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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 Ref
'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.
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |