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.

No comments: