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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 Ref
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'.
| 2611 | It is currently held that quantifying over something implies belief in its existence [Ayer] |
| 19486 | We can use quantification for commitment to unnameable things like the real numbers [Quine] |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| 1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
| 5747 | "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
| 12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |