Page 226 - Encyclopedia of Philosophy of Language

Truth and Meaning
An expression or concept is vague if it has borderline cases, where it neither definitely applies nor definitely fails to apply. For example, tall is vague because some people are neither definitely tall nor definitely not tall. If a term is not vague, it is precise. Vagueness is one source of logical paradoxes. It constitutes a major challenge to the attempt to describe natural languages by means of formal semantics.
1. Kinds of Vagueness
Vagueness must be distinguished from ambiguity, unspecificity, and context-dependence. Competent speakers associate an ambiguous term with at least two separate meanings, each of which may be precise; a vague term may be associated withjust one meaning, a vague one. The vagueness of tall is not ambiguity; the ambiguity of bank is not vagueness. An unspecific term covers a wide range of cases, but is not vague unless its boundary is blurred. Although acute [angle] is unspecific, it is not vague. A context-dependent term draws different boundaries in different contexts; this too is not a matter of blurriness. That 'less than 97 miles away' applies to Glasgow if said in Edinburgh and not if said in London does not make the phrase vague; equally, 'not far away' may be vague even as said by a particular speaker in a particular place with a particular purpose in mind.
A term is extensionally vague if it has borderline cases. It is intensionally vague if it could have such cases. Borderlines are of different kinds. Consider the word lake: a certain body of water may be neither definitely a lake nor definitely not a lake; a given lake may neither definitely contain nor definitely not contain a certain drop of water. Borderline cases give a term first-order vagueness. If some cases are neither definitely borderline cases nor definitely not border- line cases, the term has second-order vagueness. Higher orders of vagueness are defined similarly.
Almost any word in natural language is at least slightly vague in some respect. Used as a technical term, 'vague' is not pejorative. Indeed, vagueness is a desirable feature of natural languages. Vague words often suffice for the purpose in hand, and too much precision can lead to time-wasting and inflexibility. Although specific words need to be made less vague for specific purposes, there is no question of making one's whole language perfectly precise. Any linguistic stipulations intended to introduce such precision would themselves have to be couched in one's pre- existing vague language.
Attempts have been made to measure vagueness experimentally, by gathering statistics about variation
between speakers in their application of terms and variation over time or indecision at a time in given speakers. However, such effects would be expected even for precise terms, owing to ignorance, error, or confusion. In the absence of a filter for these extraneous effects, the statistics do not cast much light on vagueness.
2. ParadoxesofVagueness
V agueness provokes paradoxes. The best-known is attributed to Eubulides, a contemporary of Aristotle. The removal of one grain from a heap apparently still leaves a heap; thus if grains are removed one by one from a heap of 10,000 grains, at each stage there should still be a heap; yet eventually no heap is left. Similar paradoxes can be constructed for most vague terms. They are known as 'sorites' (from Greek sdros 'heap').
A sorites paradox may be conceived as an argument with an apparently true major premise (e.g., For every positive number n.ifn grains made a heap then n —l grains made a heap), an apparently true minor premise (e.g., Ten thousand grains made a heap) and an appar- ently false conclusion (e.g., One grain made a heap). Yet the argument apparently consists of a series of valid steps of elementary logic (from the major prem- ise and n grains made a heap to n —l grains made a heap), and should therefore preserve truth from prem- ises to conclusion. A major test of a theory of vague- ness is its ability to diagnose sorites paradoxes. Which appearance is misleading and why? Is one of the prem- ises false, or the conclusion true, or the argument invalid?
The obvious solution is to deny the major premise. However, this commits one by standard logic to asserting that for some n, n grains made a heap and n— 1 did not. Given the vagueness of'heap,' how can one grain make such a difference?
3. Theories of Vagueness
It is often assumed that vague statements are neither true nor false in borderline cases. If so, they are coun- terexamples to the principle of bivalence, according to which every statement is either true or false. Since the best-developed attempts to give formal semantics for natural languages assume bivalence, they are chal- lenged by the phenomenon of vagueness.
Commitment to bivalence has led some phil- osophers, notably Frege, to deny coherent meaning to vague terms. Thus systematic semantic descriptions can be given only of ideally precise, and therefore artificial, languages. However, most theories of vague-
204
Vagueness T. Williamson