, Volume 148, Issue 3, pp 507–524 | Cite as

Meaning Approached Via Proofs

  • Dag PrawitzEmail author


According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence.


Main Idea Main Part Simple Structure Logical Basis Natural Deduction 
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  1. Church, A. 1956Introduction to Mathematical LogicPrinceton University PressPrincetonGoogle Scholar
  2. Cozzo, C. 1994Meaning and ArgumentAlmqvist & WiksellStockholmGoogle Scholar
  3. Dummett, M.: 1973, The Justification of Deduction, The British Academy, London (republished in M. Dummett, Truth and Other Enigmas, Duckworth, London 1978).Google Scholar
  4. Dummett, M.: 1976, ‘What is a Theory of Meaning II’, in G. Evans et al. (eds.), Truth and Meaning, Oxford, pp. 67–137 (republished in M. Dummett, The Seas of Language, Clarendon Press, Oxford 1993).Google Scholar
  5. Dummett, M.: 1983, ‘Language and Truth’, in R. Harris (ed.), Approaches to Language, Oxford (republished in M. Dummett, The Seas of Language, Clarendon Press, Oxford 1993).Google Scholar
  6. Dummett, M. 1991The Logical Basis of MetaphysicsDuckworthLondonGoogle Scholar
  7. Gentzen, G.: 1934, ‘Untersuchungen Über das Logische Schließen’, Mathematische Zeitschrift 39, 176–210 and 405–431.Google Scholar
  8. Kreisel, G.,  et al. 1962‘Foundations of Intuitionistic Logic’Nagel, E. eds. Logic, Methodology and Philosophy of ScienceStanford University PressStanford198210Google Scholar
  9. Martin-Löf, P.: 1985, ‘On the Meanings of the Logical Constants and the Justification of the Logical Laws’, in Atti degli Incontri di Logica Matematica, Siena, Vol. 2, pp. 203–281 (reprinted in Nordic Journal of Philosophical Logic 1, 11–60).Google Scholar
  10. Martin-Löf, P.,  et al. 1995‘Verificationism Then and Now’Köhler, E. eds. The Foundational Debate: Complexity and Constructivity in Mathematics and PhysicsKluwerDordrecht187196Google Scholar
  11. Martin-Löf, P. 1998‘Truth and Knowability: on the PrinciplesC and K of Michael Dummett’Dales, H. G.Olivieri, G. eds. Truth in MathematicsClarendon PressOxford105114Google Scholar
  12. Prawitz, D. 1971‘Ideas and Results in Proof Theory’Fenstad, J. E. eds. Proceedings of the Second Scandinavian Logic SymposiumNorth-HollandAmsterdam235307Google Scholar
  13. Prawitz, D.,  et al. 1973‘Towards a Foundation of a General Proof Theory’Suppes, P. eds. Logic, Methodology, and Philosophy of Science IVNorth-HollandAmsterdam225250Google Scholar
  14. Prawitz, D. 1974‘On the Idea of a General Proof Theory’Synthese.276377CrossRefGoogle Scholar
  15. Prawitz, D. 1987‘Dummett on a Theory of Meaning’Taylor, B. eds. Michael Dummett, Contributions to PhilosophyKluwerDordrecht117165Google Scholar
  16. Prawitz, D. 1995‘Quine and Verificationism’Inquiry.37487494CrossRefGoogle Scholar
  17. Prior, A. N.: 1960, ‘The Runabout Inference-Ticket’, Analysis 24.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of PhilosophyStockholm UniversityStockholmSweden

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