> Because if you show that the converse of Goldbach's conjecture is not provable, you have actually proven Goldbach's conjecture (since you have shown that ther

> Because if you show that the converse of Goldbach's conjecture is not provable, you have actually proven Goldbach's conjecture (since you have shown that there is no counterexample!). Lets hypothetize that Goldbach's conjecture is true and unprovable (let's call it S1). In that case, the following statments are both true: C1) It is impossible to prove S1. C2) It is impossible to prove the converse of S1. (since in this case S1 is true, the converse is actually false, so cannot be proven). Now, if we go into meta-proofs, we may be able to prove C1 (whether or not S1 is true). But we will never be able to prove C2 (if S1 is true and unprovable, C2 will also be true and unprovable). Now, if S1 is actually false, We may actually at some point find a proof of that. But that's not really so interesting. The interesting part is that there DOES exist statements like this that ARE true AND unprovable (even if we don't know which statments), we just don't know WHAT statments those are.