Sorry Godfrey, I take the opportunity to explain the use of CT in the search of the observability conditions. But I know people are not familiar with mathematical logic. Computer science is not well known either.


On 01 Sep 2005, at 17:49, [EMAIL PROTECTED] wrote:

Hi Bruno,

I appreciate your effort on my behalf but I am afraid I do not understand anything of your
"explanation" below! Sorry!

Godfrey Kurtz
(New Brunswick, NJ)

-----Original Message-----
From: Bruno Marchal <[EMAIL PROTECTED]>
Sent: Thu, 1 Sep 2005 15:54:40 +0200
Subject: Re: subjective reality

On 31 Aug 2005, at 17:11, [EMAIL PROTECTED] wrote:

This I don't quite follow. Sorry! How are "conditions of observability" defined by CT?

This is obviously technical, but in a nutshell (see more in the papers): By the UD Argument (UDA, Universal Dovetailer Argument), we know, assuming comp, that all atomic or primitive observer moment corresponds to the states accessible by the Universal Dovetailer (CT is used here). This can be shown (with CT) equivalent to the set of true *Sigma_1 arithmetical sentences* (i.e those provably equivalent, by the lobian machines, to sentences having the shape EnP(n) with P decidable. For a lobian machine, the provability with such atomic sentences is given(*) by the theory G + (p -> Bp). Now, a propositional event will correspond to a proposition A true in all accessible observer-moments (accessible through consistent extensions, not through the UD!). And this in the case at least one such accessible observer-moments exists (the non cul-de-sac assumption). Modally (or arithmetically the B and D are the arithmetical provability and consistency predicates), this gives BA & DA. This gives the "conditions of observability" (as illustrated by UDA), and this gives rise to one of the 3 arithmetical quantum logic. The move from Bp to Bp & Dp is the second Theaetetical move. Dp is ~B~p. Read D Diamond, and B Box; or B=Provable and D=Consistent, in this setting (the interview of the universal lobian machine). Part of this has been motivated informally in the discussion between Lee and Stathis (around the "death thread"). Apology for this more "advanced post" which needs more technical knowledge in logic and computer science.


(*) EnP(n) = it exists a natural number n such that P(n) is true. If p = EnP(n), explain why p -> Bp is true for lobian, or any sufficiently rich theorem prover machine. This should be intuitively easy (try!). Much more difficult: show that not only p - > Bp will be true, but it will also be *provable* by the lobian machine. The first exercise is very easy, the second one is very difficult (and I suggest the reading of Hilbert Bernays Grundlagen, or Boolos 1993, or Smorinsky 1985 for detailled explanations).

PS: I must go now, I have students passing exams. I intent to comment Russell's post hopefully tomorrow or during the week-end.

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