Philosopher of mathematics and science, born in Debrecen, E Hungary. He moved to England after the Hungarian uprising in 1956, and taught at the London School of Economics, where he became a professor in 1969. His best-known work is Proofs and Refutations (1976), a collection of articles demonstrating the creative and informal nature of real mathematical discovery.
For other people with the same name, see Lakatos (disambiguation).Imre Lakatos (November 9, 1922 – February 2, 1974) was a philosopher of mathematics and science.
Life
Lakatos was born Imre Lipschitz to a Jewish family in Debrecen, Hungary in 1922. 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).
After his release, Lakatos returned to academic life, doing mathematical research and translating George Pólya's How to Solve It into Hungarian.
After the Soviet Union invaded Hungary in November 1956, Lakatos fled to Vienna, and later reached England.
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.
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.
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 (ISBN 0-226-46774-0).
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.
What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. (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.
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.
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'. 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.
Falsificationism, (Popper's theory), proposed that scientists put forward theories and that nature 'shouts NO' in the form of an inconsistent observation. 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 Newton's three laws of motion, which define quantities such as force. Within the Newtonian system (research program) 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.
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. If it can do this then Lakatos claims they are progressive.
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. ISBN 0-521-07826-1 Lakatos (1976). ISBN 0-521-29038-4 Lakatos (1977). Cambridge: Cambridge University Press Lakatos (1978). Imre Lakatos and the Guises of Reason.
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