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Full Idea
Through our variables of quantification we are quite capable of committing ourselves to entities which cannot be named individually at all in the resources of our language; witness the real numbers.
Gist of Idea
We can use quantification for commitment to unnameable things like the real numbers
Source
Willard Quine (On Carnap's Views on Ontology [1951], p.205)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.205
A Reaction
The real numbers are uncountable, and thus cannot all be named. This is quite an impressive point. I've always had doubts about the existence of real numbers, on the grounds that they could never all be named.
| 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] |