george
Posts:
800
Registered:
8/5/08
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Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 13, 2012 8:16 PM
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On Oct 13, 4:30 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> You still owe me some BASE THEOREMS, otherwise all your "proofs" are
> Oracular.
No, I don't. I can just say that rule "EM" (that is what I choose to
call it)
allows me to infer P V ~P *FROM*NOTHING*.
Moreover, I can call the universal generalization of that (with P as
the variable) an inference rule (if I want to)
and say that if P is ANY WFF WHATSOEVER in the first-order langauge I
am using, then
P V ~P is inferred, as the conclusion of this inference rule, and as a
theorem,
FROM NOTHING.
That does NOT make anything "oracular" and it does NOT make anything a
"logical axiom".
I can [AND DO] JUST say that it is an inference rule that any
instance of a propositional tautology is a theorem.
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