2008/4/17 Phillip Gawlowski <cmdjackryan / googlemail.com>:
> -----BEGIN PGP SIGNED MESSAGE-----
>  Hash: SHA1
>
>
> 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
>
>
>  - --
>  Phillip Gawlowski
>  Twitter: twitter.com/cynicalryan
>
>  ~   "When life gives you a lemon, make lemonade." -Susie "I say, when
>  life gives you a lemon, wing it right back and add some lemons of your
>  own!" -Calvin
>
> -----BEGIN PGP SIGNATURE-----
>  Version: GnuPG v1.4.8 (MingW32)
>  Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
>
>  iEYEARECAAYFAkgHYacACgkQbtAgaoJTgL9mbgCgkK2JMounvNuucP9HMaLPHcvC
>  YjoAn2okGjTi/OAGWGiz5kQl5hm6w0f3
>  =zHaV
>  -----END PGP SIGNATURE-----
>
>



-- 
http://ruby-smalltalk.blogspot.com/

---
Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein