Concepts

The topic of concepts lies at the intersection of semantics and philosophy of mind. A concept is supposed to be a constituent of a thought (or ‘proposition') rather in the way that a word is a constituent of a sentence that typically expresses a thought. Indeed, concepts are often thought to be the meanings of words (and will be designated by enclosing the words for them in brackets: [city] is expressed by ‘city' and by ‘metropolis'). However, the two topics can diverge: non-linguistic animals may possess concepts, and standard linguistic meanings involve conventions in ways that concepts do not. Concepts seem essential to ordinary and scientific psychological explanation, which would be undermined were it not possible for the same concept to occur in different thought episodes: someone could not even recall something unless the concepts they have now overlap the concepts they had earlier. If a disagreement between people is to be more than ‘merely verbal', their words must express the same concepts. And if psychologists are to describe shared patterns of thought across people, they need to advert to shared concepts. Concepts also seem essential to categorizing the world, for example, recognizing a cow and classifying it as a mammal. Concepts are also compositional: concepts can be combined to form a virtual infinitude of complex categories, in such a way that someone can understand a novel combination, for example, [smallest sub-atomic particle], by understanding its constituents. Concepts, however, are not always studied as part of psychology. Some logicians and formal semanticists study the deductive relations among concepts and propositions in abstraction from any mind. Philosophers doing ‘philosophical analysis' try to specify the conditions that make something the kind of thing it is - for example, what it is that makes an act good - an enterprise they take to consist in the analysis of concepts. Given these diverse interests, there is considerable disagreement about what exactly a concept is. Psychologists tend to use ‘concept' for internal representations, for example, images, stereotypes, words that may be the vehicles for thought in the mind or brain. Logicians and formal semanticists tend to use it for sets of real and possible objects, and functions defined over them; and philosophers of mind have variously proposed properties, ‘senses', inferential rules or discrimination abilities. A related issue is what it is for someone to possess a concept. The ‘classical view' presumed concepts had ‘definitions' known by competent users. For example, grasping [bachelor] seemed to consist in grasping the definition, [adult, unmarried male]. However, if definitions are not to go on forever, there must be primitive concepts that are not defined but are grasped in some other way. Empiricism claimed that these definitions were provided by sensory conditions for a concept's application. Thus, [material object] was defined in terms of certain possibilities of sensation. The classical view suffers from the fact that few successful definitions have ever been provided. Wittgenstein suggested that concept possession need not consist in knowing a definition, but in appreciating the role of a concept in thought and practice. Moreover, he claimed, a concept need not apply to things by virtue of some closed set of features captured by a definition, but rather by virtue of ‘family resemblances' among the things, a suggestion that has given rise in psychology to ‘prototype' theories of concepts. Most traditional approaches to possession conditions have been concerned with the internal states, especially the beliefs, of the conceptualizer. Quine raised a challenge for such an approach in his doctrine of ‘confirmation holism', which stressed that a person's beliefs are fixed by what they find plausible overall. Separating out any particular beliefs as defining a concept seemed to him arbitrary and in conflict with actual practice, where concepts seem shared by people with different beliefs. This led Quine himself to be sceptical about talk of concepts generally, denying that there was any principled way to distinguish ‘analytic' claims that express definitional claims about a concept from ‘synthetic' ones that express merely common beliefs about the things to which a concept applies. However, recent philosophers suggest that people share concepts not by virtue of any internal facts, but by virtue of facts about their external (social) environment. For example, people arguably have the concept [water] by virtue of interacting in certain ways with H2O and deferring to experts in defining it. This work has given rise to a variety of externalist theories of concepts and semantics generally. Many also think, however, that psychology could generalize about people's minds independently of the external contexts they happen to inhabit, and so have proposed ‘two-factor theories', according to which there is an internal component to a concept that may play a role in psychological explanation, as opposed to an external component that determines the application of the concept to the world. 1 Concepts as shareable constituents of thought Constituents of thought. It is widely thought that ‘intentional' explanation in terms of such states as belief, thought and desire affords the best explanation of the behaviour and states of people, many animals and perhaps some machines: someone drinks water because they have a thirst which they think water will quench. By and large, philosophers and psychologists such as Fodor (1975, 1991) or Peacocke (1992) who are interested in intentional explanation take themselves to be committed to the existence of concepts, whereas those sceptical of this form of explanation, for example, Quine (1960), tend to avoid them ( Animal language and thought; Cognitive development; Intentionality). Suppose one person thinks that water dissolves salt, and another that it does not. Call the thing that they disagree about a ‘proposition' - for example, [Water dissolves salt]. It is in some sense shared by them as the object of their disagreement, and it is expressed by the sentence that follows the verb ‘thinks that'. Concepts are the constituents of such propositions (in at least one understanding of them; see Propositions, sentences and statements), just as the words ‘water', ‘dissolves' and ‘salt' are constituents of the sentence. Thus, these people could have these beliefs only if they had, inter alia, the concepts [water], [dissolves], [salt]. Just which sentential constituents express concepts is a matter of some debate. The central cases that are discussed tend to be the concepts expressed by predicates or general terms, such as ‘is water' or ‘x dissolves y', terms potentially true of many different individual things. But there are presumably concepts associated with logical words (for example, [not], [some]), as well as with individual things (for example, [Rome], [2]). Shareability. If we are to make sense of processes of reasoning and communication, and have a basis for generalization in a cognitive psychology, then concepts must be shareable. Consequently, concepts need to be distinguished from the particular ideas, images, sensations that, consciously or unconsciously, pass through people's minds at a particular time. The concept [cat] could not be some individual experience someone has, since in that case no two people could share it and a single person probably could not have the same one twice. Just what kind of shareable object a concept might be is a matter of considerable disagreement among theorists. In much of the psychological literature, where the concern is often with features of actual mental processing, concepts are regarded as mental representations, on such as words or images. It will be important with respect to this and later proposals to invoke a distinction from the study of language between types and tokens ( Type/token distinction). A linguistic token, such as an inscription of ‘café' on a door, has a specific spacetime location: one can ask when and where it occurs; whereas a linguistic type - the word ‘café' - like any ‘universal', is an abstract object outside space and time. One can erase a token of the word ‘café', but the type word would still exist. Similarly, concepts could be regarded as internal representation types that have individual ideas as their specific tokens. On this view, you and I could share the concept [water] if you and I have tokens of the same representation type in our minds or brains. There is a good deal of discussion in psychology as to whether concepts in this sense are (type) words, phrases, pictures, maps, diagrams or other kinds of representations, for example, ‘prototypes' or ‘exemplars' ( §7 below; and Smith and Medin (1981); Rips (1995) for reviews of the psychological literature). But many philosophers take the view that these mental representation types would no more be identical to concepts than are the type words in a natural language. Words in a language are usually individuated syntactically, allowing both spoken and written tokens of a word to be of the same type, and syntactically identical tokens (for example, of ‘bank') to be ambiguous, or of different semantic types. Moreover, different syntactic types - for example, ‘city', ‘metropolis' - can be synonymous, that is, be of the same semantic type. Similarly, one person might express the concept [city] by a mental representation ‘city', another by ‘metropolis'; still another perhaps by a mental image of bustling boulevards. But, for all that, they might have the same concept [city]: one could believe and another doubt that cities are healthy places to live. Moreover, different people could employ the same representation to express different concepts: one person might use an image of bustling boulevards to express [city], another to express [pollution]. So, on the standard philosophical reading (which we shall follow here), concepts are to be individuated differently from the representations that express them. However, although concepts understood in this latter way are arguably also indispensable to psychology, they raise different issues from those concerning representations that standardly interest psychologists. Questions about representations typically involve just the issues that psychologists have tended to investigate: processing time, ease of judgment, susceptibility to errors. If one person represents cities and their relations ‘spatially', where another represents them by names and descriptions, this may explain differences in how rapidly the two of them can answer questions about cities; but, again, presumably they both still have the concept [city]. Just why they would, what the possession conditions for [city] or any concept might be, is not easy to say ( §5): the point here is that they seem to involve issues different from the issue of identifying a syntactically defined representation. This difference between the psychologist's and philosopher's typical interest is sometimes obscured by ambiguous phrasing. When Kant identifies ‘analytic' claims (or claims that express the ‘analysis' of a concept) as those in which one concept is ‘contained in' another, he glosses this by saying: ‘I have merely to analyse the concept, that is, to become conscious to myself of the manifold which I always think in that concept' (1781/1787: A7). In our terms, this could be read as a claim about representations, or (presumably what he intended) about the concepts they express. My mental representation of freedom might invariably involve an image of dancing people, but surely neither Kant nor I would want to say that the analysis of my concept of freedom involved dancing. Conversely, there is no reason that a good analysis should serve as a representation in ordinary, rapid reasonings (for example, identifying something as a bird): indeed, vivid images might serve better. 2 Meanings of words As most of our examples suggest, concepts are presumed to serve as the meanings of linguistic items, underwriting relations of translation, definition, synonymy, antinomy and semantic implication (Katz 1972). Indeed, much work in the semantics of natural languages ( Jackendoff 1987) takes itself to be addressing ‘conceptual structure'. This is partly motivated by Grice's (1957) proposal to understand linguistic meaning ultimately in terms of the intentions with which speakers produce linguistic tokens: ‘good' means what it does at least partly because of what users of the word have intended to mean by it; that is, because of the concept they have intended to express ( Meaning and communication; Grice, H.P. §2). One problem with this role for concepts is that it is by no means clear just what a theory of meaning is supposed to involve. Some of the issues are exactly the issues we are considering here. However, some issues seem peculiar to language: for example, how much of what is understood in the uttering of a sentence is part of its meaning, or semantics, and how much is part of its use, and so an issue of pragmatics? ( Pragmatics.) If I say of someone ‘He is not very good at chess', is the meaning simply that ‘It is not the case that he is very good', or ‘He is bad at chess'? 3 Concepts and analysis Objects of analysis. At least since Plato's Euthyphro, philosophers have been fascinated by a certain sort of question about constitutiveness: in virtue of what is something the kind of thing it is - for example, what is ‘essential' to something's being good, a piece of knowledge, a free act? Obviously, not just any truth about the target phenomenon will suffice as an answer: to take Plato's Euthyphro example, merely the fact that the gods love the good is no reason to think that that is what makes something good, any more than that all bachelors eat is what makes them bachelors ( Conceptual analysis). Some philosophers think such questions are answered by natural science. This certainly seems to be true in the case of ‘natural kinds' such as water or polio, which arguably have ‘real essences' largely independently of us ( Kripke [1972] 1980; Putnam 1975; Essentialism). But many concepts, such as [magic], [freedom], [soul] may not pick out any real kind of thing at all (much less one studiable by science): in these cases, all that seems shareable by different possessors of the concept is some belief or other. But even in the natural science cases, some conceptual analysis seems to many unavoidable, if only to determine exactly what the science is about (what makes an investigation one about water, or polio, or consciousness; Bealer 1987). There is a related question that concepts are also sometimes recruited to answer; not a metaphysical question about ‘the nature of things', but an epistemological one about how people seem to know a priori (or ‘independently of experience') various necessary truths, for example, that there is an infinity of prime numbers or that equiangular triangles are equilateral ones. However, it should be seen as a substantive and controversial hypothesis, to which we will return, whether this epistemological interest should coincide with the above metaphysical one ( A priori; §5 below). Philosophers have also sometimes hoped that conceptual analysis would help (dis)solve certain philosophical questions about, for example, truth, free will, personal identity, either by clarifying the commitments of the relevant concepts, or by showing that they were somehow defective. A once popular strategy was to show that the application of a concept was not ‘verifiable' (§5 below). A more recent strategy is to show that the application of a purported concept would be unintelligible, as in the case of [absolute space] (Peacocke 1992: ch. 8). Whatever its ultimate philosophical benefits, conceptual analysis does seem to involve the sort of facts that are relevant to the question of concept possession. Returning to our pair of people who represent cites differently: what seems relevant to the question of whether, despite their different representations, they still have the same concept [city] is what sorts of things they believe are essential to being a city; what things they would and would not count as cities (which is not to say that this would be decisive; see §5). This difference can lend an air of unreality to philosophical as opposed to psychological discussions of concepts, depending, as it does, upon difficult questions about what (one would think) is possible in various often very outlandish situations. Vagueness. One supposed defect of many concepts should be set aside from the start. The belief in constitutive analyses of a concept is often thought to be undermined by the existence of difficult, borderline cases for its application (Wittgenstein 1953: §§66-7; Smith and Medin 1981: 31). Now, it certainly cannot be denied that the world is full of genuine borderline cases: ‘Is drizzle rain?', ‘Are viruses alive?'. Arguably, the world does not supply determinate answers: all kinds in the world may have vague boundaries, any precise delimitation of which may depend upon human decision. But this does not imply that all applications of concepts are up to human decision, much less that there are no defining essences of the phenomena they pick out. [Unmarried adult male] may be a perfectly good analysis of [bachelor] not only despite hard cases, but because the hard cases for the one correspond exactly to the hard cases for the other. ( Vagueness.) 4 Referential views One candidate for the common object of people's thoughts has been simply the referents of their representations, that is, the objects in the world picked out by them. Someone might say that two representations express the same concept if and only if they refer to the same thing(s) in the world. Putting aside the difficult problem of explaining ‘reference', this seems an appealing suggestion, clearest in the case of (token) proper names such as ‘Aristotle' where the name refers to a specific person ( proper names). When we turn to predicates, however, things are not so clear. There are a number of different candidates for what counts as the ‘referent' of a predicate and so of the concept it would express: (1) its extension, (2) its intension (as function), and (3) the property that all the (possible) objects satisfying it have in common. Extensions. The ‘extension' is the set of actual objects that satisfy the concept. For example, the extension of [city] might be the set of cities: {Paris, London, Madrid,…}. Russell (1956) proposed an account of ‘propositions' according to which they were composed of real objects in the world combined with properties ( also Kaplan 1979). Extensional logicians such as Goodman (1951) and Quine (1960) think that sets of actual objects are all that are needed for serious science: all that needs to be mentioned are actual lions, tigers and quarks. They realize that this suggestion clashes with our ordinary understanding. [Cordate] is not the same as [renate], despite the fact that (let us suppose) all and only actual creatures with kidneys are creatures with hearts ([renate] and [cordate] are ‘coextensive'). It seems reasonable to require concepts to cover possible cases, for example, possible creatures that are renates but do not have hearts. Goodman would not agree, since, as he famously argues (1951: 5), ‘the notion of "possible" cases, of cases that do not exist but might have existed, is far from clear' ( Counterfactual conditionals; Goodman, N. §3). But he and Quine would also be wary of talk of concepts generally; and semanticists such as Kaplan (1979) and Salmon (1986) are anxious to avoid introducing talk of them into talk of the semantics of language. Intensions as functions. Although one might agree that modal notions such as possibility and necessity are not as clear as one would like, it is by no means agreed that science can actually dispense with them. Many philosophers think that the laws essential to causal explanation in any science require modal and counterfactual talk. But, especially in psychology, it seems doubtful that extensions would perform all the explanatory work concepts are needed to perform. Whether or not biology need worry about the possibility of renates lacking hearts, someone could think something is a renate without thinking it has a heart. Consequently, many philosophers have claimed that, in addition to extensions, there must be ‘intensions', or entities distinguished more finely than mere extensions permit ( Intensional entities; Intensional logics). Intensions have been defined in a number of ways. One approach is in terms of ‘senses' or ‘modes of presentation', to which we shall turn shortly (§5 below). Another approach simply amplifies the extensional characterization to include sets of possible as well as actual objects. Modal logicians and formal semanticists such as Montague (1974), D. Lewis (1972) and Stalnaker (1984), interested in presenting a formal account of the semantics of natural languages, have regarded intensions as functions that map a possible world to the extension of the concept in that world ( Semantics, possible worlds). However, mere appeals to possibilia may still not cut things finely enough: for there are concepts that are different even though they apply to all the same things in all possible worlds, for example, [equiangular triangle] and [equilateral triangle], or, following Kripke ([1972] 1980), [water] and [H2O]; or, to take cases of necessarily empty extensions, [square circle] and [married bachelor], which both refer to nothing in all possible worlds. Particularly interesting examples of this latter category have been suggested by Kripke ([1972] 1980) and Slote (1975), who argue in different ways that nothing could possibly satisfy the specific demands of [unicorn] or [monster]. How are we to distinguish these concepts by reference to possible objects? Properties. Some philosophers think the appropriate reference for predicate concepts is not provided by the objects that the concepts pick out (whether in the actual or merely possible worlds), but rather by the properties those objects share. Thus, [city] is not individuated by the set of all actual or possible cities, but rather by the property, ‘being a city'. Historically, concepts have not always been clearly distinguished from properties, both being regarded as ‘universals' ( Universals). Thus, the mortality one found widespread among men was often assumed to be the same as the concept [mortality] that was a constituent of one's fears. Sometimes this identification seems terminological, as in Frege (1892a) (who uses ‘concept' in a quite special way and discusses ‘senses' independently), but at other times it is substantive, as in Carnap (1952). Most writers these days would distinguish the two (Putnam 1970; Bealer 1982), even if they also think that there is a property for every concept. An interesting issue raised by Frege (1892a) that does seem common to both general concepts and properties is the difficulty of specifying exactly what sort of entities they are. As Frege noted, they seem to be incomplete, or ‘unsaturated', having places in them awaiting completion by objects, in the way that predicates in language, such as ‘x loves y', have variables awaiting substitution with names (such as ‘Romeo' and ‘Juliet'). This issue becomes important when we try to specify how general and singular concepts combine to form a thought, or how properties and objects combine to constitute facts (Russell 1903: ch. 4; Wittgenstein 1921). Many worry that appealing to properties to individuate concepts is gratuitous metaphysics, a free invention of a property for every concept, encouraged by the loose presumption that properties, such as ‘immortality', can exist even without being instantiated. To answer this charge, philosophers often claim that properties are provided by the actual causal structure of the world: having kidneys and having a heart enter differently into causal relations, as perhaps do equiangularity and equilaterality (Sober 1982). Particularly philosophers of mind such as Dretske (1981, 1988), Millikan (1984) and Fodor (1991), interested in causal interactions between an organism and the world, find this way of thinking about concepts attractive ( Semantics, informational; Semantics, teleological). However, it is not clear that causal properties will suffice. Are all our concepts really of causally efficacious properties? What about the concept [an inefficacious property]? Or concepts of secondary properties ([red], [sweet]), or ethics and aesthetics ([good], [comical]), which, many have argued, do not pick out genuine causal properties? Or consider, again, necessarily coextensive concepts such as [water] and [H2O] - which arguably correspond to the same property - or [round square] and [married bachelor], which arguably correspond to none. How could they differentially enter into the causal structure of the world? Or should we suppose that properties can be distinguished even though they are indistinguishable not only in the actual, but in all possible worlds? Are there any constraints? Moreover, even if we could distinguish concepts by properties, that would not suffice for conceptual analysis. Plato's Euthyphro question - is something good because the gods love it, or do they love it because it is good? - brings this out nicely, since the question remains even if we assume that that gods love the good in all possible worlds (so that [good] and [god-beloved] are necessarily coextensive): the direction of analysis still needs to be specified. 5 Possession conditions: external v. internal Many philosophers might not think that Plato's Euthyphro question needs an answer: for purposes of logic, and perhaps even formal semantics, appeal to any of these external phenomena (extensions, intensions or properties) may suffice, ‘analysis' be hanged. However, if concepts are to play a role in psychology, then one at least wants to know what sort of relation someone must bear to these external phenomena in order to qualify as a competent user of the concept. This is a question about the possession conditions for a concept to which many have thought analyses are crucial. In considering possession conditions, special care is needed with the peculiar idiom ‘concept of x' and the ontology it involves. Psychologists often speak of such things as the child's ‘concept of causality'. This could mean the representation the child employs of the concept [causality] that the child shares with adults; or it could mean any of the extension, intension or rule that children associate with the English word ‘cause'; or it could mean (as in fact it very often does mean) merely the standard beliefs - what some call the ‘conception' - that children associate with the extension, intension: [causality]. Which of these is intended all depends upon what entity one thinks of as the concept and what a mere accompaniment of it. What cannot be seriously intended is the suggestion that a child has a concept [causality] that is both identical to but different from the adults'. (What invites confusion here is the ‘of' that implies no relation: just as ‘the nation of China' means ‘the nation, China', so ‘the concept of x' often means ‘the concept, [x]'.) It might be thought that none of the external identifications of concepts could ever be viable for psychology, since psychology is about what is ‘in the mind' (or ‘in the head'), not what is in the world external to it ( Jackendoff 1987: 126). This would be an error. We have already seen one way in which it cannot be true: in so far as concepts are shareable, they must be distinguished from individual mental episodes. But still it might be thought that a concept must be a type of internally specified mental state, since, after all, surely psychology aims to talk about individual minds, even if it categorizes them in various ways. However, an interest in characterizing what is going on in the mind need not exclude alluding to external objects: the fact that extensions or properties may be external to the head is no reason to think them unsuitable candidates for classifying things that are in the head, just as classifying various words in a book as ‘about Vienna' does not prevent those words from existing entirely inside the book. There have been a variety of external relations that philosophers have proposed that would link internal representations to external phenomena in a way that might constitute concept possession. Influential articles by Kripke ([1972] 1980, 1982), Putnam (1975) and Burge (1979) have given rise to a variety of externalist theories of concepts, which look to such facts as actual causal history (Devitt 1981), various co-variation conditions (Dretske 1981, 1988; Fodor 1991) and evolutionary selection (Millikan 1984; Papineau 1987). However, in so far as they rely on real phenomena in the external world, they are subject to certain limitations that many feel can only be surmounted by appealing to some kind of conditions that are ‘in the head'. Intensions: ‘senses'. What argues for the need for some internal condition on concept is the difficulty for any purely external account of capturing psychologically real distinctions. The examples of necessarily unextended concepts, such as [round square], suggest that the mind can somehow make distinctions for which there is no possible external reality. Consequently, many philosophers have argued that, in addition to the referent of a general term, there must also be (following Frege 1892b) its ‘sense', or ‘mode of presentation' (occasionally ‘intension' is used here as well; see Sense and reference). Thus, what really seems to distinguish [equiangular triangles] and [equilateral triangles] is not the actual or possible things to which they refer, but rather the way the mind conceives them: it is one thing to think of something as (or qua) an equilateral triangle, another to think of it qua an equiangular triangle (which is why the proof that they are necessarily co extensive is informative). And this obviously helps with the problem of the necessarily coextensive: what distinguishes, for example, [water] and [H2O] are the different ‘ways of thinking', not reflected in any even possible difference in the world. For some (for example, Peacocke 1992) concepts are senses so understood. But, of course, we then need a theory of senses. 6 The classical view and empiricism One conception of senses is provided by the classical view of concepts. This view has two independent parts that are not always clearly distinguished, one making a claim about the nature of concepts, the other about what is to possess them: (a) concepts have an ‘analysis' consisting of conditions that are necessary and sufficient for their satisfaction; and (b) these ‘defining' conditions are known to any competent user. An interesting, but problematic, example has been [knowledge], whose analysis was traditionally thought to be [justified true belief], but which has turned out to be far subtler, due to counterexamples raised by philosophers such as Gettier (1963) ( Knowledge, concept of). The example of [knowledge] brings out an important caveat for the classical view: the proper analysis of a concept need not be readily available to a competent user of it. It was not easy for Athenians to reply to Plato's inquiries about [good], nor for recent philosophers to reply to Gettier. According to a reasonable version of the classical view, a competent user's knowledge of an analysis may be ‘tacit' or ‘unconscious', rather like the ‘knowledge' people have of the grammatical rules of their language, which they seem dependably to obey despite being unable to articulate them ( Evans 1981; Katz 1971; Knowledge, tacit; Unconscious mental states). For Plato, the analyses could only be extracted from someone by a process of ‘dialectic', involving consideration of various examples and arguments to a point of ‘reflective equilibrium' (Bealer 1987: 322; Jackson and Pettit 1995). The classical view, however, has always had to face the difficulty of primitive concepts: how are they to be defined? An influential (but not the only possible) answer was provided by seventeenth-century British empiricists, who claimed that all the primitives were sensory. Indeed, the classical view has often been uncritically burdened with this further claim, or, anyway, the claim that all concepts are ‘derived from experience'. Locke (1689), Berkeley (1710) and Hume (1739-40) seemed to take this to mean that concepts were somehow composed of introspectible mental items - ‘images', ‘impressions' - that were ultimately decomposable into basic sensory parts. Berkeley ([1710] 1982: 13) noticed a problem with this approach that every generation has had to rediscover: if a concept is a sensory impression, like an image, then how does one distinguish a general concept [triangle] from a more particular one - say, [isosceles triangle] - that would serve in imagining the general one? In any case, images seem quite hopeless for capturing the concepts associated with logical terms (what is the image for negation or for possibility?). Whatever the role of images, concepts and our competence with them involve something more ( Imagery). Indeed, in addition to images and impressions and other sensory items, a full account of concepts needs to consider issues of logical structure. This is precisely what the logical positivists did, focusing on logically structured propositions and transforming the empiricist claim into their famous ‘verifiability theory of meaning': the meaning of a proposition is the means by which it is confirmed or refuted, ultimately by sensory experience; the concept expressed by a predicate is the statement of the (perhaps logically complex) sensory conditions under which people confirm or refute whether something satisfies it ( Meaning and verification). Thus, [acid] might be analysed by reference to tendencies to cause litmus paper to turn red; [belief] by observable behavioural dispositions ( Behaviourism, analytic); [material object] by enduring possibilities of sensation ( phenomenalism). This once popular position has come under much attack in the last fifty years. Few, if any, successful ‘reductions' of ordinary concepts (such as [material object], [cause]) to purely sensory concepts have ever been achieved, and there seems to be a pattern to the failures (Chisholm 1957). There have been four main diagnoses: (1) the classical search for ‘necessary and sufficient' conditions is misguided and ought to be replaced by an appreciation of the role of a concept in our reasonings and theories of the world; (2) concepts should be regarded as ‘family resemblance' structures, or ‘prototypes', (3) because of the ‘holism of confirmation', attempts to analyse concepts in terms of any verification conditions cannot succeed; and (4) we should stop looking for characterizations of concepts in terms of epistemic conditions, but rather, more metaphysically, in terms of the actual phenomena in the world to which people are referring, but about which they might be ignorant (thus, we would abandon clause (b) of the classical view, which requires analyses to be known by competent users). We will discuss each in turn. 7 Inferential roles and prototypes Inferential roles. The first alternative, inspired by Wittgenstein's famous dictum, ‘the meaning of a word is its use' (1953: §43), treats concepts as involving some or other role of a representation, either in a theory or in thought. Thus, many (for example, Kuhn 1962) have argued that someone possesses a concepts such as [witch] or [phlogiston] only if they understand the theories in which they play a role, or can reason with it in certain appropriate ways ( Semantics, conceptual role). A vexing problem with this approach has been the fact that it is hard to identify just which roles are essential to a concept. It would appear that people can be wrong and/or disagree about almost anything: Berkeley claimed that material objects were ideas, some creationists that people are not animals, some nominalists that numbers are concrete objects. If people are genuinely to disagree with these views, they must share the relevant concepts; otherwise their use of the same words would be equivocal, their disagreement ‘merely verbal'. But then it seems very hard to insist upon any specific inferential role being essential to possessing a concept. Prototypes. Another proposal also inspired by Wittgenstein (1953: §66) is to appeal to ‘family resemblances' among the things to which a concept applies: he claimed that games, for example, share no single property, but are similar to each other in various ways that cluster together (some involve winning/losing, others mere entertainment; some are played in groups, others alone). This speculation was taken by psychologists (for example, Rosch 1973; Smith and Medin 1981) to be a testable psychological hypothesis. They showed that people respond differently (in terms of response time and other measures) to questions about whether, for example, penguins rather than robins are birds, in a fashion that suggested that concept membership was a matter not of possessing a classical analysis, but of ‘distance' from a ‘prototype' or typical ‘exemplar'. Thus, a robin satisfies many more of the features of a typical bird than does a penguin and so is a ‘better' member of the category; and a malicious lie is a better case of a lie than a well-intentioned one. It has not always been clear precisely what sort of thing a prototype or exemplar might be. One must take care not to import into the mind procedures, such as comparing one actual bird with another, that make sense only outside of it. Presumably either a prototype or an exemplar is some sort of representation (a list, or an ‘image') indicating selected properties, and a metric for determining the distance of a candidate from those properties. Some writers have exploited the resources of ‘fuzzy set theory' to capture the intended structure, whereby membership of a category is understood not as an ‘all or none' affair, but as a matter of degree: everything satisfies every concept to some degree, however small ( Zadeh 1982; Fuzzy logic). Quite apart from specifying just what the view involves, there are, however, a number of problems with appeals to prototypicality as a theory of concepts. In the first place, loosening the conditions on a concept's application from ‘defining' conditions to mere ‘family resemblances' risks leaving that application far too unconstrained. Everything after all bears some resemblance to everything else (Goodman 1970): returning to Wittgenstein's example, anything, x, resembles standard games in some way or other (if only in belonging to some arbitrary set that contains all games and that thing x!). The question is which resemblances are essential to the concept, and which merely accidental - a question that returns us to the question the classical view tries to answer ( Essentialism). Second, prototypes seem poor candidates for handling the crucial phenomenon of conceptual combination: the prototype for [tropical fish] does not seem constructible from the prototypes for [tropical] and [fish], yet someone could grasp [tropical fish] none the less (Osherson and Smith 1982). Third, prototypicality, which presumably involves distances among a complex cluster of diverse properties, must be distinguished from both vagueness and estimation. As we have already observed (§1), nearly every concept admits of vague cases, in which it is not clear whether the concept applies. But this does not imply that the concept does not have a (correspondingly vague) definition. Similarly, estimation of whether or not something satisfies a concept is a question that arises with regard to any concept. But it is clearly not a metaphysical issue of the actual conditions something must satisfy in order to satisfy a concept, but rather an epistemological one concerning the belief or epistemic probability that something satisfies the conditions, given certain evidence ( Realism and antirealism). The sight of someone with a toupee may mean that there is a 90 per cent probability that he is actually 50 per cent bald, or a 40 per cent probability that he is actually 95 per cent bald. The question of whether [bald] has a classical analysis is untouched by this issue as well (Rey 1983). 8 Metaphysics v. epistemology These latter distinctions may turn on the different interests we have already noted (§1) in psychologists' and philosophers' use of ‘concept', applying respectively to representations or to their shareable meanings. The fact that people are quicker to say that robins rather than penguins are birds may tell us something about people's representations of [bird], but nothing about the definition of the concept [bird] itself, that is, what is in fact required to satisfy that concept (on reflection, after all, most of us agree that penguins are bona fide birds, despite our initial hesitation). This is not to say that the definitional issue is not relevant to psychology: what people take to be required to be a bird is as much a psychological issue as how they figure out whether those requirements have been met. It is just that prototype theory seems to be addressed largely to the latter issue, the classical view to the former. However, the differences may be deeper than merely terminological. As the example of estimation shows, it is extremely easy to conflate metaphysical issues about the conditions for something's satisfying a concept with the epistemic ones of estimating whether something actually satisfies those conditions. One reason is that English can encourage running the two together, phrasing the metaphysical question as ‘What determines what is what?' and the epistemic one as ‘How does someone determine what is what?'. A second reason is that epistemic conditions are as likely to ‘come to mind' in thinking with a concept as are its defining conditions ( §1 above). But a more important reason is that empiricism made a policy of connecting the two: the defining conditions for a concept were to be stated in terms of experiential evidence. As anti-empiricists from Plato on have argued, however, many of our concepts seem to ‘transcend experience', in that they seem to be graspable and sometimes applicable in the absence of it. For lack of any genuine Euclidean triangles in the world, it is unclear how our concept of them could be derived from experience. And even instantiated concepts such as [material object], [causation] and [prehistoric] seem to go far beyond mere sensory experience: we seem to be able to think coherently about material objects causally interacting in prehistoric times, even in the absence of any sensory evidence of that interaction. In any case, many of our concepts transcend their stereotypes: most of us understand the concept [female doctor], and recognize that [even number] has a perfectly good definition, despite our demonstrable reliance on stereotypes in both cases (Armstrong, Gleitman and Gleitman 1983). Moreover, it can often seem arbitrary and unduly restrictive to tie a concept to any particular method of verification (or confirmation). Taking a page from Pierre Duhem (1914), Quine (1953) argued that ‘our beliefs confront the tribunal of experience only as a corporate body': litmus paper turning red confirms that a solution is acidic only in conjunction with a great deal of background chemical and physical theory; indeed, Quine claims, only in conjunction with the whole of a person's system of beliefs (a view called ‘confirmation holism'; see Analyticity; Confirmation theory; Quine, W.V.). Hence, if a concept is to be analysed as its verification conditions, its meaning would be similarly holistic (‘meaning holism'). Given that no two persons' beliefs are likely to be precisely the same, this has the consequence that no two people ever share precisely the same concepts - and no one could, strictly speaking, remember the same thing over any amount of time that included a change of any belief! Fodor and LePore (1992) have recently argued that this sort of conceptual (or semantic) holism would undermine serious psychology, but, fortunately, that the arguments for it are less than compelling ( Holism: mental and semantic; Atomism, ancient). 9 Difficulties for an internalist approach Even if one distinguishes epistemological from metaphysical issues in determining concept identity, there remain a number of problems for any purely internalist theory of concepts. Whether classical or prototypical, any internalist theory of concepts requires distinguishing internal features - beliefs, inferential roles, prototypes - that are essential to (or defining of) a concept from those that are accidental, and many feel that it really is this distinction that is undermined by Quine's observations about holism. Indeed, ‘sameness of concept' for Quine becomes by and large an ‘indeterminate' issue ( Radical translation and radical interpretation). The most one might expect is a similarity of inferential role between symbols in different theories or symbol systems (Harman 1972; Block 1986): which similarities are selected may vary for different explanatory tasks, and may be a pragmatic affair. A second problem emerged from the externalist approaches of Kripke ([1972] 1980), Putnam (1975) and Burge (1979), and has come to be represented by Putnam's example of ‘twin earth' (1975): suppose there were a planet exactly like the earth in every way except that, wherever the earth has H2O, twin earth has a different, but superficially similar chemical XYZ. Putnam argues that twin-earthlings would not mean by the word ‘water' what we mean (for example, their tokens of the sentence ‘Water is wet' would not have the same truth-conditions as ours), despite the fact that, ex hypothesi, twin-earthlings would have our same internal structure. (Burge (1979) and Stich (1983) present less outlandish examples.) As Putnam famously put it, ‘meanings just ain't in the head'; rather, he argues, they depend at least in part upon the relations between internal states and external phenomena. In view of both these examples, and the Quinian worries, Fodor (1991, 1998) opts for an entirely ‘atomistic' account of concepts, arguing that concepts have no ‘analyses' whatsoever: they are simply ways in which people are directly related to individual properties in their environments, any one of which they might enjoy without the others. In principle, someone might have the concept [bachelor] and no other concepts at all, much less any ‘analysis' of it, simply by virtue of having some internal state that is causally connected with bachelorhood in the local environment. Such a view goes hand in hand with Fodor's rejection of not only verificationist, but any empiricist, account of concept learning and construction. Indeed, given the failure of empiricist constructions, Fodor (1975, 1979) argues that concepts are not constructed or ‘derived from experience' at all, but are (nearly enough) all innate ( nativism). Devitt (1995) defends a more moderate, ‘molecularist' position, allowing that many innate primitives are non-sensory (for example, [cause], [object]) but that others are susceptible to definition, especially in view of the thereby enlarged primitive base. 10 Two-factor theories and a modified classical view Although externalism does seem to account both for the stability of concepts through variation in belief and for variations in concept due to variations in environment, it still must confront the issues we mentioned earlier (§5) that invite internalism, namely, that there seem to be more distinctions in the mind than are available in the external world. An increasingly popular approach is to separate the internal and external work concepts are asked to perform. According to ‘two-factor' theories, ‘concepts' should be regarded as having two components: one ‘in the head', consisting of an internal representation playing a certain psychological role; and the other, some sort of co-variational law or evolutionary fact that, in a historical context, determines the reference and truth-conditions of the concept. (Sometimes ‘concept' is restricted to the internal factor, ‘content' to the external; and ‘two-factor theory' is sometimes applied only to those views in which the two factors are relatively independent of one another.) A two-factor theory leaves a place for a modified classical view, as well as for something like philosophical analysis. The internal factor would determine a full semantic content to a conceptual representation only in a particular context, so that the full analysis of (the content of) a concept might await empirical investigation of that context and not be available to its user. But this is perhaps as it should be: philosophical analysis of ‘the nature of' a phenomenon may depend both upon the internal rule one is deploying and the actual phenomenon that, in a context, the rule picks out (Bealer 1987; Jackson and Pettit 1995).