Vagueness

In philosophy, vagueness refers to an important problem in semantics, metaphysics and philosophical logic. Definitions of this problem vary. A predicate is sometimes said to be vague if the bound of its extension is indeterminate, or appears to be so. The predicate 'is tall' is vague because there seems to be no particular height at which someone becomes tall. Alternately, a predicate is sometimes said to be vague if there are borderline cases of its application, such that in these cases competent speakers of the language may faultlessly disagree over whether the predicate applies. The disagreement over whether a hotdog is a sandwich suggests that “sandwich” is vague. In philosophy, vagueness refers to an important problem in semantics, metaphysics and philosophical logic. Definitions of this problem vary. A predicate is sometimes said to be vague if the bound of its extension is indeterminate, or appears to be so. The predicate 'is tall' is vague because there seems to be no particular height at which someone becomes tall. Alternately, a predicate is sometimes said to be vague if there are borderline cases of its application, such that in these cases competent speakers of the language may faultlessly disagree over whether the predicate applies. The disagreement over whether a hotdog is a sandwich suggests that “sandwich” is vague. Vagueness is commonly demonstrated by the Sorites paradox. A standard form of this paradox features a 2000-man sequence of progressively taller men, starting with a paradigm case of a short man at one extreme, say George Costanza, and at the other extreme, a paradigm case of a tall one, say Kramer. Sorites paradoxes exploit the intuition that some vague predicates are tolerant with respect to small enough differences on a dimension decisive of their application. This principle may seem to hold on the basis that (for example) no particular height is more justified than others in its vicinity as a cut-off for shortness. This intuition has been called the No Sharp Boundaries thesis about vague predicates and plays a prominent role in theories of vagueness. The Sorites paradox dates to the fourth century BCE and is attributed to Eubulides of Melitus. It has received a resurgence of attention since 1975, when three papers published in Synthese effectively conceived the contemporary study of vagueness. The problem posed by vagueness is to explain its particular kind of indeterminacy. Does vagueness render large portions of ordinary language meaningless? Likely not, since we frequently use vague language to great effect in ordinary discourse. If not, what is vagueness, at the level of predicate logic? How is it to be modeled without contradiction, and without sacrificing too much of classical logic? Is vagueness semantic, metaphysical or epistemic?