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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 Ref
'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?).
| 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] |