The Games of Logic and the Games of Inquiry*

Abstract

Truth-definitions play a crucial role in the foundations of logic and semantics. Tarsik-type truth-definitions are not possible to formulate in a usual first-order language for itself, and they have been criticized because they do not account for what makes them definitions of truth. It has been suggested that truth should instead be characterized by reference to the «language-games» of verification and falsification. The author's game-theoretical semantics (GTS) here explained for formal first-order languages, can be thought of as a realization of this idea. More technically speaking, GTS can also be thought of as a systematization of the well-known aepsilon-delta, definitions in the foundations of analysis. In GTS, truth is not defined by reference to winning a play of a game, but as the existence of a winning strategy in the game for the verifier. In a first-order language, the game-theoretical truth-condition of a sentence S can accordingly be expressed by an explicit second-order (sigma-one-one) sentence asserting the existence of the Skolem function of S. The semantical games of GTS must be distinguished not only from the «games» of formal proof (which serve to establish logical rather than material truth) but also from the «games» in volved in our ordinary activities of verification and falsification. The latter have been modelled as games of inquiry by the author, and they are essentially epistemic games where the meaning of truth is taken for granted and where the aim of the game is to come to know certain truths. To assimilate them to the semantical games constitutive of (material) truth is a form of Meno's paradox.