Abstract

In his philosophical history of nineteenth-century mathematics, Proofs and Persuasions: The Logic of Mathematical Discovery, Imre Lakatos asserts that mathematical criticism was the driving force in the growth of mathematical knowledge during the nineteenth century, and provided the impetus for some of the deepest conceptual reformulations of the century. The philosophy of mathematics represented by Proofs and Refutations also presents a rich analysis of how mathematics can be thought of as an essentially historical discipline. Despite protestations by Lakatos that he completely discarded Hegel when he discovered the work of Karl Popper, his philosophy of error closely resembles Hegel's in the Phenomenology of Spirit. According to Lakatos, the impact of proofs and refutations on naive concepts is to erase them completely and replace them by proof-generated concepts. His historical point about proofs and refutations is that this pattern in the growth of mathematical knowledge is a relatively recent innovation. Hegel's and Lakatos' shared vision of theoretical knowledge is that rather than being the inspired work of timeless, totally subjective, intellectual intuition , it is, more often than not, mediated by a lengthy history of speculation and failure