, Volume 187, Issue 3, pp 821-832
Date: 22 Apr 2011

Between proof and truth

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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.

An erratum to this article can be found at http://dx.doi.org/10.1007/s11229-011-0043-1.