On 9/23/2011 10:24 AM, Bruno Marchal wrote:
On 22 Sep 2011, at 21:12, Stephen P. King wrote:
On 9/22/2011 11:22 AM, Jason Resch wrote:
On Thu, Sep 22, 2011 at 7:55 AM, Stephen P. King
<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:
On 9/22/2011 1:19 AM, Jason Resch wrote:
Sure, let us consider this similarity to Leibniz'
"per-established harmony" idea. Could you sketch your thoughts
on the similarity that you see? I have my own thoughts about
pre-established harmony, but I see, in Craig's ideas, other
concepts similar to those of Leibniz that do relate to a notion
of "harmony" and other somewhat unrelated concepts but not
necessarily include the "pre-established" aspect. I haev an
argument against the concept of "pre-established" as Leibniz
From what I understand of Craig's theory it describes a difference
between first person and third person experience/reality. Each
being two sides of the same coin, where first person experience is
the interior side of what its like to be the material. The first
person experience of is indeterminable (and possibly relies on the
indeterminism of physics?) and can cause physical changes above and
beyond what can be predicted by any third-person physics. While we
are a machine according to this theory, we are a special machine due
to our history as organisms and the special properties of the
carbon, hydrogen, oxygen, nitrogen, etc. which form the basis of our
biochemistry. Functional equivalence is either not possible, or
will lead to various brain disorders or zombies.
Excellent post!! But can you see how this is really not so
different from Bruno's "result"?! Bruno just substitutes (N, +, *) of
matter and the 1p experience is the 'inside dream" of Arithmetic.
I am not sure what you are saying. I just give a deductive argument
that if my (generalized) brain can be emulated by a material digital
device, then physics is a branch of number's psychology, itself a
branch of number theory (or combinator theory, etc.).
I understand and follow that argument. My problem is that I cannot
get my mental picture to work for this argument in the case of multiple
entities. This is why I have claimed that your argument is correct but
solipsistic. To my shame I do not know how to translate my mental
pictures into writen symbolic representations yet. I am still learning
the proper mathematical language. I may have mentioned before that my
thought are like proprioceptive sensations and visual images and my
memory dyslexia makes learning symbolic languages very difficult.
Just today I found some of my old notes and references. I didn't
understand these at the time but I knew that they where important. Now I
do understand them a a bit more and I believe that I might be able to
show the problem that I am thinking of for you, but it is not easy.
Same basic outline, very different semantics, but a radically
My argument does not depend on interpretation. That is why it is a proof.
I understand that, but logically consistent results can follow from
false premises. My problem is in the assumptions that you are making in
your initial premises, that numbers (or equivalent) and arithmetic can
exist as ontological primitives and that computations do not require
some form of physical implementation. What I see is that neither numbers
nor matter is primitive, both are emergent in a way from a neutral
primitive that is neither. My reasoning follows lines similar to those
that Bertrand Russell used in his idea of neutral monism.
Craig does make a big deal about "special properties" but the
properties of carbon, etc. do matter when it comes to real
functionality. While it is true that we can build universal Turing
machine equivalents out of practically anything, explaining and
modeling the physical world is not about computations that do not
require resources or can run forever or such "ideal" things,
It is. Or you have to find the flaw. I am, as always, open to search
it with you, step by step.
OK, I accept your challenge. It will help me learn to write the
mathematical symbols to do this. I must overcome my disabilities.
it is about how all this stuff that has particular properties
interacts with each other. We simply cannot dismiss all of the
details that encompass our reality by just invoking computational
We have no choice. Of course, we can, like Craig, just assume that
comp is false.
But I do not thing think that comp is 'false", I think it to be
incomplete. My evidence is that comp must assume situations that are in
gross conflict with physical reality, such the ability to be implemented
without requiring the consumption of resources. Even a perfect
reversible computer must have memory available in some fashion.
What is that truism? The Devil is in the Details!
My own thesis follows this same outline, except that I propose
that the topological spaces are the "outside" and algebras (which
would include Bruno's (N, +, *) and minds are the inside. This
outline dispenses with the problem of psycho-physical parallelism
that I will make a comment on below. There is no need to explain why
or how matter and mind are harmonized or synchronized when,
ultimately, they are jsut two different (behaviorally and
structuraly) aspect of each other, all of this follow from M. Stone's
My idea is a bit tricky because we have to treat topological
spaces (such as the totally disconnected compact Hausdorff spaces
dual to Boolean logics)
I think you have good intuition here, but you need to develop them.
Note that there are semantic of G and S4Grz in term of totally
disconnected Hausdorff spaces, or the Cantor scattered space which
ground that intuition, and the Stone duality, in the frame of
self-reference, as I think I have already told you (work of Blok and
Thank you, I am studying hard but find that the books are not
written in a pedagogical way, they are more like "look-up tables" that
one is supposed to memorize. Such memorization has always been
impossible for me. :-( With regards to the /Blok/-/Esakia/ Theorem and
isomorphism. Could you recommend a good book? I have found several in
I am also studying the Hennesy-Milner Property, as it is almost exactly
what I have in mind with my crude bisimulation algebra.
both as the form and content of 1p and as mathematical objects. This
is not a problem because math is all about representing 1p and more!
This makes sense because mathematical representations can both
represent themselves and be what they represent. WE see this
explained in a round about way in Stephen Wolfram's essay on
intractability and physics.
The basic idea of the essay is that physical systems are,
effectively, the best possible computational model of themselves. We
do not need to postulate computations separate from the physical
processes themselves, if we are going to stay int eh semi-classical
realm. If we wish to go to a fully quantum model, they the
wavefunction (and its evolution) of a physical system is the
computation itself of that system.
Vaughan Pratt argued that QM is just a consequence of the way
that the stone duality is implemented. I am just taking this ideas
and exploring them for flaws and falsification, but to do so I have
to be able to fully explain them (not an easy job!) but that is what
is necessary to claim that I understand them.
This assessment of Craig's idea seems accurate from what I can
tell at the start but falls down on the epiphenomena bit AFAIK...
Jason said that Craig's theory entails consciousness is an
epiphenomenon. I wait Craig's reply, given that he gives a role to the
subjectivity. It "insists", Craig told us. No idea what *that* means,
but I think he introduce that idea for escaping the accusation of
making consciousness an epiphenomenon. To be sure Stathis has
convincingly show that Craig is not coherent on this (and so can say
Consciousness to Craig is an epiphenomenon, since he has said there
is no reason to evolve this tehnicolor cartesian theater.
I need to get his comment on this statement about the Cartesian
The similarity I see to the pre-established harmony is that Liebniz
posits two realities, a physical reality and reality of
experiences. Each follows their own laws independently of the
other, but physics does not affect or could not implement a mind,
nor is the mind really affecting physics. Instead, physical law is
such that it coincides with what a mind would do even if there were
no mind, and the mind experiences what physical law would suggest
even if there were no physical world. It is analagous to a
matrix-world where we experiencing a pre-recorded life and
experiencing everything of that individual. Liebniz postulated his
idea when it became clear that Newton's laws suggested a
conservation of not only energy (as Descartes was aware) but also
momentum. Therefore an immaterial soul could have no affect on
physics. This led Leibniz to the idea that God setup both to
necessarily agree before hand.
About this pre-established harmony: Leibniz proposed it as a way
to select the "best of possible worlds", given all possible, and
explain the synchrony of events (that his hypothesis of Monads
required to exist) between monads.
Recall that the monads are "windowless" and to not exchange
substances. (BTW, this effectively makes them totally disconnected
spaces if we consider the topological implication of this property of
windowlessness!) Monads have both internal aspects (defining 1p
content) and external aspects (defining physical reality) that , as
you point out "... follow their own laws independently of the other,
but physics does not affect or could not implement a mind, nor is the
mind really affecting physics"; but if we follow my thesis there
would be no minds without physics nor physics without minds per se,
as the duality between algebras and topological spaces is a form of
"natural transformation" between Categories. Yes, there would be
physics for monads that do not have self-awareness - such as
electrons and quarks, but self-awareness is a higher order
computational modeling process that need not be instantiated (pace
Russell) but is possible given sufficient topological and, dually,
algebraic structure. So this thesis implies a very weak form of
It can be proven that Leibniz's pre-ordained harmony implies a
logical contradiction and thus is flawed: even an omnipotent god
cannot perform computations of infinite NP-Complete problems in zero
time - which is exactly what is required to have god establish the
harmony of the universe prior to creating it or as you wrote: "God
setup both to necessarily agree before hand". How can one perform a
task that requires an eternity to complete the set up in the first
place? It cannot ever begin!
The alternative to Leibniz' self-contradicting explanation is to
consider that the NP-Complete computation as running for eternity,
NP-completeness concerns polynomial tractability. I have never
understood why you refer to it.
Can you see how the idea of a "harmony" or "orchestration", as
Leibniz discussed, is a solution to a Np-complete problem? The fact that
it is an optimization problem over N variables where each and every
combination of the variables must be compared with every other. I use
the ideas found on this wiki page, for example:
For a computation of the type that Leibniz envisioned, it seems
obvious that one must some an NP-complete problem that has an infinite
number of variables. It not only has to simulate all possible worlds but
it also has to compare all of them to each other so that one can be
found that the world is such that there are no observable violations of
physical law in it, aka Harry-Potterims or White Rabbits. The Boolean
version of this is SAT.
it never begins and it never ends - kinda like Bruno's UD* - and 1p
are finite instances or "streams" of this eternal computational
process. Each stream instantiates a Monad and the psycho-physical
parallelism is the natural result of the Stone duality between the
insidge (logical algebras) and the outside (topological spaces), no
need to have an explanation of mind and body interactions! All the
neat stuff follows from considering how minds interact with each
other. The appearance of a "beginning of time (and space!)" that we
seem to have is simply an artifact of the finiteness of our 1p.
One interesting and strange twist of this idea is that it implies
that we never actually observe the outside aspects of monads (Leibniz
does mention this in his Monadology), we only experience the internal
representations of them. This twist is a form of the argument that we
find in the Matrix thought-experiment that since we cannot prove that
we are not in a matrix we should assume that we are and work out the
consequences. This idea also seems consistent with Russell's thesis
that "the set of all the universes that make up the Multiverse,
contains no information at all, and is in fact Nothing; it is just
from the inside, as mere descriptions – bits of strings – that we
are, that there /seems/, from our point of view, to be something."
Consciousness exists, so there is something. It can't be an illusion,
given that an illusion requires consciousness. But Russell is right in
the sense that the "everything" philosophy minimize the TOE
I agree that that is one of the necessary compoments of the process
of consciousness, but it alone is insufficient. One's model of
consciousness must allow for interactions between multiple minds and
recursive self-modeling and maybe more. Compactness of the topological
dual spaces also seems necessary.
Recall how Observer moments are finite?
Not Bostrom 1-OM, which are infinite in the mechanist theories.
3-OM are just (relative) computational states.
Umm, I forgot about that. I need to understand what motivated
Bostom's definition of OMs. I do not understand the concept of 3-OMs.
How can the content of experience be public? Your explanation in terms
of the diary seems to ignore the fact that without the invariance of
structure with respect to transitivity (that matter generates) it is not
possible to have a diary or record of any kind, so how can OMs be public
in the situation of "(relative) computational states"? How, exactly, are
the individual computational states related with each other. I know that
you discuss the Goedel's numbering scheme and how it can code relations,
but how does this work without the invariance with respect to
transitivity to act as a separable mapping between the numbers
themselves and the Goedelian Bew(p)? Similarly, how is a computation
"implemented" without any notion of transitivity at all?
This is what I do not understand of UDA and is why I believe it is
incomplete. I see repeated uses of words, in your papers, that imply
transitivity but the definitions of computation and arithmetic that you
use do not allow it to exist. I am confused! Either Change exists or it
Does this not imply that there is an event horizon effect in the
history of an observer whose 1p is given in terms of OMs? This is an
effective cut-off on information that follows from its ability to
only resolve a finite amount of information, which is just another
way of saying that OMs are finite. Thus this idea implies that the
"singularity" of the Big bang never happened nor necessarily exists,
an interesting and counter-intuitive implication! (Penrose and
Hawking's singularity theorems work only if gravity exists at
infinitesimal size/ infinite energy scale and this is, on its face,
merely an idealization.) We would see an event horizon in our most
distant past, but not because there is an infinite gravitational
gradient behind it. Because of this (and considerations such as those
that Russell explains in his book), my thesis implies the "perfect
cosmological principle" that any average observer would see pretty
much the same thing as any other no matter where in a universe it
found itself. All observers would see an event horizon in their
distant past and would see a universe that they believe is middle aged.
This idea also how the appearence of a Cartesian theater effect,
that (pace Dennett) actually explains something without an actual
infinite regress of explanations! Basically, the homunculus of the
Cartesian Theater model is proposed to be something like a "strange
attractor" on the configuration space or, by the dually, computation
space of the brain. The attractor is a computational model of the
global behavior of the brain and is capable of computing simulations
of itself since, if we believe in computational universality, a model
of a computation is a computation too. So the experience that we have
of being a "driver in a body" makes sense, given that what we
actually experience of the world is the brain's Virtual Reality
simulation of the world *and* this simulation is a computation
capable of simulating itself,
A computation does not necessarily simulate itself, although universal
machine can simulate their own computations.
I agree, I am pointing to the universal machines in this claim
about the Cartesian theater. This is the reason why I claim that
self-awareness and consciousness are this identical. Self-awareness
requires universality whereas basic consciousness does not. So this
implies that there are 1-OM that do not involve self-awareness at all.
It is this idea that I see replicated in Graig's idea of "sense".
albeit at a lower resolution and level of complexity. Since the brain
has access to finite physical resoulces to run the computations there
will be a short truncation of the regress of simulations within
simulations; maybe only 3 to 4 recursions, I figure, at the most.
Kleene's theorem is the tool for cutting the infinite regression in
computer science. AUDA's self-reference, and intensional variants of
it, is 100% based on this theorem, even if it is hidden in the
arithmetical soundness and completeness theorem of Solovay.
Ah yes, the beautiful *Kleene recursion theorems.* But it seems
that they only work for well-founded set theories. This is the source of
the measurement problem that you face, it is demonstrated well by the
Banach-Tarsky paradox. Bisimulation requires non-well founded logics and
sets generally, so this method of preventing regress is not available.
There are alternatives but they are not so easy to state.
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