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.