Re: Simple yet Profound Metatheorem

David C. Ullrich wrote:

> You post a "theorem" that's obviously false, where
> "obviously false" means that it takes no effort whatever to
> find a counterexample, counterexamples are simply obvious.

Your "refutation" is meaningless as it refers to the truth of an
Atomic Formula. It is not provable because it is not interpreted but
then it also lacks a truth value and it is meaningless to talk about
P==|-P when P can have unquantified free variables.

C-B

> And in reply to an utterly simple counterexample all you
> can say is that it's not a very good counterexample
> because it's too trivial. Huh.
>
> Hint: An utterly trivial counterexample here is better
> because it better illustrates how _obviously_ false the
> theorem was.
>
> Another hint: Credibility-wise it doesn't seem like a good
> idea for you to point out that a "Godel sentence" gives
> a counterexample. Because all this started with your
> amazing profundities about Godel this and Godel that -
> if I were you I'd hope that nobody _noticed_ that what
> I was saying was obviously inconsistent with Godel's
> theorems.
>
> >By that logic, you can say that a
> >system is incomplete because it has a propositional variable with no
> >meaning and thus no proof of it or its negation.
>
> Yes, if the question were whether propositional logic was complete
> the answer would be obviously not, because an atomic formula
> is neither a tautology nor an anti-tautology.
>
> >That's not what we're talking about.
>
> Giggle. Translation: Let's not talk about the really really obvious
> counterexamples to my assertions. Instead let's restrict discussion
> to counterexamples that depend on non-trivial results in logic -
> that way we'll still sound smart, even though what we said was
> obviously wrong.
>
> Tee-hee.
>
> >C-B
> >
> >> ************************
> >>
> >> David C. Ullrich
>
>
> ************************
>
> David C. Ullrich

.

Relevant Pages
Quantcast