[headsonpikes]

I'm reasonably certain that you are unfamiliar with Godel's Proof.

There is nothing left-wing or nihilistic in Godel's lucid, brief proof for the incompleteness of any non-contradictory formal system.

It was part of Symbolic Logic II when I was an undergrad.

Nothing communist about Godel.

I can't believe that I have to post this.

[js1138]

I can't believe that I have to post this.

js1138's Law: The first to post a negative comment on a science thread hasn't read the article.

[general_re]

I can't believe that I have to post this.

Depressing, innit? ;)

[snarks_when_bored]

...Godel's lucid, brief proof for the incompleteness of any non-contradictory formal system...

Two (friendly) comments. First, Gödel's proof was stunning, but not brief (nor was it lucid in the ordinary meaning of that word). Second, the formal system has to be strong enough to express natural number arithmetic with multiplication; systems weaker than that—say, systems that include only the operation of addition—can be proved to be both complete and consistent.

Here's a useful link to an article by R.B. Braithwaite which provides some background and details on Gödel's Incompleteness Theorem:

Introduction [to Gödel's Theorem]