The aim of this paper is to reconcile two claims that have long been thought to be incompatible: that we compositionally determine the meaning of complex expressions from the meaning of their parts, and that prototypes are components of the meaning of lexical terms such as fish, red, and gun. Hypotheses and are independently plausible, but most researchers think that reconciling them is a difficult, if not hopeless task. In particular, most linguists and philosophers agree that is not negotiable; so (...) they tend to reject. Recently, there have been some attempts to reconcile these claims, but they all adopt an implausibly weak notion of compositionality. Furthermore, parties to this debate tend to fall into a problematic way of individuating prototypes that is too externalistic. In contrast, I propose that we can reconcile and if we adopt, instead, an internalist and pluralist conception of prototypes and a context-sensitive but strong notion of compositionality. I argue that each of this proposals is independently plausible, and that, when taken together, provide the basis for a satisfactory account of prototype compositionality. (shrink)

While holism and atomism are often treated as mutually exclusive approaches to semantic theory, the apparent tension between the two usually results from running together distinct levels of semantic explanation. In particular, there is no reason why one can’t combine an atomistic conception of what the semantic values of our words are (one’s “descriptive semantics”), with a holistic explanation of why they have those values (one’s “foundational semantics”). Most objections to holism can be shown to apply only to holistic version (...) of descriptive semantics, and do not tell against any sorts of holistic foundational semantics. As Davidson’s work will be used to illustrate, by clearly distinguishing foundational and descriptive semantics, one can capture the most appealing features of both holism and atomism. (shrink)

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address (...) arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)

The purpose of this paper is twofold: (i) we argue that the structure of commonsense knowledge must be discovered, rather than invented; and (ii) we argue that natural language, which is the best known theory of our (shared) commonsense knowledge, should itself be used as a guide to discovering the structure of commonsense knowledge. In addition to suggesting a systematic method to the discovery of the structure of commonsense knowledge, the method we propose seems to also provide an explanation for (...) a number of phenomena in natural language, such as metaphor, intensionality, and the semantics of nominal compounds. Admittedly, our ultimate goal is quite ambitious, and it is no less than the systematic ‘discovery’ of a well-typed ontology of commonsense knowledge, and the subsequent formulation of the longawaited goal of a meaning algebra. (shrink)

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...) the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. (shrink)