On 9/19/2012 2:39 PM, Bruno Marchal wrote:
Dear Bruno,

Your remarks raise an interesting question: Could it be that both the object and the means to generate (or perceive) it are of equal importance ontologically?

Yes. It comes from the embedding of the subject in the objects, that any monist theory has to do somehow.

In computer science, the "universal" (in the sense of Turing) association i -> phi_i, transforms N into an applicative algebra. The numbers are both perceivers and perceived according of their place x and y in the relation of phi_x(y).

You can define the applicative operation by x # y = phi_x(y). The combinators are not far away from this, and provides intensional and extensional models.

I remind you that phi_i represent the ith computable function in some effective universal enumeration of the partial computable functions. You can take LISP, or c++ to fix the things.

Dear Bruno,

You are highlighting of the key property of a number, that it can both represent itself and some other number. My question becomes, how does one track the difference between these representations? You speak of measures, but I have never seen how relative measures are discussed or defined in modal logic. It seems to me that if we have the possibility of a Godel numbering scheme on the integers, then we lose the ability to define a global index set on subsets of those integers unless we can somehow call upon something that is not a number and thus not directly representable by a number..




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