Brent Meeker wrote:

>OK.  So do you invoke an anthropic principle in the step (computer law)
>=> (mind law) ...

Let us a say a Church Turing Markov -tropic principle, eventually.
If you want I (re)define the physical by what is observable
by a sound universal machine. And observable is eventually
defined by a measure on her set on consistent extension, and I
must add "as seen by her". 


>and then hope to show that will entail the step (mind
>law) => (physical law)?  

It seems to me that the UDA entails that "reversal".
We must recover physical laws and physical sensations from the 
discourse of "average" sound universal
machine about their most probable computational neighborhood.


>And why do you take this approach rather than
>(number law) => (computer law) => (physical law) => (mind law)?

Just for the "kantian" reason that I can access only to my first
person knowledge, even when I just look to a needle of a physical
measuring apparatus. The UDA shows I must integrate on all
computational histories going through, similar enough, from
a first person point of view, states. Those states-point of
view are psychological concept.
It could still be possible that, in fine,

              (physical law) <=> (mind law)  

That could happen if our level of description is very low.
But then we will know it, without having put the mind-body
problem under the rug.

What is very promising with the arithmetical transformation is that
all logics are doubled (G and G*, Z and Z*, ...) so that we get 
information on both communicable and incommunicable propositions. 
The arithmetical quantisation seems to put light on both 
qualia and quanta.

Also, independently, Maudlin and me have shown in some more
direct way that, with comp, there is no hope for (physical law) 
=> (mind law). (It is the crackpot proof in Jacques Mallah's 
terms!, look in the archive at key words like "Maudlin", 
"movie", "crackpot". (But with Occam it is not necessary).

 
>Perhaps you could briefly elucidate what you think goes into each " =>
>"?  For example, I assume that the step (number law) => (computer law)
>is motivated by saying our TOE must be finitely describable and so it
>must lie in a subset of all mathematics that is most explicitly defined
>by computation.  Is this right?

Mmh ...
Arithmetical truth is not finitely describable and I doubt there
is a TOE for any first person plenitude (Levy's term).
You should realise that Godel shows that the structure
(N, +, x, >, =, 0)  is far more complex than the equivalent
structure for the reals, which are completely captured by the
notion of archimedian algebraicaly closed field. Natural numbers
are in a sense much more complex than reals. We have no TOE for
them.

The step "(number law) => (computer law)" comes from the fact that
you can, by chosing some number encoding (like Godel's one) embed
proposition on programs in pure arithmetical terms.

An example is Godel's encoding of provability, which I promise 
George to discuss about, and so will I ASAP or perhaps later. But in
a nutshell, Godel did build, uniquely from the symbole O, =, X, +, x, s,
(intended for the successor function) an arithmetical predicate
B(x,y) meaning x is the godel number of a proof for the formula
with godel number y. So that provable(y) is just the arithmetical
sentence ExB(x,y).   (E = the existencial quantifier).

I'm not sure I can give "precise" meaning to an expression
like "all mathematics". Perhaps this is the Cantor "inconsistenz".
But I don't ask mathematics to be made explicit by computations.

In fact most of the truth *about* computations are not reachable by
univoquely determined computations. This is the foremost
origin of the gap between G and G*. Computerland, which
is just an intentional variant of numberland, is not computable,
not finitely describable.
A brain, or any "implementation" of a universal machine is really
nothing other than a door on many (many) realities.

Bruno

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