The Existential Assertion of Existence

Russell's theory that unicorns have one horn is false on his theory, and Russell wanted it to be false. In fact, we all feel intuitively that it must be false, not because there is a present king of France who is hairless but because there is no presentKing of France. But for Russell you would have to analyze the sentence in such a way that it managed to get rid of the implication that there are actually unicorns.