Dear Bruno,

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. *Any system* that can implement a unitary transformation would have a mind by my definition. 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>



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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