`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.`

Bruno

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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 notunderstand anything of your"explanation" below! Sorry! Godfrey Kurtz (New Brunswick, NJ) -----Original Message----- From: Bruno Marchal <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] Cc: everything-list@eskimo.com 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 ofobservability" defined by CT?This is obviously technical, but in a nutshell (see more in thepapers):By the UD Argument (UDA, Universal Dovetailer Argument), we know,assuming comp, that all atomic or primitive observer momentcorresponds to the states accessible by the Universal Dovetailer(CT is used here). This can be shown (with CT) equivalent to theset of true *Sigma_1 arithmetical sentences* (i.e those provablyequivalent, by the lobian machines, to sentences having the shapeEnP(n) with P decidable. For a lobian machine, the provability withsuch atomic sentences is given(*) by the theory G + (p -> Bp). Now,a propositional event will correspond to a proposition A true inall accessible observer-moments (accessible through consistentextensions, not through the UD!). And this in the case at least onesuch accessible observer-moments exists (the non cul-de-sacassumption). Modally (or arithmetically the B and D are thearithmetical provability and consistency predicates), this gives BA& DA. This gives the "conditions of observability" (as illustratedby UDA), and this gives rise to one of the 3 arithmetical quantumlogic. 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 andD=Consistent, in this setting (the interview of the universallobian machine). Part of this has been motivated informally in thediscussion between Lee and Stathis (around the "death thread").Apology for this more "advanced post" which needs more technicalknowledge in logic and computer science.Bruno(*) 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 anysufficiently rich theorem prover machine. This should beintuitively easy (try!). Much more difficult: show that not only p -> Bp will be true, but it will also be *provable* by the lobianmachine. The first exercise is very easy, the second one is verydifficult (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 tocomment Russell's post hopefully tomorrow or during the week-end.http://iridia.ulb.ac.be/~marchal/________________________________________________________________________Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.

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