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/
