证明与反驳

简介

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.

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