Identity universalism and ontological explosion

I show that the combination of unrestricted composition and composition as identity is formally analogous to Frege’s second-order theory of objects and properties, including a commitment to an exact analogue of Basic Law V. I argue that although the view manages to avert a corresponding version of Russell’s paradox, it nonetheless remains in conflict with the Cantorian insight about cardinality underlying the paradox. I argue that such a conflict can be dissipated by thinking about the view in terms of fundamentality.