Wilfrid Sellars and Willard Van Quine long disagreed over the nature of ontological commitment in scientific inquiry. Particularly, they disagreed over whether abstract entities such as numbers, sets, or classes should be admitted into scientific ontology. In Quine’s view, positing such platonic entities is necessary in order for scientific inquiry to progress and for scientific knowledge to increase. Sellars, on the other hand, sees such a view as a form of platonic realism and eschews it in favor of a more austere nominalism about the ontological status of abstracta. I summarize the reasons for each philosopher’s view, drawing on a dialogue between them regarding the ontological status of abstracta. I argue that Quine’s justifications for his pragmatically-based realism do little to evade Sellars’ charge that such a view commits one to an empirically unjustifiable platonistic ontology. In Sellars’ view, an adequate philosophy of science requires an adequate philosophy of mind, and this implies that we cannot locate unobservable platonic abstracta on an ontological continuum with the unobservable theoretical entities posited in scientific theories (e.g., neutrinos or positrons). Those who are committed to the ideals of scientific realism and methodological naturalism must grapple with the question Sellars posed to Quine: “if sets are basic objects, how does the mind get in touch with them?”

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