# What are some ways of understanding plural predication (and what are some academic resources on the matter)?

The particular case I'm thinking about has to do with existence. Peter Van Inwagen writes:

'When I say that affirmation of existence is denial of the number zero, I mean only that to say that Fs exist is to say that the number of Fs is not zero. For example, in my view, ‘Horses exist’ is equivalent to ‘The number of horses is not zero.’

This is in response to Frege's position, that an affirmative general existential such as 'horses exist' is to be understood as ascribing to the concept horse the property of 'having more than one instance'. Van Inwagen thinks it's misleading to reduce the existence of real horses to a property that belongs to a concept, and not the actual objects that exist.

Vallicella writes in response to this: 'What I don’t understand is how “more than zero” can attach to a plurality as a plurality, as opposed to a one-over-many such as a concept. A plurality as a plurality is not one item but a mere manifold of items: There is simply nothing there to serve as logical subject of the predicate “more than zero”'.

I sort of agree with Vallicella here, but as I was looking for a bit more detail, he unfortunately continues with: 'But to discuss this further would take us far afield into the topic of plural predication.'

So, I was wondering what sort of general 'views' or 'positions' of plural predication could deal with this issue.

• Peter van Inwagen, “Being, Existence, and Ontological Commitment”, in Metametaphysics: New Essays on the Foundations of Ontology, ed. Chalmers et al. (Oxford University Press, 2009), 483. Italics in original
• William Vallicella, "Existence: Two Dogmas of Analysis", in Neo-Aristotelian Perspectives in Metaphysics, ed. Novak et al. (Routledge, 2014), 48
• Plural Quantification is a good overview/introduction to some relevant material, though the distinction between quantifiers and predicates might make seeing the relevance a little iffy (c.f., however, quantifiers as second-order predicates, as with Frege per your reference). Commented Jul 19, 2023 at 4:21
• Thank you so much. Not sure why I did not come across that already haha. Commented Jul 20, 2023 at 1:48