Proofs and Refutations

Introduction

The text grew out of Imre Lakatos’s Cambridge doctoral thesis (1961) and appeared in four parts in the British Journal for the Philosophy of Science in 1963–64; after his death in 1974 John Worrall and Elie Zahar edited it as a book. In an imaginary classroom a teacher and pupils named after Greek letters discuss Euler’s conjecture that for every polyhedron the numbers of vertices, edges and faces satisfy V – E + F = 2. Each counterexample – a cube with a cubic hole, a picture frame – forces a choice: dismiss it as a “monster”, restrict the theorem, or improve the concept of polyhedron and the proof. Lakatos applies Popper’s fallibilism to mathematics, against formalist views of it.

More works by Imre Lakatos

• 1970Falsification and the Methodology of Scientific Research Programmes