Topoi

, Volume 13, Issue 2, pp 127–133

Intuitionistic mathematics does not needex falso quodlibet

  • Neil Tennant
Article
  • 90 Downloads

Abstract

We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.

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References

  1. Milne, P.: 1994, ‘Intuitionistic Relevant Logic and Perfect Validity’,Analysis (in press).Google Scholar
  2. Prawitz, D.: 1965,Natural Deduction: A Proof-Theoretical Study, Almqvist and Wiksell, Stockholm.Google Scholar
  3. Tennant, N.: 1978,Natural Logic, Edinburgh University Press, Edinburgh.Google Scholar
  4. Tennant, N.: 1980, ‘A Proof-Theoretic Approach to Entailment’,Journal of Philosophical Logic 9, 185–209.CrossRefGoogle Scholar
  5. Tennant, N.: 1984, ‘Perfect Validity, Entailment and Paraconsistency’,Studia Logica 43, 179–198.CrossRefGoogle Scholar
  6. Tennant, N.: 1987a, ‘Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic’,Journal of Symbolic Logic 52, 665–680.CrossRefGoogle Scholar
  7. Tennant, N.: 1987b,Anti-Realism and Logic, Clarendon Press, Oxford.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Neil Tennant
    • 1
  1. 1.The Ohio State University and Churchill CollegeCambridge

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