Le 18-oct.-06, à 16:27, 1Z a écrit :
>
>> Bruno: In computer science, a
>> fixed universal machine plays the role of a coordinate system in
>> geometry. That's all. With Church Thesis, we don't even have to name
>> the particular universal machine, it could be a universal cellular
>> automaton (like the game of life), or Python, Robinson Aritmetic,
>> Matiyasevich Diophantine universal polynomial, Java, ... rational
>> complex unitary matrices, universal recursive group or ring, billiard
>> ball, whatever.
>
> Peter: Ye-e-es. But if all this is taking place in Platonia, the
> only thing it *can* be is a number. But *that* number can't
> be associated with a computaiton by *another* machine,
> or you get infinite regress.
I don't think so. Remember that I assume arithmetical realism. This
means that I take the arithmetical truth as being true independently of
me. This means not only that the propositions saying that such numbers
exists or not are true independently of me, but also that propositions
asserting that such or such relations between numbers exist are true
independently of me (you, ...).
Now, and I agree this is perhaps more subtle, propositions like "x is a
computational states reachable by y in the context z", or "x is
reachable by a DU" can be translated in term of such relations between
numbers, under the form of pure arithmetical sentences. And this is
enough for both the UDA reasoning to proceed, and the arithmetical
lobian interview to be completed.
So the infinite regress is avoided by the facts that purely
arithmetical truth (and even just provability) are already turing
universal. The universal computational "behavior" of the numbers is
naturally encoded through the additive and multiplicative relations
among numbers. Godel did show this through its arithmetization" of
metamathematics, and Matiyasevich has succeeded in showing that such
universal computational relation can even be encoded through a
polynomial equation. That is more than enough to justify, assuming
comp, why numbers will "feel" like if subjective time, matter, taxes
and death "exists", from their own point of view. To solve the riddle
of "matter and consciousness" the only (big) problem which remains
consists in showing how the laws of physics will emerge in the
empirically correct stable relative proportions. But that was the point
I want to show, except that I have actually already derive a bit of
comp physics to say that the quantum weirdness confirms the comp hyp
until now. The advantage of getting the comp-physics through such an
arithmetical interview is that it gives the quanta/qualia nuances, like
it gives all n-person point of views, etc.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Oct 20 2006 - 09:55:30 PDT