On the Cardinality Argument Against Quidditism

Robert Black argues against quidditism on the grounds that the quidditist is either committed to proper-class many possible worlds and proper-class many possible fundamental properties or must adopt an unacceptably arbitrary restriction on the number of possible fundamental properties. In this paper, I examine Black’s cardinality argument against quidditism and argue that quidditists and non-quidditists alike have reason to reject a key premise of that argument. While it may be the case that the quidditist is committed to nomically indiscernible possible worlds that mark distinctions that make no difference to the physicist, it does not appear that the cardinality of the class of possible worlds or the class of possible fundamental properties postulated by the quidditist is any more problematic than that postulated by the non-quidditist.