On Sun, 28 Oct 2012 04:23:28 -0700, JRStern <JRStern@foobar.invalid> wrote:
>On Sun, 28 Oct 2012 07:31:24 +0000 (UTC), "Peter Webb" ><webbfamilyDIEspamDie@optusnet.com.au> wrote: > >>> 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. >>> >>> J. >> >>Its a theorem in ZF. It doesn't need an axiom. > >It seems a little involved to be the kind of thing we like to call a >theorem,
> and I believe it was Poincare who said it (or was he just >broad-brushing all of Cantor?) only works by assuming its conclusion.
I don't believe that. Any evidence at all?
>What would it take to make Poincare happy with this one particular >theorem? > >I think there may be another line of criticisms that the diagonal >argument asserts certain properties to the two-dimensional lists of >numbers on which it draws diagonals, that cannot really be assumed so >freely. > >This is separate from what may still be true about ZFC and CH, after >all Cantor started without the diagonal argument and maybe he was >better off that way after all.