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Ralf Busse, Class Nominalism, Wolterstorff's Objection, and Combinatorial Worlds, The Philosophical Quarterly, Volume 66, Issue 265, October 2016, Pages 680–700, https://doi.org/10.1093/pq/pqw016
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Abstract
Wolterstorff's objection (WO) to Class Nominalism says that properties cannot be identical to classes because classes have their members essentially while properties typically do not have their instances essentially. I develop a two-step solution to WO on behalf of actualist nominalism: part one shows that the actualist nominalist can mimic Lewis's reply to WO by identifying abundant properties with classes of ersatz individuals in combinatorial ersatz worlds. Part two shows that the possibilia-generating recombination can be based on perfectly natural classes of actual particulars instead of sparse universals: to consider a particular as instantiating a natural class is not to consider it as possibly being one of the things in that class but as being like those things; instantiation is not membership but a ‘qualitative’ relationship defined by a resemblance-like primitive that compares particulars, as they might be, to pluralities of actual particulars, as they actually are.
