Re: Simple yet Profound Metatheorem

David C. Ullrich wrote:
> On 14 Dec 2005 18:10:58 -0800, "Charlie-Boo" <chvol@xxxxxxx> wrote:

> >Prove ( P = |- Q ) => |- ( P = Q )
>
> Various people have asked what the heck this means.
> You should _say_ what it means, instead of replying
> with questions.

You are way too loose with your tongue.

1. "Various people have asked what the heck this means.": Only one
person asked a question, viz, "What does this mean?".

2. "instead of replying with questions.": I had yet to respond to
that one question.

3. I posed one question, in response to the statement that my theorem
is ill-formed. As the statement did not say what constructs in the
theorem are ill-formed, I asked if he was referring to the use of |- as
an operator in a wff.

At no point did I reply to a question with a question.

> Hint: My best attempt at deciphering it leads to
> something obviously false:
>
> "If P equals 'Q has a proof' then there is a
> proof of 'P equals Q'."

That's it. What was so hard about that?

> Obviously false, since if P equals 'Q has a proof'
> then P does not equal Q.

Why is that false? (Once again, what you are so adamantly convinced of
is just not so.)

> So that must not be what you mean.

Thanks for the vote of confidence.

> >(P and Q have the same sets of free variables.) This simple theorem (I
> >created 12/1/05) provides the link between Theory of Computation and
> >Proof Theory (Incompleteness in Logic) that theoreticians such as
> >myself have been looking for since the 1930's. (Each Theory of
> >Computation theorem becomes an Incompleteness theorem in Logic,
> >providing almost trivial formal derivation of the exact results of
> >Godel, Rosser and Smullyan.)
>
> Awesome.

Would it be awesome (interesting, new, useful) if it were true?

C-B

> >Hint: Consider the equivalent ( P = |-Q ) => ( P = |- P )
>
>
> ************************
>
> David C. Ullrich

.

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