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Subject: Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
From: George Greene <gree...@email.unc.edu>
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On Oct 13, 4:30=A0pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> These are just INFERENCES mind you.
>
> You still owe me some BASE THEOREMS, otherwise all your "proofs" are
> Oracular.

NO, I DON'T.

In the NON-logical context, in the SET THEORY or NUMBER THEORY (Peano
Arithmetic)
or group theory OR ANY OTHER AXIOMATIC THEORY context, in the context
of anything
for which you might actually be USING first-order logic, any
investigation TO WHICH you might
be APPLYING first-order logic, what YOU are calling a "base theorem"
is called AN AXIOM.
That's what axioms ARE FOR.  They are true DESPITE not having any
proofs (other than "it's an axiom".)

In the pure-logical context, there is no difference between a logical
axiom and the conclusion of an inference
rule that infers/derives that conclusion FROM AN EMPTY set of
premises.
I'm NOT being ORACULAR when I insist that P V ~ P
is true, withOUT any proof in a FIRST-order system.  P V ~P
*is*ZEROth*-order, to start with.
First-order PRESUMES all that IN ONE handwave!