Hi Stephen,

On 02 Jul 2011, at 16:53, Stephen Paul King wrote:

Could you elaborate a bit more on the part where you say "...self-speeding up abilities to the machine with respect to the most probable continuation/universal-machine"? What defines the "most probable"?

The universal dovetailing, or equivalently the true sigma_ sentences and their proofs, and relative proof. This follows from the UD argument. The logic of "probability one" can already be characterized by the logic of the "arithmetical quantization" BDp with p a Sigma_1 propositions. It gives an arithmetical non boolean sort of quantum logic.I think that if you search on the name of "Goldblatt" in the archive you might find longer explanation that I have already given to you on this, if I remember well.

I am just translating a problem in philosophy/theology into a problem in math by using the comp hypothesis to justify the use of computer science and mathematical logic.

I have taken a look at the Steve Vickers slides you pointed too. It is rather complex and does not seem related to comp in an easy way. It it can be related at all, it has to be related through the S4Grz1 ("universal soul, the "pure" first person") and X1* ("universal feeler") arithmetical points of view.



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