Article Title：Vagueness and blurry sets
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 S-1 to the effect that 'Bob is bald' is x true, for x in [0,1], there should be a further statement S-2 which tells us how true S-1 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 su 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, 0.3), 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.
Keywords: blurry sets; degree functions; degrees of truth; fuzzy logic; fuzzy sets; higher-order vagueness; logic; sorites paradox; truth; type n fuzzy logic; vagueness
DOI: 10.1023/B:LOGI.0000021717.26376.3f
Source：JOURNAL OF PHILOSOPHICAL LOGIC
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