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Full Idea
The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted.
Gist of Idea
We could have unrestricted quantification without having an all-inclusive domain
Source
Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1)
Book Ref
'Absolute Generality', ed/tr. Rayo,A/Uzquiano,G [OUP 2006], p.2
A Reaction
Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant).
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |