A modality called 'negation'

Francesco Berto*

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 (the admissible) negations. The approach unifies in a philosophically motivated picture the following results: nothing can be called a negation properly if it does not satisfy (Minimal) 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.

Original languageEnglish
Pages (from-to)761-793
Number of pages33
JournalMind
Volume124
Issue number495
DOIs
Publication statusPublished - 3 Jun 2015

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Modality
Negation
Compatibility
Split
Quantifiers
Logical Pluralism
Logic
Encoding
Double Negation
Operator
Accessibility
Modal Operators
Constructivist

ASJC Scopus subject areas

  • Philosophy

Cite this

A modality called 'negation'. / Berto, Francesco.

In: Mind, Vol. 124, No. 495, 03.06.2015, p. 761-793.

Research output: Contribution to journalArticle

Berto, F 2015, 'A modality called 'negation'', Mind, vol. 124, no. 495, pp. 761-793. https://doi.org/10.1093/mind/fzv026
Berto, Francesco. / A modality called 'negation'. In: Mind. 2015 ; Vol. 124, No. 495. pp. 761-793.
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