Le 24-mai-07, à 19:32, Mohsen Ravanbakhsh a écrit :

> 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.



They cannot *know* that. The first person associated to each system is  
different of the other. Unless you mean something *very* general by  
"similar".






> Then both have the reason to believe in each others statements, with  
> the improvement that the new system is COMPLETE.


Why? Only if S2 is much more simple than S1, can S1 be complete on S2.  
No system can be complete on itself or on anything similar to itself.





> 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 n 
> or disprove it, so you tell 
>  THEM that their statement is true.


If that is a proof, then you are inconsistent. If it is an intuition,  
or a prayer, a hope, a bet, or anything like that, then it is ok, but  
you don't need to system for that. S1 can use the very similar system  
S1 itself.
The apparent infinite regression is soleved by the traditional  
diagonalisation technics. Look in the archive for both
diagonalisation  and
diagonalization
in the archive. Or ask (and be patient :)




> 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 a simulation is not a proof, especially if the simulation doesn't  
halt.




> But in the logical sense ONE system wont be able to overcome the incomp 
> leteness, 
> 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.


Here I do agree (but from a different reasoning). See later, or,  
meanwhile, search for "Plotinus" or "guardian angel" or "hypostases".

Very shortly, the lobian-godelian incompleteness forces the distinction  
between:

p
Bp
Bp & p
Bp & Dt
(Bp & p) & Dt

which makes a total of eight  notions of "self" (8, not 5, because 3 of  
them splits in two different logic due to incompleteness. B is for  
"beweisbar" and correspond to Goel arithmetical provability predicate.

You can read them as

truth
provability
knowability
observability
sensibility

or, with Plotinus (300 AD):

ONE
INTELLECT
SOUL
INTELLIGIBLE MATTER
SENSIBLE MATTER

With the provable versus true distinction (the  [ ] / [ ]*   
distinction), the hypostases are:


                                one
discursive Intellect                    divine Intellect
                                soul
intell. matter                          intell. matter
sensible mat.                           sensible mat

AND THEN, éadding the comp assumption leads to the comp physics, for  
the soul and both matter hypostases, and it is enough to cmpare the  
comp-physics with the empirical physics to evaluate the degree of  
plausibility of comp. And that's my point.

Bruno


http://iridia.ulb.ac.be/~marchal/

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