Andrew,

Let me try to be a little more precise or helpful.

I just said,

On 03 Feb 2011, at 15:15, Bruno Marchal wrote:

Yes, but your point in step 8 is that a physical universe is *too little*, but with omega point it is not too little, it is as rich as arithmetically possible.

Not at all. the point is that in step seven, you can still argue for comp + mat, by postulating that the material universe is too little. If you believe at the start that the (apparent) universe is enough big to contain the UD*, then the reversal is done, and we are already in the "omega point" of arithmetic, and you should then see that physics is a branch of number theory (indeed the branch of the first person sharable number's belief, say).

++++++++++

In step seven what is proved is that

MEC + 'big universe' entails that physic is a branch of computer science.
Do you see that?
Step 5 plays the big role there. You don't need to be annihilated for having your continuations determined by the first person comp indeterminacy on UD*, once a UD, a fortiori an omega point, is in the physical universe.

In step eight, the assumption of the existence of a big universe is eliminated. Roughly because no universal machine at all can distinguish arithmetical reality from anything else. This throws away the need of any universe. Physics has to be justified by number relations only (numbers or any elementary terms of a Sigma_1 complete theory).

OK?

With the whole UDA1-8, you should understand that all what has been done, by the use of MEC, is a reduction of the mind body problem to a body problem in computer science.

At first sight we might think that we are just very close to a refutation of comp, because, as I think you have intuited, there might be an avalanche of first person 'white rabbits' that is aberrant, or just "white noisy" experiences.

To find a proper measure on the consistent continuations is very difficult, and that is why I have restricted myself to the search of the logic of the certainties, for Löbian machines. Löban machines are chosen because they have enough introspection power and cognitive abilities to describe what they can prove about their certainties, and what they can infer interrogatively. That is not entirely trivial and relies mainly on the work of Gödel, Löb and Solovay (and Post, Turing, Kleene, etc.)

Don't hesitate to ask any question if anything seems insufficiently clear.

Bruno


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



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