George Levy wrote:
>
>
>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
The dovetailer is only supposed to generate all *computable* functions
though, correct? And the diagonalization of the (countable) set of all
computable functions would not itself be computable.
Jesse
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Received on Tue May 30 2006 - 16:03:38 PDT