Abstract

In ordinary conversation, we describe all sorts of different things as vague: you can have vague plans, vague ideas and vague aches and pains. In philosophy of language, in contrast, it is parts of language – words, expressions and so on – that are said to be vague. One classic example of a vague term is the word ‘heap’. A single grain clearly does not make a heap, and a million grains does make a heap, but where exactly does the boundary lie? How many grains do you need to make a heap? There seems to be no precise answer to this question, and because the term is imprecise in this way, we call it vague. Vague terms are extremely common in natural language. The term ‘bald’ is vague, because there is no precise number of hairs that mark the boundary between ‘bald’ and ‘not bald’; the term ‘hot’ is vague because there is no precise temperature that something must reach to count as hot – and so on. As we have seen, adjectives can be vague, but so can nouns, adverbs and perhaps all parts of language. To find terms which are precise rather than vague, we need to look to the languages of logic and mathematics. We can use vague terms to construct paradoxes known as sorites paradoxes. From an obviously true premise, such as that a collection of 1 million grains is a heap, together with the claim that ‘heap’ has no sharp boundary, we can derive the absurd conclusion that just 1 grain counts as a heap. Any theory of vagueness must offer some solution to this paradox. Some of the most popular theories of vagueness include supervaluationism, the degree theory of truth and the epistemic theory, and many of the available theories demand a radical rethink of classical accounts of logic and language.