Truthmakers and Consequence
We compare Tarski’s notion of logical consequence (preservation of truth) with that of Prawitz (transformability of warrants for assertion). The latter is our point of departure for a definition of consequence in terms of the transformability of truthmakers (verifications) relative to all models. A sentence’s Tarskian truth-in-M coincides with its having an M-relative truthmaker. An M-relative truthmaker serves as a winning strategy or game plan for player T in the ‘material game’ played on that sentence against the background of the model M. We enter conjectures about soundness and completeness of Classical Core Logic with respect to the notion of consequence that results when the domain is required to be decidable. We consider whether the truthmaker semantics threatens a slide to realism. We work with examples of core proofs whose premises are given M-relative truthmakers; and show how these can be systematically transformed into a truthmaker for the proof’s conclusion.