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Imre Lakatos
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Imre Lakatos (November 9, 1922 – February 2, 1974) was a philosopher of mathematics and science, most famous today worldwide for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations', and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes.
tos was born Imre (Avrum) Lipschitz to a Jewish family in Debrecen, Hungary in 1922.
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Imre Lakatos (November 9, 1922 – February 2, 1974) was a philosopher of mathematics and science, most famous today worldwide for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations', 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 last name 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.
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, published after his death, is based on this work.
Lakatos never obtained British Citizenship, in effect remaining stateless.
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 John Watkins. 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 highly-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 brain haemorrhage, aged just 51. The Lakatos Award was set up by the school in his memory.
In January 1971 he became editor of the internationally prestigious British Journal for the Philosophy of Science until his death in 1974, after which it was then edited jointly for many years by his LSE colleagues John 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.
Proofs and refutations
Lakatos' philosophy of mathematics was inspired by both Hegel's and Marx' dialectic, Karl Popper's theory of knowledge, and the work of mathematician George Polya.
The book Proofs and Refutations is based on his doctoral thesis. 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. 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 'quote' famous mathematicians such as Cauchy.
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.)
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 publication in 1976, 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. One of the major problems perceived by critics is that the pattern of mathematical research depicted in Proofs and Refutations does not faithfully represent most of the actual activity of contemporary mathematicians.
Research programmes
Lakatos' contribution to the philosophy of science was an attempt to resolve the perceived conflict between Popper's falsificationism and the revolutionary structure of science described by Kuhn. Popper's theory as often reported (inaccurately)
implied that scientists should give up a theory as soon as they encounter any falsifying evidence, immediately replacing it with increasingly 'bold and powerful' new hypotheses. However, Kuhn described science as consisting of periods of normal science in which scientists continue to hold their theories in the face of anomalies, interspersed with periods of great conceptual change. Popper acknowledged that excellent new theories may be inconsistent with apparently empirically well supported older theories. For example, he pointed out in Objective Knowledge (p.200) that Newton's theories were inconsistent with Kepler's third law. However, whereas Kuhn implied that good scientists ignored or discounted evidence against their theories Popper regarded counter evidence as something to be dealt with, either by explaining it, or eventually modifying the theory. Popper was not describing actual behaviour of scientists, but what a scientist should do. Kuhn was mostly describing actual behaviour.
Lakatos sought a methodology that would harmonize these apparently contradictory points of view, a methodology that could provide a rational account of scientific progress, consistent with the historical record.
For Lakatos, what we think of as a 'theory' may actually be a succession of slightly different theories and experimental techniques developed over time, that share some common idea, or what Lakatos called their 'hard core'. Lakatos called such changing collections 'Research Programmes'. The scientists involved in a programme will attempt to shield the theoretical core from falsification attempts behind a protective belt of auxiliary hypotheses. Whereas Popper was generally regarded as disparaging such measures as 'ad hoc', Lakatos wanted to show that adjusting and developing a protective belt is not necessarily a bad thing for a research programme. Instead of asking whether a hypothesis is true or false, Lakatos wanted us to ask whether one research programme is better than another, so that there is a rational basis for preferring it. He showed that in some cases one research programme can be described as progressive while its rivals are degenerative. A progressive research programme is marked by its growth, along with the discovery of stunning novel facts, development of new experimental techniques, more precise predictions, etc. A degenerative research program is marked by lack of growth, or growth of the protective belt that does not lead to novel facts.
Lakatos claimed that he was actually expounding Popper's ideas, which had themselves developed over time. He contrasted Popper0, the crude falsificationist, who existed only in the minds of critics and followers who had not understood Popper's writings, Popper1, the author of what Popper actually wrote, and Popper2, who was supposed to be Popper as reinterpreted by his pupil Lakatos, though many commentators believe that Popper2 just is Lakatos. The idea that it is often not possible to show decisively which of two theories or research programmes is better at a particular point in time whereas subsequent developments may show that one is 'progressive' while the other is 'degenerative', and therefore less acceptable was a major contribution both to philosophy of science and to history of science. Whether it was Popper's idea or Lakatos' idea, or, most likely, a combination, is of less importance.
Lakatos was following Pierre Duhem's idea that one can always protect a cherished belief from hostile evidence by redirecting the criticism toward other things that are believed. (See Confirmation holism and Duhem-Quine thesis). This difficulty with falsificationism had been acknowledged by Popper.
Falsificationism, (Popper's theory), proposed that scientists put forward theories and that nature 'shouts NO' in the form of an inconsistent observation. According to Popper, it is irrational for scientists to maintain their theories in the face of Nature's rejection, yet this is what Kuhn had described them as doing. But for Lakatos, "It is not that we propose a theory and Nature may shout NO rather we propose a maze of theories and nature may shout INCONSISTENT". This inconsistency can be resolved without abandoning our Research Programme by leaving the hard core alone and altering the auxiliary hypotheses. One example given is Newton's three laws of motion. Within the Newtonian system (research programme) these are not open to falsification as they form the programme's hard core. This research programme provides a framework within which research can be undertaken with constant reference to presumed first principles which are shared by those involved in the research programme, and without continually defending these first principles. In this regard it is similar to Kuhn's notion of a paradigm.
Lakatos also believed that a research programme contained 'methodological rules', some that instruct on what paths of research to avoid (he called this the 'negative heuristic') and some that instruct on what paths to pursue (he called this the 'positive heuristic').
Lakatos claimed that not all changes of the auxiliary hypotheses within research programmes (Lakatos calls them 'problem shifts') are equally as acceptable. He believed that these 'problem shifts' can be evaluated both by their ability to explain apparent refutations and by their ability to produce new facts. If it can do this then Lakatos claims they are progressive. However if they do not, if they are just 'ad-hoc' changes that do not lead to the prediction of new facts, then he labels them as degenerate.
Lakatos believed that if a research programme is progressive, then it is rational for scientists to keep changing the auxiliary hypotheses in order to hold on to it in the face of anomalies. However, if a research programme is degenerate, then it faces danger from its competitors, it can be 'falsified' by being superseded by a better (i.e. more progressive) research programme. This is what he believes is happening in the historical periods Kuhn describes as revolutions and what makes them rational as opposed to mere leaps of faith (as he believed Kuhn took them to be).
The Milton Friedman neoclassical economics case study
In August 1972 a case study of the methodology of neoclassical economics by Lakatos's London School of Economics colleague Spiro Latsis published in The British Journal for the Philosophy of Science found Milton Friedman's methodology to be 'pseudo-scientific' in terms of Lakatos's evaluative philosophy of science, according to which the demarcation between scientific and pseudo-scientific theories consists of their at least predicting testable empirical novel facts or not. Latsis claimed Friedman's instrumentalist methodology of neoclassical economics had never predicted any novel facts. In its defence in a three-page letter to Latsis in December 1972, Friedman counter-claimed that the neoclassical monopoly competition model had in fact shown empirical progress by predicting phenomena not previously observed that were also subsequently confirmed by empirical evidence.But he notably never actually identified any specific economic phenomenon as an example of any such successfully predicted positive novel fact.
In early 1973, as Editor of the Journal, Lakatos invited Friedman to submit a discussion note based on his December 1972 letter to Latsis for publication in a symposium on the issue of the scientific status or not of neoclassical economics . Lakatos even assured Friedman he would have the last word. But Friedman never took up Lakatos's invitation. Three years later, in 1976 Friedman was awarded the Nobel Prize for Economics without this outstanding charge of 'pseudo-science' ever having been publicly conclusively rebutted. The citation for Friedman's prize said it was awarded "for his achievements in the fields of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilisation policy." But four Nobel Prize laureates protested at Friedman's award, and most notably the 1974 joint laureate of the Economics award, Gunnar Myrdal, complained that Friedman's prize (and also Hayek's) was undeserved because the economics did not qualify as a science, thus apparently concurring with Latsis's judgment that Friedman's economics was 'pseudo-scientific'.
Criticism
Feyerabend
Paul Feyerabend argued that Lakatos' methodology was not a methodology at all, but merely "words that sound like the elements of a methodology." He argued that Lakatos' methodology was no different in practice from epistemological anarchism, Feyerabend's own position. He wrote in Science in a Free Society (after Lakatos' death) that: Lakatos realized and admitted that the existing standards of rationality, standards of logic concluded, were too restrictive and would have hindered science had they been applied with determination. He therefore permitted the scientist to violate them (he admits that science is not "rational" in the sense of these standards). However, he demanded that research programmes show certain features in the long run — they must be progressive.... I have argued that this demand no longer restricts scientific practice. Any development agrees with it. Lakatos and Feyerabend planned to produce a joint work where Lakatos developed a rationalist description of science and Feyerabend attacking it. According to Feyerabend, Lakatos' unexpected demise threw Feyerabend into a depression.
Selected works
- Howson, Colin, Ed. Method and Appraisal in the Physical Sciences: The Critical Background to Modern Science 1800-1905 Cambridge University Press 1976 ISBN 0521211107
- Kampis, Kvaz & Stoltzner (eds) Vienna Circle Institute Library, Kluwer 2002 ISBN 1-4020-0226
- Lakatos, Musgrave ed. (1970). Criticism and the Growth of Knowledge. Cambridge: Cambridge University Press. ISBN 0-521-07826-1
- Lakatos (1976). Proofs and Refutations. Cambridge: Cambridge University Press. ISBN 0-521-29038-4
- Lakatos (1978). The Methodology of Scientific Research Programmes: Philosophical Papers Volume 1. Cambridge: Cambridge University Press
- Lakatos (1978). Mathematics, Science and Epistemology: Philosophical Papers Volume 2. Cambridge: Cambridge University Press. ISBN 0-521-21769-52
- Latsis, Spiro J. Ed. Method and Appraisal in Economics Cambridge University Press 1976 ISBN 0521210763
- Motterlini, Matteo FOR AND AGAINST METHOD Imre Lakatos and Paul Feyerabend Chicago University Press, 1999 ISBN 0-226-46774-0
- Zahar, Elie Einstein's Revolution: A study in heuristic Open Court 1988
Archives
Imre Lakatos' papers are held at the His personal is also held at the School.
See also
Further information
- Brendan Larvor (1998). Lakatos: An Introduction. London: Routledge. ISBN 0-415-14276-8
- John Kadvany (2001). Imre Lakatos and the Guises of Reason. Durham and London: Duke University Press. ISBN 0-8223-2659-0; author's Web site: http://www.johnkadvany.com.
- Teun Koetsier (1991). Lakatos' Philosophy of Mathematics: A Historical Approach. Amsterdam etc: North Holland. ISBN 0-444-88944-2
- Szabo, Arpad The Beginnings of Greek Mathematics (Tr Ungar) Reidel & Akademiai Kiado, Budapest 1978 ISBN 963 05 1416 8
External links
- (including an MP3 audio file) – Lakatos' 1973 Open University BBC Radio talk on the subject
- The Autumn 2006 MIT Press journal Perspectives on Science devoted to articles on this topic, with article abstracts.
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