Heather Burnett · Vagueness and Scale Structure within the Delineation Approach to Gradability in Natural Language
In this presentation, I present a new theory of the relationship between context-sensitivity, vagueness, and adjectival scale structure set within the Delineation semantics framework (Kamp, 1975; Klein, 1980, among others). From an empirical point of view, I argue that the four principle subclasses of adjectival predicates (relative adjectives (ex. tall), total absolute adjectives (ex. dry), partial absolute adjectives (ex. wet), and non-scalar adjectives (ex. atomic)) can be distinguished along three dimensions: 1) how their criteria of application can vary depending on context; 2) how they display the characteristic properties of vague language; and 3) what the properties of their associated orders (a.k.a. scales) are. It has been known for a long time in the literature (cf. Unger (1975), Pinkal (1995), Kennedy (2007), McNally (2011) a.o.) that there exist connections between context-sensitivity, vagueness, and scale structure; however, a formal system that expresses these connections has yet to be developed. By combining insights into the relationship between context-sensitivity and scalarity from the delineation semantics framework with insights into the relationship between tolerance relations and the Sorites paradox from Cobreros, Égré;, Ripley & van Rooij (2012)’s Tolerant, Classical, Strict (TCS) framework, I propose such a logical system. Using this framework, I show that the association of particular classes of adjectives with their particular kinds of scales can be derived from their context-sensitivity and vagueness properties. In other words, I argue that from independently necessary theories of context-sensitivity and vagueness, we arrive at a full theory of gradability and scale structure in the adjectival domain.