Showing posts with label theorem. Show all posts
Showing posts with label theorem. Show all posts

Tuesday, September 29, 2009

Incompleteness

I'm with Gödel, said Pliny the Elder. The world is not everything that is the case. I haven't received my book yet, although I've paid for it, and that's a fact.

I don't think Gödel's theorem was concerned with things that hadn't arrived yet, I said doubtfully. I think it was only to do with arithmetical truths. That some things arithmetical are true but unprovable, in any consistent theory.

Well, said Pliny, It's true but unprovable that I haven't got my book. How do you prove that you haven't got something?

You're right you can't, I agreed. But it's not the Incompleteness Theory.

Yes it is, said Pliny. My transaction in buying the book is incomplete without the book. And you can't tell me that a monetary transaction is not arithmetical.

I think you have won the argument, I said. Gödel's theorem is more useful than I thought.