On Thu, Apr 17, 2008 at 12:13 PM, Robert Dober <robert.dober / gmail.com> wrote:
> 2008/4/17 Phillip Gawlowski <cmdjackryan / googlemail.com>:
>
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>  >
>  > Robert Dober wrote:
>  >  |>  1. P Q        Premise
>  >  |>  2. P ¢ª (Q ¢ª ¢ÌP)         Premise
>  >  | De falsum quodlibet, nice try ;)
>  >  | IOW You can prove anything with a wrong premise as false -> X is
>  >  | always true indeed what you proved was
>  >  | false -> (P && !P)
>  >  | which is correct of course.
>  >
>  >  Outside of propositional logic, yes. But I did warn that this doesn't
>  >  necessarily apply, too, and provided a link for thorough critique of the
>  >  proof by the reader. :)
>  Oops I missed it, nice trick anyway.
>
> >
>  >
>  >  | Is it really called an axiom? An axiom cannot be proven, it should be
>  >  | called a Theorem.
>  >
>  >  Sorry, my mistake. It *is* a theorem. Still a misnomer since the theorem
>  >  is more of a paradox.
>  I see no paradox in it, the paradox is the proof of the theorem right?
>  The theorem itself just says that such paradoxes will occur in a
>  complete system, but I admit it is difficult to accept that as not
>  being paradoxal itself. :=)
>  IIRC even Bertrand Russel did not believe Gdel's theorem and there
>  were other prominent mathematicians defying it.
>  Gdel was waaaay ahead of his time.
>
>  Cheers
>  Robert

Fascinating conversation!  It comes up every once in a while in
database talk lists.

Formal logic system proves that it cannot prove everything that's true
within the system (It's not talking about itself, is it? :).

I love it!

Todd