Vagueness and Blurry Sets
Smith (Nicholas J.J.)
Source: Journal of Philosophical Logic 33 (2004) 165-235
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Philosophers Index Abstract

    This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S1 to the effect that 'Bob is bald' is x true, for x in [0,1], there should be a further statement S2 which tells us how true S1 is, and so on---that is, it accommodates higher-order vagueness---without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic---as opposed to the semantics---of vague discourse is classical. I model the extension of a vague predicate P as a BLURRY SET, this being a function which assigns a degree of membership or DEGREE FUNCTION to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence (0.3,0.2), for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.

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