Proofs and Refutations
Proofs and Refutations first came to public notice as an article in the British Journal for the Philosophy of Science. Based on part of Lakatos’ Cambridge PhD thesis Essays in the Logic of Mathematical Discovery (which he completed in 1961) it was published in four parts during 1963 and 1964. Long though this essay was, it only dealt with the informal history of the Euler conjecture (see below). The objection that modern mathematics is formal and does not suffer the uncertainties and refutations of informal mathematics was therefore left unanswered. Later in his life Lakatos hoped to write a book on the philosophy of mathematics but, distracted by developments in the philosophy of science and troubled in his later years by ill health, he never managed to produce a manuscript. After his death John Worrall and Elie Zahar undertook to gather what material they considered to be suitable into a single volume in lieu of the proposed work. Thus the original British Journal essay together with selections from the PhD thesis were published in 1976 as Proofs and Refutations: the Logic of Mathematical Discovery. In their introduction the editors express the hope that the extra chapters can meet the objection that Lakatos’ work only applies to informal mathematics.