20th Amsterdam Colloquium, Amsterdam
According to the logical pluralist, there may be more than one legitimate answer to the question of whether a given deductive argument is valid. The pluralist faces a challenge, though, to explain how this could be so. In this paper I show that by adopting the ‘built-in opponent’ conception of deduction, a specific multi-agent dialogical account of our deductive practices, we can address the explanatory challenge: the different logics arise out of different norms effecting our argumentative and explanatory practices. In order to clarify our position we introduce Prover-Skeptic games, a novel kind of dialogue game introduced by Sørensen & Urzyczyn. Unlike traditional Lorenzen and Hintikka style dialogue games, theses are games of ‘proof-construction’ as opposed to ‘formula-evaluation’, and thus they connect up better with the built-in opponent view of our deductive practices. We give a uniform adequacy result for a class of substructural implicational logics relative to Prover-Skeptic games, with the changes in the structural rules in play being reflected in a uniform manner in the dialogue game.