On Sat, 27 Oct 2012 22:58:21 +0100, Frederick Williams <email@example.com> wrote:
>JRStern wrote: >> >> Are there any such published? >> >> I can see in the archives here it's a common topic, and I have my own >> crackpot theories which certainly overlap a lot of the more popular >> objections. >> >> I don't want to prove or assert or reject any statement about the >> countability of reals, I just want to consider the validity of the >> diagonalization argument. >> >> Has anybody put that out in a refereed journal or a respectable >> publisher? Even if it's just a prettier rejection of crank theories, >> it would seem worthwhile. > >In his lifetime Cantor was opposed by some very competent mathematics: >Brouwer, K\"onig, Kronecker, Poincar\'e, Weyl.
Yes, and I agree with most of them, only those are intuitionist/constructivist, and they rejected large parts or all of Cantor's cardinals, reasoning, and I suppose necessarily reject ZFC.
I want to see if within ZFC, the diagonal argument itself is valid.
I suppose at worst it could be made an optional axiom, or some statement of principle could be added as an additional axiom to allow it to be true.