Semantic Indecision

Abstract

Linguistic vagueness results from aggregating many judgments into one. Thus, vagueness is a type of decision problem, and the sorites paradox—most famous of vagueness phenomena—is a paradox of collective decision making. The sorites paradox reflects this judgement-aggregating character of vagueness. In the case of vague predicates like healthy, the “judgments” are the rankings of contextually salient entities along some scale (like “health”) and the “dimensions” are relevant criteria (like blood pressure and heart rate). The sorites paradox is paradoxical because it tracks changes along one dimension (“a person with slightly higher blood pressure than a healthy person is healthy”) while ignoring others. The aggregation of many judgments into one is also a feature of Condorcet’s paradox, a paradox of collective decision making. If three equal blocks of voters have certain preferences among the available candidates, then the judgment-aggregating procedure—a vote—fails to deliver an outcome. Condorcet’s paradox and the sorites paradox are two sides of the same coin. Both paradoxes arise from the decision problems inherent in aggregating many judgments along many dimensions. And in both cases, plausible constraints on the aggregation process—well developed in the theory of social choice—lead to paradox.