Encyclopedia
Imre Lakatos was a
philosopher of
mathematics and of
science.
Life
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. He became an active
communist during the
Second World War. He changed his last name once again to
Lakatos to reflect communist values and in honor of Géza Lakatos.
After the war, he continued his education in Budapest . 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 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 and John Watkins.
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 is an analysis of the history of science [i]. ...
". According to Musgrave, Thomas Kuhn was so popular during the 60's that people attended his lectures in adjacent lecture theatres listening to him via a sound system.
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.
Parts of his correspondence with his friend and critic Paul Feyerabend have been published in
For and Against Method .
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.
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 programs
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 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.
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 Programs'. 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
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, , 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"
1. 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
Newton's three
laws of motion, which define quantities such as force. Within the Newtonian system these are not open to falsification as they form the programs 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 and some that instruct on what paths to pursue .
Lakatos claimed that not all changes of the auxiliary hypotheses within research programs 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
2. 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 research program. 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 .
Notes
1. Lakatos, Musgrave ed. , Pg. 130
2. 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. Empirically progressiveness is if some of this content is corroborated.
Selected works
- Lakatos, Musgrave ed. . Criticism and the Growth of Knowledge. Cambridge: Cambridge University Press. ISBN 0-521-07826-1
- Lakatos . Proofs and Refutations. Cambridge: Cambridge University Press. ISBN 0-521-29038-4
- Lakatos . The Methodology of Scientific Research Programmes: Philosophical Papers Volume 1. Cambridge: Cambridge University Press
- Lakatos . Mathematics, Science and Epistemology: Philosophical Papers Volume 2. Cambridge: Cambridge University Press. ISBN 0-521-21769-5
See also
- Scientific Community Metaphor, an approach to programming influenced by Lakatos's work on research programmes.
Further information
- Brendan Larvor . Lakatos: An Introduction. London: Routledge. ISBN 0-415-14276-8
- John Kadvany . 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.
External links
