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Re: unable to prove?
Posted:
Aug 25, 2012 11:24 AM
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"David C. Ullrich" wrote:
>
> On Fri, 24 Aug 2012 20:14:13 +0100, Frederick Williams
> <freddywilliams@btinternet.com> wrote:
>
> >TS742 wrote:
> >>
> >> Are some hypotheses unprovable?
> >
> >Idiots like me may say, "no, the hypothesis 0 =/= 0 is unprovable".
> >
> >Do you mean "are some truths unprovable?"? I don't know. Some may
> >claim that the truths of mathematics ae just those statements that are
> >provable.
> >
> >> Or do they all have a proof that is
> >> just not found yet? The Riemann hypothesis comes to mind.
> >
> >Let's suppose that RH is true. "RH is unprovable" may mean various
> >things:
> >(1) Humans could prove it were it not for the fact that they will become
> >extinct before they do so. (And that "could" means what?)
> >(2) Humans can't prove it because their brains are too feeble. (But the
> >giraffe-like beings on planet Scorrrf (my keyboard doesn't have the
> >diacritics that the first and third "r"s should have) prove it as
> >homework in their first year a school.)
> >(3) A computer (built and programmed by another computer) proved it
> >after running for sixty years, but no one is foolhardy enough to claim
> >that they understand what that computer is doing or that it is bug-free.
> >(4) No machine or creature in this universe or any other will ever prove
> >it.
> >
> >What about the continuum hypothesis in place of RH?
>
> In my opinion (with which many diisagree) it's not clear that CH
> _is_either true or false in any absolute sense. If so then it's
> much more problematic here.
And that is precisely why I mentioned it!
--
The animated figures stand
Adorning every public street
And seem to breathe in stone, or
Move their marble feet.
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