Bruno Marchal wrote:
> On 24 Jul 2011, at 22:08, benjayk wrote:
>>> OK. Remember the goal, to find the, or a, TOE.
>>> What I suggest, at least, is that with comp, any first order logical
>>> specification of any universal machine, will do.
>> Well, okay. I just get the feeling that a TOE doesn't really exist.  
>> You
>> "just" have a theory that manages to state this very clearly, and  
>> logically.
> You might try to take literally what I say. I was saying that each  
> universal numbers (like FORTRAN, Conway's game of life, LISP, prolog,  
> Robinson arithmetic, etc.) are TOE. To fix the things I have chosen  
> Robinson Arithmetic.
> The theory of everything is basically a bit of classical logic and the  
> axioms:
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0
> x*s(y)=(x*y)+x
> Another one is mainly
> Kxy = x
> Sxyz = xz(yz)
> That gives rich ontologies in which internal observers "project  
> realities". With comp we have to embed the mathematician (the little  
> ego!) in arithmetics, and the laws of mind and matter does not depend  
> on the choice of the first initial universal system.
> All computations contains all computations by all universal systems,  
> that is why the tehological matter (including physics) does not depend  
> on the initial choice. It does not mean that there is no TOE. Only a  
> lot, which are equivalent  for the fundamental matter. They lead all  
> to the same hypostases, once you accept the classical theory of  
> knowledge (Theaetetus).

We can debate the terms. I think calling universal systems a TOE is a bit of
a stretch. The notion of a TOE usually is used in a reductionist sense, as a
theory that can be used to predict everything. I don't think this can be
done through universal systems. It appears to me COMP allows for
uncomputable, and therefore unpredictable phenomena. 
I am critical of the very notion of a TOE. It doesn't make much sense. Even
current physics clearly shows that results of experiments can't be predicted
precisely. So is the TOE supposed to give a perfect probability
distribution? But what is this even supposed to mean?

COMP shows, as you said, that there are unbridgeable gaps, which really
means there is something left unexplained, and unexplainable. So no theory
can explain everything. But we can show the necessity of there being a gap.
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