Anyone who believes they may need assistance in attending or fully participating in the workshop should contact the graduate coordinator in advance (djagannathan@uchicago.edu).

The Logical Foundations of Adjectival Scale Structure

Abstract: In this presentation, I present a new theory of the relationship between context-sensitivity, vagueness, and adjectival scale structure. 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 (Klein (1980), a.o.) 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.

Just about every theorist holds that vague terms are context-sensitive to some extent. What counts as “tall”, “rich”, and “bald” depends on the ambient comparison class, paradigm cases, and/or the like. To take a stock example, a given person might be tall with respect to European entrepreneurs and downright short with respect to professional basketball players. It is also generally agreed that vagueness remains even after comparison class, paradigm cases, etc. are fixed, and so this context sensitivity does not solve the problems with vague terms.

In this talk, I’ll briefly sketch the main features of my broadly contextualist account of vagueness and that of Agustin Rayo and the late Ruth Manor, showing how those relate to, and reinforce, each other, noting a seeming difference. A key item used to articulate my own view is David Lewis’s notion of conversational score. This is used to track which borderline cases have been called in the course of a conversation. Manor alludes to Lewis’s notion of accommodation, a key aspect of the kinematics of conversation, and Rayo speaks of common ground. I’ll show how the conversational score could be employed to develop and extend Manor’s view, showing how vague terms, as she construes them, are (or can be) deployed in conversation, consistent with both the underlying indeterminacy of the terms and normal communicative goals.

To help develop the view further, I’ll invoke Craige Roberts’s notion of retrievability, a tool developed to show how definites, such as definite descriptions, singular pronouns, and proper names, are deployed in conversation, in a Lewis-style scorekeeping framework. This, I think, is exactly the right way to understand conversations in what Manor calls non-sorities situations and, to invoke my own view, in sorites situations as well.

As a reminder, the workshop will return to the theme of vagueness next Friday, March 1st at the usual time and place, with a talk on “Vagueness, open-texture, and retrievability” by Stewart Shapiro, O’Donnell Professor of Philosophy at the Ohio State University.

Matt Teichman’s talk will instead be on February 8th, at the same time and place, and the remainder of our schedule this quarter will be as advertised in the schedule.

And here is our preliminary schedule for Winter Quarter.