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

Authors
Elia Zardini
Universidade de Lisboa
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.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-008-9156-z
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References found in this work BETA

Introduction to Non-Classical Logic.Graham Priest - 2001 - Cambridge University Press.
Fuzzy Logic and Approximate Reasoning.L. A. Zadeh - 1975 - Synthese 30 (3-4):407-428.
The Logic of Inexact Concepts.J. A. Goguen - 1969 - Synthese 19 (3-4):325-373.
The Justification of Deduction.Michael A. E. Dummett - 1974 - In Michael Dummett (ed.), Truth and Other Enigmas. Oxford University Press.

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Citations of this work BETA

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
Naive Modus Ponens.Elia Zardini - 2013 - Journal of Philosophical Logic 42 (4):575-593.
Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.

View all 40 citations / Add more citations

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