Dear Russell,

    Isn't the key feature of a "self-aware system" the ability to generate 
some form of representation of itself within itself? Would it not be a 
simple matter of a system being able to generate some form of simulation of 
itself such that there is both a similarity and a difference between the 
system and its simulation of itself?
    The similarity, it seems to me, would be merely a matter of faithful and 
predictible simulation of the system; the difference might be a difference 
in state, resolution or some other measure.

    For me the question has always been how does one "overcome 
Incompleteness" when it is impossible for a simulated system to be identical 
to its simulator unless the two are one and the same. Given this identity, 
how then does any notion of provability arise when all that exists is a 
tautology, A=A.

    BTW, have you ever taken a look at Jon Barwise's treatment of the Liar 
Paradox?

http://en.wikipedia.org/wiki/Jon_Barwise

Kindest regards,

Stephen

----- Original Message ----- 
From: "Russell Standish" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, May 24, 2007 10:12 PM
Subject: Re: Overcoming Incompleteness


>
> 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


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