The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, others ‘thin’ and ontologically peripheral—and examine this distinction in relation to some notable ‘ontic’ accounts of explanation. I also discuss the issue in the broader context of other ‘explanationist’ realist arguments.

中文翻译：

---

论数学的“不可或缺的解释作用”

关于数学实在论必不可少的论证的文献经常提到数学的“不可或缺的解释作用”。我认为我们应该从科学解释的具体概念的角度来审视解释性不可或缺的概念。原因是解释性的必要性本身并不足以证明危及的本体论结论的合理性。为了表明这一点，我引入了不同类型解释角色之间的区别——一些“厚”和本体论承诺，另一些“薄”和本体论边缘——并检查这种区别与一些值得注意的“本体”解释解释的关系。我还在其他“解释主义”现实主义论证的更广泛背景下讨论了这个问题。