On 31 Jul 2011, at 16:14, benjayk wrote:

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.
"just" have a theory that manages to state this very clearly, and

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

0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)

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.

Just to be precise, the TOE is not the universal system, but some first order classical logic, with equality, extension of the chosen universal system. OK. (the UMs and the LUMs are more like hero and heroin in the dramas the TOE allows)

The notion of a TOE usually is used in a reductionist sense, as a
theory that can be used to predict everything.

A TOE should do that, in principle at least.
Of course it should be able to predict everything which is predictible, in the right condition. No one asks for a TOE which can predict things which are not predictible. No TOE can predict that you will feel to be, just after the duplication, in W or in M.

I don't think this can be
done through universal systems. It appears to me COMP allows for
uncomputable, and therefore unpredictable phenomena.

A lot. All surprises hide surprises.

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?

The exact contrary. Comp is not just a change in 'perspective' (Aristotle -> Plato), but the discovery of a creative bomb (the UM). With comp we begin to know that we don't know what we are doing. We can (machines can) understand that by trying to control it, we make it less controllable. A bit like a mother with a baby. That is not something entirely new, but here it appears in the 3-theories.

COMP shows, as you said, that there are unbridgeable gaps, which really
means there is something left unexplained, and unexplainable.

Absolutely so (assuming comp). comp = CT + "yes doctor". CT subsumes arithmetic.

So no theory
can explain everything. But we can show the necessity of there being a gap.

OK. You are right. I will abandon the label TOE, for TOAE. Theory of almost everything.

But, you know, it is more than the necessity for a gap, it is the discovery that the gap 'kick back', it has a geometry, it is "something" and machines have access to it, they can point mathematical telescope on it, also.

Comp leads to a generalization of Everett's idea to apply QM to the observer. Comp applies arithmetic and meta-arithmetic (a part of arithmetic by Post, Gödel, Kleene & Co.) to the 'body' of the mathematician, or at least the one who say yes doctor to a doctor which serendipitously opts for the correct level, in a mathematical precise sense: in this case it inherits of the hypostases, and the logic of it determine the views you can have from inside. But the simplest thing you can say on those views is that they all make us more ignorant. The "concrete" relative Löbian machines get interesting on the border of the computable and non computable, where very deep sharable histories develop, in all case, from all views some mysteries subsists, and some key mystery, the gap, have a quasi life of its own. But *that* fact, that there are mysteries, is no more a mystery. And in that sense, comp provides, I think, the first coherent picture of almost everything, from God (oops!) to qualia, quanta included, and this by assuming only seven arithmetical axioms.
And the point is not that this is true, but that this is testable.
Comp, not so much unlike salvia perhaps, put you naked in front of the unknown. But not without tools.


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