Comment on AI cooperation in practice

Sat, 31 Jul 2010 13:40:11 GMT

An automated proof-checker can identify some correct proofs - but not all of them.

That's a consequence of "Tarski's Undefinability of Truth Theorem":

No. That's not what Tarski's theorem says. Tarski's theorem is a statement about first-order arithmetic descriptions of truth (it can be generalized slightly beyond that but this is the easiest way of thinking about it). It asserts that there's no first-order description of what statements are true in a system that lies in the system.

Proof checking is a very different issue. Proof checking is straightforward. Indeed, most of the time we insist that axiomatic systems have proofs checkable as a primitive recursive function. We can do this in Peano Arithmetic for example, and in PA every proof can be verified by a straightforward algorithm.

Discuss