This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne ( 2018 ), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from ‘If A were true, then C would be true’ to ‘If A and B were true, then C would be true’), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics.

中文翻译：

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反事实逻辑与数学的必要性

本文关注的是反事实逻辑及其对数学断言模态状态的影响。这是对 Yli-Vakkuri 和 Hawthorne（2018 年）雄心勃勃的计划的最直接回应，他们试图确定数学致力于其自身的必要性。我证明了他们的假设将反事实条件分解为物质条件。这种崩溃导致反事实强化的成功（从“如果 A 是真的，那么 C 将是真的”推论到“如果 A 和 B 是真的，那么 C 将是真的”），这在反事实逻辑中是有争议的，并且在纯数学和应用数学中有反例。我最后讨论了数学语言中反事实条件的可有可无性。