Vagueness and Borderline Cases

Abstract

Vagueness is ubiquitous in natural language. It seems incompatible with classical, bivalent logic, which tells us that every statement is either true or false, and none is vaguely true. Yet we do manage to reason using vague natural language. In fact, the majority of our day-to-day reasoning involves vague terms and concepts. There is a puzzle here: how do we perform this remarkable feat of reasoning? I argue that vagueness is a kind of semantic indecision. In short, that means we cannot say exactly who is bald and who is not because we have never decided the precise meaning of the word 'bald'--there are some borderline cases in the middle, which might be bald or might not. That is a popular general strategy for addressing vagueness. Those who use it, however, do not often say what they mean by 'borderline case'. It is most frequently used in a loose way to refer to in-between items: those people who are neither clearly bald nor clearly not bald. But under that loose description, the notion of borderline cases is ambiguous, and some of its possible meanings create serious problems for semantic theories of vagueness.Here, I clarify the notion of a borderline case, so that borderline cases can be used profitably as a key element in a successful theory of vagueness. After carefully developing my account of borderline cases, I demonstrate its usefulness by proposing a theory of vagueness based upon it. My theory, vagueness as permission, explains how classical logic can be used to model even vague natural language.