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Imre Lakatos ((ハンガリー語:Lakatos Imre) (:ˈlɒkɒtoʃ ˈimrɛ); November 9, 1922 – February 2, 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes. ==Life== Lakatos was born Imre (Avrum) Lipschitz 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. He avoided Nazi persecution of Jews by changing his name to Imre Molnár. His mother and grandmother died in Auschwitz. He became an active communist during the Second World War. He changed his surname once again to ''Lakatos'' (Locksmith) in honor of Géza Lakatos. After the war, from 1947 he worked as a senior official in the Hungarian ministry of education. He also continued his education with a PhD at Debrecen University awarded in 1948, and also attended György Lukács's weekly Wednesday afternoon private seminars. He also studied at the Moscow State University under the supervision of Sofya Yanovskaya in 1949. When he returned, however, 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. More of Lakatos' activities in Hungary after World War II have recently become known. In fact, Lakatos was a hardline Stalinist and, despite his young age, had an important role between 1945 and 1950 (his own arrest and jailing) in building up the Communist rule, especially in cultural life and the academia, in Hungary.〔http://www.amazon.com/Chocolate-Chess-Unlocking-Lakatos-Bandy/dp/9630588196〕 After his release, Lakatos returned to academic life, doing mathematical research and 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 received a doctorate in philosophy in 1961 from the University of Cambridge. The book ''Proofs and Refutations: The Logic of Mathematical Discovery'', published after his death, is based on this work. Lakatos never obtained British Citizenship. In 1960 he was appointed to a position in the London School of Economics, 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. Published in 1970, the 1965 Colloquium included well-known speakers delivering papers in response to Thomas Kuhn's ''"The Structure of Scientific Revolutions"''. Lakatos remained at the London School of Economics until his sudden death in 1974 of a heart attack,〔Donald Gillies. ''Imre Lakatos. Paul K. Feyerabend. On the Threshold of Science: For and Against Method'', by Matteo Motterlini. ''The British Journal of the Philosophy of Science''. Vol. 47, No. 3, Sep., 1996. http://www.jstor.org/stable/687992〕 aged just 51. The Lakatos Award was set up by the school in his memory. 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,〔See Lakatos's 5 Jan 1971 letter to Paul Feyerabend p233-4 in Motterlini's 1999 ''For and Against Method''〕 after which it was then edited jointly for many years by his LSE colleagues John W. N. Watkins and John Worrall, Lakatos's ex-research assistant. His last LSE lectures in scientific method in Lent Term 1973 along with parts of his correspondence with his friend and critic Paul Feyerabend have been published in ''For and Against Method'' (ISBN 0-226-46774-0). Lakatos and his colleague Spiro Latsis organised an international conference devoted entirely to historical case studies in Lakatos's methodology of research programmes in physical sciences and economics, to be held in Greece in 1974, and which still went ahead following Lakatos's death in February 1974. These case studies in such as Einstein's relativity programme, Fresnel's wave theory of light and neoclassical economics, were published by Cambridge University Press in two separate volumes in 1976, one devoted to physical sciences and Lakatos's general programme for rewriting the history of science, with a concluding critique by his great friend Paul Feyerabend, and the other devoted to economics.〔These were respectively ''Method and Appraisal in the Physical Sciences: The Critical Background to Modern Science 1800-1905'' Colin Howson (Ed)and ''Method and Appraisal in Economics'' Spiro J. Latsis (Ed)〕 ==Proofs and refutations, mathematics== (詳細はHegel's and Marx's dialectic, by Karl Popper's theory of knowledge, and by the work of mathematician George Polya. The 1976 book ''Proofs and Refutations'' is based on the first three chapters of his four chapter 1961 doctoral thesis ''Essays in the logic of mathematical discovery''. But its first chapter is Lakatos's own revision of its chapter 1 that was first published as ''Proofs and Refutations'' in four parts in 1963-4 in ''The British Journal for the Philosophy of Science''. It is largely taken up by a fictional dialogue set in a mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties of polyhedra, namely that for all polyhedra the number of their (V)ertices minus the number of their (E)dges plus the number of their (F)aces is 2: (V – E + F = 2). The dialogue is meant to represent the actual series of attempted proofs which mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Often the students paraphrase famous mathematicians such as Cauchy, as noted in Lakatos's extensive footnotes. Lakatos termed the polyhedral counter examples to Euler's formula Monsters and distinguished three ways of handling these objects: Firstly, monster-barring, by which means the theorem in question could not be applied to such objects. Secondly, monster-adjustment whereby by making a re-appraisal of the monster it could be made to obey the proposed theorem. Thirdly, exception handling, a further distinct process. Interestingly, these distinct strategies has been taken up in qualitative physics, where the terminology of monsters has been applied to apparent counter-examples, and the techniques of monster-barring and monster-adjustment recognized as approaches to the refinement of the analysis of a physical issue. 〔(【引用サイトリンク】url=http://harveycohen.net/dragons/Lakatosian_Monsters.htm )〕 What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (If axioms are given for a branch of mathematics, however, Lakatos claimed that proofs from those axioms were tautological, i.e. logically true.)〔See, for instance, Lakatos' ''A renaissance of empiricism in the recent philosophy of mathematics'', section 2, in which he defines a Euclidean system to be one consisting of all logical deductions from an initial set of axioms and writes that "a Euclidean system may be claimed to be true".〕 Lakatos proposed an account of mathematical knowledge based on the idea of heuristics. In ''Proofs and Refutations'' the concept of 'heuristic' was not well developed, although Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs, and sometimes called his philosophy 'quasi-empiricism'. However, 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. Therefore, he fundamentally disagreed with the 'formalist' conception of proof which prevailed in Frege's and Russell's logicism, which defines proof simply in terms of ''formal'' validity. On its first publication as a paper in ''The British Journal for the Philosophy of Science'' in 1963-4, ''Proofs and Refutations'' became highly influential on new work in the philosophy of mathematics, although few agreed with Lakatos' 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. Lakatos, Worrall and Zahar use Poincaré (1893)〔Poincaré, H. (1893). "Sur la Généralisation d'un Théorème d'Euler relatif aux Polyèdres", ''Comptes Redus de Seances de l'Academie des Sciences'', 117 p. 144, as cited in Lakatos, Worrall and Zahar, p. 162〕 to answer one of the major problems perceived by critics, namely that the pattern of mathematical research depicted in ''Proofs and Refutations'' does not faithfully represent most of the actual activity of contemporary mathematicians.〔Lakatos, Worrall and Zahar (1976), ''Proofs and Refutations'' ISBN 0-521-21078-X, pp. 106-126, note that Poincaré's formal proof (1899) "Complèment à l'Analysis Situs", ''Rediconti del Circolo Matematico di Palermo'', 13, pp. 285-343, rewrites Euler's conjecture into a tautology of vector algebra.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Imre Lakatos」の詳細全文を読む スポンサード リンク
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