The Semantics of Comparatives: A Difference-Based Approach

Abstract

Abstract Degree semantics has been developed to study how the meanings of measurement and comparison are encoded in natural language. Within degree semantics, this paper proposes a difference-based (or subtraction-based) approach to analyze the semantics of comparatives. The motivation is the measurability and comparability of differences involved in comparatives. The main claim is that comparatives encode a subtraction equation among three scalar values: two measurements along an interval scale and the difference between them. We contribute two innovations: (i) using interval arithmetic to implement subtraction, and (ii) analyzing comparative morpheme -er/more as an additive particle, denoting the default, most general, positive difference. Our analysis inherits existing insights in the literature. Moreover, the innovations bring new conceptual and empirical advantages. In particular, we address the interpretation of comparatives containing than-clause-internal quantifiers and various kinds of numerical differentials. We also account for three puzzles with regard to the scope island issue, the monotonicity of than-clauses, and the discourse status of the standard in comparison.