Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
dilettante

Posts: 141
Registered: 5/15/12
Re: unable to prove?
Posted: Aug 25, 2012 11:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
news:c3qh38lilvho3lnar8gvo1po7rbhmokflr@4ax.com...
> 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.


This has always been a little disconcerting for me. I've read that it was
proved that CH is independent of the usual axioms of set theory, or
something like that. It seems to me that if the real numbers are a well
defined object, then its power set should be a well defined object, and it
should be the case that either some member of that power set has cardinality
between that of the naturals and that of the reals, or not. If such an
animal did exist, it should be at least possible for someone to exhibit it
in some way - "here it is, now what about that independence?" The fact that
this isn't so is very strange to me, but there are more things in heaven and
earth than are dreamt of in our philosophy, Horatio.
Any thoughts on how to better grasp this little conundrum?
>
>





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.