis it is more justifiedto believe given the evidence (or the comparativeacceptability of hypotheses given the evidence)from the question of what the comparative signifi-cance is of evidence for one hypothesis comparedwith the evidence’s significance for another hypoth-esis. It is the latter question that the likelihoodapproach actually addresses, and it is sometimessuggested that the degree to which an E supportsan H compared with the support of E for an H 0is measured by the likelihood ratio, PðE jHÞ=PðE jH 0Þ: Also, likelihood measures of degree ofconfirmation of single hypotheses have been pro-posed, such as LðH;EÞ ¼ PðE jHÞ=PðE jØHÞ;or the log of this ratio. (see Fitelson 2001 andForster and Sober 2002 for recent discussion andreferences.)Another possible response to the problem of

priors is to point to convergence theorems (as inde Finetti 1937) and argue that initial settings ofpriors does not matter in the long run. Accordingto such theorems, if a number of agents set dif-ferent priors, are exposed to the same series ofevidence, and update their subjective probabil-ities (degrees of belief ) in certain ways, then, al-most certainly, their subjective probabilities will

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eventually converge on each other and, under cer-tain circumstances, upon the truth.The problem of old evidence (Glymour 1980;

Good 1968, 1985) arises in cases in which P(E ) ¼1. It is a theorem of probability theory that in suchcases P(H jE ) ¼ P(H ), for any hypothesis H, sothat in the Bayesian conception of confirmationas formulated above, an E with probability 1 can-not confirm any hypothesis H. But this seems torun against intuition in some cases. An often-citedsuch case is the confirmation that Einstein’s generaltheory of relativity apparently was informed by al-ready known facts about the behavior of the perihe-lion of the planet Mercury. One possible Bayesiansolution to the problem, suggested by Glymour(1980), would be to say that it is not the alreadyknown E that confirms the H after all, but rather anewly discovered logical or explanatory relationbetween the H and the E. Other solutions havebeen proposed, various versions of the problemhave been distinguished (see Earman 1992 for adiscussion), and the problem remains one of livelydebate.

ELLERY EELLS

References

Bayes, Thomas (1764), ‘‘An Essay Towards Solving a Prob-lem in the Doctrine of Chance,’’ Philosophical Transac-tions of the Royal Society of London 53: 370–418.

de Finetti, Bruno (1937), ‘‘La prevision: Ses lois logiques,ses sources subjectives,’’ Annales de l’Institute HenriPoincare 7: 1–68.

Duhem, Pierre (1914), The Aim and Structure of PhysicalTheory. Princeton, NJ: Princeton University Press.

Earman, John (1992), Bayes or Bust: A Critical Examina-tion of Bayesian Confirmation Theory. Cambridge, MA,and London: MIT Press.

Edwards, A. W. F. (1972), Likelihood. Cambridge: Cam-bridge University Press.

Eells, Ellery (1982), Rational Decision and Causality. Cam-bridge and New York: Cambridge University Press.

Fitelson, Branden (2001), Studies in Bayesian ConfirmationTheory. Ph.D. dissertation, University of Wisconsin–Madison.

Forster, Malcolm, and Elliott Sober (2002), ‘‘Why Likeli-hood?’’ in M. Taper and S. Lee (eds.), The Nature ofScientific Evidence. Chicago: University of ChicagoPress.

Glymour, Clark (1980), Theory and Evidence. Princeton,NJ: Princeton University Press.

Good, I. J. (1967), ‘‘The White Shoe Is a Red Herring,’’The British Journal for the Philosophy of Science 17: 322.

——— (1968), ‘‘Corroboration, Explanation, Evolv-ing Probability, Simplicity, and a Sharpened Razor,’’British Journal for the Philosophy of Science 19: 123–143.

——— (1985), ‘‘A Historical Comment Concerning NovelConfirmation,’’ British Journal for the Philosophy of Sci-ence 36: 184–186.

Goodman, Nelson (1965), Fact, Fiction, and Forecast. NewYork: Bobbs-Merrill.

Hempel, Carl G. ([1945] 1965), ‘‘Studies in the Logic ofConfirmation,’’ in Aspects of Scientific Explanation andOther Essays in the Philosophy of Science. New York:Free Press, 3–51. Originally published in Mind 54: 1–26and 97–121.

Jeffrey, Richard C. ([1965] 1983), The Logic of Decision.Chicago and London: University of Chicago Press.

Joyce, James M. (1999), The Foundations of Causal DecisionTheory. Cambridge and New York: Cambridge Univer-sity Press.

Nicod, Jean (1930), Foundations of Geometry and Induction.New York and London: P. P. Wiener.

Quine, W. V. (1969), ‘‘Natural Kinds,’’ in Ontological Rela-tivity and Other Essays. New York: Columbia UniversityPress.

Ramsey, Frank Plumpton (1931), ‘‘Truth and Probability,’’in R. B. Braithwaite (ed.), The Foundations of Mathe-matics and Other Logical Essays. London: Routledgeand Kegan Paul, 156–198.

Royall, Richard (1997), Statistical Evidence: A LikelihoodParadigm. Boca Raton, FL: Chapman and Hall.

Savage, Leonard ([1954] 1972), The Foundations of Statis-tics. New York: Dover Publications.

See also Bayesianism; Carnap, Rudolf; DecisionTheory; Dutch Book Argument; Epistemology;Hempel, Carl Gustav; Induction, Problem of; Induc-tive Logic; Probability

CONNECTIONISM

Connectionist models, also known as modelsof parallel distributed processing (PDP) and arti-ficial neural networks (ANN), have merged intothe mainstream of cognitive science since the

mid-1980s. Connectionism currently represents oneof two dominant approaches (symbolic modeling isthe other) within artificial intelligence used to dev-elop computational models of mental processes.

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Unlike symbolic modeling, connectionist modelingalso figures prominently in computational neuro-science (where the preferred term is neural networkmodeling).

Connectionist modeling first emerged in the pe-riod 1940–1960, as researchers explored possibleapproaches to using networks of simple neuronsto perform psychological tasks, but it fell into de-cline when limitations of early network designsbecame apparent around 1970. With the publica-tion of the PDP Research Group volumes (Ru-melhart, McClelland, et al. 1986; McClelland,Rumelhart, et al. 1986), connectionism was rescuedfrom over a decade of popular neglect, and the waywas opened for a new generation to extend theapproach to fresh explanatory domains. (For acollection of historically significant papers fromthese neglected years and before, see Anderson andRosenfeld 1988; Anderson, Pellionisz, and Rosen-feld 1990.) Despite some early claims that connec-tionism constitued a new, perhaps revolutionary,way of understanding cognition, the veritableflood of network-based research has ultimately oc-curred side by side with other, more traditional,styles of modeling and theoretical frameworks.

The renaissance in connectionist modeling is aresult of convergence from many different fields.Mathematicians and computer scientists attempt todescribe the formal, mathematical properties of ab-stract network architectures. Psychologists and neu-roscientists use networks to model behavioral,cognitive, and biological phenomena. Roboticistsalso make networks the control systems for manykinds of embodied artificial agents. Finally, engi-neers employ connectionist systems in many in-dustrial and commercial applications. Researchhas thus been driven by a broad spectrum ofconcerns, ranging from the purely theoretical toproblem-solving applications for problems invarious scientific domains to application-based orengineering needs.

Given these heterogeneous motivations, and therecent proliferation of network models, analytictechniques, applications, and theories, it is appro-priate to ask whether connectionism constitutes acoherent research program or is instead primarilya modeling tool. Following Lakatos, connection-ism could be construed as a research program in-volving a set of core theoretical principles aboutthe role of networks in explaining and understand-ing cognition, a set of positive and negative heur-istics that guide research, an ordering of theimportant commitments of connectionist model-ing, and a set of principles and strategies dictatinghow recalcitrant empirical results are to be

accounted for (see Lakatos, Imre; Research Pro-grams). The greater the disunity in these factors,the less connectionism resembles a research pro-gram, and the more it appears to be a convenienttool for modeling certain phenomena. If it is a mod-eling tool, connectionism need not commitmodelersto having anything in common beyond their use ofthe particular mathematical and formal apparatusitself.This article will briefly describe the features of

prevalent connectionist architectures and discuss anumber of challenges to the use of thesemodels. Onechallenge comes from symbolicmodels of cognition,which present an alternative representational frame-work and set of processing assumptions. Anothercomes from a purportedly nonrepresentationalframework, that of nonlinear dynamical systemstheory. Finally, there is the neuroscientific chal-lenge to the disciplinary boundaries drawn around‘‘cognitive’’ modeling by some connectionist psy-chologists. The status of connectionism is assessedin light of these challenges.

The Properties of Connectionist Models

Connectionist networks are built up from basiccomputational elements called units or nodes,which are linked to each other via weighted con-nections, called simply weights. Units take on avariable numerical level of activation, and theypass activation to each other via the weights.Weights determine how great an effect one unithas on other units. This effect may be positive(excitatory) or negative (inhibitory). The net inputa unit receives at a time is the weighted sum of theactivations on all of the units that are active andconnected to it. Given the net input, an activationfunction (often nonlinear or imposing a threshold)determines the activation of the unit. In this way,activation is passed in parallel throughout the net-work. Connectionist networks compute functionsby mapping vectors of activation values onto othersuch vectors.Multilayer feedforward networks are the most

intensively studied and widely used class of con-temporary models. Units are arranged into layers,beginning with an input layer and passing througha number of intermediate hidden layers, terminat-ing with an output layer. There are no reciprocalconnections, so activation flows unidirectionallythrough the network. The modeler assigns repre-sentational significance to the activation vectors atthe input and output layers of a network, therebyforging the link between the model and the cogni-tive task to be explained.

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For example, Sejnowski and Rosenberg’sNETtalk architecture is designed to map graphe-mic inputs (letters) onto phonemic outputs. It con-sists of an input layer of seven groups of 29 units, ahidden layer of 80 units, and an output layer of 26units. Each layer is completely connected to thenext one. Vectors of activity in the network repre-sent aspects of the letter-reading task. The inputgroups are used to represent the seven letters of textthat the network is perceiving at a time, and theoutput layer represents the phoneme correspondingto the fourth letter in the input string. The task ofthe network is to pronounce the text correctly,given the relevant context. When the values of theweights are set correctly, the network can producethe appropriate phoneme-representing vectors inresponse to the text-representing vectors.Simple networks can be wired by hand to com-

pute some functions, but in networks containinghundreds of units, this is impossible. Connectionistsystems are therefore usually not programmed inthe traditional sense, but are trained by fixing alearning rule and repeatedly exposing the networkto a subset of the input-output mappings it isintended to learn. The rule then systematicallyadjusts the network’s weights until its outputs arenear the target output values. One way to classifylearning rules is according to whether they requirean external trainer. Unsupervised learning (e.g.,Hebbian learning) does not require an externaltrainer or source of error signals. Supervisedlearning, on the other hand, requires that somethingoutside the network indicate when its performanceis incorrect. The most popular supervised learningrule currently in use is the backpropagation rule.In backpropagation learning, the network’s

weights are initially set to random values (withincertain bounds). The network is then presentedwith patterns from the training environment.Given random weights, the network’s response willlikely be far from the intended mapping. The differ-ence between the output and the target is computedby the external trainer and used to send an errorsignal backward through the network. As the signalpropagates, the weights between each layer areadjusted by a slight amount. Over many train-ing cycles, the network’s performance graduallyapproaches the target. When the output is withinsome criterion distance of the target, training ceases.Since the error is being reduced gradually, back-propagation is an instance of a gradient-descentlearning algorithm.Backpropagation-trained networks have been

successful at performing in many domains, includ-ing past-tense transformation of verbs, generation

of prototypes from exemplars, single word read-ing, shape-from-shading extraction, visual objectrecognition, modeling deficits arising in deep dys-lexia, and more. Their formal properties are wellknown. However, they suffer from a number ofproblems. Among these is the fact that learningvia backpropagation is extremely slow, and in-creasing the learning-rate parameter typicallyresults in overshooting the optimum weights forsolving the task.

Another problem facing feedforward networksgenerally is that individual episodes of processinginputs are independent of each other except forchanges in weights resulting from learning. Butoften a cognitive agent is sensitive not just to whatit has learned over many episodes, but to what itprocessed recently (e.g., the words prior to the pre-ceding one). The primary way sensitivity to contexthas been achieved in feedforward networks has beento present a constantly moving window of input.For example, in NETtalk, the input specified thethree phonemes before and three phonemes afterthe one to be pronounced. But this solution isclearly a kludge and suffers from the fact that itimposes a fixed window. If sensitivity to the itemfour back is critical to correct performance, thenetwork cannot perform correctly.

An alternative architecture that is increasinglybeing explored is the simple recurrent network(SRN) (Elman 1991). SRNs have both feedforwardand recurrent connections. In the standard model,an input layer sends activity to a hidden layer,which has two sets of outgoing connections: oneto other hidden layers and eventually on to theoutput layer, and another to a specialized contextlayer. The weights to the units in the context layerenable it to construct a copy of the activity in thehidden units. The activation over these units is thentreated as an additional input to the same hiddenunits at the next temporal stage of processing. Thisallows for a limited form of short-term memory,since activity patterns that were present during theprevious processing cycle have an effect on the nextcycle. Since the activity on the previous cycle wasitself influenced by that on a yet earlier cycle, thisallows for memory extending over several previousprocessing epochs (although sensitivity to morethan one cycle back will be diminished).

Once trained in a variation of backpropagation,many SRNs are able to discover patterns in tempo-rally ordered sets of events. Elman (1991) hastrained SRNs on serially presented words in anattempt to teach them to predict the grammaticalcategory of the next word in a sentence. The net-works can achieve fairly good performance at

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this task. Since the networks were never suppliedinformation about grammatical categories, thissuggests that they induced a representation of amore abstract similarity among words than waspresent in the raw training data. There are manyother kinds of neural network architecture. (Forfurther details on their properties and applications,see Anderson 1995; Bechtel and Abrahamsen2002.)

Connectionism and Symbolic Models

Within cognitive science, symbolic models of cog-nition have constituted the traditional alternativeto connectionism. In symbolic models, the basicrepresentational units are symbols having bothsyntactic form and typically an intuitive semanticsthat corresponds to the elements picked out bywords of natural language. The symbols are dis-crete and capable of combining to form complexsymbols that have internal syntactic structure. Likethe symbol strings used in formal logic, these com-plex symbols exhibit variable binding and scope,function-and-argument structure, cross-reference,and so on. The semantics for complex symbols iscombinatorial: The meaning of a complex symbolis determined by the meanings of its parts plus itssyntax. Finally, in symbolic models the dynamics ofthe system are governed by rules that transformsymbols into other symbols by responding to theirsyntactic or formal properties. These rules areintended to preserve the truth of the structuresmanipulated. Symbolic models are essentiallyproof-theoretic engines.

Connectionist models typically contain unitsthat do not individually represent lexicalized se-mantic contents. (What are called localist net-works are an exception. In these, individual unitsare interpretable as expressing everyday propertiesor propositions. See Page 2000.) More comm-only, representations with lexicalized content aredistributed over a number of units in a network(Smolensky 1988). In a distributed scheme, individ-ual units may stand for repeatable but nonlexica-lized microfeatures of familiar objects, which arethemselves represented by vectors of such features.In networks of significant complexity, it may bedifficult, if not impossible, to discern what contenta particular unit is carrying.

In networks, there is no clear analog to the sym-bolicist’s syntactic structures. Units acquire andtransmit activation values, resulting in larger pat-terns of coactivation, but these patterns of units donot themselves syntactically compose. Also, there isno clear program/data distinction in connectionist

systems. Whether a network is hand-wired ortrained using a learning rule, the modificationsare changes to the weights between units. The newweight settings determine the future course of acti-vation in the network and simultaneously consti-tute the data stored in the network. There are noexplicitly represented rules that govern the system’sdynamics.Classical theorists (Fodor and Pylyshyn 1988)

have claimed that there are properties of cognitionthat are captured naturally in symbolic modelsbut that connectionist models can capture themonly in an ad hoc manner, if at all. Among theseproperties are the productivity and the systemati-city of thought. Like natural language, thought isproductive, in that a person can think a potentiallyinfinite number of thoughts. For example, one canthink that Walt is an idiot, that Sandra believesthat Walt is an idiot, that Max wonders whetherSandra believes that Walt is an idiot, and so on.Thought is also systematic, in that a person whocan entertain a thought can also entertain manyother thoughts that are semantically related to it(Cummins 1996). If a person can think that Rexadmires the butler’s courage, that person can alsothink that the butler admires Rex’s courage. Any-one who can think that dogs fear cats can thinkthat cats fear dogs, and so on. Unless each thoughtis to be learned anew, these capacities need somefinite basis.Symbolicists argue that this basis is composition-

ality: Thought possesses a combinatorial syntaxand semantics, according to which complex thou-ghts are built up from their constituent concepts,and those concepts completely determine the mean-ing of a complex thought. The compositionalityof thought would explain both productivity andsystematicity. Grasping the meaning of a set ofprimitive concepts and grasping the recursiverules by which they can be combined is sufficientfor grasping the infinite number of thoughts thatthe concepts and rules can generate. Similarly,grasping a syntactic schema and a set of constituentconcepts explains why the ability to entertain onethought necessitates the ability to entertain others:Concepts may be substituted into any permissiblerole slot in the schema.The challenge symbolicists have put to con-

nectionists is to explain productivity and syste-maticity in a principled fashion, without merelyimplementing a symbolic architecture on top ofthe connectionist network (for one such implemen-tation, see Franklin and Garzon 1990). One optionthat some connectionists pursue is to deny thatthought is productive or systematic, as symbolicists

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characterize these properties. For example, onemight deny that it is possible to think any system-atically structured proposition. Although one cancompose the symbol string ‘‘The blackberry ate thebear,’’ that does not entail that one is able to thinksuch a thought. But clearly much of thought exhi-bits some degree of productivity and systematicity,and it is incumbent on connectionists to offer someaccount of how it is achieved.Connectionists have advanced a number of pro-

posals for explaining productivity and syste-maticity. Two of the most widely discussed arePollack’s recursive auto-associative memories(RAAMs) and Smolensky’s tensor product net-works (Pollack 1990; Smolensky, 1991). RAAMsare easier to understand. An auto-associative net-work is one trained to produce the same patternon the output layer as is present on the input layer.If the hidden layer is smaller than the input andoutput layers, then the pattern produced on thehidden layer is a compressed representation of theinput pattern. If the input layer contains threetimes the number of units as the hidden layer,then one can treat the input activation as consistingof three parts constituting three patterns (e.g., fordifferent words) and recursively compose thehidden pattern produced by three patterns withtwo new ones. In such an encoding, one is implicitlyignoring the output units, but one can also ignorethe input units and supply patterns to the hiddenunits, allowing the RAAM to generate a pattern onthe output units. What is interesting is that evenafter several cycles of compression, one can, byrecursively copying the pattern on one-third ofthe output units back onto the hidden units, re-create with a fair degree of accuracy the originalinput patterns.If RAAMs are required to perform many cycles

of recursive encoding, the regeneration of the orig-inal pattern may exhibit errors. But up to thispoint, the RAAM has exhibited a degree of pro-ductivity by composing representations of com-plex structures from representations of their parts.One can also use the compressed patterns in otherprocessing (e.g., to train another feedforward net-work to construct the compressed representationof a passive sentence from the corresponding ac-tive sentence). RAAMs thus exhibit a degree ofsystematicity. But the compressed representationsare not composed according to syntactic princi-ples. Van Gelder (1990), accordingly, construesthem as manifesting functional, not explicit,compositionality.Symbolicists have rejected such functional

compositionality as inadequate for explaining

cognition. In many respects, this debate hasreached a standoff. In part its resolution will turnon the issue posed earlier: To what degree dohumans exhibit productivity and systematicity?But independently of that issue, there are seriousproblems in scaling up from connectionist net-works designed to handle toy problems to onescapable of handling the sort of problems humansdeal with regularly (e.g., communicating in naturallanguages). Thus, it is not clear whether solutionssimilar to those employed in RAAMs (or in SRNs,which also exhibit a degree of productivity andsystematicity) will account for human perfor-mance. (Symbolic models have their own problemsin scaling, and so are not significantly better off inpractice.)

Connectionism and Dynamical Systems Theory

Although the conflict between connectionists andsymbolicists reached a stalemate in the 1990s, with-in the broader cognitive science community a kindof accord was achieved. Connectionist approacheswere added to symbolic approaches as parts of themodeling toolkit. For some tasks, connectionistmodels proved to be more useful tools than symbol-ic models, while for others symbolic modelscontinued to be preferred. For yet other tasks, con-nectionist models were integrated with symbolicmodels into hybrids.

As this was happening, a new competitoremerged on the scene, an approach to cognitionthat challenged both symbolic and connectionistmodeling insofar as both took seriously that cogni-tive activity involved the use of some form of repre-sentation. Dynamical systems theory suggested thatrather than construing cognition as involvingsyntactic manipulation of representations or pro-cessing them through layers of a network, oneshould reject the notion of representation altogeth-er. The alternative these critics advanced was tocharacterize cognitive activity in terms of a (typi-cally small) set of variables and to formulate (typi-cally nonlinear) equations that would relate thevalues of different variables in terms of how theychanged over time. In physics, dynamical systemstheory provides a set of tools for understanding thechanges over time of such systems of variables. Forexample, each variable can be construed as defining adimension in a multidimensional state space, andmany systems, although starting at different pointsin this space, will settle onto a fixed point or into acycle of points. These points are known as attrac-tors, and the paths to them as the transients. Thestructure of the state space can often be represented

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geometrically—for example, by showing differentbasins, each of which represents starting states thatwill end up in a different attractor.

Connectionist networks, especially those employ-ing recurrent connections, are dynamical systems,and some connectionist modelers have embracedthe tools of dynamical systems theory for describingtheir networks. Elman, for example, employs suchtools to understand how networks manage to learnto respect syntactic categories in processing streamsof words. Others have made use of some of themore exotic elements in dynamical systems theory,such as activitation functions that exhibit deter-ministic chaos, to develop new classes of networksthat exhibit more complex and interesting patternsof behavior than simpler networks (e.g., jumpingintermittently between two competing interpreta-tions of an ambiguous perceptual figure such asthe duck-rabbit (see van Leeuwen, Verver, andBrinkers 2000)). Some particularly extreme dynami-cists, however, contend that once one has character-ized a cognitive system in thisway, there is no furtherpoint to identifying internal states as representationsand characterizing changes as operations on theserepresentations. Accordingly, they construe dyna-mical systems theory as a truly radical paradigmshift for cognitive science (van Gelder 1995).

This challenge has been bolstered by some nota-ble empirical successes in dynamical systems mod-eling of complex cognition and behavior. Forexample, Busemeyer and Townsend (1993) offer amodel of decision under uncertainty, decision fieldtheory, that captures much of the empirical dataabout the temporal course of decision makingusing difference equations containing only sevenparameters for psychological quantities such asattention weight, valence, preference, and so on.Connectionist models, by contrast, have activationstate spaces of as many dimensions as they haveunits. There are dynamical systems models of manyother phenomena, including coordination of fingermovement, olfactory perception, infants’ steppingbehavior, the control of autonomous robot agents,and simple language processing. The relative sim-plicity and comprehensibility of their models moti-vates the antirepresentational claims advanced bydynamical systems theorists.

There is reason, though, to question dynamicalsystems theory’s more radical challenge to cogni-tive modeling. One can accept the utility of char-acterizing a system in terms of a set of equationsand portraying its transitions through a multidi-mensional state space without rejecting the utilityof construing states within the system as represen-tational and the trajectories through state space in

terms of transitions between representations. Thisis particularly true when the system is carrying outwhat one ordinarily thinks of as a complex reason-ing task such as playing chess, where the task isdefined in terms of goals and the cognizer can beconstrued as considering different possible movesand their consequences. To understand why a cer-tain system is able to play chess successfully, ratherthan just recognizing that it does, the commonstrategy is to treat some of its internal states as rep-resenting goals or possible moves. Moreover, inso-far as these internal states are causally connectedin appropriate ways, they do in fact carry informa-tion (in what is fundamentally an informational-theoretic sense, in which the state covaries withreferents external to the system), which is thenutilized by other parts of the system. In systemsdesigned to have them, these information-carryingstates may arise without their normal cause (aswhen a frog is subjected to a laboratory with bul-lets on a string moving in front of its eyes). In thesesituations the system responds as it would if thestate were generated by the cause for which theresponse was designed or selected. Such internalstates satisfy a common understanding of what arepresentation is, and the ability to understand whythe system works successfully appeals to theserepresentations. If this construal is correct, thendynamical systems theory as well is not an alterna-tive to connectionist modeling, but should be con-strued as an extension of the connectionist toolkit(Bechtel and Abrahamsen, 2002).

Connectionism and Neuroscience

Connectionist models are often described as beingneurally inspired, as the term ‘‘artificial neuralnetworks’’ implies. More strongly, many connec-tionists have claimed that their models enjoy aspecial sort of neural plausibility. If there is a signif-icant similarity between the processing in ANNsand the activity in real networks of neurons, thismight support connectionism for two reasons.First, since the cognitive description of the systemclosely resembles the neurobiological description, itseems that connectionist models in psychologyhave a more obvious account about how the mindmight supervene on the brain than do symbolicmodels (see Supervenience). Second, connectionistmodels might provide a fairly direct characteriza-tion of the functioning of the neural level itself(e.g., the particular causal interactions among neu-rons). This functioning is not easily revealed bymany standard neuroscience methods. For exam-ple, localization of mental activity via functional

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magnetic resonance imaging can indicate whichbrain regions are preferentially activated duringcertain tasks, but this alone does not give informa-tion about the specific computations being carriedout within those regions. Connectionist modelingof brain function thus might supplement otherneurobiological techniques.This strategy can be illustrated within the domain

of learning andmemory.Neuropsychological studiessuggest that the destruction of structures in the medi-al temporal lobes of the brain, especially the hippo-campus, results in a characteristic pattern ofmemorydeficits. These include (i) profound anterograde am-nesia for information presented in declarative or ver-bal form, such as arbitrary paired associates, as wellas memory for particular experienced events moregenerally (episodic memory); (ii) preserved implicitmemory for new information, such as gradually ac-quired perceptual-motor skills; and (iii) retrogradeamnesia for recently acquired information, with rel-ative preservation of memories farther back in time.This triad of deficits was famously manifested byH.M., a patient who underwent bilateral removal ofsections of his medial temporal lobes in the early1950s in order to cure intractable epilepsy. SinceH.M., this pattern of deficits has been confirmed inother human and animal studies.McClelland, McNaughton, and O’Reilly (1995)

offer an explanation of these deficits based on conne-ctionist principles. One feature of backpropagation-trained networks is that once they are trained onone mapping, they cannot learn another mappingwithout ‘‘unlearning’’ the previously stored knowl-edge. This phenomenon is known as catastrophicinterference. However, catastrophic interfence canbe overcome if, rather than fully training a networkon one mapping, then training it on another, thetraining sets are interleaved so that the network isexposed to both mappings in alternation. Whenthe training environment is manipulated in thisway, the network can learn both mappings withoutoverwriting either one.As a model of all learning and memory, this

technique suffers from being slow and reliant on afortunate arrangement of environmental con-tingencies. However, McClelland et al. (1995) sug-gest that learning in the neocortex may becharacterized by just such a process, if there is aneural mechanism that stores, organizes, and pre-sents appropriately interleaved stimuli to it. Theyconjecture that this is the computational functionof the hippocampus. Anatomically, the hippo-campus receives convergent inputs from manysensory centers and has wide-ranging efferent con-nections to the neocortex. The pattern of deficits

resulting from hippocampal lesions could beexplained on the assumption that the hippocampushas a method of temporarily storing associationsamong stimuli without catastrophic interference.Ablation of the hippocampus results in antero-grade amnesia for arbitrary associations and de-clarative information because the neocortex aloneis incapable of learning these without the appro-priately interleaved presentation. Implicit learningis preserved because it does not require rapid inte-gration of many disparate representations into asingle remembered experience; further, it typicallytakes many trials for mastery, as is also the casewith backpropagation learning. Finally, the tem-porally graded retrograde amnesia is explained bythe elimination of memory traces that are tem-porarily stored in the hippocampus itself. Oldermemories have already been integrated into theneocortex, and hence are preserved.

McClelland et al. (1995) did not model the hip-pocampus directly; rather, they implemented it as ablack box that trained the neocortical networkaccording to the interleaving regimen. Othershave since presented more elaborate models.Murre, Graham, and Hodges (2001) have imple-mented a system called TraceLink that features anetwork corresponding to a simplified single-layerhippocampus, the neocortex, and a network ofneuromodulatory systems (intended to correspondto the basal forebrain nuclei). TraceLink accountsfor the data reviewed by McClelland et al. (1995),and also predicts several phenomena associatedwith semantic dementia. Other models incor-porating a more elaborate multilayer hippocampalnetwork have been presented by Rolls and Treves(1998) and O’Reilly and Rudy (2001). These mod-els collectively support the general framework setout by McClelland et al. (1995) concerning thecomputational division of labor between the hippo-campus and the neocortex in learning and memory.

These studies of complementary learning systemssuggest a useful role for network-based modeling inneuroscience. However, this role is presently limit-ed in several crucial respects. The models currentlybeing offered are highly impoverished comparedwith the actual complexity of the relevant neuro-biological structures. Assuming that these net-works are intended to capture neuron-levelinteractions, they are several orders of magnitudeshort of the number of neurons and connections inthe brain. Further, the backpropagation rule itselfis biologically implausible if interpreted at the neu-ronal level, since it allows individual weights totake on either positive or negative values, whileactual axonal connections are either excitatory or

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inhibitory, but never both. There is no networkmodel that captures all of the known causal prop-erties of neurons, even when the presence of glialcells, endocrine regulators of neural function, andother factors are abstracted away.

A common response to these objections is tointerpret networks as describing only select pat-terns of causal activity among large populationsof neurons. In many cases, this interpretation isappropriate. However, there are many kinds ofnetwork models in neuroscience, and they can beinterpreted as applying to many different levels oforganization within the nervous system, includingindividual synaptic junctions on dendrites, particu-lar neurons within cortical columns, and interac-tions at the level of whole neural systems. No singleinterpretation appears to have any special priorityover the others. The specific details of the networkarchitecture are dictated in most cases by the par-ticular level of neural analysis being pursued, andtheorists investigate multiple levels simultaneously.There are likely to be at least as many distinct kindsof possible connectionist models in neuroscience asthere are distinct levels of generalization within thenervous system.

Conclusions

At the beginning of this article, the question wasasked whether connectionism is best thought of asa research program, a modeling tool, or somethingin between. Considering the many uses to whichnetworks have been put, and the many disciplinesthat have been involved in cataloguing their proper-ties, it seems unlikely that there will be any commonunity of methods, heuristics, principles, etc., amongthem. Ask whether a neuroscientist using networksto model the development of receptive fields in thesomatosensory systemwould have anything in com-mon with a programmer training a network to takecustomers’ airline reservations. Each of these mightbe a neural network theorist, despite having nothingsignificant in common besides the formal apparatusthey employ. Across disciplines, then, connection-ism lacks the characteristic unity one would expectfrom a research program.

The question may be asked again at the level ofeach individual discipline. This article has not sur-veyed every field in which networks have played asignificant role but has focused on their uses inartificial intelligence, psychology, and neurosci-ence. Even within these fields, the characteristicunity of a research program is also largely absent,if one takes into account the diverse uses that aremade of networks.

In psychology, for instance, there are some con-nectionists who conceive of their models asproviding a theory of how mental structures mightfunctionally resemble, and therefore plausibly su-pervene in, the organization of large-scale neuronalstructures (see Psychology). However, there are justas many theorists who see their work as being only,in some quite loose sense, neurally inspired. Theorganization of the NETtalk network is not partic-ularly neurally plausible, since it posits a simplethree-layered linear causal process leading fromthe perception of letters to the utterance of pho-nemes. Being a connectionist in psychology doesnot appear to require agreement on the purpose ofthe models used or the possible data (e.g., neurobi-ological) that might confirm or disconfirm them.This is what one might expect of a tool rather than aresearch program.It is perhaps ironic that this state of affairs was

predicted by Rumelhart, one of the theorists whorevitalized connectionism during the 1980s. In a1993 interview, Rumelhart claimed that as networksbecomemore widely used in a number of disciplines,‘‘there will be less and less of a core remaining forneural networks per se andmore of, ‘Here’s a persondoing good work in [her] field, and [she’s] usingneural networks as a tool’ ’’ (Anderson and Rosen-feld 1998, 290). Within the fields, in turn, networkmodeling will ‘‘[d]isappear as an identifiable sepa-rate thing’’ and become ‘‘part of doing science ordoing engineering’’ (291). Such a disappearance,however, may not be harmful. Connectionist net-works, like other tools for scientific inquiry, are tobe evaluated by the quality of the results they pro-duce. In this respect, they have clearly proven them-selves a worthy, and sometimes indispensible,component of research in an impressive variety ofdisciplines.

DAN WIESKOPF AND WILLIAM BECHTEL

References

Anderson, James A. (1995), An Introduction to Neural Net-works. Cambridge, MA: MIT Press.

Anderson, James A., and Edward Rosenfeld (eds.) (1988),Neurocomputing: Foundations of Research, vol. 1. Cam-bridge, MA: MIT Press.

——— (1998), Talking Nets: An Oral History of NeuralNetworks. Cambridge, MA: MIT Press.

Anderson, James A., Andras Pellionisz, and EdwardRosenfeld (eds.) (1990), Neurocomputing: Directions forResearch, vol. 2. Cambridge, MA: MIT Press.

Bechtel, William, and Adele Abrahamsen (2002), Connec-tionism and the Mind: Parallel Processing, Dynamics, andEvolution in Networks. Oxford: Basil Blackwell.

Busemeyer, Jerome R., and James T. Townsend (1993),‘‘Decision Field Theory: A Dynamic-Cognitive

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Approach to Decision Making in an Uncertain Environ-ment,’’ Psychological Review 100: 423– 459.

Cummins, Robert (1996), ‘‘Systematicity,’’ Journal of Phi-losophy 93: 591–614.

Elman, Jeffrey L. (1991), ‘‘Distributed Representations,Simple Recurrent Networks, and Grammatical Struc-ture,’’ Machine Learning 7: 195–225.

Fodor, Jerry A., and Zenon Pylyshyn (1988), ‘‘Connection-ism and Cognitive Architecture: A Critical Analysis,’’Cognition 28: 3–71.

Franklin, Stan, and Max Garzon (1990), ‘‘Neural Comput-ability,’’ in O. M. Omidvar (ed.), Progress in NeuralNetworks, vol. 1. Norwood, NJ: Ablex, 127–145.

McClelland, James L., Bruce L. McNaughton, and RandallC. O’Reilly (1995), ‘‘Why There Are ComplementaryLearning Systems in the Hippocampus and Neocortex:Insights from the Successes and Failures of Connection-ist Models of Learning and Memory,’’ PsychologicalReview 102: 419– 457.

McClelland, James L., David E. Rumelhart, and the PDPResearch Group (1986), Parallel Distributed Processing:Explorations in the Microstructure of Cognition, vol. 2.Cambridge, MA: MIT Press.

Murre, Jacob, Kim S. Graham, and John R. Hodges (2001),‘‘Semantic Dementia: Relevance to Connectionist Mod-els of Long-Term Memory,’’ Brain 124: 647–675.

O’Reilly, Randall C., and J. W. Rudy (2001), ‘‘ConjunctiveRepresentations in Learning and Memory: Principles ofCortical and Hippocampal Function,’’ Psychological Re-view 108: 311–345.

Page, M. (2000), ‘‘Connectionist Modeling in Psychology:A Localist Manifesto,’’ Behavioral and Brain Sciences 23:443–512.

Pollack, Jordan B (1990), ‘‘Recursive Distributed Represen-tations,’’ Artificial Intelligence 46: 77–105.

Rolls, Edmund T., and Alessandro Treves (1998), NeuralNetworks and Brain Function. Oxford: Oxford UniversityPress.

Rumelhart, David E., James L. McClelland, and the PDPResearch Group (1986), Parallel Distributed Processing:Explorations in the Microstructure of Cognition, vol. 1.Cambridge, MA: MIT Press.

Smolensky, Paul (1988), ‘‘On the Proper Treatment ofConnectionism,’’ Behavioral and Brain Sciences 11: 1–74.

——— (1991), ‘‘Connectionism, Constituency, and theLanguage of Thought,’’ in Barry Loewer and GeorgesRey (eds.), Meaning in Mind: Fodor and His Critics.Oxford: Basil Blackwell.

van Gelder, Timothy (1990), ‘‘Compositionality: A Connec-tionist Variation on a Classical Theme,’’ Cognitive Sci-ence 14: 355–384.

——— (1995), ‘‘What Might Cognition Be, If Not Compu-tation?’’ Journal of Philosophy 111: 345–381.

van Leeuwen, Cees, S. Verver, and M. Brinkers (2000), ‘‘Vi-sual Illusions, Solid/Outline Invariance andNon-Station-ary Activity Patterns,’’ Connection Science 12: 279–297.

See also Artificial Intelligence; Cognitive Science;Neurobiology; Psychology, Philosophy of; Superve-nience

CONSCIOUSNESS

Consciousness is extremely familiar, yet it is at thelimits—beyond the limits, some would say—ofwhat one can sensibly talk about or explain. Per-haps this is the reason its study has drawn contri-butions from many fields, including psychology,neuroscience, philosophy, anthropology, culturaland literary theory, artificial intelligence, physics,and others. The focus of this article is on the vari-eties of consciousness, different problems that havebeen raised about these varieties, and prospects forprogress on these problems.

Varieties of Consciousness

Creature vs. State ConsciousnessOne attributes consciousness both to people

and to their psychological states. An agent can beconscious (as opposed to unconscious), and that

agent’s desire for a certain emotional satisfactionmight be unconscious (as opposed to conscious).Rosenthal (1992) calls the former creatureconsciousness and the latter state consciousness.Most, but not all, discussion of consciousness inthe contemporary literature concerns state con-sciousness rather than creature consciousness.Rosenthal (1992) goes on to propose an explana-tion of state consciousness in terms of creatureconsciousness, according to which a state is con-scious just in case an agent who is in the stateis conscious of it—but this proposal has provedcontroversial (e.g., Dretske 1993).

Essential vs. Nonessential ConsciousnessFocusing on conscious states, one may distin-

guish those that are essentially conscious from

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those that are (or might be) conscious but notessentially so. The distinction is no doubt vague,but, to a first approximation, a state is essentiallyconscious just in case being in the state entails thatit is conscious, and is not essentially conscious justin case this is not so.

Sensations are good candidates for states thatare essentially conscious. If an agent is in pain,this state would seem to be conscious. (This is notto deny that the agent might fail to attend to it.)Beliefs, knowledge, and other cognitive states aregood candidates for states that might be consciousbut not essentially so. One may truly say that anagent knows the rules of his language even thoughthis knowledge is unconscious. Perception presentsa hard case, as is demonstrated by the phenomenonof blindsight, in which subjects report that they donot see anything in portions of the visual field andyet their performance on forced-choice tasks sug-gests otherwise (Weiskrantz 1986). Clearly someinformation processing is going on in such cases,but it is not obvious that what is going on is properlydescribed as perception, or at least as perceptualexperience. It is plausible to suppose that indecisionabout how to describe matters here derives in partfrom indecision about whether perceptual states orexperiences are essentially conscious.

Transitive vs. Intransitive ConsciousnessIn the case of creature consciousness, one may

speak of someone’s being conscious simpliciter andof someone’s being conscious of something or other.Malcolm calls the first ‘‘intransitive’’ and the second‘‘transitive’’ consciousness (e.g., Armstrong andMalcolm 1984). To say that a person is conscioussimpliciter is a way of saying that the person isawake or alert. So the study of creature intransitiveconsciousness may be assimilated to the study ofwhat it is to be alert. The denial of consciousnesssimpliciter does not entail a denial of psychologicalstates altogether. If an agent is fast asleep on acouch, one may truly say both that the agent isunconscious and that the agent believes that snowis white. Humphrey (1992) speculates that thenotion of intransitive consciousness is a recentone, perhaps about two hundred years old, butpresumably people were on occasion intransitivelyconscious (i.e., alert or awake) prior to that date.

To say that a person is conscious of somethingseems to be a way of saying that the person knowsor has beliefs about that thing. To say that one isconscious of a noise overhead is to say that oneknows there is a noise overhead, though perhapswith the accompanying implication that one knows

this only vaguely. So the study of creature trans-itive consciousness may be assimilated to the studyof knowledge or beliefs. It is sometimes suggestedthat ‘‘consciousness’’ and ‘‘awareness’’ are syno-nyms. This is true only on the assumption thatwhat is intended is creature transitive conscious-ness, since awareness is always by someone ofsomething.

Intentional vs. Nonintentional ConsciousnessWhile the transitive/intransitive distinction has

no obvious analogue in the case of state conscious-ness—a state is not itself awake or alert, nor is itaware of anything—a related distinction is thatbetween intentional and nonintentional consciousstates. An intentional conscious state is of some-thing in the sense that it represents the world asbeing a certain way—such states exhibit ‘‘inten-tionality,’’ to adopt the traditional word. A non-intentional conscious state is a state that does notrepresent the world as being in some way. It issometimes suggested that bodily sensations (itches,pains) are states of this second kind, while percep-tual experiences (seeing a blue square on a redbackground) are cases of the first. But the matteris controversial given that to have a pain in one’sfoot seems to involve among other things re-presenting one’s foot as being in some conditionor other, a fact that suggests that even here thereis an intentional element in consciousness (seeIntentionality).

Phenomenal vs. Access ConsciousnessBlock (1995) distinguishes two kinds of state

consciousness: phenomenal consciousness and ac-cess consciousness. The notion of a phenomenallyconscious state is usually phrased in terms of‘‘What is it like . . . ?’’ (e.g., Nagel 1974, ‘‘What isit like to be a bat?’’). For a state to be phenome-nally conscious is for there to be something it isakin to being, in that state. In the philosophicalliterature, the terms ‘‘qualia,’’ ‘‘phenomenal char-acter,’’ and ‘‘experience’’ are all used as rough syn-onyms for phenomenal consciousness in this sense,though unfortunately there is no terminologicalconsensus here.For a state to be access conscious is, roughly, for

the state to control rationally, or be poised tocontrol rationally, thought and behavior. For crea-tures who have language, access consciousnessclosely correlates with reportability, the ability toexpress the state at will in language. Block suggests,among other things, that a state can be phenome-nally conscious without its being access conscious.

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For example, suppose one is engaged in intenseconversation and becomes aware only at noonthat there is a jackhammer operating outside—atfive to twelve, one’s hearing the noise is phenome-nally conscious, but it is not access conscious.Block argues that many discussions both inthe sciences and in philosophy putatively aboutphenomenal consciousness are in fact about accessconsciousness. Block’s distinction is related to onemade by Armstrong (1980) between experience andconsciousness. For Armstrong, consciousness is at-tentional: A state is conscious just in case oneattends to it. However, since one can have an expe-rience without attending to it, it is possible todivorce experience and consciousness in this sense.Within the general concept of access consci-

ousness, a number of different strands may bedistinguished. For example, an (epistemologically)normative interpretation of the notion needs to beseparated from a nonnormative one. In the formercase, the mere fact that one is in an access-consciousstate puts one in a position to know or justifiablybelieve that one is; in the latter, being in an access-conscious state prompts one to think or believe thatone is—here there is no issue of epistemic appraisal(see Epistemology). Further, an actualist interpre-tation of the notion needs to be separated from acounterfactual one. In the former case, what isat issue is whether one does know or think thatone is in the state; in the latter, what is at issue iswhether one would, provided other cognitive con-ditions were met. Distinguishing these variousnotions leads naturally into other issues. For exam-ple, consider the claim that it is essentially true ofall psychological states that if one is in them, onewould know that one is, provided one reflects andhas the relevant concepts. That is one way ofspelling out the Cartesian idea (recently defendedby Searle [1992]) that the mind is ‘‘transparent’’ toitself.There are hints both in Block (1995) and in

related discussion (e.g., Davies and Humphreys1993) that the phenomenal/access distinction is in(perhaps rough) alignment with both the intention-al/nonintentional and the essential/nonessentialdistinction. The general idea is that phenomenallyconscious states are both essentially so and nonin-tentional, while access-conscious states are neither.In view of the different interpretations of accessconsciousness, however, it is not clear that this isso. Psychological states might well be both essen-tially access conscious and phenomenally con-scious. And, as indicated earlier, perhaps allconscious states exhibit intentionality in someform or other.

Self-consciousnessTurning back from state consciousness to crea-

ture consciousness, a notion of importance here isself-consciousness, i.e., one’s being conscious ofoneself as an agent or self or (in some cases) aperson. If to speak of a creature’s being ‘conscious’of something is to speak about knowledge orbeliefs, to attribute self-consciousness is to attri-bute to a creature knowledge or beliefs that thecreature is a self or an agent. This would presum-ably require significant psychological complexityand perhaps cultural specificity. Proposals likethose of Jaynes (1976) and Dennett (1992)—thatconsciousness is a phenomenon that emerges onlyin various societies—are best interpreted as con-cerning self-consciousness in this sense, whichbecomes more natural the more one complicatesthe underlying notion of self or agent. (Parallelremarks apply to any notion of group conscious-ness, assuming such a notion could be made clear.)

Problems of Consciousness

If these are the varieties of consciousness, it is easyenough to say in general terms what the pro-blems of consciousness are, i.e., to explain or un-derstand consciousness in all its varieties. Butdemands for explanation mean different things todifferent people, so the matter requires furtherexamination.

To start with, one might approach the issue froman unabashedly scientific point of view. Conscious-ness is a variegated phenomenon that is a pervasivefeature of the mental lives of humans and othercreatures. It is desirable to have an explanation ofthis phenomenon, just as it is desirable to have anexplanation of the formation of the moon, or theorigin of HIV/AIDS. Questions that might beraised in this connection, and indeed have beenraised, concern the relation of consciousness toneural structures (e.g., Crick and Koch 1998), theevolution of consciousness (e.g., Humphrey 1992),the relation of consciousness to other psychologicalcapacities (e.g., McDermott 2001), the relation ofconsciousness to the physical and social environ-ment of conscious organisms (e.g., Barlow 1987),and relations of unity and difference among con-scious states themselves (e.g., Bayne and Chalmers2003).

The attitude implicit in this approach—that con-sciousness might be studied like other empiricalphenomena—is attractive, but there are at leastfour facts that need to be confronted before it canbe completely adopted:

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1. No framework of ideas has as yet beenworked out within which the study of con-sciousness can proceed. Of course, this doesnot exclude the possibility that such a frame-work might be developed in the future, but itdoes make the specific proposals (such as thatof Crick and Koch 1998) difficult to evaluate.

2. In the past, one of the main research tasks inpsychology and related fields was to studypsychological processes that were not con-scious. This approach yielded a number offruitful lines of inquiry—e.g., Chomsky’s(1966) idea that linguistic knowledge is to beexplained by the fact that people haveunconscious knowledge of the rules of theirlanguage—but will presumably have to beabandoned when it comes to consciousnessitself.

3. As Block (1995) notes, the standard conceptof consciousness seems to combine a numberof different concepts, which in turn raises thethreat that consciousness in one sense will beconfused with consciousness in another.

4. The issue of consciousness is often thought toraise questions of a philosophical nature, andthis prompts further questions about whethera purely scientific approach is appropriate.

What are the philosophical aspects of the issue ofconsciousness? In the history of the subject, theissue of consciousness is usually discussed in thecontext of another, the traditional mind–bodyproblem. This problem assumes a distinction be-tween two views of human beings: the materialistor physicalist view, according to which humanbeings are completely physical objects; and thedualist view, according to which human beingsare a complex of both irreducibly physical andirreducibly mental features. Consciousness, then,emerges as a central test case that decides theissue. The reason is that there are a number ofthought experiments that apparently make it plau-sible to suppose that consciousness is distinct fromanything physical. An example is the inverted spec-trum hypothesis, in which it is imagined that twopeople might be identical except for the fact thatthe sensation provoked in one when looking atblood is precisely the sensation provoked in theother when looking at grass (Shoemaker 1981). Ifthis hypothesis represents a genuine possibility, it isa very short step to the falsity of physicalism,which, setting aside some complications, entailsthat if any two people are identical physically, theyare identical psychologically. On the other hand, ifthe inverted spectrum is possible, then two people

identical physically may yet differ in respect ofcertain aspects of their conscious experience, andso differ psychologically. In short, physicalists arerequired to argue that the inverted spectrum hy-pothesis does not represent a genuine possibility.And this places the issue of consciousness at theheart of the mind–body problem.In contemporary philosophy of mind, the tradi-

tional mind–body problem has been severely criti-cized. First, most contemporary philosophers donot regard the falsity of physicalism as a live option(Chalmers [1996] is an exception), so it seems absurdto debate something one already assumes to be true.Second, some writers argue that the very notionswithin which the traditional mind–body problem isformed aremisguided (Chomsky 2000). Third, thereare serious questions about the legitimacy ofsupposing that reflection of possible cases such asthe inverted spectrum could even in principle decidethe question of dualism or materialism, which areapparently empirical, contingent claims about thenature of the world (Jackson 1998).As a result of this critique, many philosophers

reject the mind–body problem in its traditionalguise. However, it is mistaken to infer from thisthat concern with the inverted spectrum and relatedideas has likewise been rejected. Instead, the theo-retical setting of these arguments has changed. Forexample, in contemporary philosophy, the invertedspectrum often plays a role not so much in thequestion of whether physicalism is true, but ratherin questions about whether phenomenal conscious-ness is in principle irreducible or else lies beyondthe limits of rational inquiry. The impact of philo-sophical issues of this kind on a possible science ofconsciousness is therefore straightforward.In the philosophical debates just alluded to, the

notion of consciousness at issue is phenomenalconsciousness. In other areas of philosophy, othernotions are more prominent. In epistemology,for example, an important question concerns theintuitive difference between knowledge of one’sown mental states—which seems in a certain senseprivileged or direct—and knowledge of the externalworld, including the minds of others. This questionhas been made more acute by the impact of exter-nalism, the thesis that one’s psychological statesdepend constitutively on matters external to thesubject, factors for which direct knowledge is notplausible (Davies 1997). Presumably these issueswill be informed by the study of access conscious-ness. Similarly, in discussions of the notion of per-sonal identity and related questions about how andwhy persons are objects of special moral concern,the notion of self-consciousness plays an important

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role. One might also regard both access consci-ousness and self-consciousness as topics forstraightforward scientific study.

Prospects for Progress

Due to the influence of positivist and postpositivistphilosophy of science in the twentieth century, itwas at one time common to assume that some or allquestions of consciousness were pseudo-questions.Recently it has been more common to concede thatthe questions are real enough. But what are thechances of progress here?In light of the multifariousness of the issues, a

formulaic answer to this question would be inap-propriate. Access consciousness seems to be a mat-ter of information processing, and there is reasonto suppose that such questions might be addressedusing contemporary techniques. Hence, many wri-ters (e.g., Block 1995) find grounds for cautiousoptimism here, though this might be tempereddepending on whether access consciousness is con-strued as involving a normative element. In the caseof self-consciousness, the issue of normativity isalso present, and there is the added complicationthat self-consciousness is partly responsive to ques-tions of social arrangements and their impact onindividual subjects.But it is widely acknowledged that the hardest

part of the issue is phenomenal consciousness. Herethe dominant strategy has been an indirect one ofattempting to reduce the overall number of pro-blems. One way to implement this strategy is toattempt to explain the notion of phenomenal con-sciousness in terms of another notion, say, accessconsciousness or something like it. Some philoso-phers suggest that puzzlement about phenomenalconsciousness is a cognitive illusion, generated by afailure to understand the special nature of conceptsof phenomenal consciousness, and that once thispuzzlement is dispelled, the way will be clear for astraightforward identification of phenomenal andaccess consciousness (e.g., Tye 1999). Others arguethat discussions of phenomenal consciousness ne-glect the extent to which conscious states involveintentionality, and that once this is fully appre-ciated there is no bar to adopting the view thatphenomenal consciousness is just access conscious-ness (e.g., Carruthers 2000).The attractive feature of these ideas is that if

successful, they represent both philosophical andscientific progress. But the persistent difficulty isthat the proposed explanations are unpersua-sive. It is difficult to rid oneself of the feeling thatwhat is special about concepts of phenomenal

consciousness derives from only what it is thatthey are concepts of, and this makes it unlikelythat the puzzles of phenomenal consciousness arean illusion. And, while it is plausible that phenom-enally conscious states are intentional, emphasizingthis fact will not necessarily shed light on the issue,for the intentionality of phenomenal conscious-ness might be just as puzzling as phenomenalconsciousness itself.

However, even if one agrees that phenomenalconsciousness represents a phenomenon distinctfrom these other notions, and therefore requires aseparate approach, there is still a way in which onemight seek to implement the strategy of reducingthe number of problems, for, as noted earlier, phe-nomenal consciousness is thought to present both aphilosophical and a scientific challenge. But what isthe relation between these two issues? It is commonto assume that the philosophical problem needs tobe removed before one can make progress on thescience. But perhaps the reverse is true. If the phil-osophical problems can be seen to be a reflectionpartly of ignorance in the scientific domain, there isno reason to regard them as a further impedimentto scientific study. This might not seem like muchof an advance. But the study of consciousness hasbeen hampered by the feeling that it presents aproblem of a different order from more straightfor-ward empirical problems. In this context, to com-bat that assumption is to move forward, thoughslowly.

DANIEL STOLJAR

References

Armstrong, D. (1980), ‘‘What Is Consciousness?’’ in TheNature of Mind and Other Essays. Ithaca, NY: CornellUniversity Press, 55–67.

Armstrong, D., and N. Malcolm (1984), Consciousness andCausality. Oxford: Blackwell.

Barlow, H. (1987), ‘‘The Biological Role of Consciousness,’’in C. Blakemore and S. Greenfield (eds.), Mindwaves.Oxford: Basil Blackwell.

Bayne, T., and D. Chalmers (2003), ‘‘What Is the Unity ofConsciousness?’’ in A. Cleeremans (ed.), The Unityof Consciousness: Binding, Integration and Dissociation.Oxford: Oxford University Press.

Block, N. (1995), ‘‘On a Confusion About a Functionof Consciousness,’’ Behavioral and Brain Sciences 18:227–247.

Chalmers, D. (1996), The Conscious Mind. New York: Ox-ford University Press.

Chomsky, N. (1966), Aspects of the Theory of Syntax. Cam-bridge, MA: MIT Press.

——— (2000), New Horizons in the Study of Mind andLanguage. Cambridge: Cambridge University Press.

Crick, F., and C. Koch (1990), ‘‘Towards a NeurobiologicalTheory of Consciousness,’’ Seminars in the Neuros-ciences 2: 263–275.

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Carruthers, P. (2000), Phenomenal Consciousness: A Natu-ralistic Theory. Cambridge: Cambridge University Press.

Davies, M. (1997), ‘‘Externalism and Experience,’’ in N.Block, O. Flanagan, and G. Guzeldere (eds.), The Na-ture of Consciousness: Philosophical Debates. Cam-bridge, MA: MIT Press, 309–328.

Davies, M., and G. Humphreys (1993), ‘‘Introduction,’’ inM. Davies and G. Humphreys (eds.), Consciousness:Psychological and Philosophical Essays. Oxford: Black-well.

Dennett , D. (1992), Consciousness Explained. Boston: Lit-tle, Brown and Co.

Dretske, D. (1993), ‘‘Conscious Experience,’’ Mind 102:263–283.

Humphrey, N. (1992), A History of the Mind. New York:Simon and Schuster.

Jackson, J. (1998), From Metaphysics to Ethics. Oxford:Clarendon.

Jaynes, J. (1976), The Origin of Consciousness in the Breakdo-wn of the Bicameral Mind. Boston: HoughtonMifflin Co.

McDermott, D. (2001), Mind and Mechanism. Cambridge,MA: MIT Press.

Nagel, T. (1974), ‘‘What Is It Like to Be a Bat?’’ Philosophi-cal Review 83: 7–22.

Rosenthal, D. (1992), ‘‘A Theory of Consciousness,’’ inN. Block, O. Flanagan, and G. Guzeldere (eds.), TheNature of Consciousness: Philosophical Debates. Cam-bridge, MA: MIT Press, 729–754.

Searle, R. (1992), The Rediscovery of the Mind. Cambridge,MA: MIT Press.

Shoemaker, S. (1981), ‘‘The Inverted Spectrum,’’ Journal ofPhilosophy 74: 357–381.

Tye, M. (1999), ‘‘Phenomenal Consciousness: The Explan-atory Gap as a Cognitive Illusion,’’ Mind 108: 432.

Weiskrantz, L. (1986), Blindsight. Oxford: Oxford Univer-sity Press.

See also Cognitive Science; Connectionism; Inten-tionality; Psychology, Philosophy of

CONSERVATION BIOLOGY

Conservation biology emerged in the mid-1980s asa science devoted to the conservation of biologicaldiversity, or biodiversity. Its emergence was preci-pitated by a widespread concern that anthro-pogenic development, especially deforestation inthe tropics (Gomez-Pompa, Vazquez-Yanes, andGuevera 1972), had created an extinction crisis: asignificant increase in the rate of species extinction(Soule 1985). From its beginning, the primary ob-jective of conservation biology was the design ofconservation area networks (CANs), such as na-tional parks, nature reserves, and managed-usezones that protect areas from anthropogenictransformation.

Conservation biology, then, is a normative disci-pline, in that it is defined in terms of a practicalgoal in addition to the accumulation of knowledgeabout a domain of nature. In this respect, it isanalogous to medicine (Soule 1985). Like medi-cine, conservation biology performs its remedialfunction in two ways: through intervention (forexample, when conservation plans must bedesigned for species at risk of imminent extinction)and through prevention (for example, when plansare designed to prevent decline in species numberslong before extinction is imminent).

The normative status of conservation biologydistinguishes it from ecology, which is not definedin terms of a practical goal (see Ecology). More-over, besides using the models and empirical resultsof ecology, conservation biology also draws uponsuch disparate disciplines as genetics, computerscience, operations research, and economics in de-signing and implementing CANs. Each of thesefields contributes to a comprehensive frameworkthat has recently emerged about the structure ofconservation biology (see ‘‘The Consensus Frame-work’’ below).Different views about the appropriate target of

conservation have generated distinct methodologieswithin conservation biology. How ‘biodiversity’ isdefined and, correspondingly, what conservationplans are designed will partly reflect ethical viewsabout what features of the natural world are valu-able (Norton 1994; Takacs 1996). There exists,therefore, a close connection between conservationbiology and environmental ethics.

The Concept of Biodiversity

‘Biodiversity’ is typically taken to refer to diversityat all levels of biological organization: molecules,


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cells, organisms, species, and communities (e.g.,Meffe and Carroll 1994). This definition does not,however, provide insight into the fundamental goalof conservation biology, since it refers to allbiological entities (Sarkar and Margules 2002).Even worse, this definition does not exhaust allitems of biological interest that are worth preserv-ing: Endangered biological phenomena, such as themigration of the monarch butterfly, are not includ-ed within this definition (Brower and Malcolm1991). Finally, since even a liberally construed no-tion of biodiversity does not capture the ecosystemprocesses that sustain biological diversity, somehave argued that a more general concept of bio-logical integrity, incorporating both diversity ofentities and the ecological processes that sustainthem, should be recognized as the proper focus ofconservation biology (Angermeier and Karr 1994).In response to these problems, many conserva-

tion biologists have adopted a pluralistic approachto biodiversity concepts (Norton 1994; Sarkar andMargules 2002; see, however, Faith [2003], whoargues that this ready acceptance of pluralismconfuses the [unified] concept of biodiversity withthe plurality of different conservation strategies).Norton (1994), for example, points out that anymeasure of biodiversity presupposes the validityof a specific model of the natural world. The exis-tence of several equally accurate models ensures theabsence of any uniquely correct measure. Thus, heargues, the selection of a biodiversity measureshould be thought of as a normative political deci-sion that reflects specific conservation values andgoals. Sarkar and Margules (2002) argue that theconcept of biodiversity is implicitly defined by thespecific procedure employed to prioritize places forconservation action (see ‘‘Place Prioritization’’below). Since different contexts warrant differ-ent procedures, biodiversity should similarly beunderstood pluralistically.

Two Perspectives

Throughout the 1980s and early 90s, the disciplinewas loosely characterized by two general ap-proaches, which Caughley (1994) described as the‘‘small-population’’ and ‘‘declining-population’’paradigms of conservation. Motivated significantlyby the legal framework of the Endangered SpeciesAct of 1973 and the National Forest ManagementAct of 1976, the small-population paradigm origi-nated and was widely adopted in the United States(Sarkar 2005). It focused primarily on individualspecies threatened by extinction. By analyzing their

distributions and habitat requirements, conservat-ion biologists thought that ‘‘minimum viable popu-lations’’ could be demonstrated, that is, populationsizes below which purely stochastic processeswould significantly increase the probability of ex-tinction (see ‘‘Viability Analysis’’ below). It quicklybecame clear, however, that this methodology wasinadequate. It required much more data than couldbe feasibly collected for most species (Caughley1994) and, more importantly, failed to considerthe interspecies dynamics essential to most species’survival (Boyce 1992).

Widely followed in Australia, the declining-population paradigm focused on deterministic, rath-er than stochastic, causes of population decline(Sarkar 2005). Unlike the small-population para-digm, its objective was to identify and eradicatethese causes before stochastic effects became signif-icant. Since the primary cause of population declinewas, and continues to be, habitat loss, conservationbiologists, especially in Australia, became princi-pally concerned with protecting the full comple-ment of regional species diversity and requiredhabitat within CANs. With meager monetaryresources for protection, conservation biologistsconcentrated on developing methods that identifiedrepresentative CANs in minimal areas (see ‘‘PlacePrioritization’’ below).

The Consensus Framework

Recently, a growing consensus about the structureof conservation biology has emerged that combinesaspects of the small-population and declining-population paradigms into a framework that em-phasizes the crucial role computer-based placeprioritization algorithms play in conservationplanning (Margules and Pressey 2000; Sarkar2005). The framework’s purpose is to make conser-vation planning more systematic, thereby replacingthe ad hoc reserve design strategies often employedin real-world planning in the past. It focuses onensuring the adequate representation and persis-tence of regional biodiversity within the socioeco-nomic and political constraints inherent in suchplanning.

Place Prioritization

The first CAN design methods, especially withinthe United States, relied almost exclusively on is-land biogeography theory (MacArthur and Wilson1967) (see Ecology). It was cited as the basis forgeometric design principles intended to minimize


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extinction rates in CANs as their ambient regionswere anthropogenically transformed (Diamond1975). Island biogeography theory entails that theparticular species composition of an area is con-stantly changing while, at an equilibrium betweenextinction and immigration, its species richnessremains constant. The intention behind designprinciples inspired by the theory, therefore, was toensure persistence of the maximum number of spe-cies, not the specific species the areas currentlycontained. However, incisive criticism of the theory(Gilbert 1980; Margules, Higgs, and Rafe 1982)convinced many conservation biologists, especiallyin Australia, that representation of the specific spe-cies that areas now contain, rather than the persis-tence of the greatest number of species at somefuture time, should be the first goal of CAN design.Computer-based place prioritization algorithmssupplied a defensible methodology for achievingthe first goal and an alternative to the problematicreliance on island biogeography theory in CANdesign.

Place prioritization involves solving a resourceallocation problem. Conservation funds are usuallysignificantly limited and priority must be given toprotecting some areas over others. The ExpectedSurrogate Set Covering Problem (ESSCP) and theMaximal Expected Surrogate Covering Problem(MESCP) are two prioritization problems typicallyencountered in biodiversity conservation planning(Sarkar 2004). Formally, consider a set of indi-vidual places called cells fcj : j ¼ 1; . . . ; ng; cellareas faj : j ¼ 1; . . . ; ng; biodiversity surrogatesL ¼ fsi : i ¼ 1; . . . ;mg; representation targets, onefor each surrogate fti : i ¼ 1; . . . ;mg; probabilitiesof finding si at cj fpij : i ¼ 1; . . . ;m; j ¼ 1; . . . ; ng;and two indicator variables Xj( j ¼ 1; . . . ; nÞ andYiði ¼ 1; . . . ;mÞ defined as follows:

Xj ¼ 1; if cj 2 G;0; otherwise;

�

Yi ¼1; if

Xcj2G

pij > ti;

0; otherwise:

8<:

ESSCP is the problem:

MinimizeXnj¼1

ajXj such thatXnj¼1

Xjpij � ti f

or 8si 2 L:

Informally, find the set of cells G with the smal-lest area such that every representation target issatisfied. MESCP is the problem:

MaximizeXmi¼1

Yi such thatXnj¼1

Xj ¼ M;

where M is the number of protectable cells. Infor-mally, given the opportunity to protect M cells,find those cells that maximize the number of repre-sentation targets satisfied.The formal precision of these problems allows

them to be solved computationally with heuristicor exact algorithms (Margules and Pressey 2000;Sarkar 2005). Exact algorithms, using mixed integerlinear programming, guarantee optimal solutions:the smallest number of areas satisfying the problemconditions. Since ESSCP andMESCP are NP hard,however, exact algorithms are computationally in-tractable for practical problems with large datasets.Consequently, most research focuses on heuristicalgorithms that are computationally tractable forlargedatasets butdonotguaranteeminimal solutions.The most commonly used heuristic algorithms are

‘‘transparent,’’ so called because the exact criterionby which each solution cell is selected is known.These algorithms select areas for incorporationinto CANs by iteratively applying a hierarchical setof conservation criteria, such as rarity, richness, andcomplementarity. Rarity, for example, requires selec-ting the cell containing the region’smost infrequentlypresent surrogates, which ensures that endemic taxaare represented. The criterion most responsible forthe efficiency of transparent heuristic algorithms iscomplementarity: Select subsequent cells that com-plement those already selected by adding the mostsurrogates not yet represented (Justus and Sarkar2002). In policymaking contexts, transparency facil-itates more perspicuous negotiations about compet-ing land uses, which constitutes an advantage overnontransparent heuristic prioritization proceduressuch as those based on simulated annealing.Methodologically, the problem of place prioriti-

zation refocused theoretical research in conserva-tion biology from general theories to algorithmicprocedures that require geographically explicit data(Sarkar 2004). In contrast to general theories,which abstract from the particularities of individu-al areas, place prioritization algorithms demon-strated that adequate CAN design criticallydepends upon these particularities.

Surrogacy

Since place prioritization requires detailed infor-mation about the precise distribution of a region’sbiota, devising conservation plans for specific areaswould ideally begin with an exhaustive series offield surveys. However, owing to limitations of


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time, money, and expertise, as well as geographicaland sociopolitical boundaries to fieldwork, suchsurveys are usually not feasible in practice. Theselimitations give rise to the problem of discovering a(preferably small) set of biotic or abiotic land attri-butes (such as subsets of species, soil types, vegeta-tion types, etc.) the precise distribution of which isrealistically obtainable and that adequately repre-sents biodiversity as such. This problem is referredto as that of finding surrogates or ‘‘indicators’’ forbiodiversity (Sarkar and Margules 2002).This challenge immediately gives rise to two im-

portant conceptual problems.Given the generality ofthe concept of biodiversity as such, the first problemconcerns the selection of those entities that should betaken to represent concretely biodiversity in a partic-ular planning context. These entities will be referredto as the true surrogate, or objective parameter, as it isthe parameter that one is attempting to estimate inthe field. Clearly, selection of the true surrogate ispartly conventional andwill depend largely on prag-matic and ethical concerns (Sarkar and Margules2002); in most conservation contexts the true surro-gate will typically be species diversity, or a species atrisk. Once a set of true surrogates is chosen, theset of biotic and/or abiotic land attributes that willbe tested for their capacity to represent the truesurrogates adequately must be selected; these areestimator surrogates, or indicator parameters.The second problem concerns the nature of the

relation of representation that should obtain be-tween the estimator and the true surrogate: Whatdoes ‘representation’mean in this context and underwhat conditions can an estimator surrogate be saidto represent adequately a true surrogate? Once thetrue and estimator surrogates are selected and a pre-cise (operational) interpretation of representation isdetermined, the adequacy with which the estimatorsurrogate represents the true surrogate becomes anempirical question. (Landres, Verner, and Thomas[1988] discuss the import of subjecting one’s choice ofestimator surrogate to stringent empirical testing.)Very generally, two different interpretations of

representation have been proposed in the conserva-tion literature. The more stringent interpretation isthat the distribution of estimator surrogates shouldallow one to predict the distribution of true surro-gates (Ferrier andWatson 1997). The satisfaction ofthis condition would consist in the construction of awell-confirmed model from which correlations be-tween a given set of estimator surrogates and a givenset of true surrogates can be derived. Currently suchmodels have met with only limited predictive suc-cess; moreover, since such models can typically beused to predict the distribution of only one surrogate

at a time, they are not computationally feasible forpractical conservation planning, which must deviseCANs to sample a wide range of regional biodiver-sity. Fortunately, the solution to the surrogacyproblem does not in practice require predictionsof true-surrogate distributions.

A less stringent interpretation of representationassumes only that the set of places prioritized onthe basis of the estimator surrogates adequatelycaptures true-surrogate diversity up to some speci-fied target (Sarkar and Margules 2002). The ques-tion of the adequacy of a given estimator surrogatethen becomes the following: If one were to con-struct a CAN that samples the full complement ofestimator-surrogate diversity, to what extent doesthis CAN also sample the full complement of true-surrogate diversity? Several different quantitativemeasurements can be carried out to evaluate thisquestion (Sarkar 2004). At present, whether ade-quate surrogate sets exist for conservation planningremains an open empirical question.

Viability Analysis

Place prioritization and surrogacy analysis helpidentify areas that currently represent biodiversity.This is usually not, however, sufficient for success-ful biodiversity conservation. The problem is thatthe biodiversity these areas contain may be in irre-versible decline and unlikely to persist. Since princi-ples of CANdesign inspired by island biogeographytheory were, by the late 1980s, no longer believed toensure persistence adequately, attention subse-quently turned, especially in the United States, tomodeling the probability of population extinc-tion. These principles became known as populationviability analysis (PVA).

PVA models focus primarily on factors affectingsmall populations, such as inbreeding depression,environmental and demographic stochasticity, ge-netic drift, and spatial structure. Drift andinbreeding depression, for example, may reducethe genetic variation required for substantial evol-vability, without which populations may be moresusceptible to disease, predation, or future environ-mental change. PVA modeling has not, however,provided a clear understanding of the generalimport of drift and inbreeding depression to popu-lation persistence in nature (Boyce 1992). Unfortu-nately, this kind of problem pervades PVA. In atrenchant review, for instance, Caughley (1994) con-cluded that the predominantly theoretical workdone thus far in PVA had not been adequatelytested with field data and that many of the teststhat had been done were seriously flawed.


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Models used for PVA have a variety of differentstructures and assumptions (see Beisinger andMcCullough 2002). As a biodiversity conservationmethodology, however, PVA faces at least threegeneral difficulties:

1. Precise estimation of parameters common toPVA models requires enormous amounts ofquality field data, which are usually unavail-able (Fieberg and Ellner 2000) and cannot becollected, given limited monetary resourcesand the imperative to take conservation actionquickly. Thus, with prior knowledge beinguncommon concerning what mechanisms areprimarily responsible for a population’s dy-namics, PVA provides little guidance abouthow to minimize extinction probability.

2. In general, the results of PVA modeling areextremely sensitive to model structure and pa-rameter values. Models with seemingly slight-ly different structure may make radicallydifferent predictions (Sarkar 2004), and dif-ferent parameter values for one model mayproduce markedly different predictions, aproblem exacerbated by the difficulties dis-cussed under (1).

3. Currently, PVA models have been developedalmost exclusively for single species (occa-sionally two) and rarely consider more thana few factors affecting population decline.Therefore, only in narrow conservation con-texts focused on individual species would theypotentially play an important role. Successfulmodels that consider the numerous factorsaffecting the viability of multiple-species as-semblages, which are and should be the pri-mary target of actual conservation planning,are unlikely to be developed in the near future(Fieberg and Ellner 2000).

For these reasons and others, PVA has not thusfar uncovered nontrivial generalities relevant toCAN design. Consequently, attention has turnedto more pragmatic principles, such as designingCANs to minimize distance to anthropogenicallytransformed areas. This is not to abandon the im-portant goals of PVA or the need for sound theoryabout biodiversity persistence, but to recognizethe weaknesses of existing PVA models and theimperative to act now given significant threats tobiodiversity.

Multiple-Criterion Synchronization

The implementation and maintenance of CANsinevitably take place within a context of competing

demands upon the allocation and use of land. Con-sequently, successful implementation strategiesshould ideally be built upon a wide consensusamong agents with different priorities with respectto that usage. Thus, practical CAN implementationinvolves the attempt to optimize the value of aCAN amongst several different criteria simulta-neously. Because different criteria typically con-flict, however, the term ‘‘synchronization’’ ratherthan ‘‘optimization’’ is more accurate. Themultiple-constraint synchronization problem involves de-veloping and evaluating procedures designed tosupport such decision-making processes.One approach to this task is to ‘‘reduce’’ these

various criteria to a single scale, such as monetarycost. For example, cost-benefit analysis has at-tempted to do this by assessing the amount anagent is willing to pay to improve the conservationvalue of an area. In practice, however, such esti-mates are difficult to carry out and are rarelyattempted (Norton 1987). Another method, basedonmultiple-objective decision-makingmodels, doesnot attempt to reduce the plurality of criteria to asingle scale; rather it seeks merely to eliminate thosefeasible CANs that are suboptimal when evaluatedaccording to all relevant criteria. This method, ofcourse, will typically not result in the determinationof a uniquely best solution, but it may be able toreduce the number of potential CANs to one that issmall enough so that decision-making bodies canbring other implicit criteria to bear on their ultimatedecision (see Rothley 1999 and Sarkar 2004 forapplications to conservation planning).

JUSTIN GARSON AND JAMES JUSTUS

References

Angermeier, P. L., and J. R. Karr (1994), ‘‘Biological Integ-rity versus Biological Diversity as Policy Directives,’’BioScience 44: 690–697.

Beisinger, S. R., and D. R. McCullough (eds.) (2002), Pop-ulation Viability Analysis. Chicago: University of Chi-cago Press.

Boyce, M. (1992), ‘‘Population Viability Analysis,’’ AnnualReview of Ecology and Systematics 23: 481–506.

Brower, L. P., and S. B. Malcolm (1991), ‘‘Animal Migra-tions: Endangered Phenomena,’’ American Zoologist 31:265–276.

Caughley, G. (1994), ‘‘Directions in Conservation Biology,’’Journal of Animal Ecology 63: 215–244.

Diamond, J. (1975), ‘‘The Island Dilemma: Lessons ofModern Biogeographic Studies for the Design of Natu-ral Reserves,’’ Biological Conservation 7: 129–146.

Faith, D. P. (2003), ‘‘Biodiversity,’’ in EdwardN. Zalta (ed.),The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/sum2003/entries/biodiversity

Ferrier, S., and G. Watson (1997), An Evaluation of theEffectiveness of Environmental Surrogates and Modelling


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Techniques in Predicting the Distribution of BiologicalDiversity: Consultancy Report to the Biodiversity Conven-tion and Strategy Section of the Biodiversity Group, Envi-ronment Australia. Arimidale, New South Wales:Environment Australia.

Fieberg, J., and S. P. Ellner (2000), ‘‘When Is It Meaningfulto Estimate an Extinction Probability?’’ Ecology 8:2040–2047.

Gilbert, F. S. (1980), ‘‘The Equilibrium Theory of IslandBiogeography: Fact or Fiction?’’ Journal of Biogeogra-phy 7: 209–235.

Gomez-Pompa, A., C. Vazquez-Yanes, and S. Guevera(1972), ‘‘The Tropical Rain Forest: A NonrenewableResource,’’ Science 177: 762–765.

Justus, J., and S. Sarkar (2002), ‘‘The Principle of Comple-mentarity in the Design of Reserve Networks to Con-serve Biodiversity: A Preliminary History,’’ Journal ofBiosciences 27: 421– 435.

Landres, P. B., J. Verner, and J. W. Thomas (1988), ‘‘Eco-logical Uses of Vertebrate Indicator Species: A Cri-tique,’’ Conservation Biology 2: 316–328.

MacArthur, R., and E. O. Wilson (1967), The Theory ofIsland Biogeography. Princeton, NJ: Princeton Universi-ty Press.

Margules, C. R., and R. L. Pressey (2000), ‘‘SystematicConservation Planning,’’ Nature 405: 242–253.

Margules, C., A. J. Higgs, and R. W. Rafe (1982), ‘‘ModernBiogeographic Theory: Are There Lessons for NatureReserve Design?’’ Biological Conservation 24: 115–128.

Meffe, G. K., and C. R. Carroll (1994), Principles of Con-servation Biology. Sunderland, MA: Sinauer Associates.

Norton, B. G. (1987), Why Preserve Natural Variety? Prin-ceton, NJ: Princeton University Press.

Norton, B. G. (1994), ‘‘OnWhat We Should Save: The Roleof Cultures in Determining Conservation Targets,’’ inP. L. Forey, C. J. Humphries, and R. I. Vane-Wright(eds.), Systematics and Conservation Evaluation. Oxford:Clarendon Press, 23–29.

Rothley, K. D. (1999), ‘‘Designing Bioreserve Networks toSatisfy Multiple, Conflicting Demands,’’ EcologicalApplications 9: 741–750.

Sarkar, S. (2004), ‘‘Conservation Biology,’’ in E. N. Zalta(ed.), The Stanford Encyclopedia of Philosophy. http://stanford.edu/entries/conservation-biology

——— (2005), Biodiversity and Environmental Philosophy.New York: Cambridge University Press.

Sarkar, S., and C. R. Margules (2002), ‘‘OperationalizingBiodiversity for Conservation Planning,’’ Journal ofBiosciences 27: 299–308.

Soule, M. E. (1985), ‘‘What Is Conservation Biology?’’BioScience 35: 727–734.

Takacs, D. (1996), The Idea of Biodiversity: Philosophies ofParadise. Baltimore: Johns Hopkins University Press.

CONSTRUCTIVE EMPIRICISM

See Instrumentalism; Realism

CONVENTIONALISM

Conventionalism is a philosophical position accord-ing to which the truth of certain propositions, suchas those of ethics, aesthetics, physics, mathematics,or logic, is in some sense best explained by appealto intentional human actions, such as linguisticstipulations. In this article, the focus will be onconventionalism concerning physics, mathematics,and logic. Conventionalism concerning empirical

science and mathematics appears to have emergedas a distinctive philosophical position only in thelatter half of the nineteenth century.

The philosophical motivations for conventional-ism are manifold. Early conventionalists such asPierre Duhem and Henri Poincare, and morerecently Adolf Grunbaum, have seen conventional-ism about physical or geometrical principles as


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justified in part by what they regard as the under-determination of a physical or geometrical theory byempirical observation (see Duhem Thesis; Poincare,Henri; Theories, Underdetermination of ). An (em-pirically) arbitrary choice of a system from amongempirically equivalent theories seems required.

A second motivation, also suggested by Duhemand Poincare, and explicitly developed later byRudolf Carnap, stems from their view that anydescription of the empirical world presupposes asuitable descriptive apparatus, such as a geometry,a metric, or a mathematics. In some cases thereappears to be a choice as to which descriptiveapparatus to employ, and this choice involves anarbitrary convention (see Carnap, Rudolf ).

A third motivation for conventionalism, em-phasized by philosophers such as Moritz Schlick,Hans Hahn, and Alfred Ayer, is that appeal toconventions provides a straightforward explana-tion of a priori propositional knowledge, such asknowledge of mathematical truths (see Ayer,Alfred Jules; Hahn, Hans; Schlick, Moritz).Suchtruths, it was thought, are known a priori in virtueof the fact that they are stipulated rather thandiscovered.

It is important to note that conventionalists donot regard the selection of a set of conventions tobe wholly arbitrary, with the exception of the radi-cal French conventionalist Edouard LeRoy, whodid (see Giedymin 1982, 118–28). Conventionalistsacknowledge that pragmatic or instrumental con-siderations involving human capacities or purposesmight be relevant to the adoption of a set of con-ventions (see Instrumentalism). However, they in-sist that the empirical evidence does not compelone choice rather than another.

This article focuses on several major figures andissues, but there are a number of other importantphilosophers with broadly conventionalist leanings,including Pierre Duhem, Kazimierz Ajdukiewicz,and Ludwig Wittgenstein, that for the sake of bre-vity will not here receive the attention they deserve.

Poincare and Geometric Conventionalism

The development of non-Euclidean geometries andsubsequent research into the foundations of geom-etry provided both the inspiration and the modelfor much of the conventionalism of the early twen-tieth century (see Space-Time). The central figurein early conventionalism was the French mathe-matician and philosopher Henri Poincare (seePoincare, Henri). Although a Kantian in his phil-osophy of mathematics, Poincare shared withmany late-nineteenth-century mathematicians and

philosophers the growing conviction that the disco-very of non-Euclidean geometries, such as the geo-metries of Lobatschevsky and Riemann, conjoinedwith other developments in the foundations of ge-ometry, rendered untenable the Kantian treatmentof geometrical axioms as a form of synthetic apriori intuition.The perceived failings of Kant’s analysis of

geometry did not, however, lead Poincare to anempiricist treatment of geometry. If geometrywere an experimental science, he reasoned, itwould be open to continual revision or falsifiedoutright (the perfectly invariable solids of geometryare never empirically discovered, for instance)(Poincare [1905] 1952, 49–50). Rather, geometricalaxioms are conventions. As such, the axioms (pos-tulates) of a systematic geometry constitute implicitdefinitions of such primitive terms of the system as‘‘point’’ and ‘‘line’’ (50). This notion of implicitdefinition originated with J. D. Gergonne (1818),who saw an analogy between a set of sentences withn undefined terms and a set of equations with nunknowns. The two are analogous in that the rootsthat satisfy the equations are akin to interpretationsof the undefined terms in the set of sentences underwhich the sentences are true. Of course, not everyset of equations determines a set of values, and sotoo not every set of sentences (system of axioms)constitutes an implicit definition of its primitiveterms. Poincare accommodated this fact by recog-nizing two constraints on the admissibility of a setof axioms. First, the set must be consistent, andsecond, it must uniquely determine the objectsdefined (1952, 150–3).Although the axioms were in his view conven-

tional, Poincare thought that experience nonethe-less plays a role within geometry. The genesis ofgeometrical systems is closely tied to experience, inthat the systems of geometry that are constructedare selected on the basis both of prior idealizedempirical generalizations and of the simplicity andconvenience that particular systems (such asEuclidean geometry) may afford their users ([1905]1952, 70–1; 1952, 114–5). But these empirical con-siderations do not provide a test of empirically ap-plied geometries. Once elevated to the status of aconvention, a geometrical system is not an empiricaltheory, but is rather akin to a language used, inpart, to frame subsequent empirical assertions. Asa system of implicit definitions, it is senseless tospeak of one geometry being ‘‘more true’’ thananother ([1905] 1952, 50).Poincare therefore rejected the supposition that

an empirical experiment could compel the selectionof one geometry over another, provided that both

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satisfied certain constraints. He was inspired bySophus Lie’s (1959) group-theoretic approach togeometrical transformations, according to which,given an n-dimensional space and the possible trans-formations of figures within it, only a finite group ofgeometries with differing coordinate systems arepossible for that space. Among these geometriesthere is no principled justification for selectingone (such as Plucker line geometry) over another(such as sphere geometry) (Poincare [1905] 1952,46–7). Indeed, one geometry within the groupmay be transformed into another given a certainmethod of translation, which Lie derived fromGergonne’s theory of reciprocity. Poincare con-joined the intertransformability of certain geomet-rical systems with the recognition that alternativegeometries yield different conventions governingthe notions of ‘‘distance’’ or ‘‘congruence’’ toargue that any attempt to decide by experimentbetween alternative geometries would be futile,since interpretations of the data presupposed geo-metric conventions. In a much-discussed passagehe wrote:

If Lobatchevsky’s geometry is true, the parallax of a verydistant star will be finite. If Riemann’s is true, it will benegative. These are the results which seem within thereach of experiment . . . . But what we call a straight linein astronomy is simply the path of a ray of light. If,therefore, we were to discover negative parallaxes, orto prove that all parallaxes are higher than a certainlimit, we should have a choice between two conclu-sions: we could give up Euclidean geometry, or modifythe laws of optics, and suppose that light is not rigorous-ly propagated in a straight line. ([1905] 1952, 72–3)

On one reading, advanced by Grunbaum, this pas-sage affirms that there is no fact of the matter as to whichis the ‘‘correct’’ metric, and hence supports the conven-tionality of spatial metrics. This reading is further dis-cussed below. Another reading of this passage sees in itan argument closely akin to Duhem’s argument leadingto the denial of the possibility of a ‘‘crucial experiment’’that could force the acceptance or elimination of ageometrical theory (see Duhem [1906] 1954, 180–90).Interestingly, Poincare uses the argument to support adistinction between ‘‘conventional’’ truths and empiri-cal truths, whereas Quine later adduces similar Duhe-mian considerations on behalf of his claim that there isno such distinction to be drawn (see Duhem Thesis;Quine, Willard Van Orman).

However he may have intended his parallax ex-ample, Poincare would probably have acceptedboth the conventionality of the spatial metric andthe absence of any experimental test capable ofdeciding between two alternative geometries. As afurther illustration of these issues, he proposeda well-known thought experiment ([1905] 1952,

65–7). Imagine a world consisting of a large spheresubject to the following temperature law: At thecenter of the sphere the temperature is greatest,and at the periphery it is absolute zero. The tem-perature decreases uniformly as one moves towardthe circumference in proportion to the formulaR2 – r2, where R is the radius of the sphere and rthe distance from the center. Assume further thatall bodies in the sphere are in perfect thermal equi-librium with their environment, that all bodiesshare a coefficient of dilation proportional totheir temperature, and that light in this sphere istransmitted through a medium whose index of re-fraction is 1/(R2 – r2). Finally, suppose that thereare inhabitants of this sphere and that they adopt aconvention that allows them to measure lengthswith rigid rods. If the inhabitants assume thatthese rods are invariant in length under transport,and if they further triangulate the positions in theirworld with light rays, they might well come to theconclusion that their world has a Lobatchevskiangeometry. But they could also infer that their worldis Euclidean, by postulating the universal physicalforces just described. Again, no empirical experi-ment seems adequate to establish one geometryover the other, since both are compatible with allknown possible observations given appropriateauxiliary hypotheses. Rather, a conventional choiceof a geometry seems called for. The choice will bemotivated by pragmatic factors, perhaps, but not‘‘imposed’’ by the experimental facts (Poincare[1905] 1952, 70–1).

Grunbaum’s Conventionalism: The Metricand Simultaneity

Poincare’s parallax and sphere-world examplesmotivated his view that the choice of a spatialmetric is conventional. Adolph Grunbaum hasdefended this conventionalist conclusion at length(Grunbaum 1968, 1973). Grunbaum claims thatthere is no unique metric ‘‘intrinsic’’ to a spatialmanifold, since between any two points on a realnumber line, there is an uncountably infinite con-tinuum of points. Hence, if one wishes to specify ametric for a manifold, one must employ ‘‘extrinsic’’devices such as measuring rods, and must furtherstipulate the rods’ behavior under transport.

Grunbaum defends what he takes to bePoincare’s metric conventionalism against a varietyof objections. Perhaps the most serious objection isthe claim that Poincare’s result illustrates only atrivial point about the conventionality of referringexpressions, an objection first directed againstPoincare by Arthur Eddington and subsequently

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developed by Hilary Putnam and Paul Feyerabend.Eddington objected that Poincare’s examples illu-strated not that metrical relations (such as the rela-tions of equality or of the congruence of two rods)were conventional, but rather—and only—that themeanings of words such as ‘‘equal’’ and ‘‘congru-ent’’ were conventional. This, Eddington objected,was a trivial point about semantical conventionali-ty, and the fact that the selection of differentmetrics could yield different but apparently equi-pollent geometries illustrated only that ‘‘the mean-ing assigned to length and distance has to go alongwith the meaning assigned to space’’ (Eddington1953, 9–10). Eddington suggested, and Feyerabendlater developed, a simple illustration of this pointwithin the theory of gases. Upon the discovery thatBoyle’s law:

pv ¼ RT

holds only approximately of real gases, one couldeither revise Boyle’s law in favor of van der Waal’slaw:

ðpþ a=v2Þðv� bÞ ¼ RT

or one could preserve Boyle’s law by redefiningpressure as follows:

Pressure ¼Def ðpþ a=v2Þð1� b=vÞ:ðFeyerabend; quoted in Grnbaum 1973; 34ÞThe possibility of such a redefinition, the objec-

tion proceeds, is physically and philosophicallyuninteresting. Provided that a similar move is avail-able in Poincare’s own examples with expressionslike ‘‘congruent,’’ Poincare’s examples appear toillustrate only platitudes about semantic conven-tionality.

Grunbaum tries to show that Poincare’s con-ventionalism is not merely an example of whatGrunbaum calls ‘‘trivial semantic conventionality’’by showing that the conventionality of the metricis the result of a certain absence of ‘‘intrinsic’’ str-ucture within the space-time manifold, which struc-ture can (or must) then be imposed ‘‘extrinsically’’:

And the metric amorphousness of these continua thenserves to explain that even after the word ‘‘congruent’’has been pre-empted semantically as a spatial or tempo-ral equality predicate by the axioms of congruence,congruence remains ambiguous in the sense that theseaxioms still allow an infinitude of mutually exclusivecongruence classes of intervals.

(Grunbaum 1973, 27)

Grunbaum developed a related argument to theeffect that the simultaneity relation in special

relativity (SR) involves a conventional element. Asympathetic reconstruction of the argument will beattempted here, omitting a number of details inorder to present the gist of the argument as brieflyand intuitively as possible. Within Newtonian me-chanics (NM), there is no finite limit to the speed atwhich causal signals can be sent. Further, onemight take it to be a defining feature of causalrelations that effects cannot precede their causes.This asymmetry allows for a distinction betweenevents that are temporally before or after a givenevent on a world line. There is then only one simul-taneity relation within the space-time of NMmeeting the constraints mentioned. Considerevents (or space-time points, if one prefers) a andb on two distinct parallel world lines. Event a issimultaneous with b just in case a is not causallyconnectible to any event on the future part of b’sworld line but is causally connectible to any eventon the past of b’s world line. Within SR, however,there is an upper limit to the speed of causal sig-nals. Thus the constraint that effects cannot pre-cede their causes allows any one of a continuum ofpoints along a parallel world line to be a candidatefor simultaneity with a given event on the worldline of an inertial observer. Grunbaum calls suchpoints ‘‘topologically simultaneous’’ with a point oon the observer’s world line. In claiming that si-multaneity is (to some extent) conventional withinthe SR picture, Grunbaum is in good company, asEinstein makes a claim to this effect in his original1905 paper. (It is important to distinguish the issueof the conventionality of simultaneity within SR,which has been controversial, from the (observeror frame) relativity of simultaneity within SR,which is unchallenged; see Space-Time.)Grunbaum claims that the existence of a contin-

uum of possible ‘‘planes of simultaneity’’ through agiven point is explained by, or reflects, the fact thatthe simultaneity relation is not ‘‘intrinsic’’ to themanifold of events within special relativity. Oneobjection that a number of Grunbaum’s criticssuch as Putnam (in Putnam 1975b) have had tohis treatment of conventionalism (concerningboth the metric and the simultaneity relation) isthat the notion of an intrinsic feature, which playsa crucial role for Grunbaum, is never adequatelyclarified. David Malament (1977) provides a natu-ral reading of ‘intrinsic’: An intrinsic property orrelation of a system is ‘‘definable’’ in terms of a setof basic features. The intuitive idea is that if arelation is definable from relations that are uncon-troversially intrinsic, then these ought to count asintrinsic as well. Malament goes on to show thatif one takes certain fairly minimal relations to

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be given as intrinsic, then a unique simultaneityrelation, in fact the standard one, is definablefrom them in a fairly well defined sense of ‘defin-able. ’Malament’s result has been taken by many to

have definitively settled the issue of whether simul-taneity is conventional within SR (see e.g., Norton1992). In this view, the standard simultaneity rela-tion is nonconventional, since it is definable, or‘‘logically constructible,’’ from uncontroversiallyintrinsic features of Minkowski space-time, thespace-time of SR. Furthermore, standard simulta-neity is the only such nonconventional simultaneityrelation.However, there are dissenters, including

Grunbaum. A number of authors have attackedone or another of Malament’s premises, includingfor instance the claim that simultaneity must be atransitive relation, that is, the requirement that forarbitrary events x, y, and z, if x sim y and y sim z,then x sim z. Sarkar and Stachel have shown thateven if it is allowed that simultaneity must be anequivalence relation, other simultaneity relations(the backward and the forward light cones ofevents on the given world line) are definable fromrelations that Malament takes as basic or intrinsic(see Sarkar and Stachel 1999). Peter Spirtes (1981)shows that Malament’s result is highly sensitive tothe choice of basic or intrinsic relations, which factmight be taken to undercut the significance ofMalament’s result as well.A conventionalist might raise a different sort of

objection to Malament’s results, questioning theirrelevance to a reasonable, although perhaps not theonly reasonable, construal of the question as towhether simultaneity is conventional within SR.Suppose for simplicity that any relation that oneis willing to call a simultaneity relation is an equiv-alence relation, that causes must always precedetheir effects, and that there is an upper bound tothe speed of causal influences within SR. One maynow ask whether more than one relation can bedefined (extrinsically or otherwise) on the manifoldof events (or ‘‘space-time points’’), meeting thesecriteria within SR. That is, one might ask whether,given any model M of T (roughly, Minkowskispace-time, the ‘‘standard’’ space-time of SR),there is a unique expansion of the model to amodel M0 for T 0, where T 0 adds to T sentencescontaining a symbol ‘sim’, which sentences in effectrequire that ‘sim’ be an equivalence relation andthat causes are not ‘sim’ with their effects. It is astraightforward matter to see, as Grunbaum shows(the details are omitted here), that there is no suchunique expansion ofM. The constraints mentioned

leave room for infinitely many possible inter-pretations of ‘sim’. In this sense, the simultaneityrelation (interpretation of ‘sim’) might naturally besaid to be conventional within SR. In contrast,given a model for the causal structure of NM, themeaning constraints on the concept of simultaneitythat are assumed here yield a unique expansion (aunique extension for ‘sim’).

It should be noted that the conventionality ofsimultaneity within SR and its nonconventionalitywithin NM in the sense just described reflect struc-tural differences between the two theories (or theirstandard models). Thus this form of conventional-ism appears to escape the charge that the only sensein which simultaneity is conventional is the trivialsense in which the word ‘‘simultaneous’’ can beused to denote different relations. As Grunbaumfrequently emphasizes, the interesting cases of con-ventionality arise only when one begins with analready meaningful term or concept, whose mean-ing is constrained in some nontrivial way. It alsoallows one to interpret Einstein as making a sub-stantive, yet fairly obvious point when he claimsthat the standard simultaneity relation within SR isa conventional, or stipulated, choice.

How does this version of conventionalism re-late to Malament’s arguments? It will be helpfulto note a puzzle before proceeding. Wesley Salmon(1977) argues at length that the one-way speed oflight is not empirically identifiable within SR. (Thebasic problem is that the one-way speed seemsmeasurable only by using distant synchronizedclocks, but the synchronization of distant clockswould appear to involve light signals and presup-positions about their one-way speeds.) This factappears to yield as an immediate consequence theconventionality (in the sense of empirical admissi-bility described above) of simultaneity within SR,given the various apparently admissible ways ofsynchronizing distant clocks within a referenceframe. The puzzle is this: On one hand, the stan-dard view has it that Malament’s result effectivelyproves the falsehood of conventionalism (aboutsimultaneity within SR); on the other hand,Salmon’s arguments appear to entail the truth ofconventionalism. Yet, his arguments for the empir-ical inaccessibility of the one-way speed of lightseem sound. No one has convincingly shown whatis wrong with them. All that the nonconventionalistseems able to provide is the indirect argument thatMalament is right, so Salmon (and Grunbaum)must be wrong.

In the present analysis, this puzzle is dissolved bydistinguishing two proposals, each of which mayjustifiably be called versions of conventionalism.

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One version claims that a relation (thought of as aset or extension) is conventional within a modelfor a theory if it is not intrinsic within M, where‘intrinsic’ might then be interpreted as definability(in the sense of logical constructibility) from un-controversially intrinsic relations within M. Theother version claims that the extension of a conceptis conventional within a model (or theory) if themeaning of the concept does not entail a uniqueextension for the concept within the model (orwithin all models of the theory). Call these ver-sions of conventionalism C1 and C2, respectively.Malament shows that simultaneity is notC1 conven-tional within SR (leaving aside other possibleobjections to his result). Grunbaum and Salmonshow that simultaneity is C2 conventional withinSR. Malament further considers relations definablefrom the causal connectibility relation (togetherwith the world line of an inertial observer) withinSR, and notes that only one is a nontrivial candi-date simultaneity relation (relative to the corre-sponding inertial frame). He shows there is onlyone, and that therefore there is a unique intrinsic(and hence non–C1 conventional) simultaneity re-lation within SR, the standard one. The C2 conven-tionalist may respond that although Malament haspointed out an interesting feature of a particularcandidate interpretation of the already meaningfulterm ‘‘simultaneous,’’ he has not thereby ruled outall other candidate interpretations. One should not,the C2 defender will argue, confuse the metalinguis-tic notion ‘definable within M (or T )’ with a mean-ing constraint on our concept of simultaneity, i.e., aconstraint on potential interpretations of our al-ready meaningful term ‘‘simultaneous.’’ It wouldbe absurd to claim that what was meant all alongby ‘simultaneous’ required not only that any can-didate be an equivalence relation and that it must‘‘fit with’’ causal relations in that effects may notprecede their causes, but also that for any twoevents, they are simultaneous if and only if theyare in a relation that is definable from the causalconnectibility relation.

A possible interpretation of the debate con-cerning the conventionality of simultaneity withinSR, on the present construal, is that Grunbaum,perhaps in order to avoid the charge of simplyrediscovering a form of trivial semantic conven-tionality, appealed to his notion of an intrinsicrelation. Failure to express or denote an intrinsicfeature was then said to characterize the interesting(nontrivial) cases of conventionality. This notionled to a number of difficulties for Grunbaum, cul-minating in Malament’s apparent refutation ofthe conventionality of simultaneity within SR.

However, it has been argued above that theappeal to intrinsicness turns out to be unnecessaryin order to preserve a nontrivial form of conven-tionalism, C2.Grunbaum’s arguments concerning the conven-

tionality of the space-time metric for continuousmanifolds involve more complex issues than thosein the simultaneity case. But some key elements arecommon to both disputes. Grunbaum claims thatcontinuous manifolds do not have intrinsic metrics,and critics complain that the notion of an intrinsicfeature is unclear (see e.g., Stein 1977). Some of theclaims that Grunbaum makes lend support to theidea that he is concerned with C1 conventionalism.He claims, for example, that for a discrete manifold(such that between any two points there are onlyfinitely many points), there is an intrinsic andhence nonconventional metric, where the ‘‘dis-tance’’ between any two points is the number ofpoints between them, plus one. This claim makessense to the extent that one is concerned with C1,that is, with the question of whether a relation isdefinable or logically constructible from a basic set.Grunbaum’s arguments do not seem well suited forshowing that such a metric would be C2 noncon-ventional, since nothing about the meaning of ‘dis-tance’ constrains the adoption of this as opposed toinfinitely other metrics.Another worry that might be raised concerns

Grunbaum’s insistence that distance functions de-fined in terms of physical bodies and their beha-viors under transport are extrinsic to a manifold. Ifthe manifold is a purely mathematical object, thensuch a view seems more plausible. But if one isconcerned with a physical manifold of space-timepoints, it is less obvious that physical bodies shouldbe treated as extrinsic. More importantly, even ifone grants Grunbaum that physical bodies andtheir behaviors are extrinsic to the physical space-time manifold, one might want to grant a scientistthe right to specify which features of the structuresthat are being posited are to count as basic orintrinsic. For example, Grunbaum proposes thatNewton in effect made a conceptual error in claim-ing that whether the temporal interval between onepair of instants is the same as that between anotherpair of instants is a factual matter, determined bythe structure of time itself. Since instants form atemporal continuum in Newton’s picture, there is,according to Grunbaum, no intrinsic temporalmetric, contrary to Newton’s claims. However,one can imagine a Newtonian responding withbewilderment. Does Newton not get to say whatrelations are intrinsic to the structures that he ispositing?

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It is difficult to see how to make room for anotion of intrinsicness that can do all of the philo-sophical work that Grunbaum requires of it, asStein (1977) and others argue at length. On theother hand, Grunbaum’s conventionalism aboutsimultaneity within SR remains defensible (in par-ticular, it escapes the trivialization charge as wellas Malament’s attempted refutation) if his con-clusions are interpreted in the sense of C2 conven-tionalism described above.

Mathematical and Logical Conventionalism

Up to now this discussion has focused on conven-tionalist claims concerning principles of an empiri-cal science, physics. Other propositions that haveattracted conventionalist treatment are those fromthe nonempirical sciences of mathematics andlogic. Conventionalism seems especially attractivehere, particularly to empiricists and others whofind the notion of special faculties of mathematicalintuition dubious but nevertheless wish to treatknown mathematical or logical propositions asnonempirical.The axiomatic methods that had motivated

Poincare’s geometric conventionalism discussedabove received further support with the publicationof David Hilbert’s Foundations of Geometry ([1921]1962). Hilbert disregarded the intuitive or ordinarymeanings of such constituent terms of Euclideangeometry as ‘‘point,’’ ‘‘line,’’ and ‘‘plane,’’ and in-stead proposed regarding the axioms as purely for-mal posits (see Hilbert, David). In other words, theaxioms function as generalizations about whateverset of things happens to satisfy them. In addition toallowing Hilbert to demonstrate a number of sig-nificant results in pure geometry, this method ofabstracting from particular applications had imme-diate philosophical consequences. For instance, inresponse to Gottlob Frege’s objection that withoutfixing a reference for primitive expressions like‘‘between,’’ Hilbert’s axiomatic geometry wouldbe equivocal, Hilbert wrote:

But surely it is self-evident that every theory is merely aframework or schema of concepts together with theirnecessary relations to one another, and that the basicelements can be construed as one pleases. If I think ofmy points as some system or other of things, e.g., thesystem of love, of law, or of chimney sweeps . . . andthen conceive of all my axioms as relations betweenthese things, then my theorems, e.g., the Pythagoreanone, will hold of these things as well.

(Hilbert 1971, 13)

Moritz Schlick was quick to find in Hilbert’sconclusions the possibility of generalizing conven-tionalism beyond geometry (see Schlick, Moritz).

If the reference of the primitive concepts of anaxiomatic system could be left undetermined, asHilbert had apparently demonstrated, then theaxioms would be empty of empirical content, andso knowledge of them would appear to be a priori.Like Poincare, Schlick rejected a Kantian explana-tion of how such knowledge is possible, and he sawin Hilbert’s approach a demonstration of how animplicit definition of concepts could be obtainedthrough axioms whose validity had been guaran-teed (Schlick [1925] 1985, 33). In his General Theo-ry of Knowledge Schlick distinguished explicitlybetween ‘‘ordinary concepts,’’ which are definedby ostension, and implicit definitions. Of the latter,he wrote that

[a] system of truths created with the aid of implicitdefinitions does not at any point rest on the ground ofreality. On the contrary, it floats freely, so to speak, andlike the solar system bears within itself the guarantee ofits own stability. (37)

The guaranteed stability was to be provided by aconsistency proof for a given system of axioms,which Schlick, like Poincare and Hilbert beforehim, claimed was a necessary condition in a systemof symbolism. Schlick followed Poincare in treatingthe axioms as conventions, and hence as known apriori through stipulation (Schlick [1925] 1985, 71).But he diverged markedly from Poincare in extend-ing this account to mathematics and logic as well.His basis for doing so was Hilbert’s formalizedtheory of arithmetic, which Schlick hoped (wrong-ly, as it turned out) would eventuate in a consisten-cy proof for arithmetic ([1925] 1985, 357).

The conventionalism that emerged was thus onein which true propositions known a priori wereregarded as components of autonomous symbolgames that, while perhaps constructed with an eyeto an application, are not themselves answerable toan independent reality (Schlick [1925] 1985, 37–8).Schlick thought that the laws of logic, such as theprinciples of identity, noncontradiction, and theexcluded middle, ‘‘say nothing at all about thebehavior of reality. They simply regulate how wedesignate the real’’ ([1925] 1985, 337). Schlick ac-knowledged that the negation of logical principleslike noncontradiction was unthinkable, but he sug-gested that this fact was itself a convention ofsymbolism (concerning the notion ‘unthinkable’),claiming that ‘‘anything which contradicts the prin-ciple is termed unthinkable’’ ([1925] 1985, 337).

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Although Schlick thought that the structure of asymbol system, including inference systems such aslogic, was autonomous and established by a set ofimplicit definitions, he also recognized the possibilitythat some of its primitive terms could be coordi-nated by ordinary definitions with actual objectsand properties. In this way, a conventionallyestablished symbol system could be used to describethe empirical world, and an object designated by aprimitive term might be empirically discovered tohave previously unknown features. Nonetheless,some of the properties and relations had by a primi-tive term would continue to be governed by the sys-tem conventions through which the term is implicitlydefined (Schlick [1925] 1985, 48ff ). These propertiesand relations would thus be knowable a priori.

The conventionalism of Schlick’s General Theoryof Knowledge anticipated many of the convention-alist elements of the position advanced by mem-bers of the Vienna Circle (see Vienna Circle).Philosophers such as Hahn, Ayer, and Carnapsaw in conventionalism the possibility of acknowl-edging the existence of necessary truths known apriori while simultaneously denying such proposi-tions any metaphysical significance. Inspired byWittgenstein’s analysis of necessary truths in theTractatus, Vienna Circle members identified thetruths of mathematics and logic with tautologies—statements void of content in virtue of the fact thatthey hold no matter what the facts of the worldmay be (Hahn 1980; Ayer 1952). Tautologies, inturn, were equated with analytic statements, andCircle members regarded all analytic statements aseither vacuous conventions of symbolism known apriori through stipulation or as derivable conse-quences of such conventions knowable a priorithrough proof (see Analyticity).

An especially noteworthy outgrowth of the con-ventionalism of the Vienna Circle was Carnap’sThe Logical Syntax of Language. In this bookCarnap advanced a conventionalist treatment ofthe truths of mathematics and logic through hisespousal of the principle of tolerance, which states:

In logic, there are no morals. Everyone is at liberty tobuild up his own logic, i.e., his own form of language, ashe wishes. All that is required of him is that . . . he muststate his methods clearly, and give syntactical rules in-stead of philosophical arguments.

(Carnap 1937, 52)

Carnap regarded a language as a linguisticframework that specified logical relations of conse-quence among propositions. These logical relationsare a precondition of description and investigation.In this view, there can be no question of justifying

the selection of an ideal or even unique languagewith reference to facts, since any such justification(including a specification of facts) would presup-pose a language. Mathematics is no exception tothis. As a system of ‘‘framework truths,’’ mathe-matical truths do not describe any convention-independent fact but are consequences of thedecision to adopt one linguistic framework overanother, in Carnap’s account.Conventionalism about mathematics and logic

has faced a number of important objections. Asignificant early objection was given by Poincare(1952, 166–72), who rejected Hilbert’s idea that theprinciple of mathematical induction might merelybe an implicit definition of the natural numbers(see Hilbert [1935] 1965, 193). Mathematical induc-tion should not be regarded in this way, Poincareargued, for it is presupposed by any demonstrationof the consistency of the definition of number, sinceconsistency proofs require a mathematical inducti-on on the length of formulas. Treating the induc-tion principle as itself conventional while using it toprove the consistency of the conventions of which itis a part would thus involve a petitio.Carnap’s Logical Syntax of Language sidestepp-

ed such problems by removing the demand that asystem of conventions be consistent; the principleof tolerance made no such demand, and Carnapregarded the absence of consistency proofs as oflimited significance (1937, 134). It appears that hewould have regarded a contradictory language sys-tem to be pragmatically useless but not impossible.Kurt Godel, however, raised an important objec-

tion to this strategy. Godel claimed that if mathe-matics is to be ‘‘merely’’ a system of syntacticalconventions, then the conventions must be knownnot to entail the truth or falsity of any sentenceinvolving a matter of extralinguistic empirical fact;if it does have such entailments, in Godel’s view,the truth of such sentences is not merely a syntacti-cal, conventional matter (Godel 1995, 339). If thesystem contains a contradiction, then it will implyevery empirical sentence. But according to Godel’ssecond incompleteness theorem, a consistency proofrequired to assure the independence of the systemcannot emerge from within the system itself if thatsystem is consistent (1995, 346).Recent commentators (Ricketts 1994; Goldfarb

1995) have argued that a response to this objec-tion is available from within Carnap’s conven-tionalist framework. Godel’s argument requiresacceptance of an extralinguistic domain of empiri-cal facts, which a stipulated language systemmay or may not imply. But it is doubtful thatCarnap would have accepted such a domain, for

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Carnap considered linguistic conventions, includ-ing the conventions constitutive of mathematics, asantecedent to any characterization of the facts,including facts of the empirical world. The issuesinvolved in Godel’s objection are complex and in-teresting, and a thorough and satisfactory conven-tionalist response remains to be formulated.Another objection to conventionalism about

logic was advanced by Willard V. Quine (seeQuine, Willard Van Orman). Quine objectedagainst Carnap that treating logical laws and infer-ence rules as conventional truths implicitly presup-posed the logic that such conventions wereintended to establish. Consider for instance a pro-posed logical convention MP of the form ‘‘Let allresults of putting a statement for p and a statementfor q in the expression ‘If p, then q and p, then q’ betrue.’’ In order to apply this convention to particu-lar statements A and B, it seems that one mustreason as follows: MP and if MP, then (A and ifA, then B imply B); therefore, A and if A, then Bimply B). But this requires that one use modusponens in applying the very convention that stipu-lates the soundness of this inference. Quine con-cluded that ‘‘if logic is to proceed mediately fromconventions, logic is needed for inferring logic fromthe conventions’’ (Quine 1966, 97). Quine at onepoint suggested that similar reasoning might un-dermine the intelligibility of the notion of a linguis-tic convention in general (98–9). However, afterDavid Lewis’ analysis of tacit conventions (Lewis1969), Quine acknowledged the possibility of atleast some such conventions (Quine, in Lewis1969, xii).Quine’s original objection suggests that the

conventionalist about logical truth must have anaccount of how something recognizable as a conven-tion can intelligibly be established ‘‘prior to logic.’’As with Godel’s objection, the issues are difficultand have not yet been given a fully satisfying con-ventionalist account. However, there are a variety ofstrategies that a conventionalist might explore. Onewill bementioned here. Consider an analogous case,that of rules of grammar. On one hand, one cannotspecify rules of grammar without employing a lan-guage (which has its grammatical rules). Thus onecannot acquire one’s first language by, say, readingits rules in a book. On the other hand, this fact doesnot seem to rule out the possibility that any givenrules of grammar are to some extent arbitrary, andconventionally adopted. Whether the conventional-ist can extend this line of thought to a defensibleform of conventionalism about logic remains to beconclusively demonstrated.

CORY JUHL AND ERIC LOOMIS

References

Ayer, Alfred J. (1952), Language, Truth and Logic. NewYork: Dover.

Carnap, Rudolph (1937), The Logical Syntax of Language.London: Routledge and Kegan Paul.

Duhem, Pierre ([1906] 1954), The Aim and Structure ofPhysical Theory. Translated by Philip P. Wiener. Prince-ton, NJ: Princeton University Press.

Eddington, A. S (1953), Space, Time and Gravitation. Cam-bridge: Cambridge University Press.

Gergonne, Joseph Diaz (1818), ‘‘Essai sur la theorie de ladefinition,’’ Annales de mathematiques pures et appli-quees 9:1–35.

Giedymin, Jerzy (1982), Science and Convention: Essays onHenri Poincare’s Philosophy of Science and the Conven-tionalist Tradition. Oxford: Pergamon.

Godel, Kurt (1995), ‘‘Is Mathematics Syntax of Language?’’in Solomon Feferman (ed.),Kurt Godel: CollectedWorks,vol. 3. Oxford: Oxford University Press, 334–362.

Goldfarb, Warren (1995), ‘‘Introductory Note to *1953/9,’’in Solomon Feferman (ed), Kurt Godel: Collected Works,vol. 3. Oxford: Oxford University Press, 324–334.

Grunbaum, Adolph (1968), Geometry and Chronometery inPhilosophical Perspective. Minneapolis: University ofMinnesota Press.

——— (1973), Philosophical Problems of Space and Time,2nd ed. Dordrecht, Netherlands: Reidel.

Hahn, Hans (1980), Empiricism, Logic, and Mathematics.Translated by Brian McGuinness. Dordrecht, Nether-lands: Reidel.

Hilbert, David ([1935] 1965), ‘‘Die Grundlegung der ele-mentaren Zahlenlehre,’’ in Gesammelte Abhandlungen,vol. 3. New York: Chelsea Publishing, 192–195.

——— ([1921] 1962), Grundlagen der Geometrie. Stuttgart:B. G. Teubner.

——— (1971), ‘‘Hilbert’s Reply to Frege,’’ in E. H. W.Kluge (trans., ed.), On the Foundations of Geometry andFormal Theories of Arithmetic. London: Yale UniversityPress, 10–14.

Lewis, David (1969), Convention: A Philosophical Study.Oxford: Blackwell.

Lie, Sophus (1959), ‘‘On a Class of Geometric Transforma-tions,’’ in D. E. Smith (ed.), A Source Book in Mathe-matics. New York: Dover.

Malament, David (1977), ‘‘Causal Theories of Time and theConventionality of Simultaneity,’’ Nous 11: 293–300.

Norton, John (1992), ‘‘Philosophy of Space and Time,’’ inM. H. Salmon et. al. (eds), Introduction to the Philosophyof Science. Indianapolis: Hackett.

Poincare, Henri ([1905] 1952),Science andHypothesis. Trans-lated byW. J. Greestreet. NewYork: Dover Publications.

——— (1952), Science and Method. Translated by FrancisMaitland. New York: Dover Publications.

Putnam, Hilary (1975a), ‘‘An examination of Grunbaum’sPhilosophy of Geometry,’’ in Mathematics, Matter andMethod Philosophical Papers, vol. 1. New York: Cam-bridge University Press.

——— (1975b), ‘‘Reply to Gerald Massey,’’ in Mind, Lan-guage and Reality, Philosophical Papers, vol. 2. NewYork: Cambridge UP.

Quine, Willard V. (1966), ‘‘Truth By Convention,’’ in TheWays of Paradox and Other Essays. New York: RandomHouse, 70–99.

Ricketts, Thomas (1994), ‘‘Carnap’s Principle of Tolerance,Empricism, and Conventionalism,’’ in Peter Clark andAU:43

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Bob Hale (eds.), Reading Putnam. Cambridge, MA:Blackwell, 176–200.

Salmon, Wesley (1977), ‘‘The Philosophical Significanceof the One-Way Speed of Light,’’ Nous 11: 253–292.

Sarkar, Sahotra, and John Stachel (1999), ‘‘Did MalamentProve the Non-Conventionality of Simultaneity in theSpecial Theory of Relativity?’’ Philosophy of Science 66:208–220.

Schlick, Moritz ([1925] 1985), General Theory of Knowledge.Translated by Albert E. Blumberg. La Salle, IL: OpenCourt.

Spirtes, Peter L. (1981), ‘‘Conventionalism and the Phi-losophy of Henri Poincare,’’ Ph. D. Dissertation,

Department of the History and Philosophy of Science,University of Pittsburgh.

Stein, Howard (1977), ‘‘On Space-Time and Ontology: Ex-tract from a Letter to Adolf Grunbaum,’’ in Foundationsof Space-time Theories, Minnesota Studies in the Philos-ophy of Science, vol. 8. Minneapolis: University of Min-nesota Press.

See also Analyticity; Carnap, Rudolf; Duhem The-sis; Hilbert, David; Instrumentalism; Logical Empir-icism; Poincare, Henri; Quine, Willard Van Orman;Schlick, Moritz; Space-Time; Vienna Circle

CORROBORATION

Karl R. Popper (1959) observed that insofar asnatural laws have the force of prohibitions, theycannot be adequately formalized as unrestrictedlygeneral material conditionals but incorporate amodal element of natural necessity. To distinguishbetween possible laws and mere correlations, em-pirical scientists must therefore subject them tosevere tests by serious attempts to refute them,where the only evidence that can count in favor ofthe existence of a law arises from unsucces-sful attempts to refute it. He therefore insistedupon a distinction between ‘confirmation’ and‘corroboration’ (see Popper, Karl Raimund).

To appreciate Popper’s position, it is essential toconsider the nature of natural laws as the objects ofinquiry. When laws of nature are taken to have thelogical form of unrestrictedly general material con-ditionals, such as ðxÞðRx ! BxÞ for ‘‘All ravens areblack,’’ using the obvious predicate letters Rx andBx and !, as the material conditional, then theyhave many logically equivalent formulations, suchas ðxÞðØBx ! ØRxÞ; using the same notation,which stands for ‘‘Every nonblack thing is a non-raven.’’ As Carl G. Hempel (1965) observed, if it isassumed that confirming a hypothesis requires satis-fying its antecedent and then ascertaining whetheror not its consequent is satisfied, then if logicallyequivalent hypotheses are confirmed or disconfirmedby the same evidence, a white shoe as an instance oføBx that is also øRx confirms the hypothesis ‘‘Allravens are black’’ (see Induction, Problem of ).

Popper argued that there are no ‘‘paradoxesof falsification’’ parallel to the ‘‘paradoxes of

confirmation.’’ And, indeed, the only way inwhich even a material conditional can be falsifiedis by things satisfying the antecedent but not satis-fying the consequent. Emphasis on falsificationtherefore implies that serious tests of hypothesespresuppose satisfying their antecedents, thereby sug-gesting a methodological maxim of deliberatelysearching for examples that should be most likelyto reveal the falsity of a hypothesis if it is false, suchas altering the diet or the habitat of ravens toascertain whether that would have any effect ontheir color. But Popper’s conception of laws asprohibition was an even more far reaching insightrelative to his falsificationist methodology.Popper’s work on natural necessity distinguishes

it from logical necessity, where the notion of pro-jectible predicates as a pragmatic condition is dis-placed by the notion of dispositional predicates as asemantic condition. It reflects a conception oflaws as relations that cannot be violated or chan-ged and require no enforcement. Fetzer (1981) haspursued this approach, where lawlike sentencestake the form of subjunctive conditionals, such asðxÞðRx ) BxÞ; where ) stands for the subjunctiveconditional. This asserts of everything, ‘‘If it were araven, then it would be black.’’ The truth of thisclaim, which is logically contingent, depends on adifference between permanent and transient prop-erties. It does not imply the counterpart, ‘‘If any-thing were nonblack, then it would be a nonraven.’’Among Popper’s most important contributions

were his demonstration of how his falsificationistmethodology could be extended to encompass

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statistical laws and his propensity interpretationof probability (see Probability). Distributions ofoutcomes that have very low probabilities in hypo-theses are regarded, by convention, as methodolog-ically falsifying those hypotheses, tentatively andfallibilistically. Popper entertained the prospect ofprobabilistic measures of corroboration, but likeli-hood measures provide a far better fit, since uni-versal hypotheses as infinite conjunctions have zeroprobability. Indeed, Popper holds that the appro-priate hypothesis for scientific acceptance is the onethat has the greatest content and has withstoodour best attempts at its falsification, which turnsout to be the least probable among the unfalsifiedalternatives.The likelihood of hypothesis H, given evidence

E, is simply the probability of evidence E, if hy-pothesis H is true. While probabilistic measureshave to satisfy axioms of summation and multipli-cation—for example, where mutually exclusive andjointly exhaustive hypotheses must have probabil-ities that sum to 1—likelihood measures are consis-tent with arbitrarily many hypotheses of highvalue. This approach can incorporate the laws oflikelihood advanced by Ian Hacking (1965) and adistinction between preferability for hypotheseswith a higher likelihood on the available evidenceand acceptability for those that are preferable whensufficient evidence becomes available. Acceptabil-ity is partially determined by relative likelihoods,even when likelihoods are low. Popper (1968,360–91) proposed that where E describes the out-come of a new test and B our background knowl-edge prior to that test, the severity of E as a test ofH, relative to B, might be measured by

PðE jH6BÞ� PðE jBÞ; ð1Þthat is, as the probability of E, given H and B,minus the probability of E, given B alone. Theintent of equation 1 may be more suitably capturedby a formulation that employs a symmetrical—andtherefore absolute—measure reflecting differencesin expectations with respect to outcome distribu-tions over sets of relevant trials, such as

jPðE jHÞ� PðE jBÞ j ; ð2Þwhich ascribe degrees of nomic expectability to rel-ative frequency data, for example. When B entailsE, then P(E jB) ¼ 1, and if P(E jH ) ¼ 1 as well, theseverity of any such test is minimal, i.e., 0. When Hentails E, while B entails øE, the severity of such atest is maximal, i.e., 1. The acceptance of H mayrequire the revision of B to preserve consistency.A plausible measure of the degree of corrobora-

tion C of H, given E, relative to B, would be

CðH jE6BÞ ¼ LðH jEÞ½ jPðE jHÞ� PðE jBÞ j �;ð3Þ

that is, as the product of the likelihood of H, givenE, times the severity of E as a test of H, relative toB. This is a Popperian measure, but not necessarilyPopper’s. Popper suggests (as one possibility)

CðH jE6BÞ ¼PðE jHÞ� PðE jBÞ=PðE jHÞ þ PðE jBÞ; ð4Þ

which even he does not find to be entirely satisfac-tory and which Imre Lakatos severely criticizes(Lakatos 1968, especially 408–16). When alterna-tive hypotheses are available, the appropriate com-parative measures appear to be corroborationratios

CðH2 jEÞCðH1 jEÞ ¼

LðH2 jEÞ½ jPðE jH2Þ� PðE jH1Þ j �LðH1 jEÞ½ jPðE jH1Þ� PðE jH2Þ j �

ð5Þthat reduce to the corresponding likelihood ra-

tios of L(H2jE ) divided by L(H1jE ) and assumeincreasing significance as a function of the severityof those tests, as Fetzer (1981, 222–30) explains.

Popper also proposed the propensity interpreta-tion of physical probabilities as probabilistic dis-positions (Popper 1957 and 1959). In a revisedformulation, the single-case propensity interpreta-tion supports a theory of lawlike sentences, logical-ly contingent subjunctive conditionals ascribingpermanent dispositional properties (of varyingstrength) to everything possessing a reference prop-erty (Fetzer 1981 and 1993). Propensity hypothesesare testable on the basis of the frequencies theygenerate across sequences of trials. Long runs areinfinite and short runs are finite sequences of singletrials. Propensities predict frequencies but also ex-plain them. Frequencies are evidence for thestrength of propensities.

Popper (1968) promoted the conception of sci-ence as a process of conjectures and (attempted)refutations. While he rejected the conception ofscience as a process of inductive confirmationexemplified by the work of Hans Reichenbach(1949) and Wesley C. Salmon (1967), his commit-ments to deductive procedures tended to obscurethe role of ampliative reasoning in his own posi-tion. Popper rejected a narrow conception of in-duction, according to which the basic rule ofinference is ‘‘If m/n observed As are Bs, then inferthat m/n As are Bs, provided a suitable number ofAs are tested under a wide variety of conditions.’’And, indeed, the rule he rejects restricts scientifichypotheses to those couched in observational

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language and cannot separate bona fide laws fromcorrelations.

Although it was not always clear, Popper wasnot thereby rejecting induction in the broad senseof ampliative reasoning. He sometimes tried toformalize his conception of corroboration usingthe notion of absolute (or prior) probability of theevidenceE,P(E ), which is typically supposed to be asubjective probability. Grover Maxwell (1974) evendevelops Popper’s approach using Bayes’s theorem.However, appeals to priors are inessential to forma-lizations of Popper’s measures (Fetzer 1981), and itwould be a mistake to suppose that Popper’s ac-count of severe tests, which is a pragmatic concep-tion, could be completely formalizable.

Indeed, Popper’s notion of accepting hypotheseson the basis of severe tests, no matter how tentative-ly and fallibilistically, implies ampliative reasoning.Its implementation for probabilistic hypothesesthereby requires large numbers of trials over a widevariety of conditions, which parallels the narrowinductivist conception. These results, however, mustbe subjected to severe tests to make sure the frequen-cies generated are robust and stable under variableconditions.When Volkswagens were first importedinto the United States, for example, they were allgray. The narrow inductivist rule of inference justi-fied inferring that all Volkswagens were gray, aconclusion that could not withstand severe tests.

JAMES H. FETZER

References

Fetzer, James H. (1981), Scientific Knowledge: Causation,Explanation, and Corroboration. Dordrecht, Nether-lands: D. Reidel.

——— (1993), Philosophy of Science. New York: ParagonHouse.

Hacking, Ian (1965), Logic of Statistical Inference. Cam-bridge: Cambridge University Press.

Hempel, Carl G. (1965), Aspects of Scientific Explanation.New York: Free Press.

Lakatos, Imre (1968), ‘‘Changes in the Problem of Induc-tive Logic,’’ in The Problem of Inductive Logic. Amster-dam: North-Holland, 315–417.

Maxwell, Grover (1974), ‘‘Corroboration without De-marcation,’’ in Paul A. Schilpp (ed.), The Philosophy ofKarl R. Popper, part 1. LaSalle, IL: OpenCourt, 292–321.

Popper, Karl R. (1959), The Logic of Scientific Discovery.New York: Harper & Row.

——— (1957), ‘‘The Propensity Interpretation of the Cal-culus of Probability, and the Quantum Theory,’’ in Ste-phan Korner (ed.), Observation and Interpretation in thePhilosophy of Physics. New York: Dover Publications,65–70.

——— (1959), ‘‘The Propensity Interpretation of Probabili-ty,’’British Journal for the Philosophy of Science 10: 25–42.

——— (1968), Conjectures and Refutations. New York:Harper & Row.

Reichenbach, Hans (1949), The Theory of Probability. Ber-keley and Los Angeles: University of California.

Salmon, Wesley C. (1967), The Foundations of Scien-tific Inference. Pittsburgh: University of Pittsburgh Press.

See also Confirmation Theory; Hempel, Carl Gus-tav; Induction, Problem of; Popper, Karl Raimund;Verisimilitude

COSMOLOGY

See Anthropic Principle

COUNTERFACTUALS

See Causality

COUNTERFACTUALS

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CARNAP, RUDOLF - University of Toronto · 2018. 12. 22. · CARNAP, RUDOLF (18 May 1891–14 September 1970) Rudolf Carnap (1891–1970), preeminent member of the Vienna Circle, was