Kneebone and Lakatos: at the roots of a dialectical philosophy of mathematics

This paper examines the origins of the dialectical approach to the philosophy of mathematics. While this approach is commonly taken to begin with Imre Lakatos’s Proofs and Refutations, first published as a series of articles (1963-64), it turns out that it was pre-empted by the British logician G. T. Kneebone in a pair of forgotten articles (1955; 1957) and a chapter of his book (1963). We introduce Kneebone’s dialectical approach to mathematics, and compare it to Lakatos’s. Furthermore, we give evidence from the LSE Lakatos archives that Kneebone and Lakatos were acquainted, in correspondence, and that Lakatos read and annotated Kneebone’s papers. Nonetheless, Kneebone is nowhere mentioned in Lakatos’s work. We finish on the question of why this might be.