Re: Peterson's Death Sentence

From: Parse Tree (account_at_domain.extension)
Date: 01/31/05 

Date: Mon, 31 Jan 2005 01:19:33 GMT

Noah Roberts wrote:
> Parse Tree wrote:
>
>> http://en.wikipedia.org/wiki/G%F6del%27s_completeness_theorem
>>
>> Perhaps the person you're talking to is thinking of Godel's
>> incompleteness theorem, which is much better known, but applicable to
>> mathematics, and not logic.
>
> "Gödel's completeness theorem is a fundamental theorem in mathematical
> logic proved by Kurt Gödel in 1929. It states, in its most familiar
> form, that in first-order predicate calculus every universally valid
> formula can be proved.
>
> "The word "proved" above means, in effect: proved by a method whose
> validity can be checked algorithmically, for example, by a computer..."
>
> I think maybe you didn't read the wikipedia link you just gave me; on
> the other hand, I did.

No, that's exactly what I have stated previously.

> More, and this is pretty much exactly what I was told already by the
> person stating you were using the term incorrectly:
>
> "To cleanly state Gödel's completeness theorem, one has to refer to an
> underlying set theory in order to clarify what the word "domain" in the
> definition of "universally valid" means."

Stating it is irrelevant. We know that logic is both consistent and
complete.

> Here is another quote from a different source:
> If you want to bring in Godel, it must be by an analogy. Its a poor
> analogy, ...

Not at all. The completeness theorem proves completeness. I brought it
in because you were stating that logic was somehow 'incomplete'.

> another:
> Again, technical terms ("completeness theorem") used inappropriately.
>
> Completeness theorem are theorem about particular logical systems.

Yes, and we are talking about logic. When I say that something is
logically impossible, I am talking about logic, not talking about magic,
or farting. Do you still not understand?

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