Re: [sl4] Re: More silly but friendly ideas

From: Lee Corbin (
Date: Sat Jun 28 2008 - 02:07:00 MDT

John Clark writes

>> In 1930, Gödel proved his Completeness* theorem,
>> showing that first order logic (without that
>> axiomatized arithmetical component!) is both
>> sound (anything you prove really is true)
> That is true, there are no contradictions in first order logic.
>> and complete (if it's true, you can prove it).
> BULLSHIT! First order logic is not even powerful enough to even do
> arithmetic

Listen, John, I didn't want to give the entire explanation of
what "completeness" is because it contains many qualifying
phrases pertaining to model theory and so on. What "if it's
true, then you can prove it" means "any logical consequence
of the theory has a deduction in the theory". I'm sure you
knew that.

OF COURSE it does not mean that everything in the universe
that is "true" (on whatever theory of truth you like) can be
proven in pure first order logic (first order logic without
arithmetic). You can't be *that* desperate to denounce as
BULLSHIT some portion of what someone says,
or can you?


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