On 26 Jul 2011, at 20:26, meekerdb wrote:

On 7/26/2011 9:50 AM, Bruno Marchal wrote:
Not at all. If comp is true, consciousness is not the result of a computation.

This confuses me. I understand consciousness (according to your theory) is not the result of computing some function, i.e. one of the infinitely many programs the UD is executing. Rather it is the result of all those computations. And a state of consciousness corresponds to a state of computation which occurs in infinitely many of the UD programs. But I'm not clear on what gets Godelization. Is it the UD and all the functions it computes? Or is it each program being computed?

The UD is equivalent, in arithmetic with the proof of the sigma_1 sentences. It is the basic "ontology". The Gödelization is what gives all the Bp (B_PA p, B_ZF p, B_Brent_Meeker p, etc). The "B" correponds ideally to some correct 3- description of the body, like when they talk with the doctor. Comp makes all those "B" sigma_1. The UD dovetails on such talk.

In AUDA the UD appears in the end, when we restrict the arithmetical interpretation of "p" (in "Bp", "Bp & p") to the sigma_1 propositions. You have to add p->Bp in G, giving G1, to get the corresponding complete and sound theory (by a result of Visser). This is what introduce a basic symmetry at the bottom level of physics, in the "soul" and "matter" hypostases, by making them prove p -> BDp, which makes possible an arithmetical quantization. It is an open problem (in arithmetic/provability logic) if that makes possible already a quantum topological computer (it should, if QM is 100% correct).

So the Godelization is used twice:
- to see the UD in the proof of the sigma_1 sentences by RA, and
- to see, sparsed in those UD proofs, the proofs made by more complex machines (the Löbian one) when they try to figure out "what happens", and bet on their possible consistent extension (Dp, p sigma_1). All "Bp" are sigma_1 (by comp).

Bruno


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



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