more from A.George / D.J.Velleman

Single Idea 10109

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing]

Full Idea

Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets.

Gist of Idea

ZFC can prove that there is no set corresponding to the concept 'set'

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.90


A Reaction

This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets.