Twentieth century philosophy
|Name: Imre Lakatos|
|Birth: November 9, 1922|
|Death: February 2, 1974|
|School/tradition: Critic of Falsificationism|
|Philosophy of science, Epistemology, Philosophy of mathematics, Politics|
|Method of proofs and refutations, methodology of scientific research programmes|
|George Pólya, Paul Feyerabend, Karl Popper||Paul Feyerabend|
Imre Lakatos (November 9, 1922 – February 2, 1974) was a philosopher of mathematics and science. Born in Hungary and initially educated there and in the Soviet Union, he was a Communist for a time during and after World War II, but he eventually became disenchanted with Communist bureaucracy and ideology. Eventually, at the time of the Soviet invasion of Hungary in 1956, he fled from Hungary to Vienna, and then to England. He received a doctorate from the University of Cambridge in 1961. In 1960, Lakatos was appointed to the London School of Economics and he taught there for fourteen years, until his death. It is for this work in England that he is known today.
Lakatos was born Imre 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. During the Second World War he became an active communist. He changed his last name once again to Lakatos (Locksmith) to reflect communist values and in honor of Géza Lakatos. After the war, he continued his education in Budapest (under György Lukács, among others). He also studied at the Moscow State University under the supervision of Sofya Yanovskaya. When he returned, he worked as a senior official in the Hungarian ministry of education. 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 a stateless person.
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 and John Watkins.
According to Ernst Gellner and others, Lakatos lectured on difficult and abstract subjects full of technicalities, but he did it in a way that was intelligible, fascinating, dramatic, and amusing, to a crowded lecture hall in an electric atmosphere, where gales of laughter would often erupt.
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, aged just 51.
The work of Lakatos was heavily influenced by Popper and by Pólya. His doctoral thesis, "Essays in the Logic of Mathematical Discovery," was submitted to Cambridge in 1961. The theme of his thesis, done at the suggestion of Pólya, was the history of the Euler-Descartes formula V - E + F = 2.
Lakatos published Proofs and Refutations in 1963-64, in four parts in the British Journal for Philosophy of Science. This work was based on his doctoral thesis and expounds his view of the progress of mathematics. It is structured as a series of Socratic dialogues between a teacher and a group of students. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavor. According to John Worrall, "… as well as having great philosophical and historical value, [this paper] was circulated in offprint form in enormous numbers."
During his lifetime, Lakatos refused to publish the work as a book, since he intended to improve it. However, in 1976, two years after his death, the work did appear as a book, I. Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, edited by J. Worrall and E. G. Zahar.
Worrall describes the work:
The thesis of Proofs and Refutations is that the development of mathematics does not consist (as conventional philosophy of mathematics tells us it does) in the steady accumulation of eternal truths. Mathematics develops, according to Lakatos, in a much more dramatic and exciting way—by a process of conjecture, followed by attempts to "prove" the conjecture (i.e. to reduce it to other conjectures) followed by criticism via attempts to produce counter-examples both to the conjectured theorem and to the various steps in the proof ("Imre Lakatos (1922-1974): Philosopher of Mathematics and Philosopher of Science").
Hersh says that Proofs and Refutations is:
… an overwhelming work. The effect of its polemical brilliance, its complexity of argument and self-conscious sophistication, its sheer weight of historical learning, is to dazzle the reader ("Introducing Imre Lakatos").
Lakatos wrote a number of papers on the philosophy of mathematics before moving on to write more generally on the philosophy of science. However, like his doctoral thesis, he often used historical case studies to illustrate his arguments. His article, "Cauchy and the Continuum: The Significance of Non-Standard Analysis for the History and Philosophy of Mathematics," is a notable example.
Hersh explains the point of the approach to history that Lakatos uses in this article:
The point is not merely to rethink the reasoning of Cauchy, not merely to use the mathematical insight available from Robinson's non-standard analysis to re-evaluate our attitude towards the whole history of the calculus and the notion of the infinitesimal. The point is to lay bare the inner workings of mathematical growth and change as a historical process, as a process with its own laws and its own "logic," one which is best understood in its rational reconstruction, of which the actual history is perhaps only a parody (Hersh, op. cit.).
Lakatos was extremely effective as a research supervisor to students. He inspired a group of young scholars to do original research, and he would often spend days with them perfecting their manuscripts for publication. At the time of his death, he was highly productive, with many plans to publish new work, reply to his critics, and apply his ideas in new fields.
Worrall claims that the achievement of which Lakatos would have been most proud was leaving
… a thriving research program manned, at the London School of Economics and elsewhere, by young scholars engaged in developing and criticizing his stimulating ideas and applying them to new areas (Worrall, op. cit.).
Lakatos' character is described this way:
With his sharp tongue and strong opinions he sometimes seemed authoritarian; but he was "Imre" to everyone; and he invited searching criticism of his ideas, and his writings over which he took endless trouble before they were finally allowed to appear in print (Worrall, op. cit.).
Proofs and refutations
Proofs and Refutations 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 one should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, that is, 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 knowledge accumulates, through the logic and process of proofs and refutations.
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 Gottlob Frege's and Bertrand 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 programs 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.
Lakatos' contribution to the philosophy of science was an attempt to resolve the perceived conflict between Karl Popper's "falsificationism" and the revolutionary structure of science described by Thomas S. Kuhn. Popper's theory 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.
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, and thus preserve the rationality of science in the face of the failure or Popperian falsificationism and Kuhn's irrationalism.
For Lakatos, what we think of as "theories" are actually groups of slightly different theories that share some common idea, or what Lakatos called their "hard core." Lakatos called these groups "Research Programmes" [British spelling]. Those scientists involved in the program will shield the theoretical core from falsification attempts behind a protective belt of auxiliary hypotheses. Whereas Popper generally disparaged 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 program. Instead of asking whether a hypothesis is true or false, Lakatos wanted us to ask whether a research program is progressive or degenerative. A progressive research program is marked by its growth, along with the discovery of stunning novel facts. A degenerative research program is marked by lack of growth, or growth of the protective belt that does not lead to novel facts.
Lakatos was following Willard Van Orman Quine's idea that one can always protect a cherished belief from hostile evidence by redirecting the criticism toward other things that are believed. This difficulty with falsificationism had been acknowledged by Popper.
Falsificationism, Karl 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 Natures 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 program by leaving the hard core alone and altering the auxiliary hypotheses.
One example given is Isaac Newton's three laws of motion. Within the Newtonian system (research program) these are not open to falsification as they form the program's hard core. This research program 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 program, 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 program 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 programs (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 program 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 program is degenerate, then it faces danger from its competitors; it can be "falsified" by being superseded by a better (i.e. more progressive) research program. This is what he believed is happening in the historical periods Kuhn described as revolutions and what makes them rational as opposed to mere leaps of faith (as he believed Kuhn took them to be).
Lakatos' Break with Karl Popper
Lakatos was at first a close follower and defender of Karl Popper and Popperian falsificationism. However, eventually he and Popper broke with each other, so much so that Popper denounced Lakatos somewhat bitterly and claimed that Lakatos misunderstood and misrepresented him (in The Philosophy of Karl Popper 999-1013). W.W. Bartley, III, a Popperian and editor of some of Popper's works, also wrote critically about Lakatos.
In turn, Lakatos—along with his friend and colleague Paul Feyerabend, another lapsed Popperian—came to minimize the importance of Popper and Popper's work.
Lakatos is regarded as one of the one of the most important philosophers of science in the twentieth century. His contributions include his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and his introduction of the concept of the "Research Programmes" (or research programs) which include "methodological rules" that guide the direction of scientific research.
Lakatos and Feyerabend planned to produce a joint work in which Lakatos would develop a rationalist description of science and Feyerabend would attack it. The correspondence between Lakatos and Feyerabend, where the two discussed the project, has since been reproduced, entitled For and Against Method, edited by Matteo Motterlini.
The Lakatos Award, endowed by the Latsis Foundation in memory of Imre Lakatos, is given annually for an outstanding contribution to the philosophy of science.
- Lakatos, Imre, ed. 1968. The Problem of Inductive Logic. Amsterdam: North Holland Publishing Co.
- Lakatos, Imre and Alan Musgrave, eds. 1970. Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London, 1965. Cambridge and New York: Cambridge University Press. ISBN 0521078261
- Lakatos, Imre. 1973. "Science and Pseudoscience," Broadcast June 30, 1973, as Programme 11 of The Open University Arts Course A303, "Problems in Philosophy," by the BBC. Pub. as Philosophy in the Open, ed. by Godfrey Vesey, and as the Introduction to The Methodology of Scientific Research Programmes, ed. by John Worrall and Gregory Currie.
- Lakatos, Imre. 1974. "Popper on Demarcation and Induction," 241-273 of Paul Arthur Schilpp, ed., The Philosophy of Karl Popper. The Library of Living Philosophers, Vol. XIV. La Salle IL: Open Court.
- Lakatos, Imre. 1976. Essays in Memory of Imre Lakatos, ed. by R. S. Cohen, P. K. Feyerabend, and M. W. Wartofsky. Dordrecht & Boston: D. Reidel Pub. Co. ISBN 9027706549
- Lakatos, Imre. 1976. Proofs and Refutations. Cambridge: Cambridge University Press. ISBN 0521290384
- Lakatos, Imre. 1977. The Methodology of Scientific Research Programmes: Philosophical Papers Volume 1. Ed. by John Worrall and Gregory Currie. Cambridge: Cambridge University Press.
- Lakatos, Imre. 1978. "Cauchy and the Continuum: The Significance of Non-Standard Analysis for the History and Philosophy of Mathematics," in The Mathematical Intelligencer(3), 151-161
- Lakatos, Imre. 1978. Mathematics, Science and Epistemology: Philosophical Papers Volume 2 ed. by John Worrall and Gregory Currie. Cambridge: Cambridge University Press. ISBN 0521217695
- Lakatos, Imre and Paul Feyerabend. 1999. For and Against Method: Including Lakatos’ Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence. Chicago: University of Chicago Press. ISBN 0226467740
- Feyerabend, Paul. 1975. "Imre Lakatos." British Journal for the Philosophy of Science. 26, 1-18.
- Gellner, Ernst. 1974. "Professor Imre Lakatos." The Times, London, February 8, p. 18.
- Hersh R. 1978. "Introducing Imre Lakatos." Mathematics Intelligencer 1 (3) (1978), 148-151.
- Kadvany, John. 2001. Imre Lakatos and the Guises of Reason. London: Duke University Press. ISBN 0822326590
- Koetsier, Teun. 1991. Lakatos' Philosophy of Mathematics: A Historical Approach. Amsterdam: North Holland. ISBN 0444889442
- Larvor, Brendan. 1998. Lakatos: An Introduction. London: Routledge. ISBN 0415142768
- Schilpp, Paul Arthur (ed.). 1974. The Philosophy of Karl Popper. La Salle IL: Open Court.
- Weimer, Walter B. 1979. Notes on the Metholology of Scientific Research. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Worrall, John. 1974. "Imre Lakatos (1922-1974): Philosopher of Mathematics and Philosopher of Science." Z. Allgemeine Wissenschaftstheorie 5 (2), 211-217.
All links retrieved June 24, 2019.
- Lakatos LSE Department of Philosophy, Logic and Scientific Method
- Imre Lakatos Stanford Encyclopedia of Philosophy
- John J. O'Connor and Edmund F. Robertson. Imre Lakatos at the MacTutor archive
General philosophy sources
- Stanford Encyclopedia of Philosophy
- The Internet Encyclopedia of Philosophy
- Paideia Project Online
- Project Gutenberg
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