On Jun 18, 5:11 pm, "LudovicoVan" <ju...@diegidio.name> wrote: > "Gus Gassmann" <horand.gassm...@googlemail.com> wrote in message > > news:email@example.com... > > > > > > > > > > > On Jun 18, 1:22 pm, Virgil <vir...@ligriv.com> wrote: > >> In article > >> <3694188a-d258-4273-b904-c9dc8ce80...@f14g2000yqe.googlegroups.com>, > >> WM <mueck...@rz.fh-augsburg.de> wrote: > >> > On 17 Jun., 19:36, PotatoSauce <kiwisqu...@gmail.com> wrote: > > >> > > Why are we talking about set of all sets? > > >> > Because your Platonism implies that problem unless you errect an > >> > artificial border. > > >> It is abuse of language called self-reference that produces those > >> problems, not the set theory. > > >> ZFC, NBG, Morse-Kelley and similar set theories, have no such problems. > > > Wait a minute. Am I parsing this correctly? ZFC has no problem with > > self-reference? I thought Goedel showed that any axiom system strong > > enough to encode PA can be made to be self-referential. Isn't that the > > essence of the Goedel sentence and in fact of the proof? > > Maybe it is not too incorrect to say (informally) that what is required is > an arithmetical system at least strong enough to be able to describe its own > behavior (i.e. where one can code statements and have symbols to talk about > the set of -say- provable/refutable sentences, etc. But I won't guarantee > for the details...). > > Otherwise no, self-referentiality is not a necessary ingredient to construct > undecidable statements: > > <http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems#The...>
Interesting. I'll have to try to digest that. Thanks.