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Topic: unable to prove?
Replies: 28   Last Post: Sep 18, 2012 3:54 PM

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: unable to prove?
Posted: Aug 25, 2012 11:01 AM
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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.





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