Le 22-mai-07, à 12:57, Mohsen Ravanbakhsh a écrit :

> Hi everybody,
> It seems Bruno's argument is a bit rich for some of us to digest, so I 
> decided to keep talking by posing another issue.
> By Godel's argument we know that every sufficiently powerful system of 
> logic would be incomplete, and recently there has been much argument 
> to make human an exception;


Mainly Lucas 1960 and Penrose recent books. But Emil Post found in 1921 
(!!!) both the "godelian" argument against mechanism AND the pitfal (it 
is just an error) in that argument.
Those who read french can look at my  "Conscience & Mecanisme" for a 
thorough analysis of that "error", including the natural "machine's 
answer" to that error.



> that's because we see the truth of Godelian statements ( i.e. This 
> sentence is unprovable in this system)


Of course we "see" the truth only for simple machine. Not for machine 
just a little more complex. This is used explicitly in my approach. A 
rich lobian machine (like ZF) can derived the whole theology of PA 
(whole means both the provable and unprovable part (at some level)). 
But ZF has to make a leap of faith to lift that theology on herself.


> Let's call such a system S1, and call another (powerful enough in 
> Godel's sense) system S2. and suppose S2 structurally is able to give 
> statements about the statements in S1. What does it mean? Consider S2 
> as a being able examine some statements in S2 via some operators and 
> get the result(like function calls).
>  
> My claim is:
>  
> 1.
>  S2, is able to see the truth of the Godelian statements in S1, and in 
> some sense:
> "S2 is complete against the statements of S1", because it can see that 
> S1 at last wont be able to evaluate our Godelian statement and so the 
> statement would be correct.

You are correct (up to some details I want bore you right now)

>  
> 2.
> We humans are vulnerable to the Godelian statements like all other 
> logical systems.


Yes. As far as we are correct!


> We have our paradoxes too.
> Consider the same Godelian statement for yourself as a system 
> (i.e. "You can't prove me" or some similar sentences like "This 
> sentence is false")


Better:    This sentence is not provable by you.
Is that sentence true? Can you prove it?

>  
> 3.in the first claim consider the first system to have the same 
> attitude toward the second one, I mean let there be a loop (some how 
> similar to Hofstadter's Strange loops as the foundation of self)
> Is it complete of not? 


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 (imo).

I have to go. Don't hesitate to make any comments. If I am slow to 
answer, it just means I'm a bit busy, not that I consider some question 
don't have to be answered. Thanks for the interest,

Bruno









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


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