Between proof and truth
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We consider two versions of truth as grounded in verification procedures: Dummett’s notion of proof as an effective way to establish the truth of a statement and Hintikka’s GTS notion of truth as given by the existence of a winning strategy for the game associated with a statement. Hintikka has argued that the two notions should be effective and that one should thus restrict one’s attention to recursive winning strategies. In the context of arithmetic, we show that the two notions do not coincide: on the one hand, proofs in PA do not yield recursive winning strategies for the associated game; on the other hand, there is no sound and effective proof procedure that captures recursive GTS truths. We then consider a generalized version of Game Theoretical Semantics by introducing games with backward moves. In this setting, a connection is made between proofs and recursive winning strategies. We then apply this distinction between two kinds of verificationist procedures to a recent debate about how we recognize the truth of Gödelian sentences.
- Bonnay D. (2004) Preuves et jeux sémantiques. Philosophia Scientiae 8(2): 105–123
- Coquand T. (1995) A semantics of evidence for classical arithmetic. Journal of Symbolic Logic 60(1): 325–337 CrossRef
- Dummett, M. (1978a). The philosophical basis of intuitionistic logic. In Truth and other enigmas London: Duckworth.
- Dummett, M. (1978b). The philosophical significance of Gödel’s theorem. In Truth and other enigmas, London: Duckworth.
- Hintikka J. (1996) The principles of mathematics revisited. Cambridge University Press, Boston CrossRef
- Krivine J. L. (2003) Dependent choice, ‘quote’ and the clock. Theoretical Computer Science 308: 259–276 CrossRef
- Milne P. (2007) On Gödel sentences and what they say. Philosophia Mathematica, III 15: 193–226 CrossRef
- Tennant N. (2002) Deflationism and the Gödel phenonmena. Mind 111(443): 551–582 CrossRef
- van Benthem, J. (2001). Logic in games, Lecture notes. Amsterdam: ILLC.
- Between proof and truth
Volume 187, Issue 3 , pp 821-832
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- Springer Netherlands
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- Game theoretical semantics
- Games with backward moves
- Recursive winning strategies
- Gödel’s sentence
- Logical consequence
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