ABSTRACT
Platonists differ considerably in their views about the diversity, modal status, and intrinsic nature of abstracta. This chapter presents some of the most significant of these divisions. Other platonist options fall between the two rough categories of metaphysical platonism and anti-nominalism. But these two quite different strains of platonism face distinctive challenges, which are inherited by many of the views that fall between them. Metaphysical Platonists will address worries about epistemic, semantic, or cognitive access by leaning heavily on the distinctive character of abstract entities. And, while metaphysical platonists can wheel out elaborate views about the nature of abstracta to allay concerns about non-uniqueness, anti-nominalists are more likely to reject these concerns as hair-splitting. Unlike metaphysical platonists, they can comfortably opt for a kind of pragmatic indifference. For those more interested in providing metaphysical explanations, any viable nominalism must replace abstract entities with either a largesse of ideology or additional concrete entities.
