AFAIK, every statement must be either true or false (or a paradox, but that's not what I am talking about now), by the law of the excluded middle.
The statement "The king of France is bald." is false, because there is no king of France. But then, by the same law, shouldn't "The king of France is not bald.", that is, "The king of France has hair.", be true?
The only possibility I can think of to solve this confusion is that the opposite of a statement is not what we usually think it is, and as "The king of France is bald." means "The king of France exists." and "If he does exist, he is bald.", that is "If the king of France exists, then he is bald.".
Maybe as "If the king of France exists, then he is bald." equals "The king of France doesn't exist and/or he is bald.", the opposite should be (by DeMorgan's laws) "The king of France exists and he isn't bald.", but that's even more awkward.
So what should the opposite of this should be? The converse? The inverse? The contrapositive cannot be, it would be false as well. Can you give me a hand here?