On 04 Jan 2009, at 03:09, Stephen Paul King wrote:
>
> Hi Günther,
>
>Nice post! Coments soon.
>
>Speaking of Svozil's work, please see: Cristian S. Calude, Peter H.
> Hertling and Karl Svozil, ``Embedding Quantum Universes in Classical
> Ones'',
> Foundations of Physics 29(3), 349-390 (1999) [abstract], [CrossRef
> DOI:10.1023/A:1018862730956], [pdf], [pdf], [tex], [ps].
Nice work. It is in the line of the beautiful theorem of Kochen and
Specker.
>
>
>How can we derive quantum logics from purely integer (or even real
> number) based logics? This paper seems to yeild a no-go theorem!
And this confirms the MEC prediction (or re-prediction) that the logic
of the physical reality cannot be boolean.
I recall you that the material hypostases, when interpreted in
arithmetic, gives quantum like logics. There is no reason to suppose
they can be embedded in Boolean logics. The no-go theorems shows that
quantum logic cannot be embedded in classical logic in observable
value preserving way.
Such no go-theorems cannot be applied to the AUDA arithmetical
quantization, which concerns the way self-observing machine have to
structure the comp physical reality. Remember the result by
Goldblatt(*) 1974: there is a boolean way to interpret "epistemically"
quantum logic (by the modal logic B). The arithmetical quantization,
which captures the first person (plural) points of view, gives a modal
logic B (without necessitation rule). It would be a nice research
project to show that this extends the no-go theorems to the comp
physical quantum logics. This would confirm the highly non boolean
(and non Aristotelian) nature of matter, or appearance of matter.
The mechanist quantum logic is not derived from numbers, but from
numbers personal points ov view: what numbers can observe and share
when they observe themselves, and this with a very general notion of
observation.
It is like the MWI, the most weird is the quantum world, the more we
can believe that comp is correct, given that comp entails a rather
highly non classical view of the physical reality.
All right? More generally and perhaps more simply the no-go theorems
forbid a classical reality, it does not forbid a classical *theory*
about a non classical reality. The (meta)logic of quantum mechanics
itself is classical. If you believed that the non go theorems is a
problem for comp, it means that you could be confusing levels with
metalevels. All right?
Best,
Bruno
PS Kim, Günther, I will comment your posts with some details asap, but
I have some new year activities ...
(*) Goldblatt, R. I. (1974). Semantic Analysis of Orthologic. Journal
of Philosophical Logic, 3:19-35. Also in Goldblatt, R. I. (1993).
Mathematics of Modality. CSLI Lectures Notes, Stanford California,
page 81-97.
>
> - Original Message -
> From: "Günther Greindl"
> To:
> Sent: Saturday, January 03, 2009 5:53 PM
> Subject: Re: Boltzmann Brains, consciousness and the arrow of time
>
>
>
> Hi Bruno,
>
> first of all thanks for the long answer, and yes, it was very helpful.
>
> You described the production of all reals with a very vivid imagery;
> it
> showed a glimpse of the vastness of the UD. And, I agree, _in the
> limit_
> there will be an infinite number of histories. So, as we have to also
> take into account infinite delay, we must take this limit into account
> and have infinite histories going through a "state" (do I understand
> you
> correctly?).
>
> As to the interacting programs: do you consider them purely because
> they
> are part of UD or do you think this is a possible way to share
> histories?
>
> (I am interested in this because I find COMP very convincing, though I
> am still a bit worried about solipsism).
>
> I am also preparing a few thoughts (in a later post, but see hints
> below) on how consciousness might supervene on large parts of past
> causal histories, thereby also steering a bit away from solipsism
> (arguing via the concept of external realism from analytic philosophy,
> summarized by Putnam's "meaning is not in the head").
>
> I also have another question (related to the above issue of
> solipsism):
>
> We have considered COMP and MAT and seen that the two are not really
> compatible.
>
> But you also say that with COMP, the universe itself is not computable
> (I understand why, and I agree with your reasoning as you have
> presented
> it).
>
> But I have one "worry": what if the subsitution level is "at the
> bottom"
> of the universe - (for a moment drawing on materialist intuitions,
> the
> universe in the "normal" sense and not considering infinite histories
> for the moment).
>
> If the universe is a computation, then also an individual in the
> universe is part of this computation. But this individual can't be
> "duplicated" because of the quantum no-cloning theorem (that is what I
> mean with "at the bottom" - not above the quantum level).
>
> Svozil for
