Fuzzy Logic and Higher-Order Vagueness

In Petr Cintula, Chris Fermüller, Lluis Godo & Petr Hájek (eds.), Logical Models of Reasoning with Vague Information. pp. 1--19 (2011)
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Abstract

The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need to understand the true nature and source of the problem. Two possible sources are discussed: the problem stems from the very nature of vagueness—from the defining features of vague predicates; or the problem stems from the way in which the meanings of predicates are determined—by the usage of speakers together with facts about their environment and so on. I argue that the latter is the true source of the problem, and on this basis that fuzzy plurivaluationism is the correct solution.

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Nicholas J. J. Smith
University of Sydney

References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Vagueness and contradiction.Roy A. Sorensen - 2001 - New York: Oxford University Press.
Theory change and the indeterminacy of reference.Hartry Field - 1973 - Journal of Philosophy 70 (14):462-481.
Vagueness and Contradiction.Roy Sorensen - 2005 - Philosophy and Phenomenological Research 71 (3):695-703.
On the coherence of vague predicates.Crispin Wright - 1975 - Synthese 30 (3-4):325--65.

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