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Abstract

Vagueness is semantic indecision, David Lewis said. This dissertation vindicates this insight by applying social choice theory, the branch of economics concerning collective decision making, to account for linguistic vagueness. Vagueness effects are analogues to cycles that sometimes arise in collective decisions. Cycles (e.g. A is preferred to B is preferred to C is preferred to A) may arise in a collective body like a legislature whenever such a body tries to choose among three or more proposals. Though cycles paralyze decision making, the economist Kenneth Arrow proved that (under certain conservative assumptions) cycles are unavoidable., ,Cycling is a failure of transitivity, the property that requires if A is related to B, and B is related to C, then A is related to C. Like cycling, vagueness effects depend on intransitivities: if A looks to be as tall as B, and if B looks to be as tall as C, it may not be the case that A looks to be as tall as C. Vagueness effects like the sorites paradox (how many people can move to a little city before it is no longer little?), borderline cases (what is the biggest little city?), and higher-order vagueness (when is a city definitely little, as opposed to just little?) all involve failures of transitivity. , ,Arrow's result explains these failures. From the view of choice theory, the semantic choosers are vague predicates such as healthy, and the chosen are different measures by which to determine what counts as healthy. Adjectives like healthy involve evaluations of multiple different criteria in context, such as blood pressure or cholesterol (this is why it is possible to say things like healthy with respect to cholesterol). Speakers compare contextually relevant entities according to these criteria, counting as healthy the entities that rank sufficiently high on sufficiently many, sufficiently important dimensions. These adjectives can therefore be interpreted as choice functions subject to Arrow's result. Replace voters with the different criteria and legislative proposals with contextually relevant entities, and Arrow's result reconstructs itself in the semantics of gradable adjectives. , ,Vagueness is therefore indecision. And this indecision is semantic in nature: vagueness effects follow from standard assumptions about the meaning of gradable adjectives plus reasonable assumptions about aggregating many criteria into one. Where many previous approaches to vagueness have focused on the range of the function healthy---the set of truth values---the indecisional approach that I propose focuses instead on this function's domain, most relevantly the set of degrees. When this domain depends on multiple component dimensions (like blood pressure and heart rate for "healthy"), these component dimensions must be aggregated into one healthiness scale much in the same way that voters' preferences must be aggregated to produce a collective decision. Vagueness effects follow, and are even expected, from reasonable constraints on this aggregation process.

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