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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