On 01 Aug 2012, at 17:11, Stephen P. King wrote:
On 8/1/2012 3:14 AM, Bruno Marchal wrote:
On 31 Jul 2012, at 20:28, Stephen P. King wrote:
Your statement here demonstrates that I have entirely failed
to communicate my thoughts so that you could understand them. You
are arguing against a straw man. What you write here as
"Stephen's idea" is as Wolfgang Pauli might say: "not even wrong".
I am proposing that numbers and arithmetical truth are (at least)
relational structures within the realm of the mind, the mind of
observers which are not exclusive to humans.
But what is mind? I fail to understand you because you fail to give
a theory that I could explain to my niece. You fail to give me what
we accept as existing and how we derive the phenomenology. You
refer to paper which postulate too much to address the mind-body
problem in the comp setting.
Dear Bruno,
A mind is, for example, the subject of books such as David
Chalmer's "The Conscious Mind" with the addition that a mind is *at
least* representable as a Boolean Algebra. I full-throatily endorse
Chalmer's definitions and ideas. I have already defined "existence"
as *that which is necessarily possible*.
So you assume classical set theory.
I think the Boolean algebra better describe the laws of thought than
the laws of mind, more related to the self-reference abilities of the
machines.
*Any system* that can implement a unitary transformation would
have a mind by my definition.
So you agree that elementary arithmetic has a mind?
No, not alone. Elementary arithmetic is a necessary component of
a mind but it is not sufficient to be a mind.
Then you contradict that *any system* which implement a unitary
transformation would have a mind.
A mind has a "becoming" aspect that cannot be captured by fixed and
static relational schemata.
That can make sense in a an atemporal ontology. The mind of the
numbers, as seen by the numbers, has more than one becoming aspects.
Elementary arithmetic represents the primitive act of counting,
I really mean addition and multiplication. Counting alone is not
enough (not Turing universal).
but is not the counting itself.
You mean it is not human counting? I agree.
Human counting, with comp, involves very big numbers, having long
computational histories.
We must never mistake an object for its representation unless the
two are actually the same thing, as in the case of a physical system
being its own best possible simulation.
Keep in mind that I use only "simulation" in its digital meaning. I
have no idea what you mean by a "physical system". I don't assume
"physical systems", and as you known I show that with comp the notion
appears to be an emerging one.
Here you seem to assume analysis and physics. In the comp setting,
once we say "yes" to the doctor, we have to explain analysis and
physics in term of Diophantine equation. Be it with numbers or with
combinators, we live on the "continuum border of a digital structure",
so to speak.
This is a very subtle point that I need to explain better. A self-
simulation is a form of automorphism. Some of the algebra of such is
in a paper found here: webpages.charter.net/Outlaw/An Algebra of
Bisimulation.pdf
(It is an easy theorem that elementary arithmetic implements all
unitary transformations, but this remark is trivial and does not
solve the mind-body problem, but it makes it formulable in
arithmetic or in arithmetical terms).
There is no "mind-body" problem once one accepts the Stone
duality relationship as representing the mind-body relationship. All
that is left is the interaction between minds problem (or its dual
interacting bodies problem),
I doubt this. Like Craig you symmetrize mind and matter, but comp, or
just self-reference makes the big picture less symmetrical. The
relation is more akin to the relation between a volume and a surface.
The dualism that I am advocating is explained in Vaughan Pratt's
paper http://boole.stanford.edu/pub/ratmech.pdf and is a
rehabilitation of Descartes failed version by dropping the idea of
a "primitive substance" and using the natural duality of
Categories to co-define "minds" and "bodies". Becoming is
considered to be the fundamental primitive. This idea of becoming
is explained here: http://www.metasciences.ac/time_XIV.pdf
Going from a third person view to a first person view transforms
(by 1-indeterminacy) an "and" into an "or" like in "Paul is in W
and Paul is in M" to "Paul feels to be in W or Paul feels to be in
M".
The 3p is an abstraction from the mutual non-contradiction of
many 1p.
But you have only 3p object in front of you, you have to project 1p
there, by non solipsism. You rely on 3p-data.
It is not a primitive.
To do science you have to share axioms on a small amount of 3p things.
Those are what I call primitive.
I can only hope my audience agree that 2+6=8, and things like that (+
the yes doctor in this case).
Is that a particular case of Vaughan Pratt's duality?
Pratt does not explore the 1-ideterminacy as he assumes spaces
from the start (using the Chu space representation).
? (this means he is not aware of the comp mind body problem, but that
happens).
Pratt's discussion is weak for this (and some other) reasons and I
am trying to strengthen the theory. Your 1-indeterminacy is a way to
define spaces
Not at all. It is a consequence of comp, and we have to take into
account. It leads to the fact that the idea of space is emergent from
the statistical interference of infinities of computation.
It is an open problem if that sum on computations (nuanced for each
povs) give rise to a stable physical universe comparable to the one we
observed.
if and only if the interaction problem is assumed to be solved first.
That's the point. may point is that comp makes this mandatory, and
thanks to Gödel, Löb and Solovay, we can already interview the (rich)
universal machines on the question, and that gives the shadow of the
shadow of the answer. Even simpler more fundamental problems than
interaction have to be solved first.
We cannot assume that there exist (are necessarily possible) a
plurality of "locations" prior to the copy/paste operation.
After UDA we definitely know that there is none. A "location" is
directly determined by infinities of arithmetical relations.
One must assume a space and then localize "Paul" in it.
Not at all. Not after UDA. before UDA, we assume only that our brain
are digitally emulable by our environment, staying agnostic on the
nature of that environment.
In other words, only until and unless W and M (and so forth) are
defined is it possible for sentences like "Paul is in W and Paul is
in M" and "Paul feels to be in W or Paul feels to be in M" to be
meaningful.
It is enough we can distinguish them in the common sense of the terms,
to get the UDA point. It is the point of that reasoning.
You are introducing difficulties were there are none. You could have
asked Galilee to define light for interpreting what he pretends to see
through a telescope.
With comp no machines can distinguish "real", virtual, arithmetical,
for a short run. You are presuming we need something physical, but
then the reasoning will just show that the relevant part of your body,
for your mind, is not Turing emulable.
We cannot just assume prior necessary possibility (existence) as
generating the reality of the locations. Reality requires a
collection of entities to whom the locations are incontrovertible
(no mutual contradictions).
This implies a circular relationship between observers and
locations! This is not problematic nor pathological as long as one
is operating with the proper logic and set theory: the Non-Well
Founded Set theory as explained by Jon Barwise et al. (You might
have noticed a reference to the Liar Paradox in Pratt's paper, this
was a hint to the NWF set construction...)
With comp the self-reference is well founded enough. No need to
involve set theory at the bottom, but it is handy for the semantics of
self-reference indeed, at the epistemological level, where, with comp,
the laws of physics originate and develops.
Don't interpret my saying as a solution proposal of a problem. I only
translate a problem into another one, assuming an hpothesis. But the
translation changes the perspective, going from aristotelian
naturalism to a more neoplatonist Pythagorism. To be short.
Be careful to distinguish the math needed for the basic ontology, and
the metalevel math needed to describe the internal processes and their
internal perspective raised by that basic ontology, once comp is
assumed.
Bruno
http://iridia.ulb.ac.be/~marchal/
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