1999 | OriginalPaper | Buchkapitel
Negation, Absurdity and Contrariety
verfasst von : Neil Tennant
Erschienen in: What is Negation?
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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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.