On 12/12/2012 7:27 AM, Richard Ruquist wrote:
On Tue, Dec 11, 2012 at 10:08 AM, Bruno Marchal<marc...@ulb.ac.be>  wrote:

On 10 Dec 2012, at 19:03, Richard Ruquist wrote:

On Mon, Dec 10, 2012 at 11:42 AM, Bruno Marchal<marc...@ulb.ac.be>  wrote:

On 10 Dec 2012, at 16:17, Richard Ruquist wrote:

Roger Bruno,
How is consciousness related to god?
It seems like the beginning of an infinite god regression.

God = Truth (Plato). OK? With the CTM, arithmetical truth is enough (and
tiny provable part is enough for the ontology).

I would say that consciousness is a form of knowledge.
Knowledge intersects belief and truth. (It is a private undefinable
with CTM).
The knower in you is the "inner God", which is God restricted by the
universal window of your brain/body.

I don't know if God (truth) is conscious, but without God (truth) I doubt
could be conscious, even if most of the content of my consciousness is
(except on the indubitable fixed point, and perhaops the sharablke oart
math, arithmetic, perhaps).

I have no certainties, and that is why I use the arithmetical translation
Plotinus in such conversation, with
God = Arithmetical Truth
Believable = (sigma_1) provable = universal (Löbian) machine
Knowable = the same, but true (unlike proved) = the inner god = the
universal soul
intelligible matter = the same as 'believable", but together with
sensible matter = the same as intelligible matter, but as true

That gives eight modalities, as they divided by incompleteness (except
and the Soul).

If Gödel's incompleteness theorem was wrong, all those modalities would
collapse. Despite the modalities extension is the same set of
propositions, the machine cannot knows that, and this change drastically
logic of the modalities.
Roughly speaking, "God" obeys classical logic, the "Universal Soul" obeys
intuitionist logic, and the two matters obeys (different) quantum logics,
perhaps even linear (with some luck!)

Bruno, thanks. That helps alot.
In case you have not already guessed I am trying to marry CTM, string
theory and monadology/Indra'sJewels, in order to improve my paper on
incompletenes/consciousness: http://vixra.org/pdf/1101.0044v1.pdf

This will work only if you derived the axioms of string theory from
arithmetic, unless your theory contradicts the comp or CTM theory.
First of all, your request seems to contradict the definition of axiom
to claim that they should be derived from arithmetic (meaning CTM I

Here from Davies 2005 is what I consider to be appropriate ST axioms:
A. The universes are described by quantum mechanics.
B. Space has an integer number of dimensions. There is one dimension of time.
C. Spacetime has a causal structure described by pseudo-Riemannian geometry.
D. There exists a universe-generating mechanism subject to some form
of transcendent physical law.
E. Physics involves an optimization principle (e.g. an action
principle) leading to well defined laws, at least at relatively low
F.The multiverse and its constituent universes are described by mathematics.
G.The mathematical operations involve computable functions and standard logic.
H.There are well-defined “states of the  world” that have properties
which may be specified mathematically.
I. The basic physical laws, and the underlying principle/s from which
they derive, are independent of the states.
J. At least one universe contains observers, whose observations
include sets of rational numbers that are related to the (more
general) mathematical objects describing the universe by a specific
and restricted projection rule, which is also mathematical.

I do not claim the ability to defend all these axioms

This bespeaks a confusion. Axioms are mathematical assumptions. You don't have to defend them; you assume them and build a model on them. Then you see if your model is consistent with the know facts (if not, too bad) and does it successfully predict some new facts (if so, great!).

or even
understand them all for that matter. But I think a little more needs
to be said about A.

Quantum theory must be based on complex variables and not real numbers
or quaternions for example.

I don't see how you can rule out quaternions, or even octonions, since they include complex numbers.

Again from Davies 2005 "In addition, one
can consider describing states in a space defined over different
fields, such as the reals (Stueckelberg, 1960) or the quaternions
(Adler, 1995) rather than
the complex numbers. These alternative schemes possess distinctly
different properties. For example, if entanglement is defined in terms
of rebits rather than qubits, then states that are separable in the
former case may not  be separable in the latter (Caves, Fuchs and
Rungta (2001) “Entanglement of formation of an arbitrary state of two
rebits,” Found. of Physics Letts. 14, 199.,2001). And as I recently
learned, in quantum information theory, "Negative quantum entropy can
be traced back to “conditional” density matrices which admit
eigenvalues larger than unity" for quantum entangled systems

This is not so esoteric. It's just accounting. There's no negative money, but you still have negative entries in your bank account. If you have two systems and to calculate the total entropy you get some number. Then if you learn that one of them is entangled with the other and is perfectly correlated with it, you have to subtract off that duplicated entropy.

It is not clear that your simple arithmetic axioms can derive complex

They don't even entail real numbers. But just as computers can deal with real numbers as approximations, so they can approximate complex, quaternion, octonion, and other number systems. And they do this finitely.

and if they can then the resulting universes seem not to
have unique properties especially concerning entanglement, which is an
essential feature of my approach to resolving the paradox between MWI
and SWI. BTW I consider MWI to apply to the mental realm and SWI to
apply to the physical realm in a mind/brain duality with the two
realms being connected by BEC entanglement.
I am not sure why you single out Peano Arithmetic in your paper. Logician
use Peano Arithmetic like biologist use the bacterium Escherichia Coli, as a
good represent of a very simple Löbian theory.
I singled out PA because that was the limit of what I knew of Godel's
math at the time that I wrote that paper two years ago.
Gödel used Principia Mathematica, and then a theory like PA can be shown
essentially undecidable: adding axioms does not change incompleteness. That
is why it applies to us, as far as we are correct. It does not apply to
everyday reasoning, as this use a non monotonical theory, with a notion of
updating our beliefs.

Not all undecidable theory are essentially undecidable. Group theory is
undecidable, but abelian group theory is decidable.

Bruno, is there an general, meta-mathematical theory about what axioms will produce a decidable theory and which will not?



At the time that I wrote that paper, I considered to step from Godel's
incompleteness of consistent discrete real number systems to
consciousness to be a 'leap of faith'. Since becoming a little
familiar with your CTM, I have not been able to discern if you make
the same leap or not. Can you help me here?


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