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Negation on the Australian Plan

Journal of Philosophical Logic volume 48, pages 1119–1144 (2019)Cite this article

Abstract

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.

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Authors and Affiliations

  1. Department of Philosophy, University of St Andrews, St Andrews, UK

    Francesco Berto

  2. Institute for Logic, Language and Computation (ILLC), University of Amsterdam, Amsterdam, The Netherlands

    Francesco Berto

  3. Department of Philosophy, University of Melbourne, Melbourne, Australia

    Greg Restall

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  1. Francesco Berto
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Correspondence to Francesco Berto.

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Berto, F., Restall, G. Negation on the Australian Plan. J Philos Logic 48, 1119–1144 (2019). https://doi.org/10.1007/s10992-019-09510-2

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Keywords

  • Negation
  • Compatibility semantics
  • Kripke semantics
  • Non-classical logics
  • Many-valued logics
  • Modal logics