Bruno Marchal wrote:
>Meanwhile, I
>would like to ask George and the others if they have a good
>understanding of the present thread, that is on the fact that growing
>functions has been well defined, that each sequence of such functions
>are well defined, and each diagonalisation defines quite well a precise
>programmable growing function (growing faster than the one in the
>sequence it comes from).
>Just a tiny effort, and I think we will have all we need to go into the
>"heart of the matter", and to understand why comp makes our "universe"
>a godelized one in the Smullyan sense.
>
>
To speak only for myself, I think I have a sufficient understanding of
the thread. Essentially you have shown that one cannot form a set of all
numbers/functions because given any set of numbers/functions it is
always possible, using diagonalization, to generate new
numbers/functions: the Plenitude is too large to be a set. This leads to
a problem with the assumption of the existence of a Universal Dovetailer
whose purpose is to generate all functions. I hope this summary is accurate.
George
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Received on Tue May 30 2006 - 14:43:56 PDT