The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of "construction" is proposed and compared with related notions, in particular with Frege's concept of "function" and Carnap's concept of "intensional isomorphism." It is argued that constructions constitute the proper subject matter of (...) both logic and mathematics, and that a coherent semantic account of mathematical formulas cannot be given without assuming that they serve as names of constructions. (shrink)

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

In Furnishing the Mind, Jesse Prinz attempts to swing the pendulum back toward empiricism.

Philosophers from Hume, Kant, and Wittgenstein to the recent realists and antirealists have sought to answer the question, What are concepts? This book provides a detailed, systematic, and accessible introduction to an original philosophical theory of concepts that Christopher Peacocke has developed in recent years to explain facts about the nature of thought, including its systematic character, its relations to truth and reference, and its normative dimension. Particular concepts are also treated within the general framework: perceptual concepts, logical concepts, and (...) the concept of belief are discussed in detail. The general theory is further applied in answering the question of how the ontology of concepts can be of use in classifying mental states, and in discussing the proper relation between philosophical and psychological theories of concepts. Finally, the theory of concepts is used to motivate a nonverificationist theory of the limits of intelligible thought. Peacocke treats content as broad rather than narrow, and his account is nonreductive and non-Quinean. Yet Peacocke also argues for an interactive relationship between philosophical and psychological theories of concepts, and he plots many connections with work in cognitive psychology. (shrink)

1 There is a Standard Objection to the idea that concepts might be prototypes (or exemplars, or stereotypes): Because they are productive, concepts must be compositional. Prototypes aren't compositional, so concepts can't be prototypes (see, e.g., Margolis, 1994).2 However, two recent papers (Osherson and Smith, 1988; Kamp and Partee, 1995) reconsider this consensus. They suggest that, although the Standard Objection is probably right in the long run, the cases where prototypes fail to exhibit compositionality are relatively exotic and involve phenomena (...) which any account of compositionality is likely to find hard to deal with; for example, the effects of quantifiers, indexicals, contextual constraints, etc. KP are even prepared to indulge a guarded optimism: "... when a suitably rich compositional theory... is developed, prototypes will be seen ... as one property among many which only when taken altogether can support a compositional theory of combination" (p.56). In this paper, we argue that the Standard Objection to prototype theory was right after all: The problems about compositionality are insuperable in even the most trivial sorts of examples; it is therefore as near to certain as anything in cognitive science ever gets that the structure of concepts is not statistical. Theories of categorization, concept acquisition, lexical meaning and the like, which assume the contrary simply don't work. We commence with a general discussion of the constraints that an account of concepts must meet if their compositionality is to explain their productivity. We'll then turn to a criticism of proposals that OS2 and KP make for coping with some specific cases. (shrink)

The renowned philosopher Jerry Fodor, a leading figure in the study of the mind for more than twenty years, presents a strikingly original theory on the basic constituents of thought. He suggests that the heart of cognitive science is its theory of concepts, and that cognitive scientists have gone badly wrong in many areas because their assumptions about concepts have been mistaken. Fodor argues compellingly for an atomistic theory of concepts, deals out witty and pugnacious demolitions of rival theories, and (...) suggests that future work on human cognition should build upon new foundations. This lively, conversational, and superbly accessible book is the first volume in the Oxford Cognitive Science Series, where the best original work in this field will be presented to a broad readership. Concepts will fascinate anyone interested in contemporary work on mind and language. Cognitive science will never be the same again. (shrink)

This article provides a critical overview of competing theories of conceptual structure (definitional structure, probabilistic structure, theory structure), including the view that concepts have no structure (atomism). We argue that the explanatory demands that these different theories answer to are best accommodated by an organization in which concepts are taken to have atomic cores that are linked to differing types of conceptual structure.

Concepts: Core Readings traces the develoment of one of the most active areas of investigation in cognitive science. This comprehensive volume brings together the essential background readings on concepts from philosophy, psychology, and linguistics, while providing a broad sampling of contemporary research. The first part of the book centers around the fall of the Classical Theory of Concepts in the face of attacks by W.V.O. Quine, Ludwig Wittgenstein, Eleanor Rosch, and others, emphasizing the emergence and development of the Prototype Theory (...) and the controversies it spurred. The second part surveys a broad range of contemporary theories—Neoclassical Theories, the Prototype Theory, the Theory-Theory, and Conceptual Atomism. (shrink)

In Concepts, Kinds, and Cognitive Development, Frank C. Keil provides a coherent account of how concepts and word meanings develop in children, adding to our understanding of the representational nature of concepts and word meanings at all ages. Keil argues that it is impossible to adequately understand the nature of conceptual representation without also considering the issue of learning. Weaving together issues in cognitive development, philosophy, and cognitive psychology, he reconciles numerous theories, backed by empirical evidence from nominal kinds studies, (...) natural-kinds studies, and studies of fundamental categorical distinctions. He shows that all this evidence, when put together, leads to a better understanding of semantic and conceptual development. The book opens with an analysis of the problems of modeling qualitative changes in conceptual development, investigating how concepts of natural kinds, nominal kinds, and artifacts evolve. The studies on nominal kinds document a powerful and unambiguous developmental pattern indicating a shift from a reliance on global tabulations of characteristic features to what appears to be a small set of defining ones. The studies on natural kinds document an analogous shift toward a core theory instead of simple definition. Both sets of studies are strongly supported by cross cultural data. While these patterns seem to suggest that the young child organizes concepts according to characteristic features, Keil argues that there is a framework of conceptual categories and causal beliefs that enables even very young children to understand kinds at a deeper, theoretically guided, level. This account suggests a new way of understanding qualitative change and carries strong implications for how concepts are represented at any point in development. A Bradford Book. (shrink)

In this interpretive analysis, Ravin argues that thematic roles are not valid semantic entities, and that syntax and semantics are indeed autonomous and independent of one another. Suggesting a decompositional approach to lexical semantics in the spirit of Katz's semantic theory, the book considers such theoretical issues as indeterminacy and ambiguity, lexical configuration rules, and lexical projection, and analyzes the semantic content of event concepts such as causation, action, and change.

Semantic Structures is a large-scale study of conceptual structure and its lexical and syntactic expression in English that builds on the theory of Conceptual...

This entry provides an overview of theories of concepts that is organized around five philosophical issues: (1) the ontology of concepts, (2) the structure of concepts, (3) empiricism and nativism about concepts, (4) concepts and natural language, and (5) concepts and conceptual analysis.

Given the fundamental role that concepts play in theories of cognition, philosophers and cognitive scientists have a common interest in concepts. Nonetheless, there is a great deal of controversy regarding what kinds of things concepts are, how they are structured, and how they are acquired. This chapter offers a detailed high-level overview and critical evaluation of the main theories of concepts and their motivations. Taking into account the various challenges that each theory faces, the chapter also presents a novel approach (...) to concepts that is organized around two ideas. The first is a pluralistic view of differing types of conceptual structure. The second is a model that treats concepts as atomic representations that are linked to various types of conceptual structures. (shrink)