Full Idea
Ontological commitment is carried by first-order quantifiers; a second-order quantifier needn't be taken to be a first-order quantifier in disguise, having special items, collections, as its range. They are two ways of referring to the same things.
Gist of Idea
First- and second-order quantifiers are two ways of referring to the same things
Source
George Boolos (To be is to be the value of a variable.. [1984], p.72)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.72
A Reaction
If second-order quantifiers are just a way of referring, then we can see first-order quantifiers that way too, so we could deny 'objects'.