With the meager ontological commitments, the deflationary nominalist fares very well on the ontological front. One source of concern is how meager the deflationary nominalist's ontology ultimately is. For instance, platonists would insist that mathematical objects are ontologically independent of our psychological processes and linguistic practices, and—using the criterion of ontological commitment offered by the deflationary nominalist—they would insist that these objects do exist. Similarly, modal realists (such as Lewis 1986) would also argue that possible worlds are ontologically independent of us in the relevant sense, thus concluding that these objects also exist. Deflationary nominalists will try to resist these conclusions. But unless their arguments are successful at this point, the concern remains that the deflationary nominalist may have a significantly more robust ontology—given the proposed criterion of ontological commitment—than advertised.