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Imre Lakatos (November 9, 1922 – February 2, 1974) was a 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) 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. 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: The Logic of Mathematical Discovery, 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,[1] 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.[2]

Proofs and refutations
Main article: 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 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 '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 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)[3] 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.[4]

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 (inaccurately) reported 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[5] (at page 200) that "in Newton's theory Kepler's laws are only approximately valid – that is, strictly invalid – if we take into account the mutual attraction between the planets", so that (in precise terms) 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 degenerating. 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 degenerating 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 extending Popper's ideas, which had themselves developed over time. He contrasted Popper, 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 'degenerating', 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 theory (or part of one) from hostile evidence by redirecting the criticism toward other theories or parts thereof. (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"[6]. 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 took the view 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 took the view 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[7]. 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 took the view 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 says is happening in the historical periods Kuhn describes as revolutions and what makes them rational as opposed to mere leaps of faith (as he considered that Kuhn took them to be).

Pseudoscience

According to the demarcation criterion of pseudoscience originally proposed by Lakatos, a theory is pseudoscientific if it fails to make any novel predictions of previously unknown phenomena, in contrast with scientific theories which at least predict some novel fact(s), whether or not they are confirmed.[8] Within the class of scientific theories, progressive scientific theories are those which have their novel facts confirmed and degenerate scientific theories are those whose predictions of novel facts are refuted. Hence Lakatos based his criterion of science on the view that the aim of science is the growth of knowledge of phenomena, whereby a theory is pseudoscientific if it does not even attempt such and makes no novel predictions. As he put it:

"A given fact is explained scientifically only if a new fact is predicted with it....The idea of growth and the concept of empirical character are soldered into one." See pages 34–5 of The Methodology of Scientific Research Programmes, 1978.

Lakatos's own key examples of pseudoscience were Ptolemaic astronomy, Velikowsky's planetary cosmogony, Freudian psychoanalysis, 20th century Soviet Marxism[9], Lysenko's biology, Bohr's Quantum Mechanics post-1924, astrology, psychiatry, sociology and neo-classical economics. And in his 1973 LSE Scientific Method Lecture 1[10] he also claimed that "nobody to date has yet found a demarcation criterion according to which Darwin can be described as scientific", thus implying Darwin's theory of evolution did not satisfy Lakatos's own criterion of at least predicting some novel fact(s), and so either it was pseudoscientific or else there was something wrong with Lakatos's criterion.

Almost 20 years after Lakatos's 1973 'challenge' on the scientificity of Darwin, in her 1991 The Ant and the Peacock (pp31–2), LSE lecturer and ex-colleague of Lakatos, Helena Cronin, attempted to establish Darwinian theory was empirically scientific in respect of at least being supported by evidence of likeness in the diversity of life forms in the world, allegedly explained by descent with modification. She notably first admitted that in respect of "our usual idea of corroboration as requiring the successful prediction of novel facts...Darwinian theory was not strong on temporally novel predictions"[11] and certainly did not identify any. But she then asserted it was scientific on the weaker Zahar criterion of providing independent novel explanation of old already well known facts.[12] However, she even more notably then also failed to demonstrate that it provided any confirmed nomological-deductive explanation of any old facts of likeness within evolutionary diversity whatever, only making a mere assertion that it did so, but without proof. In fact not only with respect to predicting/explaining likeness in diversity, but in fact nowhere in her book did Cronin provide any example or demonstration of Darwinian theory successfully predicting any novel fact nor of it independently novelly explaining any old known fact about anything whatsoever in terms of the standard positivist nomological-deductive model of scientific predictions and explanations advocated by her.[13]

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.[14] Latsis claimed that Friedman's instrumentalist methodology of neoclassical economics had never predicted any novel facts.[15] In its defense 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.[16] But he notably never actually identified any specific economic phenomenon as an example of any such successfully predicted positive novel fact.[17]

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.[18] But Friedman never took up Lakatos's invitation. Three years later, in 1976, Friedman was awarded the Nobel Prize for Economics "for his achievements in the fields of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy".[19]

Criticism

Feyerabend

Paul Feyerabend argued that Lakatos's methodology was not a methodology at all, but merely "words that sound like the elements of a methodology."[20] He argued that Lakatos's methodology was no different in practice from epistemological anarchism, Feyerabend's own position. He wrote in Science in a Free Society (after Lakatos's 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.[21]

Lakatos and Feyerabend planned to produce a joint work in which Lakatos would develop a rationalist description of science and Feyerabend would attack it. According to Feyerabend, Lakatos's unexpected demise threw Feyerabend into a depression.

Notes

1. ^ See Lakatos's 5 Jan 1971 letter to Paul Feyerabend p233-4 in Motterlini's 1999 For and Against Method
2. ^ 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)
3. ^ 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
4. ^ 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.
5. ^ K R Popper (1972), Objective knowledge: an evolutionary approach.
6. ^ Lakatos, Musgrave ed. (1970), Pg. 130
7. ^ As an added complication he further differentiates between empirical and theoretical progressiveness. Theoretical progressiveness is if the new 'theory has more empirical content then the old. Empirical progressiveness is if some of this content is corroborated. (Lakatos ed., 1970, P.118)
8. ^ See/hear Lakatos's 1973 Open University BBC Radio talk Science and Pseudoscience at his LSE website @ www.lse.ac.uk/lakatos
9. ^ Lakatos notably only condemned specifically Soviet Marxism as pseudoscientific, as opposed to Marxism in general. In fact at the very end of his very last LSE lectures on Scientific Method in 1973, he finished by posing the question of whether Trotsky's theoretical development of Marxism was scientific, and commented that "Nobody has ever undertaken a critical history of Marxism with the aid of better methodological and historiographical instruments. Nobody has ever tried to find an answer to questions like: were Trotsky's unorthodox predictions simply patching up a badly degenerating programme, or did they represent a creative development of Marx's programme ? To answer similar questions, we would really need a detailed analysis which takes years of work. So I simply do not know the answer, even if I am very interested in it."[p109 Motterlini 1999] However, in his 1976 On the Critique of Scientific Reason Feyerabend claimed Lenin's development of Marxism in his auxiliary theory of colonial exploitation had been 'Lakatos scientific' because it was "accompanied by a wealth of novel predictions (the arrival and structure of monopolies being one of them)." And he continued by claiming both Rosa Luxemburg's and Trotsky's developments of Marxism were close to what Lakatos regarded as scientific: "And whoever has read Rosa Luxemburg's reply to Bernstein's criticism of Marx or Trotsky's account of why the Russian Revolution took place in a backward country (cf also Lenin [1968], vol 19, pp99ff.) will see that Marxists are pretty close to what Lakatos would like any upstanding rationalist to do..." [See footnote 9, p315 of Howson (Ed) 1976]
10. ^ Published in For and Against Method: Imre Lakatos and Paul Feyerabend Motterlini (Ed) University of Chicago Press 1999
11. ^ In fact she was thoroughly equivocal about whether it did or did not make any novel predictions, only saying " For the most part this evidence was already well known, thoroughly documented by pre-Darwinian natural history.[Italics added]" So if only for the most part, then what other part of the evidence, if any, was not already well known, but had been novelly predicted ? Cronin did not say.
12. ^ In 1973 Elie Zahar had proposed Lakatos's criterion that the prediction of novel facts is a necessary condition of a theory being scientific should be diluted to make independent novel explanations of old known facts a sufficient condition of scientificity, a proposal that was partly endorsed by Lakatos that year. The declared motivation of this revision was to explain the Einsteinian GTR revolution in mechanics, which Zahar apparently dated to 1915 by when it had made no novel predictions, and hence was apparently an anomaly for Lakatos's criterion of scientific revolutions as requiring the successful prediction of novel facts. But it had explained the old fact of the anomalous perihelion of Mercury in 1915. However Zahar's [1973] had notably failed to establish the GTR revolution happened in 1915 in any great majority conversion of the scientific community that year, rather than post-1919 say, by when it was thought to have successfully predicted the novel fact and degree of gravitational lensing, allegedly confirmed by Eddington's 1919 eclipse experiment. Moreover in the second outing of the application of Zahar's new criterion to try and explain the heliocentric revolution in a joint paper with Lakatos, it had again failed to do so. But this time its attempted explanation of a scientific revolution was historically unsynchronised by a draconian two millenia or so too late rather than only at least three years early as in the GTR revolution case. For on the Lakatos & Zahar account of it, Aristarchus's simple heliocentric model had satisfied that criterion in its novel explanation of planetary stations and retrogressions and of the bounded elongations of Venus and Mercury.
13. ^ So if Cronin's 1991 attempted application of Zahar's criterion was its third outing, then it also failed that test inasmuch as there was indeed a Darwinian revolution as Cronin believes, but Darwinian theory has neither made any novel predictions nor provided any novel hypothetico-deductive explanations of old facts, but rather merely provided metaphysical speculation about evolutionary possibilities in the kind of empirically unilluminating Kiplingesque ‘Just-so’ stories it has been accused of.
14. ^ Situational Determinism in Economics S.J Latsis The British Journal for the Philosophy of Science, 23, p207-45. As Editor of the Journal Lakatos had been primarily responsible for its contents since August 1971.
15. ^ Thus on the basis of Lakatos's evaluation of Marxian economics by the same yardstick as 'degenerate' science because allegedly all its novel predictions were empirically refuted and their refutation not progressively resolved, on the same threefold graded criteria of 'progressive-science' and 'degenerate-science' and 'pseudo-science', Friedman's economics was in effect evaluated as being even less 'scientific' than Marx's, that is as 'pseudoscience' as opposed to 'degenerate science', because it had allegedly never even made any theoretically novel predictions that could possibly be refuted, a necessary condition of being 'scientific' in Lakatos's normative methodology. In fact Lakatos’s LSE colleague, the econometrician and now Labour parliamentary peer Baron Meghnad Desai, then evaluated Marxian economics as a progressive scientific research programme in both his 1974 ‘’Marxian Economics’’ and its 1979 second edition. But he notably failed to identify any successfully predicted novel fact(s) that had rendered it progressive science and which thus empirically countermanded the relatively negative evaluations of both Popper and Lakatos. However, in 1976 Feyerabend claimed that contrary to John Worrall's 1975 repetition of Lakatos's claim that Marxism's auxiliary hypotheses to eliminate refuting instances were not content increasing, that in fact such as its theory of imperialism and colonial exploitation to explain the apparent refutation of its law of the falling rate of profit was "accompanied by a wealth of novel predictions (the arrival and structure of monopolies being one of them.)", and which Feyerabend apparently regarded as having been confirmed.(See p315 and its notes 8 & 9 of Feyerabend’s On the Critique of Scientific Reason in Howson's 1976 Method and Appraisal in the Physical Sciences.)
16. ^ His 6 December 1972 letter is held in Folder 36 of Box 29 of the Hoover Institution Archives' Milton Friedman Papers at Stanford University, created by Friedman himself and his wife in 1992. This Folder also contains a two-page reply to Friedman's letter by Latsis dated 27 January 1973
17. ^ The only example he gave of "predictions of phenomena not formerly observed" was a prediction of Chamberlin's monopolistic competition model that "the standard explanation for the Standard Oil monopoly was wrong", which he said had been theoretically predicted by Aaron Director, his brother-in-law, and empirically confirmed by Magee. But he failed to identify exactly what novel phenomenon was thereby positively predicted and confirmed.
18. ^ Lakatos's 2 February 1973 letter of invitation is held in Folder 32 of Box 29.
19. ^ Nobel Prize Committee Press Release announcing Milton Friedman as the 1976 winner http://nobelprize.org/nobel_prizes/economics/laureates/1976/press.html
20. ^ See How to Defend Society Against Science
21. ^ Paul Feyerabend (1978). Science in a Free Society. London: NLB. ISBN 0860910083