Re: Mathematical Logic, Podnieks'page ...

From: Bruno Marchal <>
Date: Sun, 04 Jul 2004 17:08:41 +0200

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.

Received on Sun Jul 04 2004 - 11:05:09 PDT

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