An argument for vagueness with holes

Abstract

Linguistic vagueness is a consequence of aggregating many judgments into one. For example, whether something is a heap depends on judgments along at least two dimensions, height and width. Results from social choice theory—a branch of economics dealing with collective decision making—show that such judgment aggregations face significant limitations. Topologically, these limitations stem from “holes” in the structure of multidimensional domains over which judgment aggregations occur. Semantically, these limitations manifest as vagueness effects like susceptibility to the sorites paradox.