Logic after Wittgenstein

Wittgenstein's later rejection of the externalist Tractarian picture of logic according to which all rationally analysable discourse is properly understood as truth-functional rules out any conception of logic as the study of universal features of discourse. Given later references to 'the logic of our language', some conception of logic appears to survive even on Wittgenstein's later view. However, given his rejection of any conception of philosophical theory as explanatory or hypothetical, Wittgenstein seems to be forced into descriptivism. Despite these constraints, I attempt to show that a valuable account of logic consistent with Wittgenstein's critique can be identified. That possibility raises the question: can any conception of formal logic as valuable modulo natural language survive Wittgenstein's later change of heart? Taking Wittgenstein's rejection of Tractarian conceptions seriously, logic is relativised to language-games in general and, perhaps, localised to particular language-games. Looking at logic in this way opens up the possibility of uncovering inferential structures distinct from those which form the traditional logical-epistemological dichotomy. Here I outline a formal logical framework consistent with all of the foregoing points in terms of which analogues of inferential structures (traditional and non-traditional) can be constructed. Taking third-person ascriptions of psychological predicates as a testcase, I try to show that the formal framework (a system of formal dialogue) has a flexibility which augurs well for future logical investigations into linguistic practices without presupposing knowledge of the kinds of inferential structures which such investigations might reveal. Hence, my claim that the system in question represents logic after (the later) Wittgenstein.