Kneebone and Lakatos: At the Roots of a Dialectical Philosophy of Mathematics

In this article, we examine 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 in 1963–64, it was preempted by the British logician G. T. Kneebone in a pair of forgotten articles in 1955 and 1957 and a chapter of his 1963 book. We introduce Kneebone’s dialectical approach to mathematics and compare it with Lakatos’s. Furthermore, we give evidence from the Lakatos archives at the London School of Economics 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 with the question of why this might be.