You are right when it comes to the combination of two independent systems A and B. What the original poster's idea was a self-simulating, or self-aware system. In this case, consider the liar type paradox:
I cannot prove this statement Whilst I cannot prove this statement, I do know it is true, simply because if I could prove the statement it would be false. To know that it is true, I am using self-reference about my own proof capabilities. I don't think anyone yet has managed a self aware formal system, although self-reproducing systems have been known since the 1950s, and are popularly encountered in the form of computer viruses. There has to be some relationship between a self-reproducing system and a self-aware system... Cheers On Thu, May 24, 2007 at 09:45:45PM -0400, Jesse Mazer wrote: > > 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 <[EMAIL PROTECTED]> > >Reply-To: [EMAIL PROTECTED] > >To: [EMAIL PROTECTED] > >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 [EMAIL PROTECTED] > >Australia http://www.hpcoders.com.au > >---------------------------------------------------------------------------- > > > >> > > _________________________________________________________________ > Like the way Microsoft Office Outlook works? You'll love Windows Live > Hotmail. > http://imagine-windowslive.com/hotmail/?locale=en-us&ocid=TXT_TAGHM_migration_HM_mini_outlook_0507 > > > -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
