论文标题
数学的深刻分歧
Deep Disagreement in Mathematics
论文作者
论文摘要
反对有理解决的分歧，通常被称为``深度分歧''，一直是认识论和非正式逻辑上许多工作的重点。在本文中，我认为他们也应该受到数学哲学家的关注。我将数学上是否存在深刻分歧的问题与关于是否可以在数学上有革命的更熟悉的辩论联系起来。我使用关于Shinichi Mochizuki关于ABC猜想的作品的争议作为两个现象的潜在例子，对两个问题提出了肯定的答案。最后，我通过调查了通过美德理论方法来解决非正式逻辑和数学实践的数学深度分歧的前景。
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.
