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C

CARNAP, RUDOLF

(18 May 1891–14 September 1970)

Rudolf Carnap (1891–1970), preeminent member in Germany (Carnap 1963a). In early childhood he of the Vienna Circle, was one of the most influen- was educated at home by his mother, Anna Carnap tial figures of twentieth-century philosophy of (neePROOF´ Do¨rpfeld), who had been a schoolteacher. science and analytic philosophy (including the phi- From 1898, he attended the Gymnasium at Bar- losophies of language, logic, and mathematics). men, where the family moved after his father’s The Vienna Circle was responsible for promulgat- death that year. In school, Carnap’s chief interests ing a set of doctrines (initially in the 1920s) that were in mathematics and Latin. From 1910 to 1914 came to be known as logical positivism or logical Carnap studied at the Universities of Jena and empiricism (see Logical Empiricism; Vienna Cir- Freiburg, concentrating first on philosophy and cle). This set of doctrines has provided the point mathematics and, later, on philosophy and physics. of departure for most subsequent developments in Among his teachers in Jena were Bruno Bauch, a the philosophy of science. Consequently Carnap prominent neo-Kantian, and Gottlob Frege, a must be regarded as one of the most important founder of the modern theory of quantification in philosophers of science of the twentiethFIRST century. logic. Bauch impressed upon him the power of Nevertheless, his most lasting positive contribu- Kant’s conception that the geometrical structure tions were in the philosophy of logic and mathe- of space was determined by the form of pure intui- matics and the philosophy of language. Meanwhile, tion. Though Carnap was impressed by Frege’s his systematic but ultimately unsuccessful attempt ongoing philosophical projects, Frege’s real (and to construct an inductive logic has been equally lasting) influence came only later through a study influential, since its failure has convinced most phi- of his writings. Carnap’s formal intellectual work losophers that such a project must fail. was interrupted between 1914 and 1918 while he did Carnap was born in 1891 in Ronsdorf, near Bar- military service during World War I. His political men, now incorporated into the city of Wuppertal, views had already been of a mildly socialist/pacifist

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CARNAP, RUDOLF

nature. The horrors of the war served to make them Circle) (see Schlick, Moritz), the geometry of physi- more explicit and more conscious, and to codify cal space was regarded as an empirical matter. Car- them somewhat more rigorously. nap included a discussion of the role of non- Euclidean geometry in Einstein’s theory of general Space relativity. By distinguishing among intuitive, math- ematical, and physical spaces, Carnap attempted to After the war, Carnap returned to Jena to begin resolve the apparent differences among philoso- research. His contacts with Hans Reichenbach and phers, mathematicians, and physicists by assigning others pursuing philosophy informed by current the disputing camps to different discursive domains. science began during this period (see Reichenbach, In retrospect, this move heralded what later became Hans). In 1919 he read Whitehead and Russell’s the most salient features of Carnap’s philosophical Principia Mathematica and was deeply influenced work: tolerance for diverse points of view (so long as by the clarity of thought that could apparently they met stringent criteria of clarity and rigor) and be achieved through symbolization (see Russell, an assignment of these viewpoints to different Bertrand). He began the construction of a putative realms, the choice between which is to be resolved axiom system for a physical theory of space-time. not by philosophically substantive (e.g., epistemo- The physicists—represented by Max Wien, head of logical) criteria but by pragmatic ones (see Conven- the Institute of Physics at the University of Jena— tionalism). were convinced that the project did not belong in physics. Meanwhile, Bauch was equally certain that The Constructionist Phase it did not belong in philosophy. This incident was instrumental in convincing Carnap of the institu- During the winter of 1921, Carnap read Russell’s tional difficulties faced in Germany of doing inter- Our Knowledge of the External World. Between disciplinary work that bridged the chasm between 1922 and 1925, this work led him (Carnap 1963a) philosophy and the natural sciences. It also probably to begin the analysis that culminated in Der logische helped generate the attitude that later led the logical Aufbau der Welt ([1928] 1967), which is usually empiricists to dismiss much of traditional philoso- regarded as Carnap’s first major work. The purpose phy, especially metaphysics. By this point in his intel- of the Aufbau was to construct the everyday world lectual development (the early 1920s) Carnap was from a phenomenalist basis (see Phenomenalism). already a committed empiricist who, nevertheless, The phenomenalist basis is an epistemological accepted both the analyticity of logic and mathemat- choice (§§54, 58). Carnap distinguished between ics and the Frege-Russell thesis of logicism, which four domains of objects: autopsychological, physi- required that mathematics be formally constructed cal, heteropsychological, and cultural (§58). The and derived from logic (see Analyticity). firstPROOF of these consists of objects of an individual’s Faced with this lack of enthusiasm for his original own psychology; the second, of physical entities project in Jena, Carnap (1922) abandoned it to write (Carnap does not distinguish between everyday ma- a dissertation on the philosophical foundations of terial objects and the abstract entities of theoretical geometry, which was subsequently published as physics); the third consists of the objects of some Der Raum. Most traditional commentators have other individual’s psychology; and the fourth, regarded the dissertation as a fundamentally neo- of cultural objects (geistige Gegensta¨nde), which Kantian work because it included a discussion of include historical and sociological phenomena. ‘‘intuitive space,’’ determined by pure intuition, in- From Carnap’s ([1928] 1967) point of view, ‘‘[a]n dependent of all contingent experience, and distinct object ... is called epistemically primary relative to from both mathematical (or formal)FIRST space and another one ... if the second one is recognized physical space (see Friedman 1999). However, re- through the mediation of the first and thus presup- cent reinterpretations argue for a decisive influence poses, for its recognition, the recognition of the of Husserl (Sarkar 2003). In contrast to Kant, first’’ (§54). Autopsychological objects are episte- Carnap restricted what could be grasped by pure mically primary relative to the others in this sense. intuition to some topological and metric properties Moreover, physical objects are epistemically pri- of finite local regions of space. He identifies this mary to heteropsychological ones because the latter intuitive space with an infinitesimal space and goes can be recognized only through the mediation of on to postulate that a global space may be con- the former—an expression on a face, a reading in structed from it by iterative extension. In agreement an instrument, etc. Finally, heteropsychological with Helmholtz and Moritz Schlick (a physicist- objects are epistemically primary relative to cultur- turned-philosopher, and founder of the Vienna al ones for the same reason.

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CARNAP, RUDOLF

The main task of the Aufbau is construction, Since the elex are elementary, they cannot be which Carnap ([1928] 1967) conceives of as the further analyzed to define what would be regarded converse of what he regarded as reduction (which as constituent qualities of them such as partial is far from what was then—or is now—conceived sensations or intensity components of a sensation. of as ‘‘reduction’’ in Anglophone philosophy) (see Had the elex not been elementary, Carnap could Reductionism): have used ‘‘proper analysis’’ to define such quali- ... ties by isolating the individuals into classes on the [A]n object is ‘reducible’ to others if all statements basis of having a certain (symmetric) relationship about it can be translated into statements which speak with each other. Carnap defines the process of AU:1 only about these other objects ... .Byconstructing a concept from other concepts, we shall mean the indica- ‘‘quasi-analysis’’ to be formally analogous to prop- tion of its ‘‘constructional definition’’ on the basis of er analysis but only defining ‘‘quasi-characteristics’’ other concepts. By a constructional definition of the or ‘‘quasi-constituents’’ because the elex are unana- concept a on the basis of the concepts b and c,we lyzable. Thus, if an elex is both c in color and t in mean a rule of translation which gives a general indica- temperature, c or t can be defined as classes of every tion how any propositional function in which a occurs elex having c or t, respectively. However, to say may be transformed into a coextensive propositional that c or t is a quality would imply that an elex is function in which a no longer occurs, but only b and c. analyzable into simpler constituents. Quasi-analysis If a concept is reducible to others, then it must indeed be proceeds formally in this way (as if it is proper possible to construct it from them (§35). analysis) but defines only quasi-characteristics, However, construction and reduction present thus allowing each elex to remain technically unan- different formal problems because, except in some alyzable Quasi-analysis based on the relation ‘‘part degenerate cases (such as explicit definition), the similarity’’ (Ps), itself defined from Rs, is the cen- transformations in the two directions may not tral technique of the Aufbau. It is used eventually have any simple explicit relation to each other. to define sense classes and, then, the visual sense, The question of reducibility/constructibility is dis- visual field places, the spatial order of the visual tinct from that of epistemic primacy. In an impor- field, the order of colors and, eventually, sensa- tant innovation in an empiricist context, Carnap tions. Thus the physical domain is constructed argues that both the autopsychological and physi- out of the autopsychological. Carnap’s accounts cal domains can be reduced to each other (in his of the construction between the other two domains sense). Thus, at the formal level, either could serve remain promissory sketches. as the basis of the construction. It is epistemic Carnap was aware that there were unresolved primacy that dictates the choice of the former. technical problems with his construction of the Carnap’s task, ultimately, is to set up a construc- physical from the autopsychological, though he tional system that will allow the construction of probablyPROOF underestimated the seriousness of these the cultural domain from the autopsychological problems. The systematic problems are that when through the two intermediate domains. In the Auf- a quality is defined as a class selected by quasi- bau, there are only informal discussions of how the analysis on the basis of a relation: (i) two (different) last two stages of such a construction are to be qualities that happen always to occur together executed; only the construction of the physical (say, red and hot) will never be separated, and from the autopsychological is fully treated formal- (ii) quality classes may emerge in which any two ly. As the basic units of the constructional system, members bear some required relation to each Carnap chose what he calls ‘‘elementary experi- other, but there may yet be no relation that holds ences’’ (Elementarerlebnisse, or elex) (an extended between all members of the class. Carnap’s re- discussion of Carnap’s constructionFIRST is to be found sponse to these problems was extrasystematic: In in Goodman 1951, chapter 5). These are supposed the complicated construction of the world from the to be instantaneous cross-sections of the stream of elex, he hoped that such examples would never or experience—or at least bits of that stream in the only very rarely arise. Nevertheless, because of smallest perceivable unit of time—that are incapable these problems, and because the other construc- of further analysis. The only primitive relation tions are not carried out, the attitude of the Aufbau that Carnap introduces is ‘‘recollection of similarity’’ is tentative and exploratory: The constructional AU:2 (Rs). (In the formal development of the system, system is presented as essentially unfinished. (Good- Rs is introduced first and the elex are defined man 1951 also provides a lucid discussion of these as the field of Rs.) The asymmetry of Rs is eventu- problems.) ally exploited by Carnap to introduce temporal Some recent scholarship has questioned whether ordering. Carnap had any traditional epistemological

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CARNAP, RUDOLF

concerns in the Aufbau. In particular, Friedman Viennese Positivism (e.g., 1992) has championed the view that Carnap’s concerns in that work are purely ontological: In 1926, at Schlick’s invitation, Carnap moved to The Aufbau is not concerned with the question of Vienna to become a Privatdozent (instructor) in the source or status of knowledge of the external philosophy at the University of Vienna for the world (see Empiricism); rather, it investigates the next five years (see Vienna Circle). An early version bases on which such a world may be constructed of the Aufbau served as his Habilitationsschrift. He (see Richardson 1998). Both Friedman and was welcomed into the Vienna Circle, a scientific Richardson—as well as Sauer (1985) and Haack philosophy discussion group organized by (and (1977) long before them—emphasize the Kantian centered around) Schlick, who had occupied the roots of the Aufbau. If this reinterpretation is cor- chair for philosophy of the inductive sciences since rect, then what exactly the Aufbau owes to Russell 1922. In the meetings of the Vienna Circle, the type- (and traditional empiricism) becomes uncertain. script of the Aufbau was read and discussed. What However, as Putnam (1994, 281) also points out, Carnap seems to have found most congenial in the this reinterpretation goes too far: Though the proj- Circle—besides its members’ concern for science ect of the Aufbau is not identical to that of Russell’s and competence in modern logic—was their rejec- external world program, there is sufficient con- tion of traditional metaphysics. Over the years, gruence between the two projects for Carnap to besides Carnap and Schlick, the Circle included have correctly believed that he was carrying out Herbert Feigl, Kurt Go¨del, Hans Hahn, Karl Russell’s program. In particular, the formal con- Menger, Otto Neurath, and Friedrich Waismann, structions of the Aufbau are a necessary prerequi- though Go¨del would later claim that he had little site for the development of the epistemology that sympathy for the antimetaphysical position of the Russell had in mind: One must be able to construct other members. The meetings of the Circle were the world formally from a phenomenalist basis characterized by open, intensely critical, discussion before one can suggest that this construction with no tolerance for ambiguity of formulation or shows that the phenomena are the source of knowl- lack of rigor in demonstration. The members of the edge of the world. Moreover, this reinterpretation Circle believed that philosophy was a collective ignores the epistemological remarks scattered enterprise in which progress could be made. These throughout the Aufbau itself, including Carnap’s attitudes, even more than any canonical set of posi- concern for the epistemic primacy of the basis he tions, characterized the philosophical movement— begins with. Savage (2003) has recently pointed out initially known as logical positivism and later as that the salient difference between Russell’s and logical empiricism—that emerged from the work of Carnap’s project is that whereas the former chose the members of the Circle and a few others, espe- sense data as his point of departure, the latter chose ciallyPROOF Reichenbach. However, besides rejecting tra- elementary experiences. But this difference is simply ditional metaphysics, most members of the Circle a result of Carnap’s having accepted the results of accepted logicism and a sharp distinction between Gestalt psychology as having definitively shown analytic and synthetic truths. The analytic was what may be taken as individual experiential bases; identified with the a priori; the synthetic with the other than that, that is, with respect to the issue of a posteriori (see Analyticity). A. J. Ayer, who at- empiricism, it has no philosophical significance. tended some meetings of the Circle in 1933 (after In any case, by this time of his intellectual devel- Carnap had left—see below), returned to Britain opment, Carnap had fully endorsed not only the and published Language, Truth and Logic (Ayer logicism of the Principia, but also the form that 1936) (see Ayer, Alfred Jules). This short book Whitehead and Russell had given to logic (that is, did much to popularize the views of the Vienna FIRST Circle among Anglophone philosophers, though it the ramified theory of types including the axioms of infinity and reducibility) in that work. However, lacks the sophistication that is found in the writings Poincare´ also emerges as a major influence during of the members of the Circle, particularly Carnap. this period. Carnap did considerable work on the Under Neurath’s influence, during his Vienna conceptual foundations of physics in the 1920s, and years, Carnap abandoned the phenomenalist lan- some of this work—in particular, his analysis of the guage he had preferred in the Aufbau and came to relationship between causal determination and the accept physicalism (see Neurath, Otto; Physical- structure of space—shows strong conventionalist ism). The epistemically privileged language is one attitudes (Carnap 1924; see also 1923 and 1926) in which sentences reporting empirical knowledge (see Conventionalism; Poincare´, Henri). of the world (‘‘protocol sentences’’) employ terms

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CARNAP, RUDOLF

referring to material bodies and their observable the status of the principle itself is, that is, whether properties (see Protocol Sentences). From Carnap’s it is meaningful by its own criterion of meaningful- point of view, the chief advantage of a physicalist ness. Carnap, as well as other members of the language is its intersubjectivity. Physicalism, more- Vienna Circle including Hahn and Neurath, rea- over, came hand-in-hand with the thesis of the lized that a weaker criterion of meaningfulness was ‘‘unity of science,’’ that is, that the different empir- necessary. Thus began the program of the ‘‘liberal- ical sciences (including the social sciences) were ization of empiricism.’’ There was no unanimity merely different branches of a single unified science within the Vienna Circle on this point. The differ- (see Unity of Science Movement). To defend this ences between the members are sometimes de- thesis, it had to be demonstrated that psychology scribed as those between a conservative ‘‘right’’ could be based on a physicalist language In an wing, led by Schlick and Waismann, which rejected important paper only published somewhat later, both the liberalization of empiricism and the epis- Carnap ([1932] 1934) attempted that demonstration temological antifoundationalism of the move to (see Unity and Disunity of Science). Carnap’s adop- physicalism, and a radical ‘‘left’’ wing, led by Neur- tion of physicalism was final; he never went back ath and Carnap, which endorsed the opposite to a phenomenalist language. However, what he views. The ‘‘left’’ wing also emphasized fallibilism meant by ‘‘physicalism’’ underwent radical trans- and pragmatics; Carnap went far enough along this formations over the years. By the end of his life, it line to suggest that empiricism itself was a proposal meant no more than the adoption of a nonsolipsistic to be accepted on pragmatic grounds. This differ- language, that is, one in which intersubjective is ence also reflected political attitudes insofar as possible (Carnap 1963b). Neurath and, to a lesser extent, Carnap viewed In the Vienna Circle, Wittgenstein’s Tractatus was science as a tool for social reform. discussed in detail. Carnap found Wittgenstein’s The precise formulation of what came to be rejection of metaphysics concordant with the views called the criterion of cognitive significance took he had developed independently. Partly because of three decades (see Hempel 1950; Carnap 1956 and Wittgenstein’s influence on some members of the 1961) (see Cognitive Significance). In an important Circle (though not Carnap), the rejection of meta- pair of papers, Testability and Meaning, Carnap physics took the form of an assertion that the sen- (1936–1937) replaced the requirement of verifica- tences of metaphysics are meaningless in the sense of tion with that of confirmation; at this stage, he being devoid of cognitive content. Moreover, the made no attempt to quantify the latter. Individual decision whether a sentence is meaningful was to terms replace sentences as the units of meaning. be made on the basis of the principle of verifiability, Universal generalizations are no longer problemat- which claims that the meaning of a sentence is given ic; though they cannot be conclusively verified, by the conditions of its (potential) verification (see theyPROOF can yet be confirmed. Moreover, in Testability Verifiability). Observation terms are directly mean- and Meaning, theoretical terms no longer require ingful on this account (see Observation). Theoreti- explicit definition from observational ones in order cal terms acquire meaning only through explicit to acquire meaning; the connection between the definition from observation terms. Carnap’s major two may be indirect through a system of implicit innovation in these discussions within the Circle was definitions. Carnap also provides an important to suggest that even the thesis of realism—asserting pioneering discussion of disposition predicates. the ‘‘reality’’ of the external world—is meaningless, a position not shared by Schlick, Neurath, or Reich- The Syntactic Phase enbach. Problems generated by meaningless ques- tions became the celebrated ‘‘pseudo-problemsFIRST’’ of Meanwhile, in 1931, Carnap had moved to Prague, philosophy (Carnap [1928] 1967). where he held the chair for natural philosophy at Wittgenstein’s principle of verifiability posed the German University until 1935, when, under the fairly obvious problems in any scientific context. shadow of Hitler, he emigrated to the United States. No universal generalization can ever be verified. Toward the end of his Vienna years, a subtle but Perhaps independently, Karl Popper perceived the important shift in Carnap’s philosophical interests same problem (see Popper, Karl Raimund). This had taken place. This shift was from a predominant led him to replace the requirement of verifiability concern for the foundations of physics to that for with that of falsifiability, though only as a criterion the foundations of mathematics and logic, even to demarcate science from metaphysics, and not though he remained emphatic that the latter were as one to be also used to demarcate meaningful important only insofar as they were used in the from meaningless claims. It is also unclear what empirical sciences, especially physics.

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CARNAP, RUDOLF

In Vienna and before, following Frege and last few sections of Syntax also present a few Russell, Carnap espoused logicism in its convention- results regarding the syntax of any language and al sense, that is, as the doctrine that held that the also discuss the philosophical ramifications of the concepts of mathematics were definable from those syntactic point of view. (Sarkar 1992 attempts a of logic, and the theorems of mathematics were de- comprehensible reconstruction of the notoriously rivable from the principles of logic. In the aftermath difficult formalism of Syntax.) of Go¨del’s (1931) incompleteness theorems, how- Language I, which Carnap calls ‘‘definite,’’ is ever, Carnap abandoned this type of logicism and intended as a neutral core of all logically interesting opted instead for the requirement that the concepts languages, neutral enough to satisfy the strictures of mathematics and logic always have their custom- of almost any intuitionist or constructivist. It per- ary (that is, everyday) interpretation in all contexts. mits the definition of primitive recursive arithmetic He also began to advocate a strong conventionalism and has bounded quantification (for all x up to regarding what constituted ‘‘logic.’’ some upper bound) but not much more. Its syntax Besides the philosophical significance of Go¨del’s is fully constructed formally. Language II, which results, what impressed Carnap most about that is ‘‘indefinite’’ for Carnap, is richer. It includes work was Go¨del’s arithmetization of syntax. Down- Language I and has sufficient resources for the playing the distinction between an object language formulation of all of classical mathematics, and is and its metalanguage, Carnap interpreted this pro- therefore nonconstructive. Moreover, Carnap per- cedure as enabling the representation of the syntax mits descriptive predicates in each language. Thus, of a language within the language itself. At this the resources of Language II are strong enough to point Carnap had not yet accepted the possibility permit, in principle, the formulation of classical of semantics, even though he was aware of some of physics. The important point is that because of Tarski’s work and had had some contact with the the principle of tolerance, the choice between Lan- Polish school of logic. In this context, the represen- guages I and II or, for that matter, any other tation of the syntax of a language within itself sug- syntactically specified language, is not based on gested to Carnap that all properties of a language factual considerations. If one wants to use mathe- could be studied within itself through a study of matics to study physics in the customary way, Lan- syntax. guage II is preferable, since as yet, nonconstructive These positions were codified in Carnap’s major mathematics remains necessary for physics. But the work from this period, The Logical Syntax of Lan- adoption of Language II, dictated by the pragmatic guage (Carnap 1934b and 1937). The English trans- concern for doing physics, does not make Language lation includes material that had to be omitted I incorrect. This was Carnap’s response to the foun- from the German original due to a shortage of dational disputes of mathematics: By tolerance they paper; the omitted material was separately published arePROOF defined out of existence. in German as papers (Carnap 1934a and 1935). The price paid if one adopts the principle of Conventionalism about logic was incorporated tolerance is a radical conventionalism about what into the well-known principle of tolerance: constitutes logic. Conventionalism, already appar- ent in Carnap’s admission of both a phenomenalist It is not our business to set up prohibitions but to arrive at and a physicalist possible basis for construction in conventions [about what constitutes a logic] ... . In logic, there are no morals. Every one is at liberty to the Aufbau, and strongly present in the works on build up his own logic, i.e., his own form of language, the foundations of physics in the 1920s, had now as he wishes. All that is required is that, if he wishes to been extended in Syntax to logic. As a conse- discuss it, he must state his method clearly, and give quence, what might be considered to be the most syntactic rules instead of philosophicalFIRST arguments. important question in any mathematical or empirical context—the choice of language—became prag- (Carnap 1937, 51–52; emphasis in the original) matic. This trend of relegating troublesome ques- Logic, therefore, is nothing but the syntax of tions to the realm of pragmatics almost by fiat, language. thereby excusing them from systematic philosophi- In Syntax, the principle of tolerance allows cal exploration, became increasingly prevalent in Carnap to navigate the ongoing disputes between Carnap’s views as the years went on. logicism, formalism, and intuitionism/constructiv- Syntax contained four technical innovations in ism in the foundations of mathematics without logic that are of significance: (i) a definition of abandoning any insight of interest from these analyticity that, as was later shown by S. C. Kleene, schools. Carnap begins with a detailed study of mimicked Tarski’s definition of truth for a forma- the construction of two languages, I and II. The lized language; (ii) a proof, constructed by Carnap

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CARNAP, RUDOLF

independently of Tarski, that truth cannot be de- transformations on sentences: those involving fined as a syntactic predicate in any consistent for- ‘‘the method of derivation’’ or ‘‘d-method,’’ and malized language; (iii) a rule for infinite induction those involving the ‘‘method of consequence’’ or (in Language I) that later came to be called the ‘‘c-method.’’ Both of these were supposed to be omega rule; and (iv), most importantly, a generali- syntactic, but there is a critical distinction between zation of Go¨del’s first incompleteness theorem that them. The former allows only a finite number of has come to be called the fixed-point lemma. With elementary steps. The latter places no such restric- respect to (iv), what Carnap proved is that in a tion and is, therefore, more ‘‘indefinite.’’ Terms language strong enough to permit arithmetization, defined using the d-method (‘‘d-terms’’) include for any syntactic predicate, one can construct a ‘‘derivable,’’ ‘‘demonstrable,’’ ‘‘refutable,’’ ‘‘resolu- sentence that would be interpreted as saying that ble,’’ and ‘‘irresoluble’’; the corresponding c-terms it satisfies that predicate. If the chosen predicate is are ‘‘consequence,’’ ‘‘analytic,’’ ‘‘contradictory,’’ unprovability, one gets Go¨del’s result. ‘‘L-determinate,’’ and ‘‘synthetic.’’ After the con- Besides the principle of tolerance, the main phil- version to semantics, Carnap proposed that the osophical contribution of Syntax was the thesis c-method essentially captured what semantics that philosophy consisted of the study of logical allowed; the c-terms referred to semantic concepts. syntax. Giving a new twist to the Vienna Circle’s Thus semantics involves a kind of formalization, claim that metaphysical claims were meaningless, though one that is dependent on stronger inference Carnap argues and tries to show by example that rules than the syntactical ones. In this sense, as sentences making metaphysical claims are all syn- Church (1956, 65) has perceptively pointed out, AU:3 tactically ill-formed. Moreover, since the arithme- Carnap—and Tarski—reduce semantics to formal tization procedure shows that all the syntactic rules rules, that is, syntax. Thus emerges the interpreta- of a language can be formulated within the lan- tion of deductive logic that has since become the guage, even the rules that determine what sentences textbook version, so commonly accepted that is has are meaningless can be constructed within the lan- become unnecessary to refer to Carnap when one guage. All that is left for philosophy is a study of uses it. For Carnap, the semantic move has an the logic of science. But, as Carnap (1937) puts it: important philosophical consequence: Philosophy ‘‘The logic of science (logical methodology) is noth- is no longer to be replaced just by the syntax of the ing else than the syntax of the language of science.... language of science; rather, it is to be replaced by the To share this view is to substitute logical syntax syntax and the semantics of the language of science. for philosophy’’ (7–8; emphasis in original). The Carnap’s (1947) most original—and influential— claims of Syntax are far more grandiose—and work in semantics is Meaning and Necessity, where more flamboyant—than anything in the Aufbau. the basis for an intensional semantics was laid down. LargelyPROOF following Frege, intensional concepts are Semantics distinguished from extensional ones. Semantical rules are introduced and the analytic/synthetic dis- In the late 1930s Carnap abandoned the narrow tinction is clarified by requiring that any definition syntacticism of Syntax and, under the influence of of analyticity must satisfy the (meta-) criterion that Tarski and the Polish school of logic, came to accept analytic sentences follow from the semantical rules semantics. With this move, Carnap’s work enters its alone. By now Carnap had fully accepted that final mature phase. For the first time, he accepted semantic concepts and methods are more funda- that the concept of truth can be given more than mental than syntactic ones: The retreat from the pragmatic content. Thereupon, he turned to the flamboyance of Syntax was complete. The most systematization of semantics withFIRST characteristic important contribution of Meaning and Necessity vigor, especially after his immigration to the United was the reintroduction into logic, in the new inten- States, where he taught at the University of Chicago sional framework, of modal concepts that had been from 1936 to 1952. In his contribution to the Inter- ignored since the pioneering work of Lewis (1918). national Encyclopedia of Unified Science (Carnap In the concluding chapter of his book, Carnap intro- 1939), on the foundations of logic and mathematics, duced an operator for necessity, gave semantic rules the distinctions among syntactic, semantic, and for its use, and showed how other modal concepts pragmatic considerations regarding any language such as possibility, impossibility, necessary implica- are first presented in their mature form. tion, and necessary equivalence can be defined from Introduction to Semantics, which followed in this basis. 1942, develops semantics systematically. In Syntax By this point, Carnap had begun to restrict his Carnap had distinguished between two types of analyses to exactly constructed languages, implicitly

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abandoning even a distant hope that they would only with respect to a class of terms, a theoretical have any direct bearing on natural languages. The language, an observation language, correspondence problem with the latter is that their ambiguities rules between them, and a theory. Relativization to made them unsuited for the analysis of science, a theory is critical to avoiding the problems that which, ultimately, remained the motivation of all beset earlier attempts to find such a criterion. Car- of Carnap’s work. Nevertheless, Carnap’s distinc- nap proves several theorems that are designed to tion between the analytic and the synthetic came show that the criterion does capture the distinction under considerable criticism from many, including between scientific and nonscientific discourse. This Quine (1951), primarily on the basis of considera- criterion was criticized by Roozeboom (1960) and tions about natural languages (see Analyticity; Kaplan (1975), but these criticisms depend on Quine, Willard Van Orman). Though philosophical modifying Carnap’s original proposal in impor- fashion has largely followed Quine on this point, at tant ways. According to Kaplan, Carnap accepted least until recently, Carnap was never overly im- his criticism, though there is apparently no in- pressed by this criticism (Stein 1992). The analytic/ dependent confirmation of that fact. However, synthetic distinction continued to be fundamental Carnap (1961) did turn to a different formalism to his views, and, in a rejoinder to Quine, Carnap (Hilbert’s e-operator) in what has been interpreted argued that nothing prevented empirical linguistics as his last attempt to formulate such a criterion from exploring intensions and thereby discovering (Kaplan 1975), and this may indicate dissatisfac- cases of synonymy and analyticity (Carnap 1955). tion with the 1956 attempt. If so, it remains unclear Carnap’s (1950a) most systematic exposition of why: That attempt did manage to avoid the techni- his final views on ontology is also from this period. cal problems associated with the earlier attempts of A clear distinction is maintained between questions the logical empiricists (see Cognitive Significance). that are internal to a linguistic framework and questions that are external to it. The choice of a Probability and Inductive Logic linguistic framework is to be based not on cognitive but on pragmatic considerations. The external From 1941 onward Carnap also began a systematic question of ‘‘realism,’’ which ostensibly refers to attempt to analyze the concepts of probability and the ‘‘reality’’ of entities of a framework in some to formulate an adequate inductive logic (a logic of sense independent of it, rather than to their ‘‘reali- confirmation), a project that would occupy him for ty’’ within it after the framework has been accept- the rest of his life. Carnap viewed this work as an ed, is rejected as noncognitive (see Scientific extension of the semantical methods that he had Realism). This appears to be an anti-‘‘realist’’ posi- been developing for the last decade. This under- tion, but it is not in the sense that within a frame- scores an interesting pattern in Carnap’s intellectu- work, Carnap is tolerant of the abstract entities alPROOF development. Until the late 1930s Carnap viewed that bother nominalists. The interesting question syntactic categories only as nonpragmatically spec- becomes the pragmatic one, that is, what frame- ifiable; questions of truth and confirmation were works are fruitful in which contexts, and Carnap’s viewed as pragmatic. His conversion to semantics attitude toward the investigation of various alter- saw the recovery of truth from the pragmatic to the native frameworks remains characteristically and semantic realm. Now, confirmation followed truth consistently tolerant. down the same pathway. Carnap continued to explore questions about the In Logical Foundations of Probability (1950b), nature of theoretical concepts and to search for a his first systematic analysis of probability, Carnap criterion of cognitive significance, preoccupations distinguished between two concepts of probability: of the logical empiricists that dateFIRST back to the ‘‘statistical probability,’’ which was the relevant Vienna Circle. Carnap (1956) published a detailed concept to be used in empirical contexts and gener- exposition of his final views regarding the relation ally estimated from the relative frequencies of between the theoretical and observational parts of events, and ‘‘logical probability,’’ which was to be a scientific language. This paper emphasizes the used in contexts such as the confirmation of scien- methodological and pragmatic aspects of theoreti- tific hypotheses by empirical data. Though the latter cal concepts. It also contains his most subtle, concept, usually called the ‘‘logical interpreta- though not his last, attempt to explicate the notion tion’’ of probability, went back to Keynes (1921), of the cognitive significance of a term and thus Carnap provides its first systematic explication (see establish clearly the boundary between scientific Probability). and nonscientific discourse. However, the criterion Logical probability is explicated from three he formulates makes theoretical terms significant different points of view (1950b, 164–8): (i) as a

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conditional probability c(h,e), which measures the logic, often with several collaborators, over the degree of confirmation of a hypothesis h on the next decade. There were significant modifications basis of evidence e (if c(h,e) ¼ r, then r is deter- of his earlier attempts to formulate a systematic mined by logical relations between h and e); (ii) as a inductive logic (see Carnap and Jeffrey 1971 and rational degree of belief or fair betting quotient (if Jeffrey 1980. An excellent introduction to this part c(h,e) ¼ r, then r is a fair bet on h if e correctly of Carnap’s work on inductive logic is Hilpinen describes the total knowledge available to a bettor); 1975). Obviously impressed by the earlier work of and (iii) as the limit of relative frequencies in some Ramsey and de Finetti, Carnap (1971a) returned to cases. According to Carnap, the first of these, which the second of his three 1950 explications of logical specifies a confirmation function (‘‘c-function’’), is probability and emphasized the use of inductive the concept that is most relevant to the problem logic in decision problems. of induction. In the formal development of the More importantly, Carnap, in A Basic System of theory, probabilities are associated with sentences Inductive Logic (1971b and 1980), finally recog- of a formalized language. nized that attributing probabilities to sentences In Foundations, Carnap (1950b) believed that a was too restrictive. If a conceptual system uses unique measure c(h,e) of the degree of confirmation real numbers and real-valued functions, no lan- can be found, and he even proposed one (viz., guage can express all possible cases using only Laplace’s rule of succession), though he could not sentences or classes of sentences. Because of this, prove its uniqueness satisfactorily. His general he now began to attribute probabilities to events or strategy was to augment the standard axioms of propositions (which are taken to be synonymous). the probability calculus by a set of ‘‘conventions This finally brought some concordance between on adequacy’’ (285), which turned out to be equiv- his formal methods and those of mathematical sta- alent to assumptions about the rationality of tisticians interested in epistemological questions. degrees of belief that had independently been pro- Propositions are identified with sets of models; posed by both Ramsey and de Finetti (Shimony however, the fields of the sets are defined using 1992). In a later work, The Continuum of Inductive the atomic propositions of a formalized language. Methods, using the conventions on adequacy and Thus, though probabilities are defined as measures some plausible symmetry principles, Carnap (1952) of sets, they still remain relativized to a particular managed to show that all acceptable c-functions formalized language. Because of this, and because could be parameterized by a single parameter, a the languages considered remain relatively simple real number, l 2 [0,1]. The trouble remained (mostly monadic predicate languages), much of this that there is no intuitively appealing a priori strate- work remains similar to the earlier attempts. gy to restrict l to some preferably very small subset By this point Carnap had abandoned the hope of [0,1]. At one point, Carnap even speculated ofPROOF finding a unique c-function. Instead, he distin- that it would have to be fixed empirically. Unfor- guished between subjective and objective app- tunately, some higher-order induction would then roaches in inductive logic. The former emphasizes be required to justify the procedure for its estima- individual freedom in the choice of necessary con- tion, and potentially, this leads to infinite regress ventions; the latter emphasizes the existence of lim- (see Confirmation Theory; Inductive Logic). itations. Though Carnap characteristically claimed Carnap spent 1952–54 at the Institute for Ad- to keep an open mind about these two approaches, vanced Study at Princeton, New Jersey, where he his emphasis was on finding rational a priori prin- continued to work on inductive logic, often in col- ciples that would systematically limit the choice of laboration with John Kemeny. He also returned to c-functions. Carnap was still working on this proj- the foundations of physics, apparentlyFIRST motivated ect when he died on September 14, 1970. He had by a desire to trace and explicate the relations not finished revising the last sections of the second between the physical concept of entropy and an part of the Basic System, both parts of which were abstract concept of entropy appropriate for induc- published only posthumously. tive logic. His discussion with physicists proved Toward the end of his life, Carnap’s concern for to be disappointing and he did not publish his political and social justice had led him to become an results. (These were edited and published by Abner active supporter of an African American civil rights Shimony [Carnap 1977] after Carnap’s death.) organization in Los Angeles. According to Stegmu¨l- In 1954 Carnap moved to the University of Cali- ler (1972, lxvi), the ‘‘last photograph we have of fornia at Los Angeles to assume the chair that had Carnap shows him in the office of this organization, become vacant with Reichenbach’s death in 1953. in conversation with various members. He was the There he continued to work primarily on inductive only white in the discussion group.’’

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The Legacy be counterproductive; and his program of natura- lizing epistemology has yet to live up to its initial Thirty-five years after Carnap’s death it is easier to promise. Putnam’s ‘‘internal realism’’ is based on assess Carnap’s legacy, and that of logical empiri- and revives Carnap’s views on ontology, and Kuhn cism, than it was in the 1960s and 1970s, when a is perhaps now better regarded as having contribu- new generation of analytic philosophers and philo- ted significantly to the sociology rather than to the sophers of science apparently felt that they had to epistemology of science. reject that work altogether in order to be able to However, to note that some of the traditionally define their own philosophical agendas. This reac- fashionable objections to Carnap and logical em- tion can itself be taken as evidence of Carnap’s piricism cannot be sustained does not show that seminal influence, but, nevertheless, it is fair to that work deserves a positive assessment on its say that Carnap and logical empiricism fell into a own. There still remains the question: What, exact- period of neglect in the 1970s from which it began ly, did Carnap contribute? The answer turns out to to emerge only in the late 1980s and early 1990s. be straightforward: The textbook picture of deduc- Meanwhile it became commonplace among philo- tive logic that is in use today is the one that Carnap sophers to assume that Carnap’s projects had produced in the early 1940s after he came to ac- failed. knowledge the possibility of semantics. The fixed- Diagnoses of this failure have varied. For some it point lemma has turned out to be an important was a result of the logical empiricists’ alleged in- minor contribution to logic. The reintroduction of ability to produce a technically acceptable criterion modal logic into philosophy opened up new vistas for cognitive significance. For others, it was be- for Kripke and others in the 1950s and 1960s. cause of Quine’s dicta against the concept of ana- Carnap’s views on ontology continue to influence lyticity and the analytic/synthetic distinction (see philosophers today. Moreover, even though the Analyticity; Quine, Willard Van Orman). Some project of inductive logic seems unsalvageable to took Popper’s work to have superseded that of most philosophers, it is hard to deny that Carnap Carnap and the logical empiricists (see Popper, managed to clarify significantly the ways in which Karl Raimund). Many viewed Kuhn’s seminal concepts of probability must be deployed in the work on scientific change to have shown that the empirical sciences and why the problem of in- project of inductive logic was misplaced; they, and ductive logic is so difficult. But, most of all, Carnap others, generally regarded Carnap’s attempt to ex- took philosophy to a new level of rigor and plicate inductive logic to have been a failure (see clarity, accompanied by an open-mindedness (codi- Kuhn, Thomas; Scientific Change). Finally, a new fied in the principle of tolerance) that, unfortunate- school of ‘‘scientific realists’’ attempted to escape ly, is not widely shared in contemporary analytic Carnap’s arguments against external realism (see philosophy.PROOF Scientific Realism). SAHOTRA SARKAR There can be little doubt that Carnap’s project of founding inductive logic has faltered. He never claimed that he had gone beyond preliminary References explorations of possibilities, and, though there has been some work since, by and large, epistemolo- Ayer, A. J. (1936), Language, Truth and Logic. London: gists of science have abandoned that project in Gollancz. Carnap, R. (1922), Der Raum. Berlin: von Reuther and favor of less restrictive formalisms, for instance, Reichard. those associated with Bayesian or Neyman- ——— (1923), ‘‘U¨ ber die Aufgabe der Physik und die Pearson statistics (see Bayesianism; Statistics, Phi- Anwendung des Grundsatzes der Einfachsteit,’’ Kant- losophy of). But, with respect to everyFIRST other case Studien 28: 90–107. mentioned in the last paragraph, the situation is far ——— (1924), ‘‘Dreidimensionalita¨t des Raumes und Kau- salita¨t: Eine Untersuchung u¨ber den logischen Zusam- less clear. It has already been noted that Carnap’s menhang zweier Fiktionen,’’ Annalen der Philosophie und final criterion for cognitive significance does not philosophischen Kritik 4: 105–130. suffer from any technical difficulty no matter ——— (1926), Physikalische Begriffsbildung. Karlsruhe, what its other demerits may be. Quine’s dicta Germany: Braun. against analyticity no longer appear as persuasive ——— ([1928] 1967), The Logical Structure of the World and Pseudoproblems in Philosophy. Berkeley and Los as they once did (Stein 1992); Quine’s preference Angeles: University of California Press. for using natural—rather than formalized— ——— ([1932] 1934. The Unity of Science. London: Kegan language in the analysis of science has proved to Paul, Trench, Trubner & Co.

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——— (1934a), ‘‘Die Antinomien und die Unvollsta¨ndig- Goodman, N. (1951), The Structure of Experience. Cam- keit der Mathematik,’’ Monatshefte fu¨r Mathematik und bridge, MA: Harvard University Press. Physik 41: 42–48. Haack, S. (1977), ‘‘Carnap’s Aufbau: Some Kantian Reflec- ——— (1934b), Logische Syntax der Sprache. Vienna: tions,’’ Ratio 19: 170–175. Springer. Hempel, C. G. (1950), ‘‘Problems and Changes in the Em- ——— (1935), ‘‘Ein Gu¨ltigskriterium fu¨r die Sa¨tze der piricist Criterion of Meaning,’’ Revue Internationale de klassischen Mathematik,’’ Monatshefte fu¨r Mathematik Philosophie 11: 41–63. und Physik 42: 163–190. Hilpinen, R. (1975), ‘‘Carnap’s New System of Inductive ——— (1936–1937), ‘‘Testability and Meaning,’’ Philoso- Logic,’’ in J. Hintikka (ed.), Rudolf Carnap, Logical phy of Science 3 and 4: 419–471 and 1–40. Empiricist: Materials and Perspectives. Dordrecht, Neth- ——— (1937), The Logical Syntax of Language. London: erlands: Reidel, 333–359. Kegan Paul, Trench, Trubner & Co. Jeffrey, R. C. (ed.) (1980), Studies in Inductive Logic and ——— (1939), Foundations of Logic and Mathematics. Chi- Probability (Vol. 2). Berkeley and Los Angeles: Univer- cago: University of Chicago Press. sity of California Press. ——— (1947), Meaning and Necessity: A Study in Semantics Kaplan, D. (1975), ‘‘Significance and Analyticity: A and Modal Logic. Chicago: University of Chicago Press. Comment on Some Recent Proposals of Carnap,’’ in ——— (1950a), ‘‘Empiricism, Semantics, and Ontology,’’ J. Hintikka (ed.), Rudolf Carnap, Logical Empiricist: Revue Internationale de Philosophie 4: 20–40. Materials and Perspectives. Dordrecht, Netherlands: ——— (1950b), Logical Foundations of Probability. Chi- Reidel, 87–94. cago: University of Chicago Press. Keynes, J. M. (1921), A Treatise on Probability. London: ——— (1952), The Continuum of Inductive Methods. Chi- Macmillan & Co. cago: University of Chicago Press. Lewis, C. I. (1918), A Survey of Symbolic Logic. Berkeley ——— (1955), ‘‘Meaning and Synonymy in Natural Lan- and Los Angeles: University of California Press. guages,’’ Philosophical Studies 7: 33–47. Putnam, H. (1994), ‘‘Comments and Replies,’’ in P. Clark ——— (1956), ‘‘The Methodological Character of Theoret- and B. Hale (eds.), Reading Putnam. Oxford: Blackwell, ical Concepts,’’ in H. Feigl and M. Scriven (eds.), The 242–295. Foundations of Science and the Concepts of Psychology Quine, W. V. O. (1951), ‘‘Two Dogmas of Empiricism,’’ and Psychoanalysis. Minneapolis: University of Minne- Philosophical Review 60: 20–43. sota Press, 38–76. Richardson, A. (1998), Carnap’s Construction of the World. ——— (1961), ‘‘On the Use of Hilbert’s e-Operator in Scien- Cambridge: Cambridge University Press. tific Theories,’’ in Y. Bar-Hillel, E. I. J. Poznanski, M. O. Roozeboom, W. (1960), ‘‘A Note on Carnap’s Meaning Rabin, and A. Robinson (eds.), Essays on the Founda- Criterion,’’ Philosophical Studies 11: 33–38. tions of Mathematics. Jerusalem: Magnes Press, 156–164. Sarkar, S. (1992), ‘‘‘The Boundless Ocean of Unlimited ——— (1963a), ‘‘Intellectual Autobiography,’’ in P. A. Possibilities’: Logic in Carnap’s Logical Syntax of Lan- Schilpp (ed.), The Philosophy of Rudolf Carnap.La guage,’’ Synthese 93: 191–237. Salle, IL: Open Court, 3–84. ——— (2003), ‘‘Husserl’s Role in Carnap’s Der Raum,’’ in ——— (1963b), ‘‘Replies and Systematic Expositions,’’ in T. Bonk (ed.), Language, Truth and Knowledge: Contri- P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap.La butions to the Philosophy of Rudolf Carnap. Dordrecht, Salle, IL: Open Court, 859–1013. Netherlands: Kluwer, 179–190. ——— (1971a), ‘‘Inductive Logic and Rational Decisions,’’ Sauer,PROOF W. (1985), ‘‘Carnap’s ’Aufbau’ in Kantianishcer in R. Carnap and R. C. Jeffrey (eds.), Studies in Inductive Sicht,’’ Grazer Philosophische Studien 23: 19–35. Logic and Probability (Vol. 1). Berkeley and Los Savage, C. W. (2003), ‘‘Carnap’s Aufbau Rehabilitated,’’ in Angeles: University of California Press, 5–31. T. Bonk (ed.), Language, Truth and Knowledge: Contri- ——— (1971b), ‘‘A Basic System of Inductive Logic, Part I,’’ butions to the Philosophy of Rudolf Carnap. Dordrecht, in R. Carnap and R. C. Jeffrey (eds.), Studies in Inductive Netherlands: Kluwer, 79–86. Logic and Probability (Vol. 1). Berkeley and Los Angeles: Shimony, A. (1992), ‘‘On Carnap: Reflections of a Meta- University of California Press, 33–165. physical Student,’’ Synthese 93: 261–274. ——— (1977), Two Essays on Entropy. Berkeley and Los Stegmu¨ller, W. (1972), ‘‘Homage to Rudolf Carnap,’’ in Angeles: University of California Press. R. C. Buck and R. S. Cohen (eds.), PSA 1970. Dordrecht, ——— (1980), ‘‘A Basic System of Inductive Logic, Part Netherlands: Reidel, lii–lxvi. II,’’ in R. C. Jeffrey (ed.), Studies in Inductive Logic and Stein, H. (1992), ‘‘Was Carnap Entirely Wrong, After All?’’ Probability (Vol. 2). Berkeley and Los Angeles: Univer- Synthese 93: 275–295. sity of California Press, 8–155. FIRST Carnap, R., and R. C. Jeffrey (eds.) (1971), Studies in Inductive Logic and Probability (Vol. 1). Berkeley and See also Analyticity; Confirmation Theory; Cogni- Los Angeles: University of California Press. tive Significance; Conventionalism; Hahn, Hans; Friedman, M. (1992), ‘‘Epistemology in the Aufbau,’’ Hempel, Carl Gustav; Induction, Problem of; Induc- Synthese 93: 191–237. tive Logic; Instrumentalism; Logical Empiricism; ——— (1999), Reconsidering Logical Empiricism. New Neurath, Otto; Phenomenalism; Protocol sen- York: Cambridge University Press. Go¨del, K. (1931), ‘‘U¨ ber formal unentscheidbare Sa¨tze der tences; Quine, Willard Van Orman; Reichenbach, Principia Mathematica und verwandter Systeme 1,’’ Hans; Scientific Realism; Schlick, Moritz; Space- Monatshefte fu¨r Mathematik und Physik 38: 173–198. Time; Verifiability; Vienna Circle

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CAUSALITY

Arguably no concept is more fundamental to science objectively deterministic but subjectively uncertain. than that of causality, for investigations into cases of Another difference lies in the distinction between existence, persistence, and change in the natural teleological (intentional, goal-oriented) and nonte- world are largely investigations into the causes of leological causality: While the broadly physical these phenomena. Yet the metaphysics and episte- sciences tend not to cite motives and purposes, the mology of causality remain unclear. For example, plant, animal, human, and social sciences often ex- the ontological categories of the causal relata have plicitly do. Contemporary treatments of teleological been taken to be objects (Hume [1739] 1978), events causality generally aim at avoiding the positing of (Davidson 1967), properties (Armstrong 1978), pro- anything like entelechies or ‘‘vital forces’’ (of the cesses (Salmon 1984), variables (Hitchcock 1993), sort associated with nineteenth-century accounts and facts (Mellor 1995). (For convenience, causes of biology), and also at avoiding taking teleological and effects will usually be understood as events in goals to be causes that occur after their effects (see what follows.) Complicating matters, causal rela- Salmon 1989, sec. 3.8, for a discussion). In Wright’s tions may be singular (‘‘Socrates’ drinking hemlock (1976) account of ‘‘consequence etiology,’’ teleolog- caused his death’’) or general (‘‘Drinking hem- ical behaviors (e.g., stalking a prey) are not caused lock causes death’’); hence the relata might be tokens by future catchings (which, after all, might not (e.g., instances of properties) or types (e.g., types of occur), but rather by the fact that the behavior in events) of the category in question. Other questions question has been often enough successful in the up for grabs are: Are singular causes metaphysically past that it has been evolutionarily selected for. and/or epistemologically prior to general causes or Experience or inferences may also be operative in vice versa (or neither)? What grounds the intuitive guiding behavior. While teleological causes raise asymmetry of the causal relation? Are macrocausal interesting questions for the causal underpinnings relations reducible to microcausal relations? And of behavior (especially concerning whether a perhaps most importantly: Are causal facts (e.g., naturalistically acceptable account of intentionality the holding of causal relations) reducible to non- can be given), the focus in what follows will be on causal facts (e.g., the holding of certain spatiotem- nonteleologicalPROOF causality, reflecting the primary poral relations)? concern of contemporary philosophers of causation.

Some Issues in Philosophy of Causality: The Varieties of Causation Singular vs. General Causation Is all singular causation ultimately general? Causes can apparently contribute to effects in a Different answers reflect different understandings variety of ways: by being background or standing of the notion of ‘production’ at issue in the platitude conditions, ‘‘triggering events,’’ omissions, factors ‘‘Causes produce their effects.’’ In generalist (or that enhance or inhibit effects, factors that remove a covering-law) accounts (see the sections on ‘‘Hume common preventative of an effect, etc.FIRST Traditionally and Pearson: Correlation, Not Causation’’ and accounts of causation have focussed on triggering ‘‘Contemporary Philosophical Accounts of Causal- events, but contemporary accounts are increasingly ity: Generalist Accounts’’ below), causal production expected to handle a greater range of this diversity. is a matter of law: Roughly, event C causes event E There may also be different notions of cause char- just in case C and E are instances of terms in a law acteristic of the domains of different sciences (see connecting events of C ’s type with events of E ’s Humphreys 1986; Suppes 1986): The seemingly in- type. The generalist interpretation is in part moti- deterministic phenomena of quantum physics may vated by the need to ground inductive reasoning: require treatment different from either the seeming- Unless causal relations are subsumed by causal ly deterministic processes of certain natural sciences laws, one will be unjustified in inferring that events or the ‘‘quasi-deterministic’’ processes characteris- of C ’s type will, in the future, cause events of E ’s tic of the social sciences, which are presumed to be type. Another motivation stems from thinking that

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identifying a sequence of events as causal requires antirealist is a matter of dispute, one philosopher’s identifying the sequence as falling under a (possibly reductive elimination being another’s reductive in- unknown) law. troduction.) By way of contrast, nonreductive gen- Alternatively, singularists (see ‘‘Singularist Ac- eralists (often called realists—see ‘‘Causal Powers, counts’’ below) interpret causal production as invol- Capacities, Universals, Forces’’ below) take the ving a singular causal process (variously construed) modally robust causal connection between event that is metaphysically prior to laws. Singularists types to be an irreducible feature of reality (see also argue for the epistemological priority of sin- Realism). Singularists also come in reductive or gular causes, maintaining that one can identify a realist varieties (see ‘‘Singularist Accounts’’ below). sequence as causal without assuming that the se- A second question of reducibility concerns quence falls under a law, even when the sequence whether a given account of causation aims to pro- violates modal presuppositions (as in Fair’s [1979] vide a conceptual analysis of the concept (hence to case: Intuitively, one could recognize a glass’s account for causation in bizarre worlds, containing breaking as causal, even if one antecedently thought magic, causal action at a distance, etc.) or aims to glasses of that type were unbreakable). account for the causal relation in the actual world, Counterfactual accounts (see ‘‘Counterfactual Ac- in terms of physically or metaphysically more fun- counts’’ below) analyze singular causes in terms of damental entities or processes. These different aims counterfactual conditionals (as a first pass, event C make a difference in what sort of cases and coun- causes event E just in case if C had not occurred, terexamples philosophers of causation take to then E would not have occurred). Whether a coun- heart when developing or assessing theories. A terfactual account should be considered singularist, common intermediate methodology focuses on however, depends on whether the truth of the coun- central cases, leaving the verdict on far-fetched terfactuals is grounded in laws connecting types of cases as ‘‘spoils for the victor.’’ events or in, e.g., propensities (objective single-case A third question of reducibility concerns whether chances) understood as irreducible to laws. Yet macrocausal relations (holding between entities, or another option is to deny that either singular or expressed by laws, in the special sciences) are re- general causes are reducible to the other, and go on ducible to microcausal relations (holding between to give independent treatments of each type (as in entities, or expressed by laws, in fundamental phys- Sober 1984). ics). This question arises from a general desire to understand the ontological and causal underpin- nings of the structured hierarchy of the sciences, Reduction vs. Nonreduction and from a need to address, as a special case, the There are at least three questions of reducibility ‘‘problem of mental causation,’’ of whether and at issue in philosophical accounts of causation, howPROOF mental events (e.g., a feeling of pain) can be which largely cut across the generalist/singularist causally efficacious vis-a`-vis certain effects (e.g., distinction. The first concerns whether causal grimacing) that appear also to be caused by the facts (e.g., the holding of causal relations) are re- brain events (and ultimately, fundamental physical ducible to noncausal facts (e.g., the holding of events) upon which the mental events depend. certain spatiotemporal relations). Hume’s general- Causal reductionists (Davidson 1970; Kim 1984) ist reduction of causality (see ‘‘Hume and Pearson: suggest that mental events (more generally, macro- Correlation, Not Causation’’ below) has a projec- level events) are efficacious in virtue of superven- tivist or antirealist flavor: According to Hume, the ing on (or being identical with) efficacious physical seeming ‘‘necessary connexion’’ between cause and events. Many worry, however, that these appro- effect is a projection of a psychologicalFIRST habit of aches render macro-level events causally irrelevant association between ideas, which habit is formed (or ‘‘epiphenomenal’’). Nonreductive approaches to by regular experience of events of the cause type macro-level causation come in both physicalist and being spatially contiguous and temporally prior to nonphysicalist varieties (Wilson 1999 provides an events of the effect type. Contemporary neo overview; see Physicalism). Some physicalists posit Humeans (see ‘‘Hempel: Explanation, Not Causa- a relation (e.g., the determinable/determination re- tion’’ and ‘‘Probabilistic Relevance Accounts’’ lation or proper parthood) between macro- and below) dispense with Hume’s psychologism, focus- micro-level events that entails that the set of causal ing instead on the possibility of reducing causal powers of a given macrolevel event M (roughly, the relations and laws to objectively and noncausally set of causal interactions that the event, in appropri- characterized associations between events. (Whe- ate circumstances, could enter into) is a proper sub- ther such accounts are appropriately deemed set of those of the micro-level event P upon which M

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depends. In this ‘‘proper subset’’ strategy, the fact effects and, in accordance with what Reichenbach that the sets of causal powers are different provides called ‘‘the principle of the common cause,’’ the some grounds for claiming that M is efficacious in probabilistic dependence of the effects on each its own right, but since each individual causal power other is ‘‘screened off ’’—goes away—when the of M is identical with a causal power of P, the two common cause is taken into account. Such forks events are not in causal competition. In another are, he claimed, always (or nearly always) open to nonreductive strategy—emergentism—the causal the future and closed to the past. Others have efficacy of at least some macro-level events (nota- suggested that the direction of causation is fixed bly, mental events) is due to their having genuinely by the direction of increasing entropy, or (more new causal powers not possessed by the physical speculatively) by the direction of quantum collapse events on which the mental events depend (see of the wave packet. Alternatively, Price (1992) sug- Emergence). When the effect in question is physi- gests that human experience of manipulating cal, such powers violate the causal closure of causes provides a basis for the (projected) belief the physical (the claim that every physical effect that causality is forward directed in time (see has a fully sufficient physical cause); but such a ‘‘Counterfactuals and Manipulability’’ below). All violation arguably is not at odds with any cher- these accounts nonstipulatively explain the usual ished scientific principles, such as conversation temporal direction of causal processes. But neither laws (see McLaughlin 1992). stipulative nor nonstipulative appeals to temporal direction seem to explain the asymmetry of causa- Features of Causality: Asymmetry, Temporal tion, which intuitively has more to do with causes Direction, Transitivity producing their effects (in some robust sense of ‘production’) than with causes being prior to their Intuitively, causality is asymmetric: If event C effects. Nonreductive accounts in which causality causes event E, then E does not cause C. Causality involves manifestations of powers or transfers of also generally proceeds from the past to the future. energy (or other conserved quantities) may be bet- How to account for these data remains unclear. ter situated to provide the required explanation, if The problem of explaining asymmetry is particu- such manifestations or transfers can be understood larly pressing for accounts that reductively analyze as directed (which remains controversial). causality in terms of laws of association, for it is Another feature commonly associated with cau- easy to construct cases in which the laws are revers- sality is transitivity: If C causes D, and D causes E, ible but the causation is not (see, for example, then C causes E. This assumption has come into Bromberger’s [1962] case in which the height h of question of late, largely due to the following sort of a flagpole is correlated with the length l of the case (see Kvart 1991): A man’s finger is severed in a shadow it casts, and vice versa, and intuitively factoryPROOF accident; a surgeon reattaches the finger, h causes l but l does not cause h). Both the asym- which afterward becomes perfectly functional. The metry and the temporal direction of causality can accident caused the surgery, and the surgery caused be accommodated (as in Hume) by stipulatively the finger’s functionality; but it seems odd to say that identifying causal with temporal asymmetry: the accident caused the finger’s functionality. The Causes differ from their effects in being prior to precise bearing of such cases on the transitivity claim their effects. But this approach rules out simulta- remains unclear (see Hall 2000 for a discussion). neous and backward causation, which are generally taken to be live possibilities; and it also rules out Challenges to Causality: Galileo, Newton, and reducing the direction of time to the (general) di- Maxwell—How, Not Why rection of causation, which some (e.g.,FIRST Reichenbach 1956) have wanted to do. The approach is also From the ancient through modern periods, ac- methodologically unsatisfactory, insofar as it fails counts of natural phenomena proceeded by citing to provide a basis for a unified resolution of pro- the powers and capacities of agents, bodies, and blems facing associationist accounts (e.g., the pro- mechanisms to bring about effects (see Hankinson blems of joint effects and of preemption discussed in 1998; Clatterbaugh 1999). Galileo’s account of the ‘‘Hume and Pearson: Correlation, Not Causation’’ physics of falling bodies initiated a different ap- below). proach to scientific understanding, which became Other strategies use physical processes to explain a matter of determining how certain measurable the temporal direction of causation. Reichenbach quantities were functionally correlated (the ‘‘how’’ appealed to the direction of ‘‘conjunctive forks’’: of things, or the kinematics), as opposed to deter- processes in which a common cause produces joint mining the causal mechanisms responsible for these

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correlations (the ‘‘why’’ of things, or the dynam- notwithstanding the availability of interpretations ics). This descriptive approach enabled scientific of scientific theories as purely descriptive, there are theories to be formulated with relatively high pre- compelling reasons (say, the need to avoid a sus- cision, which in turn facilitated predictive and ret- pect action at a distance) for taking the causally rodictive success; by way of contrast, explanations explanatory posits of scientific theories (e.g., fields in terms of (often unobservable) causal mechan- and forces) ontologically seriously. The deeper isms came to be seen as explanatorily otiose at questions here, of course, concern how to assess best and unscientific at worst. the ontological and causal commitments of scien- Newton’s famous claim in the Principia ([1687] tific theories; and at present there is no philosophi- 1999), ‘‘Hypotheses non fingo’’ (‘‘I frame no cal consensus on these important matters. In any hypotheses’’), regarding gravitation’s ‘‘physical case it is not enough, in assessing whether causes causes and seats’’ is often taken as evidence that he are implicated by physical theories, to note that advocated a descriptivist approach (though he terms like ‘‘cause’’ don’t explicitly appear in the speculated at length on the causes of gravitational equations of the theory, insofar as the commitments forces in the Optics). And while Maxwell drew of a given theory may transcend the referents of the heavily upon Faraday’s qualitative account of terms appearing in the theory, and given that many causally efficacious electromagnetic fields (and terms—force, charge, valence—that do appear are associated lines of force) in the course of develop- most naturally defined in causal terms (‘force,’ for ing his theories of electricity and magnetism, he example, is usually defined as that which causes later saw such appeals to underlying causes as heu- acceleration). It is also worth noting that the appar- ristic aids that could be dropped from the final ent symmetry of many equations, as well as the fact quantitative theory. that cause terms do not explicitly appear in scien- Such descriptivist tendencies have been encour- tific equations, may be artifacts of scientists’ using aged by perennial worries about the metaphysical the identity symbol as an all-purpose connective and epistemological presuppositions of explicitly between functional quantities, which enables the causal explanations (see ‘‘Causal Powers, Capaci- quantities to be manipulated using mathematical ties, Universals, Forces’’ below) and the concomi- techniques but is nonetheless implicitly understood tant seeming availability of eliminativist or as causally directed, as in f ¼ ma. reductivist treatments of causal notions in scientific Nor does scientific practice offer decisive illumi- laws. For example, Russell (1912) influentially ar- nation of whether scientific theorizing is or is not gued that since the equations of physics do not committed to causal notions: As with Maxwell, it contain any terms explicitly referring to causes or remains common for scientists to draw upon ap- causal relations and moreover (in conflict with the parently robustly causal notions when formulating presumed asymmetry of causality) appear to be orPROOF explaining a theory, even while maintaining that functionally symmetric (one can write a ¼ f /m as the theory expresses nothing beyond descriptive well as f ¼ ma), causality should be eliminated as functional correlations of measurable quantities. ‘‘a relic of a bygone age.’’ Jammer (1957) endorsed Perhaps it is better to attend to what scientists do a view in which forcebased dynamics is a sophisti- rather than what they say. That they rarely leave cated form of kinematics, with force terms being matters at the level of descriptive laws linking mere ‘‘methodological intermediaries’’ enabling the observables is some indication that they are not convenient calculation of quantities (e.g., accelera- concerned with just the ‘‘how’’ question—though, tions) entering into descriptions. And more recent- to be sure, the tension between descriptive and ly, van Fraassen (1980) has suggested that while causal/explanatory questions may recur at levels explanations going beyond descriptionsFIRST may serve below the surface of observation. various pragmatic purposes, these have no onto- logical or causal weight beyond their ability to ‘‘save the phenomena.’’ Hume and Pearson: Correlation, Not Causation Whether science really does, or should, focus on the (noncausally) descriptive is, however, deeply The Galilean view of scientific understanding as controversial. Galileo himself sought for explana- involving correlations among measurable quanti- tory principles going beyond description (see ties was philosophically mirrored in the empiricist Jammer 1957 for a discussion), and notwithstand- view that all knowledge (and meaning) is ultimately ing Newton’s professed neutrality about their grounded in sensory experience (see Empiricism). physical seats, he took forces to be the ‘‘causal The greatest philosophical challenge to causality principle[s] of motion and rest.’’ More generally, came from Hume, who argued that there is no

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experience of causes being efficacious, productive, preempting Billy’s rock from doing so), how is one or powerful vis-a`-vis their effects; hence ‘‘we only to rule out Billy’s rockthrowing as a cause? learn by experience the frequent conjunction of The above cases indicate that lawful sufficiency objects, without being ever able to comprehend alone does not satisfy causality. One response is to any thing like connexion between them’’ ([1748] adopt an account of events in which these are finely 1993, 46). In place of realistically interpreted ‘‘pro- individuated, so that, for example, the bottlebreak- ducing’’ theories of causation (see Strawson 1987 ing resulting from Suzy’s rockthrowing turns out to for a taxonomy), Hume offered the first regularity be of a different event type than a bottlebreaking theory of causation, according to which event C resulting from Billy’s rockthrowing (in which case causes event E just in case C and E occur, and Billy’s rockthrowing does not instantiate a rock- events of C ’s type have (in one’s experience) been throwing–bottlebreaking law, and so does not universally followed by, and spatially contiguous count as a cause). Another response incorporates to, events of E ’s type. (As discussed, such constant a proviso that the lawful sufficiency at issue is that conjunctions were the source of the psychological of the circumstances (as in Mackie’s ‘‘INUS’’ con- imprinting that was, for Hume, the ultimate locus dition account, in which a cause is an insufficient of causal connection.) Hume’s requirement of con- but necessary part of a condition that is, in the tiguity may be straightforwardly extended to allow circumstances, unnecessary but sufficient for the for causes to produce distant effects, via chains of effect). spatially contiguous causes and effects. Nor is lawful sufficiency alone necessary for cau- Hume’s requirement of universal association is sality, as the live possibility of irreducibly probabi- not sufficient for causation (night always follows listic causality indicates. This worry is usually day but night does not cause day). Nor is Hume’s sidestepped by a reconception of laws according requirement necessary, for even putting aside to which these need express only some lawlike pat- the requirement that one experience the association tern of dependence; but this reconception makes it in question, there are many causal events that hap- yet more difficult for regularity theorists to distin- pen only once (e.g., the big bang). The immediate guish spurious from genuine causes and laws (see move of neo-Humeans (e.g., Hempel and Oppen- ‘‘Probabilistic Relevance Accounts’’ below for heim 1948; Mackie 1965) is to understand the gen- developments). One neo-Humean response is to eralist component of the account in terms of laws allow certain a priori constraints to enter into de- of nature, which express the lawful sufficiency of termining what laws there are in a world (as in the the cause for the effect, and where (reflecting ‘‘best system’’ theory of laws of Lewis 1994) in Hume’s reductive approach) the sufficiency is not which the laws are those that systematize the phe- to be understood as grounded in robust causal nomena with the best combination of (predictive) production. One wonders, though, what is ground- strengthPROOF and (formal) simplicity, so as to accom- ing the laws in question if associations are neither modate probabilistic (and even uninstantiated) necessary nor sufficient for their holding and ro- laws (see also ‘‘Hempel: Explanation, Not Causa- bust production is not allowed to play a role. If the tion’’ below). laws are grounded in brute fact, it is not clear that The view that causation is nothing above (appro- AU:4 the reductive aim has been served (but see the priately complex) correlations was widespread fol- discussion of Lewis’s account of laws, below). lowing the emergence of social statistics in the In any case, neo-Humean accounts face several nineteenth century and was advanced by Karl problems concerning events that are inappropriate- Pearson, one of the founders of modern statistics, ly deemed causes (‘‘spurious causes’’). One is the in 1890 in The Grammar of Science. Pearson’s en- problem of joint effects, as when a virusFIRST causes first dorsement of this view was, like Hume’s, inspired a fever, and then independently causes a rash: Here by a rejection of causality as involving mysterious the fever is lawfully sufficient for, hence incorrectly productive powers, and contributed to causes (as deemed a cause of, the rash. Another involves opposed to associations) being to a large extent violations of causal asymmetry: Where events of expunged from statistics and from the many the cause’s type are lawfully necessary for events sciences relying upon statistics. An intermediate of the effect’s type, the effect will be lawfully suffi- position between these extremes, according to cient for (hence inappropriately deemed a cause of ) which causes are understood to go beyond correla- the cause. Cases of preemption also give rise to tions but are not given any particular metaphysical spurious causes: Suzy’s and Billy’s rockthrowings interpretation (in particular, as involving pro- are each lawfully sufficient for breaking the bottle; ductive powers), was advanced by the evolutio- but given that Suzy’s rock broke the bottle (thereby nary biologist Sewall Wright, the inventor of path

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analysis. Wright (1921) claimed that path analysis low probability, as in Scriven’s case (discussed by not only enabled previously known causal relations him prior to Hempel’s extension, and developed in to be weighted, but moreover enabled the testing of Scriven 1975), where the probability of paresis causal hypotheses in cases where the causal rela- given syphilis is low, but when paresis occurs, syph- tions were (as yet) unknown. Developed descen- ilis is the reason. A similar point applies to many dants and variants of Wright’s approach have quantum processes. Such cases gave rise to two found increasing favor of late (see ‘‘Bayesian Net- different approaches to handling probabilistic ex- works and Causal Models’’ below), contributing to planation (or causation, by those inclined to accept some rehabilitation of the notion of causality in the this notion). One approach (see Railton 1978) social sciences. locates probabilistic causality in propensities; the other (see ‘‘Probabilistic Relevance Accounts’’ be- Hempel: Explanation, Not Causation low) in more sophisticated probabilistic relations. At this point the line between accounts that are Logical empiricists were suspicious of causation reductive (in the sense of reducing causal to non- understood as a metaphysical connection in nature; causal goings-on) and nonreductive, as well as the instead they located causality in language, in- line between singularist and generalist accounts, terpreting causal talk as talk of explanation (see begins to blur. For while a propensity-based ac- Salmon 1989 for a discussion). On Hempel and count of causality initially looks nonreductive and Oppenheim’s (1948) influential D-N (deductive- singularist, some think that propensities can be nomological) model of scientific explanation, accommodated in a sophisticated associationist ac- event C explains event E just in case a statement count of laws; and while an account based on rela- expressing the occurrence of E is the conclusion of tions of probabilistic relevance initially looks an argument with premises, one of which expresses reductive and generalist, whether it is so depends the holding of a universal generalization to the on how the probabilities are interpreted (as given effect that events of C ’s type are associated with by frequencies, irreducible propensities, etc.). events of E ’s type and another of which expresses the fact that C occurred (see Explanation). Contemporary Philosophical Accounts of Imposing certain requirements on universal gen- Causality: Generalist Accounts eralizations (e.g., projectibility) enabled the D-N account to avoid cases of spurious causation due Probabilistic Relevance Accounts to accidental regularities (S ’s being a screw in A natural response to Scriven-type cases is to Smith’s car does not explain why S is rusty, even understand positive causal relevance in terms of if all the screws in Smith’s car are rusty). Hempel probability raising (Suppes 1970): Event C causes suggested various strategies for how the D-N ac- eventPROOFE just in case the probability of events of E ’s count might avoid admitting spurious causes type is higher given events of C ’s type than with- (explanations) associated with cases of asymmetry out. (Other relevance relations, such as being a and preemption. For example, if one is willing to negative causal factor, can be defined accordingly.) let causal asymmetry depend on temporal asymme- A common objection to such accounts (see Rosen try, one can avoid admitting the length of the shad- 1978) proceeds by constructing cases ‘‘the hard ow as explaining the height of the flagpole by way,’’ in which it seems that causes lower the prob- noting that the length of the shadow at T depends ability of their effects (e.g., where a mishit golf ball AU:5 on the height of the flagpole at T Àe, while no such ricochets off a tree, resulting in a hole-in-one; or relationship holds between the height of the flag- where a box contains a radioactive substance S that e AU:6 pole at T and the length of the shadowFIRST at T À . produces decay particles but the presence of S To accommodate the possibility of irreducibly excludes the more effective radioactive substance 0 probabilistic associations, as well as explanations S ). Such cases can often be handled, however, by AU:7 (characteristic of the social sciences) proceeding locating a neutral context (where the golf ball is not under conditions of partial uncertainty, Hempel hit at all, or where no radioactive substance is in (1965) proposed an inductive-statistical (I-S) the box) relative to which events of the given type model, in which event C explains event E if C do raise the probability of events of the effect type. occurs and it is an inductively grounded law that A more serious problem for probability-raising the probability of an event of type E given an event accounts is indicated by Simpson’s paradox, of type C is high (see Explanation; Inductive according to which any statistical relationship be- Logic). This account is subject to counterexamples tween two variables may be reversed by including in which a cause produces an effect but with a additional factors in the analysis. The ‘‘paradox’’

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reflects the possibility that a variable C can be reductive versions of probabilistic accounts with positively correlated with a variable E in a popula- circularity. Attempts have been made to provide a tion and yet C be negatively correlated with E in noncircular means of specifying the relevant back- every partition of the population induced by a third ground contexts (e.g., Salmon 1984), but it is ques- variable X. Just this occurred in the Berkeley sex tionable whether these attempts succeed, and many discrimination case. Relative to the population of are presently prepared to agree with Cartwright: all men and women applying to graduate school at ‘‘No causes in, no causes out.’’ the University of California, Berkeley, being male As mentioned, probabilistic accounts may or (C ) was positively correlated with being admitted may not be reductive, depending on whether the (E ). But relative to every partition of the popula- probabilities at issue are understood as grounded in tion containing the men and women applying to a associations (as in Suppes 1970) or else in powers, particular department (X ), this correlation was re- capacities, or propensities (as in Humphreys 1989 versed. In this case the difference between the gen- and Cartwright 1989). In the latter interpretation, eral and specific population statistics reflected the further divisions are introduced: If the propensities fact that while in every department it was easier for are taken to be irreducible to laws (as in Cart- women to be admitted than men, women were wright’s account), then the associated probabilistic more likely to apply to departments that were relevance account is more appropriately deemed harder (for everyone) to get into. The general pop- singularist. Complicating the taxonomy here is the ulation statistic was thus confounded: Being a fact that most proponents of probabilistic accounts male, simpliciter, was not in fact causally relevant are not explicit as regards what analysis should be to getting into graduate school at UC Berkeley; given of the probabilities at issue. rather (assuming no other confounding was at issue), applying to certain departments rather than others was what was relevant. Bayesian Networks and Causal Models To use probabilistic accounts as a basis for test- Philosophical worries concerning whether statis- ing hypotheses and making predictions—and espe- tical information adequately tracks causal influence cially in order to identify effective strategies are echoed in current debates over the interpreta- (courses of action) in the social sciences and, in- tion of the statistical techniques used in the social deed, in everyday life—statistical confounding sciences. As noted above (‘‘Hume and Pearson: needs to be avoided. Cartwright (1979) suggested Correlation, Not Causation’’), these techniques that avoiding confounding requires that the rele- have frequently been interpreted as relating exclu- vant probabilities be assessed relative to back- sively to correlations, but increasingly researchers ground contexts within which all other causal in computer science, artificial intelligence, and sta- factors (besides the variable C, whose causal rele- tisticsPROOF (see Spirtes, Glymour, and Scheines 1993; vance is at issue) are held fixed. (Of course, reduc- Pearl 2000) have developed nonreductive interpre- tionists need to be able to specify these background tations of these approaches as encoding explicitly contexts without appealing to distinctly causal fac- causal information and that appear to lead to im- AU:8 tors; see below.) Opinions differ regarding whether proved hypothesis testing and prediction of effects events of type C must raise the probability of under observation and intervention. events of type E in at least one such context, in a Another advantage claimed for such accounts is AU:9 majority of contexts, or in every such context. So that they provide a means of avoiding confounding one might take C to be a positive causal factor for without imposing the often impracticable require- AU:10 E just in case p(E|C^Xi)  p(E|C ^Xi) for all ment that the relevant probabilities be assessed background contexts Xi, with strictFIRST inequality for against background contexts taking into account at least one Xi. In this approach, smoking would be all causal factors, it rather being sufficient to take a positive causal factor for having lung cancer just into account all common causal factors. As a simple in case smoking increases the chance of lung cancer illustration, suppose that A and B are known to in at least one background context and does not causally influence C, as in Figure 1. lower it in any background context. To judge whether D influences C, Cartwright AU:12 Practically, Cartwright’s suggestion has the dis- generally recommends holding fixed both A and advantage that one is frequently not in a position B, while Spirtes et al. (1993) instead recommend to control for all alternative causal factors (though holding fixed only A. Cartwright allows, however, in some circumstances one can avoid having to do that attention to just common causal factors is this; see ‘‘Bayesian Networks and Causal Models’’ possible when the causal Markov condition (dis- below). Philosophically, the requirement threatens cussed below) holds. As will be seen shortly, this

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all variables X, where X is not one of V ’s des- cendants, P(V |Pn^X ) ¼ P(V |Pn). (In particular, AU:15 where V is a joint effect, conditioning on the causal parents of V screens off the probabilistic influence of the other joint effects on V.) Here again there is the practical problem that in the social sciences, AU:11 Fig. 1. where the approaches are supposed to be applica- ble, one is often not in a position to specify states with sufficient precision to guarantee that the condition is met. A metaphysical problem is that condition must hold in order to implement the (contrary to Reichenbach’s apparent assumption causal modeling approach. So, the restriction to that the condition holds in all cases involving a common causal factors is not really an advantage common cause of joint effects) the causal Markov over Cartwright’s account. condition need not hold in cases of probabilistic In the causal modeling approach, one starts causation: When a particle may probabilistically with a set of variables (representing properties) decay either by emitting a high-energy electron and a probability distribution over the variables. and falling into a lowenergy state or by emitting This probability distribution, partially interpreted a low-energy electron and falling into a different with prior causal knowledge, is assumed to reflect a energy state, the joint effects in either case will causal structure (a set of laws expressing the causal not be probabilistically independent of each other, relations between the variables, which laws may be even conditioning on the cause; and certain cases expressed either graphically or as a set of structur- of macrocausation appear also to violate the ally related functional equations). Given that cer- condition. AU:13 tain conditions (discussed below) hold between the A second assumption of the causal modeling probabilities and the causal structure, algorithmic technique is what Spirtes et al. (1993) call ‘‘faith- techniques are used to generate the set of all causal fulness’’ (also known as ‘‘stability’’ in Pearl 2000), structures consistent with the probabilities and the according to which probabilistic dependencies prior causal knowledge. Techniques also exist for faithfully reveal causal connections. In particular, extracting information regarding the results of if Y is probabilistically independent of X, given X ’s interventions (corresponding to manipulations of parents, then X is assumed not to cause Y. Again, variables). this condition cannot be assumed to hold in all While causal modeling approaches may lead to cases, since some variables (properties) may some- improved causal inference concerning complex sys- times prevent and sometimes produce an effect (as tems (in which case they are of some epistemologi- whenPROOF birth control pills are a cause of thrombosis cal interest), it is unclear what bearing they have on yet also prevent thrombosis, insofar as pregnancy the metaphysics of causality. Spirtes et al. (1993) causes thrombosis and the pills prevent pregnancy). present their account not so much as an analysis of In circumstances where the positive and negative causality as a guide to causal inference. Pearl contributions of X to Y are equally effective, the (2000), however, takes the appeal to prior causal probabilistic dependence of effect on cause may intuitions to indicate that causal modeling cancel out, and thus X may inappropriately be approaches are nonreductive (and moreover based taken not to be causally relevant to Y. on facts about humans’ cognitive capacities to make effective causal inferences in simple cases). In any case, the potential of causal modelsFIRST to pro- Causal Powers, Capacities, Universals, Forces vide a basis for a general theory of causality is As mentioned, some proponents of probabilistic limited by the fact that certain strong conditions relevance accounts endorse metaphysical interpre- need to be in place in order for the algorithms to be tations of the probabilities at issue. Such positions correctly applied. fall under the broader category of nonreductive One of these is the causal Markov condition (of (‘‘realist’’) covering-law theories, in which laws ex- which Reichenbach’s [1956] ‘‘principle of the com- press (or are grounded in) more than mere associa- mon cause’’ was a special case), which says that tions. The job such accounts face is to provide an AU:14 once one conditions on the complete set Pn alternative basis for causal laws. Among other pos- of ‘‘causal parents’’ (direct causes) of a variable sibilities, these bases are taken to be relations of V, V will be probabilistically independent of all necessitation or ‘‘probabilification’’ among univer- other variables except V’s descendants; that is, for sals (Dretske 1977; Tooley 1977; Armstrong 1978),

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(law-based) capacities or powers associated with the best explanation—often of the patterns of asso- objects or properties (Shoemaker 1980; Martin ciation appealed to by reductivist accounts. 1993), or fundamental forces or interactions (Bohm 1957; Strawson 1987). Singularist Accounts Such accounts sidestep many of the problems associated with reductive coveringlaw accounts. Singularists reject the claim that causes follow laws Since laws are not just a matter of association, a in the order of explanation, but beyond this there realist has the means to deny, in the virus–fever– is considerable variety in their accounts. Contra rash case, that there is a law connecting fevers with Hume, Anscombe (1971) takes causation to be a rashes; similarly, in cases of preemption a realist (primitive) relation that may be observed in cut- may claim that, for example, Billy’s rockthrowing tings, pushings, fallings, etc. It is worth noting that and the bottle’s breaking did not instance the law in a primitivist approach to causality is compatible question (even without endorsing a fine-grained with even a strict empiricism (compare Hume’s account of event individuation). Of course, much primitivist account of the resemblance relation). depends here on the details of the proposed ac- The empiricist Ducasse (1926) also locates causa- count of laws. In the Dretske-Tooley-Armstrong tion in singular observation, but nonprimitively: account, causal laws are contingent, brute relations A cause is the change event observed to be im- between universals. Some find this less than satisfy- mediately prior and spatiotemporally contiguous ing from a realist point of view, insofar as it is to an effect event. While interesting in allowing compatible with, for example, the property of hav- for a nonassociative, nonprimitivist, empiricist cau- ing spin 1 bestowing completely different causal sality, Ducasse’s account is unsatisfactory in allow- powers (say, all those actually bestowed by having ing only the coarse-grained identification of causes 1 spin 2) on its possessing particulars. Other realists (as some backward temporal segment of the entire are more inclined to see the nature of properties observed change); hence it fails to account for most and particulars as essentially dependent on the ordinary causal judgments. Note that singularists causal laws that actually govern them, a view basing causation on observation need not assert that is quite plausible for scientific entities: ‘‘[C] that one’s knowledge of causality proceeds only ausal laws are not like externally imposed legal via observations of the preferred sort; they rather restrictions that, so to speak, merely limit the generally maintain that such experiences are suffi- course of events to certain prescribed paths ... . cient to account for one’s acquiring the concept of [T]he causal laws satisfied by a thing ... are inex- causation, then allow that causation need not be tricably bound up with the basic properties of the observed and that confirming singular causal thing which helps to define what it is’’ (Bohm claims may require attention to associations. 1957, 14). PROOFAnother singularist approach takes causation to The primary problem facing realist accounts is be theoretically inferred, as that relation satisfying that they require accepting entities and relations (something like) the Ramsey sentence consisting of (universals, causal powers, forces) that many phi- the platitudes about causality involving asymme- losophers and scientists find metaphysically ob- try, transitivity, and so on (see Tooley 1987). One scure and/or epistemologically inaccessible. How problem here is that, as may be clear by now, such one evaluates these assessments often depends on platitudes do not seem to uniformly apply to all one’s other commitments. For example, many tra- cases. Relatedly, one may wonder whether they are ditional arguments against realist accounts (e.g., consistent; given the competing causal intuitions Hume’s arguments) are aimed at showing that driving various accounts of causality, it would be these do not satisfy a strict epistemologicalFIRST stan- surprising if they were. dard, according to which the warranted posit of a Finally, a wide variety of singularist accounts contingent entity requires that the entity be directly understand causality in terms of singular processes. accessible to experience (or a construction from Such accounts are strongly motivated by the intui- entities that are so accessible). But if inference to tion that in a case of preemption such as that of the existence of an unexperienced entity (as the best Suzy and Billy, what distinguishes Suzy’s throw as a AU:16 explanation of some phenomena) is at least some- cause is that it initiates a process ending in the bottle times an acceptable mode of inference, such a breaking, while the process initiated by Billy’s throw strict epistemological standard (and associated never reaches completion (see Menzies 1996 for a arguments) will be rejected; and indeed, positive discussion). Commonly, process singularists at- arguments for contemporary realist accounts of tempt (like Ducasse) to provide a nonprimitivist causality generally proceed via such inferences to causality that is both broadly empiricist, in not

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appealing to any properly metaphysical elements, actually occurring (which occurrences, as above, and nonassociationist, in recognition of the diffcul- are assumed); hence standard counterfactual acc- ties that associationist accounts have (both with ounts do not have a nontrivial notion of coun- preemption and with distinguishing genuine causal- terfactual sufficiency. A nontrivial notion of ity from accidental regularity). Hence they typically counterfactual sufficiency can be obtained by ap- fill in the ‘‘process’’ intuition by identifying causal- peal to nested counterfactuals (see Vihvelin 1995): ity with fundamental physical processes, including C causes E only if, if neither C nor E had occu- transfers or interactions, as in Fair’s (1979) account rred, then (if C had occurred, then E would have of causation as identical with the transfer of energy occurred). AU:17 momentum, Salmon’s (1984) ‘‘mark transmission’’ account, and Dowe’s (1992) account in which the transfer of any conserved quantity will suffice. Problems, Events, and Backtrackers An objection to the claim that physical proce- While counterfactual accounts are often moti- sses are sufficient for causality is illustrated by vated by a desire to give a reductive account of Cartwright’s (1979) case of a plant sprayed with causality that avoids problems with reductive cov- herbicide that improbably survives and goes on to ering-law accounts (especially those of joint effects flourish (compare also Kvart’s 1991 finger-severing and of preemption), it is unclear whether counter- case, discussed previously). While transfers and factual accounts do any better by these problems. interactions of the requisite sort can be traced First, consider the problem of joint effects. Sup- from spraying to flourishing, intuitively the former pose a virus causes first a fever, then a rash, and did not cause the latter; however, accepting that that the fever and rash could only have been caused the spraying did cause the flourishing may not be by the virus. It seems correct to reason in the an overly high price to pay. A deeper worry concerns following ‘‘backtracking’’ fashion: If the fever had the epistemological question of how accounts not occurred, then the viral infection would not of physical process link causation understood as have occurred, in which case the rash would involving theoretical relations or processes of not have occurred. But then the counterfactual fundamental physics with causation as ordinarily ‘‘If the fever had not occurred, the rash would not experienced. Fair suggests that ordinary experience have occurred’’ turns out true, which here means involves macroprocesses, which are in turn reducible that the fever causes the rash, which is incorrect. to the relevant physical processes; but even sup- Proponents of counterfactual accounts have posing that such reductions are in place, ordinary responses to these objections, which require accept- causal judgments do not seem to presuppose them. ing controversial accounts of the truth conditions for counterfactuals (see Lewis 1979). Even so, the responsesPROOF appear not to succeed (see Bennett 1984 Counterfactual Accounts for a discussion). Counterfactual accounts of causality take as their Second, consider the problem of preemption. In starting point the intuition that a singular cause the Suzy-Billy case, it seems correct to reason that makes an important difference in what happens. if Suzy had not thrown her rock, then Billy’s rock As a first pass, C causes E (where C and E are would have gotten through and broken the bottle. actually occurring events) only if, were C not to Hence the counterfactual ‘‘If Suzy’s throw had not occur, then E would not occur. As a second pass, C occurred, the bottlebreaking would not have oc- causes E only if C and E are connected by a chain curred’’ turns out false; so Suzy’s rockthrowing of such dependencies (see Lewis 1973), so as to turns out not to be a cause, which is incorrect. In ensure that causation is transitive (thatFIRST is, causa- cases (as here) of so-called ‘‘early preemption,’’ tion is the ‘‘ancestral,’’ or transitive closure, of where it makes sense to suppose that there was an counterfactual dependence). In addition to the re- intermediate event D between the effect and the quirement of counterfactual necessity of causes for cause on which the effect depended, this result effects, counterfactual accounts also commonly can be avoided: Although the breaking does not impose a requirement of counterfactual sufficiency counterfactually depend on Suzy’s rockthrowing, of causes for effects: If C were to occur, then there is a chain of counterfactual dependence link- E would occur. Insofar as counterfactual accounts ing the breaking to Suzy’s rockthrowing (and no are standardly aimed at reducing causal to non- such chain linking the breaking to Billy’s), and so causal relations, and given plausible assumptions her throw does end up being a cause (and Billy’s concerning evaluation of counterfactuals, the does not). But the appeal to an intermediate event latter requirement is satisfied just by C and E ’s seems ad hoc and in any case cannot resolve cases

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of ‘‘late preemption.’’ Lewis (developing an idea ——— (1970), ‘‘Mental Events,’’ in L. Foster and J. Swan- broached in Paul 1998) eventually responded to son (eds.), Experience and Theory. Amherst: Mass- achusetts University Press. Reprinted in Davidson such cases by allowing that an event may be (2001), Essays on Actions and Events. Oxford: Oxford counted as a cause if it counterfactually influences University Press, 207–224. the mode of occurrence of the effect (e.g., how or Dowe, Phil (1992), ‘‘Wesley Salmon’s Process Theory of when it occurs), as well as if it counterfactually Causality and the Conserved Quantity Theory,’’ Philos- influences the occurrence of the effect, simpliciter. ophy of Science 59: 195–216. Dretske, Fred (1977), ‘‘Laws of Nature,’’ Philosophy of Science 44: 248–268. Counterfactuals and Manipulability Ducasse, C. J. (1926), ‘‘On the Nature and Observability of Where counterfactual accounts may be most use- the Causal Relation,’’ Journal of Philosophy 23: 57–68. ful is in providing a basis for understanding or Fair, David (1979), ‘‘Causation and the Flow of Energy,’’ Erkenntnis 14: 219–250. formalizing the role that manipulability plays in Hall, Ned (2000), ‘‘Causation and the Price of Transitivity,’’ the concept of causation. One such approach sees Journal of Philosophy 97: 198–222. counterfactuals as providing the basis for an epis- Hankinson, R. J. (1998), Cause and Explanation in Ancient temological, rather than a metaphysical, account of Greek Thought. Oxford: Oxford University Press. causation (see Pearl 2000 for a discussion). The Hempel, Carl (1965), In Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New idea here is that counterfactuals nicely model the York: Free Press. role manipulability (actual or imagined) plays in Hempel, Carl, and Paul Oppenheim (1948), ‘‘Studies in the causal inference, for a natural way to determine Logic of Explanation,’’ Philosophy of Science 15: 135–175. whether a counterfactual is true is to manipulate Hitchcock, Christopher (1993), ‘‘A Generalized Probabilis- conditions so as to actualize the antecedent. An- tic Theory of Causal Relevance,’’ Synthese 97: 335–364. Hume, David ([1739] 1978), A Treatise of Human Nature. other approach takes counterfactuals to provide a Edited by L. A. Selby-Bigge. Oxford: Oxford University basis for a generalist account of causal explanation Press. (see Woodward 1997), according to which such ——— ([1748] 1993), An Enquiry Concerning Human Un- explanations track stable or invariant connections derstanding. Edited by Eric Steinberg. Indianapolis: and the notion of invariance is understood none- Hackett Publishing. Humphreys, Paul (1986), ‘‘Causation in the Social Sciences: pistemologically in terms of a connection’s con- An Overview,’’ Synthese 68: 1–12. tinuing to hold through certain counterfactual (not ——— (1989), The Chances of Explanation. Princeton, NJ: necessarily human) ‘‘interventions.’’ Whether the Princeton University Press. notion of manipulability is itself a causal notion, Jammer, Max (1957), Concepts of Force. Cambridge, MA: and so bars the reduction of causal to noncausal Harvard University Press. Kim, Jaegwon (1984), ‘‘Epiphenomenal and Supervenient facts, is still an open question. Causation,’’ Midwest Studies in Philosophy IX: Causa- JESSICA WILSON PROOFtion and Causal Theories, 257–270. ——— (1993), Supervenience and Mind: Selected Philosoph- References ical Essays. Cambridge: Cambridge University Press. AU:18 Kvart, Igal (1991), ‘‘Transitivity and Preemption of Causal Anscombe, G. E. M. (1971), Causality and Determination. Relevance,’’ Philosophical Studies LXIV: 125–160. Cambridge: Cambridge University Press. Lewis, David (1973), ‘‘Causation,’’ Journal of Philosophy Armstrong, David M. (1978), Universals and Scientific Re- 70: 556 –567. alism, vol. 2: A Theory of Universals. Cambridge: Cam- ——— (1979), ‘‘Counterfactual Dependence and Time’s bridge University Press. Arrow,’’ Nouˆs 13:455– 476. Bennett, Jonathan (1984), ‘‘Counterfactuals and Temporal ——— (1983), Philosophical Papers, vol. 1. Oxford: Oxford Direction,’’ Philosophical Review 93: 57–91. University Press. Bohm, David (1957), Causality and Chance in Modern Phys- ——— (1994), ‘‘Humean Supervenience Debugged,’’ Mind ics. London: Kegan Paul. 1: 473– 490. Bromberger, Sylvain (1962), ‘‘What AreFIRST Effects?’’ in Mackie, John L. (1965), ‘‘Causes and Conditions,’’ Ameri- Ronald J. Butler (ed.), Analytical Philosophy, vol. 1. can Philosophical Quarterly 2: 245–264. Oxford: Oxford University Press. Martin, C. B. (1993), ‘‘Power for Realists,’’ in Keith Cam- Cartwright, Nancy (1979), ‘‘Causal Laws and Effective bell, John Bacon, and Lloyd Reinhardt (eds.), Ontology, Strategies,’’ Nouˆs 13: 419–438. Causality, and Mind: Essays on the Philosophy of D. M. ——— (1989), Nature’s Capacities and Their Measurement. Armstrong. Cambridge: Cambridge University Press. Oxford: Clarendon Press. McLaughlin, Brian (1992), ‘‘The Rise and Fall of British Clatterbaugh, Kenneth (1999), The Causation Debate in Emergentism,’’ in Ansgar Beckerman, Hans Flohr, and Modern Philosophy, 1637–1739. New York: Routledge. Jaegwon Kim (eds.), Emergence or Reduction? Essays on Davidson, Donald (1967), ‘‘Causal Relations,’’ Journal of the Prospects of Nonreductive Physicalism. Berlin: De Philosophy 64: 691–703. Reprinted in Davidson (2001), Gruyter, 49–93. Essays on Actions and Events. Oxford: Oxford University Mellor, D. H. (1995), The Facts of Causation. Oxford: Press, 149–162. Oxford University Press.

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Menzies, Peter (1996), ‘‘Probabilistic Causation and the Sober, Elliott (1984), ‘‘Two Concepts of Cause,’’ in Peter D. Pre-Emption Problem,’’ Mind 105: 85–117. Asquith and Philip Kitcher (eds.), PSA 1984. East Lan- Newton, Isaac ([1687] 1999), The Principia: Mathematical sing, MI: Philosophy of Science Association, 405–424. Principles of Natural Philosophy. Translated by I. Sosa, Ernest, and Michael Tooley (eds.) (1993), Causation. Bernard Cohen and Anne Whitman. Berkeley and Los Oxford: Oxford University Press.. Angeles: University of California Press. Spirtes, P., C. Glymour, and R. Scheines (1993), Causation, Paul, Laurie (1998), ‘‘Keeping Track of the Time: Emend- Prediction, and Search. New York: Springer-Verlag. ing the Counterfactual Analysis of Causation,’’ Analysis Strawson, Galen (1987), ‘‘Realism and Causation,’’ Philo- LVIII: 191–198. sophical Quarterly 37: 253–277. Pearl, Judea (2000), Causality. Cambridge: Cambridge Uni- Suppes, Patrick (1970), A Probabilistic Theory of Causality. versity Press. Amsterdam: North-Holland. Price, Huw (1992), ‘‘Agency and Causal Asymmetry,’’ Mind ——— (1986), ‘‘Non-Markovian Causality in the Social 101: 501–520. Sciences with Some Theorems on Transitivity,’’ Synthese Railton, Peter (1978), ‘‘A Deductive-Nomological Model of 68: 129–140. Probabilistic Explanation,’’ Philosophy of Science 45: Tooley, Michael (1977), ‘‘The Nature of Laws,’’ Canadian 206–226. Journal of Philosophy 7: 667–698. Reichenbach, Hans (1956), The Direction of Time. Berkeley ——— (1987), Causation: A Realist Approach. Oxford: and Los Angeles: University of California Press. Oxford University Press. Rosen, Deborah (1978), ‘‘In Defense of a Probabilistic van Fraassen, Bas (1980), The Scientific Image. Oxford: Theory of Causality,’’ Philosophy of Science 45: 604–613. Oxford University Press. Russell, Bertrand (1912), ‘‘On the Notion of Cause,’’ Pro- Vihvelin, Kadhri (1995), ‘‘Causes, Effects, and Counterfac- ceedings of the Aristotelian Society 13: 1–26. tual Dependence,’’ Australasian Journal of Philosophy Salmon, Wesley (1984), Scientific Explanation and the 73: 560–583. Causal Structure of the World. Princeton, NJ: Princeton Wilson, Jessica (1999), ‘‘How Superduper Does a Physical- University Press. ist Supervenience Need to Be?’’ Philosophical Quarterly ——— (1989), ‘‘Four Decades of Scientific Explanation,’’ 49: 33–52. in Philip Kitcher and Wesley Salmon (eds.), Scientific Woodward, James (1997), ‘‘Explanation, Invariance, and AU:19 Explanation,3–219. Intervention,’’ Philosophy of Science 64 (Proceedings): Scriven, Michael (1975), ‘‘Causation as Explanation,’’ Nouˆs S26–S41. 9: 238–264. Wright, Larry (1976), Teleological Explanation. Berkeley Shoemaker, Sydney (1980), ‘‘Causality and Properties,’’ in and Los Angeles: University of California Press. Peter van Inwagen (ed.), Time and Cause. Dordrecht, Wright, Sewall (1921), ‘‘Correlation and Causation,’’ Jour- Netherlands: D. Reidel, 109–135. nal of Agricultural Research 20: 557–585. PROOF CHAOS THEORY

See Prediction FIRST CHEMISTRY, PHILOSOPHY OF

Although many influential late-nineteenth- and (Gaston Bachelard, Pierre Duhem, Emile Myerson, early-twentieth-century philosophers of science Wilhelm Ostwald, Michael Polanyi), they sel- were educated wholly or in part as chemists dom reflected directly on the epistemological,

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methodological, or metaphysical commitments of The history of chemistry also raises a number of their science. Subsequent philosophers of science interesting questions about the character of knowl- followed suit, directing little attention to chemistry edge and understanding in the science. Whereas in comparison with physics and biology despite the philosophers have historically identified theoretical industrial, economic, and academic success of the knowledge with laws or sets of propositions, the chemical sciences. Scattered examples of philo- history of chemistry shows that there are different sophical reflection on chemistry by chemists do kinds of knowledge that function as a base for exist; however, philosophically sensitive historical understanding. Much of chemistry is experimental, analysis and sustained conceptual analysis are rela- and much of what is known to be true arises in tively recent phenomena. Taken together, these two experimental practice independently of or only in- developments demonstrate that chemistry addres- directly informed by theoretical knowledge. When ses general issues in the philosophy of science and, chemists have theorized, they have done so freely, in addition, raises important questions in the in- using and combining phenomenological, construc- terpretation of chemical theories, concepts, and tive (in which the values of certain variables are experiments. given by experiment or other theory), and deduc- Historians of chemistry have also raised a num- tive methods. Chemists have rarely been able to ber of general philosophical questions about chem- achieve anything like a strict set of axioms or first istry. These include issues of explanation, ontology, principles that order the phenomena and serve as reduction, and the relative roles of theories, experi- their explanatory base (Bensaude-Vincent and ments, and instruments in the advancement of the Stengers 1996; Gavroglu 1997; Nye 1993). science. Historical research has also raised the issue of Worries about the explanatory nature of the al- whether theory has contributed most to the prog- chemical, corpuscularian, and phlogiston theories ress of chemistry. While philosophers often point to are well documented (cf. Bensaude-Vincent and the conceptual ‘‘revolution’’ wrought by Lavoisier Stengers 1996; Brock 1993). Lavoisier and—to a as an example of progress, historians more often lesser extent historically—Dalton initiated shifts in point to the ways in which laboratory techniques the explanatory tasks and presuppositions of the have been an important motor of change in chemis- science. For instance, prior to Lavoisier many che- try, by themselves or in tandem with theoretical mists ‘‘explained’’ a chemical by assigning it to a shifts (Bensaude-Vincent and Stengers 1996; Nye type associated with its experimental dispositions 1993). For example, during the nineteenth century, (e.g., flammability, acidity, etc.). After Lavoisier substitution studies, in which one element is re- and Dalton, ‘‘explanation’’ most often meant the placed by another in a compound, were driven isolation and identification of a chemical’s constitu- largely by experimental practices. Theoretical con- ents. Eventually, the goal of explanation changed to ceptsPROOF did not, in the first instance, organize the the identification of the transformation processes in investigation (Klein 1999). Similar remarks can be the reactants that gave rise to the observed properties made regarding the coming of modern experimental of the intermediaries and the products. It is at that techniques such as various types of chromatogra- time that chemists began to write the now familiar phy and spectroscopy (Baird 2000; Slater 2002). reaction equations, which encapsulate this change. Chemists often characterize a molecule using such These transformations cannot be described simply as techniques, and while the techniques are grounded the coming of new theories; they also involved in physical theory, the results must often be inter- changes in explanatory presuppositions and lan- preted in chemical language. These examples lead guages, as well as new experimental techniques back to questions about the nature of chemical (Bensaude-Vincent and Stengers 1996;FIRST Nye 1993). knowledge. Arguably, the knowledge appears to Thinking in terms of transformation processes be a mix of ‘‘knowing how’’ and ‘‘knowing that’’ led chemists to postulate atoms as the agents of which is not based solely in the theory (chemical or the transformation process. But atoms were not physical) available at the time. observable in the nineteenth century. How is the A number of the philosophical themes raised in explanatory power of these unobservable entities the history of chemistry continue to reverberate in accounted for? Also, do chemical elements retain current chemistry. For instance, what is the proper their identity in compounds (Paneth 1962)? Some- ontological base for chemical theory, explanation, thing remains the same, yet the properties that and practice? While many chemists would unfail- identify elements (e.g., the green color of chlo- ingly resort to molecular structure as the explana- rine gas) do not exist in compounds (e.g., sodium tion of what is seen while a reaction is taking chloride, or common table salt). place, this conception can be challenged from two

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directions. From one side, echoing the eighteenth- with relatively few electrons or with high degrees century conception of the science, chemistry begins of symmetry can be calculated with a high degree of in the first instance with conceptions and analyses faithfulness to the complete theoretical description. of the qualitative properties of material stuff For most chemical systems, various semi-empirical (Schummer 1996; van Brakel 2001). One might methods must be used to get theoretically guided call the ontology associated with this conception a results. More often than not, it is the experimental metaphysically nonreductive dispositional realism, practice independent of any theoretical calculation since it focuses on properties and how they appear that gets the result. Strictly theoretical predictions under certain conditions and does not attempt to of novel properties are rather rare, and whether interpret them in any simpler terms. In this concep- they are strictly theoretical is a matter that can be tion, reference to the underlying molecular struc- disputed. A case in point is the structure of the CH2 ture is subsidiary or even otiose, since the focus is molecule. Theoretical chemists claimed to have on the observable properties of the materials. predicted novel properties of the molecule, viz., its Given that molecular structure is difficult to justify nonlinear geometry, prior to any spectroscopic within quantum mechanics (see below), one can evidence (Foster and Boys 1960). While it is true argue that it is justifiable to remain with the ob- that the spectroscopic evidence was not yet avail- servable properties. If this view is adopted, howev- able, it may have been the case that reference to er, the justification of the ontology of material stuff analogous molecules allowed the researchers to set becomes a pressing matter. Quantum mechanics the values for some of the parameters in the equa- will not supply the justification, since it does not tions. So the derivation may not have been as a deliver the qualitative properties of materials. Fur- priori as it seemed. ther, it still seems necessary to account for the Like the other special sciences, chemistry raises phenomenal success that molecular explanati- the issue of reductionism quite forcefully. Howev- ons afford in planning and interpreting chemical er, perhaps because most philosophers have accept- structures and reactions. ed at face value Dirac’s famous dictum that From the other side, pure quantum mechanics chemistry has become nothing more than the appli- makes it difficult to speak of the traditional atoms- cation of quantum mechanics to chemical problems within-a-molecule approach referred to in the reac- (cf. Nye 1993, 248), few seem to be aware of the tion equations and structural diagrams (Primas difficulties of making good on that claim using the 1983; Weininger 1984). Quantum mechanics tells tools and concepts available in traditional philo- us that the interior parts of molecules should not sophical analyses of the sciences. No one doubts be distinguishable; there exists only a distribution that chemical forces are physical in nature, but of nuclear and electronic charges. Yet chemists rely connecting the chemical and physical mathematical on the existence and persistence of atoms and mole- structuresPROOF and/or concepts proves to be quite a cules in a number of ways. To justify these prac- challenge. Although problems involving the rela- tices, some have argued that one can forgo the tion between the physical and the chemical sur- notion of an atom based on the orbital model and round a wide variety of chemical concepts, such instead identify spatial regions within a molecule as aromaticity, acidity (and basicity), functional bounded by surfaces that have a zero flux of energy groups, and substituent effects (Hoffmann 1995), across the surfaces (Bader 1990). Currently, it is an three examples will be discussed here to illustrate open question whether this representation falls nat- the difficulties: the periodic table, the use of orbi- urally out of quantum mechanics, and so allows tals to explain bonding, and the concept of molec- one to recover atoms as naturally occurring sub- ular shape. Each also raises issues of explanation, stituents of molecules, or whetherFIRST the notion of representation, and realism. ‘atom’ must be presupposed in order for the identi- Philosophers and scientists commonly believe fication to be made. Here again there is a question that the periodic table has been explained by— of the character of the theory that will give the and thus reduced to—quantum mechanics. This is desired explanation. taken to be an explanation of the configuration of A number of examples supporting the claim that the electrons in the atom, and, as a result of this, an quantum mechanics and chemistry are uneasy bed- explanation of the periodicity of the table. In the fellows will be discussed below as they relate to the first case, however, configurations of electrons in issue of reductionism, but their relationship also atoms and molecules are the result of a particular raises forcefully the long-standing issue of how the- approximation, in which the many-electron quan- ory guides chemical practice. Even in this era of tum wavefunction is rewritten as a series of one- supercomputers, only the energy states of systems electron functions. In practice, these one-electron

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functions are derived from the hydrogen wavefunc- approximation that was the basis for the assign- tion and, upon integration, lead to the familiar ment into the s, p, and d orbitals in the first place. It spherical s orbital, the dumbbell-shaped p orbitals, thus becomes an open question whether quantum and the more complicated d and f orbitals. Via the mechanics, via the Aufbau principle, has explained Pauli exclusion principle, which states that the spins the chemical periodicities encapsulated in the table. are to be paired if two electrons are to occupy one Similar questions about the tenuous relation be- orbital and no more than two electrons may occupy tween physics and chemistry surround the concept an orbital, electrons are assigned to these orbitals. of bonding. At a broad level, chemists employ two If the approximation is not made (and quantum seemingly inconsistent representations, the valence mechanics tells us it should not be, since the ap- bond (VB) and molecular orbital (MO) theories, to proximation relies on the distinguishability of elec- explain why atoms and molecules react. Both are trons), the notion of individual quantum numbers— calculational approximations inherited from atom- and thus configurations—is no longer meaningful ic physics. The relations between the two theories AU:20 (Richman 1999). In addition, configurations them- and respective relations to the underlying quantum selves are not observable; absorption and emission mechanics raise many issues of theory interpreta- spectra are observed and interpreted as energy tion and realism about the chemical concepts (see transitions between orbitals of different energies. below). Subsidiary concepts such as resonance are In the second case, quantum mechanics explains also invoked to explain the finer points of bonding. only part of the periodic table, and often it does not Chemists have offered competing realist interpreta- explain the features of the table that are of most tions of this concept, and philosophers have offered interest to chemists (Scerri 1998). Pauli’s introduc- various realist and instrumentalist interpretations tion of the fourth quantum number, ‘‘spin’’ or of it as well (Mosini 2000). ‘‘spin angular momentum,’’ leads directly to the More specifically, a host of philosophical issues Aufbau principle, which states that the periodic are raised within the molecular orbital theory. table is constructed by placing electrons in lower Here, bonding is pictured as due to the interaction energy levels first and then demonstrating that of electrons in various orbitals. As noted earlier, atoms with similar configurations have similar the familiar spherical and dumbbell shapes arise chemical properties. In this way, one can say that only because of the orbital approximation. Howev- since chlorine and fluorine need one more electron er, there is no reason to expect that the hydrogenic to achieve a closed shell, they will behave similarly. wavefunctions will look anything like the molecu- However, this simple, unqualified explanation suf- lar ones (Bader 1990; Woody 2000). After the fers from a number of anomalies. First, the filling hydrogenic wavefunctions have been chosen as sequence is not always strictly obeyed. Cobalt, the basis for the calculation, they must be pro- nickel, and copper fill their shells in the sequence cessedPROOF mathematically to arrive at a value for the 3d74s2,3d84s2,3d104s1. The superscripts denote the energy of the orbital that is at all close to the number of electrons in the subshell; the s shell can experimentally observed value. The molecular hold a maximum of two electrons and the five d wave equation is solved by taking linear combina- orbitals ten. The observed order of filling is curious tions of the hydrogenic wavefunctions, forming the from the perspective of the unmodified Aufbau product of these combinations (the ‘‘configuration principle for a number of reasons. The 4s shell, interaction’’ approach), and using the variational which is supposed to be higher in energy than the method to produce a minimal energy solution to 3d shell, has been occupied and closed first. Then, the equation. The familiar orbitals appear only there is the ‘‘demotion’’ of one 4s electron in nickel when these three steps in the complete solution to a 3d electron in copper. Second,FIRST configurations have been omitted (Woody 2000). Thus, the idea are supposed to explain why elements falling into that the familiar orbitals are responsible for the the same group behave similarly, as in the example bonding is thrown into question. Yet the orbitals of chlorine and fluorine. Yet nickel, palladium, and classify and explain how atoms and molecules bond platinum are grouped together because of their extremely well. That they do provide deep, unified, marked chemical similarities despite the fact that and fertile representations and explanations seems their outer shells have different configurations (4s2, curious from the perspective of fundamental quan- 5s0 and 6s1, respectively). These and other anoma- tum mechanics. Clearly, more analysis is required lies can be resolved using alternative derivations to understand the relation clearly. If one insists on more closely tied to fundamental quantum me- a philosophical account of reduction that requires chanics, but the derivations require that the the mathematical or logical derivability of one the- orbital approximation be dropped, and it was that ory from another, how orbitals achieve their power

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remains obscure. Even when one abandons that parameterization, albeit in different ways. How is it philosophical account, it is not clear how the repre- that such parameterizations uncover useful patterns sentations have the organizing and explanatory in the data? Are they explanatory? When are they power they do (see Reductionism). acceptable and when not (Ramsey 1997)? These and As a final illustration of the difficulty of connect- a host of similar questions remain to be answered. ing physics and chemistry in any sort of strict fash- Other epistemological and ontological issues ion, consider the concept of molecular shape. raised in the practice of chemistry remain virtually Partly through the tradition of orbitals described unexplored. For instance, the question of whether above and partly through a historical tradition of one molecule is identical to another is answered by oriented bonding that arose well before the concept referring to some set of properties shared by the of orbitals was introduced, chemists commonly ex- two samples. Yet the classification of two mole- plain many behaviors of molecules as due to their cules as of the ‘‘same’’ type will vary, since different three-dimensional orientiation in space. Molecules theoretical representations and experimental tech- clearly react as if they are oriented in three-dimen- niques detect quite different properties (Hoffmann À sional space. For example, the reaction I þ CH3Br 1995). For instance, reference can be made to the À ! ICH3 þ Br is readily explained by invoking the space-filling property of molecules, their three- notion that the iodine ion (IÀ) attacks the carbon dimensional structure, or the way they respond to (C) on the side away from the bromine (Br) atom. an electric field. Additionally, the determination of (This can be detected by substituting deuterium sameness must be made in light of the question, For atoms for one of the hydrogens [H] and measuring what function or purpose? For instance, two mole- subsequent changes in spectroscopic properties.) cules of hemoglobin, which are large biological As noted before, however, such explanations are molecules, might have different isotopes of oxygen suspect within quantum mechanics, since talk of at one position. While this difference might be useful oriented bonds and quasi-independent substituents in order to discover the detailed structure of the in the reaction is questionable. Orientations must hemoglobin molecule, it is usually irrelevant when be ‘‘built into’’ the theory by parameterizing some talking about the molecule’s biological function. of the theoretical variables. Unfortunately, there is How the explanatory practices of chemistry stand no strict quantum mechanical justification for the in relation to the available philosophical accounts method by which orientation in space is derived. and to the practices of other sciences remains an Orientation relies on a notion of a nuclear frame important question. Chemical explanations are surrounded by electrons. This notion is constructed very specific, often lacking the generality invoked via the Born-Oppenheimer approximation, which in philosophical accounts of explanation. Moreover, provides a physical rationale for why the nuclear chemists invoke a wide variety of models, laws, the- positions should be slowly varying with respect to ories,PROOF and mechanisms to explain the behavior and the electronic motions. In some measurement structure of molecules. Finally, most explanations regimes, the approximation is invalid, and correct require analogically based and/or experimentally predictions are achieved only by resorting to a derived adjustments to the theoretical laws and reg- more general molecular Hamiltonian. In more ularities in order for the account to be explanatory. common measurement regimes, the approximation As mentioned earlier, chemistry is an extremely is clearly valid. But, as with the issues involved in experimental science. In addition to unifying and the case of the periodic table and orbitals, the fragmenting research programs in chemistry, new physics alone do not tell us why it is valid. There laboratory techniques have dramatically changed is a physical justification for the procedure, but this the epistemology of detection and observation in justification has no natural representationFIRST with the chemistry (e.g., from tapping manometers to read- available physical theory (Weininger 1984). Should ing NMR [nuclear magnetic resonance] outputs). As justification based on past experience be trusted, or yet, however, there is no overarching, complete should the theory correct the interpretive practice? study of the changes in the epistemology of experi- In any case, the chemistry is consistent with, but mention in chemistry: for example, what chemists not yet derivable from, the physics. count as observable (and how this is connected to All three examples are connected with a method- what they consider to be real), what they assume ological issue mentioned earlier, viz., the type of counts as a complete explanation, what they assume theory that chemists find useful. As previously counts as a successful end to an experiment, etc. noted, chemists often must parameterize the physi- Additionally, what are the relations between cal theories at their disposal to make them useful. academic and industrial chemistry? What are the All three of the cases described above involve such relative roles of skill, theory, and experiment in

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these two arenas of inquiry? Last but not least, there Foster, J. M., and S. F. Boys (1960), ‘‘Quantum Variational are pressing ethical questions. The world has been Calculations for a Range of CH2 Configurations,’’ Reviews of Modern Physics 32: 305–307. transformed by chemical products. Chemistry has Gavroglu, K. (1997), ‘‘Philosophical Issues in the History of blurred the distinction between the natural and the Chemistry,’’ Synthese 111: 283–304. artificial in confusing ways (Hoffmann 1995). For Hoffmann, R. (1995), The Same and Not the Same. New instance, catalytically produced ethanol is chemical- York: Columbia University Press. ly identical with the ethanol produced in fermenta- Klein, U. (1999), ‘‘Techniques of Modeling and Paper- Tools in Classical Chemistry,’’ in M. Morgan and tion. So is the carbon dioxide produced in a forest M. Morrison (eds.), Models as Mediators. New York: fire and in a car’s exhaust. Why are there worries Cambridge University Press, 146–167. about the exhaust fumes but not the industrially Mosini, V. (2000), ‘‘A Brief History of the Theory of Reso- produced ethanol? Is this the appropriate attitude? nance and of Its Interpretation,’’ Studies in History and Last but not least, chemicals have often replaced Philosophy of Modern Physics 31B: 569–581. Nye, M. J. (1993), From Chemical Philosophy to Theoretical earlier dangerous substances and practices; witness Chemistry. Berkeley and Los Angeles: University of the great number of herbicides and insecticides California Press. available at the local garden center and the prescrip- Paneth, F. (1962), ‘‘The Epistemological Status of the Con- tion medicines available at the pharmacy. Yet these cept of Element,’’ British Journal for the Philosophy of replacements are often associated with a cost. One Science 13: 1–14, 144–160. Primas, H. (1983), Chemistry, Quantum Mechanics and Re- need think only of DDT or thalidomide to be flung ductionism. New York: Springer Verlag. headlong into ethical questions regarding the harm- Ramsey, J. (1997), ‘‘Between the Fundamental and the fulness and use of human-made products. Phenomenological: The Challenge of ‘Semi-Empirical’ Many of the above topics have not been ana- Methods,’’ Philosophy of Science 64: 627–653. lyzed in any great depth. Much remains to done to Scerri, E. (1998), ‘‘How Good Is the Quantum Mechanical Explanation of the Periodic System?’’ Journal of Chemi- explore the methodology and philosophy of the cal Education 75: 1384–1385. chemical sciences. Schummer, J. (1996), Realismus und Chemie. Wuerzburg: JEFFRY L. RAMSEY Koenigshausen and Neumann. Slater, L. (2002), ‘‘Instruments and Rules: R. B. Woodward References and the Tools of Twentieth-century Organic Chemis- AU:21 try,’’ Studies in History and Philosophy of Science 33: Bader, R. (1990), Atoms in Molecules: a Quantum Theory. 1–32. New York: Oxford University Press. van Brakel, J. (2001), Philosophy of Chemistry: Between the Baird, D. (2000), ‘‘Encapsulating Knowledge: The Direct Manifest and the Scientific Image. Leuven, Belgium: Reading Spectrometer,’’ Foundations of Chemistry 2: Leuven University Press. 5–46. Weininger, S. (1984), ‘‘The Molecular Structure Conundrum: Bensaude-Vincent, B., and I. Stengers (1996), A History of Can Classical Chemistry Be Reduced to Quantum Chemistry. Translated by D. van Dam. Cambridge, MA: PROOFChemistry?’’ Journal of Chemical Education 61: 939–944. Harvard University Press. Woody, A. (2000), ‘‘Putting Quantum Mechanics to Work Bhushan, N., and S. Rosenfeld (2000), Of Minds and Mole- in Chemistry: The Power of Diagrammatic Representa- cules: New Philosophical Perspectives on Chemistry. New tion,’’ Philosophy of Science 67(suppl): S612–S627. York: Oxford University Press. Brock, W. (1993), The Norton History of Chemistry. New See also Explanation; Laws of Nature; Quantum York: W. W. Norton. Mechanics; Reductionism

CHOMSKY,FIRST NOAM

(7 December 1928–)

Avram Noam Chomsky received his Ph.D in lin- Technology since 1955, where he is currently Insti- guistics from the University of Pennsylvania and tute Professor. Philosophers are often familiar with has been teaching at Massachusetts Institute of the early work of Chomsky (1956, 1957, 1959a,

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and 1965), which applied the methods of formal One of the ways in which these assumptions language theory to empirical linguistics, but his translated into theory was in the order that vari- work has also incorporated a number of philo- ous levels of linguistic description were to be sophical assumptions about the nature of scien- tackled. The American Structuralists identified tific practice—many of which are defended in his four levels: phonemics (intuitively the study of writings. sound patterns), morphemics (the study of words, This essay will first describe the development and their prefixes and suffixes), syntax (the study of evolution of Chomsky’s theory of generative lin- sentence-level structure), and discourse (the study guistics, highlighting some of the philosophical of cross-sentential phenomena). The idea was that assumptions that have been in play. It will then proper methodology would dictate that one begin turn to some of the methodological debates in gen- at the level of phonemics, presumably because it erative linguistics (and scientific practice more is closer to the data; then proceed to construct generally), focusing on Chomsky’s role in these a theory of morphemics on the foundations of debates. phonemics; then proceed to construct a theory of syntax, etc. Notice the role that the concepts of logical em- The Development and Evolution of piricism played in this proposed methodology. One Generative Grammar finds radical reductionism in the idea that every level must be reducible to the more basic phonemic A number of commentators have suggested that level; verificationism in the contention that the Chomsky’s early work in generative linguistics phonemic level is closely tied to sense experience; initiated a kind of Kuhnian paradigm shift in lin- and discovery procedures in the suggestion that guistic theory. While Chomsky himself would re- this overall order of inquiry should be adopted ject this characterization (at least for his initial (see Reductionism; Verificationism). work in generative grammar), it is instructive to Chomsky rejected most if not all of these examine the development of generative linguistics, assumptions early on (see Chomsky [1955] 1975, for it provides an excellent laboratory for the introduction, for a detailed discussion). As regards study of the development of a young science, and discovery procedures, for example, he rejected in particular it illuminates some of the philosophi- them while still a matriculating graduate student, cal prejudice that a young science is bound to then holding a position in the Harvard Society of encounter. Fellows: Chomsky’s role in the development of linguistic theory and cognitive science generally can best be By 1953, I came to the same conclusion [as Morris appreciated if his work is placed in the context of PROOFHalle]if the discovery procedures did not work, it was not because I had failed to formulate them correctly, but the prevailing intellectual climate in the 1950s—one ... in which behaviorism held sway in psycho- because the entire approach was wrong. [S]everal years of intense effort devoted to improving discovery logy departments and a doctrine known as Ameri- procedures had come to naught, while work I had been can Structuralism was prevalent in linguistics doing during the same period on generative grammars departments. and explanatory theory, in almost complete isolation, American Structuralism, in particular as articu- seemed to be consistently yielding interesting results. lated by Bloomfield (1933 and 1939), adopted a (1979: 131) number of key assumptions that were in turn Chomsky also rejected the assumption that all adopted from logical empiricism (see Logical Em- processes should be ‘‘observable’’— early theories piricism). Newmeyer (1986, ch. 1) notes that the of transformational grammar offered key examples following assumptions were in play:FIRST of unobservable processes. For example, in his . All useful generalizations are inductive gener- ‘‘aspects theory’’ of generative grammar (Chomsky alizations. 1965), the grammar is divided into two different . Meanings are to be eschewed because they are ‘‘levels of representation,’’ termed initially deep occult entities—that is, because they are not structure and surface structure. The deep-structure directly empirically observable. representations were generated by a context-free . Discovery procedures like those advocated in phase structure grammar—that is, by rules (of de- logical empiricism should be developed for the composition, ‘‘!’’) of the following form, where S proper conduct of linguistic inquiry. stands for sentence, NP for noun phrase, VP for . There should be no unobserved processes. verb phrase, etc.

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S ! NP VP broke with prevailing methodology in structuralist linguistics and, indeed, behaviorist psychology, by VP ! VNP allowing intuitions rather than publicly available NP ! John behaviors as data. Generative grammar subsequently evolved in re- NP ! Bill sponse to a number of internal pressures. Crucially, V ! saw the number of transformations began to proliferate in a way that Chomsky found unacceptable. Why These rewriting rules then generated linguistic unacceptable? Early on in the development of gen- representations of the following form: erative grammar, Chomsky had made a distinction between 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, it must not merely describe the facts, but must do so t ð1Þ in a way that explains how humans are able to learn languages. Thus, linguistics was supposed to be embeddable into cognitive science more broad- ly. But if this is the case, then there is a concern about the unchecked proliferation of rules—such rule systems might be descriptively adequate, but Crucially for Chomsky, the objects of analysis in they would fail to account for how we learn lan- linguistic theory were not the terminal strings of guages (perhaps due to the burden of having to words, but rather phrase markers—structured learn all those language-specific rules). objects like (1). Transformational rules then oper- Chomsky’s initial (1964 and 1965) solution to this ated on these deep-structure representations to problem involved the introduction of conditions on yield surface-structure representations. So, for ex- transformations (or constraints on movement), with ample, the operation of passivization would take a the goal of reducing the complexity of the descrip- deep-structure representation like (1) and yield the tive grammar. In Chomsky (1965), for example, the surface-structure representation (abstracting from recursive power of the grammar is shifted from the detail) in (2): transformations to the phrase structure rules alone. In the ‘‘extended standard theory’’ of the 1970s, there was a reduction of the phrase structure com- ponentPROOF with the introduction of ‘‘X-bar theory,’’ and a simplification of the constraints on move- ð2Þ ment. This was followed by a number of proposals to reduce the number and types of movement rules themselves. This came to a head (Chomsky 1977 and 1981a) with the abandonment of specific transfor- mations altogether for a single rule (‘‘move-a’’), The sentence in (3) is therefore a complex object which stated, in effect, that one could move any- consisting of (at a minimum) an ordered pair of the thing anywhere. This one rule was then supplemen- two representations corresponding to (1) and (2): ted with a number of constraints on movement. As Chomsky and a number of other generative linguists Bill was seen by John:FIRSTð3Þ were able to show, it was possible to reduce a great Clearly, Chomsky was committed not only to number of transformations to a single-rule move-a ‘‘unobserved’’ processes in the guise of transforma- and to a handful of constraints on movement. tions, but also to unobserved levels of representa- Chomsky (1981b, 1982, and 1986a) synthesized tion. No less significant was the nature of the data subsequent work undertaken by linguists working that Chomsky admitted—not utterances or written in a number of languages, ranging from the romance strings, but rather speakers’ judgments of accept- languages to Chinese and Japanese, showing that ability and meaning. Thus, (3) is not a datum be- other natural languages had similar but not identical cause it has been written or spoken, but rather constraints, and it was hypothesized that the varia- because speakers have intuitions that it is (would tion was due to some limited parametric variation be) an acceptable utterance. Here again, Chomsky among human languages. This work established the

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‘‘principles and parameters’’ framework of genera- biological processes (like sphere packing in cell divi- tive grammar. To get an idea of this framework, sion) but also that such factors might be involved consider the following analogy: Think of the lan- across the board—even including the human brain guage faculty as a prewired box containing a num- and its language faculty. ber of switches. When exposed to environmental In broadest outline, the minimalist program data, new switch settings are established. Applying works as follows: There are two levels of linguistic this metaphor, the task of the linguist is to study representation, phonetic form (PF) and logical the initial state of the language faculty, determine form (LF), and a well-formed sentence (or linguis- the possible parametric variations (switch settings), tic structure) must be an ordered pair of and account for language variation in terms of a these representations (where p is a phonetic form limited range of variation in parameter settings. In and l is the logical form). PF is taken to be the Chomsky’s view (2000, 8), the principles-and-para- level of representation that is the input to the meters framework ‘‘gives at least an outline of a performance system (e.g., speech generation), and genuine theory of language, really for the first LF is, in Chomsky’s terminology, the input to the time.’’ Commentators (e.g., Smith 2000, p. xi) conceptual/intensional system. Since language is, if have gone so far as to say that it is ‘‘the first really nothing else, involved with the pairing of sounds novel approach to language of the last two and a and meanings, these two levels of representation half thousand years.’’ In what sense is it a radical are conceptually necessary. A minimal theory departure? For the first time it allowed linguists to would posit no other levels of representation. get away from simply constructing rule systems for It is assumed that each sentence (or better, struc- individual languages and to begin exploring in a ture, S) is constructed out of an array or numera- deep way the underlying similarities of human lan- tion, N, of lexical items. Some of the items in the guages (even across different language families), to numeration will be part of the pronounced (writ- illuminate the principles that account for those ten) sentence, and others will be part of a universal similarities, and ultimately to show how those prin- inventory of lexical items freely inserted into all ciples are grounded in the mind/brain. numerations. Given the numeration N, the compu- In Chomsky’s view, the principles-and-parameters tational system (CHL) attempts to derive (compute) framework has yielded a number of promising well-formed PF and LF representations, con- results, ranging from the discovery of important verging on the pair . The derivation is similarities between prima facie radically different said to converge at a certain level if it yields a languages like Chinese and English to insights into representation that is interpretable at that level. If the related studies of language acquisition, lan- it fails to yield an interpretable representation, the guage processing, and acquired linguistic deficits derivation crashes. Not all converging derivations (e.g., aphasia). Perhaps most importantly, the yieldPROOF structures that belong to a given language principles-and-parameters framework offered a L. Derivations must also meet certain economy way to resolve the tension between the two goals conditions. of descriptive adequacy and explanatory adequacy. Chomsky (2000, 9) notes that the import of the Still working within the general principles-and- minimalist program is not yet clear. As matters parameters framework, Chomsky (1995 and 2000, currently stand, it is a subresearch program within ch. 1) has recently articulated a research program the principles-and-parameters framework that is that has come to be known as the ‘‘minimalist showing some signs of progress—at least enough program,’’ the main idea behind which is the work- to encourage those working within the program. ing hypothesis that the language faculty is not the As always, the concerns are to keep the number product of messy evolutionary tinkeringFIRST—for ex- of principles constrained, not just to satisfy eco- ample, there is no redundancy, and the only nomy constraints, but to better facilitate the resources at work are those that are driven by ‘‘con- embedding of linguistics into theories of language ceptual necessity.’’ Chomsky (1995, ch. 1) initially acquisition, cognitive psychology, and, perhaps seemed to hold that in this respect the language most importantly, general biology. faculty would be unlike other biological functions, but more recently (2001) he seems to be drawn to D’Arcy Thompson’s theory that the core of evolu- Some Conceptual Issues in Generative tionary theory consists of physical/mathematical/ Grammar chemical principles that sharply constrain the possi- ble range of organisms. In this case, the idea would While Chomsky would argue that he does not be not only that those principles constrain low-level have a philosophy of science per se and that his

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philosophical observations largely amount to com- Not only is the notion of an E-language prob- mon sense, a number of interesting debates have lematic, but it will not help to retreat to talk about arisen in the wake of his work. The remainder of E-dialects. The problem is that what counts as a this essay will review some of those debates. separate 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’’ On the Object of Study rhymes with ‘‘matter’’ but not with ‘‘madder.’’ For AU:22 Chomsky (1986) draws the distinction between others, the facts do not cut in this way. Do they the notions of I-language and E-language, where I- speak the same dialect as Chomsky or not? There language is the language faculty discussed above, is no empirical fact of the matter here; it all construed as a chapter in cognitive psychology and depends on individuals’ desires to identify linguis- ultimately human biology. E-language, on the tically with each other. Even appeals to mutual other hand, comprises a loose collection of theories intelligibility will not do, since what we count as that take language to be a shared social object, intelligible will depend much more on our patience, established by convention and developed for pur- our ambition, and our familiarity with the practices poses of communication; or an abstract mathemat- of our interlocutors than it will on brute linguistic ical object of some sort. facts. In Chomsky’s view (widely shared by linguists), If the notion of E-language and E-dialect are the notion of a ‘language’ as it is ordinarily con- incoherent, is it possible to construct a notion of strued by philosophers of language is fundamental- E-idiolect?—that is, to identify idiolects by external ly incoherent. We may talk about ‘‘the English criteria like an individual’s spoken or written lan- language’’ or ‘‘the French language’’ but these are guage? Apparently not. Included in what a person loose ways of talking. Typically, the question of says or writes are numerous slips of the tongue, who counts as speaking a particular language is performance errors, etc. How are we to rule those determined more by political boundaries than ac- out of the individual’s E-idiolect? Appeal to the tual linguistic variation. For example, there are agent’s linguistic community will not do, since dialects of German that, from a linguistic point that would in turn require appeal to an E-language, of view, are closer to Dutch than to standard and for the reasons outlined above, there is no German. Likewise, in the Italian linguistic situa- meaningful way to individuate E-languages. In tion, there are a number of so-called dialects only the I-language approach, however, the problem of some of which are recognized as ‘‘official’’ lan- individuating I-idiolects takes the form of a coher- guages by the Italian government. Are the official ent empirical research project. The idiolect (I- languages intrinsically different from the ‘‘mere’’ idiolect) is determined by the parametric state dialects? Not in any linguistic sense. The decision ofPROOFA’s language faculty, and the language faculty to recognize the former as official is entirely a thus determines A’s linguistic competence. Speech political decision. In the words attributed to Max production that diverges from this competence Weinreich: A language is a dialect with an army can be attributed to performance errors. Thus, the and a navy. In this case, a language is a dialect with competence/performance distinction is introduced substantial political clout and maybe a threat of to illuminate the distinction between sounds and separatism. interpretations that are part of A’s grammar and Chomsky (1994 and 2000, ch. 2) compares talk those that are simply mistakes. The E-language of languages (i.e., E-languages) to saying that two perspective has no similar recourse. cities are ‘‘near’’ each other; whether two cities are near depends on our interests andFIRST our mode of transportation and very little on brute facts of The Underdetermination of Theory by Evidence geography. In the study of language, the notion One of the first philosophical issues to fall out of ‘sameness’ is no more respectable than that of from the development of generative grammar has ‘nearness’in geography. Informally we might group been the dispute between Quine (1972) and AU:23 together ways of speaking that seem to be similar Chomsky (1969 and 2000, ch. 3) on the indetermi- (relative to our interests), but such groupings have nacy of grammar. Similar to his argument for no real scientific merit. As a subject of natural the indeterminacy of meaning, Quine held that inquiry, the key object of study has to be the lan- there is no way to adjudicate between two descrip- guage faculty and its set of possible parametric tively adequate sets of grammatical rules. So, for variations. example, imagine two rule sets, one envisioning

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structures like (1) above, and another positing the agent and its environment) (see Supervenience). following: Chomsky has argued that all scientifically inter- esting psychological and linguistic properties supervene upon individualist (intrinsic) properties. In particular, there is a brute fact about the state of an individual’s language faculty, and that fact is ð4Þ determined in turn by facts about the individual in isolation—not by the environment in which the individual is embedded. Because the language fac- ulty is part of our biological endowment, the nature of the representations utilized by the language fac- Chomsky maintained that Quine’s argument is ulty are fixed by biology and are not sensitive to simply a recapitulation of the standard scientific environmental issues such as whether one is problem of the underdetermination of theory by moving about on Earth or a phenomenologically evidence. And in any case it is not clear that there identical planet with a different microstructure are no linguistic tests that would allow us to choose (e.g., Putnam’s ‘‘Twin Earth’’). between (1) and (4)—there are, after all, ‘‘constitu- Thus Chomsky takes issue with philosophers like ency tests’’ (e.g., involving movement possibilities) Burge (1986), who argues in Individualism and Psy- that would allow us to determine whether the XP chology that the content of the representations pos- or the VP is the more plausible constituent. ited in psychology are determined at least in part by Even if there are several grammars that are con- environmental factors. Chomsky holds that if the sistent with the available linguistic facts (the facts notion of content involves externalist or environ- are not linguistic behavior, for Chomsky, but intui- mental notions, then it is not clear that it can play tions about acceptability and possible interpreta- an interesting role in naturalistic inquiry in cognitive tion), we still have the additional constraint of psychology (see Psychology, Philosophy of ). which theory best accounts for the problem of If environmentalism is to be rejected in psychol- language acquisition, acquired linguistic deficits ogy, then it naturally must be rejected in the se- (e.g., from brain damage), linguistic processing, mantics of natural language as well. That is: if the etc. In other words, since grammatical theory is task of the linguist is to investigate the nature of I- embedded within cognitive psychology, the choice language; if the nature of I-language is a chapter of between candidate theories can, in principle, be cognitive psychology; and if cognitive psychology radically constrained. But further, even if there is an individualistic rather than a relational science, were two descriptively adequate grammars, each semantics will want to eschew relational properties likePROOF reference (where ‘reference’ is construed as a of which could be naturally embedded within cog- nitive psychology, there remain standard best- relation between a linguistic form and some object theory criteria (simplicity, etc.) that can help us to in the external environment). Thus Chomsky (1975 adjudicate between the theories. and 2000) rejects the notion of reference that has been central to the philosophy of language for the past three decades, characterizing it as an ill-defined Intrinsic Versus Relational Properties in technical notion (certainly one with no empirical Linguistics applications), and, following Strawson, suggests In the philosophy of science, it is routine to make that in the informal usage, individuals ‘refer’ but the distinction between ‘‘intrinsic’’ and ‘‘relational’’ linguistic objects do not (see Reference, Theories of ). properties. So, for example, the restFIRST mass of an This conclusion has immediate results for the object would be an intrinsic property and its weight notion of theory change in science. If the notion of would be a relational property (since it depends reference is suspect or incoherent, then it can hardly upon the mass of the body that the object is stand- be employed in an account of theory change (as in ing on). Similarly, in the philosophy of psychology Putnam 1988). How then to make sense of theory there is a common distinction between ‘‘individual- change? Chomsky (2000) suggests the following: istic’’ and ‘‘externalist’’ properties. So, for example, Some of the motivation for externalist approaches there is the question of whether psychological derives from the concern to make sense of the history states supervene on individualistic properties (in- of science. Thus, Putnam argues that we should take the trinsic properties that hold of the individual in early Niels Bohr to have been referring to electrons in isolation) or whether they supervene on ‘‘extern- the quantum-theoretic sense, or we would have to ‘‘dis- alist’’ properties (in effect, on relations between the miss all of his 1900 beliefs as totally wrong’’ (Putnam

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1988), perhaps on a par with someone’s beliefs about unselected functions that are determined from angels, a conclusion that is plainly absurd ... . structure (see Function). Agreeing ... that an interest in intelligibility in scientific discourse across time is a fair enough Inductive Versus Abductive Learning concern, still it cannot serve as the basis for a A number of debates have turned on whether general theory of meaning; it is, after all, only one language acquisition requires a dedicated language concern among many, and not a central one for the faculty or whether ‘‘general intelligence’’ is enough study of human psychology. Furthermore, there to account for our linguistic competence. Chomsky are internalist paraphrases. Thus we might say considers the general-intelligence thesis hopelessly that in Bohr’s earlier usage, he expressed beliefs vague, and argues that generalized inductive that were literally false, because there was nothing learning mechanisms make the wrong predictions of the sort he had in mind in referring to electrons; about which hypotheses children would select in a but his picture of the world and articulation of it number of cases. Consider the following two exam- was structurally similar enough to later con- ples from Chomsky (1975 and [1980] 1992a): ceptions so that we can distinguish his beliefs about electrons from beliefs about angels. (43) The man is tall ð5Þ (see Putnam, Hilary). Is the man tall? ð6Þ

Against Teleological Explanation in Linguistics Chomsky observes that confronted with evi- A number of philosophers and linguists have dence of question formation like that (5)–(6) and thought that some progress can be made in the given a choice between hypothesis (H1) and (H2), understanding of language by thinking of it as the generalized inductive learning mechanism will principally being a medium of communication. select (H1): Chomsky rejects this conception of the nature of Move the first ‘‘is’’ to the front of the sentence: language, arguing that the language faculty is not for communication in any interesting sense. Of ðH1Þ course, by rejecting the contention that language is a social object established for purposes of com- Move the first ‘‘is’’ following the first NP : ðH2Þ munication, Chomsky has not left much room for to the front of the sentence thinking of language in this way. But he also rejects But children apparently select (H2), since in standard claims that I-language must have evolved forming a question from (7), they never make the for the selectional value of communication; he error of producing (8), but always opt for (9): regards such claims as without basis in fact. On PROOF this score, Chomsky sides with Gould (1980), The man who is here is tall: ð7Þ Lewontin (1990), and many evolutionary biologists in supposing that many of our features (cognitive ÃIs the man who here is tall? ð8Þ or anatomical) did not necessarily evolve for selec- tional reasons, but may have been the result of Is the man who is here tall? ð9Þ arbitrary hereditary changes that have perhaps been co-opted (see Evolution). Thus the langu- Note that this is true despite the fact that the age faculty may not have evolved for purposes of only data they have been confronted with previous communication but may have been co-opted for to encountering (7) is simple data like (5)–(6). that purpose, despite its nonoptimalFIRST design for Chomsky’s conclusion is that whatever accounts communicative purposes. for children’s acquisition of language, it cannot be In any case, Chomsky cautions that even if there generalized inductive learning mechanisms, but was selectional pressure for the language faculty to rather must be a system with structure-dependent serve as a means of communication, selection is but principles/rules. Chomsky (1975, ch.1; 2000, 80) one of many factors in the emerging system. Cru- compares such learning to Peircian abduction. In cially (2000, 163), ‘‘physical law provides narrow other contexts this has been cast as a thesis about channels within which complex organisms may the ‘‘modularity’’ of language—that is, that there is vary,’’ and natural selection is only one factor a dedicated language acquisition device, and it, that determines how creatures may vary within rather than some vague notion of general intelli- these constraints. Other factors (as Darwin himself gence, accounts for our acquisition of language (see noted) will include nonadaptive modifications and Evolutionary Psychology).

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Putnam (1992) once characterized Chomsky’s distinguish between problems that in principle fall with- notion of a mental organ like the language faculty in its range, and mysteries that do not. The distinction is as being ‘‘biologically inexplicable,’’ but Chomsky relative to humans; rats and Martians have different ([1980] 1992b) has held that it is merely ‘‘unex- problems and mysteries and, in the case of rats, we plained’’ and not inexplicable; in his view the even know a fair amount about them. The distinction language faculty is thus on the same footing as also need not be sharp, though we certainly expect it to exist, for any organism and any cognitive faculty. The many other features of our biology (see Abduction; successful natural sciences, then, fall within the inter- Inductive Logic). section of the scope of SFF and the nature of the world; they treat the (scattered and limited) aspects of the world The Science-Forming Faculty that we can grasp and comprehend by naturalistic inqui- On a more general and perhaps more abstract ry, in principle. The intersection is a chance product of level, Chomsky has often spoken of a ‘‘science- human nature. Contrary to speculations since Peirce, forming faculty,’’ parallel to our language faculty. there is nothing in the theory of evolution, or any other The idea is that science could not have formed in intelligible source, that suggests that it should include answers to serious questions we raise, or even that we response to mere inductive generalizations, but that should be able to formulate questions properly in areas human beings have an innate capacity to develop of puzzlement. (2000, ch. 4) scientific theories (Chomsky credits C. S. Peirce with this basic idea). Despite Star Trekkian The question of what the ‘‘natural’’ sciences are, assumptions to the contrary, extraterrestrials pre- then, might be answered, narrowly, by asking what sumably do not have a science-forming faculty like they have achieved; or more generally, by inquiry we do, and may go about theorizing in entirely into a particular faculty of (the human) mind, with different ways, which would not be recognized as its specific properties. ‘‘scientific’’ by humans. While the science-forming faculty may be limit- The Mind/Body Problem and the Question of ed, Chomsky would not concede that its limits are Physicalism necessarily imposed by the selectional pressures of Chomsky has consistently defended a form of our prehistoric past. Just as the language faculty methodological monism (he is certainly no dualist); may not have evolved principally in response to but for all that, he is likewise no materialist. In selectional pressures, so too the science-forming Chomsky’s view the entire mind/body question is faculty may have emerged quite independently of ill-formed, since there is no coherent notion of selectional considerations. As Chomsky (2000, physical body. This latter claim is not in itself ch. 6) notes (citing Lewontin 1990), insects may unique; Crane and Mellor (1990) have made a seem marvelously well adapted to flowering plants, similarPROOF point. There is a difference, however; for but in fact insects evolved to almost their current Crane and Mellor, developments in twentieth- diversity and structure millions of years before century science have undermined physicalism, but flowering plants existed. Perhaps it is a similar for Chomsky the notion of physical body was situation with the science-forming faculty. That is, already undermined by the time of Newton: perhaps it is simply a matter of good fortune for us that the science-forming faculty is reliable and Just as the mechanical philosophy appeared to be trium- useful, since it could not have evolved to help us phant, it was demolished by Newton, who reintroduced with quantum physics, for example. a kind of ‘‘occult’’ cause and quality, much to the dis- may of leading scientists of the day, and of Newton himself. The Cartesian theory of mind (such as it was) The Limits of Science was unaffected by his discoveries, but the theory of body The notion of a science-formingFIRST faculty also was demonstrated to be untenable. To put it differently, raises some interesting questions about the limits Newton eliminated the problem of ‘‘the ghost in the of our ability to understand the world. Since what machine’’ by exorcising the machine; the ghost was we can know through naturalistic endeavors is unaffected. (2000, 84) bounded by our science-forming faculty, which in In Chomsky’s view, then, investigations into the turn is part of our biological endowment, it stands mind (in the guise of cognitive science generally or to reason that there are questions that will remain linguistics in particular) can currently proceed mysteries to us—or at least outside the scope of without worrying about whether they hook up naturalistic inquiry: with what we know about the brain, or even fun- Like other biological systems, SFF [the science-forming damental particles. The unification of science faculty] has its potential scope and limits; we may remains a goal, but in Chomsky’s view it is not

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the study of mind that must be revised so as to the criteria for rationality and justification from the study conform to physical theory, but rather physical of scientific success. Beyond that boundary, everything theory may eventually have to incorporate what changes; the critic applies independent criteria to sit in we learn in our study of the mind. According to judgment over the theories advanced and the entitities Chomsky this is parallel to the situation that held they postulate. This seems to be nothing more than a prior to the unification of chemistry and physics; it kind of ‘‘methodological dualism,’’ far more pernicious than the tradtional metaphysical dualism, which was a was not chemistry that needed to be modified to scientific hypothesis, naturalistic in spirit. Abandoning account for what we know about physics, but in this dualist stance, we pursue inquiry where it leads. fact just the opposite: (2000, 112)

Large-scale reduction is not the usual pattern; one PETER LUDLOW should not be misled by such dramatic examples as the reduction of much of biology to biochemistry in the middle of the twentieth century. Repeatedly, the more ‘‘fundamental’’ science has had to be revised, some- References AU:24 times radically, for unification to proceed. (2000, 82) Bloomfield, L. (1933), Language. New York: Holt, Rine- hart and Winston. ——— (1939), Linguistic Aspects of Science: International Conclusion Encyclopedia of Unified Science (Vol. 1, No. 4). Chicago: University of Chicago Press. The influence of Chomsky’s work has been felt in a Burge, T. (1986), ‘‘Individualism and Psychology,’’ Philo- number of sciences, but perhaps the greatest in- sophical Review 95: 3–45. fluence has been within the various branches of Chomsky, N. ([1955] 1975), The Logical Structure of Lin- guistic Theory. Chicago: University of Chicago Press. cognitive science. Indeed, Gardner (1987) has ——— (1956), ‘‘Three Models for the Description of Lan- remarked that Chomsky has been the single most guage,’’ I.R.E. Transactions of Information Theory IT-2: important figure in the development of cognitive 113–124. science. Some of Chomsky’s impact is due to his ——— (1957), Syntactic Structures. The Hague: Mouton. role in arguing against behaviorist philosophers ——— (1959a), ‘‘On Certain Formal Properties of Gram- mars,’’ Information and Control 2: 137–167. such as Quine; some of it is due to work that led ——— (1959b), ‘‘Review of B. F. Skinner, Verbal Behav- to the integration of linguistic theory with other ior,’’ Language 35, 26–57. sciences; some of it is due to the development of ——— (1964), Current Issues in Linguistic Theory. The formal tools that were later employed in disciplines Hague: Mouton & Co. ranging from formal language theory (cf. the ——— (1965), Aspects of the Theory of Syntax. Cambridge, MA: MIT Press. ‘‘Chomsky Hierarchy’’) to natural language proces- ——— (1968), Language and Mind. New York: Harcourt sing; and some of it is due to his directly engaging PROOFBrace Jovanovich. psychologists on their own turf. (One classic exam- ——— (1969), ‘‘Quine’s Empirical Assumptions,’’ in ple of this was Chomsky’s [1959b] devastating re- D. Davidson and J. Hintikka (eds.), Words and Objec- view of Skinner’s [1957] Verbal Behavior. See also tions: Essays on the Work of W.V. Quine. Dordrecht, Netherlands: D. Reidel. his contributions to Piatelli-Palmerini 1980) (See ——— (1975), Reflections on Language. New York: Pan- Behaviorism). theon. With respect to his debates with various philoso- ——— (1977), ‘‘Conditions on Rules of Grammar,’’ in phers, Chomsky has sought to expose what he has Essays on Form and Interpretation. Amsterdam: Elsevier taken to be double standards in the philosophical North-Holland, 163–210. ——— (1979), Language and Responsibility. New York: literature. In particular he has held that while other Pantheon. sciences are allowed to proceed where inquiry takes ——— (1980), Rules and Representations. New York: them without criticism by armchairFIRST philosophers, Columbia University Press. matters change when the domain of inquiry shifts ——— (1981a), Lectures on Government and Binding. Dor- to mind and language: drecht, Netherlands: Foris Publications. ——— (1981b), ‘‘Principles and Parameters in Syntactic The idea is by now a commonplace with regard to Theory,’’ in N. Horstein and D. Lightfoot (eds.), Expla- physics; it is a rare philosopher who would scoff at its nation in Linguistics: The Logical Problem of Language Acquisition. London: Longman. weird and counterintuitive principles as contrary to right ——— (1982), Some Concepts and Consequences of the thinking and therefore untenable. But this standpoint Theory of Government and Binding. Cambridge, MA: is commonly regarded as inapplicable to cognitive sci- MIT Press. ence, linguistics in particular. Somewhere in-between, ——— (1986a), Barriers. Cambridge, MA: MIT Press. there is a boundary. Within that boundary, science is ——— (1986b), Knowledge of Language. New York: self-justifying; the critical analyst seeks to learn about Praeger.

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——— (1988), Language and Problems of Knowledge: The Gould, S. J. (1980), The Panda’s Thumb: More Reflections Managua Lectures. Cambridge, MA: MIT Press. in Natural History. New York: W. W. Norton. ——— ([1980] 1992a), ‘‘On Cognitive Structures and Their Lewontin, R. (1990), ‘‘The Evolution of Cognition,’’ in Development,’’ in B. Beakley and P. Ludlow (eds.), The D. N. Osherson and E. E. Smith (eds.), An Invitation to Philosophy of Mind: Classical Problems/Contemporary Cognitive Science (Vol. 3). Cambridge, MA: MIT Press, Issues. Cambridge, MA: MIT Press, 393–396. 229–246. ——— ([1980] 1992b), ‘‘Discussion of Putnam’s Com- Newmeyer, Frederick (1986), Linguistic Theory in America ments,’’ in B. Beakley and P. Ludlow (eds.), The Philos- (2nd ed.). San Diego: Academic Press. ophy of Mind: Classical Problems/Contemporary Issues. Piatelli-Palmerini, M. (ed.) (1980), Language and Learning: Cambridge, MA: MIT Press, 411–422. The Debate between Jean Piaget and Noam Chomsky. ——— ([1988] 1992c), ‘‘From Language and Problems of Cambridge, MA: Harvard University Press. Knowledge,’’ in B. Beakley and P. Ludlow (eds.), The Putnam, H. (1988), Representation and Reality. Cambridge, Philosophy of Mind: Classical Problems/Contemporary MA: MIT Press. Issues. Cambridge, MA: MIT Press, 47–50. ——— ([1980] 1992), ‘‘What Is Innate and Why: Comments ——— (1994), ‘‘Noam Chomsky,’’ in S. Guttenplan (ed.), on the Debate,’’ in B. Beakley and P. Ludlow (eds.), The A Companion to the Philosophy of Mind. Oxford: Black- Philosophy of Mind: Classical Problems/Contemporary well, 153–167. Issues. Cambridge, MA: MIT Press. ——— (1995), The Minimalist Program. Cambridge, MA: Skinner, B. F. (1957), Verbal Behavior. New York: Appleton- MIT Press. Century-Crofts. ——— (2000), New Horizons in the Study of Language and Smith, N. (2000), Foreword, in Chomsky, New Horizons in Mind. Cambridge: Cambridge University Press. the Study of Language and Mind. Cambridge: Cambridge ——— (2001), ‘‘Beyond Explanatory Adequacy,’’ MIT Oc- University Press. casional Papers in Linguistics, no. 20. MIT Department of Linguistics. See also Behaviorism; Cognitive Science; Innate- Crane, T., and D. H. Mellor (1990), ‘‘There Is No Question Acquired Distinction; Linguistics, Philosophy of; of Physicalism,’’ Mind 99: 185–206. Psychology, Philosophy of; Physicalism Gardner, H. (1987), The Mind’s New Science: A History of the Cognitive Revolution. New York: Basic Books.

CLASSICAL MECHANICS PROOF

Over the centuries classical mechanics has been a mathematical refinement during the nineteenth steady companion of the philosophy of science. It century, classical mechanics gave birth to the com- has played different parts, ranging (i) from positing bination of formal analysis and philosophical its principles as a priori truths to the insight— interpretation that distinguished the modern phi- pivotal for the formation of a modern philosophy losophy of science from the earlier Naturphiloso- of science—that modern physics requires a farewell phie. The works of Helmholtz, Mach, and Poincare´ to the explanatory ideal erected upon mechanics; molded the historical character of the scientist-phi- (ii) from the physiological analyses of mechanical losopher that would fully bloom during the emer- experiences to axiomatizations accordingFIRST to the gence of relativity theory and quantum mechanics strictest logical standards; and (iii) from the me- (see Mach; Quantum Mechanics; Poincare´; Space- chanistic philosophy to conventionalism (see Con- Time). ventionalism; Determinism; Space-Time). Core Mechanics became ‘‘classical’’ at the latest with the structures of modern science, among them differen- advent of quantum mechanics. Already relativistic tial equations and conservation laws, as well as core field theory had challenged mechanics as the lead- themes of philosophy, among them determinism and ing scientific paradigm. Consequently, present-day the ontological status of theoretical terms, have philosophers of science usually treat classical me- emerged from this context. Two of the founders of chanics within historical case studies or as the first classical mechanics, Galileo and Newton, have often touchstone for new proposals of a general kind. been identified with the idea of modern science as Nonetheless, there are at least two lines on which a whole. Owing to its increasing conceptual and classical mechanics in itself remains a worthy topic

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for philosophers. On the one hand, ensuing from no mathematical derivation whatsoever could substantial mathematical progress during the twen- replace experience. tieth century, classical mechanics has developed Pivotal for bringing about modern experimental into the theory of classical dynamical systems. science was Galileo’s successful criticism of Aristo- Among the problems of interest to formally mind- telian mechanics. Aristotle had divided all natural ed philosophers of science are the relationships motions into celestial motions, which were circular between the different conceptualizations, issues of and eternal, and terrestrial motions, which were stability and chaotic behavior, and whether classi- rectilinear and finite. Each of the four elements cal mechanics is a special case of the conceptual (earth, water, fire, air) moved toward its natural structures characteristic of other physical theories. place. Aristotle held that heavy bodies fell faster On the other hand, classical mechanics or semiclas- than light ones because velocity was determined by sical approaches continue to be applied widely by the relation of motive force (weight) and resistance. working scientists and engineers. Those real-world All forces were contact forces, such that a body applications involve a variety of features that sub- moving with constant velocity was continuously stantially differ from the highly idealized textbook acted upon by a force from the medium. Resistance models to which physicists and philosophers are guaranteed that motion remained finite in extent. typically accustomed, and they require solution Thus there was no void, nor motion in the void. strategies whose epistemological status is far from Galileo’s main achievement was the idealization of obvious. a constantly accelerated motion in the void that is Often classical mechanics is used synonymously slowed down by the resistance of the medium. This with Newtonian mechanics, intending that its con- made free fall amenable to geometry. For today’s tent is circumscribed by Newton’s famous three reader, the geometrical derivation of the law is laws. The terms analytical mechanics and rational clumsy; the ratio of different physical quantities mechanics stress the mathematical basis and theo- v ¼ s/t (where s stands for a distance, t for a time AU:25 retical side of mechanics as opposed to practical interval, and v for a velocity) was not yet meaning- mechanics, which originally centered around the ful. Galileo expressly put aside what caused bodies traditional simple machines: lever, wedge, wheel to fall and referred to experimentation. Historians and axle, tackle block, and screw. But the domain and philosophers have broadly discussed what and of mechanics was being constantly enlarged by the how Galileo reasoned from empirical evidence. invention of new mechanical machines and tech- Interpreters wondered, in particular, whether the nologies. Most expositions of mechanics also in- thought experiment establishing the absurdity of clude the theory of elasticity and the mechanics of the Aristotelian position was conclusive by itself continua. The traditional distinction between me- or whether Galileo had simply repackaged empiri- chanics and physics was surprisingly long-lived. calPROOF induction in the deductive fashion of geometry. One reason was that well into the nineteenth centu- Huygens’ most important contribution to me- ry, no part of physics could live up to the level of chanics was the derivation of the laws of impact formal sophistication that mechanics had achieved. by invoking the principle of energy conservation. Although of little importance from a theoretical His solution stood at the crossroads of two tradi- point of view, it is still common to distinguish statics tions. On the one hand, it solved the foundational (mechanical systems in equilibrium) and dynamics problem of Cartesian physics, the program of that are subdivided into a merely geometrical part, which was to reduce all mechanical phenomena to kinematics, and kinetics. contact forces exchanged in collision processes. On the other hand, it gave birth to an approach based Ancient Greek and Early ModernFIRST Mechanics upon the concept of energy, which became an al- ternative to the Newtonian framework narrowly In Greek antiquity, mechanics originally denoted understood. the art of voluntarily causing motions against the The work of Kepler has repeatedly intrigued nature of the objects moved. Other than physics, it philosophers of diverging orientations. Utilizing was tractable by the methods of Euclidean geome- the mass of observational data collected by Brahe, try. Archimedes used mechanical methods to deter- Kepler showed that the planetary orbits were ellip- mine the center of mass of complex geometrical ses. Kepler’s second law states that the line joining shapes but did not recognize them as valid geomet- the sun to the planet sweeps through equal areas in rical proofs. His Euclidean derivation of the law equal times, and the third law states that the square of the lever, on the other hand, sparked severe of the periods of revolution of any two planets criticism from Mach ([1883] 1960), who held that are in the same proportion as the cubes of their

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semi-major axes. All three laws were merely kine- space and time. Within Kant’s transcendental phi- matical. In his Mysterium cosmographicum, Kepler losophy, Euclidean space-time emerged from pure ([1596] 1981) identified the spacings of the then intuition a priori. This was the stand against known six planets with the five platonic solids. It which twentieth-century philosophy of science rebel- will be shown below that the peculiar shape of led, having relativity theory in its support (see the solar system given Newton’s laws of univer- Space-Time). sal gravitation can be explained without refer- Admitting that the laws were suggested by pre- ence to Kepler’s metaphysical belief in numerical vious experiences, some interpreters, including harmony. Poincare´, considered them as mere conventions (see Conventionalism). Positing absolute Euclidean On the Status of Newton’s Laws space, the first law states how inertial matter moves in it. But it is impossible to obtain knowledge about The most important personality in the history of space independent of everything else. Thus, the first classical mechanics was Newton. Owing to the law represents merely a criterion for choosing a activities of his popularizers, he became regarded suitable geometry. Mach ([1883] 1960) rejected as the model scientist; this admiration included a absolute space and time as metaphysical. All ob- devotion to the methodology of his Philosophiae servable motion was relative, and thus, at least in naturalis principia mathematica (Newton [1687, principle, all material objects in the universe were 1713] 1969), outlined in a set of rules preceding mutually linked. Mach’s principle, as it became book III. But interpreters disagree whether Newton called, influenced the early development of general really pursued the Baconian ideal of science and relativity but is still controversial among philoso- licensed induction from phenomena or must be sub- phers (see Barbour and Pfister 1995; Pooley and sumed under the later descriptivist tradition that Brown 2002). To Mach’s mind, the three laws were emerged with Mach ([1883] 1960) and Kirchhoff highly redundant and followed from a proper em- (1874). At any rate, the famous declaration not piricist explication of Newton’s definitions of mass to feign hypothesis targeted the Cartesian and and force. Defining force, with Newton, as an ac- Leibnizian quest for a metaphysical basis of the tion exerted upon a body to change its state, that is, principles of mechanics. as an acceleration, the first and second laws can be After the model of Euclid, the Principia began straightforwardly derived. Mach rejected Newton’s with eight definitions and three axioms or laws. definition of mass as quantity of matter as a pseudo- Given Newton’s empiricist methodology, interpre- definition and replaced it with the empirical insight ters have wondered about their epistemological that mass is the property of bodies determin- status and the logical relations among them. Cer- ing acceleration. This was equivalent to the third tainly, the axioms were neither self-evident truths law.PROOF Mach’s criticism became an important moti- nor mutually independent: vation for Einstein’s special theory of relativity. Yet, even the members of the Vienna Circle dis- 1. Every body continues in its state of rest or agreed whether this influence was formative or uniform motion in a right (i.e., straight) line, Mach merely revealed the internal contradictions unless it is compelled to change that state by of the Newtonian framework (see Vienna Circle). forces impressed upon it. As to the second law, one may wonder whether 2. The change of motion is proportional to the the forces are inferred from the observed phenom- motive force impressed and is made in the ena of motion or the motions are calculated from direction of the right line in which that force given specific forces. Textbooks often interpret the is impressed. second law as providing a connection from forces 3. To every action there is alwaysFIRST opposed an to motion, but this is nontrivial and requires a equal reaction; or the mutual actions of two proper superposition of the different forces and a bodies upon each other are always equal, and due account of the constraints. The opposite inter- directed to contrary parts. pretation has the advantage of not facing the noto- The proper philosophical interpretation of these rious problem of characterizing force as an entity three laws remained contentious until the end of in its own right, which requires a distinction be- the nineteenth century. Kant claimed to have tween fundamental forces from fictitious or inertial deduced the first and third laws from the synthetic forces. a priori categories of causality and reciprocity, re- Book III of Newton’s Principia introduced the spectively. The absolute distinction between rest law of universal gravitation, which finally unified and motion in the first law was based on absolute the dynamics of the celestial and terrestrial spheres.

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CLASSICAL MECHANICS

But, as it stood, it involved an action at a distance 1785, Laplace explained the remaining chief anoma- through the vacuum, which Newton regarded lies in the solar system and provided a (flawed) as the greatest absurdity. To Bentley he wrote: indirect proof for the stability of the solar system ‘‘Gravity must be caused by an Agent acting from the conservation of angular momentum according to certain Laws; but whether this Agent (cf. Wilson 1995). be material or immaterial, I have left to the Consid- One might draw an inductivist lesson from this eration of my readers’’ (Cohen 1958, 303). Given the history and conceive the increased precision in the law of universal gravity, the peculiar shape of the core parameters of the solar system, above all the solar system was a matter of initial conditions, a planetary masses, as a measure of explanatory suc- fact that Newton ascribed to the contrivance of a cess for the theory containing them (cf. Harper and voluntary agent. Smith 1995). Yet, the historically more influential The invention of the calculus was no less impor- lesson for philosophers consisted in the ideal of tant for the development of mechanics than was the Laplace’s Demon, the intellect that became the law of gravitation. But its use in the Principia was executive officer of strict determinism: not consistent and intertwined with geometrical arguments, and it quickly turned out that Leibniz’s Given for one instant an intelligence which could com- version of the calculus was far more elegant. That prehend all the forces by which nature is animated and the respective situation of the beings who compose it— British scientists remained loyal to Newton’s flux- an intelligence sufficiently vast to submit these data to ions until the days of Hamilton proved to be a analysis—it would embrace in the same formula the substantial impediment to the use of calculus in greatest bodies of the universe and those of the lightest science. atom; for it, nothing would be uncertain, and the future, as the past, would be present to its eyes. Celestial Mechanics and the Apparent (Laplace [1795] 1952, 4) Triumph of Determinism But the Demon is threatened by idleness in many No other field of mechanics witnessed greater tri- ways. If the force laws are too complex, determin- umphs of prediction than celestial mechanics: the ism becomes tautologous; if Newton’s equations return of Halley’s comet in 1758; the oblateness of cannot be integrated, perturbative and statistical the Earth in the 1740s; and finally the discovery of strategies are mandatory; calculations could still Neptune in 1846 (cf. Grosser 1962). However, be too complex; exact knowledge of the initial while Neptune was found at the location that the state of a system presupposes that the precision of anomalies in the motion of Uranus had suggested, measurement could be increased at will. Le Verrier’s prediction of a planet Vulcan to ac- A further idealization necessary to make the count for the anomalous perihelion motion of LaplacianPROOF ideal thrive was the point mass approach Mercury failed. Only general relativity would pro- of Boscovich ([1763] 1966). But some problems vide a satisfactory explanation of this anomaly (see cannot be solved in this way—for instance, whether Space-Time). a point particle moving in a head-on orbit directed But in actual fact little follows from Newton’s at the origin of a central force is reflected by the axioms and the inverse square law of gravitation singularity or goes right through it. In many cases, alone. Only the two-body problem can be solved celestial mechanics treats planets as extended bod- analytically by reducing it to a one-body problem ies or gyroscopes rather than point masses. Non- for relative distance. The three-body problem re- rigid bodies or motion in resisting media require quires approximation techniques, even if the mass even further departures from the Laplacian ideal. of one body can be neglected. To ensureFIRST the conver- As Mark Wilson put it, ‘‘applied mathematicians gence of the respective perturbation series became are often forced to pursue roundabout and shakily a major mathematical task. In his lunar theory, rationalized expedients if any progress is to be Clairaut could derive most of the motion of the made’’ (2000, 296). lunar apsides from the inverse-square law, provided Only some of these expedients can be mathemat- the approximation was carried far enough. But ically justified. This poses problems for the rela- d’Alembert warned that further iterations might tionship of mathematical and physical ontology. fail to converge; hence subsequent analysts cal- Often unsolvable equations are divided into tracta- culated to higher and higher orders. D’Alembert’s ble satellite equations. Continuum mechanics is a derivation of the precession and nutation of the case in point. The Navier-Stokes equations are Earth completed a series of breakthroughs around virtually intractable by analytic methods; Prandtl’s 1750 that won Newton’s law a wide acceptance. In boundary layer theory splits a flow in a pipe into

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CLASSICAL MECHANICS

one equation for the fluid’s boundary and one for of work as an empirical specification of the instinc- the middle of the flow. Prandtl’s theory failed in the tive experience that perpetual motion is impossible, case of turbulence, while statistical investigations Planck (1887) stressed the independence and uni- brought useful results. Accordingly, in this case versality of the principle of energy conservation. predictability required abandoning determinism Planck later lauded Mach’s positivism as a useful altogether years before the advent of quantum antidote against exaggerated mechanical reduc- mechanics (cf. von Mises 1922). tionism but called for a stable world view erected upon unifying variational principles and invariant From Conserved Quantities to Invariances: quantities. Force and Energy Group theory permitted mathematical physicists to ultimately drop any substantivalist connotation The framework of Newton’s laws was not the only of conserved quantities, such as energy. The main conception of mechanics used by 1800 (cf. Grattan- achievement was a theorem of Emmy Noether that Guinness 1990). There were purely algebraic ver- identified conserved quantities, or constants of mo- sions of the calculus based on variational problems tion, with invariances under one-parameter group developed by Euler and perfected in Lagrange’s transformations (cf. Arnold 1989, 88–90). Analytical Mechanics ([1788] 1997). Engineers de- veloped a kind of energy mechanics that emerged Variational Principles and Hamiltonian from Coulomb’s friction studies. Lazare Carnot de- Mechanics veloped it into an alternative to Lagrange’s reduc- tion of dynamics to equilibrium, that is, to statics. In 1696–7 Johann Bernoulli posed the problem of Dynamics should come first, and engineers had to finding the curve of quickest descent between two deal with many forces that did not admit a potential points in a homogeneous gravitational field. While function. his own solution used an analogy between geomet- The nature of energy—primary entity or just rical optics and mechanics, the solutions of Leibniz inferred quantity—was no less in dispute than and Jacob Bernoulli assumed that the property of that of force. Both were intermingled in content minimality was present in the small as in the large, and terminology. The eighteenth century was arriving thus at a differential equation. The title of strongly influenced by the vis viva controversy Euler’s classic treatise describes the scope of the launched by Leibniz. What was the proper quantity variational calculus: The Method of Finding Curved in the description of mechanical processes: mv or Lines That Show Some Property of Maximum or mv2 (where m ¼ mass and v ¼ velocity)? After the Minimum (1744). The issue of minimality sparked Leibniz-Clarke correspondence, the issue became philosophical confusion. In 1746 Pierre Moreau de associated with atomism and the metaphysical MaupertuisPROOF announced that in all natural processes R R character of conserved quantities. In the nineteenth the quantity vds ¼ v2dt attains its minimum; he century, ‘energy,’ or work, became a universal interpreted this as a formal teleological principle principle after the discovery of the mechanical that avoided the outgrowths of the earlier physi- equivalent of heat. Helmholtz gave the principle a cotheology of Boyle and Bentley. Due to his defec- more general form based upon the mechanical tive examples and a priority struggle, the principle conception of nature. For many scientists this sug- lost much of its credit. Lagrange conceived of it gested a reduction of the other domains of physical simply as an effective problem-solving machinery. science to mechanics. But this program failed in There was considerable mathematical progress electrodynamics. during the nineteenth century, most notably by Through the works of Ostwald andFIRST Helm, the Hamilton, Gauss, and Jacobi. Only Weierstrass concept of energy became the center of a movement found the first sufficient condition for the varia- that spellbound German-speaking academia from tional integral to actually attain its minimum value. the 1880s until the 1900s. But, as Boltzmann untir- In 1900, Hilbert urged mathematicians to sys- ingly stressed, energeticists obtained the equations tematically develop the variational calculus (see of motion only by assuming energy conservation in Hilbert, David). He made action principles a core each spatial direction. But why should Cartesian element of his axiomatizations of physics. Hilbert coordinates have a special meaning? and Planck cherished the principles’ applicability, Two historico-critical studies of the energy con- after appropriate specification, to all fields of re- cept set the stage for the influential controversy versible physics; thus they promised a formal uni- between Planck and Mach (1908–1910). While fication instead of the discredited mechanical Mach ([1872] 1911) considered the conservation reductionism.

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There exist differential principles, among them draw conclusions about modal characteristics. d’Alembert’s principle and Lagrange’s principle of Albeit well versed in their mathematical intri- virtual work, that reduce dynamics to statics, and cacies, logical empiricists treated action principles integral action principles that characterize the ac- with neglect in order to prevent an intrusion of tual dynamical evolution over a finite time by the metaphysics (Sto¨ltzner 2003). stationarity of an integral as compared with other The second-order Euler-Lagrange equations, possible evolutions. Taking Mq as the space of all which typically correspond to the equations estab- possible motions q(t) between two points in config- lished by way of Newton’s laws, can be reformu- uration space, the action principle states that the lated as a pair of first-order equations, Hamilton’s actual motionR q extremizes the value of the integral equations, or a single partial differential equation, b ; ; _ W½qŠ ¼ a Fðt qðtÞ qðtÞÞdt in comparison with all viz., the Hamilton-Jacobi equation. Hamilton’s possible motions, the varied curves (q þ dq)2Mq equations emerge from the so-called Legendre (the endpoints of the interval [a, b] remain fixed). transformation, which maps configuration space If one views the philosophical core of action ðq; q_Þ into phase space ðq; pÞ, thus transforming principles in a temporal teleology, insofar as a the derivative of position q_ into momentum p.If AU:27 particle’s motion between a and b is also deter- this transformation fails, constraints may be pres- mined by the fixed state, this contradicts the fact ent. The core property of Hamilton’s equations is that almost all motions that can be treated by way their invariance under the so-called canonical trans- of action principles are reversible. Yet, already the formations. The canonical transformation ðq; pÞ! mathematical conditions for an action principle to ðQ; PÞ that renders the Hamiltonian H(Q,P) ¼ be well defined suggest that the gist of the matter T þ V equal to zero leads to the Hamilton-Jacobi lies in its global and modal features. Among the equation. Its generator W ¼ S – Et (where Et is the necessary conditions is the absence of conjugate total energy) can be interpreted as an action func- AU:28 points between a and b through which all varied tional corresponding to moving wave fronts in or- curves have to pass. Sufficient conditions typically dinary space that are orthogonal to the extremals involve a specific field embedding of the varied of the variational problem (cf. Lanczos 1986). curves; also the continuity properties of the q 2 The analogy between mechanics and geometric Mq play a role. Thus initial and final conditions optics is generic and played an important role in have to be understood in the same vein as bound- Schro¨dinger’s justification of his wave equation. ary conditions for partial differential equations Hamilton-Jacobi theory was also a motivation for AU:26 that have to be specified beforehand so that the Bohm’s reformulation of the de Broglie pilot wave solution cannot be grown stepwise from initial theory (see Quantum Mechanics). For periodical data. motions one can use S to generate a canonical There are also different ways of associating the transformationPROOF that arrives at action and angle possible motions. In Hamilton’s principle, F is the variables ðJ; oÞ, where J ¼ rpdq. This integral Lagrangian L ¼ T – V, where T is the kinetic and V was quantized in the older Bohr-Sommerfeld the potential energy; time is not varied such that all quantum theory. The space of all possible motions possible motions take equal time but correspond to associated with a variational problem Mq can be higher energies than the actual motion. For the considered as an ensemble of trajectories. Arguing original principle of least action, F equals T, and that in quantum theory all possible motions are one obtains the equations of motion only by as- realized with a certain possibility provides some suming energy conservation, such that at equal intuitive motivation for the Feynman path integral total energy the varied motions take a longer time approach (see Quantum Field Theory). than the actual ones. FIRST Variational principles played a central role in Butterfield (2004) spots three types of modality several philosophically influential treatises of me- in the sense of David Lewis (1986) here. While all chanics in the late nineteenth century. Most radical action principles involve a modality of changed ini- was that of Heinrich Hertz ([1894] 1956), who used tial conditions and changed problems, Hamilton’s Gauss’s (differential) principle of least constraints principle also involves changed laws because the to dispense with the notion of force altogether. varied curves violate energy conservation. Energe- There were no single mass points but only a system ticists and Mach ([1883] 1960) held that u is unique- of mass points connected by constraints. Hertz’s ly determined within Mu as compared with the problem was to obtain a geometry of straight line other motions that appear pairwise or with higher for this system of mass points. This task was compli- degeneracy, but they disagreed whether one could cated by Hertz’s Kantian preference for Euclidean

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CLASSICAL MECHANICS

geometry as a basis for the non-Euclidean geometry intricacies of variational calculus do not evaporate; of mass points. Contemporaries deemed Hertz’s they transform into obstructions of and conditions AU:29 geometrization of mechanics a ‘‘God’s eye view.’’ for the application of the whole geometrical Boltzmann (1897 and 1904) praised its coherence machinery, e.g., how far a local flow can be extend- but judged Hertz’s picture as inapplicable to pro- ed. The constants of the motion define invariant blems easily tractable by means of forces. submanifolds that restrict the flow to a manifold of Hertz held that theoretical pictures had to be lower dimension; they act like constraints. If a logically permissible, empirically correct, and ap- Hamiltonian system has, apart from total energy, propriate (that is, sufficiently complete and sim- enough linearly independent constants ofP motion ; m @ = ple). Boltzmann criticized permissibility as an and if their Poisson brackets fF Gg¼ i¼1ð F unwarranted reliance upon a priori laws of thought @qi@G=@pi À @G=@qi@F=@piÞ mutually vanish, the and held instead that pictures were historically ac- system is integrable (the equations of motion can quired and corroborated by success. Around 1900, be solved) and the invariant submanifold can be treating theories (e.g., atomism) as pictures repre- identified with a higher-dimensional torus. sented an alternative to mechanical reductionism The geometrical structure of Hamiltonian me- and positivist descriptivism, until the idea of co- chanics is kept together by the symplectic form i ordinative definitions between symbolic theory o ¼ dq 6dpi that is left invariant by canonical and empirical observations won favor (see Vienna transformations. It plays a role analogous to the Circle). metric in relativity theory. The skew-symmetric product 6 of forms and the exterior derivative d Mathematical Mechanics and Classical are the main tools of the Cartan calculus and per- Dynamical Systems mit an entirely coordinate-free formulation of dy- namics. Many equations thus drastically simplify, After classical mechanics was finally dethroned as but quantitative results still require the choice of a the governing paradigm of physics, its course specific chart. became largely mathematical in kind and was Mathematical progress went hand in hand with a strongly influenced by concepts and techniques de- shift of emphasis from quantitative to qualitative veloped by the new-frontier theories of physics: results that started with Poincare´’s work on the relativity theory and quantum physics. There was n-body problem. Some deep theorems of Hamilto- substantial progress in the variational calculus, nian mechanics become trivialities in this new lan- but the main inspirations came from differential guage, among them the invariance of phase space geometry, group theory, and topology, on the volume (Liouville’s theorem) and the fact that al- one hand, and probability theory and measure the- most all points in a phase space volume eventually— ory, on the other. This has led to some rigorous inPROOF fact, infinitely often—return arbitrarily close to results on the n-body problem. The advent of the their original position (Poincare´ recurrence) (see modern computer not only opened a new era of also Statistical Mechanics). celestial mechanics, it also revealed that chaotic For the small number of mass points character- behavior, ignored by physicists in spite of its early istic of celestial mechanics, there has been major discovery by Poincare´, occurred in a variety of progress along the lines of the questions asked by simple mechanical systems. Thirring (1992, 6): ‘‘Which configurations are sta- Geometrization has drastically changed the ble? Will collisions ever occur? Will particles ever appearance of classical mechanics. Configuration escape to infinity? Will the trajectory always remain space and phase space have become the tangent in a bounded region of phase space?’’ In the two- and cotangent bundles on which tensors,FIRST vector body problem, periodic elliptic motions, head-on fields, and differential forms are defined. Coordi- collisions, and the hyperbolic and parabolic trajec- nates have turned into charts, and the theory of tories leading to infinity are neatly separated by differentiable manifolds studies the relationships initial data. between the local level, where everything looks For the three-body problem the situation is Euclidean, and the global level, where topological already complex; there do not exist sufficient con- obstructions may arise. The dynamics acting on stants of motion. Two types of exact solutions were these bundles are expressed in terms of flows de- quickly found: The particles remain collinear fined by vector fields, which gives a precise mean- (Euler) or they remain on the vertices of an equilat- ing to variations. The picture of flows continues eral triangle (Lagrange). The equilateral configura- Hamilton-Jacobi theory. This elucidates that the tion is realized by the Trojan asteroids, Jupiter and

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the sun. In general, however, even for a negative References total energy, two bodies can come close enough to Arnold, Vladimir I (1989), Mathematical Methods of Clas- expel the third to infinity. In the four-body pro- sical Mechanics, 2nd ed. New York and Berlin: Springer. blem, there exist even collinear trajectories on Barbour, Julian B., and Herbert Pfister (eds.) (1995), which a particle might reach spatial infinity in a Mach’s Principle: From Newton’s Bucket to Quantum finite time (Mather and McGehee 1975). Five bod- Gravity. Boston and Basel: Birkha¨user. Boltzmann, Ludwig (1897 and 1904), Vorlesungen u¨ber die ies, one of them lighter than the others, can even be Principe der Mechanik. 2 vols. Leipzig: Barth. arranged in such a manner that this happens with- Boscovich, Ruder J. ([1763] 1966), A Theory of Natural out any previous collisions because the fifth parti- Philosophy. Cambridge, MA: MIT Press. cle oscillates faster and faster between the two Butterfield, Jeremy (2004), ‘‘Some Aspects of Modality in escaping planes, in each of which two particles Analytical Mechanics,’’ in Michael Sto¨ltzner and Paul Weingartner (eds.), Formale Teleologie und Kausalita¨t. rotate around one another (Xia 1992; Saari 2005). Paderborn, Germany: Mentis. Both examples blatantly violate special relativity. Cohen, I. Bernhard (ed.) (1958), Isaac Newton’s Papers and But rather than hastily resort to arguments of Letters on Natural Philosophy. Cambridge, MA: Harvard what is ‘physical,’ the philosopher should follow University Press. the mathematical physicist in analyzing the logical Euler, Leonhard (1744), Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes sive Solutio structure of classical mechanics, including collisions Problematis Isoperimetrici Latissimo Sensu Accepti. and other singularities. Lausanne: Bousquet. Can an integrable system remain stable under Grattan-Guinness, Ivor (1990), ‘‘The Varieties of Mechanics perturbation? In the 1960s Kolmogorov, Arnold, by 1800,’’ Historia Mathematica 17: 313–338. and Moser (KAM) gave a very general answer that Grosser, Morton (1962), The Discovery of Neptune. Cam- bridge, MA: Harvard University Press. avails itself of the identification of integrable sys- Harper, William, and George E. Smith (1995), ‘‘Newton’s tems and invariant tori. The KAM theorem shows New Way of Inquiry,’’ in J. Leplin (ed.), The Creation that sufficiently small perturbations deform only of Ideas in Physics: Studies for a Methodology of the invariant tori. If the perturbation increases, Theory Construction. Dordrecht, Netherlands: Kluwer, the tori in resonance with it break first; or more 113–166. Hertz, Heinrich ([1894] 1956), The Principles of Mechanics: precisely, the more irrational the ratio of the fre- Presented in a New Form. New York: Dover Publica- quency of an invariant torus (in action and angle tions. variables) and the frequency of the perturbation, Kepler, Johannes ([1596] 1981), Mysterium cosmographi- the more stable is the respective torus. If all invari- cum. New York: Abaris. ant tori are broken, the system becomes chaotic (cf. Kirchhoff, Gustav Robert (1874), Vorlesungen u¨ber analy- tische Mechanik. Leipzig: Teubner. Arnold 1989; Thirring 1992). The KAM theorem Lagrange, Joseph Louis ([1788] 1997), Analytical Mechan- also provides the rigorous basis of Kepler’s associ- ics. Dordrecht, Netherlands: Kluwer. ation of planetary orbits and platonic solids. The Lanczos,PROOF Cornelius (1986), The Variational Principles of ratios of the radii of platonic solids to the radii of Mechanics. New York: Dover. inscribed platonic solids are irrational numbers of a Laplace, Pierre Simon de ([1795] 1952), A Philosophical Essay on Probabilities. New York: Dover. kind that is badly approximated by rational num- Lewis, David (1986), On the Plurality of Worlds. Oxford: bers. And, indeed, among the asteroids between Blackwell. Mars and Jupiter, one finds significant gaps for Mach, Ernst ([1872] 1911), History and Root of the Principle small ratios of an asteroid’s revolution time to of the Conservation of Energy. Chicago: Open Court. that of the perturbing Jupiter. ——— ([1883] 1960), The Science of Mechanics: A Critical and Historical Account of Its Development. La Salle, IL: If all invariant tori have broken up, the only Open Court. German first edition published by Broc- remaining constant of motion is energy, such that khaus, Leipzig, 1883. the system begins to densely cover the energy shell Mather, John, and Richard McGehee, ‘‘Solutions of the FIRST Collinear Four-Body Problem Which Become Unbound- and becomes ergodic. No wonder that concepts of statistical physics, among them ergodicity, entropy, ed in Finite Time,’’ in Ju¨rgen Moser (ed.), Dynamical Systems Theory and Applications. New York: Springer, and mixing, have been used to classify chaotic be- 573–587. havior, even though chaotic behavior does not suc- Newton, Isaac ([1687, 1713] 1969), Mathematical Principles cumb to statistical laws. They are supplemented by of Natural Philosophy. Translated by Andrew Motte topological concepts, such as the Hausdorff dimen- (1729) and revised by Florian Cajori. 2 vols. New sion, and concepts of dynamical systems theory, York: Greenwood. AU:30 Planck, Max (1887), Das Princip der Erhaltung der Energie, such as bifurcations (nonuniqueness of the time 2nd ed. Leipzig: B. G. Teubner. evolution) and attractors (in the case of dissipative Pooley, Oliver, and Harvey Brown (2002), ‘‘Relationalism systems where energy is no longer conserved). Rehabilitated? I: Classical Mechanics,’’ British Journal MICHAEL STO¨ LTZNER for the Philosophy of Science 53: 183–204.

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Saari, Donald G. (2005), Collisions, Rings, and Other New- Wilson, Curtis (1995), ‘‘The Dynamics of the Solar System,’’ tonian N-Body Problems. Providence, RI: American in Ivor Grattan-Guinness (ed.), Companion Encyclopedia Mathematical Society. of the History and Philosophy of the Mathematical Sto¨ltzner, Michael (2003), ‘‘The Principle of Least Action Sciences. London: Routledge. as the Logical Empiricists’ Shibboleth,’’ Studies in Wilson, Mark (2000), ‘‘The Unreasonable Uncooperative- History and Philosophy of Modern Physics 34: 285– ness of Mathematics in the Natural Sciences,’’ The 318. Monist 83 (2000): 296–314. See also his very instructive Thirring, Walter (1992), A Course in Mathematical Physics 1: entry ‘‘Classical Mechanics’’ in the Routledge Encyclope- Classical Dynamical Systems, 2nd ed. Translated by dia of Philosophy. Evans M. Harrell. New York and Vienna: Springer. Xia, Zhihong (1992), ‘‘The Existence of Noncollision Sin- von Mises, Richard (1922), ‘‘U¨ ber die gegenwa¨rtige Krise gularities in Newtonian Systems,’’ Annals of Mathemat- der Mechanik,’’ Die Naturwissenschaften 10: 25–29. ics 135: 411–468.

COGNITIVE SCIENCE

Cognitive science is a multidisciplinary approach to Key External Questions the study of cognition and intelligence that emerg- ed in the late 1950s and 1960s. ‘‘Core’’ cognitive There are three basic groups of external questions: science holds that the mind/brain is a kind of com- those concerning the nature of a scientific field X, puter that processes information in the form of those concerning the relations of X to other scientif- mental representations. The major disciplinary par- ic fields, and those concerning the scientific merits ticipants in the cognitive science enterprise are of X. An interesting feature of such discussions psychology, linguistics, neuroscience, computer is that they often draw on, and sometimes even science, and philosophy. Other fields that are some- contribute to, the literature on a relevant prior times included are anthropology, education, math- meta-question. For example, discussions concer- ematics, biology, and sociology. ningPROOF the scientific nature of a particular X (e.g., There has been considerable philosophical dis- cognitive science) may require prior conside- cussion in recent years that relates, in one way or ration of the question, What is the best way to another, to cognitive science. Arguably, not all of characterize X (in general) scientifically (e.g., in this discussion falls within the tradition of philoso- terms of its theories, explanations, paradigm, phy of science. There are two fundamentally differ- research program)? ent kinds of question that philosophers of science typically raise about a specific scientific field: ‘‘ex- What Is Cognitive Science? ternal’’ questions and ‘‘internal’’ questions. If one There are many informal descriptions of cogni- assumes that a scientific field provides a framework tive science in the literature, not based on any of inquiry, external questions willFIRST be about that serious consideration of the relevant meta-question framework as a whole, from some external point (e.g., Simon 1981; Gardner 1985). The only system- of view, or about its relation to other scientific atic formal treatment of cognitive science is that frameworks. In contrast, an internal question will of von Eckardt (1993), although there have been be one that is asked within the framework, either attempts to describe aspects of cognitive psychology with respect to some entity or process that constitu- in terms of Kuhn’s notion of a paradigm. Rejecting tes part of the framework’s foundations or with Kuhn’s notion of a paradigm as unsuitable for the respect to some specific theoretical/empirical issue characterization of an immature field, von Eckardt that scientists committed to that framework are (1993) proposes, as an alternative, the notion of a addressing. Philosophers have dealt extensively research framework. A research framework consists with both external and internal questions associated of four sets of elements D, Q, SA, MA, where D is a with cognitive science. set of assumptions that provide a pretheoretical

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specification of the domain under study; Q is a set about evenly split.) A further area of disagreement of basic empirical research questions, formulated concerns whether cognitive science encompasses pretheoretically; SA is a set of substantive assump- only cognition/intelligence or includes all aspects of tions that embody the approach being taken in mind, including touch, taste, smell, emotion, mood, answering the basic questions and that constrain motivation, personality, and motor skills. One point possible answers to those questions; and MA is a on which there now seems to be unanimity is that set of methodological assumptions. cognitive science must address the phenomenon of One can think of what Kuhn (1970) calls ‘‘normal consciousness. science’’ as problem-solving activity. The funda- Second, a modified characterization of cognitive mental problem facing the community of research- science must describe it as evolving not only with ers committed to a research framework is to answer respect to the computational assumption (from an each of the basic empirical questions of that frame- exclusive focus on symbol systems to the inclusion work, subject to the following constraints: of connectionist devices) but also with respect to the role of neuroscience. Because cognitive science 1. Each answer is scientifically acceptable in originally emerged from cognitive psychology, arti- light of the scientific standards set down by ficial intelligence research, and generative lin- the shared and specific methodological as- guistics, in the early years neuroscience was often sumptions of the research framework. relegated to a secondary role. Currently, most non- 2. Each answer is consistent with the substan- neural cognitive scientists believe that research on tive assumptions of the research framework. the mind/brain should proceed in an interactive 3. Each answer to a theoretical question makes way—simultaneously both top-down and bottom- significant reference to the entities and pro- up. Ironically, a dominant emerging view of co- cesses posited by the substantive assumptions gnitive neuroscience seems to be that it, rather of the research framework. than cognitive science, will be the locus of an inter- According to von Eckardt (1993), cognitive sci- disciplinary effort to develop, from the bottom up, ence consists of a set of overlapping research fra- a computational or information-processing theory meworks, each concerned with one or another of the mind/brain. aspect of human cognitive capacities. Arguably, There are also research programs currently at the the central research framework concerns the study periphery of cognitive science—what might be called of adult, normal, typical cognition, with subsidiary alternative cognitive science. These are research frameworks focused on individual differences, programs that investigate some aspect of cognition group differences (e.g., expert vs. novice, male vs. or intelligence but whose proponents reject one or female), cultural variation, development, patholo- more of the major guiding or methodological as- gy, and neural realization. The description offered sumptionsPROOF of mainstream cognitive science. Three in von Eckardt (1993), summarized in Table 1, is such programs are research on situated cognition, intended to be of only the central research frame- artificial life, and the dynamical approach to cog- work. In addition, it is claimed to be a rational nition. reconstruction as well as transdisciplinary, that is, common to cognitive scientists of all disciplines. Von Eckardt claims that research frameworks can Interfield Relations Within Cognitive Science evolve and that the description in question reflects The second group of external questions typically commitments of the cognitive science community asked by philosophers of some particular scientific at only one period of its history (specifically, the field concerns the relation of that field to other late 1980s/early 1990s). FIRST scientific fields. Because cognitive science is itself Cognitive science is a very complex and rapidly multidisciplinary, the most pressing interfield ques- changing field. In light of this complexity and ch- tions arise about the relationship of the various ange, von Eckardt’s original reconstruction should, subdisciplines within cognitive science. Of the ten perhaps, be modified as follows. First, it needs to possible two-place relations among the five core be acknowledged that there exists a fundamental disciplines of cognitive science, two have received disagreement within the field as to its domain. The the most attention from philosophers: relations narrow conception, embraced by most psycholo- between linguistics and psychology (particularly gists and linguists, is that the domain is human psycholinguistics) and relations between cognitive cognition; the broad conception, embraced by arti- psychology and neuroscience. ficial intelligence researchers, is that the domain is Discussion of the relation between linguistics and intelligence in general. (Philosophers seem to be psychology 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. PROOF 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):FIRST 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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Table 1. (Continued)

. 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 adequatePROOF 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 AU:45 to X, they should be committed to Y) FIRST claim that the aims of linguistics are, first, to devel- involved in understanding and producing lan- op hypotheses (in the form of generative grammars) guage. Earlier discussion focused on syntax; more about what the native speaker of a language knows recent debates have looked at semantics. (tacitly) or that capture the native speaker’s linguis- There are several views. One, favored by tic competence and, second, to develop a theory of Chomsky himself, is that a representation of the the innate constraints on language (‘‘universal grammar of a language L constitutes a part of the grammar’’) that the child brings to bear in learning mental apparatus involved in the psychological any given language. Philosophers have focused on processes underlying language performance and, the relation of competence models to so-called per- hence, is causally implicated in the production of formance models, that is, models developed by that performance (Chomsky and Katz 1974). A sec- psychologists to describe the information processes ond, suggested by Marr (1982) and others, is that

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competence theories describe a native speaker’s lin- classical and connectionist machines count as com- guistic input-output capacity (Marr’s ‘‘computa- puters), and is there any reason to believe, at the tional’’ level) without describing the processes current stage of research, that human mind/brains underlying that capacity (Marr’s ‘‘algorithmic’’ are one sort of computer rather than another? The level). For example, the capacity to understand a view that the human mind/brain is, or is important- sentence S can be viewed as the capacity that maps ly like, a classical computer is called classicism; the a phonological representation of S onto a semantic view that it is, or is importantly like, a connection- representation S. Both views have been criticized. ist computer is called connectionism. Against the first, it has been argued that because of The theory of computation in mathematics de- the linguist’s concern with simplicity and generali- fines a number of different kinds of abstract ma- ty, it is unlikely that the formal structures utilized chines in terms of the sets of functions they can by optimal linguistic theories will be isomorphic to compute. Of these, the most relevant to cognitive the internal representations posited by psycholin- science is the universal Turing machine, which, guists (Soames 1984). A complementary point is according to the Church-Turing thesis, can com- that because processing models are sensitive to pute any function that can be computed by an architectural and resource constraints, the ways in effective method, that is, a method specified by a which they implement syntactic knowledge have finite number of exact instructions, in a finite num- turned out to be much less transparent than fol- ber of steps, carried out by a human unaided by any lowers of Chomsky had hoped (Mathews 1991). At machinery except paper and pencil and demanding best, they permit a psycholinguistic explanation of no insight or ingenuity. Many philosophers and why a particular set of syntactic rules and princi- cognitive scientists think that the notion of a com- ples correctly characterize linguistic competence. puter relevant to cognitive science can be adequately Against the second capacity view, it has been ar- captured by the notion of a Turing machine. In gued that grammars constitute idealizations (for fact, that is not the case. To say that a computer example, there are no limitations on the length of (and hence the mind/brain) is simply a device equiv- permissible sentences or on their degree of internal alent to a universal Turing machine says nothing complexity) and so do not describe actual speakers’ about the device’s internal structure, and to say linguistic capacities (Franks 1995; see Philosophy that a computer (and hence the mind/brain) is of Psychology; Neurobiology). an implementation of a Turing machine seems flat- Internal questions have been raised about both out false. There are many dissimilarities. A Turing foundational assumptions and concepts and parti- machine is in only one state at a time, while hum- cular theories and findings within cognitive science. ans are, typically, in many mental or brain states Foundational discussions have focused on the core simultaneously. Further, the memory of a Turing substantive assumptions: (1) The cognitive mind/ machinePROOF is a ‘‘tape’’ with only a simple linear stru- brain is a computational system and (2) it is a cture, while human memory appears to have a representational system. complex multidimensional structure. An alternative approach is to provide an archi- The Computational Assumption tectural characterization, but at a fairly high level of abstraction. For example, von Eckardt (1993, 114) Cognitive science assumes that the mind/brain is a claims that cognitive science’s computational as- kind of computer. But what is a computer? To sumption takes a computer to be ‘‘a device capable date, two kinds of computer have been important of automatically inputting, storing, manipulating, to cognitive science modeling—classical machines and outputting information in virtue of inputting, (‘‘conventional,’’ ‘‘von Neumann,’’ orFIRST‘‘symbol sys- storing, manipulating, and outputting representa- tem’’), and connectionist machines (‘‘parallel tions of that information,’’ where ‘‘[t]hese informa- distributed processing’’). Classical machines have tion processes occur in accordance with a finite set an architecture similar to ordinary personal com- of rules that are effective and that are, in some puters (PCs). There are separate components for sense, in the machine itself.’’ Another proposal, processing and memory, and processing occurs by due to Copeland (1996) and specifically intended the manipulation of data structures. In contrast, to include functions that a Turing machine cannot connectionist computers are more like brains, con- compute, is that a computer is a device capable of sisting of interconnected networks of neuron-like solving a class of problems, that can represent both elements. Philosophers interested in the computa- the problems and their solution, contains some tional assumption have focused on two questions: number of primitive operations (some of which What is a computer in general (such that both may not be Turing computable), can sequence

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these operations in some predetermined way, and between classicism and connectionism will no lon- has a provision for feedback (see Turing, Alan). ger hold (that is, neither the fact that a system is To the question of whether the mind/brain is a classical nor the fact that it is connectionist can, connectionist versus a classical computer, discus- taken by itself, explain systematicity, while either sion has centered around Fodor and Pylyshyn’s fact can explain systematicity when appropriately (1988) argument in favor of classicism. In their supplemented), and Fodor and Pylyshyn’s argu- view, the claim that the mind/brain is a connection- ment will be unsound. ist computer should be rejected on the grounds of the premises that The Representational Assumption 1. cognitive capacities exhibit systematicity Following Peirce (Hartshorne, Weiss, and Burks (where ‘systematicity’ is the fact that some ca- 1931–58), one can say that any representation has pacities are intrinsically connected to others— four aspects essential to its being a representation: e.g., if a native speaker of English knows how (i) It is realized by a representation bearer; (ii) it has to say ‘‘John loves the girl,’’ the speaker will semantic content of some sort; (iii) its semantic con- know how to say ‘‘The girl loves John’’) and tent is grounded somehow; and (iv) it has significance 2. this feature of systematicity cannot be ex- for (that is, it can function as a representation for) plained by reference to connectionist models the person who has it. (Peirce’s terminology was (unless they are implementations of classical somewhat different. He spoke of a representation’s models), whereas bearer as the ‘‘material qualities’’ of the repre- 3. it can be explained by reference to classical sentation and the content as the representation’s models. ‘‘object.’’) Fodor and Pylyshyn’s reasoning is that it is In Peirce, a representation has significance for ‘‘characteristic’’ of classical systems but not of con- a person insofar as it produces a certain effect or nectionist systems to be ‘‘symbol processors,’’ that ‘‘interpretant.’’ This conception of representation is, systems that posit mental representations with is extremely useful for exploring the view of cogni- constituent structure and then process these re- tive science vis-a`-vis mental representation, for it presentations in a way that is sensitive to that leads one to ask: What is the representation bearer, structure. Given such features, classical models semantic content, and ground of mental represen- can explain systematicity; but without such fea- tation, and how do mental representations have tures, as in connectionist machines, it is a mystery. significance for the people in whose mind/brains Fodor and Pylyshyn’s challenge has generated a they reside? host of responses, from both philosophers and com- A representation bearer is an entity or state that puter scientists. In addition, the argument itself hasPROOF semantic properties considered with respect to has evolved in two significant ways. First, it has its nonrepresentational properties. The representa- been emphasized that to be a counterexample to tion bearers for mental representations, according premise 2, a connectionist model must not only to cognitive science, are computational structures exhibit systematicity, it must also explain it. Second, or states. If the mind/brain is a classical computer, it has been claimed that what needs explaining is not its representation bearers are data structures; if it is just that human cognitive capacities are systematic; a connectionist computer, its explicit representa- it is that they are necessarily so (on the basis of tion bearers are patterns of activation of nodes in scientific law). a network. It is also claimed that connectionist The critical points regarding premise 3 are espe- computers implicitly represent by means of their cially important. The force of Fodor andFIRST Pylyshyn’s connection weights. argument rests on classical systems being able to do Much of the theoretical work of cognitive psy- something that connectionist systems (at a cogni- chologists consists of claims regarding the content tive, nonimplementational level) cannot. However, of the representations used in exercising one or it has been pointed out that the mere fact that a another cognitive capacity. For example, psycho- system is a symbol processer (and hence classical) linguists posit that in understanding a sentence, does not by itself explain systematicity, much less people unconsciously form representations of the the lawful necessity of it; additional assumptions sentence’s phonological structure, words, syntactic must be made about the system’s computational structure, and meaning. Although psychologists resources. Thus, if the critics are right that connec- do not know enough about mental representation tionist systems of specific sorts can also explain as a system to theorize about its semantics in the systematicity, then the explanatory asymmetry sense in which linguistics provides the formal

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semantics of natural language, if one reflects on Arguably, any adequate theory of content deter- what it is that mental representations are hypothe- mination will be able to account for the full range sized to explain—certain features of cognitive of semantic properties of mental representational capacities—one can plausibly infer that the seman- systems. On this criterion, all current theories of tics of human mental representation systems must content determination are inadequate. For exam- have certain characteristics. In particular, a case ple, theories that ground representational content can be made that people must be able to represent in an isomorphism between some aspect of a rep- (i) specific objects; (ii) many different kinds of resentation (usually, either its formal structure or objects including concrete objects, sets, properties, its functional role) and what it represents do not events and states of affairs in the world, in possible seem to be able to explain how one can represent worlds, and in fictional worlds, as well as abstract specific objects, such as a favorite coffee mug. In objects such as universals and numbers; (iii) both contrast, theories that rely on actual, historical objects (tout court) and aspects of those objects causal relations can easily explain the representa- (or something like extension and intension); and tion of specific objects but do not seem to be able (iv) both correctly and incorrectly. to explain the representation of sets or kinds of Although cognitive psychologists have concern- objects (e.g., all coffee mugs). It is precisely because ed themselves primarily with the representation single-factor theories of content determination do bearers and semantic content of mental representa- not seem to have the resources to explain all as- tions, the hope is that eventually there will be an pects of people’s representational capacities that account of how the computational states and struc- many philosophers have turned to two-factor the- tures that function as representation bearers come ories, such as theories that combine causal relations by their content. In virtue of what, for example, do with function (so-called teleofunctional theories) lexical representations represent specific words? and theories that combine causal relations with What makes an edge detector represent edges? functional role (so-called two-factor theories). Such theories are sometimes described as one or The fourth aspect of a mental representation, in another form of ‘‘semantics’’ (e.g., informational the Peircian view, is that the content of a repre- semantics, functional role semantics), but this fa- sentation must have significance for the represent- cilitates a confusion between theories of content er. In the information-processing paradigm, this and theories of what determines that content. A amounts to the fact that for each representation, preferable term is theory of content determination. there will be a set of computational consequences Philosophers have been concerned both (a) to de- of that representation being ‘‘entertained’’ or ‘‘acti- lineate the basic relation between a representation’s vated,’’ and in particular a set of computational having a certain content and its having a certain consequences that are appropriate given the content ground and (b) to sketch alternative theories of ofPROOF the representation (von Eckardt 1993, chap. 8). content determination, that is, theories of what that ground might be. A common view is that the The Viability of Cognitive Science basic relation is strong supervenience, as defined by Kim (1984). Others, such as Poland (1994), Cognitive science has been criticized on several believe that a stronger relation of realization is grounds. It has been claimed that there are phe- required. nomena within its domain that it does not have the How is the content of mental representations conceptual resources to explain; that one or more determined? Proposals appeal either exclusively or of its foundational assumptions are problematic in some combination to the structure of the repre- and, hence, that the research program grounded sentation bearer (Palmer 1978); actualFIRST historical in those assumptions can never succeed; and that (Devitt 1981) or counterfactual causal relations it can, in principle, be eliminated in favor of pure (Fodor 1987) between the representation bearer neuroscience. and phenomena in the world; actual and counter- The list of mental phenomena that, according to factual (causal, computational, inferential) rela- critics, cognitive science will never be able to ex- tions between the representation-bearer state and plain include that of people ‘‘making sense’’ in their other states in the mind/brain (Harman 1987; actions and speech, of their having sensations, Block 1987); or the information-carrying or other emotions, and moods, a self and a sense of self, functions of the representation-bearer state and consciousness, and the capabilities of insight and associated components (based on what they were creativity and of interacting closely and directly with selected for in evolution or learning) (Millikan their physical and social environments. Although 1984; Papineau 1987). no impossibility proofs have been offered, when

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cognitive science consisted simply of a top-down, are four ways of making sense of this posited se- ‘‘symbolic’’ computational approach, this explana- mantic property. The semantic property in ques- tory challenge had a fair amount of intuitive plau- tion is identical to one of the following options: sibility. However, given the increasing importance 1. the original content property, of neuroscience within cognitive science and the 2. an interpreter-dependent semiotic-semantic continuing evolution of the field, it is much less property, clear today that no cognitive science explanation 3. a pure semiotic-semantic property of the sort of such phenomena will be forthcoming. The big- posited in linguistics, or gest challenge seems to be the ‘‘explanatory gap’’ 4. some new theoretical ‘‘naturalized’’ property. posed by phenomenal consciousness (Levine 1983) (see Consciousness). However, according to Horst (1996), none of The major challenge against the computational these options will work. Options 1 and 2 are circu- assumption is the claim that the notion of a com- lar and hence uninformative. Option 3 is ruled out puter employed within cognitive science is vacuous. on the grounds that there is no reason to believe that Specifically, Putnam (1988) has offered a proof there are such properties. And option 4 is ruled out that every ordinary open system realizes every ab- on the grounds that naturalized theories of content stract finite automaton, and Searle (1990) has determination do not have the conceptual resources claimed that implementation is not an objective to deliver the kind of explanation required. relation and, hence, that any given system can be In response, it has been argued that Horst’s case seen to implement any computation if interpreted against option 3 is inadequate and that his argu- appropriately. Both claims have been disputed. For ment against option 4 shows a misunderstanding example, it has been pointed out that Putnam’s of what theories of content determination are result relies on employing both an inappropriate trying to achieve (von Eckardt 2001). Horst’s re- computational formalism (the formalism of finite ason for ruling out option 3 is that he thinks that state automata, which have only monadic states), people who believe in the existence of pure seman- an inappropriately weak notion of implementation tic properties or relations do so because there are (one that does not require the mapping from formal semantic theories that posit such properties computational to physical states to satisfy counter- and such theories have met with a certain degree of factual or lawful state–state transitions), and an success. But (he argues) when scientists develop inappropriately permissive notion of a physical models (theories) in science, they do so by a process state (one that allows for rigged disjunctions). of abstraction from the phenomena in vivo that When these parameters of the problem are made they wish to characterize. Such abstractions can more restrictive, implementations are much harder be viewed either as models of the real-world phe- to come by (Chalmers 1996). However, in defense nomenaPROOF they were abstracted from or as descrip- of Putnam, it has been suggested that this response tions of the mathematical properties of those does not get to the heart of Putnam’s challenge, phenomena. Neither view provides a license for which is to develop a theory that provides neces- new ontological claims. Thus, Horst’s argument sary and sufficient criteria to determine whether a rests on a nonstandard conception of both theory class of computations is implemented by a class of construction (as nothing but abstraction) and mod- physical systems (described at a given level). An els or theories (as purely mathematical). If, contra alternative approach to implementation might be Horst, a more standard conception is substituted, based on the notion of realization of a (mathemati- then linguists have as much right to posit pure cal) function by a ‘‘digital system’’ (Scheutz 1999). semantic properties as physicists have to posit The major challenge to the representationalFIRST as- strange subatomic particles. Furthermore, the exis- sumption is the claim that the project of finding an tence of the posited entities will depend completely adequate theory of content determination is doom- on how successful they are epistemically. ed to failure. One view is that the attempt by co- Horst’s case against option 4, again, exhibits a gnitive science to explain the intentionality of misunderstanding of the cognitive science project. cognition by positing mental representations is He assumes that the naturalistic ground N of the fundamentally confused (Horst 1996). The argu- content of a mental representation C will be such ment is basically this: According to cognitive sci- that the truth of the statement ‘‘X is N ’’ conjoined ence, a mental state, as ordinarily construed, has with the necessary truths of logic and mathematics some content property in virtue of the fact that it is will be logically sufficient for the truth of the state- identical to (supervenes on) a representational state ment ‘‘X has C ’’ and that, further, this entailment that has some associated semantic property. There will be epistemically transparent. He then argues

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against there being good prospects for a naturalistic Horst, S. W. (1996), Symbols, Computation, and Intention- theory of content on the grounds that natural- ality. Berkeley and Los Angeles: University of California Press. istic discourse does not have the conceptual resourc- Kim, J. (1984), ‘‘Concepts of Supervenience,’’ Philosophical es to build a naturalistic theory that will entail, in an and Phenomenological Research 45: 153–176. epistemically transparent way, the truths about in- Kuhn, T. (1970), The Structure of Scientific Revolutions. tentionality. However, as von Eckardt (2001) points Chicago: University of Chicago Press. out, Horst’s conception of naturalization is much Levine, J. (1983), ‘‘Materialism and Qualia: The Ex- planatory Gap,’’ Pacific Philosophical Quarterly 64: stronger than what most current theory of content 354–361. determination theorists have in mind, viz., strong Marr, D. (1982), Vision: A Computational Investigation into supervenience or realization (see Supervenience). the Human Representation and Processing of Visual In- As a consequence, his arguments that naturalization formation. San Francisco: W. H. Freeman. is implausible given the conceptual resources of Mathews, R. (1991), ‘‘Psychological Reality of Grammars,’’ in A. Kasher (ed.), The Chomskyan Turn. Oxford and naturalistic discourse are seriously misguided. Cambridge, MA: Basil Blackwell. BARBARA VON ECKARDT Millikan, R. (1984), Language, Thought, and Other Biological Categories. Cambridge, MA: MIT Press. References Palmer, S. (1978), ‘‘Fundamental Aspects of Cognitive Rep- resentation,’’ in E. Rosch and B. Lloyd (eds.), Cognition Block, N. (1987), ‘‘Functional Role and Truth Conditions,’’ and Categorization. Hillsdale, NJ: Erlbaum. Proceedings of the Aristotelian Society 61: 157–181. Papineau, D. (1987), Reality and Representation. Oxford: Chalmers, D. (1996), ‘‘Does a Rock Implement Every Blackwell. Finite-State Automaton?’’ Synthese 108: 309–333. Poland, J. (1994), Physicalism: The Philosophical Founda- Chomsky, N., and J. Katz (1974), ‘‘What the Linguist Is tions. Oxford: Oxford University Press. Talking About,’’ Journal of Philosophy 71: 347–367. Putnam, H. (1988), Representation and Reality. Cambridge, Copeland, B. (1996), ‘‘What Is Computation?’’ Synthese MA: MIT Press. 108: 336–359. Scheutz, M. (1999), ‘‘When Physical Systems Realize Func- Devitt, M. (1981), Designation. New York: Columbia tions,’’ Minds and Machines 9: 161–196. University Press. Searle, J. (1990), ‘‘Is the Brain a Digital Computer?’’ Pro- Fodor, J. (1987), Psychosemantics. Cambridge, MA: MIT ceedings and Addresses of the American Philosophical Press. Association 64: 21–37. Fodor, J., and Z. W. Pylyshyn (1988), ‘‘Connectionism Simon, H. (1981), ‘‘Cognitive Science: The Newest Science and Cognitive Architecture: A Critical Analysis,’’ in of the Artificial,’’ in D. A. Norman (ed.), Perspectives S. Pinker and J. Miller (eds.), Connections and Symbols. on Cognitive Science. Norwood, NJ: Ablex Publishing, Cambridge, MA: MIT Press, 1–71. 13–26. Franks, B. (1995), ‘‘On Explanation in the Cognitive Soames, S. (1984), ‘‘Linguistics and Psychology,’’ Linguis- Sciences: Competence, Idealization and the Failure of tics and Philosophy 7: 155–179. the Classical Cascade,’’ British Journal for the Philosophy von Eckardt, B. (2001), ‘‘In Defense of Mental Representa- of Science 46: 475–502. PROOFtion,’’ in P. Gardenfors, K. Kijania–Placek, and J. Gardner, H. (1985), The Mind’s New Science: A History of Wolenski (eds.), Proceedings of the 11th International the Cognitive Revolution. New York: Basic Books. Congress of Logic, Methodology and Philosophy of Sci- Harman, G. (1987), ‘‘(Non–Solipsistic) Conceptual Role ence. Dordrecht, Netherlands: Kluwer. Semantics,’’ in E. Lepore (ed.), New Directions in Seman- ——— (1993), What Is Cognitive Science? Cambridge, MA: tics. London: Academic Press. MIT Press. Hartshorne, C., P. Weiss, and A. Burks (eds.) (1931–58), Collected Papers of Charles Sanders Peirce. Cambridge, See also Consciousness; Physicalism; Psychology, MA: Harvard University Press. Philosophy of; Supervenience FIRST COGNITIVE SIGNIFICANCE

One of the main objectives of logical empiricism which are neither. The desired criterion would was to develop a formal criterion by which cogni- specify, and in some way justify, the logical empiri- tively significant statements, which are true or cists’ conviction that scientific statements were false, could be delineated from meaningless ones, exemplars of significance and metaphysical ones

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were decidedly not (see Logical Empiricism). their antimetaphysical agenda, the logical empiri- Finding such a criterion was crucial to logical em- cists focused on empirical significance. piricism. Without it there seemed to be no defensi- ble way to distinguish metaphysics from science and, consequently, no defensible way to exclude The Verifiability Requirement metaphysics from subjects that deserved serious The first attempts to develop the antimetaphysical philosophical attention (see Demarcation, Problem ideas of the logical empiricists into a more rigorous of ). Accordingly, several logical empiricists devoted criterion of meaningfulness were based on the attention to developing a criterion of cognitive sig- verifiability theory of meaning (see Verifiability). nificance, including Carnap, Schlick, Ayer, Hempel, Though of auxiliary importance to the rational re- and, to a lesser degree, Reichenbach. construction in the Aufbau, Carnap (1928a) Scientific developments also motivated the claimed that a statement was verifiable and thereby project in two related ways. First, physics and meaningful if and only if it could be translated biology were demonstrating that a priori metaphys- into a constructional system; for instance, by re- ical speculations about empirical matters were ducing it (at least in principle) to a system about usually erroneous and methodologically misguid- basic physical objects or elementary experiences ed. Hans Driesch’s idea of an essential entelechy (§179) (see Carnap, Rudolf). Meaningful questions was no longer considered scientifically respectable, have verifiable answers; questions that fail this re- and the intuitive appeal of the concept of abso- quirement are pseudo-questions devoid of cogni- lute simultaneity was shown to be misleading by tive content (§180). Einstein (Feigl 1969). Scientific results demon- The first explicit, semiformal criterion originated strated both the necessity and the fruitfulness of with Carnap in 1928. With the intention of demon- replacing intuitive convictions with precise, empiri- strating that the realism/idealism debate, and many cally testable hypotheses, and logical empiricists other philosophical controversies, were devoid of thought the same methodology should be applied cognitive significance, Carnap (1928b) presented a to philosophy. Formulating a defensible criter- criterion of factual content: ion that ensured the privileged epistemological status of science, and revealed the vacuity of meta- If a statement p expresses the content of an experience E, physics, was thought crucial to the progress and and if the statement q is either the same as p or can be respectability of philosophy. derived from p and prior experiences, either through Second, many scientific discoveries and emerg- deductive or inductive arguments, then we say that q is ‘supported by’ the experience E .... A statement p is said ing research programs, especially in theoretical to have ‘factual content’ if experiences which would physics, were considerably removed from everyday support p or the contradictory of p are at least conceiv- observable experience and involved abstract, math- PROOF able, and if their characteristics can be indicated. ematically sophisticated theories. The logical empiricists felt there was a need for a formal system- (Carnap 1967, 327) atization of science that could clarify theoretical Only statements with factual content are em- concepts, their interrelations, and their connection pirically meaningful. Notice that a fairly precise infer- with observation. The emerging tools of modern ential method is specified and that a statement has mathematical logic made this task seem imminently factual content if there are conceivable experiments attainable. With the desire for clarity came the that could support it. Thus, the earliest formal signif- pursuit of a criterion that could sharply distinguish icance criterion already emphasized that possible, not these scientific developments, which provided in- necessarily actual, connection to experience made sights about the world and constitutedFIRST advances in statements meaningful. knowledge, from the obfuscations of metaphysics. Carnap ([1932] 1959) made three significant Formulation of a cognitive significance criterion changes to his proposal. First, building on an earli- requires an empirical significance criterion to de- er example (1928b, §7), he developed in more detail lineate empirical from nonempirical statements and the role of syntax in determining the meaningful- a criterion of analyticity to delineate analytic ness of words and statements in natural languages. from synthetic statements (see Analyticity). Most The ‘‘elementary’’ sentence form for a word is the logical empiricists thought analytically true and simplest in which it can occur. For Carnap, a word false statements were meaningful, and most meta- had to have a fixed mode of occurrence in its physicians thought their claims were true but not elementary sentence form to be significant. Besides analytically so. In their search for a cognitive failing to connect with experience in some way, significance criterion, as the principal weapon of statements could also be meaningless because they

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contained sequences of words that violated the though conventional, has to satisfy an adequacy language’s syntactic rules, or its ‘‘logical syntax.’’ condition. The criterion is empirical because, to According to Carnap, ‘‘Dog boat in of’’ is mean- be adequate, it must classify ‘‘propositions which ingless because it violates grammatical syntax, and by universal agreement are given as significant’’ as ‘‘Our president is definitely a finite ordinal,’’ is significant, and propositions that are universally meaningless because it violates logical syntax, agreed to be nonsignificant as nonsignificant ‘president’ and ‘finite ordinal’ being members of (Ayer 1934, 345). different logical categories. The focus on syntax Ayer developed two formalizations of the criteri- led Carnap to contextualize claims of significance on. The first edition of Language, Truth, and Logic to specific languages. Two languages that differ in contained the proposal that ‘‘a statement is verifi- syntax differ in whether words and word sequences able ... if some observation-statement can be de- are meaningful. duced from it in conjunction with certain other Second, Carnap ([1932] 1959) no longer required premises, without being deducible from those statements to be meaningful by expressing con- other premises alone,’’ where an observation state- ceivable states of affairs. Rather, statements are ment is one that records any actual or possible meaningful because they exhibit appropriate dedu- observation (Ayer 1946, 11). cibility relations with protocol statements whose Following criticisms (see the following section) significance was taken as primitive and incorrigible of his earlier work, a decade later Ayer (1946) by Carnap at that time (see Protocol Sentences). proposed a more sophisticated criterion by distin- Third, Carnap did not specify exactly how signifi- guishing between directly verifiable statements and cant statements must connect to protocol state- indirectly verifiable ones. In conjunction with a set ments, as he had earlier (1928b). In 1932, Carnap of observation statements, directly verifiable state- would ascertain a word’s meaning by considering ments entail at least one observation statement the elementary sentence in which it occurred and that does not follow from the set alone. Indirectly determining what statements entailed and were verifiable statements satisfy two requirements: (1) entailed by it, the truth conditions of the statement, In conjunction with a set of premises, they entail at or how it was verified—considerations Carnap least one directly verifiable statement that does not then thought were equivalent. The relations were follow from the set alone; and (2) the premises can probably left unspecified because Carnap came to include only statements that are either analytic or appreciate how difficult it was to formalize the directly verifiable or can be indirectly verified on significance criterion, and realized that his earlier independent grounds. Nonanalytic statements that criterion was seriously flawed, as was shown of are directly or indirectly verifiable are meaningful, Ayer’s first formal criterion (see below). whereas analytic statements are meaningful but do In contrast to antimetaphysical positions that notPROOF assert anything about the world. evaluated metaphysical statements as false, Carnap believed his criterion justified a radical elimination Early Criticisms of the Verifiability Criterion of metaphysics as a vacuous enterprise. The defen- sibility of this claim depended upon the status of the The verifiability criterion faced several criticisms, criterion—whether it was an empirical hypothesis which took two general forms. The first, already men- that had to be supported by evidence or a definition tioned in the last section, questioned its status— that had to be justified on other grounds. Carnap specifically, whether the statement of the criterion ([1932] 1959) did not address this issue, though he satisfies the criterion. The second questioned its labels the criterion as a stipulation. Whether this adequacy: Does the criterion ensure that obviously stipulation was defensible in relationFIRST to other pos- meaningful statements, especially scientific ones, sible criteria or whether the statement of the crite- are labeled as meaningful and that obviously mean- rion satisfied the criterion itself were questions left ingless statements are labeled as meaningless? unanswered. Criticisms of the first form often mistook the In his popularization of the work of Carnap point of the criterion, construing it as a simple em- ([1932] 1959) and Schlick ([1932] 1979), Ayer pirical hypothesis about how the concept of mean- (1934) addressed these questions and stated that a ing is understood or a dogmatic stipulation about significance criterion should not be taken as an how it should be understood (Stace 1935). As men- empirical claim about the linguistic habits of the tioned earlier, Ayer (1934, 1946) clearly recognized AU:31 class of people who use the ‘meaning’ of a word that it was not this type of empirical claim, nor was (see Ayer, Alfred Jules; Schlick, Moritz). Rather, it it an arbitrary definition. Rather, as Hempel (1950) is a different kind of empirical proposition, which, later made clear, the criterion was intended to clarify

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and explicate the idea of a meaningful statement. As nonsignificant. Empirical impossibility, which an explication it must accord with intuitions about Schlick understood as contradictng the ‘‘laws of the meaningfulness of common statements and sug- nature,’’ does not entail nonverifiability. If it did, gest a framework for understanding how theoretical Schlick argued, the meaningfulness of a putative terms of science are significant (see Explication). statement could be established only by empirical The metaphysician can deny the adequacy of this inquiry about the laws of nature. For Schlick, this explication but must then develop a more liberal conflated a statement’s meaning with its truth. The criterion that classifies metaphysical claims as meaning of a statement is determined (‘‘bestowed’’) significant while evaluating clearly meaningless by logical syntax, and only with meaning fixed a assertions as meaningless (Ayer 1934). priori can its truth or falsity be assessed. Further- Criticisms of the second form often involved more, since some lawlike generalizations are yet to misinterpretations of the details of the criterion, be identified and lawlike generalizations are never due partially to the ambiguity of what was meant established with absolute certainty, it seems that a by ‘verifiability.’ For example, in a criticism of sharp boundary between the empirically impossible Ayer (1934), Stace (1935) argued that the verifiabil- and possible could never be determined. Hence, there ity criterion made all statements about the past would be no sharp distinction between the verifiable meaningless, since it was in principle impossible and unverifiable, which Schlick found unacceptable. to access the past and therefore verify them. His For Schlick ([1936] 1979), questions formulated argument involved two misconceptions. First, Stace according to the rules of logical grammar are construed the criterion to require the possibility of meaningful if and only if it is logically possible to conclusive verification, for instance a complete re- verify their answers. A state of affairs is logically duction of any statement to (possible) observations possible for Schlick if the statement that describes that could be directly verified. Ayer (1934) did it conforms to the logical grammar of language. not address this issue, but Schlick ([1932] 1979), Hence, meaningful questions may concern states from whose work Ayer drew substantially, empha- of affairs that contradict well-supported lawlike sized that many meaningful propositions, such as generalizations. Schlick’s position implies that the those concerning physical objects, could never be set of meaningful questions is an extension of the set verified conclusively. Accepting Neurath’s criti- of questions for which verifiable answers can be cisms in the early 1930s, Carnap accepted that no imagined. Questions about velocities greater than statement, including no protocol statement, was light are meaningful according to Schlick, but conclusively verified (see Neurath, Otto). Recall imagining how they could be verified surpasses also that Carnap (1928b) classified statements that our mental capabilities. were ‘‘supported by’’ conceivable experiences—not Schlick’s emphasis on logical possibility was conclusively verified—as meaningful. problematicPROOF because it was unclear that the verifi- Second, Stace’s argument depended on the am- cation conditions of most metaphysical statements biguity of ‘‘possible verification,’’ which made are, or entail, logical impossibilities. In contrast, early formulations of the criterion misleadingly un- Carnap ([1936–7] 1965) and Reichenbach (1938) clear (Lewis 1934). The possibility of verification claimed that metaphysical statements were nonsig- can have three senses: practical possibility, empiri- nificant because no empirically possible process of cal possibility, and logical possibility. Practical confirmation could be specified for them (see possibility was not the intended sense: ‘‘There are Reichenbach, Hans). Furthermore, if only the logi- 10,000-foot mountains on the moon’s far side’’ was cal possibility of verification were required for sig- meaningful in the 1930s, though its verification was nificance, then the nonsignificance of metaphysical practically impossible (Schlick [1932]FIRST 1979). statements could no longer be demonstrated by However, Carnap (1928a, 1928b, [1932] 1959), demanding an elucidation of the circumstances in Schlick ([1932] 1979), and Ayer (1934) were silent which they could be verified. Metaphysicians can on whether empirical or logical possibility divided legitimately respond that such circumstances may the verifiable from the unverifiable. Stace thought be difficult or impossible to conceive because they time travel was empirically impossible. The question are not empirically possible. Nevertheless, the cir- was therefore whether statements about past events cumstances may be logically possible, and hence were meaningful for which no present evidence was the metaphysical statements may be significant available, and no future evidence would be. according to Schlick’s position. In the first detailed analysis of the verifiability Faced with the problematic vagueness of the criterion, Schlick ([1936] 1979) stated that the logical early criteria, a formal specification of the criterion impossibility of verification renders a statement was thought to be crucial. Berlin (1939) pointed out

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that the early verifiability criteria were open to Beyond Verifiability: Carnap and Hempel objections from metaphysicians because the details of the experiential relevance required of meaningful While Ayer first attempted to formalize the verifi- statements were left unclear: ‘‘Relevance is not a ability criterion, Carnap ([1936–7] 1965) recognized precise logical category, and fantastic metaphysical the obvious weaknesses of verifiability-based signif- systems may choose to claim that observation data icance criteria. At roughly the same time, in the light are ‘relevant’ to their truth’’ (233). of Tarski’s rigorous semantic account of truth, With formalizations of the criterion, however, Carnap was coming to accept that a systematic came more definitive criticisms. Ayer’s (1946, 39) (that is, nonpragmatic) account might be possible first proposal was seriously flawed because it for other concepts, such as ‘confirmation.’ He sub- seemed to make almost all statements verifiable. sequently refocused the question of cognitive signif- For any grammatical statement S—for instance icance away from verifiability, which seemed to ‘‘The Absolute is peevish’’—any observation state- connote the possibility of definitive establishment of truth, to confirmability—the possibility of ob- ment O, and the conditional S ! O, S and S ! O jointly entail O, though neither of them alone usu- taining evidence, however partial, for a statement. ally does. According to Ayer’s criterion, therefore, In particular, Carnap thought a justifiable signifi- S and S ! O are meaningful except in the rare case cance criterion could be formulated if an adequate that S ! O entails O (Berlin 1939). account of the confirmation of theory by observa- Church (1949) presented a decisive criticism of tion were available. A better understanding of the Ayer’s (1946, 13) second proposal. Consider three latter would provide a clearer grasp of how scientific terms are significant due to their connection to ob- logically independent observation statements O1, O , O and any statement S. The disjunction servation and prediction and how metaphysical 2 3 concepts are not, because they lack this connection. (øO16O2)V(øS6O3) is directly verifiable, since in conjunction with O it entails O . Also, Yet, insights into the nature of confirmation of 1 3 theory by observation do not alone determine the (øO16O2)V(øS6O3) and S together entail O2. Hence, by Ayer’s criterion, S is indirectly verifiable, form of an adequate significance criterion. Rather, unless (øO 6O )V(øS6O ) alone entails O , these insights were important because Carnap 1 2 3 2 ([1936–7] 1965) radically changed the nature of the which implies øS and O3 entail O2 so that øS is directly verifiable. Thus, according to Ayer’s debate over cognitive significance. criterion, any statement is indirectly verifiable, Carnap reemphasized (from his work in 1932) and therefore significant, or its negation is directly that what expressions are cognitively significant verifiable, and thereby meaningful. depends upon the structure of language, and hence Nidditch (1961) pointed out that Ayer’s (1946) a criterion could be proposed relative to only a proposal could be amended to avoid Church’s specificPROOF language. He distinguished two kinds of (1949) criticism by specifying that the premises questions about cognitive significance: those con- could only be analytic, directly verifiable, or indi- cerning ‘‘historically given language system[s]’’ and rectly verifiable on independent grounds and could those concerning constructible ones (Carnap [1932] only be composed of such statements. Thus that 1959, 237). Answers to the two kinds of questions are evaluated by different standards. To be mean- (øO16O2)V(øS6O3) and S together entail O2 does not show that S is indirectly verifiable because ingful in the first case, an expression E must be a sentence of L, which is determined by the language’s (øO16O2)V(øS6O3) contains a statement (S) that has not been shown to be analytic, directly verifiable, syntax, and it must ‘‘fulfill the empiricist criterion of or independently verifiable on independent grounds. meaning’’ (167) for L. Carnap does not disclose the Unfortunately, Scheffler (1963) pointed out that exact form of the criterion—verifiability, testability, FIRST or confirmability—for a particular language, such according to Nidditch’s (1961) revised criterion, an argument similar to Church’s (1949) with the dis- as English. The reason for Carnap’s silence, however, was junction øO2V(S6O1) shows that any statement S is significant, unless it is a logical consequence of his belief that the second type of question posed a an observation statement. Scheffler (1963) also more fruitful direction for the debate. The second pointed out that Ayer’s second proposal makes type of question is practical, and the answers are proposals, not assertions. Carnap ([1936–7] 1965) any statement of the form S6(O1 ! O2) signifi- cant, where O , O are logically independent obser- remarked that he was no longer concerned to 1 2 argue directly that metaphysical statements are vation sentences and S is any statement. S6(O1 ! O ) entails O when conjoined with O and neither not cognitively significant (236). Rather, his strat- 2 2 1 egy was to construct a language L in which every the conjunction nor O1 entails O2 alone.

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nonanalytic statement was confirmable by some confirmation of S is not completely reducible experimental procedure. Given its designed struc- to C and (b) there is an infinite subclass C 0 of ture, L will clearly indicate how theoretical state- mutually independent sentences of C such ments can be confirmed by observational ones, and that S entails, by substitution alone, each it will not permit the construction of metaphysical member of C 0. statements. If a language such as L can be con- 3. The confirmation of a predicate P reduces to structed that accords with intuitions about the sig- the confirmation of a class of predicates Q if nificance of common statements and is sufficient for the confirmation of every full sentence of P the purposes of science, then the onus is on the with a particular argument (e.g., P(a), in metaphysician to show why metaphysical state- which a is a constant of the language) is ments are significant in anything but an emotive reducible to the confirmation of a consistent or attitude-expressing way. set of predicates of Q with the same argu- In a review paper more than a decade later, Hem- ment, together with their negations. pel (1950) construed Carnap’s ([1936–7] 1965) posi- With these definitions Carnap ([1936–7] 1965) tion as proposing a translatability criterion— showed how dispositional predicates (for instance, a sentence is cognitively significant if and only if it ‘‘is soluble in water’’) S could be introduced into an is translatable into an empiricist language (see empiricist language by means of reduction postu- Hempel, Carl). The vocabulary of an empiricist lates or finite chains of them. These postulates language L contains observational predicates, the could take the simple form of a reduction pair: customary logical constants, and any expression constructible from these; the sentence formation ð8xÞðWx !ðDx ! SxÞÞ; rules of L are those of Principia Mathematica. The ð8xÞðFx !ðRx ! ØSxÞÞ; problem Carnap ([1936–7] 1965) attempted to rec- in which W, D, F, and R designate observational tify was that many theoretical terms of science AU:32 terms and S is a dispositional predicate. (In the cannot be defined in L. solubility example, Sx ¼ ‘‘x is soluble in water’’; Hempel’s interpretation, however, slightly mis- Dx ¼ ‘‘x dissolves in water’’; Wx ¼ ‘‘x is placed in construed Carnap’s intention. Carnap ([1936–7] water’’; and R and F are other observational 1965) did not try to demonstrate how theoretical terms.) If Dx $ øRx and Wx $ Fx, then the terms could be connected to observational ones in reduction pair is a bilateral reduction sentence: order to assert translatability as a criterion of cognitive significance. Rather, in accord with the ð8xÞðWx !ðDx $ SxÞÞ: principle of tolerance (Carnap 1934) Carnap’s proj- The reduction postulates introduce, but do not ect in 1936–7 was to construct an alternative to explicitly define, terms by specifying their logical metaphysically infused language. The features of PROOF relations with observational terms. They also pro- the language are then evaluated with respect to vide confirmation relations between the two types the purposes of the language user on pragmatic of terms. For instance, the above reduction pair grounds. Although it seems to conflict with his entails that the confirmation of S reduces to that position in 1932, Carnap (1963) clarified that a of the confirmation of the set {W, D, F, R}. Carnap ‘‘neutral attitude toward various forms of language ([1936–7] 1965) defined a sentence or a predicate to based on the principle that everyone is free to use be confirmable (following definitions 1–3 above) if the language most suited to his purposes, has its confirmation reduces to that of a class of ob- remained the same throughout my life’’ (18–19). servable predicates (156–7). Reduction postulates Carnap ([1936–7] 1965) tried to formulate a provide such a reduction for disposition terms such replacement for metaphysics, rather than directly FIRST as S. The reduction pair does not define S in terms repudiate it on empiricist grounds. of observational terms. If øWx and øFx, then Sx is Three definitions were important in this regard. undetermined. However, the conditions in which S The forms presented here are slightly modified or its negation hold can be extended by adding from those given by Carnap ([1936–7] 1965): other reduction postulates to the language. Carnap 1. The confirmation of a sentence S is complete- thought that supplementing an empiricist language ly reducible to the confirmation of a class of to include terms that could be introduced by means sentences C if S is a consequence of a finite of reduction postulates or chains of them (for ex- subclass of C. ample, if Wx is introduced by a reduction pair) 2. The confirmation of S directly incompletely would adequately translate all theoretical terms of reduces to the confirmation of C if (a) the scientific theories.

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Although it set a more rigorous standard for the theoretical constructs, on to systems with hardly any debate, Carnap’s ([1936–7] 1965) proposal encoun- bearing on potential empirical findings. (74). tered difficulties. Carnap believed that bilateral re- Hempel suggested that it may be more fruitful to duction sentences were analytic, since all the compare theoretical systems according to other consequences of individual reduction sentences characteristics, such as clarity, predictive and ex- that contained only observation terms were tautol- planatory power, and simplicity. On these bases, ogies. Yet, Hempel (1951) pointed out that two the failings of metaphysical systems would be more bilateral reduction sentences together sometimes clearly manifested. entailed synthetic statements that contained only Of all the logical empiricists’ criteria, Carnap’s observation terms. Since the idea that the conjunc- (1956) criterion was the most sophisticated. It tion of two analytic sentences could entail synthetic attempted to rectify the deficiencies of his 1936–7 statements was counterintuitive, Hempel made work and thereby avoid Hempel’s pessimistic con- the important suggestion that analyticity and cog- clusions. Scientific languages were divided into two nitive significance must be relativized to a specific parts, a theoretical language LT and an observation language and a particular theoretical context. A language LO. Let VO be the class of descriptive bilateral reduction sentence could be analytic in constants of LO, and VT be the class of primitive one context but synthetic in a different context descriptive constants of LT. Members of VO desig- that contained other reduction postulates. nate observable properties and relations such as Hempel (1950) also argued that many theoretical ‘hard,’‘white,’ and ‘in physical contact with.’ The terms, for instance ‘‘gravitational potential’’ or logical structure of LO contains only an elementary ‘‘electric field,’’ could not be translated into an logic, such as a simple first-order predicate calculus. empiricist language with reduction postulates or The descriptive constants of LT, called theoreti- chains of them. Introducing a term with reduction cal terms, designate unobservable properties and postulates provides some sufficient and necessary relations such as ‘electron’ or ‘magnetic field.’ LT observation conditions for the term, but Hempel contains the mathematics required by science along claimed that this was possible only in simple cases, with the ‘‘entities’’ referred to in scientific physical, such as electric fields of a simple kind. Introducing psychological, and social theories, though Carnap a theoretical term with reduction sentences also stressed that this way of speaking does not entail unduly restricted theoretical concepts to observa- any ontological theses. A theory was construed as a tion conditions. The concept of length could not finite set of postulates within LT and represented by be constructed to describe unobservable intervals, the conjunction of its members T. A finite set of À100 for instance 1 Â 10 m, and the principles of correspondence rules, represented by the conjunc- calculus would not be constructible in such a lan- tion of its members C, connects terms of VT and VO. guage (Hempel 1951). Carnap’s ([1936–7] 1965) pro- PROOF Within this framework Carnap (1956) presented posal could not accommodate most of scientific three definitions, reformulated as: theorizing. Although ultimately untenable, adequacy condi- D1. A theoretical term M is significant relative tions for a significance criterion were included in to a class K with respect to LT, LO, T, and = Carnap’s ([1936–7] 1965) papers, generalized by C ¼df if (i) K  VT, (ii) M 2 K, and (iii) Hempel (1951) as: If N is a nonsignificant sentence, there are three sentences SM, SK 2 LT, and then all truth-functional compound sentences that SO 2 LO such that: nonvacuously contain N must be nonsignificant. It (a) SM contains M as the only descriptive follows that the denial of a nonsignificant sentence term. is nonsignificant and that a disjunction, conjunct- (b) The descriptive terms in SK belong to K. 6 6 6 FIRST (c) (SM SK T C ) is consistent. ion, or conditional containing a nonsignificant com- 6 6 6 ponent sentence is also nonsignificant. Yet Hempel (d) (SM SK T C ) logically implies SO. ø 6 6 (1951) was pessimistic that any adequate criterion (e) [(SK T C ) logically implies SO]. satisfying this condition and yielding a sharp di- D2. A theoretical term Mn is significant with chotomy between significance and nonsignificance respect to LT, LO, T, and C ¼df if there is < could be found. Instead, he thought that cognitive a sequence of theoretical constants M1, ... > significance was a matter of degree: Mn (Mi 2 VT) such that every Mi is signif- icant relative to {M1, ... MiÀ1} with respect Significant systems range from those whose entire extra- to LT, LO, T, and C. logical vocabulary consists of observational terms, D3. An expression A of LT is a significant sen- through theories whose formulation relies heavily on tence of LT ¼ df if (i) A satisfies the rules of

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formation of LT and (ii) every descriptive his intuition that deoccamization should preserve term in A is significant, as in D2. the empirical content of a theory and, therefore, not change the significance of its theoretical terms. These definitions, especially D1 (d) and (e), are The objection is as follows: If any members of V intended to explicate the idea that a significant term T are significant with respect to T, C, L , and L , must make a predictive difference. Carnap was T O then there must be at least one M that is signifi- aware that observation statements can often be de- 1 cant relative to an empty K (D2). Yet, if T6C is duced only from theoretical statements containing deoccamized such that M is resolved into two new several theoretical terms. With D2 Carnap implicitly 1 terms M and M that are never found apart, distinguishes between theoretical terms whose signif- 11 12 then the original argument that satisfied D1 can icance depends on other theoretical terms and those no longer be used, since T 06C 0 do not provide that acquire significance independently of others. In similar logical relationships for M and M indi- contrast to his work in 1936–7, and in accord with 11 12 vidually. Hence, the sequence of theoretical terms Hempel’s (1951) relativization of analyticity and required by D2 will have no first member. Subse- cognitive significance, Carnap (1956) specified that quently, no chain of implications that establishes the significance of theoretical terms is relativized to the significance of successive theoretical terms a particular language and a particular theory T. exists. Although deoccamization preserves the With the adequacy of his proposal in mind, deductive systematization of L , according to Carnap (1956, 54–6) proved an interesting result. O Carnap’s criterion it may render every theoretical Consider a language in which V is divided into T term of T 06C 0 meaningless and therefore render empirically meaningful terms V and empirically 1 T 06C 0 devoid of empirical content. meaningless terms V . Assume that C does not 2 Creath (1976) vindicated the core of Carnap’s permit any implication relation between those sen- (1956) criterion by generalizing it to accommodate tences that contain only V or V terms and those 1 O sets of terms, reformulated as: sentences that contain only V2 terms. For a given theory T that can be resolved into a class of state- D10. A theoretical term M is significant relative ments T1 that contain only terms from V1, and T2 to a class K with respect to LT, LO, T, and that contain only terms of V2, then a simple but C =df if (i) K  VT, (ii) M 2= K, (iii) there is a adequate significance criterion can be given. Any class J such that J  VT, M 2 J, but J and theoretical term that occurs only in isolated sen- K do not share any members, and (iv) there tences, which can be omitted from T without are sentences SJ, SK 2 LT, and SO 2 LO affecting the class of sentences of LO that it entails such that: in conjunction with C, is meaningless. (a) SJ contains members of J as the only The problem is that this criterion cannot be uti- PROOFdescriptive terms. 0 lized for a theory T equivalent to T that cannot be (b) The descriptive terms in SK belong to K. similarly divided. Carnap (1956), however, showed (c) (SJ6SK6T6C ) is consistent. by indirect proof that his criterion led to the desired (d) (SJ6SK6T6C ) logically implies SO. conclusion that the terms of V2 were not significant (e) ø[(SK6T6C ) logically implies SO]. 0 0 0 relative to T (LO, LT, and C ) and that therefore (f ) It is not the case that (9J )(J  J ) and the criterion was not too liberal. sentences SJ 0, SK 02 LT, and SO 0 2 LO such that: 0 (f1) SJ 0 contains only terms of J as its The Supposed Failure of Carnap descriptive terms. Kaplan (1975) raised two objections to Carnap’s (f2) The descriptive terms of SK 0 be- (1956) criterion that were designed toFIRST show that it long to K. 6 6 6 was too liberal and too restrictive. Kaplan’s first (f3) (SJ 0 SK 0 T C ) is consistent. 6 6 6 objection utilized the ‘‘deoccamization’’ of T6C. (f4) (SJ 0 SK 0 T C ) logically im- The label is appropriate, since the transformation plies SO 0. ø 6 6 of T6C into its deoccamization T 06C 0 involves (f5) [(SK 0 T C ) logically implies replacing all instances of some theoretical terms SO 0]. 0 with disjunctions or conjunctions of new terms of D2 . A theoretical term Mn is significant with the same type: an Occam-unfriendly multiplication respect to LT, LO, T and C ¼ df if there is of theoretical terms. Kaplan proved that any de- a sequence of sets (Mn 2 Jn and ductive systematization of LO by T6C is also estab- Ji  VT) such that every member of every lished by any of its deoccamizations. This motivates set Ji is significant relative to the union of

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J1 through JiÀ1 with respect to LT, LO, T but ‘‘definitional extensions are ordinarily thought and C. of as having no more empirical content than the original theory’’ (Kaplan 1975, 90). Condition (f ) ensures that each member of J is Using the same basic strategy, Rozeboom (1960) required for the significance of the entire set. demonstrated that extending T6C can transform Creath (1976) points out that any term made sig- an empirically significant term into an insignificant nificant by D1 and D2 of Carnap (1956) is made one. Consider a term M that is significant with significant by D10 and D20 and that according to respect to T, C, L , and L . Rozeboom showed the generalized criterion, Kaplan’s (1975) deocca- T O that if postulates (not necessarily definitions) are mization criticism no longer holds. added to T or to C to form T 0 or C 0, in some cases Kaplan (1975) and Rozeboom (1960) revealed an D1(e) will no longer be satisfied, and no other apparent second flaw in Carnap’s (1956) proposal: sentences S 0 , S 0 , S 0 exist by which M could be As postulates (definitions for Kaplan’s criticism) M K O independently shown to be significant. Further- are added to T6C, the theoretical terms it contains more, if T6C is maximally L consistent, no theo- may change from cognitively significant to nonsig- O retical term of L is significant, since D1(e) is never nificant or vice versa. Consider an example from T satisfied; for any S ,ifT6C is maximally L Kaplan (1975) in which V ¼ {J , P , R }; L is O O O O O O O consistent then it alone implies S . Rozeboom the class of all sentences of first-order logic with O (1960) took the strength of his criticism to depend identity that contain no descriptive constants or upon the claim that for a criterion to be ‘‘intuitively only those from V ; V ¼ {B , F , G , H , M , O T T T T T T acceptable,’’ theoretical terms must retain signifi- N }; and L is the class of all sentences of first- T T cance if T or C is extended. order logic with identity that contain theoretical Carnap (1956) can be defended in at least two terms from V . Let T be: T ways. First, as Kaplan (1975) notes, the criterion ðTÞ½ð8xÞðHT x ! FT xފ6½ð8xÞðHT x ! was restricted to primitive, nondefined theoretical ðBT xVØGT xÞފ6½ð8xÞðMT x $ NT xÞ]; terms. It was explicitly formulated to avoid criti- cisms derived from definitional extensions. Defined and let C be: terms often play an important role in scientific ðCÞ½ð8xÞðROx ! HT xފ6½ð8xÞðFT x ! JOxފ6 theories, and it could be objected that any adequate ½ð8xÞðGT x ! POxފ: criterion should apply directly to theories that con- tain them. Yet the amendment that any theoretical GT, FT, and HT are significant with respect to term within the definiens of a significant defined 6 T C relative to the empty set (see Carnap [1956] term must be antecedently shown significant quells D1) and, hence, significant with respect to LO, LT, these worries (Creath 1976). T, and C (see Carnap [1956] D2). RO is significant PROOFSecond, Carnap (1956) insisted that terms are relative to K ¼ {GT}; MT and NT are not significant. significant only within a particular language and 0 Consider a definitional extension T of T in an for a particular T and C. He did not intend to 0 0 extended vocabulary VT and language LT. After formulate a criterion of cognitive significance that adding two definitions to T: held under theory or language change. If Carnap’s

ðDEF1Þð8xÞðD1T x $ðMT x6ð9xÞFT xÞÞ (1956) work on a significance criterion was an ex- plication of the idea of meaningfulness (Hempel and 1950), the explicandum was the idea of a meani-

ðDEF2Þð8xÞðD2T x $ðMT x !ð9xÞGT xÞÞ; ngful statement of a particular language in a par- ticular theoretical context, not meaningfulness D1T is significant relative to the empty set and per se. Hence, Kaplan and Rozeboom’s objections, FIRST0 therefore significant with respect to T , C, LO, and which rely on questionable intuitions about the 0 LT (D2). D2T is significant relative to K ¼ {D1T}, invariance of significance as T6C changes, are 0 and therefore significant with respect to T , C, LO, not appropriately directed at Carnap (1956). The 0 and LT (D2). MT, which failed to be significant fact that Carnap did not attempt such an account is with respect to T, C, LO, and LT, is now signifi- not merely the result of a realization that so many 0 0 cant with respect to T , C, LO, and LT. A similar problems would thwart the project. Rather, it is a procedure makes NT significant. Kaplan thought consequence of the external/internal framework this showed that Carnap’s (1956) criterion was too that he believed was the most fruitful approach to liberal. The procedure seems able to make any the philosophical questions (Carnap 1947). theoretical term significant with respect to some Furthermore, Rozeboom’s acceptability condi- extended language and definition-extended theory, tion is especially counterintuitive, since changes in

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T or C designate changes in the connections be- Church, A. (1949), ‘‘Review of the Second Edition of Lan- tween theoretical terms themselves or theoretical guage, Truth and Logic, ’’ Journal of Symbolic Logic 14: 52–53. terms and observation terms. Additional postulates Creath, R. (1976), ‘‘Kaplan on Carnap on Significance,’’ that specify new connections, or changes in the Philosophical Studies 30: 393–400. connections, between these terms can obviously Feigl, H. (1969), ‘‘The Origin and Spirit of Logical Positiv- change the significance of a theoretical term. Scien- ism,’’ in P. Achinstein and S. F. Barker (eds.), The tific advances are sometimes made when empirical Legacy of Logical Positivism. Baltimore, MD: Johns Hopkins Press, 3–24. or theoretical discoveries render a theoretical term Hempel, C. (1950), ‘‘Problems and Changes in the Empiri- nonsignificant. cist Criterion of Meaning,’’ Revue Internationale de Phi- JAMES JUSTUS losophie 11: 41–63. ——— (1951), ‘‘The Concept of Cognitive Significance: A Reconsideration,’’ Proceedings of the American Academy References of Arts and Sciences 80: 61–77. Kaplan, D. (1975), ‘‘Significance and Analyticity,’’ in Ayer, A. J. (1934), ‘‘Demonstration of the Impossibility of J. Hintikka (ed.), Rudolf Carnap, Logical Empiricist. Metaphysics,’’ Mind 43: 335–345. Dordrecht, Netherlands: D. Reidel Publishing Co., ——— (1946), Language, Truth, and Logic, 2nd ed. New 87–94. York: Dover Publications. Lewis, C. I. (1934), ‘‘Experience and Meaning,’’ Philosophi- Berlin, I. (1939), ‘‘Verification,’’ Proceedings of the Aristo- cal Review 43: 125–146. telian Society 39: 225–248. Nidditch, P. (1961), ‘‘A Defense of Ayer’s Verifiability Carnap, R. (1928a), Der Logische Aufbau der Welt. Berlin- Principle Against Church’s Criticism,’’ Mind 70: 88–89. Schlachtensee: Weltkreis-Verlag. Reichenbach, H. (1938), Experience and Prediction. Chi- ——— (1928b), Scheinprobleme in der Philosophie: Das cago: University of Chicago Press. Fremdpsychische und der Realismusstreit. Berlin- Rozeboom, W. W. (1960), ‘‘A Note on Carnap’s Meaning Schlachtensee: Weltkreis-Verlag. Criterion,’’ Philosophical Studies 11: 33–38. ——— ([1932] 1959), ‘‘The Elimination of Metaphysics Scheffler, I. (1963), Anatomy of Inquiry. New York: Alfred Through Logical Analysis of Language,’’ in A. J. Ayer A. Knopf. (ed.), Logical Positivism. Glencoe, IL: Free Press, 60–81. Schlick, M. ([1932] 1979), ‘‘Positivism and Realism,’’ in H. ——— (1934), The Logical Syntax of Language. London: L. Mulder and B. F. B. van de Velde-Schlick (eds.), Routledge Press. Moritz Schlick: Philosophical Papers (1926–1936), vol. ——— ([1936–7] 1965), ‘‘Testability and Meaning,’’ in R. 2. Dordrecht, Netherlands: D. Reidel Publishing Co., R. Ammerman (ed.), Classics of Analytic Philosophy. 259–284. New York: McGraw-Hill, 130–195. ———([1936] 1979), ‘‘Meaning and Verification,’’ in H. L. ——— (1947), ‘‘Empiricism, Semantics, and Ontology,’’ in Mulder and B. F. B. van de Velde-Schlick (eds.), Moritz Meaning and Necessity. Chicago: University of Chicago Schlick: Philosophical Papers (1926–1936), vol. 2. Press, 205–221. Dordrecht, Netherlands: D. Reidel Publishing Co., ——— (1956), ‘‘The Methodological Character of Theoret- 456–481. ical Concepts,’’ in H. Feigl and M. Scriven (eds.), The Stace,PROOF W. T. (1935), ‘‘Metaphysics and Meaning,’’ Mind 44: Foundations of Science and the Concepts of Psychology 417–438. and Psychoanalysis. Minneapolis: University of Minne- sota Press, 38–76. See also Analyticity; Ayer, Alfred Jules; Carnap, ——— (1963), ‘‘Intellectual Autobiography,’’ in P. Schlipp Rudolf; Corroboration; Demarcation, Problem of; (ed.), The Philosophy of Rudolf Carnap. Peru, IL: Open Explication; Feigel, Herbert; Hempel, Carl; Logical Court Press, 3–86. Empiricism; Neurath, Otto; Popper, Karl; Rational ——— (1967), Logical Structure of the World and Pseudo- problems in Philosophy. Berkeley and Los Angeles: Uni- Reconstruction; Reichenbach, Hans; Schlick, Mor- versity of California Press. itz; Tarski, Alfred; Verifiability; Vienna Circle FIRST COMPLEMENTARITY

The existence of indivisible interaction quanta is a objects and the interaction with the measuring instru- crucial point that implies the impossibility of any ments that serve to define the conditions under which sharp separation between the behavior of atomic the phenomena appear. In fact, the individuality

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of the typical quantum effects finds its proper ex- the QM mathematics. That it does not M-interpret pression in the circumstance that any attempt at the QM mathematics is made painfully clear by the subdividing the phenomena will demand a change fact that the obvious conception of the QM state it in the experimental arrangement, introducing new suggests—a statistical ensemble of particles, each in possibilities of interaction between objects and a definite classical state—is provably not a possible measuring instruments, which in principle cannot M-interpretation of QM. (For example, no consis- be controlled. Consequently, evidence obtained tent sense can then be made of a superposition of under different experimental conditions cannot c-states, since it is a mathematical theorem that the be comprehended within a single picture but must QM statistics of a superposed state cannot all be be regarded as complementary in the sense that deduced from any single product of classical statis- only the totality of the phenomena exhausts the tical states.) possible information about the objects (Bohr Bohr does not offer an M-interpretation of QM. AU:33 2000, 209–10). He came to think the very idea of such an inter- Complementarity is distinctively associated with pretation incoherent. (In that sense, the term the Danish physicist Niels Bohr and his attempt to ‘‘Copenhagen interpretation’’ is a misnomer; Bohr understand the new quantum mechanics (QM) dur- does not use this label.) Equally, however, Bohr ing the heyday of its invention, 1920–1935. Physi- does not eschew all interpretive discussion of QM, cists know in practice how to extract very precise as many others do on the (pragmatic or positivist- and accurate predictions and explanations from inspired) basis that confining the use of QM strictly QM. Yet, remarkably, even today no one is con- to deriving statistics will avoid error while allowing fident about how to interpret it metaphysically science to continue. Bohr’s position is that this (‘‘M-interpret’’ it). That is, there is no compellingly too is profoundly wrong, and ultimately harmful satisfactory account of what sort of objects and to physics. Instead he offers the doctrine of comple- relations make up the QM realm, and so, ultimate- mentarity as a ‘‘framework’’ for understanding the ly, no one knows why the precise answers are as ‘‘epistemological lesson’’ of QM (not its ontological they are. In classical mechanics (CM), physicists lesson) and for applying QM consistently and as thought they had a lucidly M-interpretable theory: meaningfully as possible. (see Folse 1985 for a gen- There was a collection of clearly specified entities, eral introduction. For extensive, more technical particles, or waves that interacted continuously analyses, see Faye and Folse 1994; Honner 1987; according to simple laws of force so that the system Murdoch 1987. For one of many critiques, and the state was completely specified everywhere and at all opposing Bohrian M-interpretation, see Cushing times—indeed, specification of just instantaneous 1994.) position and momenta sufficed. Here the dynamic Although Bohr considered it necessary (‘‘un- process specified by the laws of force, expressed in avoidablePROOF’’) to continue using the key descriptive terms of energy and momentum (Bohr’s ‘‘causal concepts of CM, the epistemological lesson of QM picture’’), generated a uniquely unfolding system was that the basic conditions for their well-defined configuration expressed in terms of position and use were altered by the quantization of QM in- time (Bohr’s ‘‘space-time picture’’). To repeat this teractions into discrete unanalyzable units. This, for QM, what is needed is a collection of equivalent he argued, divided the CM state in two, the con- quantum objects whose interactions and move- ditions for the well-defined use of (1) causal (ener- ments in space-time generate the peculiar QM sta- gy-momentum) concepts and (2) configurational tistical results in ways that are as intuitively clear as (space-time) concepts being now mutually ex- they are for CM. (However, even this appealing con- clusive, so that only one kind of description could cept of CM proves too simplistic; thereFIRST is continuing be coherently provided at a time. Both kinds of metaphysical perplexity underlying physics; see description were necessary to capture all the AU:34 e.g., Earman 1986; Hooker 1991, note 13.) aspects of a QM system, but they could not be That M-interpreting QM is not easy is nicely simply conjoined as in CM. They were now illustrated by the status of the only agreed-on complementary. general ‘‘interpretation’’ to which physicists refer, Heisenberg’s uncertainty relations of QM, such D D = p; D Born’s rule. It specifies how to extract proba- as x p . h 2 where x is the uncertainly in the bilities from the QM wave function (c [‘‘psi’’]- position, Dp is the uncertainty in the momentum, function). These are normally associated with and h is Planck’s constant (or more generally the particle-like events. But without further M- commutation relations, such as ½x; p ih=2p xŠ ¼ _ interpretive support, Born’s rule becomes merely where h is again Planck’s constant, the magnitude part of the recipe for extracting numbers from of quantization), are not themselves statements

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of complementarity. Rather, they specify the Such inherent mutual exclusions should not be corresponding quantitative relationships between mistaken for merely practical epistemic exclusions complementary quantities. (some of Heisenberg’s pronouncements not- These complementary exclusions are implicit in withstanding). Suppose that the position of an QM ontologies. For instance, single-frequency investigated particle i is determined by bouncing (‘‘pure’’) waves must, mathematically, occupy all (‘‘scattering’’) another probe particle p off of it, space, whereas restricting their extent involves determining the position of i from the intersection superposing waves of different frequencies, with a of the initial and final momenta of p. However, i point-size wave packet requiring use of all frequen- will have received an altered momentum in the cies; thus, frequency and position are not uniquely interaction, and it is tempting to conclude that we cospecifiable. And since the wavelength l is the are thus excluded from knowing both the position wave velocity V (a constant) divided by the fre- and the momentum of i immediately after the in- quency vðl ¼ V=nÞ, uniquely specifying wave- teraction. But in CM the interaction may be retro- length and uniquely specifying position equally spectively analyzed to calculate the precise change are mutually exclusive. QM associates wavelength in momentum introduced by p to i, using conserva- with momentum ð p ¼ h=lÞ and energy with fre- tion of momentum, and so establish both the posi- quency (E ¼ hn) in all cases with discrete values tion and the momentum of i simultaneously. More and for both radiation (waves) and matter ( parti- generally, it is in this manner possible to correct for cles), yielding the QM exclusions. (Note, however, all measurement interactions and arrive at a com- that wave/particle complementarity is but one as- plete classical state specified independently of its pect of causal/configurational complementarity, method of measurement. This cannot, in principle, the aspect concerned with physical conditions that be done in QM, because of quantization. frame coherent superposition versus those that Faye (1991) provides a persuasive account of the frame localization.) origins of Bohr’s ideas about the applicability of Precisely why these particular associations (and physical concepts in the thought of the Danish similar QM associations) should follow from philosopher Harald Høffding (a family friend and quantization of interaction is not physically obvi- early mentor of Bohr’s) and sets out Bohr’s conse- ous, despite Bohr’s confident assertion. Of course quent approach. According to Høffding, objective such associations follow from the QM mathe- description in principle required a separation be- matics, but that presupposes rather than explains tween describing a subject and describing a known complementarity, and Bohr intended comple- object (Bohr’s ‘‘cut’’ between them) in a way that mentarity to elucidate QM. The physical and always permitted the object to be ascribed a unique mathematical roots of quantization are still only (Bohr’s ‘‘unambiguous’’) spatiotemporal location, partially understood. However, it is clear that state,PROOF and causal interaction. These ideas in turn discontinuity leads to a constraint, in principle, originated in the Kantian doctrine that an objective on joint precise specification. Consider initially description of nature requires a well-defined dis- any quantity that varies with time (t), e.g., energy tinction between the knower and the object of AU:35 (E ), so that E ¼ f ðtÞ.Then across some time in- knowledge, permitting the unique construction of terval, t1 ! t2, E will change accordingly: a well-defined object state, specified in applications E1ðt1Þ!E2ðt2Þ. of concepts from the synthetic a priori (essentially If E varies continuously, then both E and t are Newtonian) construction of the external world (see everywhere jointly precisely specifiable because Friedman 1992). We have just noted how CM for every intermediate value of t between t1 and t2 satisfies this requirement. (say, t1þn) there will be a correspondingFIRST value for Contrarily, Bohr insisted, the quantum of action E: E1þn ¼ f ðt1þnÞ. Suppose, however, that E (but creates an ‘‘indissoluble bond’’ between the mea- not t) is quantized, with no allowed value between surement apparatus (m-apparatus, including the E1 and E2. Then no intermediate E value is avail- sentient observer) and the measured (observed) able, and energy must remain undefined during at system, preventing the construction of a well- least some part of the transition period. This con- defined system state separate from observing in- clusion can be generalized to any two or more teractions. This vitiates any well-defined, global related quantities. The problem is resolved if both cut between m-apparatus and system. Creating a quantities are quantized, but there is as yet set of complementary partial cuts is the best that no satisfactory quantization of space and time can now be done. In fact, these circumstances are (Hooker 1991). generalized to all interactions between QM

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systems; the lack of a global separation is expressed interactions, and statistical descriptions reflect in their superposition, which defies reduction to (only) limited information about states and are any combination of objectively separate states. not fundamental (contrary to common readings Consequently, Bohr regarded CM as an idealized of QM). Here the objective representation of na- physics (achieved, imperfectly, only in the limit ture through invariances eliminates any inherent h !: 0) and QM as a ‘‘rational generalization’’ of reference to any subject’s point of view. Rather, it, in the sense of the principle of affinity, the in coming to know nature we also come to know Kantian methodological requirement of continuity. ourselves as knowers by being modeled in the the- Bohr’s conception of what is required of a physi- ory as some objects among others so as to remove cally intelligible theory T can thus be summarized ourselves from the form of the theory, disappear- as follows (Hooker 1991, 1994): ing as subjects. This shift in ideals of intelligibility and objectivity locates the full depth of Bohr’s BI1. Each descriptive concept A of T has a set doctrine of complementarity. of well-defined, epistemically accessible conditions CA under which it is unambigu- ously applicable. BI2. The set of such concepts collectively References exhausts, in a complementary way, the epi- Bohr, N. (2000), ‘‘Discussion with Einstein on Epistemo- AU:38 stemically accessible features of the phe- logical Problems in Atomic Physics,’’ in P. A. Schilpp nomena in the domain of T. (ed.), Albert Einstein: Philosopher-Scientist, 3rd ed. La Salle, IL: Open Court, 199–242. AU:39 BI3. There is a well-defined, unified, and essen- ——— (1961), Atomic Theory and the Description of Nature. tially unique formal structure S(T) that Cambridge: Cambridge University Press. structures and coordinates descriptions of Bub, J. (1974), The Interpretation of Quantum Mechanics. phenomena so that each description is well Dordrecht, Netherlands: Reidel. defined (the various conditions C are con- Cushing, J. T. (1994), ‘‘A Bohmian Response to Bohr’s A Complementarity,’’ in J. Faye and H. J. Folse (eds.), sistently combined), S(T ) is formally com- Niels Bohr and Contemporary Philosophy. Dordrecht, plete (Bub 1974), and BI2 is met. Netherlands: Kluwer. BI4. Bohr objectivity (BO) satisfies BI1–3 in the Earman, J. (1986), A Primer on Determinism. Dordrecht, most empirically precise and accurate way Netherlands: Reidel. available across the widest domain of phe- Faye, J. (1991), Niels Bohr: His Heritage and Legacy. Dor- drecht, Netherlands: Kluwer. nomena while accurately specifying the in- Faye, J., and H. J. Folse (eds.) (1994), Niels Bohr and teractive conditions under which such Contemporary Philosophy. Dordrecht, Netherlands: AU:36 phenomena are accessible to us. Kluwer. Folse, H. J. (1985), The Philosophy of Niels Bohr. Amster- An objective representation of nature thus reflects PROOF dam: North-Holland. the interactive access (‘‘point of view’’) of the know- Friedman, M. (1992), Kant and the Exact Sciences. Cam- ing subject, which cannot be eliminated. In coming to bridge, MA: Harvard University Press. know nature, we also come to know ourselves as Honner, J. (1987), The Description of Nature. Oxford: Clar- endon. knowers—not fundamentally by being modeled in Hooker, C. A. (1972), ‘‘The Nature of Quantum Mechani- the theory as objects (although this too happens, cal Reality: Einstein versus Bohr,’’ in R. G. Colodny in part), but by the way the very form of rational (ed.), Pittsburgh Studies in the Philosophy of Science, generalization reflects our being as knowing subjects. vol. 5. Pittsburgh, PA: University of Pittsburgh Press. A very different ideal of scientific intelligibility ——— (1991), ‘‘Physical Intelligibility, Projection, and Objectivity: The Divergent Ideals of Einstein and operates in classical physics, and in many proposed Bohr,’’ British Journal for the Philosophy of Science 42, M-interpretations of QM. Contrary toFIRST BI1, descrip- 491–511. tive concepts are taken as straightforwardly charac- ——— (1994), ‘‘Bohr and the Crisis of Empirical Intelligi- terizing external reality (describing an M, even if it is bility: An Essay on the Depth of Bohr’s Thought and a strange one). Hence, contrary to BI2, these con- Our Philosophical Ignorance,’’ in J. Faye and H. J. Folse (eds.), Niels Bohr and Contemporary Philosophy. Dor- cepts apply conjointly to describe reality complete- drecht, Netherlands: Kluwer. AU:37 ly. Contrary to BI3 and BI4, an objective theory Murdoch, D. (1987), Niels Bohr’s Philosophy of Physics. completely and accurately describes the physical Cambridge: Cambridge University Press. state at each moment in time and provides a unique C. A. HOOKER interactive dynamic history of states for all systems in its domain. Accordingly, measurements are See also Classical Mechanics; Quantum Measure- analyzed similarly as the same kinds of dynamic ment Problem; Quantum Mechanics

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COMPLEXITY

COMPLEXITY

See Unity and Disunity of Science

CONFIRMATION THEORY

When evidence does not conclusively establish (or premises or evidence provides to a conclusion or refute) a hypothesis or theory, it may nevertheless that a hypothesis has. See Carnap, Rudolf, for an provide some support for (or against) the hypothe- idea of degree of confirmation based on his pro- sis or theory. Confirmation theory is concerned posed ‘‘logical’’ interpretation of probability and almost exclusively with the latter, where conclusive degree of support.) In the theory of the logic of support (or ‘‘countersupport’’) are limiting cases of support, confirmation theory is concerned primari- AU:40 confirmation (or disconfirmation). (Included also, ly with inductive support, where the theory of de- of course, is concern for the case in which the ductive support is supposed to be more fully evidence is confirmationally irrelevant.) Typically, understood. confirmation theory concerns potential support, The concept of confirmation can be divided into the impact that evidence would have on a hypothe- a number of subconcepts, corresponding to three sis or theory if learned, where whether the evidence distinctions. First, absolute confirmation and incre- is actually learned or not is not the point; for this mentalPROOF confirmation may be distinguished. In the reason, confirmation theory is sometimes called the absolute sense, a hypothesis is confirmed by evi- logic of confirmation. (For simplicity of exposition dence if the evidence makes (or would make) the for now, theories will be considered separately hypothesis highly supported; absolute confirmation below and not explicitly mentioned until then.) is about how the evidence ‘‘leaves’’ the hypothesis. It is relevant here to point out the distinction In the incremental sense, evidence confirms a hy- between deductive logic (or deductive evaluation pothesis if the evidence makes the hypothesis more of arguments) and inductive logic (or inductive highly confirmed (in the absolute sense) than it is evaluation of arguments). In deductive logic, the (in the absolute sense) without the evidence; incre- question is just whether or not the supposed truth mental confirmation involves a comparison. Sec- of all the premises of an argument gives an absolute ond, confirmation can be thought of either guarantee of truth to the conclusionFIRST of the argu- qualitatively or quantitatively. So, in the absolute ment. In inductive logic, the question is whether the sense of confirmation, a hypothesis can be, qualita- supposed truth of all the premises of an argument tively, left more or less confirmed by evidence, gives significant support for the truth of the conclu- where quantitative confirmation theory attempts sion, where, ideally, some measure of to what de- to make sense of assigning numerical degrees of gree the premises support the conclusion (which is confirmational support (‘‘inductive probabilities’’) sometimes called the inductive probability of an to hypotheses in light of the evidence. In the incre- argument) would be provided (see Inductive mental sense of confirmation, evidence E may, Logic; Induction, Problem of; and Verisimilitude. qualitatively, either confirm, disconfirm, or be evi- As in each of these topics also, the question is one dentially irrelevant to a hypothesis H, where in the of either qualitative or quantitative support that quantitative sense, a numerical magnitude (which

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can be measured, ‘‘inductive probabilistically,’’ in and a non-G is both an F and a non-F,’’ which different ways; see below) is assigned to the Nicod’s criterion implies that nothing can confirm ‘‘boost’’ (positive or negative, if any) that E gives (a positive instance would have to be both an F and H. Finally, confirmation can be considered to be a non-F ). either comparative or noncomparative. Noncom- Thus, Hempel suggests weakening Nicod’s crite- parative confirmation concerns just one hypothe- rion. The idea that negative instances disconfirm sis/evidence pair. In comparative confirmation, one (i.e., are sufficient to disconfirm) is retained. Fur- can compare how well an E supports an H with ther, Hempel endorses the positive-instance criteri- how well an E 0 supports the same H; or one may on, according to which positive instances are compare how well an E supports an H with how sufficient for confirmation. Nicod’s criterion can well the same E supports an H 0; or one may com- be thought of as containing six parts: necessary pare how well an E supports an H with how well an and sufficient conditions for all three of confirma- E 0 supports an H 0. tion, disconfirmation, and irrelevance. The positive- The exposition below will be divided into two instance criterion is said to be one-sixth of Nicod’s main parts. The first part, ‘‘Nonprobabilistic criterion, and it does not lead to the kind of con- Approaches,’’ will concern different aspects of qual- tradiction that Nicod’s full criterion does when itative confirmation; and the second part, ‘‘Pro- conjoined with the equivalence condition. babilistic Approaches,’’ will consider some major However, the combination of the positive- quantitative approaches. Almost exclusively, as in instance criterion and the equivalence condition the literature, the issue will be incremental confir- (i.e., the proposition that the positive-instance cri- mation rather than absolute confirmation. Both terion satisfies the equivalence condition) does lead noncomparative and various kinds of comparative to what Hempel called paradoxes of confirmation, approaches will be described. also known as the Ravens paradox and Hempel’s paradox. Hempel’s famous example is the hypoth- esis H: ‘‘All ravens are black.’’ Hypothesis H is 0 Nonprobabilistic Approaches logically equivalent to hypothesis H : ‘‘All non- black things are nonravens.’’ According to the A simple and natural idea about the confirmation equivalence condition, anything that confirms H 0 of a general hypothesis of the form ‘‘All Fs are Gs’’ confirms H. According to the positive-instance is that an object confirms the hypothesis if and only criterion, nonblack nonravens (positive instances if it is both an F and a G (a ‘‘positive instance’’ of of H 0) confirm H 0. Examples of nonblack nonra- the hypothesis), disconfirms the hypothesis if and vens (positive instances of H 0) include white shoes, only if it is an F but not a G (a ‘‘negative instance’’), yellow pencils, transparent tumblers, etc. So it fol- and is evidentially irrelevant if and only if it is not lowsPROOF from the positive-instance criterion plus the even an F (no kind of instance). Hempel ([1945] equivalence condition that objects of the kinds just 1965) calls this Nicod’s criterion (Nicod 1930). An- listed confirm the hypothesis H that all ravens other natural idea about the confirmation of are black. These conclusions seem incorrect or hypotheses is that if hypotheses H and H 0 are counterintuitive, and the paradox is that the two logically equivalent, then evidence E confirms, dis- seemingly plausible principles, the positive-instance confirms, or is irrelevant to H if and only if E criterion and the equivalence condition, lead, by confirms, disconfirms, or is irrelevant to H 0, re- valid reasoning, to these seemingly implausible spectively. Hempel calls this the equivalence condi- conclusions. Further paradoxical consequences tion, and distinguishes between criteria (definitions can be obtained by noting that the hypothesis H or partial definitions) of confirmationFIRST and the con- is logically equivalent also to H 00, ‘‘All things that ditions of adequacy that the criteria should satisfy. are either a raven or not a raven (i.e., all things) are Hempel points out that Nicod’s criterion does not either black or not a raven,’’ which has as positive satisfy the equivalence condition (as long as confir- instances any objects that are black and any objects mation, disconfirmation, and evidential irrelevance that are not ravens. are mutually exclusive). For example, a hypothesis Since the equivalence condition is so plausible ‘‘All Fs are Gs’’ is logically equivalent to ‘‘All non- (if H and H 0 are logically equivalent, they can Gs are non-Fs,’’ but Nicod’s criterion implies that be thought of as simply different formulations of an object that is an F and a G would confirm the the same hypothesis), attention has focused on the former but be irrelevant to the latter, thus violating positive-instance criterion. Hempel defended the the equivalence condition. Also, ‘‘All Fs are Gs’’ is criterion, arguing that the seeming paradoxicalness logically equivalent to ‘‘Anything that is both an F of the consequences of the criterion is more of a

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psychological illusion than a mark of a logical flaw Yet, the evidence E 0 (or E) consists of positive in the criterion: instances of H 0. Since the positive-instance criterion can be for- In the seemingly paradoxical cases of confirmation, we mulated purely syntactically—in terms of simply are often not actually judging the relation of the given evidence E alone to the hypothesis H ... . [I]nstead, we the logical forms of evidence sentences and hypoth- tacitly introduce a comparison of H with a body of evi- eses and the logical relation between their forms— dence which consists of E in conjunction with additional a natural lesson of the Grue example is that information that we happen to have at our disposal. confirmation cannot be characterized purely syntactically. (It should be noted that an important (Hempel [1945] 1965, 19) feature of Hempel’s ([1945] 1965) project was the So, for example, if one is just given the informa- attempt to characterize confirmation purely syn- tion that an object is nonblack and a nonraven tactically, so that evidence E should, strictly (where it may happen to be a white shoe or a yellow speaking, be construed as evidence statements or pencil, but this is not included in the evidence), sentences, or ‘‘observation reports,’’ as he put it, then the idea is that one should intuitively judge rather than as observations or the objects of ob- the evidence as confirmatory, ‘‘and the paradoxes servation.) And a natural response to this has vanish’’ (20). To assess properly the seemingly par- been to try to find nonsyntactical features of evi- adoxical cases for their significance for the logic of dence and hypothesis that differentiate cases in confirmation, one must observe the ‘‘methodologi- which positive instances confirm and cases in cal fiction’’ (as Hempel calls it) that one is in a which they do not. And a natural idea here is to position to judge the relation between the given distinguish between predicates that are ‘‘projec- evidence alone (e.g., that an object is a positive tible’’ (in Goodman’s terminology) and those that instance of the contrapositive of a universalized are not. Goodman suggested ‘‘entrenchment’’ of conditional) and the hypothesis in question and predicates as the mark of projectibility—where a that there is no other information. This approach predicate is entrenched to the extent to which it has has been challenged by some who have argued that been used in the past in hypotheses that have been confirmation should be thought of as a relation successfully confirmed. Quine (1969) suggested among three things: evidence, hypothesis, and drawing the distinction in terms of the idea of background knowledge (see the section below on natural kinds. A completely different approach Probabilistic Approaches). would be to point out that the reason why one Given the equivalence condition, the Ravens thinks the observation of grue emeralds (E 0 or E) paradox considers the question of which of several disconfirms the grue hypothesis (H 0) is because of kinds of evidence confirm(s) what one can consider background knowledge about constancy of color to be a single hypothesis. There is another kind (inPROOF our usual concept of color) of many kinds of of paradox, or puzzle, that arises in a case of a objects, and to argue that the evidence in this case single body of evidence and multiple hypotheses. should be taken as actually confirming the hypoth- In Nelson Goodman’s (1965) well-known Grue esis H, given the Hempelian methodological fic- paradox or puzzle, a ‘new’ predicate is defined as tion. It should be pointed out that the positive- follows. Let’s say that an object A is ‘‘grue’’ if and instance criterion applies to a limited, though very only if either (i) A has been observed before a important, kind of hypothesis and evidence: uni- certain time t (which could be now or some time versalized conditionals for the hypothesis and pos- in the future) and A is green or (ii) A has not been itive instances for the evidence. And it supplies observed before that time t and A is blue. Consider only a sufficient condition for confirmation. Hem- the hypothesis H that all emeralds are green pel ([1945] 1965) generalized, in a natural way, this 0 FIRST and the hypothesis H that all emeralds are criterion to his satisfaction criterion, which applies grue. And consider the evidence E to be the obser- to different and more complex logical structures for vation of a vast number of emeralds, all of which evidence and hypothesis and provides explicit defi- have been green. Given that t is now or some time nitions of confirmation, disconfirmation, and evi- in the future, E is equivalent to E 0, that the vast dential irrelevance. Without going into any detail number of emeralds observed have all been grue. about this more general criterion, it is worth point- It is taken that E (the ‘‘same’’ as E 0) confirms H ing out what Hempel took to be evidence for its (this is natural enough) but not H 0—for in order adequacy. It is the satisfaction, by the satisfaction for H 0 to be true, exactly all of the unobserved criterion, of what Hempel took to be some intui- (by t) emeralds would have to be blue, which tively obvious conditions of adequacy for defini- would seem to be disconfirmed by the evidence. tions, or criteria, of confirmation. Besides the

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equivalence condition, two others are the en- and observation. An example of such a principle tailment condition and the special-consequence would be, ‘‘If there is an excess of electrons [theo- condition. The entailment condition says that evi- retical] on the surface of a balloon [observational], dence that logically entails a hypothesis should be then a sheet of paper [observational] will cling [ob- deemed as confirming the hypothesis. The special- servational] to it, in normal circumstances [auxilia- consequence condition says that if evidence E con- ry assumption].’’ Of course, if the prediction fails firms hypothesis H and if H logically entails hypoth- (an observational deductive consequence of a theo- esis H 0, then E confirms H 0. This last condition will ry turns out to be false), then this is supposed to be considered further in the section below on provide disconfirmation of the theory. probabilistic approaches. Two of the main issues or difficulties that have The criteria for confirmation discussed above been discussed in connection with the HD idea apply in cases in which evidence reports and hypo- have to do with what might be called distribution theses are stated in the ‘‘same language,’’ which of credit and distribution of blame. The first has Hempel took to be an observational language. State- also been called the problem of irrelevant conjunc- ments of evidence, for example, are usually referred tion. If a hypothesis H logically implies an observa- to as observational reports in Hempel ([1945] 1965). tion report E, then so does the conjunction, H6G, What about confirmation of theories, though, where G can be any sentence whatsoever. So the which are often thought of as containing two kinds basic idea of HD has the consequence that when- of vocabulary, observational and theoretical? ever an E confirms an H, the E confirms also Hypothetico-deductivism (HD) is the idea that the- H6G, where G can be any (even irrelevant) hy- ories and hypotheses are confirmed by their obser- pothesis whatsoever. This problem concerns the vational deductive consequences. This is different distribution of credit. A natural response would from the positive-instance criterion and the satis- be to refine the basic HD idea in a way to make it faction criterion. For example, ‘‘A is an F and A is sensitive to the possibility that logically weaker a G,’’ which is a report of a positive instance of the parts of a hypothesis may suffice to deductively hypothesis that all Fs are Gs, is not a deductive imply the observation report. The second issue consequence of the hypothesis. The positive- has to do with the possibility of the failure of the instance and satisfaction criteria are formulations prediction, of the observational deductive conse- of the idea, roughly, that observations that are quence of the hypothesis turning out to be false. logically consistent with a hypothesis confirm the This is also known as Duhem’s problem (Duhem hypothesis, while HD says that deductive conse- 1914) (see Duhem Thesis). If a hypothesis H plus quences of a hypothesis or theory confirm the statements of initial conditions I plus auxiliary hypothesis or theory. assumptions A plus bridge principles B logically As an example, Edmund Halley in 1705 pub- implyPROOF an observation report E (ðH6I6A6BÞ lished his prediction that a comet, now known as ) EÞ,and E turns out to be false, then what one Halley’s comet, would be visible from Earth some- can conclude is that the four-part conjunction time in December of 1758; he deduced this using H6I6A6B is false. And the problem is how in Newtonian theory. The prediction was successful, general to decide whether the evidence should be and the December 1758 observation of the comet counted as telling against the hypothesis H, the was taken by scientists to provide (further) very statements of initial conditions I, the auxiliary significant confirmation of Newtonian theory. Of assumptions A, or the bridge principles B. course, the prediction was not deduced from New- Glymour (1980) catalogues a number of issues tonian theory alone. In general, other needed pre- relevant to the assessment of HD (and accounts mises include statements of initial conditionsFIRST(in the of confirmation in general) and proposes an al- case of the example, reports of similar or related ternative deductivist approach to confirmation observations at approximately 75-year intervals) called ‘‘the bootstrap strategy,’’ which attempts and auxiliary assumptions (that the comet would to clarify the idea of different parts of a theory not explode before December 1758; that other bod- and how evidence can bear differently on them. In ies in the solar system would have only an insignif- Glymour’s bootstrap account, confirmation is a icant effect on the path of the comet; and so on). In relation among a theory T, a hypothesis H, and addition, when the theory and the observation re- evidence expressed as a sentence E, and Glymour port share no nonlogical vocabulary (say, the theo- gives an intricate explication of the idea that ‘‘E ry is highly theoretical, containing no observational confirms H with respect to T,’’ an explication that terms), then so-called bridge principles are needed is supposed to be sensitive especially to the idea to establish a deductive connection between theory that evidence can be differently confirmationally

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CONFIRMATION THEORY

relevant to different hypotheses that are parts of a Where P measures an agent’s subjective degrees complex theory. of belief, P(HjE ) is supposed to be the agent’s degree of belief in H on the assumption that E is Probabilistic Approaches true, or the degree of belief that the agent would have in H were the agent to learn that E is true. If a One influential probabilistic approach to various person’s degree of belief in H would increase if E issues in confirmation theory is called Bayesian were learned, then it is natural to say that for this confirmation theory (see Bayesianism). The basic agent, E is positively evidentially relevant to H, idea, on which several refinements may be based, even when E is not in fact learned. Of course, is that evidence E confirms hypothesis H if and different people will have different subjective prob- only if the conditional probability PðH j EÞ (de- abilities, or degrees of belief, even if the different fined as PðH6EÞjpðEÞ) is greater than the un- people are equally rational, this being due to dif- conditional probability P(H ) and where P(S )is ferent bodies of background knowledge or beliefs the probability that the statement, or proposition, possessed (albeit possibly equally justifiable or ex- or claim, or assertion, or sentence S is true (the cusable, depending on one’s experience), so that in status of what kind of entity S might be is a con- this approach to confirmation theory, confirma- cern in metaphysics or the philosophy of language, tion is a relation among three things: evidence, as well as in the philosophy of science). Disconfir- hypothesis, and background knowledge. The rea- mation is defined by reversing the inequality, and son this approach is called Bayesian is because of evidential irrelevance is defined by changing the the use that is sometimes made of a mathematical inequality to an equality. theorem discovered by Thomas Bayes (Bayes Typically in Bayesian confirmation theory, the 1764), a simple version of which is PðH j EÞ¼ function P is taken to be a measure of an agent’s PðE j HÞPðHÞ=PðEÞ. This is significant because it subjective probabilities—also called degrees of be- is sometimes easier to figure out the probability of lief, partial beliefs, or degrees of confidence. Much an evidence statement conditional on a hypothesis philosophical work has been done in the area of than it is to figure out the probability of a hypoth- foundations of subjective probability, the intent esis on the assumption that the evidence statement being to clarify or operationalize the idea that is true (for example, when the hypothesis is statisti- agents (e.g., scientists) have (or should have only) cal and the evidence statement reports the outcome more or less strong or weak beliefs in propositions, of an experiment to which the hypothesis applies). rather than simply adopting the attitudes of accep- Bayes’s theorem can be used to link these two tance or rejection of them. One approach, called converse conditional probabilities when the priors, the Dutch book argument, attempts to clarify the P(H ) and P(E ), are known (see Bayesianism). idea of subjective probability in terms of odds that PROOFBayesian confirmation theory not only provides one is willing to accept when betting for or against a qualitative definition of confirmation, discon- the truth or falsity of propositions (see Dutch Book firmation, and evidential irrelevance, but also Argument). Another approach, characterized as a suggests measures of degree of evidential support. decision theoretical approach, assumes various The most common is the difference measure: axioms regarding rational preference (transitivity, dðH;EÞ¼PðH jEÞ À PðHÞ, where confirmation, asymmetry, etc.) and some structural conditions disconfirmation, and evidential irrelevance corre- (involving the richness of the set of propositions, spond to whether this measure is greater than, less or acts, states, and outcomes, considered by an than, or equal to 0, and the degree is measured by agent) and derives, from preference data, via repre- the magnitude of the difference. Another common- sentation theorems, a probability assignment P and ly used measure is the ratio measure: rðH; EÞ¼ FIRST = a desirability (or utility) assignment DES such that PðH j EÞ PðHÞ where confirmation, disconfirma- an agent prefers an item A to an item B if and only tion, and evidential irrelevance correspond to if some kind of expected utility of A is numerically whether this measure is greater than, less than, or greater than the expected utility of B, when the equal to 1, and the degree is measured by the expected utilities are calculated in terms of the magnitude of the ratio. Other measures have been derived P and DES functions (see Decision Theo- defined as functions of likelihoods, or converse ry). Various formulas for expected utility have been conditional probabilities, P(EjH). One application proposed. (Important work in foundations of sub- of the idea of degree of evidential support has jective probability include Ramsey 1931; de Finetti been in the Ravens paradox, discussed above. 1937; Savage [1954] 1972; Jeffrey [1965] 1983; and Such definitions of degree of evidential support Joyce 1999.) provide a framework within which one can clarify

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intuitions that under certain conditions (contrapos- confirming the H while disconfirming the H 0, itive instances of the hypothesis that all ravens telling against the special-consequence condition are black [i.e., nonblack nonravens]) confirm the and also in favor of Bayesian confirmation theory hypothesis that all ravens are black, but to a mi- (e.g., Eells 1982). nuscule degree compared with positive instances Some standard objections to Bayesian confirma- (black ravens). tion theory are characterized as the problem of the What follows is a little more detail about the priors and the problem of old evidence. As to the application of Bayesian confirmation theory to the first, while it is sometimes admitted that it makes positive-instance criterion and the Ravens para- sense to assign probabilities to evidence statements dox. (see Eells 1982 for a discussion and refer- E conditional on some hypothesis H (even in the ences.) Let H be the hypothesis that all ravens absence of much background knowledge), it is are black; let RA symbolize the statement that objected that it often does not make sense to assign object A is a raven; and let BA symbolize the unconditional, or ‘‘prior,’’ probabilities to hypoth- statement that object A is black. It can be shown esis H or to evidence statements (reports of obser- that if H is probabilistically independent of RA, vation) E.IfH is a newly formulated physical (i.e., P(H jRA) ¼ P(H )), then a positive instance hypothesis, for example, it is hard to imagine (or report of one), RA 6 BA,ofH confirms H in what would justify an assignment of probability the Bayesian sense (i.e., P(H j RA6BA) > P(H )) if to it prior to evidence—but that is just what the and only if P(BA jRA) < 1 (which latter inequality suggested criterion of confirmation, Bayes’s theo- can naturally be interpreted as saying that it rem, and the measures of confirmation described was not already certain that A would be black if above require. Such issues make some favor a like- a raven). Further, on the same independence as- lihood approach to the evaluation of evidence— sumption, it can be shown that a positive instance, Edwards (1972) and Royall (1997), for instance, RA6BA, confirms H more than a contrapositive who represent a different approach and tradition instance, ø BA6øRA if and only if P(BA j RA) < P in the area of statistical inference. According to one (øRAjøBA). formulation of the likelihood account, an E con- What about the assumption of probabilistic in- firms an H more than the E confirms an H 0 if and 0 dependence of H from RA? I. J. Good (1967) has only if P(EjH ) is greater than P(EjH ). This is a proposed counterexamples to the positive-instance comparative principle, an approach that separates criterion like the following. Suppose it is believed the question of which hypothesis it is more justified that either (1) there are just a few ravens in the to believe given the evidence (or the comparative world and they are all black or (2) there are lots acceptability of hypotheses given the evidence) and lots of ravens in the world, a very, very few of from the question of what the comparative signifi- which are nonblack. Observation of a raven, even a cancePROOF is of evidence for one hypothesis compared black one (hence a positive instance of H ), would with the evidence’s significance for another hypoth- tend to support supposition 2 against supposition 1 esis. It is the latter question that the likelihood and thus undermine H, so that a positive instance approach actually addresses, and it is sometimes would disconfirm H. But in this case the indepen- suggested that the degree to which an E supports dence assumption does not hold, so that Bayesian an H compared with the support of E for an H 0 confirmation theory can help to isolate the kinds of is measured by the likelihood ratio, PðE j HÞ= situations in which the positive-instance criterion PðE j H0Þ: Also, likelihood measures of degree of holds and the kinds in which it may not. confirmation of single hypotheses have been pro- Bayesian confirmation theory can also be used to posed, such as LðH; EÞ¼PðE j HÞ=PðE j ØHÞ; assess Hempel’s proposed conditionsFIRST of adequacy or the log of this ratio. (see Fitelson 2001 and for criteria of confirmation. Recall, for example, Forster and Sober 2002 for recent discussion and his special-consequence condition, discussed references.) above: If E confirms H and H logically entails H 0, Another possible response to the problem of then E must also confirm H 0. It is a theorem of priors is to point to convergence theorems (as in probability theory that if H logically entails H 0, de Finetti 1937) and argue that initial settings of then P(H 0) is at least as great as P(H ). If the priors does not matter in the long run. According inequality is strict, then an E can increase the prob- to such theorems, if a number of agents set dif- ability of H while decreasing the probability of ferent priors, are exposed to the same series of H 0, consistent with H logically entailing H 0. This evidence, and update their subjective probabil- fact can be used to construct intuitively compel- ities (degrees of belief ) in certain ways, then, al- ling examples of an H entailing an H 0 and an E most certainly, their subjective probabilities will

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CONFIRMATION THEORY

eventually converge on each other and, under cer- Fitelson, Branden (2001), Studies in Bayesian Confirmation tain circumstances, upon the truth. Theory. Ph.D. dissertation, University of Wisconsin– Madison. The problem of old evidence (Glymour 1980; Forster, Malcolm, and Elliott Sober (2002), ‘‘Why Likeli- Good 1968, 1985) arises in cases in which P(E ) ¼ hood?’’ in M. Taper and S. Lee (eds.), The Nature of 1. It is a theorem of probability theory that in such Scientific Evidence. Chicago: University of Chicago cases P(HjE ) ¼ P(H ), for any hypothesis H,so Press. that in the Bayesian conception of confirmation Glymour, Clark (1980), Theory and Evidence. Princeton, NJ: Princeton University Press. as formulated above, an E with probability 1 can- Good, I. J. (1967), ‘‘The White Shoe Is a Red Herring,’’ not confirm any hypothesis H. But this seems to The British Journal for the Philosophy of Science 17: 322. run against intuition in some cases. An often-cited ——— (1968), ‘‘Corroboration, Explanation, Evolv- such case is the confirmation that Einstein’s general ing Probability, Simplicity, and a Sharpened Razor,’’ theory of relativity apparently was informed by al- British Journal for the Philosophy of Science 19: 123–143. ——— (1985), ‘‘A Historical Comment Concerning Novel ready known facts about the behavior of the perihe- Confirmation,’’ British Journal for the Philosophy of Sci- lion of the planet Mercury. One possible Bayesian ence 36: 184–186. solution to the problem, suggested by Glymour Goodman, Nelson (1965), Fact, Fiction, and Forecast. New (1980), would be to say that it is not the already York: Bobbs-Merrill. known E that confirms the H after all, but rather a Hempel, Carl G. ([1945] 1965), ‘‘Studies in the Logic of Confirmation,’’ in Aspects of Scientific Explanation and newly discovered logical or explanatory relation Other Essays in the Philosophy of Science. New York: between the H and the E. Other solutions have Free Press, 3–51. Originally published in Mind 54: 1–26 been proposed, various versions of the problem and 97–121. have been distinguished (see Earman 1992 for a Jeffrey, Richard C. ([1965] 1983), The Logic of Decision. discussion), and the problem remains one of lively Chicago and London: University of Chicago Press. Joyce, James M. (1999), The Foundations of Causal Decision debate. Theory. Cambridge and New York: Cambridge Univer- ELLERY EELLS sity Press. Nicod, Jean (1930), Foundations of Geometry and Induction. New York and London: P. P. Wiener. References Quine, W. V. (1969), ‘‘Natural Kinds,’’ in Ontological Rela- Bayes, Thomas (1764), ‘‘An Essay Towards Solving a Prob- tivity and Other Essays. New York: Columbia University lem in the Doctrine of Chance,’’ Philosophical Transac- Press. tions of the Royal Society of London 53: 370–418. Ramsey, Frank Plumpton (1931), ‘‘Truth and Probability,’’ de Finetti, Bruno (1937), ‘‘La pre´vision: Ses lois logiques, in R. B. Braithwaite (ed.), The Foundations of Mathe- ses sources subjectives,’’ Annales de l’Institute Henri matics and Other Logical Essays. London: Routledge Poincare´ 7: 1–68. and Kegan Paul, 156–198. Duhem, Pierre (1914), The Aim and Structure of Physical Royall, Richard (1997), Statistical Evidence: A Likelihood Theory. Princeton, NJ: Princeton University Press. PROOFParadigm. Boca Raton, FL: Chapman and Hall. Earman, John (1992), Bayes or Bust: A Critical Examina- Savage, Leonard ([1954] 1972), The Foundations of Statis- tion of Bayesian Confirmation Theory. Cambridge, MA, tics. New York: Dover Publications. and London: MIT Press. See also Bayesianism; Carnap, Rudolf; Decision Edwards, A. W. F. (1972), Likelihood. Cambridge: Cam- bridge University Press. Theory; Dutch Book Argument; Epistemology; Eells, Ellery (1982), Rational Decision and Causality. Cam- Hempel, Carl Gustav; Induction, Problem of; Induc- bridge and New York: Cambridge University Press. tive Logic; Probability FIRST CONNECTIONISM

Connectionist models, also known as models mid-1980s. Connectionism currently represents one of parallel distributed processing (PDP) and arti- of two dominant approaches (symbolic modeling is ficial neural networks (ANN), have merged into the other) within artificial intelligence used to dev- the mainstream of cognitive science since the elop computational models of mental processes.

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Unlike symbolic modeling, connectionist modeling accounted for (see Lakatos, Imre; Research Pro- also figures prominently in computational neuro- grams). The greater the disunity in these factors, science (where the preferred term is neural network the less connectionism resembles a research pro- modeling). gram, and the more it appears to be a convenient Connectionist modeling first emerged in the pe- tool for modeling certain phenomena. If it is a mod- riod 1940–1960, as researchers explored possible eling tool, connectionism need not commit modelers approaches to using networks of simple neurons to having anything in common beyond their use of to perform psychological tasks, but it fell into de- the particular mathematical and formal apparatus cline when limitations of early network designs itself. became apparent around 1970. With the publica- This article will briefly describe the features of tion of the PDP Research Group volumes (Ru- prevalent connectionist architectures and discuss a melhart, McClelland, et al. 1986; McClelland, number of challenges to the use of these models. One Rumelhart, et al. 1986), connectionism was rescued challenge comes from symbolic models of cognition, from over a decade of popular neglect, and the way which present an alternative representational frame- was opened for a new generation to extend the work and set of processing assumptions. Another approach to fresh explanatory domains. (For a comes from a purportedly nonrepresentational collection of historically significant papers from framework, that of nonlinear dynamical systems these neglected years and before, see Anderson and theory. Finally, there is the neuroscientific chal- Rosenfeld 1988; Anderson, Pellionisz, and Rosen- lenge to the disciplinary boundaries drawn around feld 1990.) Despite some early claims that connec- ‘‘cognitive’’ modeling by some connectionist psy- tionism constitued a new, perhaps revolutionary, chologists. The status of connectionism is assessed way of understanding cognition, the veritable in light of these challenges. flood of network-based research has ultimately oc- curred side by side with other, more traditional, The Properties of Connectionist Models styles of modeling and theoretical frameworks. The renaissance in connectionist modeling is a Connectionist networks are built up from basic result of convergence from many different fields. computational elements called units or nodes, Mathematicians and computer scientists attempt to which are linked to each other via weighted con- describe the formal, mathematical properties of ab- nections, called simply weights. Units take on a stract network architectures. Psychologists and neu- variable numerical level of activation, and they roscientists use networks to model behavioral, pass activation to each other via the weights. cognitive, and biological phenomena. Roboticists Weights determine how great an effect one unit also make networks the control systems for many has on other units. This effect may be positive kinds of embodied artificial agents. Finally, engi- (excitatory)PROOF or negative (inhibitory). The net input neers employ connectionist systems in many in- a unit receives at a time is the weighted sum of the dustrial and commercial applications. Research activations on all of the units that are active and has thus been driven by a broad spectrum of connected to it. Given the net input, an activation concerns, ranging from the purely theoretical to function (often nonlinear or imposing a threshold) problem-solving applications for problems in determines the activation of the unit. In this way, various scientific domains to application-based or activation is passed in parallel throughout the net- engineering needs. work. Connectionist networks compute functions Given these heterogeneous motivations, and the by mapping vectors of activation values onto other recent proliferation of network models, analytic such vectors. techniques, applications, and theories,FIRST it is appro- Multilayer feedforward networks are the most priate to ask whether connectionism constitutes a intensively studied and widely used class of con- coherent research program or is instead primarily temporary models. Units are arranged into layers, a modeling tool. Following Lakatos, connection- beginning with an input layer and passing through ism could be construed as a research program in- a number of intermediate hidden layers, terminat- volving a set of core theoretical principles about ing with an output layer. There are no reciprocal the role of networks in explaining and understand- connections, so activation flows unidirectionally ing cognition, a set of positive and negative heur- through the network. The modeler assigns repre- istics that guide research, an ordering of the sentational significance to the activation vectors at important commitments of connectionist model- the input and output layers of a network, thereby ing, and a set of principles and strategies dictating forging the link between the model and the cogni- how recalcitrant empirical results are to be tive task to be explained.

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For example, Sejnowski and Rosenberg’s of prototypes from exemplars, single word read- NETtalk architecture is designed to map graphe- ing, shape-from-shading extraction, visual object mic inputs (letters) onto phonemic outputs. It con- recognition, modeling deficits arising in deep dys- sists of an input layer of seven groups of 29 units, a lexia, and more. Their formal properties are well hidden layer of 80 units, and an output layer of 26 known. However, they suffer from a number of units. Each layer is completely connected to the problems. Among these is the fact that learning next one. Vectors of activity in the network repre- via backpropagation is extremely slow, and in- sent aspects of the letter-reading task. The input creasing the learning-rate parameter typically groups are used to represent the seven letters of text results in overshooting the optimum weights for that the network is perceiving at a time, and the solving the task. output layer represents the phoneme corresponding Another problem facing feedforward networks to the fourth letter in the input string. The task of generally is that individual episodes of processing the network is to pronounce the text correctly, inputs are independent of each other except for given the relevant context. When the values of the changes in weights resulting from learning. But weights are set correctly, the network can produce often a cognitive agent is sensitive not just to what the appropriate phoneme-representing vectors in it has learned over many episodes, but to what it response to the text-representing vectors. processed recently (e.g., the words prior to the pre- Simple networks can be wired by hand to com- ceding one). The primary way sensitivity to context pute some functions, but in networks containing has been achieved in feedforward networks has been hundreds of units, this is impossible. Connectionist to present a constantly moving window of input. systems are therefore usually not programmed in For example, in NETtalk, the input specified the the traditional sense, but are trained by fixing a three phonemes before and three phonemes after learning rule and repeatedly exposing the network the one to be pronounced. But this solution is to a subset of the input-output mappings it is clearly a kludge and suffers from the fact that it intended to learn. The rule then systematically imposes a fixed window. If sensitivity to the item adjusts the network’s weights until its outputs are four back is critical to correct performance, the near the target output values. One way to classify network cannot perform correctly. learning rules is according to whether they require An alternative architecture that is increasingly an external trainer. Unsupervised learning (e.g., being explored is the simple recurrent network Hebbian learning) does not require an external (SRN) (Elman 1991). SRNs have both feedforward trainer or source of error signals. Supervised and recurrent connections. In the standard model, learning, on the other hand, requires that something an input layer sends activity to a hidden layer, outside the network indicate when its performance which has two sets of outgoing connections: one is incorrect. The most popular supervised learning toPROOF other hidden layers and eventually on to the rule currently in use is the backpropagation rule. output layer, and another to a specialized context In backpropagation learning, the network’s layer. The weights to the units in the context layer weights are initially set to random values (within enable it to construct a copy of the activity in the certain bounds). The network is then presented hidden units. The activation over these units is then with patterns from the training environment. treated as an additional input to the same hidden Given random weights, the network’s response will units at the next temporal stage of processing. This likely be far from the intended mapping. The differ- allows for a limited form of short-term memory, ence between the output and the target is computed since activity patterns that were present during the by the external trainer and used to send an error previous processing cycle have an effect on the next signal backward through the network.FIRST As the signal cycle. Since the activity on the previous cycle was propagates, the weights between each layer are itself influenced by that on a yet earlier cycle, this adjusted by a slight amount. Over many train- allows for memory extending over several previous ing cycles, the network’s performance gradually processing epochs (although sensitivity to more approaches the target. When the output is within than one cycle back will be diminished). some criterion distance of the target, training ceases. Once trained in a variation of backpropagation, Since the error is being reduced gradually, back- many SRNs are able to discover patterns in tempo- propagation is an instance of a gradient-descent rally ordered sets of events. Elman (1991) has learning algorithm. trained SRNs on serially presented words in an Backpropagation-trained networks have been attempt to teach them to predict the grammatical successful at performing in many domains, includ- category of the next word in a sentence. The net- ing past-tense transformation of verbs, generation works can achieve fairly good performance at

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this task. Since the networks were never supplied systems. Whether a network is hand-wired or information about grammatical categories, this trained using a learning rule, the modifications suggests that they induced a representation of a are changes to the weights between units. The new more abstract similarity among words than was weight settings determine the future course of acti- present in the raw training data. There are many vation in the network and simultaneously consti- other kinds of neural network architecture. (For tute the data stored in the network. There are no further details on their properties and applications, explicitly represented rules that govern the system’s see Anderson 1995; Bechtel and Abrahamsen dynamics. 2002.) Classical theorists (Fodor and Pylyshyn 1988) have claimed that there are properties of cognition Connectionism and Symbolic Models that are captured naturally in symbolic models but that connectionist models can capture them Within cognitive science, symbolic models of cog- only in an ad hoc manner, if at all. Among these nition have constituted the traditional alternative properties are the productivity and the systemati- to connectionism. In symbolic models, the basic city of thought. Like natural language, thought is representational units are symbols having both productive, in that a person can think a potentially syntactic form and typically an intuitive semantics infinite number of thoughts. For example, one can that corresponds to the elements picked out by think that Walt is an idiot, that Sandra believes words of natural language. The symbols are dis- that Walt is an idiot, that Max wonders whether crete and capable of combining to form complex Sandra believes that Walt is an idiot, and so on. symbols that have internal syntactic structure. Like Thought is also systematic, in that a person who the symbol strings used in formal logic, these com- can entertain a thought can also entertain many plex symbols exhibit variable binding and scope, other thoughts that are semantically related to it function-and-argument structure, cross-reference, (Cummins 1996). If a person can think that Rex and so on. The semantics for complex symbols is admires the butler’s courage, that person can also combinatorial: The meaning of a complex symbol think that the butler admires Rex’s courage. Any- is determined by the meanings of its parts plus its one who can think that dogs fear cats can think syntax. Finally, in symbolic models the dynamics of that cats fear dogs, and so on. Unless each thought the system are governed by rules that transform is to be learned anew, these capacities need some symbols into other symbols by responding to their finite basis. syntactic or formal properties. These rules are Symbolicists argue that this basis is composition- intended to preserve the truth of the structures ality: Thought possesses a combinatorial syntax manipulated. Symbolic models are essentially and semantics, according to which complex thou- proof-theoretic engines. ghtsPROOF are built up from their constituent concepts, Connectionist models typically contain units and those concepts completely determine the mean- that do not individually represent lexicalized se- ing of a complex thought. The compositionality mantic contents. (What are called localist net- of thought would explain both productivity and works are an exception. In these, individual units systematicity. Grasping the meaning of a set of are interpretable as expressing everyday properties primitive concepts and grasping the recursive or propositions. See Page 2000.) More comm- rules by which they can be combined is sufficient only, representations with lexicalized content are for grasping the infinite number of thoughts that distributed over a number of units in a network the concepts and rules can generate. Similarly, (Smolensky 1988). In a distributed scheme, individ- grasping a syntactic schema and a set of constituent ual units may stand for repeatableFIRST but nonlexica- concepts explains why the ability to entertain one lized microfeatures of familiar objects, which are thought necessitates the ability to entertain others: themselves represented by vectors of such features. Concepts may be substituted into any permissible In networks of significant complexity, it may be role slot in the schema. difficult, if not impossible, to discern what content The challenge symbolicists have put to con- a particular unit is carrying. nectionists is to explain productivity and syste- In networks, there is no clear analog to the sym- maticity in a principled fashion, without merely bolicist’s syntactic structures. Units acquire and implementing a symbolic architecture on top of transmit activation values, resulting in larger pat- the connectionist network (for one such implemen- terns of coactivation, but these patterns of units do tation, see Franklin and Garzon 1990). One option not themselves syntactically compose. Also, there is that some connectionists pursue is to deny that no clear program/data distinction in connectionist thought is productive or systematic, as symbolicists

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characterize these properties. For example, one cognition. In many respects, this debate has might deny that it is possible to think any system- reached a standoff. In part its resolution will turn atically structured proposition. Although one can on the issue posed earlier: To what degree do compose the symbol string ‘‘The blackberry ate the humans exhibit productivity and systematicity? bear,’’ that does not entail that one is able to think But independently of that issue, there are serious such a thought. But clearly much of thought exhi- problems in scaling up from connectionist net- bits some degree of productivity and systematicity, works designed to handle toy problems to ones and it is incumbent on connectionists to offer some capable of handling the sort of problems humans account of how it is achieved. deal with regularly (e.g., communicating in natural Connectionists have advanced a number of pro- languages). Thus, it is not clear whether solutions posals for explaining productivity and syste- similar to those employed in RAAMs (or in SRNs, maticity. Two of the most widely discussed are which also exhibit a degree of productivity and Pollack’s recursive auto-associative memories systematicity) will account for human perfor- (RAAMs) and Smolensky’s tensor product net- mance. (Symbolic models have their own problems works (Pollack 1990; Smolensky, 1991). RAAMs in scaling, and so are not significantly better off in are easier to understand. An auto-associative net- practice.) work is one trained to produce the same pattern on the output layer as is present on the input layer. Connectionism and Dynamical Systems Theory If the hidden layer is smaller than the input and output layers, then the pattern produced on the Although the conflict between connectionists and hidden layer is a compressed representation of the symbolicists reached a stalemate in the 1990s, with- input pattern. If the input layer contains three in the broader cognitive science community a kind times the number of units as the hidden layer, of accord was achieved. Connectionist approaches then one can treat the input activation as consisting were added to symbolic approaches as parts of the of three parts constituting three patterns (e.g., for modeling toolkit. For some tasks, connectionist different words) and recursively compose the models proved to be more useful tools than symbol- hidden pattern produced by three patterns with ic models, while for others symbolic models two new ones. In such an encoding, one is implicitly continued to be preferred. For yet other tasks, con- ignoring the output units, but one can also ignore nectionist models were integrated with symbolic the input units and supply patterns to the hidden models into hybrids. units, allowing the RAAM to generate a pattern on As this was happening, a new competitor the output units. What is interesting is that even emerged on the scene, an approach to cognition after several cycles of compression, one can, by that challenged both symbolic and connectionist recursively copying the pattern on one-third of modelingPROOF insofar as both took seriously that cogni- the output units back onto the hidden units, re- tive activity involved the use of some form of repre- create with a fair degree of accuracy the original sentation. Dynamical systems theory suggested that input patterns. rather than construing cognition as involving If RAAMs are required to perform many cycles syntactic manipulation of representations or pro- of recursive encoding, the regeneration of the orig- cessing them through layers of a network, one inal pattern may exhibit errors. But up to this should reject the notion of representation altogeth- point, the RAAM has exhibited a degree of pro- er. The alternative these critics advanced was to ductivity by composing representations of com- characterize cognitive activity in terms of a (typi- plex structures from representations of their parts. cally small) set of variables and to formulate (typi- One can also use the compressed patternsFIRST in other cally nonlinear) equations that would relate the processing (e.g., to train another feedforward net- values of different variables in terms of how they work to construct the compressed representation changed over time. In physics, dynamical systems of a passive sentence from the corresponding ac- theory provides a set of tools for understanding the tive sentence). RAAMs thus exhibit a degree of changes over time of such systems of variables. For systematicity. But the compressed representations example, each variable can be construed as defining a are not composed according to syntactic princi- dimension in a multidimensional state space,and ples. Van Gelder (1990), accordingly, construes many systems, although starting at different points them as manifesting functional, not explicit, in this space, will settle onto a fixed point or into a compositionality. cycle of points. These points are known as attrac- Symbolicists have rejected such functional tors, and the paths to them as the transients.The compositionality as inadequate for explaining structure of the state space can often be represented

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geometrically—for example, by showing different terms of transitions between representations. This basins, each of which represents starting states that is particularly true when the system is carrying out will end up in a different attractor. what one ordinarily thinks of as a complex reason- Connectionist networks, especially those employ- ing task such as playing chess, where the task is ing recurrent connections, are dynamical systems, defined in terms of goals and the cognizer can be and some connectionist modelers have embraced construed as considering different possible moves the tools of dynamical systems theory for describing and their consequences. To understand why a cer- AU:41 their networks. Elman, for example, employs such tain system is able to play chess successfully, rather tools to understand how networks manage to learn than just recognizing that it does, the common to respect syntactic categories in processing streams strategy is to treat some of its internal states as rep- of words. Others have made use of some of the resenting goals or possible moves. Moreover, inso- more exotic elements in dynamical systems theory, far as these internal states are causally connected such as activitation functions that exhibit deter- in appropriate ways, they do in fact carry informa- ministic chaos, to develop new classes of networks tion (in what is fundamentally an informational- that exhibit more complex and interesting patterns theoretic sense, in which the state covaries with of behavior than simpler networks (e.g., jumping referents external to the system), which is then intermittently between two competing interpreta- utilized by other parts of the system. In systems tions of an ambiguous perceptual figure such as designed to have them, these information-carrying the duck-rabbit (see van Leeuwen, Verver, and states may arise without their normal cause (as Brinkers 2000)). Some particularly extreme dynami- when a frog is subjected to a laboratory with bul- cists, however, contend that once one has character- lets on a string moving in front of its eyes). In these ized a cognitive system in this way, there is no further situations the system responds as it would if the point to identifying internal states as representations state were generated by the cause for which the and characterizing changes as operations on these response was designed or selected. Such internal representations. Accordingly, they construe dyna- states satisfy a common understanding of what a mical systems theory as a truly radical paradigm representation is, and the ability to understand why shift for cognitive science (van Gelder 1995). the system works successfully appeals to these This challenge has been bolstered by some nota- representations. If this construal is correct, then ble empirical successes in dynamical systems mod- dynamical systems theory as well is not an alterna- eling of complex cognition and behavior. For tive to connectionist modeling, but should be con- example, Busemeyer and Townsend (1993) offer a strued as an extension of the connectionist toolkit model of decision under uncertainty, decision field (Bechtel and Abrahamsen, 2002). theory, that captures much of the empirical data about the temporal course of decision making PROOF Connectionism and Neuroscience using difference equations containing only seven parameters for psychological quantities such as Connectionist models are often described as being attention weight, valence, preference, and so on. neurally inspired, as the term ‘‘artificial neural Connectionist models, by contrast, have activation networks’’ implies. More strongly, many connec- state spaces of as many dimensions as they have tionists have claimed that their models enjoy a units. There are dynamical systems models of many special sort of neural plausibility. If there is a signif- other phenomena, including coordination of finger icant similarity between the processing in ANNs movement, olfactory perception, infants’ stepping and the activity in real networks of neurons, this behavior, the control of autonomous robot agents, might support connectionism for two reasons. and simple language processing. TheFIRST relative sim- First, since the cognitive description of the system plicity and comprehensibility of their models moti- closely resembles the neurobiological description, it vates the antirepresentational claims advanced by seems that connectionist models in psychology dynamical systems theorists. have a more obvious account about how the mind There is reason, though, to question dynamical might supervene on the brain than do symbolic systems theory’s more radical challenge to cogni- models (see Supervenience). Second, connectionist tive modeling. One can accept the utility of char- models might provide a fairly direct characteriza- acterizing a system in terms of a set of equations tion of the functioning of the neural level itself and portraying its transitions through a multidi- (e.g., the particular causal interactions among neu- mensional state space without rejecting the utility rons). This functioning is not easily revealed by of construing states within the system as represen- many standard neuroscience methods. For exam- tational and the trajectories through state space in ple, localization of mental activity via functional

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magnetic resonance imaging can indicate which resulting from hippocampal lesions could be brain regions are preferentially activated during explained on the assumption that the hippocampus certain tasks, but this alone does not give informa- has a method of temporarily storing associations tion about the specific computations being carried among stimuli without catastrophic interference. out within those regions. Connectionist modeling Ablation of the hippocampus results in antero- of brain function thus might supplement other grade amnesia for arbitrary associations and de- neurobiological techniques. clarative information because the neocortex alone This strategy can be illustrated within the domain is incapable of learning these without the appro- of learning and memory. Neuropsychological studies priately interleaved presentation. Implicit learning suggest that the destruction of structures in the medi- is preserved because it does not require rapid inte- al temporal lobes of the brain, especially the hippo- gration of many disparate representations into a campus, results in a characteristic pattern of memory single remembered experience; further, it typically deficits. These include (i) profound anterograde am- takes many trials for mastery, as is also the case nesia for information presented in declarative or ver- with backpropagation learning. Finally, the tem- bal form, such as arbitrary paired associates, as well porally graded retrograde amnesia is explained by as memory for particular experienced events more the elimination of memory traces that are tem- generally (episodic memory); (ii) preserved implicit porarily stored in the hippocampus itself. Older memory for new information, such as gradually ac- memories have already been integrated into the quired perceptual-motor skills; and (iii) retrograde neocortex, and hence are preserved. amnesia for recently acquired information, with rel- McClelland et al. (1995) did not model the hip- ative preservation of memories farther back in time. pocampus directly; rather, they implemented it as a This triad of deficits was famously manifested by black box that trained the neocortical network H.M., a patient who underwent bilateral removal of according to the interleaving regimen. Others sections of his medial temporal lobes in the early have since presented more elaborate models. 1950s in order to cure intractable epilepsy. Since Murre, Graham, and Hodges (2001) have imple- H.M., this pattern of deficits has been confirmed in mented a system called TraceLink that features a other human and animal studies. network corresponding to a simplified single-layer McClelland, McNaughton, and O’Reilly (1995) hippocampus, the neocortex, and a network of offer an explanation of these deficits based on conne- neuromodulatory systems (intended to correspond ctionist principles. One feature of backpropagation- to the basal forebrain nuclei). TraceLink accounts trained networks is that once they are trained on for the data reviewed by McClelland et al. (1995), one mapping, they cannot learn another mapping and also predicts several phenomena associated without ‘‘unlearning’’ the previously stored knowl- with semantic dementia. Other models incor- edge. This phenomenon is known as catastrophic poratingPROOF a more elaborate multilayer hippocampal interference. However, catastrophic interfence can network have been presented by Rolls and Treves be overcome if, rather than fully training a network (1998) and O’Reilly and Rudy (2001). These mod- on one mapping, then training it on another, the els collectively support the general framework set training sets are interleaved so that the network is out by McClelland et al. (1995) concerning the exposed to both mappings in alternation. When computational division of labor between the hippo- the training environment is manipulated in this campus and the neocortex in learning and memory. way, the network can learn both mappings without These studies of complementary learning systems overwriting either one. suggest a useful role for network-based modeling in As a model of all learning and memory, this neuroscience. However, this role is presently limit- technique suffers from being slow andFIRST reliant on a ed in several crucial respects. The models currently fortunate arrangement of environmental con- being offered are highly impoverished compared tingencies. However, McClelland et al. (1995) sug- with the actual complexity of the relevant neuro- gest that learning in the neocortex may be biological structures. Assuming that these net- characterized by just such a process, if there is a works are intended to capture neuron-level neural mechanism that stores, organizes, and pre- interactions, they are several orders of magnitude sents appropriately interleaved stimuli to it. They short of the number of neurons and connections in conjecture that this is the computational function the brain. Further, the backpropagation rule itself of the hippocampus. Anatomically, the hippo- is biologically implausible if interpreted at the neu- campus receives convergent inputs from many ronal level, since it allows individual weights to sensory centers and has wide-ranging efferent con- take on either positive or negative values, while nections to the neocortex. The pattern of deficits actual axonal connections are either excitatory or

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inhibitory, but never both. There is no network In psychology, for instance, there are some con- model that captures all of the known causal prop- nectionists who conceive of their models as erties of neurons, even when the presence of glial providing a theory of how mental structures might cells, endocrine regulators of neural function, and functionally resemble, and therefore plausibly su- other factors are abstracted away. pervene in, the organization of large-scale neuronal A common response to these objections is to structures (see Psychology). However, there are just interpret networks as describing only select pat- as many theorists who see their work as being only, terns of causal activity among large populations in some quite loose sense, neurally inspired. The of neurons. In many cases, this interpretation is organization of the NETtalk network is not partic- appropriate. However, there are many kinds of ularly neurally plausible, since it posits a simple network models in neuroscience, and they can be three-layered linear causal process leading from interpreted as applying to many different levels of the perception of letters to the utterance of pho- organization within the nervous system, including nemes. Being a connectionist in psychology does individual synaptic junctions on dendrites, particu- not appear to require agreement on the purpose of lar neurons within cortical columns, and interac- the models used or the possible data (e.g., neurobi- tions at the level of whole neural systems. No single ological) that might confirm or disconfirm them. interpretation appears to have any special priority This is what one might expect of a tool rather than a over the others. The specific details of the network research program. architecture are dictated in most cases by the par- It is perhaps ironic that this state of affairs was ticular level of neural analysis being pursued, and predicted by Rumelhart, one of the theorists who theorists investigate multiple levels simultaneously. revitalized connectionism during the 1980s. In a There are likely to be at least as many distinct kinds 1993 interview, Rumelhart claimed that as networks of possible connectionist models in neuroscience as become more widely used in a number of disciplines, there are distinct levels of generalization within the ‘‘there will be less and less of a core remaining for nervous system. neural networks per se and more of, ‘Here’s a person doing good work in [her] field, and [she’s] using Conclusions neural networks as a tool’’’(Anderson and Rosen- feld 1998, 290). Within the fields, in turn, network At the beginning of this article, the question was modeling will ‘‘[d]isappear as an identifiable sepa- asked whether connectionism is best thought of as rate thing’’ and become ‘‘part of doing science or a research program, a modeling tool, or something doing engineering’’ (291). Such a disappearance, in between. Considering the many uses to which however, may not be harmful. Connectionist net- networks have been put, and the many disciplines works, like other tools for scientific inquiry, are to that have been involved in cataloguing their proper- bePROOF evaluated by the quality of the results they pro- ties, it seems unlikely that there will be any common duce. In this respect, they have clearly proven them- unity of methods, heuristics, principles, etc., among selves a worthy, and sometimes indispensible, them. Ask whether a neuroscientist using networks component of research in an impressive variety of to model the development of receptive fields in the disciplines. somatosensory system would have anything in com- DAN WIESKOPF AND WILLIAM BECHTEL mon with a programmer training a network to take customers’ airline reservations. Each of these might be a neural network theorist, despite having nothing References significant in common besides the formal apparatus Anderson, James A. (1995), An Introduction to Neural Net- they employ. Across disciplines, then, connection- works. Cambridge, MA: MIT Press. FIRST Anderson, James A., and Edward Rosenfeld (eds.) (1988), ism lacks the characteristic unity one would expect from a research program. Neurocomputing: Foundations of Research, vol. 1. Cam- The question may be asked again at the level of bridge, MA: MIT Press. ——— (1998), Talking Nets: An Oral History of Neural each individual discipline. This article has not sur- Networks. Cambridge, MA: MIT Press. veyed every field in which networks have played a Anderson, James A., Andras Pellionisz, and Edward significant role but has focused on their uses in Rosenfeld (eds.) (1990), Neurocomputing: Directions for artificial intelligence, psychology, and neurosci- Research, vol. 2. Cambridge, MA: MIT Press. ence. Even within these fields, the characteristic Bechtel, William, and Adele Abrahamsen (2002), Connec- tionism and the Mind: Parallel Processing, Dynamics, and unity of a research program is also largely absent, Evolution in Networks. Oxford: Basil Blackwell. if one takes into account the diverse uses that are Busemeyer, Jerome R., and James T. Townsend (1993), made of networks. ‘‘Decision Field Theory: A Dynamic-Cognitive

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Approach to Decision Making in an Uncertain Environ- Page, M. (2000), ‘‘Connectionist Modeling in Psychology: ment,’’ Psychological Review 100: 423– 459. A Localist Manifesto,’’ Behavioral and Brain Sciences 23: Cummins, Robert (1996), ‘‘Systematicity,’’ Journal of Phi- 443–512. losophy 93: 591–614. Pollack, Jordan B (1990), ‘‘Recursive Distributed Represen- Elman, Jeffrey L. (1991), ‘‘Distributed Representations, tations,’’ Artificial Intelligence 46: 77–105. Simple Recurrent Networks, and Grammatical Struc- Rolls, Edmund T., and Alessandro Treves (1998), Neural ture,’’ Machine Learning 7: 195–225. Networks and Brain Function. Oxford: Oxford University Fodor, Jerry A., and Zenon Pylyshyn (1988), ‘‘Connection- Press. ism and Cognitive Architecture: A Critical Analysis,’’ Rumelhart, David E., James L. McClelland, and the PDP Cognition 28: 3–71. Research Group (1986), Parallel Distributed Processing: Franklin, Stan, and Max Garzon (1990), ‘‘Neural Comput- Explorations in the Microstructure of Cognition, vol. 1. ability,’’ in O. M. Omidvar (ed.), Progress in Neural Cambridge, MA: MIT Press. Networks, vol. 1. Norwood, NJ: Ablex, 127–145. Smolensky, Paul (1988), ‘‘On the Proper Treatment of McClelland, James L., Bruce L. McNaughton, and Randall Connectionism,’’ Behavioral and Brain Sciences 11: 1–74. C. O’Reilly (1995), ‘‘Why There Are Complementary ——— (1991), ‘‘Connectionism, Constituency, and the Learning Systems in the Hippocampus and Neocortex: Language of Thought,’’ in Barry Loewer and Georges Insights from the Successes and Failures of Connection- Rey (eds.), Meaning in Mind: Fodor and His Critics. ist Models of Learning and Memory,’’ Psychological Oxford: Basil Blackwell. Review 102: 419– 457. van Gelder, Timothy (1990), ‘‘Compositionality: A Connec- McClelland, James L., David E. Rumelhart, and the PDP tionist Variation on a Classical Theme,’’ Cognitive Sci- Research Group (1986), Parallel Distributed Processing: ence 14: 355–384. Explorations in the Microstructure of Cognition, vol. 2. ——— (1995), ‘‘What Might Cognition Be, If Not Compu- Cambridge, MA: MIT Press. tation?’’ Journal of Philosophy 111: 345–381. Murre, Jacob, Kim S. Graham, and John R. Hodges (2001), van Leeuwen, Cees, S. Verver, and M. Brinkers (2000), ‘‘Vi- ‘‘Semantic Dementia: Relevance to Connectionist Mod- sual Illusions, Solid/Outline Invariance and Non-Station- els of Long-Term Memory,’’ Brain 124: 647–675. ary Activity Patterns,’’ Connection Science 12: 279–297. O’Reilly, Randall C., and J. W. Rudy (2001), ‘‘Conjunctive Representations in Learning and Memory: Principles of See also Artificial Intelligence; Cognitive Science; Cortical and Hippocampal Function,’’ Psychological Re- Neurobiology; Psychology, Philosophy of; Superve- view 108: 311–345. nience

CONSCIOUSNESSPROOF

Consciousness is extremely familiar, yet it is at the agent’s desire for a certain emotional satisfaction limits—beyond the limits, some would say—of might be unconscious (as opposed to conscious). what one can sensibly talk about or explain. Per- Rosenthal (1992) calls the former creature haps this is the reason its study has drawn contri- consciousness and the latter state consciousness. butions from many fields, including psychology, Most, but not all, discussion of consciousness in neuroscience, philosophy, anthropology, cultural the contemporary literature concerns state con- and literary theory, artificial intelligence, physics, sciousness rather than creature consciousness. and others. The focus of this articleFIRST is on the vari- Rosenthal (1992) goes on to propose an explana- eties of consciousness, different problems that have tion of state consciousness in terms of creature been raised about these varieties, and prospects for consciousness, according to which a state is con- progress on these problems. scious just in case an agent who is in the state is conscious of it—but this proposal has proved controversial (e.g., Dretske 1993). Varieties of Consciousness Creature vs. State Consciousness One attributes consciousness both to people Essential vs. Nonessential Consciousness and to their psychological states. An agent can be Focusing on conscious states, one may distin- conscious (as opposed to unconscious), and that guish those that are essentially conscious from

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those that are (or might be) conscious but not this only vaguely. So the study of creature trans- essentially so. The distinction is no doubt vague, itive consciousness may be assimilated to the study but, to a first approximation, a state is essentially of knowledge or beliefs. It is sometimes suggested conscious just in case being in the state entails that that ‘‘consciousness’’ and ‘‘awareness’’ are syno- it is conscious, and is not essentially conscious just nyms. This is true only on the assumption that in case this is not so. what is intended is creature transitive conscious- Sensations are good candidates for states that ness, since awareness is always by someone of are essentially conscious. If an agent is in pain, something. this state would seem to be conscious. (This is not to deny that the agent might fail to attend to it.) Intentional vs. Nonintentional Consciousness Beliefs, knowledge, and other cognitive states are While the transitive/intransitive distinction has good candidates for states that might be conscious no obvious analogue in the case of state conscious- but not essentially so. One may truly say that an ness—a state is not itself awake or alert, nor is it agent knows the rules of his language even though aware of anything—a related distinction is that this knowledge is unconscious. Perception presents between intentional and nonintentional conscious a hard case, as is demonstrated by the phenomenon states. An intentional conscious state is of some- of blindsight, in which subjects report that they do thing in the sense that it represents the world as not see anything in portions of the visual field and being a certain way—such states exhibit ‘‘inten- yet their performance on forced-choice tasks sug- tionality,’’ to adopt the traditional word. A non- gests otherwise (Weiskrantz 1986). Clearly some intentional conscious state is a state that does not information processing is going on in such cases, represent the world as being in some way. It is but it is not obvious that what is going on is properly sometimes suggested that bodily sensations (itches, described as perception, or at least as perceptual pains) are states of this second kind, while percep- experience. It is plausible to suppose that indecision tual experiences (seeing a blue square on a red about how to describe matters here derives in part background) are cases of the first. But the matter from indecision about whether perceptual states or is controversial given that to have a pain in one’s experiences are essentially conscious. foot seems to involve among other things re- presenting one’s foot as being in some condition Transitive vs. Intransitive Consciousness or other, a fact that suggests that even here there In the case of creature consciousness, one may is an intentional element in consciousness (see speak of someone’s being conscious simpliciter and Intentionality). of someone’s being conscious of something or other. Malcolm calls the first ‘‘intransitive’’ and the second PhenomenalPROOF vs. Access Consciousness ‘‘transitive’’ consciousness (e.g., Armstrong and Block (1995) distinguishes two kinds of state Malcolm 1984). To say that a person is conscious consciousness: phenomenal consciousness and ac- simpliciter is a way of saying that the person is cess consciousness. The notion of a phenomenally awake or alert. So the study of creature intransitive conscious state is usually phrased in terms of consciousness may be assimilated to the study of ‘‘What is it like ... ?’’ (e.g., Nagel 1974, ‘‘What is what it is to be alert. The denial of consciousness it like to be a bat?’’). For a state to be phenome- simpliciter does not entail a denial of psychological nally conscious is for there to be something it is states altogether. If an agent is fast asleep on a akin to being, in that state. In the philosophical couch, one may truly say both that the agent is literature, the terms ‘‘qualia,’’ ‘‘phenomenal char- unconscious and that the agent believes that snow acter,’’ and ‘‘experience’’ are all used as rough syn- is white. Humphrey (1992) speculatesFIRST that the onyms for phenomenal consciousness in this sense, notion of intransitive consciousness is a recent though unfortunately there is no terminological one, perhaps about two hundred years old, but consensus here. presumably people were on occasion intransitively For a state to be access conscious is, roughly, for conscious (i.e., alert or awake) prior to that date. the state to control rationally, or be poised to To say that a person is conscious of something control rationally, thought and behavior. For crea- seems to be a way of saying that the person knows tures who have language, access consciousness or has beliefs about that thing. To say that one is closely correlates with reportability, the ability to conscious of a noise overhead is to say that one express the state at will in language. Block suggests, knows there is a noise overhead, though perhaps among other things, that a state can be phenome- with the accompanying implication that one knows nally conscious without its being access conscious.

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For example, suppose one is engaged in intense Self-consciousness conversation and becomes aware only at noon Turning back from state consciousness to crea- that there is a jackhammer operating outside—at ture consciousness, a notion of importance here is five to twelve, one’s hearing the noise is phenome- self-consciousness, i.e., one’s being conscious of nally conscious, but it is not access conscious. oneself as an agent or self or (in some cases) a Block argues that many discussions both in person. If to speak of a creature’s being ‘conscious’ the sciences and in philosophy putatively about of something is to speak about knowledge or phenomenal consciousness are in fact about access beliefs, to attribute self-consciousness is to attri- consciousness. Block’s distinction is related to one bute to a creature knowledge or beliefs that the made by Armstrong (1980) between experience and creature is a self or an agent. This would presum- consciousness. For Armstrong, consciousness is at- ably require significant psychological complexity tentional: A state is conscious just in case one and perhaps cultural specificity. Proposals like attends to it. However, since one can have an expe- those of Jaynes (1976) and Dennett (1992)—that rience without attending to it, it is possible to consciousness is a phenomenon that emerges only divorce experience and consciousness in this sense. in various societies—are best interpreted as con- Within the general concept of access consci- cerning self-consciousness in this sense, which ousness, a number of different strands may be becomes more natural the more one complicates distinguished. For example, an (epistemologically) the underlying notion of self or agent. (Parallel normative interpretation of the notion needs to be remarks apply to any notion of group conscious- separated from a nonnormative one. In the former ness, assuming such a notion could be made clear.) case, the mere fact that one is in an access-conscious state puts one in a position to know or justifiably believe that one is; in the latter, being in an access- Problems of Consciousness conscious state prompts one to think or believe that one is—here there is no issue of epistemic appraisal If these are the varieties of consciousness, it is easy (see Epistemology). Further, an actualist interpre- enough to say in general terms what the pro- tation of the notion needs to be separated from a blems of consciousness are, i.e., to explain or un- counterfactual one. In the former case, what is derstand consciousness in all its varieties. But at issue is whether one does know or think that demands for explanation mean different things to one is in the state; in the latter, what is at issue is different people, so the matter requires further whether one would, provided other cognitive con- examination. ditions were met. Distinguishing these various To start with, one might approach the issue from notions leads naturally into other issues. For exam- an unabashedly scientific point of view. Conscious- ple, consider the claim that it is essentially true of nessPROOF is a variegated phenomenon that is a pervasive all psychological states that if one is in them, one feature of the mental lives of humans and other would know that one is, provided one reflects and creatures. It is desirable to have an explanation of has the relevant concepts. That is one way of this phenomenon, just as it is desirable to have an spelling out the Cartesian idea (recently defended explanation of the formation of the moon, or the by Searle [1992]) that the mind is ‘‘transparent’’ to origin of HIV/AIDS. Questions that might be itself. raised in this connection, and indeed have been There are hints both in Block (1995) and in raised, concern the relation of consciousness to related discussion (e.g., Davies and Humphreys neural structures (e.g., Crick and Koch 1998), the 1993) that the phenomenal/access distinction is in evolution of consciousness (e.g., Humphrey 1992), (perhaps rough) alignment with both the intention- the relation of consciousness to other psychological FIRST capacities (e.g., McDermott 2001), the relation of al/nonintentional and the essential/nonessential distinction. The general idea is that phenomenally consciousness to the physical and social environ- conscious states are both essentially so and nonin- ment of conscious organisms (e.g., Barlow 1987), tentional, while access-conscious states are neither. and relations of unity and difference among con- In view of the different interpretations of access scious states themselves (e.g., Bayne and Chalmers consciousness, however, it is not clear that this is 2003). so. Psychological states might well be both essen- The attitude implicit in this approach—that con- tially access conscious and phenomenally con- sciousness might be studied like other empirical scious. And, as indicated earlier, perhaps all phenomena—is attractive, but there are at least conscious states exhibit intentionality in some four facts that need to be confronted before it can form or other. be completely adopted:

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1. No framework of ideas has as yet been identical physically may yet differ in respect of worked out within which the study of con- certain aspects of their conscious experience, and sciousness can proceed. Of course, this does so differ psychologically. In short, physicalists are not exclude the possibility that such a frame- required to argue that the inverted spectrum hy- work might be developed in the future, but it pothesis does not represent a genuine possibility. does make the specific proposals (such as that And this places the issue of consciousness at the of Crick and Koch 1998) difficult to evaluate. heart of the mind–body problem. 2. In the past, one of the main research tasks in In contemporary philosophy of mind, the tradi- psychology and related fields was to study tional mind–body problem has been severely criti- psychological processes that were not con- cized. First, most contemporary philosophers do scious. This approach yielded a number of not regard the falsity of physicalism as a live option fruitful lines of inquiry—e.g., Chomsky’s (Chalmers [1996] is an exception), so it seems absurd (1966) idea that linguistic knowledge is to be to debate something one already assumes to be true. explained by the fact that people have Second, some writers argue that the very notions unconscious knowledge of the rules of their within which the traditional mind–body problem is language—but will presumably have to be formed are misguided (Chomsky 2000). Third, there abandoned when it comes to consciousness are serious questions about the legitimacy of itself. supposing that reflection of possible cases such as 3. As Block (1995) notes, the standard concept the inverted spectrum could even in principle decide of consciousness seems to combine a number the question of dualism or materialism, which are of different concepts, which in turn raises the apparently empirical, contingent claims about the threat that consciousness in one sense will be nature of the world (Jackson 1998). confused with consciousness in another. As a result of this critique, many philosophers 4. The issue of consciousness is often thought to reject the mind–body problem in its traditional raise questions of a philosophical nature, and guise. However, it is mistaken to infer from this this prompts further questions about whether that concern with the inverted spectrum and related a purely scientific approach is appropriate. ideas has likewise been rejected. Instead, the theo- retical setting of these arguments has changed. For What are the philosophical aspects of the issue of example, in contemporary philosophy, the inverted consciousness? In the history of the subject, the spectrum often plays a role not so much in the issue of consciousness is usually discussed in the question of whether physicalism is true, but rather context of another, the traditional mind–body in questions about whether phenomenal conscious- problem. This problem assumes a distinction be- ness is in principle irreducible or else lies beyond tween two views of human beings: the materialist thePROOF limits of rational inquiry. The impact of philo- or physicalist view, according to which human sophical issues of this kind on a possible science of beings are completely physical objects; and the consciousness is therefore straightforward. dualist view, according to which human beings In the philosophical debates just alluded to, the are a complex of both irreducibly physical and notion of consciousness at issue is phenomenal irreducibly mental features. Consciousness, then, consciousness. In other areas of philosophy, other emerges as a central test case that decides the notions are more prominent. In epistemology, issue. The reason is that there are a number of for example, an important question concerns the thought experiments that apparently make it plau- intuitive difference between knowledge of one’s sible to suppose that consciousness is distinct from own mental states—which seems in a certain sense anything physical. An example is theFIRSTinverted spec- privileged or direct—and knowledge of the external trum hypothesis, in which it is imagined that two world, including the minds of others. This question people might be identical except for the fact that has been made more acute by the impact of exter- the sensation provoked in one when looking at nalism, the thesis that one’s psychological states blood is precisely the sensation provoked in the depend constitutively on matters external to the other when looking at grass (Shoemaker 1981). If subject, factors for which direct knowledge is not this hypothesis represents a genuine possibility, it is plausible (Davies 1997). Presumably these issues a very short step to the falsity of physicalism, will be informed by the study of access conscious- which, setting aside some complications, entails ness. Similarly, in discussions of the notion of per- that if any two people are identical physically, they sonal identity and related questions about how and are identical psychologically. On the other hand, if why persons are objects of special moral concern, the inverted spectrum is possible, then two people the notion of self-consciousness plays an important

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role. One might also regard both access consci- consciousness derives from only what it is that ousness and self-consciousness as topics for they are concepts of, and this makes it unlikely straightforward scientific study. that the puzzles of phenomenal consciousness are an illusion. And, while it is plausible that phenom- Prospects for Progress enally conscious states are intentional, emphasizing this fact will not necessarily shed light on the issue, Due to the influence of positivist and postpositivist for the intentionality of phenomenal conscious- philosophy of science in the twentieth century, it ness might be just as puzzling as phenomenal was at one time common to assume that some or all consciousness itself. questions of consciousness were pseudo-questions. However, even if one agrees that phenomenal Recently it has been more common to concede that consciousness represents a phenomenon distinct the questions are real enough. But what are the from these other notions, and therefore requires a chances of progress here? separate approach, there is still a way in which one In light of the multifariousness of the issues, a might seek to implement the strategy of reducing formulaic answer to this question would be inap- the number of problems, for, as noted earlier, phe- propriate. Access consciousness seems to be a mat- nomenal consciousness is thought to present both a ter of information processing, and there is reason philosophical and a scientific challenge. But what is to suppose that such questions might be addressed the relation between these two issues? It is common using contemporary techniques. Hence, many wri- to assume that the philosophical problem needs to ters (e.g., Block 1995) find grounds for cautious be removed before one can make progress on the optimism here, though this might be tempered science. But perhaps the reverse is true. If the phil- depending on whether access consciousness is con- osophical problems can be seen to be a reflection strued as involving a normative element. In the case partly of ignorance in the scientific domain, there is of self-consciousness, the issue of normativity is no reason to regard them as a further impediment also present, and there is the added complication to scientific study. This might not seem like much that self-consciousness is partly responsive to ques- of an advance. But the study of consciousness has tions of social arrangements and their impact on been hampered by the feeling that it presents a individual subjects. problem of a different order from more straightfor- But it is widely acknowledged that the hardest ward empirical problems. In this context, to com- part of the issue is phenomenal consciousness. Here bat that assumption is to move forward, though the dominant strategy has been an indirect one of slowly. attempting to reduce the overall number of pro- DANIEL STOLJAR blems. One way to implement this strategy is to attempt to explain the notion of phenomenal con- PROOF References sciousness in terms of another notion, say, access consciousness or something like it. Some philoso- Armstrong, D. (1980), ‘‘What Is Consciousness?’’ in The phers suggest that puzzlement about phenomenal Nature of Mind and Other Essays. Ithaca, NY: Cornell University Press, 55–67. consciousness is a cognitive illusion, generated by a Armstrong, D., and N. Malcolm (1984), Consciousness and failure to understand the special nature of concepts Causality. Oxford: Blackwell. of phenomenal consciousness, and that once this Barlow, H. (1987), ‘‘The Biological Role of Consciousness,’’ puzzlement is dispelled, the way will be clear for a in C. Blakemore and S. Greenfield (eds.), Mindwaves. straightforward identification of phenomenal and Oxford: Basil Blackwell. Bayne, T., and D. Chalmers (2003), ‘‘What Is the Unity of access consciousness (e.g., Tye 1999). Others argue Consciousness?’’ in A. Cleeremans (ed.), The Unity that discussions of phenomenal consciousnessFIRST ne- of Consciousness: Binding, Integration and Dissociation. glect the extent to which conscious states involve Oxford: Oxford University Press. intentionality, and that once this is fully appre- Block, N. (1995), ‘‘On a Confusion About a Function ciated there is no bar to adopting the view that of Consciousness,’’ Behavioral and Brain Sciences 18: 227–247. phenomenal consciousness is just access conscious- Chalmers, D. (1996), The Conscious Mind. New York: Ox- ness (e.g., Carruthers 2000). ford University Press. The attractive feature of these ideas is that if Chomsky, N. (1966), Aspects of the Theory of Syntax. Cam- successful, they represent both philosophical and bridge, MA: MIT Press. scientific progress. But the persistent difficulty is ——— (2000), New Horizons in the Study of Mind and Language. Cambridge: Cambridge University Press. that the proposed explanations are unpersua- Crick, F., and C. Koch (1990), ‘‘Towards a Neurobiological sive. It is difficult to rid oneself of the feeling that Theory of Consciousness,’’ Seminars in the Neuros- what is special about concepts of phenomenal ciences 2: 263–275.

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Carruthers, P. (2000), Phenomenal Consciousness: A Natu- McDermott, D. (2001), Mind and Mechanism. Cambridge, ralistic Theory. Cambridge: Cambridge University Press. MA: MIT Press. Davies, M. (1997), ‘‘Externalism and Experience,’’ in N. Nagel, T. (1974), ‘‘What Is It Like to Be a Bat?’’ Philosophi- Block, O. Flanagan, and G. Guzeldere (eds.), The Na- cal Review 83: 7–22. ture of Consciousness: Philosophical Debates. Cam- Rosenthal, D. (1992), ‘‘A Theory of Consciousness,’’ in bridge, MA: MIT Press, 309–328. N. Block, O. Flanagan, and G. Guzeldere (eds.), The Davies, M., and G. Humphreys (1993), ‘‘Introduction,’’ in Nature of Consciousness: Philosophical Debates. Cam- M. Davies and G. Humphreys (eds.), Consciousness: bridge, MA: MIT Press, 729–754. Psychological and Philosophical Essays. Oxford: Black- Searle, R. (1992), The Rediscovery of the Mind. Cambridge, well. MA: MIT Press. Dennett , D. (1992), Consciousness Explained. Boston: Lit- Shoemaker, S. (1981), ‘‘The Inverted Spectrum,’’ Journal of tle, Brown and Co. Philosophy 74: 357–381. Dretske, D. (1993), ‘‘Conscious Experience,’’ Mind 102: Tye, M. (1999), ‘‘Phenomenal Consciousness: The Explan- 263–283. atory Gap as a Cognitive Illusion,’’ Mind 108: 432. Humphrey, N. (1992), A History of the Mind. New York: Weiskrantz, L. (1986), Blindsight. Oxford: Oxford Univer- Simon and Schuster. sity Press. Jackson, J. (1998), From Metaphysics to Ethics. Oxford: Clarendon. Jaynes, J. (1976), The Origin of Consciousness in the Breakdo- See also Cognitive Science; Connectionism; Inten- wn of the Bicameral Mind. Boston: Houghton Mifflin Co. tionality; Psychology, Philosophy of

CONSERVATION BIOLOGY

Conservation biology emerged in the mid-1980s as The normative status of conservation biology a science devoted to the conservation of biological distinguishes it from ecology, which is not defined diversity, or biodiversity. Its emergence was preci- in terms of a practical goal (see Ecology). More- pitated by a widespread concern that anthro- over, besides using the models and empirical results pogenic development, especially deforestation in ofPROOF ecology, conservation biology also draws upon the tropics (Go´mez-Pompa, Va´zquez-Yanes, and such disparate disciplines as genetics, computer Guevera 1972), had created an extinction crisis: a science, operations research, and economics in de- significant increase in the rate of species extinction signing and implementing CANs. Each of these (Soule´ 1985). From its beginning, the primary ob- fields contributes to a comprehensive framework jective of conservation biology was the design of that has recently emerged about the structure of conservation area networks (CANs), such as na- conservation biology (see ‘‘The Consensus Frame- tional parks, nature reserves, and managed-use work’’ below). zones that protect areas from anthropogenic Different views about the appropriate target of transformation. conservation have generated distinct methodologies Conservation biology, then, is a normative disci- within conservation biology. How ‘biodiversity’ is pline, in that it is defined in termsFIRST of a practical defined and, correspondingly, what conservation goal in addition to the accumulation of knowledge plans are designed will partly reflect ethical views about a domain of nature. In this respect, it is about what features of the natural world are valu- analogous to medicine (Soule´ 1985). Like medi- able (Norton 1994; Takacs 1996). There exists, cine, conservation biology performs its remedial therefore, a close connection between conservation function in two ways: through intervention (for biology and environmental ethics. example, when conservation plans must be designed for species at risk of imminent extinction) and through prevention (for example, when plans The Concept of Biodiversity are designed to prevent decline in species numbers ‘Biodiversity’ is typically taken to refer to diversity long before extinction is imminent). at all levels of biological organization: molecules,

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cells, organisms, species, and communities (e.g., distributions and habitat requirements, conservat- Meffe and Carroll 1994). This definition does not, ion biologists thought that ‘‘minimum viable popu- however, provide insight into the fundamental goal lations’’ could be demonstrated, that is, population of conservation biology, since it refers to all sizes below which purely stochastic processes biological entities (Sarkar and Margules 2002). would significantly increase the probability of ex- Even worse, this definition does not exhaust all tinction (see ‘‘Viability Analysis’’ below). It quickly items of biological interest that are worth preserv- became clear, however, that this methodology was ing: Endangered biological phenomena, such as the inadequate. It required much more data than could migration of the monarch butterfly, are not includ- be feasibly collected for most species (Caughley ed within this definition (Brower and Malcolm 1994) and, more importantly, failed to consider 1991). Finally, since even a liberally construed no- the interspecies dynamics essential to most species’ tion of biodiversity does not capture the ecosystem survival (Boyce 1992). processes that sustain biological diversity, some Widely followed in Australia, the declining- have argued that a more general concept of bio- population paradigm focused on deterministic, rath- logical integrity, incorporating both diversity of er than stochastic, causes of population decline entities and the ecological processes that sustain (Sarkar 2005). Unlike the small-population para- them, should be recognized as the proper focus of digm, its objective was to identify and eradicate conservation biology (Angermeier and Karr 1994). these causes before stochastic effects became signif- In response to these problems, many conserva- icant. Since the primary cause of population decline tion biologists have adopted a pluralistic approach was, and continues to be, habitat loss, conservation to biodiversity concepts (Norton 1994; Sarkar and biologists, especially in Australia, became princi- Margules 2002; see, however, Faith [2003], who pally concerned with protecting the full comple- argues that this ready acceptance of pluralism ment of regional species diversity and required confuses the [unified] concept of biodiversity with habitat within CANs. With meager monetary the plurality of different conservation strategies). resources for protection, conservation biologists Norton (1994), for example, points out that any concentrated on developing methods that identified measure of biodiversity presupposes the validity representative CANs in minimal areas (see ‘‘Place of a specific model of the natural world. The exis- Prioritization’’ below). tence of several equally accurate models ensures the absence of any uniquely correct measure. Thus, he argues, the selection of a biodiversity measure The Consensus Framework should be thought of as a normative political deci- Recently, a growing consensus about the structure sion that reflects specific conservation values and of conservation biology has emerged that combines goals. Sarkar and Margules (2002) argue that the PROOF aspects of the small-population and declining- concept of biodiversity is implicitly defined by the population paradigms into a framework that em- specific procedure employed to prioritize places for phasizes the crucial role computer-based place conservation action (see ‘‘Place Prioritization’’ prioritization algorithms play in conservation below). Since different contexts warrant differ- planning (Margules and Pressey 2000; Sarkar ent procedures, biodiversity should similarly be 2005). The framework’s purpose is to make conser- understood pluralistically. vation planning more systematic, thereby replacing the ad hoc reserve design strategies often employed in real-world planning in the past. It focuses on Two Perspectives ensuring the adequate representation and persis- FIRST tence of regional biodiversity within the socioeco- Throughout the 1980s and early 90s, the discipline nomic and political constraints inherent in such was loosely characterized by two general ap- planning. proaches, which Caughley (1994) described as the ‘‘small-population’’ and ‘‘declining-population’’ paradigms of conservation. Motivated significantly Place Prioritization by the legal framework of the Endangered Species Act of 1973 and the National Forest Management The first CAN design methods, especially within Act of 1976, the small-population paradigm origi- the United States, relied almost exclusively on is- nated and was widely adopted in the United States land biogeography theory (MacArthur and Wilson (Sarkar 2005). It focused primarily on individual 1967) (see Ecology). It was cited as the basis for species threatened by extinction. By analyzing their geometric design principles intended to minimize

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extinction rates in CANs as their ambient regions Xm Xn were anthropogenically transformed (Diamond Maximize Yi such that Xj ¼ M; 1975). Island biogeography theory entails that the i¼1 j¼1 particular species composition of an area is con- where M is the number of protectable cells. Infor- stantly changing while, at an equilibrium between mally, given the opportunity to protect M cells, extinction and immigration, its species richness find those cells that maximize the number of repre- remains constant. The intention behind design sentation targets satisfied. principles inspired by the theory, therefore, was to The formal precision of these problems allows ensure persistence of the maximum number of spe- them to be solved computationally with heuristic cies, not the specific species the areas currently or exact algorithms (Margules and Pressey 2000; contained. However, incisive criticism of the theory Sarkar 2005). Exact algorithms, using mixed integer (Gilbert 1980; Margules, Higgs, and Rafe 1982) linear programming, guarantee optimal solutions: convinced many conservation biologists, especially the smallest number of areas satisfying the problem in Australia, that representation of the specific spe- conditions. Since ESSCP and MESCP are NP hard, cies that areas now contain, rather than the persis- however, exact algorithms are computationally in- tence of the greatest number of species at some tractable for practical problems with large datasets. future time, should be the first goal of CAN design. Consequently, most research focuses on heuristic Computer-based place prioritization algorithms algorithms that are computationally tractable for supplied a defensible methodology for achieving large datasets but do not guarantee minimal solutions. the first goal and an alternative to the problematic Themostcommonlyusedheuristicalgorithmsare reliance on island biogeography theory in CAN ‘‘transparent,’’ so called because the exact criterion design. by which each solution cell is selected is known. Place prioritization involves solving a resource These algorithms select areas for incorporation allocation problem. Conservation funds are usually into CANs by iteratively applying a hierarchical set significantly limited and priority must be given to of conservation criteria, such as rarity, richness, and protecting some areas over others. The Expected complementarity. Rarity, for example, requires selec- Surrogate Set Covering Problem (ESSCP) and the ting the cell containing the region’s most infrequently Maximal Expected Surrogate Covering Problem present surrogates, which ensures that endemic taxa (MESCP) are two prioritization problems typically are represented. The criterion most responsible for encountered in biodiversity conservation planning the efficiency of transparent heuristic algorithms is (Sarkar 2004). Formally, consider a set of indi- complementarity: Select subsequent cells that com- vidual places called cells fcj : j ¼ 1; ...; ng; cell : ; ...; ; plement those already selected by adding the most areas faj j ¼ 1 ng biodiversity surrogates surrogates not yet represented (Justus and Sarkar L ¼fsi : i ¼ 1; ...; mg; representation targets, one PROOF 2002). In policymaking contexts, transparency facil- for each surrogate fti : i ¼ 1; ...; mg; probabilities : ; ...; ; ; ...; ; itates more perspicuous negotiations about compet- of finding si at cj fpij i ¼ 1 m j ¼ 1 ng ing land uses, which constitutes an advantage over and two indicator variables Xj( j ¼ 1; ...; nÞ and ; ...; nontransparent heuristic prioritization procedures Yiði ¼ 1 mÞ defined as follows: such as those based on simulated annealing. 1; if c 2 G; Methodologically, the problem of place prioriti- X ¼ j j 0; otherwise; zation refocused theoretical research in conserva- tion biology from general theories to algorithmic 8 X procedures that require geographically explicit data < 1; if pij > ti; (Sarkar 2004). In contrast to general theories, Y ¼ c G i : j 2 FIRST which abstract from the particularities of individu- 0; otherwise: al areas, place prioritization algorithms demon- strated that adequate CAN design critically ESSCP is the problem: depends upon these particularities. Xn Xn Minimize ajXj such that Xjpij  ti f Surrogacy j¼1 j¼1 Since place prioritization requires detailed infor- L: or 8si 2 mation about the precise distribution of a region’s Informally, find the set of cells G with the smal- biota, devising conservation plans for specific areas lest area such that every representation target is would ideally begin with an exhaustive series of satisfied. MESCP is the problem: field surveys. However, owing to limitations of

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time, money, and expertise, as well as geographical at a time, they are not computationally feasible for and sociopolitical boundaries to fieldwork, such practical conservation planning, which must devise surveys are usually not feasible in practice. These CANs to sample a wide range of regional biodiver- limitations give rise to the problem of discovering a sity. Fortunately, the solution to the surrogacy (preferably small) set of biotic or abiotic land attri- problem does not in practice require predictions butes (such as subsets of species, soil types, vegeta- of true-surrogate distributions. tion types, etc.) the precise distribution of which is A less stringent interpretation of representation realistically obtainable and that adequately repre- assumes only that the set of places prioritized on sents biodiversity as such. This problem is referred the basis of the estimator surrogates adequately to as that of finding surrogates or ‘‘indicators’’ for captures true-surrogate diversity up to some speci- biodiversity (Sarkar and Margules 2002). fied target (Sarkar and Margules 2002). The ques- This challenge immediately gives rise to two im- tion of the adequacy of a given estimator surrogate portant conceptual problems. Given the generality of then becomes the following: If one were to con- the concept of biodiversity as such, the first problem struct a CAN that samples the full complement of concerns the selection of those entities that should be estimator-surrogate diversity, to what extent does taken to represent concretely biodiversity in a partic- this CAN also sample the full complement of true- ular planning context. These entities will be referred surrogate diversity? Several different quantitative to as the true surrogate, or objective parameter, as it is measurements can be carried out to evaluate this the parameter that one is attempting to estimate in question (Sarkar 2004). At present, whether ade- the field. Clearly, selection of the true surrogate is quate surrogate sets exist for conservation planning partly conventional and will depend largely on prag- remains an open empirical question. matic and ethical concerns (Sarkar and Margules 2002); in most conservation contexts the true surro- Viability Analysis gate will typically be species diversity, or a species at risk. Once a set of true surrogates is chosen, the Place prioritization and surrogacy analysis help set of biotic and/or abiotic land attributes that will identify areas that currently represent biodiversity. be tested for their capacity to represent the true This is usually not, however, sufficient for success- surrogates adequately must be selected; these are ful biodiversity conservation. The problem is that estimator surrogates, or indicator parameters. the biodiversity these areas contain may be in irre- The second problem concerns the nature of the versible decline and unlikely to persist. Since princi- relation of representation that should obtain be- ples of CAN design inspired by island biogeography tween the estimator and the true surrogate: What theory were, by the late 1980s, no longer believed to does ‘representation’ mean in this context and under ensure persistence adequately, attention subse- what conditions can an estimator surrogate be said quentlyPROOF turned, especially in the United States, to to represent adequately a true surrogate? Once the modeling the probability of population extinc- true and estimator surrogates are selected and a pre- tion. These principles became known as population cise (operational) interpretation of representation is viability analysis (PVA). determined, the adequacy with which the estimator PVA models focus primarily on factors affecting surrogate represents the true surrogate becomes an small populations, such as inbreeding depression, empirical question. (Landres, Verner, and Thomas environmental and demographic stochasticity, ge- [1988] discuss the import of subjecting one’schoiceof netic drift, and spatial structure. Drift and estimator surrogate to stringent empirical testing.) inbreeding depression, for example, may reduce Very generally, two different interpretations of the genetic variation required for substantial evol- representation have been proposed inFIRST the conserva- vability, without which populations may be more tion literature. The more stringent interpretation is susceptible to disease, predation, or future environ- that the distribution of estimator surrogates should mental change. PVA modeling has not, however, allow one to predict the distribution of true surro- provided a clear understanding of the general gates (Ferrier and Watson 1997). The satisfaction of import of drift and inbreeding depression to popu- this condition would consist in the construction of a lation persistence in nature (Boyce 1992). Unfortu- well-confirmed model from which correlations be- nately, this kind of problem pervades PVA. In a tween a given set of estimator surrogates and a given trenchant review, for instance, Caughley (1994) con- set of true surrogates can be derived. Currently such cluded that the predominantly theoretical work models have met with only limited predictive suc- done thus far in PVA had not been adequately cess; moreover, since such models can typically be tested with field data and that many of the tests used to predict the distribution of only one surrogate that had been done were seriously flawed.

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Models used for PVA have a variety of different demands upon the allocation and use of land. Con- structures and assumptions (see Beisinger and sequently, successful implementation strategies McCullough 2002). As a biodiversity conservation should ideally be built upon a wide consensus methodology, however, PVA faces at least three among agents with different priorities with respect general difficulties: to that usage. Thus, practical CAN implementation involves the attempt to optimize the value of a 1. Precise estimation of parameters common to CAN amongst several different criteria simulta- PVA models requires enormous amounts of neously. Because different criteria typically con- quality field data, which are usually unavail- flict, however, the term ‘‘synchronization’’ rather able (Fieberg and Ellner 2000) and cannot be than ‘‘optimization’’ is more accurate. The multiple- collected, given limited monetary resources constraint synchronization problem involves de- and the imperative to take conservation action veloping and evaluating procedures designed to quickly. Thus, with prior knowledge being support such decision-making processes. uncommon concerning what mechanisms are One approach to this task is to ‘‘reduce’’ these primarily responsible for a population’s dy- various criteria to a single scale, such as monetary namics, PVA provides little guidance about cost. For example, cost-benefit analysis has at- how to minimize extinction probability. tempted to do this by assessing the amount an 2. In general, the results of PVA modeling are agent is willing to pay to improve the conservation extremely sensitive to model structure and pa- value of an area. In practice, however, such esti- rameter values. Models with seemingly slight- mates are difficult to carry out and are rarely ly different structure may make radically attempted (Norton 1987). Another method, based different predictions (Sarkar 2004), and dif- on multiple-objective decision-making models, does ferent parameter values for one model may not attempt to reduce the plurality of criteria to a produce markedly different predictions, a single scale; rather it seeks merely to eliminate those problem exacerbated by the difficulties dis- feasible CANs that are suboptimal when evaluated cussed under (1). according to all relevant criteria. This method, of 3. Currently, PVA models have been developed course, will typically not result in the determination almost exclusively for single species (occa- of a uniquely best solution, but it may be able to sionally two) and rarely consider more than reduce the number of potential CANs to one that is a few factors affecting population decline. small enough so that decision-making bodies can Therefore, only in narrow conservation con- bring other implicit criteria to bear on their ultimate texts focused on individual species would they decision (see Rothley 1999 and Sarkar 2004 for potentially play an important role. Successful applications to conservation planning). models that consider the numerous factors PROOFJUSTIN GARSON AND JAMES JUSTUS affecting the viability of multiple-species as- semblages, which are and should be the pri- mary target of actual conservation planning, References are unlikely to be developed in the near future (Fieberg and Ellner 2000). Angermeier, P. L., and J. R. Karr (1994), ‘‘Biological Integ- rity versus Biological Diversity as Policy Directives,’’ For these reasons and others, PVA has not thus BioScience 44: 690–697. far uncovered nontrivial generalities relevant to Beisinger, S. R., and D. R. McCullough (eds.) (2002), Pop- CAN design. Consequently, attention has turned ulation Viability Analysis. Chicago: University of Chi- cago Press. to more pragmatic principles, such as designing Boyce, M. (1992), ‘‘Population Viability Analysis,’’ Annual CANs to minimize distance to anthropogenicallyFIRST Review of Ecology and Systematics 23: 481–506. transformed areas. This is not to abandon the im- Brower, L. P., and S. B. Malcolm (1991), ‘‘Animal Migra- portant goals of PVA or the need for sound theory tions: Endangered Phenomena,’’ American Zoologist 31: about biodiversity persistence, but to recognize 265–276. Caughley, G. (1994), ‘‘Directions in Conservation Biology,’’ the weaknesses of existing PVA models and the Journal of Animal Ecology 63: 215–244. imperative to act now given significant threats to Diamond, J. (1975), ‘‘The Island Dilemma: Lessons of biodiversity. Modern Biogeographic Studies for the Design of Natu- ral Reserves,’’ Biological Conservation 7: 129–146. Faith, D. P. (2003), ‘‘Biodiversity,’’ in Edward N. Zalta (ed.), Multiple-Criterion Synchronization The Stanford Encyclopedia of Philosophy. http://plato. stanford.edu/archives/sum2003/entries/biodiversity The implementation and maintenance of CANs Ferrier, S., and G. Watson (1997), An Evaluation of the inevitably take place within a context of competing Effectiveness of Environmental Surrogates and Modelling

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Techniques in Predicting the Distribution of Biological Margules, C., A. J. Higgs, and R. W. Rafe (1982), ‘‘Modern Diversity: Consultancy Report to the Biodiversity Conven- Biogeographic Theory: Are There Lessons for Nature tion and Strategy Section of the Biodiversity Group, Envi- Reserve Design?’’ Biological Conservation 24: 115–128. ronment Australia. Arimidale, New South Wales: Meffe, G. K., and C. R. Carroll (1994), Principles of Con- Environment Australia. servation Biology. Sunderland, MA: Sinauer Associates. Fieberg, J., and S. P. Ellner (2000), ‘‘When Is It Meaningful Norton, B. G. (1987), Why Preserve Natural Variety? Prin- to Estimate an Extinction Probability?’’ Ecology 8: ceton, NJ: Princeton University Press. 2040–2047. Norton, B. G. (1994), ‘‘On What We Should Save: The Role Gilbert, F. S. (1980), ‘‘The Equilibrium Theory of Island of Cultures in Determining Conservation Targets,’’ in Biogeography: Fact or Fiction?’’ Journal of Biogeogra- P. L. Forey, C. J. Humphries, and R. I. Vane-Wright phy 7: 209–235. (eds.), Systematics and Conservation Evaluation. Oxford: Go´mez-Pompa, A., C. Va´zquez-Yanes, and S. Guevera Clarendon Press, 23–29. (1972), ‘‘The Tropical Rain Forest: A Nonrenewable Rothley, K. D. (1999), ‘‘Designing Bioreserve Networks to Resource,’’ Science 177: 762–765. Satisfy Multiple, Conflicting Demands,’’ Ecological Justus, J., and S. Sarkar (2002), ‘‘The Principle of Comple- Applications 9: 741–750. mentarity in the Design of Reserve Networks to Con- Sarkar, S. (2004), ‘‘Conservation Biology,’’ in E. N. Zalta serve Biodiversity: A Preliminary History,’’ Journal of (ed.), The Stanford Encyclopedia of Philosophy. http:// Biosciences 27: 421– 435. stanford.edu/entries/conservation-biology Landres, P. B., J. Verner, and J. W. Thomas (1988), ‘‘Eco- ——— (2005), Biodiversity and Environmental Philosophy. logical Uses of Vertebrate Indicator Species: A Cri- New York: Cambridge University Press. tique,’’ Conservation Biology 2: 316–328. Sarkar, S., and C. R. Margules (2002), ‘‘Operationalizing MacArthur, R., and E. O. Wilson (1967), The Theory of Biodiversity for Conservation Planning,’’ Journal of Island Biogeography. Princeton, NJ: Princeton Universi- Biosciences 27: 299–308. ty Press. Soule´, M. E. (1985), ‘‘What Is Conservation Biology?’’ Margules, C. R., and R. L. Pressey (2000), ‘‘Systematic BioScience 35: 727–734. Conservation Planning,’’ Nature 405: 242–253. Takacs, D. (1996), The Idea of Biodiversity: Philosophies of Paradise. Baltimore: Johns Hopkins University Press.

CONSTRUCTIVE EMPIRICISM PROOF See Instrumentalism; Realism

CONVENTIONALISMFIRST

Conventionalism is a philosophical position accord- science and mathematics appears to have emerged ing to which the truth of certain propositions, such as a distinctive philosophical position only in the as those of ethics, aesthetics, physics, mathematics, latter half of the nineteenth century. or logic, is in some sense best explained by appeal The philosophical motivations for conventional- to intentional human actions, such as linguistic ism are manifold. Early conventionalists such as stipulations. In this article, the focus will be on Pierre Duhem and Henri Poincare´, and more conventionalism concerning physics, mathematics, recently Adolf Gru¨nbaum, have seen conventional- and logic. Conventionalism concerning empirical ism about physical or geometrical principles as

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justified in part by what they regard as the under- philosophers the growing conviction that the disco- determination of a physical or geometrical theory by very of non-Euclidean geometries, such as the geo- empirical observation (see Duhem Thesis; Poincare´, metries of Lobatschevsky and Riemann, conjoined Henri; Theories, Underdetermination of ). An (em- with other developments in the foundations of ge- pirically) arbitrary choice of a system from among ometry, rendered untenable the Kantian treatment empirically equivalent theories seems required. of geometrical axioms as a form of synthetic a A second motivation, also suggested by Duhem priori intuition. and Poincare´, and explicitly developed later by The perceived failings of Kant’s analysis of Rudolf Carnap, stems from their view that any geometry did not, however, lead Poincare´ to an description of the empirical world presupposes a empiricist treatment of geometry. If geometry suitable descriptive apparatus, such as a geometry, were an experimental science, he reasoned, it a metric, or a mathematics. In some cases there would be open to continual revision or falsified appears to be a choice as to which descriptive outright (the perfectly invariable solids of geometry apparatus to employ, and this choice involves an are never empirically discovered, for instance) arbitrary convention (see Carnap, Rudolf ). (Poincare´ [1905] 1952, 49–50). Rather, geometrical A third motivation for conventionalism, em- axioms are conventions. As such, the axioms (pos- phasized by philosophers such as Moritz Schlick, tulates) of a systematic geometry constitute implicit Hans Hahn, and Alfred Ayer, is that appeal to definitions of such primitive terms of the system as conventions provides a straightforward explana- ‘‘point’’ and ‘‘line’’ (50). This notion of implicit tion of a priori propositional knowledge, such as definition originated with J. D. Gergonne (1818), knowledge of mathematical truths (see Ayer, who saw an analogy between a set of sentences with Alfred Jules; Hahn, Hans; Schlick, Moritz).Such n undefined terms and a set of equations with n truths, it was thought, are known a priori in virtue unknowns. The two are analogous in that the roots of the fact that they are stipulated rather than that satisfy the equations are akin to interpretations discovered. of the undefined terms in the set of sentences under It is important to note that conventionalists do which the sentences are true. Of course, not every not regard the selection of a set of conventions to set of equations determines a set of values, and so be wholly arbitrary, with the exception of the radi- too not every set of sentences (system of axioms) cal French conventionalist Edouard LeRoy, who constitutes an implicit definition of its primitive did (see Giedymin 1982, 118–28). Conventionalists terms. Poincare´ accommodated this fact by recog- acknowledge that pragmatic or instrumental con- nizing two constraints on the admissibility of a set siderations involving human capacities or purposes of axioms. First, the set must be consistent, and might be relevant to the adoption of a set of con- second, it must uniquely determine the objects ventions (see Instrumentalism). However, they in- definedPROOF (1952, 150–3). sist that the empirical evidence does not compel Although the axioms were in his view conven- one choice rather than another. tional, Poincare´ thought that experience nonethe- This article focuses on several major figures and less plays a role within geometry. The genesis of issues, but there are a number of other important geometrical systems is closely tied to experience, in philosophers with broadly conventionalist leanings, that the systems of geometry that are constructed including Pierre Duhem, Kazimierz Ajdukiewicz, are selected on the basis both of prior idealized and Ludwig Wittgenstein, that for the sake of bre- empirical generalizations and of the simplicity and vity will not here receive the attention they deserve. convenience that particular systems (such as Euclidean geometry) may afford their users ([1905] Poincare´ and Geometric ConventionalismFIRST 1952, 70–1; 1952, 114–5). But these empirical con- siderations do not provide a test of empirically ap- The development of non-Euclidean geometries and plied geometries. Once elevated to the status of a subsequent research into the foundations of geom- convention, a geometrical system is not an empirical etry provided both the inspiration and the model theory, but is rather akin to a language used, in for much of the conventionalism of the early twen- part, to frame subsequent empirical assertions. As tieth century (see Space-Time). The central figure a system of implicit definitions, it is senseless to in early conventionalism was the French mathe- speak of one geometry being ‘‘more true’’ than matician and philosopher Henri Poincare´ (see another ([1905] 1952, 50). Poincare´, Henri). Although a Kantian in his phil- Poincare´ therefore rejected the supposition that osophy of mathematics, Poincare´ shared with an empirical experiment could compel the selection many late-nineteenth-century mathematicians and of one geometry over another, provided that both

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satisfied certain constraints. He was inspired by 65–7). Imagine a world consisting of a large sphere Sophus Lie’s (1959) group-theoretic approach to subject to the following temperature law: At the geometrical transformations, according to which, center of the sphere the temperature is greatest, given an n-dimensional space and the possible trans- and at the periphery it is absolute zero. The tem- formations of figures within it, only a finite group of perature decreases uniformly as one moves toward geometries with differing coordinate systems are the circumference in proportion to the formula possible for that space. Among these geometries R2 – r2, where R is the radius of the sphere and r there is no principled justification for selecting the distance from the center. Assume further that one (such as Plu¨cker line geometry) over another all bodies in the sphere are in perfect thermal equi- (such as sphere geometry) (Poincare´ [1905] 1952, librium with their environment, that all bodies 46–7). Indeed, one geometry within the group share a coefficient of dilation proportional to may be transformed into another given a certain their temperature, and that light in this sphere is method of translation, which Lie derived from transmitted through a medium whose index of re- Gergonne’s theory of reciprocity. Poincare´ con- fraction is 1/(R2 – r2). Finally, suppose that there joined the intertransformability of certain geomet- are inhabitants of this sphere and that they adopt a rical systems with the recognition that alternative convention that allows them to measure lengths geometries yield different conventions governing with rigid rods. If the inhabitants assume that the notions of ‘‘distance’’ or ‘‘congruence’’ to these rods are invariant in length under transport, argue that any attempt to decide by experiment and if they further triangulate the positions in their between alternative geometries would be futile, world with light rays, they might well come to the since interpretations of the data presupposed geo- conclusion that their world has a Lobatchevskian metric conventions. In a much-discussed passage geometry. But they could also infer that their world he wrote: is Euclidean, by postulating the universal physical forces just described. Again, no empirical experi- If Lobatchevsky’s geometry is true, the parallax of a very ment seems adequate to establish one geometry distant star will be finite. If Riemann’s is true, it will be negative. These are the results which seem within the over the other, since both are compatible with all reach of experiment .... But what we call a straight line known possible observations given appropriate in astronomy is simply the path of a ray of light. If, auxiliary hypotheses. Rather, a conventional choice therefore, we were to discover negative parallaxes, or of a geometry seems called for. The choice will be to prove that all parallaxes are higher than a certain motivated by pragmatic factors, perhaps, but not limit, we should have a choice between two conclu- ‘‘imposed’’ by the experimental facts (Poincare´ sions: we could give up Euclidean geometry, or modify [1905] 1952, 70–1). the laws of optics, and suppose that light is not rigorous- ly propagated in a straight line. ([1905] 1952, 72–3) PROOF On one reading, advanced by Gru¨nbaum, this pas- Gru¨nbaum’s Conventionalism: The Metric sage affirms that there is no fact of the matter as to which and Simultaneity is the ‘‘correct’’ metric, and hence supports the conven- ´ tionality of spatial metrics. This reading is further dis- Poincare’s parallax and sphere-world examples cussed below. Another reading of this passage sees in it motivated his view that the choice of a spatial an argument closely akin to Duhem’s argument leading metric is conventional. Adolph Gru¨nbaum has to the denial of the possibility of a ‘‘crucial experiment’’ defended this conventionalist conclusion at length that could force the acceptance or elimination of a (Gru¨nbaum 1968, 1973). Gru¨nbaum claims that geometrical theory (see Duhem [1906] 1954, 180–90). there is no unique metric ‘‘intrinsic’’ to a spatial Interestingly, Poincare´ uses the argument to support a manifold, since between any two points on a real distinction between ‘‘conventional’’ truths and empiri- number line, there is an uncountably infinite con- cal truths, whereas Quine later adducesFIRST similar Duhe- tinuum of points. Hence, if one wishes to specify a mian considerations on behalf of his claim that there is metric for a manifold, one must employ ‘‘extrinsic’’ no such distinction to be drawn (see Duhem Thesis; devices such as measuring rods, and must further Quine, Willard Van Orman). stipulate the rods’ behavior under transport. However he may have intended his parallax ex- Gru¨nbaum defends what he takes to be ample, Poincare´ would probably have accepted Poincare´’s metric conventionalism against a variety both the conventionality of the spatial metric and of objections. Perhaps the most serious objection is the absence of any experimental test capable of the claim that Poincare´’s result illustrates only a deciding between two alternative geometries. As a trivial point about the conventionality of referring further illustration of these issues, he proposed expressions, an objection first directed against a well-known thought experiment ([1905] 1952, Poincare´ by Arthur Eddington and subsequently

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developed by Hilary Putnam and Paul Feyerabend. relativity (SR) involves a conventional element. A Eddington objected that Poincare´’s examples illu- sympathetic reconstruction of the argument will be strated not that metrical relations (such as the rela- attempted here, omitting a number of details in tions of equality or of the congruence of two rods) order to present the gist of the argument as briefly were conventional, but rather—and only—that the and intuitively as possible. Within Newtonian me- meanings of words such as ‘‘equal’’ and ‘‘congru- chanics (NM), there is no finite limit to the speed at ent’’ were conventional. This, Eddington objected, which causal signals can be sent. Further, one was a trivial point about semantical conventionali- might take it to be a defining feature of causal ty, and the fact that the selection of different relations that effects cannot precede their causes. metrics could yield different but apparently equi- This asymmetry allows for a distinction between pollent geometries illustrated only that ‘‘the mean- events that are temporally before or after a given ing assigned to length and distance has to go along event on a world line. There is then only one simul- with the meaning assigned to space’’ (Eddington taneity relation within the space-time of NM 1953, 9–10). Eddington suggested, and Feyerabend meeting the constraints mentioned. Consider later developed, a simple illustration of this point events (or space-time points, if one prefers) a and within the theory of gases. Upon the discovery that b on two distinct parallel world lines. Event a is Boyle’s law: simultaneous with b just in case a is not causally connectible to any event on the future part of b’s pv ¼ RT world line but is causally connectible to any event holds only approximately of real gases, one could on the past of b’s world line. Within SR, however, either revise Boyle’s law in favor of van der Waal’s there is an upper limit to the speed of causal sig- law: nals. Thus the constraint that effects cannot pre- cede their causes allows any one of a continuum of ð p þ a=v2Þðv À bÞ¼RT points along a parallel world line to be a candidate for simultaneity with a given event on the world or one could preserve Boyle’s law by redefining line of an inertial observer. Gru¨nbaum calls such pressure as follows: points ‘‘topologically simultaneous’’ with a point o 2 Pressure ¼Def ðp þ a=v Þð1 À b=vÞ: on the observer’s world line. In claiming that si- ðFeyerabend; quoted in Grnbaum 1973; 34Þ multaneity is (to some extent) conventional within the SR picture, Gru¨nbaum is in good company, as The possibility of such a redefinition, the objec- Einstein makes a claim to this effect in his original tion proceeds, is physically and philosophically 1905 paper. (It is important to distinguish the issue uninteresting. Provided that a similar move is avail- of the conventionality of simultaneity within SR, whichPROOF has been controversial, from the (observer able in Poincare´’s own examples with expressions like ‘‘congruent,’’ Poincare´’s examples appear to or frame) relativity of simultaneity within SR, illustrate only platitudes about semantic conven- which is unchallenged; see Space-Time.) tionality. Gru¨nbaum claims that the existence of a contin- Gru¨nbaum tries to show that Poincare´’s con- uum of possible ‘‘planes of simultaneity’’ through a ventionalism is not merely an example of what given point is explained by, or reflects, the fact that Gru¨nbaum calls ‘‘trivial semantic conventionality’’ the simultaneity relation is not ‘‘intrinsic’’ to the by showing that the conventionality of the metric manifold of events within special relativity. One is the result of a certain absence of ‘‘intrinsic’’ str- objection that a number of Gru¨nbaum’s critics ucture within the space-time manifold, which struc- such as Putnam (in Putnam 1975b) have had to ture can (or must) then be imposed ‘‘FIRSTextrinsically’’: his treatment of conventionalism (concerning both the metric and the simultaneity relation) is And the metric amorphousness of these continua then that the notion of an intrinsic feature, which plays serves to explain that even after the word ‘‘congruent’’ a crucial role for Gru¨nbaum, is never adequately has been pre-empted semantically as a spatial or tempo- clarified. David Malament (1977) provides a natu- ral equality predicate by the axioms of congruence, congruence remains ambiguous in the sense that these ral reading of ‘intrinsic’: An intrinsic property or axioms still allow an infinitude of mutually exclusive relation of a system is ‘‘definable’’ in terms of a set congruence classes of intervals. of basic features. The intuitive idea is that if a relation is definable from relations that are uncon- ¨ (Grunbaum 1973, 27) troversially intrinsic, then these ought to count as Gru¨nbaum developed a related argument to the intrinsic as well. Malament goes on to show that effect that the simultaneity relation in special if one takes certain fairly minimal relations to

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be given as intrinsic, then a unique simultaneity leave room for infinitely many possible inter- relation, in fact the standard one, is definable pretations of ‘sim’. In this sense, the simultaneity from them in a fairly well defined sense of ‘defin- relation (interpretation of ‘sim’) might naturally be able. ’ said to be conventional within SR. In contrast, Malament’s result has been taken by many to given a model for the causal structure of NM, the have definitively settled the issue of whether simul- meaning constraints on the concept of simultaneity taneity is conventional within SR (see e.g., Norton that are assumed here yield a unique expansion (a 1992). In this view, the standard simultaneity rela- unique extension for ‘sim’). tion is nonconventional, since it is definable, or It should be noted that the conventionality of ‘‘logically constructible,’’ from uncontroversially simultaneity within SR and its nonconventionality intrinsic features of Minkowski space-time, the within NM in the sense just described reflect struc- space-time of SR. Furthermore, standard simulta- tural differences between the two theories (or their neity is the only such nonconventional simultaneity standard models). Thus this form of conventional- relation. ism appears to escape the charge that the only sense However, there are dissenters, including in which simultaneity is conventional is the trivial Gru¨nbaum. A number of authors have attacked sense in which the word ‘‘simultaneous’’ can be one or another of Malament’s premises, including used to denote different relations. As Gru¨nbaum for instance the claim that simultaneity must be a frequently emphasizes, the interesting cases of con- transitive relation, that is, the requirement that for ventionality arise only when one begins with an arbitrary events x, y, and z,ifx sim y and y sim z, already meaningful term or concept, whose mean- then x sim z. Sarkar and Stachel have shown that ing is constrained in some nontrivial way. It also even if it is allowed that simultaneity must be an allows one to interpret Einstein as making a sub- equivalence relation, other simultaneity relations stantive, yet fairly obvious point when he claims (the backward and the forward light cones of that the standard simultaneity relation within SR is events on the given world line) are definable from a conventional, or stipulated, choice. relations that Malament takes as basic or intrinsic How does this version of conventionalism re- (see Sarkar and Stachel 1999). Peter Spirtes (1981) late to Malament’s arguments? It will be helpful shows that Malament’s result is highly sensitive to to note a puzzle before proceeding. Wesley Salmon the choice of basic or intrinsic relations, which fact (1977) argues at length that the one-way speed of might be taken to undercut the significance of light is not empirically identifiable within SR. (The Malament’s result as well. basic problem is that the one-way speed seems A conventionalist might raise a different sort of measurable only by using distant synchronized objection to Malament’s results, questioning their clocks, but the synchronization of distant clocks relevance to a reasonable, although perhaps not the wouldPROOF appear to involve light signals and presup- only reasonable, construal of the question as to positions about their one-way speeds.) This fact whether simultaneity is conventional within SR. appears to yield as an immediate consequence the Suppose for simplicity that any relation that one conventionality (in the sense of empirical admissi- is willing to call a simultaneity relation is an equiv- bility described above) of simultaneity within SR, AU:42 alence relation, that causes must always precede given the various apparently admissible ways of their effects, and that there is an upper bound to synchronizing distant clocks within a reference the speed of causal influences within SR. One may frame. The puzzle is this: On one hand, the stan- now ask whether more than one relation can be dard view has it that Malament’s result effectively defined (extrinsically or otherwise) on the manifold proves the falsehood of conventionalism (about of events (or ‘‘space-time points’’),FIRST meeting these simultaneity within SR); on the other hand, criteria within SR. That is, one might ask whether, Salmon’s arguments appear to entail the truth of given any model M of T (roughly, Minkowski conventionalism. Yet, his arguments for the empir- space-time, the ‘‘standard’’ space-time of SR), ical inaccessibility of the one-way speed of light there is a unique expansion of the model to a seem sound. No one has convincingly shown what model M0 for T 0, where T 0 adds to T sentences is wrong with them. All that the nonconventionalist containing a symbol ‘sim’, which sentences in effect seems able to provide is the indirect argument that require that ‘sim’ be an equivalence relation and Malament is right, so Salmon (and Gru¨nbaum) that causes are not ‘sim’ with their effects. It is a must be wrong. straightforward matter to see, as Gru¨nbaum shows In the present analysis, this puzzle is dissolved by (the details are omitted here), that there is no such distinguishing two proposals, each of which may unique expansion of M. The constraints mentioned justifiably be called versions of conventionalism.

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One version claims that a relation (thought of as a However, it has been argued above that the set or extension) is conventional within a model appeal to intrinsicness turns out to be unnecessary for a theory if it is not intrinsic within M, where in order to preserve a nontrivial form of conven- ‘intrinsic’ might then be interpreted as definability tionalism, C2. (in the sense of logical constructibility) from un- Gru¨nbaum’s arguments concerning the conven- controversially intrinsic relations within M. The tionality of the space-time metric for continuous other version claims that the extension of a concept manifolds involve more complex issues than those is conventional within a model (or theory) if the in the simultaneity case. But some key elements are meaning of the concept does not entail a unique common to both disputes. Gru¨nbaum claims that extension for the concept within the model (or continuous manifolds do not have intrinsic metrics, within all models of the theory). Call these ver- and critics complain that the notion of an intrinsic sions of conventionalism C1 and C2, respectively. feature is unclear (see e.g., Stein 1977). Some of the Malament shows that simultaneity is not C1 conven- claims that Gru¨nbaum makes lend support to the tional within SR (leaving aside other possible idea that he is concerned with C1 conventionalism. objections to his result). Gru¨nbaum and Salmon He claims, for example, that for a discrete manifold show that simultaneity is C2 conventional within (such that between any two points there are only SR. Malament further considers relations definable finitely many points), there is an intrinsic and from the causal connectibility relation (together hence nonconventional metric, where the ‘‘dis- with the world line of an inertial observer) within tance’’ between any two points is the number of SR, and notes that only one is a nontrivial candi- points between them, plus one. This claim makes date simultaneity relation (relative to the corre- sense to the extent that one is concerned with C1, sponding inertial frame). He shows there is only that is, with the question of whether a relation is one, and that therefore there is a unique intrinsic definable or logically constructible from a basic set. (and hence non–C1 conventional) simultaneity re- Gru¨nbaum’s arguments do not seem well suited for lation within SR, the standard one. The C2 conven- showing that such a metric would be C2 noncon- tionalist may respond that although Malament has ventional, since nothing about the meaning of ‘dis- pointed out an interesting feature of a particular tance’ constrains the adoption of this as opposed to candidate interpretation of the already meaningful infinitely other metrics. term ‘‘simultaneous,’’ he has not thereby ruled out Another worry that might be raised concerns all other candidate interpretations. One should not, Gru¨nbaum’s insistence that distance functions de- the C2 defender will argue, confuse the metalinguis- fined in terms of physical bodies and their beha- tic notion ‘definable within M (or T )’ with a mean- viors under transport are extrinsic to a manifold. If ing constraint on our concept of simultaneity, i.e., a the manifold is a purely mathematical object, then constraint on potential interpretations of our al- suchPROOF a view seems more plausible. But if one is ready meaningful term ‘‘simultaneous.’’ It would concerned with a physical manifold of space-time be absurd to claim that what was meant all along points, it is less obvious that physical bodies should by ‘simultaneous’ required not only that any can- be treated as extrinsic. More importantly, even if didate be an equivalence relation and that it must one grants Gru¨nbaum that physical bodies and ‘‘fit with’’ causal relations in that effects may not their behaviors are extrinsic to the physical space- precede their causes, but also that for any two time manifold, one might want to grant a scientist events, they are simultaneous if and only if they the right to specify which features of the structures are in a relation that is definable from the causal that are being posited are to count as basic or connectibility relation. intrinsic. For example, Gru¨nbaum proposes that A possible interpretation of theFIRST debate con- Newton in effect made a conceptual error in claim- cerning the conventionality of simultaneity within ing that whether the temporal interval between one SR, on the present construal, is that Gru¨nbaum, pair of instants is the same as that between another perhaps in order to avoid the charge of simply pair of instants is a factual matter, determined by rediscovering a form of trivial semantic conven- the structure of time itself. Since instants form a tionality, appealed to his notion of an intrinsic temporal continuum in Newton’s picture, there is, relation. Failure to express or denote an intrinsic according to Gru¨nbaum, no intrinsic temporal feature was then said to characterize the interesting metric, contrary to Newton’s claims. However, (nontrivial) cases of conventionality. This notion one can imagine a Newtonian responding with led to a number of difficulties for Gru¨nbaum, cul- bewilderment. Does Newton not get to say what minating in Malament’s apparent refutation of relations are intrinsic to the structures that he is the conventionality of simultaneity within SR. positing?

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It is difficult to see how to make room for a Moritz Schlick was quick to find in Hilbert’s notion of intrinsicness that can do all of the philo- conclusions the possibility of generalizing conven- sophical work that Gru¨nbaum requires of it, as tionalism beyond geometry (see Schlick, Moritz). Stein (1977) and others argue at length. On the If the reference of the primitive concepts of an other hand, Gru¨nbaum’s conventionalism about axiomatic system could be left undetermined, as simultaneity within SR remains defensible (in par- Hilbert had apparently demonstrated, then the ticular, it escapes the trivialization charge as well axioms would be empty of empirical content, and as Malament’s attempted refutation) if his con- so knowledge of them would appear to be a priori. clusions are interpreted in the sense of C2 conven- Like Poincare´, Schlick rejected a Kantian explana- tionalism described above. tion of how such knowledge is possible, and he saw in Hilbert’s approach a demonstration of how an implicit definition of concepts could be obtained Mathematical and Logical Conventionalism through axioms whose validity had been guaran- teed (Schlick [1925] 1985, 33). In his General Theo- Up to now this discussion has focused on conven- ry of Knowledge Schlick distinguished explicitly tionalist claims concerning principles of an empiri- between ‘‘ordinary concepts,’’ which are defined cal science, physics. Other propositions that have by ostension, and implicit definitions. Of the latter, attracted conventionalist treatment are those from he wrote that the nonempirical sciences of mathematics and logic. Conventionalism seems especially attractive [a] system of truths created with the aid of implicit here, particularly to empiricists and others who definitions does not at any point rest on the ground of find the notion of special faculties of mathematical reality. On the contrary, it floats freely, so to speak, and like the solar system bears within itself the guarantee of intuition dubious but nevertheless wish to treat its own stability. (37) known mathematical or logical propositions as nonempirical. The guaranteed stability was to be provided by a The axiomatic methods that had motivated consistency proof for a given system of axioms, Poincare´’s geometric conventionalism discussed which Schlick, like Poincare´ and Hilbert before above received further support with the publication him, claimed was a necessary condition in a system of David Hilbert’s Foundations of Geometry ([1921] of symbolism. Schlick followed Poincare´ in treating 1962). Hilbert disregarded the intuitive or ordinary the axioms as conventions, and hence as known a meanings of such constituent terms of Euclidean priori through stipulation (Schlick [1925] 1985, 71). geometry as ‘‘point,’’ ‘‘line,’’ and ‘‘plane,’’ and in- But he diverged markedly from Poincare´ in extend- stead proposed regarding the axioms as purely for- ing this account to mathematics and logic as well. mal posits (see Hilbert, David). In other words, the HisPROOF basis for doing so was Hilbert’s formalized axioms function as generalizations about whatever theory of arithmetic, which Schlick hoped (wrong- set of things happens to satisfy them. In addition to ly, as it turned out) would eventuate in a consisten- allowing Hilbert to demonstrate a number of sig- cy proof for arithmetic ([1925] 1985, 357). nificant results in pure geometry, this method of The conventionalism that emerged was thus one abstracting from particular applications had imme- in which true propositions known a priori were diate philosophical consequences. For instance, in regarded as components of autonomous symbol response to Gottlob Frege’s objection that without games that, while perhaps constructed with an eye fixing a reference for primitive expressions like to an application, are not themselves answerable to ‘‘between,’’ Hilbert’s axiomatic geometry would an independent reality (Schlick [1925] 1985, 37–8). be equivocal, Hilbert wrote: FIRST Schlick thought that the laws of logic, such as the principles of identity, noncontradiction, and the But surely it is self-evident that every theory is merely a excluded middle, ‘‘say nothing at all about the framework or schema of concepts together with their necessary relations to one another, and that the basic behavior of reality. They simply regulate how we elements can be construed as one pleases. If I think of designate the real’’ ([1925] 1985, 337). Schlick ac- my points as some system or other of things, e.g., the knowledged that the negation of logical principles system of love, of law, or of chimney sweeps ... and like noncontradiction was unthinkable, but he sug- then conceive of all my axioms as relations between gested that this fact was itself a convention of these things, then my theorems, e.g., the Pythagorean symbolism (concerning the notion ‘unthinkable’), one, will hold of these things as well. claiming that ‘‘anything which contradicts the prin- (Hilbert 1971, 13) ciple is termed unthinkable’’ ([1925] 1985, 337).

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Although Schlick thought that the structure of a the selection of an ideal or even unique language symbol system, including inference systems such as with reference to facts, since any such justification logic, was autonomous and established by a set of (including a specification of facts) would presup- implicit definitions, he also recognized the possibility pose a language. Mathematics is no exception to that some of its primitive terms could be coordi- this. As a system of ‘‘framework truths,’’ mathe- nated by ordinary definitions with actual objects matical truths do not describe any convention- and properties. In this way, a conventionally independent fact but are consequences of the established symbol system could be used to describe decision to adopt one linguistic framework over the empirical world, and an object designated by a another, in Carnap’s account. primitive term might be empirically discovered to Conventionalism about mathematics and logic have previously unknown features. Nonetheless, has faced a number of important objections. A some of the properties and relations had by a primi- significant early objection was given by Poincare´ tive term would continue to be governed by the sys- (1952, 166–72), who rejected Hilbert’s idea that the tem conventions through which the term is implicitly principle of mathematical induction might merely defined (Schlick [1925] 1985, 48ff ). These properties be an implicit definition of the natural numbers and relations would thus be knowable a priori. (see Hilbert [1935] 1965, 193). Mathematical induc- The conventionalism of Schlick’s General Theory tion should not be regarded in this way, Poincare´ of Knowledge anticipated many of the convention- argued, for it is presupposed by any demonstration alist elements of the position advanced by mem- of the consistency of the definition of number, since bers of the Vienna Circle (see Vienna Circle). consistency proofs require a mathematical inducti- Philosophers such as Hahn, Ayer, and Carnap on on the length of formulas. Treating the induc- saw in conventionalism the possibility of acknowl- tion principle as itself conventional while using it to edging the existence of necessary truths known a prove the consistency of the conventions of which it priori while simultaneously denying such proposi- is a part would thus involve a petitio. tions any metaphysical significance. Inspired by Carnap’s Logical Syntax of Language sidestepp- Wittgenstein’s analysis of necessary truths in the ed such problems by removing the demand that a Tractatus, Vienna Circle members identified the system of conventions be consistent; the principle truths of mathematics and logic with tautologies— of tolerance made no such demand, and Carnap statements void of content in virtue of the fact that regarded the absence of consistency proofs as of they hold no matter what the facts of the world limited significance (1937, 134). It appears that he may be (Hahn 1980; Ayer 1952). Tautologies, in would have regarded a contradictory language sys- turn, were equated with analytic statements, and tem to be pragmatically useless but not impossible. Circle members regarded all analytic statements as Kurt Go¨del, however, raised an important objec- either vacuous conventions of symbolism known a tionPROOF to this strategy. Go¨del claimed that if mathe- priori through stipulation or as derivable conse- matics is to be ‘‘merely’’ a system of syntactical quences of such conventions knowable a priori conventions, then the conventions must be known through proof (see Analyticity). not to entail the truth or falsity of any sentence An especially noteworthy outgrowth of the con- involving a matter of extralinguistic empirical fact; ventionalism of the Vienna Circle was Carnap’s if it does have such entailments, in Go¨del’s view, The Logical Syntax of Language. In this book the truth of such sentences is not merely a syntacti- Carnap advanced a conventionalist treatment of cal, conventional matter (Go¨del 1995, 339). If the the truths of mathematics and logic through his system contains a contradiction, then it will imply espousal of the principle of tolerance, which states: every empirical sentence. But according to Go¨del’s second incompleteness theorem, a consistency proof In logic, there are no morals. EveryoneFIRST is at liberty to required to assure the independence of the system build up his own logic, i.e., his own form of language, as he wishes. All that is required of him is that ... he must cannot emerge from within the system itself if that state his methods clearly, and give syntactical rules in- system is consistent (1995, 346). stead of philosophical arguments. Recent commentators (Ricketts 1994; Goldfarb 1995) have argued that a response to this objec- (Carnap 1937, 52) tion is available from within Carnap’s conven- Carnap regarded a language as a linguistic tionalist framework. Go¨del’s argument requires framework that specified logical relations of conse- acceptance of an extralinguistic domain of empiri- quence among propositions. These logical relations cal facts, which a stipulated language system are a precondition of description and investigation. may or may not imply. But it is doubtful that In this view, there can be no question of justifying Carnap would have accepted such a domain, for

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Carnap considered linguistic conventions, includ- References ing the conventions constitutive of mathematics, as Ayer, Alfred J. (1952), Language, Truth and Logic. New AU:44 antecedent to any characterization of the facts, York: Dover. including facts of the empirical world. The issues Carnap, Rudolph (1937), The Logical Syntax of Language. involved in Go¨del’s objection are complex and in- London: Routledge and Kegan Paul. teresting, and a thorough and satisfactory conven- Duhem, Pierre ([1906] 1954), The Aim and Structure of Physical Theory. Translated by Philip P. Wiener. Prince- tionalist response remains to be formulated. ton, NJ: Princeton University Press. Another objection to conventionalism about Eddington, A. S (1953), Space, Time and Gravitation. Cam- logic was advanced by Willard V. Quine (see bridge: Cambridge University Press. Quine, Willard Van Orman). Quine objected Gergonne, Joseph Diaz (1818), ‘‘Essai sur la the´orie de la against Carnap that treating logical laws and infer- de´finition,’’ Annales de mathe´matiques pures et appli- que´es 9:1–35. ence rules as conventional truths implicitly presup- Giedymin, Jerzy (1982), Science and Convention: Essays on posed the logic that such conventions were Henri Poincare´’s Philosophy of Science and the Conven- intended to establish. Consider for instance a pro- tionalist Tradition. Oxford: Pergamon. posed logical convention MP of the form ‘‘Let all Go¨del, Kurt (1995), ‘‘Is Mathematics Syntax of Language?’’ results of putting a statement for p and a statement in Solomon Feferman (ed.), Kurt Go¨del: Collected Works, vol. 3. Oxford: Oxford University Press, 334–362. for q in the expression ‘If p, then q and p, then q’ be Goldfarb, Warren (1995), ‘‘Introductory Note to *1953/9,’’ true.’’ In order to apply this convention to particu- in Solomon Feferman (ed), Kurt Go¨del: Collected Works, lar statements A and B, it seems that one must vol. 3. Oxford: Oxford University Press, 324–334. reason as follows: MP and if MP, then (A and if Gru¨nbaum, Adolph (1968), Geometry and Chronometery in A, then B imply B); therefore, A and if A, then B Philosophical Perspective. Minneapolis: University of Minnesota Press. imply B). But this requires that one use modus ——— (1973), Philosophical Problems of Space and Time, ponens in applying the very convention that stipu- 2nd ed. Dordrecht, Netherlands: Reidel. lates the soundness of this inference. Quine con- Hahn, Hans (1980), Empiricism, Logic, and Mathematics. cluded that ‘‘if logic is to proceed mediately from Translated by Brian McGuinness. Dordrecht, Nether- conventions, logic is needed for inferring logic from lands: Reidel. Hilbert, David ([1935] 1965), ‘‘Die Grundlegung der ele- the conventions’’ (Quine 1966, 97). Quine at one mentaren Zahlenlehre,’’ in Gesammelte Abhandlungen, point suggested that similar reasoning might un- vol. 3. New York: Chelsea Publishing, 192–195. dermine the intelligibility of the notion of a linguis- ——— ([1921] 1962), Grundlagen der Geometrie. Stuttgart: tic convention in general (98–9). However, after B. G. Teubner. David Lewis’ analysis of tacit conventions (Lewis ——— (1971), ‘‘Hilbert’s Reply to Frege,’’ in E. H. W. Kluge (trans., ed.), On the Foundations of Geometry and 1969), Quine acknowledged the possibility of at Formal Theories of Arithmetic. London: Yale University least some such conventions (Quine, in Lewis Press, 10–14. 1969, xii). Lewis,PROOF David (1969), Convention: A Philosophical Study. Quine’s original objection suggests that the Oxford: Blackwell. conventionalist about logical truth must have an Lie, Sophus (1959), ‘‘On a Class of Geometric Transforma- tions,’’ in D. E. Smith (ed.), A Source Book in Mathe- account of how something recognizable as a conven- matics. New York: Dover. tion can intelligibly be established ‘‘prior to logic.’’ Malament, David (1977), ‘‘Causal Theories of Time and the As with Go¨del’s objection, the issues are difficult Conventionality of Simultaneity,’’ Nous 11: 293–300. and have not yet been given a fully satisfying con- Norton, John (1992), ‘‘Philosophy of Space and Time,’’ in ventionalist account. However, there are a variety of M. H. Salmon et. al. (eds), Introduction to the Philosophy of Science. Indianapolis: Hackett. strategies that a conventionalist might explore. One Poincare´, Henri ([1905] 1952), Science and Hypothesis. Trans- will be mentioned here. Consider an analogous case, lated by W. J. Greestreet. New York: Dover Publications. that of rules of grammar. On one hand, one cannot ——— (1952), Science and Method. Translated by Francis FIRST Maitland. New York: Dover Publications. specify rules of grammar without employing a lan- guage (which has its grammatical rules). Thus one Putnam, Hilary (1975a), ‘‘An examination of Grunbaum’s Philosophy of Geometry,’’ in Mathematics, Matter and cannot acquire one’s first language by, say, reading Method Philosophical Papers, vol. 1. New York: Cam- its rules in a book. On the other hand, this fact does bridge University Press. not seem to rule out the possibility that any given ——— (1975b), ‘‘Reply to Gerald Massey,’’ in Mind, Lan- rules of grammar are to some extent arbitrary, and guage and Reality, Philosophical Papers, vol. 2. New conventionally adopted. Whether the conventional- York: Cambridge UP. Quine, Willard V. (1966), ‘‘Truth By Convention,’’ in The ist can extend this line of thought to a defensible Ways of Paradox and Other Essays. New York: Random form of conventionalism about logic remains to be House, 70–99. conclusively demonstrated. Ricketts, Thomas (1994), ‘‘Carnap’s Principle of Tolerance, AU:43 CORY JUHL AND ERIC LOOMIS Empricism, and Conventionalism,’’ in Peter Clark and

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CORROBORATION

Bob Hale (eds.), Reading Putnam. Cambridge, MA: Department of the History and Philosophy of Science, Blackwell, 176–200. University of Pittsburgh. Salmon, Wesley (1977), ‘‘The Philosophical Significance Stein, Howard (1977), ‘‘On Space-Time and Ontology: Ex- of the One-Way Speed of Light,’’ Nouˆs 11: 253–292. tract from a Letter to Adolf Grunbaum,’’ in Foundations Sarkar, Sahotra, and John Stachel (1999), ‘‘Did Malament of Space-time Theories, Minnesota Studies in the Philos- Prove the Non-Conventionality of Simultaneity in the ophy of Science, vol. 8. Minneapolis: University of Min- Special Theory of Relativity?’’ Philosophy of Science 66: nesota Press. 208–220. Schlick, Moritz ([1925] 1985), General Theory of Knowledge. See also Analyticity; Carnap, Rudolf; Duhem The- Translated by Albert E. Blumberg. La Salle, IL: Open Court. sis; Hilbert, David; Instrumentalism; Logical Empir- Spirtes, Peter L. (1981), ‘‘Conventionalism and the Phi- icism; Poincare´, Henri; Quine, Willard Van Orman; losophy of Henri Poincare´,’’ Ph. D. Dissertation, Schlick, Moritz; Space-Time; Vienna Circle

CORROBORATION

Karl R. Popper (1959) observed that insofar as confirmation.’’ And, indeed, the only way in natural laws have the force of prohibitions, they which even a material conditional can be falsified cannot be adequately formalized as unrestrictedly is by things satisfying the antecedent but not satis- general material conditionals but incorporate a fying the consequent. Emphasis on falsification modal element of natural necessity. To distinguish therefore implies that serious tests of hypotheses between possible laws and mere correlations, em- presuppose satisfying their antecedents, thereby sug- pirical scientists must therefore subject them to gesting a methodological maxim of deliberately severe tests by serious attempts to refute them, searching for examples that should be most likely where the only evidence that can count in favor of to reveal the falsity of a hypothesis if it is false, such the existence of a law arises from unsucces- as altering the diet or the habitat of ravens to sful attempts to refute it. He therefore insisted ascertain whether that would have any effect on upon a distinction between ‘confirmation’ and theirPROOF color. But Popper’s conception of laws as ‘corroboration’ (see Popper, Karl Raimund). prohibition was an even more far reaching insight To appreciate Popper’s position, it is essential to relative to his falsificationist methodology. consider the nature of natural laws as the objects of Popper’s work on natural necessity distinguishes inquiry. When laws of nature are taken to have the it from logical necessity, where the notion of pro- logical form of unrestrictedly general material con- jectible predicates as a pragmatic condition is dis- ditionals, such as ðxÞðRx ! BxÞ for ‘‘All ravens are placed by the notion of dispositional predicates as a black,’’ using the obvious predicate letters Rx and semantic condition. It reflects a conception of Bx and !, as the material conditional, then they laws as relations that cannot be violated or chan- have many logically equivalent formulations, such ged and require no enforcement. Fetzer (1981) has as ðxÞðØBx ! ØRxÞ; using the same notation, pursued this approach, where lawlike sentences which stands for ‘‘Every nonblack thingFIRST is a non- take the form of subjunctive conditionals, such as raven.’’ As Carl G. Hempel (1965) observed, if it is ðxÞðRx ) BxÞ; where ) stands for the subjunctive assumed that confirming a hypothesis requires satis- conditional. This asserts of everything, ‘‘If it were a fying its antecedent and then ascertaining whether raven, then it would be black.’’ The truth of this or not its consequent is satisfied, then if logically claim, which is logically contingent, depends on a equivalent hypotheses are confirmed or disconfirmed difference between permanent and transient prop- by the same evidence, a white shoe as an instance of erties. It does not imply the counterpart, ‘‘If any- øBx that is also øRx confirms the hypothesis ‘‘All thing were nonblack, then it would be a nonraven.’’ ravens are black’’ (see Induction, Problem of ). Among Popper’s most important contributions Popper argued that there are no ‘‘paradoxes were his demonstration of how his falsificationist of falsification’’ parallel to the ‘‘paradoxes of methodology could be extended to encompass

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CORROBORATION

statistical laws and his propensity interpretation CðH j E6BÞ¼LðH j EÞ½ j PðE j HÞ À PðE j BÞjŠ; of probability (see Probability). Distributions of 3 outcomes that have very low probabilities in hypo- ð Þ theses are regarded, by convention, as methodolog- that is, as the product of the likelihood of H, given ically falsifying those hypotheses, tentatively and E, times the severity of E as a test of H, relative to fallibilistically. Popper entertained the prospect of B. This is a Popperian measure, but not necessarily probabilistic measures of corroboration, but likeli- Popper’s. Popper suggests (as one possibility) hood measures provide a far better fit, since uni- CðH j E6BÞ¼ versal hypotheses as infinite conjunctions have zero ð4Þ probability. Indeed, Popper holds that the appro- PðE j HÞ À PðE j BÞ=PðE j HÞþPðE j BÞ; priate hypothesis for scientific acceptance is the one that has the greatest content and has withstood which even he does not find to be entirely satisfac- our best attempts at its falsification, which turns tory and which Imre Lakatos severely criticizes out to be the least probable among the unfalsified (Lakatos 1968, especially 408–16). When alterna- alternatives. tive hypotheses are available, the appropriate com- The likelihood of hypothesis H, given evidence parative measures appear to be corroboration E, is simply the probability of evidence E, if hy- ratios

pothesis H is true. While probabilistic measures CðH2 j EÞ LðH2 j EÞ½ j PðE j H2Þ À PðE j H1ÞjŠ have to satisfy axioms of summation and multipli- ¼ CðH1 j EÞ LðH1 j EÞ½ j PðE j H1Þ À PðE j H2ÞjŠ cation—for example, where mutually exclusive and jointly exhaustive hypotheses must have probabil- ð5Þ ities that sum to 1—likelihood measures are consis- that reduce to the corresponding likelihood ra- tent with arbitrarily many hypotheses of high tios of L(H2jE ) divided by L(H1jE ) and assume value. This approach can incorporate the laws of increasing significance as a function of the severity likelihood advanced by Ian Hacking (1965) and a of those tests, as Fetzer (1981, 222–30) explains. distinction between preferability for hypotheses Popper also proposed the propensity interpreta- with a higher likelihood on the available evidence tion of physical probabilities as probabilistic dis- and acceptability for those that are preferable when positions (Popper 1957 and 1959). In a revised sufficient evidence becomes available. Acceptabil- formulation, the single-case propensity interpreta- ity is partially determined by relative likelihoods, tion supports a theory of lawlike sentences, logical- even when likelihoods are low. Popper (1968, ly contingent subjunctive conditionals ascribing 360–91) proposed that where E describes the out- permanent dispositional properties (of varying come of a new test and B our background knowl- strength) to everything possessing a reference prop- edge prior to that test, the severity of E as a test of ertyPROOF (Fetzer 1981 and 1993). Propensity hypotheses H, relative to B, might be measured by are testable on the basis of the frequencies they generate across sequences of trials. Long runs are PðE j H6BÞ À PðE j BÞ; ð1Þ infinite and short runs are finite sequences of single that is, as the probability of E, given H and B, trials. Propensities predict frequencies but also ex- minus the probability of E, given B alone. The plain them. Frequencies are evidence for the intent of equation 1 may be more suitably captured strength of propensities. by a formulation that employs a symmetrical—and Popper (1968) promoted the conception of sci- therefore absolute—measure reflecting differences ence as a process of conjectures and (attempted) in expectations with respect to outcome distribu- refutations. While he rejected the conception of tions over sets of relevant trials, suchFIRST as science as a process of inductive confirmation exemplified by the work of Hans Reichenbach j PðE j HÞ À PðE j BÞj; ð2Þ (1949) and Wesley C. Salmon (1967), his commit- which ascribe degrees of nomic expectability to rel- ments to deductive procedures tended to obscure ative frequency data, for example. When B entails the role of ampliative reasoning in his own posi- E, then P(EjB) ¼ 1, and if P(EjH ) ¼ 1 as well, the tion. Popper rejected a narrow conception of in- severity of any such test is minimal, i.e., 0. When H duction, according to which the basic rule of entails E, while B entails øE, the severity of such a inference is ‘‘If m/n observed As are Bs, then infer test is maximal, i.e., 1. The acceptance of H may that m/nAs are Bs, provided a suitable number of require the revision of B to preserve consistency. As are tested under a wide variety of conditions.’’ A plausible measure of the degree of corrobora- And, indeed, the rule he rejects restricts scientific tion C of H, given E, relative to B, would be hypotheses to those couched in observational

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COUNTERFACTUALS

language and cannot separate bona fide laws from References correlations. Fetzer, James H. (1981), Scientific Knowledge: Causation, Although it was not always clear, Popper was Explanation, and Corroboration. Dordrecht, Nether- not thereby rejecting induction in the broad sense lands: D. Reidel. of ampliative reasoning. He sometimes tried to ——— (1993), Philosophy of Science. New York: Paragon formalize his conception of corroboration using House. Hacking, Ian (1965), Logic of Statistical Inference. Cam- the notion of absolute (or prior) probability of the bridge: Cambridge University Press. evidence E, P(E ), which is typically supposed to be a Hempel, Carl G. (1965), Aspects of Scientific Explanation. subjective probability. Grover Maxwell (1974) even New York: Free Press. develops Popper’s approach using Bayes’s theorem. Lakatos, Imre (1968), ‘‘Changes in the Problem of Induc- However, appeals to priors are inessential to forma- tive Logic,’’ in The Problem of Inductive Logic. Amster- dam: North-Holland, 315–417. lizations of Popper’s measures (Fetzer 1981), and it Maxwell, Grover (1974), ‘‘Corroboration without De- would be a mistake to suppose that Popper’s ac- marcation,’’ in Paul A. Schilpp (ed.), The Philosophy of count of severe tests, which is a pragmatic concep- Karl R. Popper, part 1. LaSalle, IL: Open Court, 292–321. tion, could be completely formalizable. Popper, Karl R. (1959), The Logic of Scientific Discovery. Indeed, Popper’s notion of accepting hypotheses New York: Harper & Row. ——— (1957), ‘‘The Propensity Interpretation of the Cal- on the basis of severe tests, no matter how tentative- culus of Probability, and the Quantum Theory,’’ in Ste- ly and fallibilistically, implies ampliative reasoning. phan Korner (ed.), Observation and Interpretation in the Its implementation for probabilistic hypotheses Philosophy of Physics. New York: Dover Publications, thereby requires large numbers of trials over a wide 65–70. variety of conditions, which parallels the narrow ——— (1959), ‘‘The Propensity Interpretation of Probabili- ty,’’ British Journal for the Philosophy of Science 10: 25–42. inductivist conception. These results, however, must ——— (1968), Conjectures and Refutations. New York: be subjected to severe tests to make sure the frequen- Harper & Row. cies generated are robust and stable under variable Reichenbach, Hans (1949), The Theory of Probability. Ber- conditions.When Volkswagens were first imported keley and Los Angeles: University of California. into the United States, for example, they were all Salmon, Wesley C. (1967), The Foundations of Scien- tific Inference. Pittsburgh: University of Pittsburgh Press. gray. The narrow inductivist rule of inference justi- fied inferring that all Volkswagens were gray, a See also Confirmation Theory; Hempel, Carl Gus- conclusion that could not withstand severe tests. tav; Induction, Problem of; Popper, Karl Raimund; JAMES H. FETZER Verisimilitude PROOF COSMOLOGY

See Anthropic Principle FIRST

COUNTERFACTUALS

See Causality

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