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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...

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