Deep Disagreement in Mathematics
History and Overview
2023-02-08 v1
Abstract
Disagreements that resist rational resolution, often termed ``deep disagreements'', have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki's work on the abc conjecture as a potential example of both phenomena. I conclude by investigating the prospects for the resolution of mathematical deep disagreements in virtue-theoretic approaches to informal logic and mathematical practice.
Keywords
Cite
@article{arxiv.2210.16488,
title = {Deep Disagreement in Mathematics},
author = {Andrew Aberdein},
journal= {arXiv preprint arXiv:2210.16488},
year = {2023}
}