Imre Lakatos

Imre Lakatos (1922–1974) was a Hungarian-British philosopher of mathematics and science whose work on scientific methodology developed a sophisticated alternative to both Popper's falsificationism and Kuhn's paradigm shifts. His central contribution is the concept of research programmes: structured clusters of theories protected by a "hard core" of foundational commitments and surrounded by a "protective belt" of auxiliary hypotheses that absorb empirical challenges. A programme is progressive if it generates novel predictions that are confirmed; it is degenerative if it merely accommodates known anomalies without predictive success. On this account, scientific rationality consists not in the instant rejection of falsified theories (Popper) or in the sociological dominance of paradigms (Kuhn), but in the long-run comparison of programmes by their fertility. Lakatos objected to Kuhn that revolutions need not be irrational conversions — they are rational when practitioners migrate from a degenerating programme to a progressive one. His Proofs and Refutations (1976) demonstrates this methodology through a reconstruction of the history of Euler's polyhedron formula, showing mathematical knowledge as the progressive refinement of proofs through the discovery and incorporation of counterexamples — a dialectic of conceptual analysis in action.