# Re: Mathematical Logic, Podnieks'page ...

`At 14:20 03/07/04 -0400, Kory Heath wrote:`

Yes, but some confusions are so easy to avoid! Confusions will always appear in the middle of conversations, but I want them at least to be unexpected ones...! Anyway, I didn't mean to derail the conversation with my "jargoning"; I was just pointing out that whenever I see "platonism" in one of these conversations, I'm never sure what we're really talking about.

No problem. Let us use "arithmetical realism", (for the belief that any (close) arithmetical
formula is either true or false, independently of us). I mean first order logic formula ... for those who know what I mean (cf Podnieks page if some wants to know that urgently).

Now I recall the problem: by UDA physics (in world/state /situation A) is given by a measure on all "computationnal histories" going through A and as "seen" from A.

The strategy I have followed consist to ask a sound universal machine what she thinks about that question. I translate the "world/state/situation A" by a (finite or infinite) set of provable (DU accessible) arithmetical propositions, and I translate "all computationnal histories" by the set of all maximal consistent extensions of A. Then I show that the "measure one" or "probability one" propositions p must satisfy the following conditions:
1) to be true everywhere (= true in all maximal consistent extensions, = []p)
2) to be true somewhere (= true in some consistent extensions, = <>p)
(by Godel "1)" does not imply "2)" from the machine in A perspective!)
This is enough to prove that the "probability 1" is quantum like. The miracle comes from the
strange and counter-intuitive behavior of the Godel beweisbar (provability) [] predicate.

`Bruno`

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

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