A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures.

Six experiments explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes in common with other categories. In probabilistic terms, the hypothesis is that prototypicality is a function of the total cue validity of the attributes of items. In Experiments 1 and 3, subjects listed attributes for members of semantic categories which had been previously rated for degree of prototypicality. High positive (...) correlations were obtained between those ratings and the extent of distribution of an item's attributes among the other items of the category. In Experiments 2 and 4, subjects listed superordinates of category members and listed attributes of members of contrasting categories. Negative correlations were obtained between prototypicality and superordinates other than the category in question and between prototypicality and an item's possession of attributes possessed by members of contrasting categories. Experiments 5 and 6 used artificial categories and showed that family resemblance within categories and lack of overlap of elements with contrasting categories were correlated with ease of learning, reaction time in identifying an item after learning, and rating of prototypicality of an item. It is argued that family resemblance offers an alternative to criterial features in defining categories. (shrink)

The Hurvich-Jameson (H-J) opponent-process network offers a familiar account of the empirical structure of the phenomenological color space for humans, an account with a number of predictive and explanatory virtues. Its successes form the bulk of the existing reasons for suggesting a strict identity between our various color sensations on the one hand, and our various coding vectors across the color-opponent neurons in our primary visual pathways on the other. But anti-reductionists standardly complain that the systematic parallels discovered by the (...) H-J network are just empirical correspondences, constructed post facto, with no predictive or explanatory purchase on the intrinsic characters of qualia proper. The present paper disputes that complaint, by illustrating that the H-J model yields some novel and unappreciated predictions, and some novel and unappreciated explanations, concerning the qualitative characters of a considerable variety of color sensations possible for human experience, color sensations that normal people have almost certainly never had before, color sensations whose accurate descriptions in ordinary language appear semantically ill-formed or even self-contradictory. Specifically, these "impossible" color sensations are activation-vectors (across our opponent-process neurons) that lie inside the space of neuronally possible activation-vectors, but outside the central 'color spindle' that confines the familiar range of sensations for possible objective colors. These extra-spindle chimerical-color sensations correspond to no reflective color that you will ever see objectively displayed on a physical object. But the H-J model both predicts their existence and explains their highly anomalous qualitative characters in some detail. It also suggests how to produce these rogue sensations by a simple procedure made available in the latter half of this paper. The relevant color plates will allow you to savor these sensations for yourself. (shrink)

A similarity space is a hyperspace in which the dimensions represent various dimensions on which objects may differ. The similarity space theory of concepts is the thesis that concepts are regions of similarity spaces that are somehow realized in the brain. Proponents of such a theory of concepts include Paul Churchland and Peter Gärdenfors. This paper argues that the similarity space theory of concepts is mistaken because regions of similarity spaces cannot serve as the components of judgments. It emerges that (...) although similarity spaces cannot model concepts, they may model a kind of nonconceptual representation. (shrink)

Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general assumptions.

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are (...) convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions. (shrink)