Proofs and what they’re good for

Greg Restall (University of Melbourne)

Abstract: I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof, including (1) how it is that a proof transmits warrant (2) Lewis Carroll’s dilemma concerning Achilles and the Tortoise and the coherence of questioning basic proof rules like modus ponens, and (3) how we can avoid logical omniscience without committing ourselves to inconsistency.