On Jun 20, 7:02 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > Transfer Principle <lwal...@lausd.net> writes: > > On Jun 20, 8:51 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > >> Newberry <newberr...@gmail.com> writes: > >> > That's right. There is no formula or algorithm to construct the list. > >> > It means that you would have to flip each and every digit one by one. > >> > And that is impossible. > >> Of course, it is perfectly reasonable to accept that there is no such > >> list, because Newberry says so. > > > Ah, so it's nice to see that Newberry has joined Herc and WM in > > this ever-growing thread. > > Yes, how nice! Er, how come? Why do you think this is a nice thing? > > Honestly? It's not that I think it's a bad thing --- though, to be > honest, I think Newberry's better than the argument he gives here --- > but why do you think it's a positive development? > > > > >> Cantor was this utterly insane freak who chose not to accept Newberry's > >> word for it, and instead *prove* that there was no list of all real > >> numbers. > > > But this proof that there is no list of all real numbers must use > > the axioms of some _theory_ (such as ZFC) -- a theory which > > Newberry isn't required to accept just because Hughes says so. > > Of course he's not required to accept it. So? > > Nonetheless, it is a *theorem*, namely a theorem of ZF. > > > > > So Hughes continues to be a Herc-religionist (i.e., a religionist > > according to Herc), appealing to ZFC to prove Newberry wrong even > > though there's no reason to assume that Newberry is working in ZFC (or > > any other theory proving Cantor's Theorem). > > If Newberry means that Cantor's Theorem is not a Theorem in some other > (specified) theory, then, of course, I'd have no opinion at all, until I > saw the theory. > > So, let's ask Newberry! > > Newberry, what theory did you have in mind?
What I had in mind is that if you drop the axiom of extent you can either conclude that there is no such list or that the anti-diagonal does not exist analogously to the conclusion that the set R = {x | ~(x in x} does not exist.
BTW, Cantor did not work in ZFC and the argument given by McCullough appeared to be on the intuitive level rather than in any particular formal theory.
I will grant you that Zermelo figured how to construct a system where the diagonal argument goes through and his system is probably consistent. It is a nonsense nevertheless. All the transfinite set theory is a completely superfluous metaphysics.
> -- > Jesse F. Hughes > "I'm not going to forget what I've seen. I understand the devastation > requires more than one day's attention." > -- G. W. Bush reassures Hurricane Katrina victims. Two days, minimum.
