# RE: What's wrong with this?

```Hi Bruno,

```
```
It seems that we need to discuss more basic ideas as it
seems that my attempted explanations are not bisimulating with your
thoughts.

[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Tuesday, September 14, 2010 9:40 AM
Subject: Re: What's wrong with this?

On 12 Sep 2010, at 21:43, Stephen P. King wrote:

Hi Bruno,

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

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

Hi Bruno,

-----Original Message-----

[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal

Sent: Friday, September 10, 2010 11:16 AM

Subject: Re: What's wrong with this?

snip

***

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...

*************

[BM]
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.

[SPK]

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.

[BM]

Honesty I am a bit lost.

[SPKnew]

OK, did you make sense of the idea of representing Integer
with a sort of equivalence class that have members that are the arithmetic
generators or creators or acts that equal examples of the number? We can
think of 1 in the Platonic sense as the class of all arithmetic operations
that are equal to 1, 2 as the class of all arithmetic operations that equal
2, etc. OK, given that then it seems to follow that, say a 2 in the
operation that equals some other number is in a sense a mapping of the
entire class of 2 into that other class. Does this make sense so far?

snip
[SPK]

Let me quote something from Carlo Rovelli that I found in "Quo
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!

[BM]

?

[SPK]

How do we consider the information content of infinite sets?
Given that and the way that we see mapping from classes into classes as
pointed out about, does this not give us a notion of "the way of counting
the allowed joint possible" elements?

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

[BM]
You may elaborate, but Stone dualities are very technical hard matter.
I guess you are alluding to Vaughan Pratt's work on Chu Spaces.

[SPK]

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.

[BM]

? (like with the UD argument?).

[SPK]

I don't understand how your UDA does this. I need to study it
further. I need to understand how you obtain the notion of concurrency in
your model, for it is not sufficient to encode transitivity for a single
system, we need to show how a vast number of systems synchronize and
correlate their states with each other, otherwise our model is solipsistic;
incapable of modelizing beyond itself.

[SPK]

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.

[BM]

Different from Everett's solution? (Which appears to extend the mind-body
problem with digital mechanism).

Is Pratt a many-worlder?

[SPK]

No, Pratt's ideas follow the interaction interpretation of
John Cramer. Resent work by Aharonov, Elitzur and other is looking in this
direction. See for example:
http://a-c-elitzur.co.il/site/siteArticle.asp?ar=71

snip

[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)

[BM]
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.

[SPK]

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:
http://boole.stanford.edu/pub/dti.pdf

[BM]

This pleads for no fundamental matter, nor time.

[SPK]

Yes, but bOnly in the limit of the totality of Existence, there
is no measure or differentiation, thus no matter or time in that fundamental
sense. That’s why the dualism that I am advocating is one that degenerates
to a neutral monism in that limit. But the Totality includes the finite and
in that finite case we have matter and time.

snip

[SPK]  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.

[BM]
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.

[SPK]

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.

[BM]

Why? The experiential logic is typically transitive, and anti-symmetrical.

[SPK] Yes, that is true but in a static Platonic Idea sense. The main
problem, I suspect, obtains from the enumerability of the content of
experiential logic as I see in your Model. This makes a computation of
logical sentence something that has properties in-it-self independent of any
notion of interaction; therefore it is, in a deep sense, solipsistic. To
boil this down, we need to start with the existence of a plurality of minds,
explaining why it is necessary that there is more than just the One. You
move toward this in SIENA.pdf but not sufficiently to nail down the
reasoning.

snip

[BM]
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.

[SPK]

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
behaviors.

[BM]

On the contrary, it is explained that free-will and responsibility is
unavoidable from inside. To use the determinacy of the big whole would be
like to give a name to God, and that is explicitly making any Löbian machine
inconsistent, and worth: incorrect.

We are typically partially responsible for our normal futures.

[SPK] This subtle proof has still eluded me. I want to be sure that no one
is projecting anthropomorphic notions into the model without sufficient
reasons that these obtain.

[SPK]  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.

[BM]

Nobody said that. I said only that the natural numbers does provide a kind
of computational time, but the subjective time (and space time) comes from
the first person logic S4Grz (and S4Grz1), in the ideal case under scrutiny.

[SPK]

A Liebnitzian "order of succession" aspect of time, certainly obtain in what
you point out here, but that is cheap, for there are no a priori
alternatives in the notion of the number that is subsequent to n, for
example n +1 or n+2 have only a single and unique property. We do not see
this kind of singular one- to one and onto like map of determination in our
notions of free-will and responsibility. We see a selection process from a
menu of alternatives, alternatives that are all given concurrently. This is
a very different notion than what we see in natural numbers.

Snip

Let us deal with the rest of my critique of Plotinus's model
some other time. It  is of great interest to me as it helps me understand
details that are absent in Leibnitz' Monadology and need to be considered,
but I need to focus on developing a mutual understanding of the ideas here
so far.

Onward!

Stephen P. King

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