ABSTRACT

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power.

中文翻译：

---

数学解释中反事实解释面临的挑战

摘要

一些数学证明解释了为什么它们证明的定理成立。本文确定了数学解释的任何反事实解释的几个挑战（即，任何解释性证明根据解释揭示解释如何不同的解释，如果解释者中的事实不同）。该论文假设反数学可以是不平凡的。它认为，尽管如此，反事实说明将解释力描述为太容易实现，没有捕捉到解释的不对称性，也没有说明为什么某些证明是解释性的，而另一些则不是。关于反事实依赖的更多信息甚至可以产生更少的解释力。