Gödel's Theorem Invalid?

Monday, October 24, 2005
A paper recently made available on Arxiv claims to have found a contradiction in Gödel's proof of his most famous theorem, that the metamathematical system of Whitehead and Russel is incomplete (ie, there exist sentences that can neither be proven true nor proven false.)

I haven't read the paper, and I've got to admit that it seems very unlikely. But it's interesting to consider it at least.

7 comments:

chuck said...

Doesn't look right to me. In particular, his first logical equivalence isn't. The author may have used the wrong word, his address is in Ecuador, but still... Likewise, he uses the induction axiom to establish that the induction axiom is a tautology. Unfortunately, he doesn't seem to realize that he has done so or why the axiom is necessary. The copyright date is 2000, so I suspect the paper was rejected for publication.

Seneca the Younger said...

You've looked at it more closely than I have so far, then. But I wondered about that --- like the interminable proofs that P=NP based on linear programming optimizations.

Or squaring the circle, and it worries me a little what I'm coming up with for examples.

chuck said...

Or squaring the circle, and it worries me a little what I'm coming up with for examples.

I think it's a crank paper. Got to love some of those guys, really. They work hard and try to think about stuff, they just don't connect. You can't convince them that they are wrong, either. Oh well.

Knucklehead said...

They work hard and try to think about stuff, they just don't connect.

Well, that doesn't make us, errr..., them bad people. After all, the world is full of folks who don't do a moment's work to try and think about stuff and don't give a tinker's damn about connecting.

Sorry, just a bit of cranky from a crank.

RogerA said...

hmmm--we have explored matrix algebra, Godel's theorem--when are we going to move past the simple stuff and get into string theory. BTW--I always thought the ultimate answer was 42.

chuck said...

I always thought the ultimate answer was 42.

Rounding error. It needs to be rerun at higher precision.

crosstalk said...

No, the ultimate answer is not 42. It's 13 (to the appropriate power).

If numeric, that is.