A Modality Called ‘Negation’

Mind 124 (495):761-793 (2015)
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Abstract

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds

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Author's Profile

Franz Berto
University of St. Andrews

Citations of this work

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References found in this work

Situations and attitudes.Jon Barwise & John Perry - 1981 - Journal of Philosophy 78 (11):668-691.
Philosophy of logic.Willard Van Orman Quine - 1986 - Cambridge: Harvard University Press. Edited by Simon Blackburn & Keith Simmons.
In contradiction: a study of the transconsistent.Graham Priest - 1987 - New York: Oxford University Press.
Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
Situations and Attitudes.Jon Barwise & John Perry - 1983 - Cambridge, Mass.: MIT Press. Edited by John Perry.

View all 90 references / Add more references