数学中的深刻分歧
Deep Disagreement in Mathematics
摘要：
抵制理性解决的分歧，通常被称为“深刻的分歧”，一直是认识论和非形式逻辑中许多工作的焦点。在本文中，我认为它们也值得数学哲学家的关注。我把数学中是否会有深刻分歧的问题与一个更熟悉的辩论联系起来，即数学中是否会有革命。我提出了一个肯定的答案，这两个问题，使用争议的望月新一的工作的ABC猜想作为一个潜在的例子，这两种现象。最后，我调查的前景，解决数学的深刻分歧，在美德理论的方法，以非形式逻辑和数学实践。
英文摘要：
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.
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