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...)


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.



"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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