A Unification of Two Approaches to Vagueness: The Boolean Many-Valued Approach and the Modal-Precisificational Approach

Journal of Philosophical Logic 46 (4):419-441 (2017)
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Abstract

The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity and truth, but while the fuzzy-logic approach postulates linearly-ordered values between 0 and 1, the Boolean approach assigns to sentences values in a many-element complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a sentence is indeterminate in truth value in some world, it is taken to be true in one precisified world accessible from that world and false in another. This paper points to a way to unify these two approaches to vagueness by showing that Fine’s version of the modal-precisificational approach can be combined with the Boolean many-valued approach instead of supervaluationism, one of the most popular approaches to vagueness.

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Ken Akiba
Virginia Commonwealth University

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References found in this work

Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - New York: Cambridge University Press.
First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
Vagueness.Timothy Williamson - 1995 - British Journal for the Philosophy of Science 46 (4):589-601.

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