From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>

Date: Sun May 13 2007 - 19:38:18 EDT

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
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*> these truths, just about being able to prove that they are truths
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*> using the axioms that form a particular system. I see this as a
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*> subtle
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*> but very relevant difference.
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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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