It does not seem to 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, that is, "It is not the case that the present King of France is bald," or its logical equivalence, "The present King of France is not bald," is true. But that seems no more true than the original statement.
Is it meaningless, then? One might suppose so (and some philosophers have; see below), because it certainly does fail to denote in a sense, but on the other hand it seems to mean something that we can quite clearly understand.
Bertrand Russell, extending the work of Gottlob Frege, who had similar thoughts, proposed according to his 'theory of descriptions' that when we say "the present King of France is bald", we are making three separate assertions:
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
so "the present King of France is not bald", because it consists of a conjunction, one of whose terms is assertion 1, is also false.
The law of the excluded middle is not violated because by denying both "the King of France is bald" and "the King of France is not bald," we are not asserting the existence of some x which is neither bald nor not bald, but denying the existence of some x which is the King of France.
There is a second way of stating "the present King of France is not bald". Instead of substituting x in the sentence "x is not bald" as we have done above, we may negate (1) yielding "it is not the case that there exists an x and x is bald" (alternatively "it is not the case that there exists an x, therefore x is neither bald nor not bald". This sentence is true as opposed to the statement obtained by the previous method. Second, it is easier to see that it does not violate the law of excluded middle. Russell's analysis has been attacked by P.F. Strawson, Keith Donnellan and others, and it has been defended and refined by Stephen Neale.