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.
*Any system* that can implement a unitary transformation would have
a mind by my definition.
So you agree that elementary arithmetic has a mind?
(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).
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".
Is that a particular case of Vaughan Pratt's duality?
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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