Re: [asa] Godel's theorem [Was: Re: Dawkins, religion, and children]

From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>
Date: Sun May 13 2007 - 19:38:18 EDT

On Sun, 13 May 2007 10:55:15 -0700 PvM <pvm.pandas@gmail.com> writes:
> I believe that you are wrong. Godel says nothing about discovering
> these truths, just about being able to prove that they are truths
> using the axioms that form a particular system. I see this as a
> subtle
> but very relevant difference.

This, in technical language, is the question whether there is an
effective way to prove a theorem. There is in the propositional calculus,
a truth table. But as soon as we get into the functional calculi, there
are no effective means to derive a proof. There is an effective way to
determine whether a sequence is a proof. Note that number theory requires
a second order functional calculus. Church extended Goedel's proof to the
first order calculus.
Dave

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Received on Sun May 13 19:52:00 2007

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