You're right, I was shooting from the lip. All computations do require
a Turing Thesis, and does contain a nontrivial amount of
information. All descriptions, on the other hand, is a zero
information set, _by definition_.
As you have well pointed out, the set of all descriptions can be
computed in c time (c = cardinality of the reals) on an ordinary
Universal Turing Machine via the UD. It is, however, a nonclassical
model of computation.
Cheers
Marchal Bruno wrote:
>
> >> > From: "Russell Standish" <R.Standish.domain.name.hidden>
>
> >> >
> >> > > There is no problem is saying that all computations exist in
> >> > > "platonia" (or the plenitude). This is a zero information set, and
> >> > > requires no further explanation.
>
> Stricly speaking I disagree. The expression "all computations" needs
> Church thesis for example. And Church thesis is a non trivial bag of info.
> But I see where is the point. The "all computation set" is a zero
> information set, but is not a zero meta-information set, should we say.
> Same for "all numbers", "all sets" You still need to define axiomatically
> numbers or sets.
> There will always be some mysterious entity we need to
> postulate. That is why I postulate explicitely the Arithmetical Realism
> in comp. Too vague "Everything" could lead to inconsistencies.
>
> Bruno
>
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A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
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Received on Fri Nov 29 2002 - 17:12:53 PST