Vagueness and blurry sets

Journal of Philosophical Logic 33 (2):165-235 (2004)
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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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Author's Profile

Nicholas J. J. Smith
University of Sydney

Citations of this work

A model of tolerance.Elia Zardini - 2008 - Studia Logica 90 (3):337-368.
Worldly indeterminacy: A rough guide.Nicholas J. J. Smith & Gideon Rosen - 2004 - Australasian Journal of Philosophy 82 (1):185 – 198.
Vagueness and endurance.E. J. Lowe - 2005 - Analysis 65 (2):104-112.
Vagueness as closeness.Nicholas J. J. Smith - 2005 - Australasian Journal of Philosophy 83 (2):157 – 183.
The Sorites Paradox in Practical Philosophy.Hrafn Asgeirsson - 2019 - In Sergi Oms & Elia Zardini (eds.), The Sorites Paradox. New York, NY: Cambridge University Press. pp. 229–245.

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References found in this work

Vagueness.Timothy Williamson - 1996 - New York: Routledge.
Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Vagueness.Timothy Williamson - 1995 - British Journal for the Philosophy of Science 46 (4):589-601.

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