Full Idea
Quine said higher-order logic is 'set theory in sheep's clothing', and there is concern about the ontology that is involved. One approach is to deny quantificational ontological commitments, or say that the entities involved are first-order objects.
Gist of Idea
Various strategies try to deal with the ontological commitments of second-order logic
Source
comment on Willard Quine (Existence and Quantification [1966]) by B Hale / C Wright - Logicism in the 21st Century 8
Book Reference
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.197
A Reaction
[compressed] The second strategy is from Boolos. This question seems to be right at the heart of the strategy of exploring our ontology through the study of our logic.