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Single Idea 13451

[filed under theme 4. Formal Logic / F. Set Theory ST / 1. Set Theory ]

Full Idea

The two best understood conceptions of set are the Iterative Conception and the Limitation of Size Conception.

Gist of Idea

The two best understood conceptions of set are the Iterative and the Limitation of Size

Source

Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)

Book Ref

'Absolute Generality', ed/tr. Rayo,A/Uzquiano,G [OUP 2006], p.7


The 6 ideas from Rayo,A/Uzquiasno,G

We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]
Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]