Imre Lakatos

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Lore & Background

Lakatos was born Imre Lipsitz to a Jewish family in Debrecen, Hungary, in 1922. He received a degree in mathematics, physics, and philosophy from the University of Debrecen in 1944. In March 1944, the Germans invaded Hungary, and Lakatos, along with Éva Révész, his then-girlfriend and subsequent wife, formed a Marxist resistance group. In May of that year, the group was joined by Éva Izsák, a 19-year-old Jewish antifascist activist. Lakatos, considering that there was a risk that she would be captured and forced to betray them, decided that her duty to the group was to commit suicide; a member of the group took her to Debrecen and gave her cyanide. During the occupation, Lakatos avoided Nazi persecution by changing his surname to Molnár. His mother and grandmother were murdered in Auschwitz. He changed his surname once again to Lakatos in honor of Géza Lakatos. After the war, from 1947, he worked as a senior official in the Hungarian Ministry of Education. He earned a PhD at Debrecen University in 1947 and attended György Lukács's weekly Wednesday afternoon private seminars. He studied at Moscow State University under Sofya Yanovskaya in 1949. When he returned, he found himself on the losing side of internal arguments within the Hungarian communist party and was imprisoned on charges of revisionism from 1950 to 1953. Lakatos was a hardline Stalinist and had an important role between 1945 and 1950 in building up Communist rule, especially in cultural life and academia. After his release, he returned to academic life, translating George Pólya's How to Solve It into Hungarian. Still nominally a communist, his political views had shifted markedly, and he was involved with at least one dissident student group in the lead-up to the 1956 Hungarian Revolution. After the Soviet Union invaded Hungary in November 1956, Lakatos fled to Vienna and later reached England. He lived there for the rest of his life but never achieved British citizenship. He received a PhD in philosophy in 1961 from the University of Cambridge; his doctoral thesis was entitled Essays in the Logic of Mathematical Discovery, and his doctoral advisor was R. B. Braithwaite. The book Proofs and Refutations: The Logic of Mathematical Discovery, published after his death, is based on this work. In 1960, he was appointed to a position in the London School of Economics (LSE), where he wrote on the philosophy of mathematics and the philosophy of science. The LSE philosophy of science department at that time included Karl Popper, Joseph Agassi and J. O. Wisdom. It was Agassi who first introduced Lakatos to Popper under the rubric of his applying a fallibilist methodology of conjectures and refutations to mathematics in his Cambridge PhD thesis. With co-editor Alan Musgrave, he edited the often cited Criticism and the Growth of Knowledge, the Proceedings of the International Colloquium in the Philosophy of Science, London, 1965. In January 1971, he became editor of the British Journal for the Philosophy of Science, which J. O. Wisdom had built up before departing in 1965, and he continued as editor until his death in 1974. Lakatos and his colleague Spiro Latsis had organized an international conference in Greece in 1975, and it went ahead despite his death. It was devoted entirely to historical case studies in Lakatos's methodology of research programmes in the physical sciences and economics. He remained at LSE until his sudden death in 1974 of a heart attack at the age of 51. The Lakatos Award was set up by the school in his memory. His last lectures along with parts of his correspondence with Paul Feyerabend have been published in For and Against Method.

Reader's Guide

Lakatos's philosophy of mathematics was inspired by both Hegel's and Marx's dialectic, by Karl Popper's theory of knowledge, and by the work of mathematician George Pólya. The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery. Its first chapter is Lakatos's own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–64 in the British Journal for the Philosophy of Science. It is largely taken up by a fictional dialogue set in a mathematics class, where students attempt to prove the formula for the Euler characteristic in algebraic topology (V − E + F = 2). The dialogue represents the actual series of attempted proofs that mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Lakatos termed the polyhedral counterexamples to Euler's formula monsters and distinguished three ways of handling these objects: monster-barring, monster-adjustment, and exception handling. What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. He proposed an account of mathematical knowledge based on the idea of heuristics. He also conceived of the mathematical community as carrying on a kind of dialectic to decide which mathematical proofs are valid and which are not, fundamentally disagreeing with the 'formalist' conception of proof that prevailed in Frege's and Russell's logicism. On its first publication as an article in 1963–64, Proofs and Refutations became highly influential on new work in the philosophy of mathematics, although few agreed with Lakatos's strong disapproval of formal proof. Before his death, he had been planning to return to the philosophy of mathematics and apply his theory of research programmes to it. In a 1966 text Cauchy and the continuum, Lakatos re-examines the history of the calculus, with special regard to Augustin-Louis Cauchy and the concept of uniform convergence, in the light of non-standard analysis. Lakatos is critical of those who would see Cauchy's proof, with its failure to make explicit a suitable convergence hypothesis, merely as an inadequate approach to Weierstrassian analysis.

Did You Know?

• Lakatos changed his surname to Molnár to avoid Nazi persecution during the German occupation of Hungary; his mother and grandmother were murdered in Auschwitz.
• He was imprisoned on charges of revisionism from 1950 to 1953 after finding himself on the losing side of internal arguments within the Hungarian communist party.
• Lakatos never achieved British citizenship despite living in England for the rest of his life after fleeing the 1956 Soviet invasion of Hungary.
• His doctoral advisor at the University of Cambridge was R. B. Braithwaite, and his 1961 PhD thesis was titled Essays in the Logic of Mathematical Discovery.
• The Lakatos Award was established by the London School of Economics in his memory after his sudden death from a heart attack at age 51.