Criteria for naturalness in conceptual spaces

Conceptual spaces are a frequently applied framework for representing concepts. One of its central aims is to find criteria for what makes a concept natural. A prominent demand is that natural concepts cover convex regions in conceptual spaces. The first aim of this paper is to analyse the convexity thesis and the arguments that have been advanced in its favour or against it. Based on this, I argue that most supporting arguments focus on single-domain concepts (e.g., colours, smells, shapes). Unfortunately, these concepts are not the primary examples of natural concepts. Building on this observation, the second aim of the paper is to develop criteria for natural multi-domain concepts. The representation of such concepts has two main aspects: features that are associated with the concept and the probabilistic correlation pattern which the concept captures. Conceptual spaces, together with probabilistic considerations, provide a helpful framework to approach these aspects. With respect to feature representation, the existence of characteristic features (i.e., that apples have a specific taste) is essential. Moreover, natural concepts capture peaks of a probabilistic distribution over complex spaces. They carve up nature at its joints, that is, at areas with no or low probabilistic density. This last aspect is shown to be closely related to the convexity demand.

Automated summary

This paper analyzes the convexity thesis in conceptual spaces and develops criteria for natural multi-domain concepts. It discusses the representation of characteristic features and the probabilistic correlation pattern in conceptual spaces.