Abstract

Quantities are ubiquitous and an important part of our understanding about the world – we talk of engine horsepower, size, mileage, price of cars; GDP, population, area of countries; wingspan, weight, surface area of birds, and so on. In this paper, we present a sketch of a theory of quantity – cognitively sound representations and principles for generating those representations. We present evidence from psychology, natural language, and ecological constraints to argue for a cognitively plausible representation of quantities. We then propose a general principle of how to make the necessary and relevant distinctions. Structured models of retrieval, similarity, and generalization, and in general models involving symbolic representations, do not handle quantities adequately. That is an artifact of poor representations of quantity, and we believe that the representations proposed here will make these models more quantity-aware. This investigation is at the intersection of qualitative reasoning, cognitive psychology, and linguistics, and builds on existing evidence in these fields to potentially contribute to the understanding of quantities in all the three. 1

Citations