A Cardinal worry for Permissive Metaontology

Permissivist metaontology proposes answering customary existence questions in the affirmative. Many of the existence questions addressed by ontologists concern the existence of theoretical entities which admit precise formal specification. This causes trouble for the permissivist, since individually consistent formal theories can make pairwise inconsistent demands on the cardinality of the universe. We deploy a result of Gabriel Uzquiano’s to show that this possibility is realised in the case of two prominent existence debates, and propose rejecting permissivism in favour of substantive ontology conducted on a cost-benefit basis. Quine declared the ontological question to be ‘what is there?’. The answer was even briefer ‘everything’, with the metaphysical hard graft consisting in filling in the details. [5] Since On What there Is the majority strand in analytic metaphysics has devoted its attentions to the Quinean details, to assaying the existents. Thousands upon thousands of words have been devoted to the question of whether properties exist, others to which (if any) mereological fusions are among the furniture of reality, still others to the supposed existence of mathematical objects – to mention just three of the most prominent existence questions considered by metaphysicians.. This research project finds itself called into question, however, by a growing constituency of permissivists. For the permissivist, the existence questions commonly asked