Vagueness by Numbers ? No Worries NICHOLAS

Theories of vagueness based upon fuzzy set theory countenance a continuum of degrees of truth, usually represented by the real numbers between 0 and 1 inclusive (with 0 representing falsity simpliciter and 1 representing truth simpliciter). Keefe (1998) argues against such theories of vagueness. 1 Keefe writes: Take the vague predicate 'tall': I claim that any numbers assigned in an attempt to capture the vagueness of 'tall' do no more than serve as another measure of height. More generally, in so far as it is possible to assign numbers which respect certain truths about, for example, comparative relations, this is no more than a measure of an attribute related to, or underlying, the vague predicate. The purpose of this note is to show that Keefe's claim here is false: the numbers that we assign to objects to measure their heights serve a quite distinct purpose from the numbers that the fuzzy theory assigns to objects to measure their degrees of tallness; and in general, the numbers that we assign to objects to measure their possession of a quantity Q serve a quite distinct purpose from the numbers that the fuzzy theory assigns to objects to measure their degree of possession of property P, where an object's possession of P is determined by its possession of Q (so Q might be mass and P the property of being heavy, Q might be hair-count and P the property of being bald, and so on). 2 Keefe notes that 'In many paradigm cases of a vague predicate F there is a corresponding measurable attribute related to F in such a way that the truth-value status of Fx … is determined by x's quantity of that attribute. For example, the truth-value status of " a is tall " is determined by, or supervenes on, a's height … similarly for the relation between " a is hot " and a's temperature' (Keefe 1998, p.575). I agree. Keefe continues: But although the measure of the underlying quantity may determine the applicability of the vague predicate, it does not follow that this measure is reflected in non-classical numerical truth-values … Are degree theorists thus mistaken in claiming that vague predicates come in degrees? I suggest that there is a sense in which F can be said to come in degrees—call it coming in degrees m —whenever there is a measure of the attribute F-ness, and where things …