Gödel proved that there are true sentences that cannot be proved.
Suppose I told you that the Goldbach conjecture is one of those. (The Goldbach conjecture supposes that every even integer number can be expressed as the sum of two odd primes.)
Is that logically possible? (And, no, I haven't proved it!)
Before the Pythagorean Theorem was proved, somebody might have said that it was "true but cannot be proved". How do you prove that something cannot be proved ? The conjecture that every even integer is the sum of two odd primes could conceivably be proved by mathematical induction. It might be proved that way sometime in the future. A single counterexample might disprove it sometime in the future.
So I don't think anybody can say right now that it is either true or not provable/disprovable.
Posted by Penny
on 2004-08-22 12:27:19