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!)

Yes, you are missing something.  For example, it is not logically possible for the conjecture "there are a finite number of primes" to be true but not provable.  So while SOME conjecture must be true and not provable, it is different to state that a specific conjecture can be true and not provable. 

Posted by David Shin on 2004-10-15 20:17:45