Higher-order one-many problems in Plato's Philebus and recent Australian metaphysics

We discuss the one-many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one-many relationships between universals themselves: instantiation, subkind and part, and thereby construct three new ‘problems of the one and the many’ (an Eidetic Dispersal Problem, a Genus-Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy.