On Thu, 28 Mar 2013 09:24:38 -0700 (PDT), email@example.com wrote:
>On Thursday, March 28, 2013 3:11:31 PM UTC, Frederick Williams wrote: > >> ... >> If groups could have classes for the collection of their elements, and >> >> if we call such groups "Groups", then we couldn't call the collection of >> >> Groups a set or a class, could we? >... > >I don't see why not. Without further restrictions, the collection of Groups would seem to be too big to be a set, but your Groups could form a class, I would think. >Classes are allowed to contain other classes after all.
Really? In what version of set theory?
>Of course, we get Russell-type paradoxes if we allow entities to contain themselves, whether the entities be sets or classes. > >Paul Epstein