Prioritizing Platonism

Some see concrete foundationalism as providing the central task for sparse ontology, that of identifying which concreta ground other concreta but aren’t themselves grounded by concreta. There is, however, potentially much more to sparse ontology. The thesis of abstract foundationalism, if true, provides an additional task: identifying which abstracta ground other abstracta but aren’t themselves grounded by abstracta. We focus on two abstract foundationalist theses—abstract atomism and abstract monism—that correspond to the concrete foundationalist theses of priority atomism and priority monism. We show that a consequence of an attractive package of views is that abstract reality has a particular mereological structure, one capable of underwriting both theses. We argue that, of abstract foundationalist theses formulated in mereological terms, abstract atomism is the most plausible.