"David C. Ullrich" wrote: > > On Fri, 24 Aug 2012 20:14:13 +0100, Frederick Williams > <firstname.lastname@example.org> 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.