LingLang Lunch (2/25/2015): Timothy Grinsell (University of Chicago)

Verdicts, Voters, and Vectors: Three Sources of Evidence for One Theory of Vagueness

This talk presents three sources of evidence for the notion that linguistic vagueness results from the aggregation of a set of judgments. The word healthy, for instance, aggregates judgments along a number of contextually supplied “dimensions,” including blood pressure, cholesterol, etc. (with the relevant dimensions contextually determined). Given certain weak assumptions, the combinatorial problems associated with aggregating judgments along multiple dimensions explain healthy’s vagueness effects.

I present three sources of evidence for this view. The first comes from jury verdicts. In some cases, juries are required to assign percentage values to a defendant’s negligence, representing that portion of fault attributable to the defendant (e.g. 80% negligent). A study of about 800 jury verdicts (Best & Donohue 2012) shows that juries tend to assign these percentages in clumpy ways. This clumpiness provides evidence for a discontinuous scale structure, consistent with the aggregation hypothesis. Second, the well-known distinction between “absolute” and “relative” adjectives (Rotstein & Winter 2004, Kennedy & McNally 2005) provides evidence that unidimensionality reduces or eliminates vagueness effects, consistent with research in political science (like the Median Voter Theorem) that unidimensionality eliminates the aggregation problem (Sen 1970). Third, a topological view of the aggregation problem (Chichilnisky 1982) finds support in the representation of concepts as continuous spaces, in which dimensions are vectors (Gärdenfors 2000, 2014).