Re: subjective reality

From: Bruno Marchal <>
Date: Thu, 1 Sep 2005 15:54:40 +0200

On 31 Aug 2005, at 17:11, 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
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


(*) 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.
Received on Thu Sep 01 2005 - 10:03:03 PDT

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