Re: Peterson's Death Sentence

From: Noah Roberts (nroberts_at_dontemailme.com)
Date: 01/30/05 

Date: Sat, 29 Jan 2005 23:48:47 -0800

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.

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."

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, ...

another:
Again, technical terms ("completeness theorem") used inappropriately.

Completeness theorem are theorem about particular logical systems.

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