Comparative Concepts

Abstract

Comparative concepts (such as 'greener than'or 'higher than') are fundamental to our grasp of associated categorical concepts ('green', 'high', respectively). Some comparative concepts seem natural, whereas other ones seem rather gerrymandered---e.g., compare 'x is greener than y'and 'x and y are such that either (i) x and y are inspected before midday and x is greener than y, or (ii) x and y are inspected after midday and x is bluer than y'. What kind of cognitive structures under your ability to order objects? And why do we order objects the way we do, and not in other ways? The aim of this talk is to outline an account of comparative concepts within a conceptual spaces framework. The account bears for one on the account of naturalness for comparative concepts. For another, it bears on the theory of gradable concepts, i.e., the type of categorical concepts expressed by gradable terms in natural language. The approach is novel in that it carries some basic assumptions from Peter Gärdenfors'conceptual spaces account of categorical concepts over to comparative concepts (in his monograph 'Conceptual Spaces'[2000]). The offered approach is more general both (i) in that it supplies a framework for motivating various types of categorisation rules for gradable concepts, and (ii) in that it gives a model that subsumes ungraded categorisation as a limiting case.