Comment on Exponentiation goes wrong first

Tue, 14 Dec 2010 15:37:02 GMT

If you can prove that a theory has no models, then you can prove a contradiction in a finite number of steps. It's interesting to contemplate the minimum number of steps -- these are busy-beaver type numbers.

In the language of model theory, Nelson believes that one can prove that Peano arithmetic has no models. He does not believe one can prove that Peano arithmetic minus induction has no models.

But we do not have to have a model, or even to know any model theory, to "talk about something."

Discuss