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France is a democracy, and has no King.

The phrase "the present King of France" comes from an example by Bertrand Russell, an apparent paradox raising some interesting questions about the law of the excluded middle, denotation, and so on.

Consider the statement "The present King of France is bald." Is this statement true? Is it false? It is meaningless?

It surely can't be true, for there is no present King of France. But if it is false, then one would suppose that the negation of the statement is true, that is, "The present King of France has hair (is not bald)." But that doesn't seem any more true than the original statement.

Is it meaningless, then? One might suppose so, because it certainly does fail to denote in a sense, but on the other hand it sure seems to mean something that we can quite clearly understand.

Russell, extending the work of Gottlob Frege, who had similar thoughts, proposed that when we say "the present king of France is bald", we are making three separate assertions:

   1.) there is an x such that x is the king of France
   2.) there is no y, y not equal x, such that y is the king
       of France (ie. x is the only king of France)
   3.) x is bald.

Since assertion 1. is plainly false, and our statement is the conjunction of all three assertions, our statement is false.

Similarly, for "the present king of France is not bald", we have the identical assertions 1. and 2. plus

   3.) x is not bald

so "the present king of France is not bald", entailing, as it does, assertion 1. ("there is a king of France") is also false.

The law of the excluded middle is not violated because by denying both of these, we are not asserting the existence of some x which is neither bald nor not bald.

If only Misplaced Pages had a professional philosopher as editor in chief, we could get a full explanation of these mysteries.