Skip to main content
Log in

Meaning Approached Via Proofs

Synthese Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • A. Church (1956) Introduction to Mathematical Logic Princeton University Press Princeton

    Google Scholar 

  • C. Cozzo (1994) Meaning and Argument Almqvist & Wiksell Stockholm

    Google Scholar 

  • Dummett, M.: 1973, The Justification of Deduction, The British Academy, London (republished in M. Dummett, Truth and Other Enigmas, Duckworth, London 1978).

  • 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).

  • 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).

  • M. Dummett (1991) The Logical Basis of Metaphysics Duckworth London

    Google Scholar 

  • Gentzen, G.: 1934, ‘Untersuchungen Über das Logische Schließen’, Mathematische Zeitschrift 39, 176–210 and 405–431.

    Google Scholar 

  • G. Kreisel (1962) ‘Foundations of Intuitionistic Logic’ E. Nagel (Eds) et al. Logic, Methodology and Philosophy of Science Stanford University Press Stanford 198–210

    Google Scholar 

  • 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).

  • P. Martin-Löf (1995) ‘Verificationism Then and Now’ E. Köhler (Eds) et al. The Foundational Debate: Complexity and Constructivity in Mathematics and Physics Kluwer Dordrecht 187–196

    Google Scholar 

  • P. Martin-Löf (1998) ‘Truth and Knowability: on the PrinciplesC and K of Michael Dummett’ H. G. Dales G. Olivieri (Eds) Truth in Mathematics Clarendon Press Oxford 105–114

    Google Scholar 

  • D. Prawitz (1971) ‘Ideas and Results in Proof Theory’ J. E. Fenstad (Eds) Proceedings of the Second Scandinavian Logic Symposium North-Holland Amsterdam 235–307

    Google Scholar 

  • D. Prawitz (1973) ‘Towards a Foundation of a General Proof Theory’ P. Suppes (Eds) et al. Logic, Methodology, and Philosophy of Science IV North-Holland Amsterdam 225–250

    Google Scholar 

  • D. Prawitz (1974) ArticleTitle‘On the Idea of a General Proof Theory’ Synthese. 27 63–77 Occurrence Handle10.1007/BF00660889

    Article  Google Scholar 

  • D. Prawitz (1987) ‘Dummett on a Theory of Meaning’ B. Taylor (Eds) Michael Dummett, Contributions to Philosophy Kluwer Dordrecht 117–165

    Google Scholar 

  • D. Prawitz (1995) ArticleTitle‘Quine and Verificationism’ Inquiry. 37 487–494 Occurrence Handle10.1080/00201749408602369

    Article  Google Scholar 

  • Prior, A. N.: 1960, ‘The Runabout Inference-Ticket’, Analysis 24.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dag Prawitz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prawitz, D. Meaning Approached Via Proofs. Synthese 148, 507–524 (2006). https://doi.org/10.1007/s11229-004-6295-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-004-6295-2

Keywords

Navigation