At 19:22 04/03/04 -0500, Stephen Paul King wrote:
>Dear Bruno,
>
> While I am VERY impressed by your reasoning, I must insist that it is
>necessary to make this aspect of COMP falsifiable.
Which aspect? We were just talking about Godel's incompleteness theorem
(which btw concerns more general things than just consistent machine )
>How is it decided
>empirically that entity X can not prove that P?
I don't think it is an empirical question.
>This reminds me of the
>statement "all crows are not non-black". It seems to me that we are putting
>ourselves in the impossible position of having to prove a negative.
>
> It is one thing to be able to point to mathematical proofs germane to
>mathematics proper but when we are trying to create models that are to be
>quantifiably predictive, we simply can not postulate such entities as
>"Platonia" and Arithmetic Realism as a basis.
I don't understand why. What I have shown is that the comp postulate
(Arithmetical Realism, Church thesis, +"Yes Doctor") entails that
physics is given by a measure on the comp histories.
The comp histories are pure mathematical object. Physical
space/time appears as internal relative modalities.
(Some others in the everything-list list seem to arrive toward similar
conclusions).
Then I use the Godel-Lob-Solovay-Boolos-Goldblatt-Visser theorems
in self-reference logic to isolate the logic of the "probability one"
(on the comp histories)
and it gives a system AQL (say) close to Quantum Logic.
The real question is : how close?
It is a matter of time to show if AQL is rich enough to justify, for
exemple, the possibility of quantum computing in the
neighborhood of all observers.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Fri Mar 05 2004 - 09:11:13 PST