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, [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]>
To: [EMAIL PROTECTED]
Cc: [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.
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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