The Semantics of Comparatives: A Difference-Based Approach

1 Degree semantics has been developed to study how the meanings of 2 measurement and comparison are encoded in natural language. Within degree 3 semantics, this paper proposes a difference-based (or subtraction-based) approach 4 to analyze the semantics of comparatives. The motivation is the measurability and 5 comparability of differences involved in comparatives. The main claim is that 6 comparatives encode a subtraction equation among three scalar values: two 7 measurements along an interval scale and the difference between them. We 8 contribute two innovations: (i) using interval arithmetic to implement subtraction, 9 and (ii) analyzing comparative morpheme -er/more as an additive particle, denoting 10 the default, most general, positive difference. Our analysis inherits existing insights 11 in the literature. Moreover, the innovations bring new conceptual and empirical 12 advantages. In particular, we address the interpretation of comparatives containing 13 than-clause-internal quantifiers and various kinds of numerical differentials. We also 14 account for three puzzles with regard to the scope island issue, the monotonicity of 15 than-clauses, and the discourse status of the standard in comparison. 16