Prove that either
a) this problem is solvable
or
b) this problem is unsolvable
(In reply to
Well..... by Dulanjana)
> The only possible situations are given by "a" and "b" (No other situation can occur). So if one is false the other is True. A truth is provable. Therefore this problem is solvable.
Not so. Goedel managed to really irritate the mathematics community by essentially proving that there are well-formed propositions in number theory and formal logic which can neither be proven true nor false. Essentially, he found a way to translate "This is a false statement" into the language of mathematics. There are other examples of such weirdness. For example, it's impossible to write a computer program that will determine reliably whether another computer program will enter an infinite loop. I'd also be impressed by any computer program that can solve the MU puzzle I had previously submitted, without special help.
Self-referential problems often lead to a hairy mess. Clearly, the way to attack this problem is not by assuming (b), as it leads to a contradiction. What's not so clear is whether we can go through (a), which does not lead to any contradictions, but does not necessarily provide enough positive statements to generate a proof.
re: Well.....
