# Universal Numbers (was: computationalism and supervenience

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Le 05-sept.-06, à 19:59, 1Z a écrit :```
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>
>
> Stathis Papaioannou wrote:
>
>> Under one mapping, the physical system implements a program which
>> thinks, "I am now experiencing my first second of life". Under a
>> different mapping, it implements a program which thinks, "I am now
>> experiencing my second second of life".
>
> And who is doing all the interpreting ?

The program itself.
And who interprets the program?
The universal numbers (= +/- the "godel numbers" of the universal
machines).
(Note: from the program first person pov, it is the most *probable*
universal numbers which will count).

And who interprets the universal numbers?

I can show that if you believe in the independent truth of even a tiny
recursively enumerable subset of the set of the true arithmetical
propositions, then you should understand that that tiny part of
Arithmetic does, or better, cannot not do the interpretation of the
universal numbers.

Incompleteness follows, and self-referentially correct universal
numbers cannot not gamble on many form of self-indeterminateness (p,
Bp, Bp & p, Bp & ~B~p, Bp & ~B~p & p, ...): the n-person point of views
(similar to Plotinus' hypostases, I have discovered since).

Comp restricts the interpretation of "p" on true Sigma1 sentences (the
arithmetical version of turing-equivalence). B is the arithmetical
Godel-Lob predicate of provability.

With the comp (sigma1) restriction,  it is exactly the same
arithmetical sentences which are true (p), provable (Bp), known (Bp &
p), observed (Bp & ~B~p), feeled (Bp & ~B~p & p), but incompleteness
(the G* \minus G gap) makes it impossible for any self-referentially
correct universal number to either prove, know, observe, or feel that
equivalence, but only to bet on it for some self survival purpose, or
not.
Realities could emerge from (extensional) arithmetical truth through
its unavoidable many internal angle or (intensional, modal) variant.
Strictly speaking one for each universal numbers. It is striking that
they all obeys similar laws with respect to their self-referential
abilities: B is an indexical(*).

(*) But still a third person one bearing on a third person!  But the
fact that B is an indexical does explain a basic relationship which
"first person based TOE" like George, David, ... I think.

Bruno

http://iridia.ulb.ac.be/~marchal/

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