**Topic:**

**HUMAN SEMANTICS**

## Vagueness and Blurry Sets

By Nicholas J. J. Smith

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 xtrue, for xin [0,1], there should be a further statement S2which 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 Pas ablurry 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 [lang] 0.3,0.2 [rang] , for example, represents the degree to which it is true to say that it is 0.2 true that ois Pto 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 nfuzzy logic, vagueness

Source: Journal of Philosophical Logic

Read it

Posted by Tony Marmo
at 06:12 BST