Vagueness and Blurry Sets
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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.