David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 90 (3):337 - 368 (2008)
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 (zeroth-order) “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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References found in this work BETA
Graham Priest (2001). Introduction to Non-Classical Logic. Cambridge University Press.
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Citations of this work BETA
Elia Zardini (2013). Naive Modus Ponens. Journal of Philosophical Logic 42 (4):575-593.
David Ripley (2015). Anything Goes. Topoi 34 (1):25-36.
Pablo Cobreros, Paul Egré, David Ripley & Robert Rooij (2012). Tolerance and Mixed Consequence in the S'valuationist Setting. Studia Logica 100 (4):855-877.
Paul Égré (forthcoming). Vagueness: Why Do We Believe in Tolerance? Journal of Philosophical Logic:1-17.
Elia Zardini (2014). Context and Consequence. An Intercontextual Substructural Logic. Synthese 191 (15):3473-3500.
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