We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work (...) by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods. (shrink)

Lakatos’ (Lakatos, 1976) model of mathematical conceptual change has been criticized for neglecting the diversity of dynamics exhibited by mathematical concepts. In this work, I will propose a pluralist approach to mathematical change that re-conceptualizes Lakatos’ model of proofs and refutations as an ideal dynamic that mathematical concepts can exhibit to different degrees with respect to multiple dimensions. Drawing inspiration from Godfrey-Smith’s (Godfrey-Smith, 2009) population-based Darwinism, my proposal will be structured around the notion of a conceptual population, the opposition between (...) Lakatosian and Euclidean populations, and the spatial tools of the Lakatosian space. I will show how my approach is able to account for the variety of dynamics exhibited by mathematical concepts with the help of three case studies. (shrink)