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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.
| 22153 | Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter] |
| 19485 | Names have no ontological commitment, because we can deny that they name anything [Quine] |
| 19486 | We can use quantification for commitment to unnameable things like the real numbers [Quine] |
| 19487 | Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine] |