Re: Is Godel's Theorem surprising?

Charlie Silver wrote:

>       Why should it be so surprising that PA is incomplete, and even (in a

sense) incompletable?

Because the axioms are "complete." The working mathematician has no new
axiom to add to those of PA. I expect that all statements provable in
classical number theory can be proved in PA. So if you believe that all true
statements are decidable somehow, which is probably part of every
mathematician's emotional constitution, then PA would be seen as complete.

Bob Lubarsky