A model of tolerance

Studia Logica 90 (3):337-368 (2008)
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Abstract

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non- existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the consequence relation. A lattice-theoretical framework for a whole family of “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic.

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Elia Zardini
Complutense University of Madrid

References found in this work

Introduction to Non-Classical Logic.Graham Priest - 2001 - Cambridge and New York: Cambridge University Press.
Anti-realism and logic: truth as eternal.Neil Tennant - 1987 - New York: Oxford University Press.
The justification of deduction.Michael Dummett - 1973 - In Truth and Other Enigmas. London: Oxford University Press.
An Introduction to Non-Classical Logic.Graham Priest - 2001 - Bulletin of Symbolic Logic 12 (2):294-295.
Fuzzy logic and approximate reasoning.L. A. Zadeh - 1975 - Synthese 30 (3-4):407-428.

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