KNOWLEDGE VS. INQUIRY: COMMENT ON BRENDAN LARVOR'S CRITICISM OF HEGEL'S PHILOSOPHY OF MATHEMATICS

abstract

I agree with Brendan Larvor that Hegel "radically misunderstood the nature of mathematics"--a misunderstanding that derived from his failure to appreciate the heuristic side of the discipline. Larvor fruitfully utilizes Imre Lakatos' more balanced interpretation of mathematical inquiry, but he does not point out that Lakatos did not explicitly disavow Popper's epistemological Darwinism. I argue that only a theory of CORRECTION, whose principles are not to be found in the Darwinian approach, will provide an adequate framework both for a theory of productive inquiry in philosophy of science, and for a plausible interpretation of dialectic in Hegel's logic.