Abstract

Two proofs are given which show that if some set of truths fall under finitely many concepts (so-called Collectivity), then they all fall under at least one of them even if we do not know which one. Examples are given in which the result seems paradoxical. The first proof crucially involves Moorean propositions while the second is a reconstruction and generalization of a proof due to Humberstone free from any reference to such propositions. We survey a few solution routes including Tennant-style restriction strategies. It is concluded that accepting Collectivity for some set of truths while also denying that any of the involved concepts in isolation capture all of them requires that one of these concepts cannot be closed under conjunction elimination. This is surprising since the paper surveys several applications in which Collectivity and the latter closure condition seemed jointly satisfiable for concepts of actual philosophical interest.