From: Hal Finney (hal@finney.org)
Date: Thu May 30 2002 - 00:54:39 MDT
Damien writes:
> If a statement is declared a theorem (as I understand it), it must be true,
> by fiat definition, *for those limited logical purposes*.
No, I'm afraid you've got it backwards. What you have described would
be more like an axiom. A theorem is, by convention, something which
is mathematically proven, based on whatever axioms are relevant. It is
the opposite of something which is assumed by fiat.
Normally the theorem is stated first, followed immediately by the proof.
The theorem's truth rests ultimately on the validity of the proof,
and the truth of the axioms.
Hal
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