Proofs as Dialogues: The Enduring Significance of Lakatos for the Philosophy of Mathematical Practice
摘要
This paper discusses the enduring significance of Lakatos’ account of mathematical knowledge in in Proofs and Refutations for the philosophy of mathematical practice. While the account has been criticized for being historically inaccurate and for relying on contentious (idealist) assumptions, I argue that it remains an insightful source for philosophers of mathematical practice. In particular, I spell out how Lakatosian proofs and refutations have inspired the formulation of a dialogical account of deduction and mathematical proof, as presented in my book The Dialogical Roots of Deduction. In particular, Lakatos’ account provides the conceptual tools for an analysis of the intricate interplay between adversariality and cooperation in practices of mathematical proof. I conclude by highlighting some of the differences between Lakatos’ Hegelian idealism and the pragmatism that underpins my dialogical account of deduction.