Re: Simple yet Profound Metatheorem

David C. Ullrich wrote:
> On 19 Dec 2005 07:31:22 -0800, "Charlie-Boo" wrote:

> I don't know whether you've noticed this, but others have:

Name 2.

> You complain that I'm just quibbling about syntax,
> and at the same time you ignore most of my comments
> about the substance of your Simple yet Profound Metatheorem...

Glad you agree it's profound.

> Oh for heaven's sake. How was I supposed to know that that two
> []'s meant entirely different things?

Sorry, I thought you knew all about Logic.

> >> > Thm. ((|- P) = (|- Q)) => |- (P=Q)
> >
> >> This is obviously false.
> >> If neither P nor Q is provable (so that
> >> ((|- P) = (|- Q)) is true) it certainly
> >> does not follow that P==Q _is_ provable.
> >
> >Let's suppose that P is "1>2" and Q is "2>3". Then P==Q is
> >(1>2)==(2>3) which IS provable.

> Huh?

I said, let's suppose that P is "1>2" and Q is "2>3". Then P==Q is
(1>2)==(2>3) which IS provable.

> I didn't say that it is never the case that P==Q is
> provable. I said that this does not follow from the assumption
> that neither P nor Q is provable.

I was just illustrating my thinking with a specific example. A better
counterexample for you (than meaningless propositional variables) would
be P is any Godel sentence and Q is FALSE.

> David C. Ullrich

.

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