----- Original Message -----
From: "Russell Standish" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, May 25, 2007 12:14 AM
Subject: Re: Overcoming Incompleteness
> On Thu, May 24, 2007 at 11:53:59PM -0400, Stephen Paul King wrote:
>> For me the question has always been how does one "overcome
>> Incompleteness" when it is impossible for a simulated system to be
>> to its simulator unless the two are one and the same.
> Is it though? If the simulated system is different from the original,
> then indeed I would agree with you.
It was the difference that i was trying to focus on... "Bisimulation"
is, after all, a form of identity if exact.
> In the case of human self-awareness, I thought it was implemented not
> by simulation as such, but by decoupling the actual inputs and outputs
> from the real world, and then feeding the scenario input into the
> actual brain circuit, and examine the output _without_ actually moving
> a muscle. It has something to do with the "mirror" neurons, and it
> really is quite a neat trick (at least Dennett thinks so, and I tend
> to agree).
Ok, but that is it that is "generating" and "examining" the inputs and
outputs? I am trying to frame this in software terms...
> Not being into supernatural explanations, I think a perfectly
> mechanical, or formal model should be able to capture this
> ability. But how to do it without running into infinite regress is the
> challenge. And if and when we have this formal model, we can then see
> this idea of solving incompleteness has any merit. I'm as sceptical as
> anyone, but I do believe the case is more subtle than to be destroyed
> by a couple of lines of handwaving argument :).
We avoid infinite regress by having only finite computational resourses.
X can only generate a simulation of itself with a resolution whose upper
bound is determined by the resourses that X has available within the span of
of the simulation of X. Remember, X is not a static entity...
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