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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