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!)
...example of a "sentence that is true but cannot be proved" is Democritus' statement that everything that happens in the Universe has a natural and logical explanation. That statement is the truest and most unprovable statement ever made.
Posted by Penny
on 2004-08-22 12:35:20