Fuzzy Logic and Higher-Order Vagueness

In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications. pp. 1--19 (2011)

Authors
Nicholas J. J. Smith
University of Sydney
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.
Keywords vagueness  fuzzy logic
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Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Vagueness and Contradiction.Roy Sorensen - 2005 - Philosophy and Phenomenological Research 71 (3):695-703.
Theory Change and the Indeterminacy of Reference.Hartry Field - 1973 - Journal of Philosophy 70 (14):462-481.
On the Coherence of Vague Predicates.Crispin Wright - 1975 - Synthese 30 (3-4):325--65.

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