LAKATOS, IMRE
(1922–1974)

Life

Imre Lakatos did important work in the 1960s and 1970s in the philosophy both of mathematics and science. He was born Imré Lipsitz in Debrecen Hungary, and by the time he left for England after the Hungarian Uprising in 1956, he had already lived a complex, charged, and controversial life. A convinced and influential Marxist, he had been unofficial leader of a group of young Jews in hiding from the Nazis after the invasion in 1944. As a high ranking official in the Ministry of Education after the war, he was involved in significant and controversial education reform before being arrested by the secret police in 1953 and held for three years under appalling conditions, sometimes in solitary confinement, in Recsk—the worst of the Gulag-style camps in Hungary.

He studied mathematics, physics, and philosophy at the University of Debrecen, graduating in 1944. He obtained a first PhD (with highest honors) from the Eötvös Collegium in 1947—this for a thesis on the sociology of science that he later insisted was worthless. After leaving Hungary in 1956, he obtained a Rockefeller Foundation grant to study for a second PhD at the University of Cambridge. From 1959 onward he regularly attended Karl Popper's seminar at the London School of Economics (LSE). Popper became the most important influence on him; amongst other things, Popper's Open Society views reinforced the decline of his faith in Marxism that had begun in 1956. Lakatos accepted a lectureship in logic at LSE in 1960 and was promoted to a personal chair (in Logic, with special reference to the philosophy of mathematics) in 1970. He was only fifty-one years old and still teaching at LSE at the sadly early time of his death from a heart attack in 1974.

Philosophy of Mathematics

Lakatos's Cambridge PhD thesis became the basis for his Proofs and Refutations. This work, published initially in the form of journal articles in 1963–1964 and in book form only posthumously in 1976, constitutes his major contribution to the philosophy of mathematics. A dialogue between a group of frighteningly bright students and their teacher, it reconstructs the process by which Euler's famous conjecture about polyhedra (that they all satisfy the formula: number of vertices plus number of faces minus the number of edges equals two) was proved and, in the process, heavily modified and transformed. Lakatos's claim was that although the eventual proof of the theorem in mathematics may be cast as a straightforward deduction, the process by which the proof is found is a more exciting process, involving counterexamples, reformulations, counterexamples to the reformulations, and careful analysis of failed proofs leading to further modifications of the theorem. Any number of interesting claims about both the history and philosophy of mathematics are thrown in to the mix—sometimes in the main text, sometimes in one of the voluminous footnotes. The work is a literary tour de force.

The extent to which Proofs and Refutation s represents a distinctive epistemological view that might challenge more traditional accounts in the philosophy of mathematics, such as logicism or formalism, is a controversial one. Lakatos sometimes described himself as extending Popper's fallibilist-falsificationist view of science into the field of mathematics, and there are even hints of Lakatos's Hegelian past in some of the claims about the autonomous development of mathematics. An alternative view, however, is that the main significance of his work is to cast light simply, though importantly, on the development of mathematics—on how mathematical truth is arrived at—and that it has nothing distinctive to say about the epistemological status of mathematical truths once they have been arrived at. But even if this alternative view is correct, there is a good of undoubtedly epistemological significance in some of the particular issues raised (for example, what he calls the problem of translation highlighting issues about how the formal systems, within which effectively infallible proof can be achieved, relate to the informal mathematics said to be captured by those formal systems).

Philosophy of Science

As indicated, Lakatos thought of himself for some years as extending Popperianism, developed as an account of natural science, into the seemingly unlikely field of mathematics. However, he eventually began to discern faults in Popper's philosophy of natural science. Most significantly, in comparing Popper's views with those of Thomas Kuhn, Lakatos came to realize that Popper's view on the way that evidence impacts on scientific theories is seriously awry.

Lakatos claimed that science is best viewed as consisting not of single, isolated theories but rather of broader research programs. A hard core of principles characterizes such a program, but this needs to be supplemented by an evolving protective belt of more specific and auxiliary assumptions in order to come into contact with experiment. When the latest theory produced by a program proves to be inconsistent with some empirical result, then the standard response of the program's proponents will be to retain the hard core and look to modify some element of the protective belt. This is a process much closer to Kuhn's idea of adverse experimental results being treated as anomalies than to the standard Popperian idea of falsification. However, while Popper used his framework to defend the idea that theory-change in science is a rational process, Lakatos believed that to accept Kuhn's account of paradigms and paradigm shifts was in effect to abandon the view that the development of science is rational. Kuhn's view, he (in)famously claimed, makes theory-change a matter of mob psychology. He was therefore led to make the important distinction between progressive and degenerating programs. The latest Newtonian theory was inconsistent with observations of Uranus's orbit; Newtonians reacted not by giving up the basic theory but by postulating a new planet.

Philip Gosse (1810–1888) realized that claim that God created the world essentially as it now is in 4004 BC is inconsistent with what Darwinians believed to be the fossil record; Gosse reacted not by surrendering the basic creationist theory (hard core), but by postulating that the alleged fossils were parts of God's initial creation. The first was a great scientific success; the second bears the clear hallmark of pseudoscience. Why? Lakatos's answer is that the Newtonian shift was progressive: It not only solved the anomaly of Uranus but made extra predictions (of the existence of a new and hitherto unsuspected planet) that could be tested empirically and were indeed confirmed (by the discovery of Neptune). Gosse's shift is degenerating: All it does is reconcile the basic creationist theory with observation but permits no independent test. The development of science consists of the replacement of degenerating programs by progressive ones. There are many other interesting aspects of the methodology, particularly concerning the role of heuristic principles, and of whether it does satisfactorily save the rationality of science.

See also Epistemology; Hegel, Georg Wilhelm Friedrich; Kuhn, Thomas; Logic, History of: Precursors of Modern Logic: Euler; Marx, Karl; Newton, Isaac; Philosophy of Science; Popper, Karl Raimund.

Bibliography

works by lakatos

With Alan Musgrave, eds. Criticism and the Growth of Knowledge. Cambridge, U.K.: Cambridge University Press, 1970.

Proofs and Refutations. The Logic of Mathematical Discovery, edited by John Worrall and E.G. Zahar. Cambridge, U.K.: Cambridge University Press, 1976.

The Methodology of Scientific Research Programmes and Mathematics, Science and Epistemology. Philosophical Papers. Vols. 1 and 2, edited by John Worrall and Gregory Currie. Cambridge, U.K.: Cambridge University Press, 1978.

With Paul Feyerabend. For and Against Method: Including Lakatos's Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence, edited and with an introduction by Matteo Motterlini. Chicago, IL: University of Chicago Press. 1999.

works by others

Kampis, George, Ladislav Kvasz, and Michael Stölzner, eds. Appraising Lakatos: Mathematics, Methodology and the Man. Dordrecht, Netherlands: Kluwer, 2002.

Larvor, Brendon. Lakatos: An Introduction. London: Routledge, 1998.

John Worrall (2005)

Lakatos, Imre 1922-1974

BIBLIOGRAPHY

The pivotal philosophical debate of twentieth-century Anglo-American philosophy originated with Thomas Kuhn’s 1962 The Structure of Scientific Revolutions. Kuhn (1922–1996), along with Imre Lakatos and Paul Feyerabend (1924–1994), made the history and sociology of science central to conceptions of scientific progress and rationality. Lakatos, a Hungarian émigré who escaped the failed 1956 revolution, became Karl Popper’s (1902–1994) best and favored student, but he joined forces with Kuhn and Feyerabend against Popper’s refusal to see scientific method as having historical roots and hence being subject to change. Lakatos maintained Popper’s anti-positivist view that scientific knowledge has no epistemological foundation, but that progress occurred through continual criticism and revision. Lakatos made the historicism in that view explicit by critically elaborating Popper’s approach into an interpretative method for the history of science and mathematics. Instead of Popper’s ahistorical “logic of scientific discovery” Lakatos saw an historically changing logic of criticism and the growth of scientific knowledge. But like Popper and Feyerabend, and unlike Kuhn, Lakatos recommended a normative conception of scientific method, analogous to normative philosophical models of political or civic processes. Lakatos created his critical theory of science using a sui generis historiographical approach for reconstructing the scientific present as a value-laden history of progress and decline.

The historiographical toolkit is Lakatos’s methodology of scientific research programs. In contrast to Popper’s confrontations of falsifiable theories, with their risky predictions and hence potential refutations, Lakatos argued that individual theories are poorly chosen “units” for scientific change. In practice, as Kuhn and Feyerabend dramatically demonstrated, the best theories can be formally inconsistent; they may contradict stable observations or received theories, or they may violate traditional canons of scientific method—not all at once, but individually or opportunistically, as needed for theory improvement. Lakatos also assumed no theory-neutral observational basis to conclusively refute a single theory. Hence there was no guarantee that confirmatory or refuting data might not itself be reinterpreted and overturned, thus making conclusive refutation of single theories either impossible or subject to unrealistic and overcomplex methodological criteria.

This messy and chaotic milieu of chronic uncertainty requires the intelligence and flexibility of working scientists, whose theories Lakatos organized in terms of longterm research programs. These need not coincide with projects of individual researchers. Instead, they are a post festum historical reconstruction used to characterize scientifically recognized progress or failure. Lakatos proposes a philosophical model to characterize just what, in longterm patterns of theory choice, empirical discovery, and interpretation, led to a recognition, perhaps erroneous, by scientific communities as achievement or decline. A research program, then, was defined as a series of theories that were loosely united by a shared hard core of key principles, ranging from inchoate metaphysical ideas to favored modeling approaches; a positive heuristic of plans for generating theoretical improvements, and turning theories into operational models for addressing open problems, hopefully creating novel confirmations or predictions; ancillary touchstone and observational theories, used to interpret and organize a changing basis of theory-laden “facts” relevant to the program; a protective belt of theories or models insulating the program from critical attack; perhaps ad hoc theories or models needed as temporary fixes; an inventory of Kuhnian puzzles, contradictions, and anomalies awaiting resolution; and an environment of competing research programs against which relative progress is gauged.

Thus “scientific” describes not individual theories, but sequences of theories in time, not necessarily coordinated by any single individual or group. Such science, then, is either progressive or degenerating, the outcome measured by the presence or absence of novel confirmations, persistent puzzles and contradictions, powerful model development, and more or less ad hoc fixes—all of these judged relative to competing programs with a shared domain of problems, relevant phenomena, and research objectives. Lakatos’s historiography of research programs is a theory of modern scientific progress in which a role for scientific truth is reduced in proportion to the Faustian ambitions of theoreticians and experimenters.

Lakatos and others rewrote episodes from the histories of various sciences, using research program categories: the phlogiston and oxygen programs of Joseph Priestley (1733–1804) and Antoine-Laurent Lavoisier (1743–1794); the wave and corpuscular programs for light; nineteenth-century atomic-versus-phenomenological theories of heat; modern plate tectonics; classical political economy from Adam Smith (1723–1790) to David Ricardo (1772–1823) and Karl Marx (1818–1883); and several segments of twentieth-century physics. These projects led to successes and failures, the latter occurring when a major change, like the replacement of classical physics with relativity theory, or the emergence of modern science altogether, is forced into Lakatos’s research program categories, which can be thought of as a nuanced conception of Kuhn’s “normal science,” and absent Kuhn’s confusing normative views. Lakatos saw this historical work as “scientific,” meaning that methodological reflection itself was an ongoing, theory-laden activity of understanding the “phenomena” of the scientific past. As in science proper, no perfect match is expected between historical theory and historical data, implying, as Lakatos points out, no “true” scientific consciousness: our knowledge of science is imperfect and uncertain, just as in science proper. Lakatos’s dialectical histories demonstrated that understanding past knowledge is possible only through some contemporary normative criteria for what counts as scientific, whether clearly articulated or not. His project was to make that condition of historical knowledge his primary lesson for the new philosophy of science. Lakatos and others carried out this project by using the methodology of scientific research programs as a historiographical guide and toolkit. Feyerabend identified the characteristic feature of modern scientific knowledge as a constantly expanding horizon of facts. Lakatos thought it best to comprehend that post-Renaissance process using normative and philosophical concepts that make historical knowledge an object of rational, even scientific, self-understanding.

SEE ALSO Kuhn, Thomas; Philosophy of Science; Popper, Karl; Science; Scientific Method

BIBLIOGRAPHY

Kuhn, Thomas S. 1962. The Structure of Scientific Revolutions .Chicago: University of Chicago Press.

Lakatos, Imre. 1976. Proofs and Refutations: The Logic of Mathematical Discovery. Eds. John Worrall and Elie Zahar. New York: Cambridge University Press.

Lakatos, Imre. 1978. Mathematics, Science, and Epistemology.Eds. John Worrall and Gregory Currie. New York:Cambridge University Press.

Lakatos, Imre. 1978. The Methodology of Scientific Research Programmes. Eds. John Worrall and Gregory Currie. New York: Cambridge University Press.

Lakatos, Imre, and Alan Musgrave, eds. 1970. Criticism and the Growth of Knowledge. New York: Cambridge University Press.

Popper, Karl Raimund. 1959. Logic of Scientific Discovery. New York: Basic Books.

John Kadvany