I definitely don't think the two systems could be complete, since (handwavey
argument follows) if you have two theorem-proving algorithms A and B, it's
trivial to just create a new algorithm that prints out the theorems that
either A or B could print out, and incompleteness should apply to this too.
Jesse
>From: Russell Standish <lists.domain.name.hidden>
>Reply-To: everything-list.domain.name.hidden
>To: everything-list.domain.name.hidden
>Subject: Re: Overcoming Incompleteness
>Date: Thu, 24 May 2007 23:59:23 +1000
>
>
>Sounds plausible that self-aware systems can manage this. I'd like to
>see this done as a formal system though, as I have a natural mistrust
>of handwaving arguments!
>
>On Thu, May 24, 2007 at 10:32:29AM -0700, Mohsen Ravanbakhsh wrote:
> > Thanks for your patience! , I know that my arguments are somehow
> > raw and immature in your view, but I'm just at the beginning.
> >
> > *S1 can simulate S2, but S1 has no reason to believe whatever S2 says.
> > There is no problem.
> > **Hofstadter "strange loop" are more related to arithmetical
> > self-reference or general fixed point of recursive operator*
> >
> > OK then it, becomes my own idea!
> > Suppose S1 and S2 are the same systems, and both KNOW that the other one
>is
> > a similar system. Then both have the reason to believe in each others
> > statements, with the improvement that the new system is COMPLETE. We've
>not
> > exploited any more powerful system to overcome the incompleteness in our
> > system.
> > I think this is a great achievement!
> > It's actually like this: YOU believe in ME. THEY give
> > you a godelian statement (You theoretically can not prove this
> > statement) you give it to ME and then see that I can neither prove it
> > nor disprove it, so you tell
> > THEM that their statement is true.
> > But the wonder is in what we do just by ourselves. We have a THEORY OF
>MIND.
> > You actually do not need to ask me about the truth of that statement,
>you
> > just simulate me and that's why I can see the a godelian statement is at
> > last
> > true. But in the logical sense ONE system wont be able to overcome the
> > incompleteness,
> > so I might conclude:
> > I'M NOT ONE LOGICAL SYSTEM!
> > This is how we might rich a theory of self. A loopy(!) and multi(!)
>self.
> >
> >
> >
> > *
> >
> > *Mohsen Ravanbakhsh
> >
> > >
>
>--
>
>----------------------------------------------------------------------------
>A/Prof Russell Standish Phone 0425 253119 (mobile)
>Mathematics
>UNSW SYDNEY 2052 hpcoder.domain.name.hidden
>Australia http://www.hpcoders.com.au
>----------------------------------------------------------------------------
>
>>
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Received on Thu May 24 2007 - 21:46:03 PDT