Lakatos was a philosopher who, perhaps more than most, left a legacy not only in publications but in the minds of colleagues. He was a forceful person who was clearly more interested in engaging in and furthering debate than in laying down written tablets for others to digest.

His first (and lasting) intellectual interest lay in the philosophy of mathematics and his distinctive views on this found a ready home in the London School of Economics where, deploying a similar approach, he developed a deeper interest in the philosophy of science. ‘Criticism’, ‘heuristic’, ‘problem’, ‘conjecture’, ‘proofs and refutations’ (the title of his book on the philosophy of mathematics), were concepts fitting the Popperian model of science (except, importantly, ‘proof’).

Orthodox accounts and histories of mathematics, according to Lakatos, distort the nature of the subject. Mathematics has been seen by philosophers and by some mathematicians as involving ‘certainty’, a feature reflecting its supposed deductive structure with theorems being rigorously deduced from indubitable axioms and postulates. Concomitantly, discovery of mathematical truth is seen as either totally rational (deduction) or as blind guessing. Lakatos challenges both these dogmatisms. The ‘real’ history of mathematics, revealed by case studies, shows the subject to be quasi-empirical and less than purely formal. Furthermore, in criticizing mathematical claims, the mathematician is not necessarily combating a completed deductive system, but helping to articulate it, perhaps by means of ‘concept-stretching’ or by finding ‘counter-examples’ which do not stand as falsifications of the theory but as heuristic challenges to it. For example, contemporaries saw Euclid’s system, not as an attempt to reach infallible foundations, but as a challenge to Parmenides and Zeno, a challenge itself subject to such quasiempirical criticism. All mathematics is conjectural and ‘the vehicle of progress is bold speculations, criticism, controversy between rival theories, problemshifts’ (1978, vol. 2, p. 30).

Holding fast to Popper’s belief in a universal criterion of scientific rationality (contrary to contemporaries Kuhn, Feyerabend and Polanyi), he saw himself as developing the Popperian methodological research programme with a greater emphasis on (rationally reconstructed) history, using case studies: ‘Philosophy of science without history of science is empty; history of science without philosophy is blind’ (1978, vol. 1, p. 102).

Lakatos’s lasting achievement in philosophy of science undoubtedly lies in his postulation of ‘research programmes’ as the key to understanding the progress of (theoretical) science. ‘My concept of a “research programme” may be construed as an objective, “third world” reconstruction of Kuhn’s socio-psychological concept of “paradigm”’ (ibid., p. 91). Whereas Popper had postulated individual theories as the focus for falsification (which made a theory scientific), Lakatos held that research programmes (embracing a series of theories), which contained falsifiable and unfalsifiable parts, were a better tool for simultaneously acknowledging both the lastingness of scientific theories and the rationality of their rejection. ‘Criticism does not—and must not—kill as fast as Popper imagined’ (ibid., p. 92).

A research programme—I will use Lakatos’s example of Newtonianism—comprises a ‘hard core’ (the three Laws of Motion and the Law of Gravitation), an unfalsifiable part to which the ‘negative heuristic’ forbids challenge, a set of ‘problem-solving techniques’ (mathematical apparatus) and a ‘protective belt’ of auxiliary hypotheses and initial conditions (geometrical optics, theory of atmospheric refraction) which is falsifiable and against which the falsity-seeking modus tollens of Popper is targeted. The ‘positive heuristic’ directs a scientist to make progressive modifications in the protective belt. Theory, not data, is primary in the formulation of research programmes. Where, then, is the rationality in scientific change? A research programme is ‘theoretically progressive’ if each new theory in the programme has excess empirical content over its predecessor, i.e. predicts some novel fact; it is ‘empirically progressive’ if some of this excess content is corroborated (Newton predicted the return of Halley’s comet).

What is important for Lakatos in both mathematics and science, is not falsification but heuristic criticism leading to better theories. True to his Hegelian background, which weakened in influence at the LSE, the notion that a theory was ‘born refuted’ he regarded with insouciance: what mattered was the heuristic value of a refuted theory. Neither corrobations nor refutations are a clearcut matter of a logical relation between statements, but partly depend on context: ‘Important criticism is always constructive: there is no refutation without a better theory’ (ibid., p. 6). Research prorgrammes have had a mixed reception. Whilst philosophers have responded positively to the attempt to have rationality and history at the same time, seen as advice to scientists research programmes seem to forbid nothing. Seen, as Lakatos preferred, as a rational reconstruction of the history of science, they seem to close to a sociological approach for rational comfort. However, philosophers of science havea deployed Lakatosian thinking in their work and research programmes have become part of the lore of philosophy of science.

Sources: Turner.