Hi Bruno,

-----Original Message-----
From: everything-list@googlegroups.com
[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Saturday, September 11, 2010 11:36 AM
To: everything-list@googlegroups.com
Subject: Re: What's wrong with this?

On 11 Sep 2010, at 00:42, Stephen P. King wrote:

> Hi Bruno,
> -----Original Message-----
> From: everything-list@googlegroups.com 
> [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
> Sent: Friday, September 10, 2010 11:16 AM
> To: everything-list@googlegroups.com
> Subject: Re: What's wrong with this?
> On 09 Sep 2010, at 14:37, Stephen P. King wrote:
>> Hi Bruno,
>>      My thought is to look at the transformation group around which some 
>> property is invariant to act as a generator of the properties of the, 
>> say, quark.
> [BM]
> Good idea. That is related with the importance of group theory and
> (soon) category theory in physics.
>> For simple numbers this would be a permutation over fields, one field 
>> per number,
> [BM]
> Why? We may have use combinators instead of numbers. Their role are 
> intensional, and representational. Their intrinsic mathematical 
> structure certainly plays some role, but I don't see why to use them 
> directly to mirror physics. Even if that works (by chance) it would 
> hidden the mind-body problem. Of course it might be very interesting, 
> and the relation between physics and number theory suggest that such 
> approach have their merits.
> [SPK]
>       YES!!! You nailed it! Let me paste a little note here that I just
> wrote up. I apologize in advance for the crudeness of this.
> ***
> Integers as Arithmetic Equivalence Classes and implications
> by S. P. King
> 9/10/2010
> Zero-ness
> _______
> 0 + 0 = 0
> 0 - 0 = 0
> 0^1 - 0^1 = 0
> 1 - 1 = 0
> 2 - 2 = 0
> 3 - 3 = 0
> ...
> 0 x 0 = 0
> _______
> One-ness
> _______
> 0 + 1 = 1
> 1^1 + 0 = 1
> 1 - 0 = 1
> 1^1 - 0 = 1
> 2 - 1 = 1
> 3 - 2 = 1
> 4 - 3 = 1
> .
> 1 x 1 = 1
> 2 / 2 = 1
> 3 / 3 = 1
> 4 / 4 = 1
> .
> _____
> Two-ness
> ________
> 1 + 1 = 2
> 1^1 + 1^1 = 2
> 0 + 2 = 2
> 3 - 1 = 2
> 4 - 2 = 2
> 5 - 3 = 2
> .
> 4 / 2 = 2
> 6 / 3 = 2
> 8 / 4 = 2
> ..
> _______
> Etc.
> External symmetry = 3rd person aspect.
>       Each Class has aleph_null tuples and thus has the same cardinality.
> We could use the permutation symmetry over the cardinality to  
> identify an
> external or 3rd person notion of Integer. This would generate a  
> notion of
> that is an Integer that is invariant to a change from one of the N  
> classes
> to another.
>       What would be the internal symmetry?
> Internal Symmetries = 1st person aspect.
>       Note that we can substitute equivalent elements of the tuples with
> each other by the use of bracketing or some other push/pop method.  
> This
> would ultimately show that the tuples are combinations of "images"  
> of each
> other's elements so that there is 1) no primitive atom and 2) that the
> pattern of similarities and differences over this tapestry of  
> combinatorics
> would encode the operations of Arithmetic. Property 1 is the reason  
> I use
> non-well founded set theory, by the way...
> *************
It is difficult for me to follow. In ZF there is no atom, yet it is  
well-founded. Non well-foundedness is motivate by introducing set  
having themselves as elements, or having elements having elements ...  
having elements having the starting set as an element.


        Yes, in my example above it seems to be the case that the N-ness
classes can have themselves as elements and so forth. For example, in the
Zero-ness class, there is a couple of 0s that are equaling 0 when added,
subtracted or multiplied. Is this not an example of an element having itself
as an element? My wording might be incorrect according to the usual
definition of class, etc. but I hope that my meanings are communicated.

>       It is my suspicion that the mind-body problem is caused by a lack of
> understanding of what is involved. It is far too easy to throw up  
> one's
> hands and settle for some silly eliminatism; Ignorance is Bliss.  
> Notice that
> both the internal and external symmetry notions here yield a kind of
> indefiniteness that Plotinus would point to, as per your  
> discussions, to
> define Matter.

You should elaborate, but you should make clear the relation between  
math and philosophy/theology.

        Yes, I agree but I am sure that you can see that this is very
difficult to do.

> But what about the information content itself of the
> relations themselves? Is Information identical to Indeterminateness?
Information is a tricky word having different meaning in different  
theories. It can be a measure of surprise, like in the old Shannon  
theory, or something related to meaning, like in logics and in the  
press. We can relate all that, but then we have to be almost formal  
for not falling in the traps of non genuine analogies.

        Let me quote something from Carlo Rovelli that I found in "Quo Vadis
Quantum Mechanics?" referring to C. E. Shannon's 1949 book:

"...the definition of Shannon, not the popular one, but the one in his book,
where you have two systems with many states, and there is a possible state
of the couple but there is only a restricted subset of all joint states.
Information is simply the way of counting the allowed joint possible states.
The fact that there is a common allowed state tells you that if you know
something about one system you also know something about the other one. This
is exactly what you need in communication theory when you have a channel, a
receiver and a transmitter. So I have two systems. If there is a quantum
correlation of the two, I can say that, if this system is UP, the other is
DOWN, and vice versa. This is what I mean by information, period."

        I am attempting to be faithful to this definition.

        Interestingly, it seems that since the equivalence classes that I
pointed out above are countably infinite then the property that any proper
subset of infinity is isomorphic to the infinity would apply and this would
make the notion of information for such classes to vanish, no? It would be a
zero-information system of sorts! 

> It
> seems to me that the answer is a resounding NO! I claim that it is  
> its Dual.
> Thus I advocate a form of mind-matter dualism in terms of an
> Information-Matter dualism following the lines of the Pontryagin and  
> Stone
> dualities. http://en.academic.ru/dic.nsf/enwiki/327868
You may elaborate, but Stone dualities are very technical hard matter.  
I guess you are alluding to Vaughan Pratt's work on Chu Spaces.


        Yes, it is Pratt's idea that inspires this thinking. What he has
found is that is possible to solve the problem of Cartesian Dualism, but in
solving the problem we chance the notion of "substance" into one that is
emergent from underlying Process and not taken to be a primitive. What
convinced me of the validity of his idea is that it offers a very neat and
novel solution to the measurement problem of QM. To me it is the utility of
a metaphysical principle in advancing understanding that goes toward the
necessity of its assumptions/axiom, just as you have shown how the ideas of
Plato ,Plotinus and Theaetetus are useful.

>> but this seems to not really resolve the question entirely.
> [BM]
> I am not sure I have a clear idea of the question, here.
> [SPK]
>       Am I making any sense so far?
>> It
>> makes me suspicious of the entire Platonic program, for what would  
>> act
>> as the universal generator of "twoness" as distinguished from
>> "threeness" be in-itself? Why not some kind of nominalism that
>> transforms asymptotically into universalism?
> [BM]
> You lost me.
> You know how I work. I start from an assumption about some link  
> between
> consciousness and Turing 'machine', and from this I derived step by  
> step a
> frame which is closer to Plato and Plotinus than to Aristotle, at  
> least on
> the "Matter" notion.
> [SPK]
>       Yes and I use the assumption that any 1st person "content" of
> consciousness can be show to be equivalent to the content of some  
> virtual
> reality generated by a Turing Machine (given with sufficient physical
> resources)
But this has been shown not working. You cannot both capture  
consciousness by Turing machine states, and at the same time to invoke  
a notion of physical resource. It is the whole point of most of my  
posts. Physical resource including space and time have to be recovered  
from the math of (abstract) computer science.


        No no no! I am not "capturing consciousness by Turing machine"! I am
pointing at the content, using Descartes' brain in a vat and related
gedankenexperiments to show how there is an equivalence relation between the
content of experience (minus "agency" notions, self-awareness, etc.)  and
the content of what can be generated by universal Virtual reality machines,
as explained by D. Deutsch in Fabric of Reality, that can be used. The
notion of a physical resource is allowed because I am assuming that both
mind (crudely an information structure, like a Boolean algebra) and matter
(crudely as a Cantor dust or completely disconnected Hausdorff space) are
both equally existent and "real". The idea in Pratt's work is that Logic and
Time (the evolution of physical systems) form a duality see:

> and following your arguments will agree that while the content
> itself is computable, *which one of the computations it is* that is  
> the
> actual generator of the particular content of a particular point of  
> view is not computational.
I am OK, here.


        OK, so if we can extract the symmetry groups from the possible
relations between 'many' and find that those include the symmetry groups
that we find in physics, would this not give us a way to think of physical
laws as emergent from interactions in a way that is parallel to Kant's idea?
But for this to work, two conditions must be show to be of prior necessity:
a plurality of systems that we can associate with observers (in a generic
non-anthropomorphic sense) and a means to derive notions of "substance
exchange". That is what I am working towards.

> These thoughts tie back to the point about
> indeterminateness that Plotinus brilliantly made and you point out.
Yes. Note that the idea of relating matter to indeterminacy is already  
in Aristotle. Alas, Aristotle and/or its successors have reified it  
metaphysically. That is, imo, what makes the mind-body problem  


        I disagree. What makes the mind-body problem insoluble is the
assumption that 'substance' is primitive. We can see this in Descartes
attempt at dualism. By taking res extensa and res cognitas as primitive
substances, Descartes was unable to close the gap between them, for within
the notion of substance one must have another substance that is of both
aspects to bridge between them and this necessity stultifies the entire
project; what is the point of separate substances if there is a third
substance that is both? Cartesian dualism fails because it is just an
incoherent monism. OTOH, if we consider Mind and Matter in terms of their
logics and dynamics and see that there is a relation between these two
aspects that preserves their differences all the while there is a
parallelism a solution can obtain. But this alternative requires a different
metaphysical underpinning; this point is what I am arguing below.

>       Your modelization so far seems to only consider a "frozen"
> perspective and there is scant mention of how the model is extended  
> to cover
> a plurality of entities, except for the diamond^alpha aspect mentioned
> below. As far as I can tell, your Model offers a logical structure  
> to a new
> version of the individual Leibnizian Monad (
> http://www.iep.utm.edu/leib-met/#H8  ) that I am trying to develop,  
> but only
> in the static sense. There is no dynamic in it.
The 'sensible' modalities, like Bp & p, and Bp & Dp & p, introduces an  
internal dynamic. S4Grz is not just a logic of knowledge, it is a  
logic of evolving knowledge, or time. It is due to the "& p". It makes  
the first person intuitionist, the builder of its mental reality.


        It may exist there Bruno, but it is by no means explicit. The fact
that we can map Bp & p, etc. to some abstract structure and use the
orderings of those relations to act as a quotienting does nothing to obtain
the experiential transitivity that is explicit in the 1st person. This is
just a very sophisticated form of eliminatism unless we assume, even
tacitly, a fundamental Becoming. We find explicit examples of this in
discussions of Chris Isham's paper on Topos. See: Isham, C. J. (1993),
“Canonical Quantum Gravity and the Problem of Time”, in L. A. Ibort and M.
A. Rodríguez (eds.), Integrable Systems, Quantum Groups, and Quantum Field
theories. Dordrecht: Kluwer Academic Publishers, 157-288. And

        My problem is that I do not have a good understanding of S4Grz.
Could you point me to papers on it that I might obtain online?

> I think that this is
> intentional since you are taking an explicit Platonic Idea stance in  
> the
> Modelization of Plotinusian Statics. I appreciate that, but  
> understand that
> unless we can derive change from changelessness within our  
> modelizing we are
> doomed to eliminatism when it comes to our 1st and 3rd notions  
> temporal
> transitivity, duration and causality.
That's right, but the nice thing is that the first person notion  
automatically provides an internal dynamics.


        Ummm, I am not so sure that is a correct statement of the
relationship. From what I have been able to understand so far, the 1st
person notion entails an internal dynamic because of its self-referencing
maps. My point is that the mere existence of automorphisms or self-mappings
alone is insufficient. We need a ground within which these would act;
otherwise we just have the equivalent of a dust with no hope of

> It is my contention that it is
> impossible to derive change from changelessness,
Even physicalists can accept this though. Many physicists don't  
believe in time. It emerges for local observers when embedded in the  
block-static reality.
Of course we accept the (non trivial) ordering of the natural numbers,  
which can be seen as the Mother of all computational times.


        So does this allow us to not consider the alternative? This is so
frustrating, we have a beautiful way of deriving the appearance of
changelessness from fundamental change, by using the notion of automorphisms
within a wider context of morphism, and this is rejected out of hand? That
is about the most irrational thinking that I can witness! The only
explanation that I can think of for this is that the hope of an impersonal
determinism that obtains from the block-static reality doctrine allows it
adherents to avoid all notions of personal responsibility for their
        As to the non-trivial ordering of numbers, it should be obvious that
there does not exist a unique ordering over the class of possible 1st person
experiences, or computational strings; the class is not equivalent to a
simply connected space which is, essentially, what is required for a unique
ordering to be possible. We see this in physics in the Foliation Problem of
General Relativity and in differential topology. See:
www.cmp.caltech.edu/~dannyc/papers/fpams.pdf.gz  we are fooling ourselves if
we think that time is just the ordering of natural numbers. Again, we can
ignore this and retreat into pseudo-monorealism - that only I exist - and
use that solipsism to conclude that any other alternative is just a
diffeomorphism of one's own notion of the natural ordering. This might
explain the irrational resistance to the reality of the implications of a
finite speed of Light that we find in many people.

        I think that the notion of Person that Plotinus uses to consider his
hypostases conceals this problem. By assuming personhood he is
surreptitiously introducing the 1st person self-mapping. This is equivalent
to assuming a fundamental Becoming grundladen within one's basic axioms. I
recall a conversation that I have with a writer that was arguing that time
did not exist. I pointed out that his model involved the computation of
optimizations over infinite collections of interactions and how this was the
mother of all NP-Complete problems and quoted to him his own words taken
from a discussion of how computational intensive it was for him to obtain
solutions to small examples of these optimizations on his physical desktop
computer and was taken aback by his complete incomprehension of this point.
One cannot consider that the mere existence of a solution to an infinite
NP-Complete problem is sufficient grounds to argue that the computation
itself need not ever occur, because that solution is not alone, it exists
mixed up with all of the infinite number of alternatives and the physical
act of running a machine is what manifests that One solution. The same
argument applies to the  Universal Dovetailer. 


Kindest regards,


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