What Is Existence?

Abstract

This paper has a negative and a positive claim. The negative claim is that the Frege-Russell account of existence as a higher-order predicate is mistaken and should be abandoned, even with respect to general statements of existence such as “Flying mammals exist” (where statements of this sort are supposed to be best accommodated by the account). The Frege-Russell view seems to be supported by two ideas. First, the idea that existence is entirely expressed by the existential quantifier of standard predicate logic. Second, the idea that the existential quantifier is a higher-order predicate, a predicate of predicates, not of individuals. I think that both ideas are wrong but will focus on the latter. By construing prima facie first-order statements such as “Flying Mammals exist” as higher-order predications such as “The Fregean Concept Flying Mammal maps at least one individual onto the True”, the Frege-Russell view commits one merely on the basis of the meaning it assigns to the existence predicate – to abstract objects such as concepts (Gottlob Frege), or propositional functions (Bertrand Russell), or classes (Rudolf Carnap), or properties, kinds, and so on. This cannot be right, I think. The positive claim of the present paper is that, at least in the context of first-order discourse, the existence predicate is just what it seems to be: a bona fide first-order predicate (pace Kant, Hume, Frege, Russell and others). Three important ideas about existence are shared with the Frege-Russell conception of existence, though.