The seminar is cancelled.
In my book The Dialogical Roots of Deduction (CUP, 2020), I presented a dialogical account ofductive reasoning, drawing on findings from philosophy, history, psychology and cognitive science, and mathematical practice. According to this account, deductive arguments can be viewed as corresponding to dialogues between two (fictive) characters, Prover and Skeptic. Prover seeks to prove that the conclusion follows deductively from the premises, while Skeptic examines each step in the argument critically to ensure that it is valid and sufficiently clear. It turns out that these two characters, Prover and Skeptic, are not only fictive: they can be viewed as embodied by real-life mathematicians. Indeed, the Prover-Skeptic dialogues offer a compelling description of actual practices of proof in mathematics, such as peer review and (adversarial) collaboration. In this talk, I present a dialogical account of proofs in mathematical practices following the Prover-Skeptic dialogues, including a discussion of four case studies: the reception of Gödel's incompleteness results, Wiles' proof of Fermat's Last Theorem, a failed proof of the inconsistency of Peano Arithmetic, and Mochizuki's (purported) proof of the ABC conjecture.
