Mathematicalnominalists have argued that we can reformulate scientific theories without quantifying over mathematical objects.However, worries about the nature and meaningfulness of these nominalistic reformulations have been raised, like Burgess and Rosen’s dilemma. In this paper, I’ll review (what I take to be) a kind of emerging consensus response to this dilemma: appeal to the idea of different levels of analysis and explanation, with philosophy providing an extra layer of analysis “below” physics, much as physics does below chemistry. I’ll argue that one can address certain lingering worries for this approach by appeal to the apparent usefulness of a distinction between foundational and non-foundational contexts within mathematics and certain (admittedly controversial) arguments for Potentialism about set theory.

中文翻译：

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位势论集合论和唯名论困境


数学唯名主义者认为，我们可以在不量化数学对象的情况下重新表述科学理论。然而，人们对这些唯名论重新表述的性质和意义的担忧已经出现，比如伯吉斯和罗森的困境。在本文中，我将回顾（我所认为的）对这一困境的一种新兴共识回应：诉诸不同层次的分析和解释的想法，哲学在物理学“之下”提供了额外的分析层，就像物理低于化学一样。我认为，人们可以通过诉诸数学中基础和非基础背景之间的区别以及关于集合论的势能论的某些（诚然有争议的）论证的明显有用性来解决对这种方法的某些挥之不去的担忧。