Re: virus: Re: The Fall of Buddhism : Honesty, Science and Objectivism

Lee Daniel Crocker (
Wed, 12 Mar 1997 22:32:43 -0800 (PST)

> See Godel's Theorem.
> Any consistent system will have truths it can't deal with; any complete
> system will allow some non-truths.
> Something near that, anyway.

To be precise, Godel's proof showed that any axiomatic system large
enough to express assertions of basic number theory must also be
capable of expressing assertions which are /true/ in the system but
not /provable/ in the system. It cannot show what those assertions
are--if it could, it would be proving them--but it can prove that
they exist. That was what Godel did--first, he proved using the
axioms of number theory that there existed a mathematical theorem
expressible in the system that was true, but could not be proven by
it. Then he generalized that result to all such systems.

At no point did Godel ever question the validity of proof, or of the
validity of symbolic logic itself, or of deductive reasoning; indeed,
his proof is a very paragon of it (although Smullyan's version in
_What is the Name of this Book_ is a lot easier to read. I'd better
not mention that Smullyan also wrote _The Tao is Slient_ or we'll
start that damned thread again. Oops, I guess I did anyway).

Lee Daniel Crocker <>