On 9/19/2012 2:39 PM, Bruno Marchal wrote:
Your remarks raise an interesting question: Could it be that both
the object and the means to generate (or perceive) it are of equal
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
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.
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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