Hi Bruno,

`I appreciate your effort on my behalf but I am afraid I do not`

`understand anything of your`

"explanation" below! Sorry!

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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 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.`

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 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.`

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

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