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

Authors
Franz Berto
University of St. Andrews
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
Keywords Negation  Logical pluralism  Modality  Possible worlds semantics  Compatibility semantics
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DOI 10.1093/mind/fzv026
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References found in this work BETA

Situations and Attitudes.Jon Barwise & John Perry - 1981 - Journal of Philosophy 78 (11):668-691.
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In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
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Citations of this work BETA

HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
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A Survey of Logical Realism.Tuomas E. Tahko - 2021 - Synthese 198 (5):4775-4790.
There is More to Negation Than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.

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