The Problem of Geometric Representation of Similarity in Peter Gärdenfors' Conceptual Spaces Theory

Abstract

The concept of similarity is undoubtedly one of the cornerstones of contemporary cognitive science. Although it plays an important role in most of the cognitive activities of man, the issue of the appropriate representation of similarities is an extremely difficult task. One approach to the issue of similarity representation is based on the geometric model used in Gärdenfors’ conceptual spaces theory. However, the criticism of the geometrical model of similarity still seems to remain valid, and the model itself is regarded, by many critics, as an inadequate tool for representing mental phenomena. The primary objective of the article is to propose a model of similarity which would be insensitive to this criticism. The first part is devoted to basic assumptions of the conceptual spaces theory and the axioms of its model of similarity. In the second part I present the most common critical arguments against the geometrical model of similarity and then introduce a geometric model of similarity immune to the criticism.