Denis Bonnay

Hintikka makes a distinction between two kinds of games: truthconstituting games and truth-seeking games. His well-known game-theoretical semantics for first-order classical logic and its independence-friendly extension belongs to the first class of games. In order to ground Hintikka’s claim that truth-constituting games are genuine verification and falsification games that make explicit the language games underlying the use of logical constants, it would be desirable to establish a substantial link between these two kinds of games. Adapting a result from Thierry Coquand, we propose such a link, based on a slight modification of Hintikka’s games, in which we allow backward playing for ∃loïse. In this new setting, it can be proven that sequent rules for first-order logic, including the cut rule, are admissible, in the sense that for each rule, there exists an algorithm which turns winning strategies for the premisses into a winning strategy for the conclusion. Thus, proofs, as results of truth-seeking games, can be seen.

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities

L’A. revient, dans le prolongement de son ouvrage L’anthropologie logique de Quine (qui plaçait l’accent sur la traduction, la logique et le principe de charité chez Quine) sur un élément souvent négligé de la thèse d’indétermination de la traduction, à savoir la reconstruction/identification des connecteurs logiques par l’assentiment et le dissentiment. Après avoir examiné diverses objections à l’utilisation par Quine des « fonctions de verdict » dans la traduction, l’A. en vient à la véritable motivation de Quine dans son recours à l’assentiment, qui émerge dans l’ouvrage méconnu the roots of reference. Quine revient, par cet usage de l’assentiment, à la question de l’analyticité et à sa critique des « Deux dogmes », qu’il nuance, dans son oeuvre tardive, par la suggestion d’une analyticité non seulement naturalisée, mais socialisée.