CDR: Godel & Turing - a final point

[Jim Choate]

On Thu, 9 Nov 2000, Jim Choate wrote:

> 
> On Wed, 8 Nov 2000, Sampo A Syreeni wrote:
> 
> > You are talking about two very different problems, here. Gödel/Turing sorta
> > things are about problems where quantifiers over an infinite set are
> > permitted.
> 
> No, it is exactly the same thing. Godel applies to ANY set of axioms and
> conjectures. It is universal.
> 
> Godel clearly applies to Boolean algebra. The theorems we are speaking of
> are applied to Boolean algebra. The theorems require either a universal
> consistency or evaluator, either is prohibited by Godel's.
> 
> In the particular case we are speaking of we are talking about the
> situation where the language consists of "all
> consistent/valid/evaluatable/assignable boolean sentences".
> 
> Hence, somebody did a naughty...

If you have a 'language' that is provably consistent then you know that
that language is not complete or 'universal'. There MUST!!! be sentences
which are not included in the listing.

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