True nominalism: Referring versus coding

One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don't invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for two alleged nominalist views: Field's fictionalism ([1980], [1989a]), and Frank Arntzenius and Cian Dorr's geometricalism (Arntzenius and Dorr [2012]). Central to our competing approach to nominalism is a distinction between terms that refer to objects and ones that instead code empirical phenomena while being referentially empty. We next contrast our approach to nominalism, which uses this term-grained distinction between coding and referring, with approaches (to nominalism) that instead attempt to make a sentencegrained distinction between mathematical and non-mathematical content. We show the latter approach (derived from the work of Kitcher, Maddy, and Sober) fails to be responsive to objections raised by van Fraassen. In the end, only one last approach to nominalism is left standing.