Identity universalism and ontological explosion

Abstract Call the combination of Unrestricted Composition and Composition as Identity Identity Universalism . I examine in detail some important features of this view in connection with Russell’s paradox and Cantor’s theorem, which have been of interest in the recent literature. I begin by showing that Identity Universalism entails an ontological explosion principle about plurals and mereology that’s exactly analogous to Frege’s infamous Basic Law V. I identify how Identity Universalism, unlike Frege’s system, nonetheless manages to avoid falling prey to a corresponding version of Russell’s paradox. I then argue that although Identity Universalism manages to forestall the letter of the paradox, it nonetheless remains in direct conflict with the Cantorian insight about cardinality at the basis of the paradox, which in this setting is the plural version of Cantor’s theorem. But I offer reasons why identity universalists needn’t be overly concerned about this. On the one hand, the same features of the view that preclude a derivation of the paradox also preclude a derivation of the theorem. On the other, identity universalists may help themselves to resources from recent discussions in fundamental metaphysics to articulate their understanding of reality, which may help allay concerns about their manifest anti-Cantorianism.