In many ontological debates there is a familiar challenge. Consider a debate over X s. The “small” or anti-X side tries to show that they can paraphrase the pro-X or “big” side’s claims without any loss of expressive power. Typically though, when the big side adds whatever resources the small side used in their paraphrase, the symmetry breaks down. The big side plus small’s resources is a more expressively powerful and thus more theoretically fruitful theory. In this paper, I show that there is a very general solution to this problem, for the small side. Assuming the resources of set theory, small can successfully paraphrase big. This result depends on a theorem about models of set theory with urelements. After proving this theorem, I discuss some of its philosophical ramifications.

在许多本体论辩论中，都有一个熟悉的挑战。考虑关于X s的辩论。“小”或反X方面试图表明他们可以解释pro- X或“大方”的主张，而不会丧失任何表达能力。但是，通常情况下，当大方添加其解释中使用的任何资源时，对称性就会破坏。大方加小方的资源是一种更具表现力的理论，因此在理论上也更有成果。在本文中，我表明对于小问题，有一个非常通用的解决方案。假设有集合论的资源，那么小可以成功地解释大。该结果取决于关于带有urelements的集合论模型的一个定理。在证明了这个定理之后，我讨论了它的一些哲学分支。