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Negation, Absurdity and Contrariety

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What is Negation?

Part of the book series: Applied Logic Series ((APLS,volume 13))

Abstract

I argue for a rule-based account of negation answering to both constructivist and relevantist demands. We can give such an account in terms of basic contrarieties, and by co-inductively defining proofs and disproofs, without having to make explicit appeal to the absurdity constant ┴. If we do make such an appeal, it is to ┴ only as a structural punctuation marker within deductions, a device that allows us to assimilate disproofs to the general class of proofs. ┴ does not, in this rôle, need to be governed by any ‘introduction’ or ‘elimination’ rules of its own. Nor does ┴ need to be treated as a propositional constant eligible for embedding within other sentences. But even if we do treat ┴ as an embeddable propositional constant, it does not follow that negation can, let alone should, be defined in terms of it. Negation should be taken as primitive, and one should explain how a grasp of its sense arises from one’s prior grasp of primitive metaphysical contrarieties within an interpreted language.

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© 1999 Springer Science+Business Media Dordrecht

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Tennant, N. (1999). Negation, Absurdity and Contrariety. In: Gabbay, D.M., Wansing, H. (eds) What is Negation?. Applied Logic Series, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9309-0_10

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  • DOI: https://doi.org/10.1007/978-94-015-9309-0_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5169-1

  • Online ISBN: 978-94-015-9309-0

  • eBook Packages: Springer Book Archive

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