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 Thu Sep 01 2005 - 11:51:29 PDT