David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Philosophical Logic 33 (2):165-235 (2004)
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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References found in this work BETA
Timothy Williamson (1994). Vagueness. Routledge.
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Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
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Nicholas J. J. Smith (2008). Vagueness and Degrees of Truth. Oxford University Press.
Citations of this work BETA
Elia Zardini (2008). A Model of Tolerance. Studia Logica 90 (3):337 - 368.
Nicholas J. J. Smith (2005). Vagueness as Closeness. Australasian Journal of Philosophy 83 (2):157 – 183.
Giovanni Boniolo & Silvio Valentini (2008). Vagueness, Kant and Topology: A Study of Formal Epistemology. Journal of Philosophical Logic 37 (2):141 - 168.
Maureen Donnelly (2009). Mereological Vagueness and Existential Vagueness. Synthese 168 (1):53 - 79.
Patrick Grim (2005). The Buried Quantifier: An Account of Vagueness and the Sorites. Analysis 65 (286):95–104.
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