Full Idea
I suggest we give up on the account of ontological claims in terms of existential quantification. The commitment to the integers is not an existential but a universal commitment, to each of the integers, not to some integer or other.
Gist of Idea
Ontological claims are often universal, and not a matter of existential quantification
Source
Kit Fine (The Question of Ontology [2009], p.167)
Book Reference
'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.167
A Reaction
In classical logic it is only the existential quantifier which requires the domain to be populated, so Fine is more or less giving up on classical logic as a tool for doing ontology (apparently?).