more on this theme | more from this thinker
Full Idea
There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases.
Gist of Idea
Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals
Source
Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1)
Book Ref
'Absolute Generality', ed/tr. Rayo,A/Uzquiano,G [OUP 2006], p.4
| 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] |