Re: Godel proved maths inconsistent not incompleteness theorem

On Tue, 6 May 2008 19:10:35 -0700 (PDT), Charlie-Boo
<shymathguy@xxxxxxxxx> wrote:

On May 6, 8:07 pm, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
There are an infinite number of theorems generated in one step?
How?

Never heard of the axiom scheme of induction?  Or regularity?  Or
separation?

An axiom scheme is not an axiom. Furthermore, if there can be an
infinite number of axioms, then we cannot write a proof generator in
general in the first place, as I said earlier.

Yes, you said that. It's hilarious. There _are_ infinitely many
axioms in ZF, and we _can_ write proof checkers and proof
generators.

This was the case I
had in mind.

Then it is not an axiomatic system and if it were you couldn't
program them in general anyway as I said.

Er, right.  Sure.  

It has to be r.e. You are going way beyond a list of axioms and rules
of inference. See http://en.wikipedia.org/wiki/Finitary

C-B

--
Jesse F. Hughes
"Contrariwise," continued Tweedledee, "if it was so, it might be, and
if it were so, it would be; but as it isn't, it ain't. That's logic!"
                                                     -- Lewis Carroll

David C. Ullrich
.

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