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*.
*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. A mind has a "becoming"
aspect that cannot be captured by fixed and static relational schemata.
Elementary arithmetic represents the primitive act of counting, but is
not the counting itself. 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. 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
<stephe...@webpages.charter.net/Outlaw/An%20Algebra%20of%20Bisimulation.pdf>:
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),
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
<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. It is not a primitive.
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 theChu space <http://chu.stanford.edu/>
representation). 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 if and only if the interaction problem is
assumed to be solved first.
We cannot assume that there exist (are necessarily possible) a
plurality of "locations" prior to the copy/paste operation. One must
assume a space and then localize "Paul" in it. 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. 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 <http://plato.stanford.edu/entries/nonwellfounded-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...)
Bruno
On 7/31/2012 6:05 AM, Bruno Marchal wrote:
I was just opposing Stephen's idea with the comp idea that numbers
and arithmetical truth is a (human) mental construct necessitating
some primitive time, space or physical reality. With comp, I argue
that arithmetical truth is simpler and can explain why the numbers
(or better the person associated to those numbers) construct ideas
of time and space, and why they can believe in some genuine way in
them, and be deluded in believing that they are primitive.
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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