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
On 01 Sep 2005, at 17:49, kurtleegod.domain.name.hidden 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 <marchal.domain.name.hidden>
> To: kurtleegod.domain.name.hidden
> Cc: everything-list.domain.name.hidden
> Sent: Thu, 1 Sep 2005 15:54:40 +0200
> Subject: Re: subjective reality
>
>
> On 31 Aug 2005, at 17:11, kurtleegod.domain.name.hidden 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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Received on Fri Sep 02 2005 - 05:59:33 PDT