This leads us to Godel's second theorem, only formal versions of
number theory which assert their own consistency are inconsistent....
All of these limitative theorems like Godel's Incompleteness,
Church's Undecidability, Turing's Halting, Tarski's Truth all
suppose some criticality with respect to representing your own
structure, that if you model it at the granularity that you
can sufficiently reason about it, then you can gurantee that
you can never represent yourself totally--because using that
structure you can always prove that 1) your modeling theory
is inconistent, or 2) there exists something outside of it
meaning it will always be incomplete.
I just thought it was a clever analogy wrt the good and evil God thread,
and might encourage a comment or two instead of some stickler.
Greg
Koen Holtman wrote:
>
> On Fri, 2 Jul 1999, Gregory Alan Bolcer wrote:
>
> > Godel's theorem. Any system (or universe) can be proven either
> > consistent or complete, but not both.
>
> Ack! That is not Godel's theorem. Plus it is false.
>
> > Once you can formalize a universe,
> > then you can prove that there's always something outside of it.
>
> Not even false.
>
> >
> > Greg
>
> Koen.