Semantic closure

Studia Logica 43 (1-2):117 - 129 (1984)
Abstract
This paper argues for tlie claims that a) a natural language such as English is semanticaly closed b) semantic closure implies inconsistency. A corollary of these is that the semantics of English must be paraconsistent. The first part of the paper formulates a definition of semantic closure which applies to natural languages and shows that this implies inconsistency. The second section argues that English is semeantically closed. The preceding discussion is predicated on the assumption that there are no truth value gaps. The next section of the paper considers whether the possibility of these makes any difference to the substantive conclusions of the previous sections, and argues that it does not. The crux of the preceding arguments is that none of the consistent semantical accounts that have been offered for solving the semantical paradoxes is a semantic ofEnglish. The final section of the paper produces a general argument as to why this must always be the case.
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DOI 10.1007/BF00935745
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References found in this work BETA
Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Semantical Paradox.Tyler Burge - 1979 - Journal of Philosophy 76 (4):169-198.
Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.

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Citations of this work BETA
A System of Paraconsistent Logic Equipped with Classical Negation.Toshiharu Waragai & Hitoshi Omori - 2009 - Journal of the Japan Association for Philosophy of Science 36 (1):9-18.
Richard (Routley) Sylvan: Writings on Logic and Metaphysics.Dominic Hyde - 2001 - History and Philosophy of Logic 22 (4):181-205.

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