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The phrase the present King of France, the classical example of an unsatisfied definite description, comes from an example due to Bertrand Russell, an apparent paradox raising some interesting questions about the law of the excluded middle, denotation, and so on.

France is a republic, and has no king. 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 (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.

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:

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", because it consists of a conjunction, one of whose terms is assertion 1. ("there is a King of France") 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.

However, though Russell's analysis has been widely accepted by philosophers, there has been some dissent. P. F. Strawson, in particular, argued that Russell had misrepresented what one means when one says "The present King of France is bald." According to Strawson, this sentence is not contradicted by "No one is the present King of France," for the former sentence contains not an existential assertion, but attempts to use "the present King of France" as a referring (or denoting) phrase. Since there is no present King of France, the phrase fails to refer, and so the sentence is neither true nor false, but meaningless.

A fine resolution to the dispute between Russell and Strawson is provided by Keith Donnellan. According to Donnellan, there are two distinct ways we may use a definite description such as "the present King of France," and thus makes his distinction (to be illustrated below) between the "referring" and the "nonreferring" use of a definite description. He argues that Russell and Strawson both make the mistake of attempting to analyse sentences removed from context. We can mean different things by the same sentence used in different situations: for example, suppose Smith has been brutally murdered. When the person who discovers Smith's body says, "Smith's murderer is insane," we may understand this as the nonreferring use of the definite description "Smith's murderer," and analyse the sentence according to Russell. This is because the discoverer might equivalently have worded the assertion, "Whoever killed Smith is insane." Now consider another speaker: suppose Jones, though innocent, has been arrested for the murder of Smith, and is now on trial. When a reporter sees Jones talking to himself outside the courtroom, and describes what she sees by saying, "Smith's murderer is insane," we may understand this as the referring use of the definite description, for we may equivalently reword the reporter's assertion thus: "That person whom I see talking to himself, and who I believe murdered Smith, is insane." In this case, we should not accept Russell's analysis as correctly representing the reporter's assertion. On Russell's analysis, the sentence is to be understood as the conjunction of

1. there is an x such that x murdered Smith;
2. there is no y, y not equal x, such that y murdered Smith; and
3. x is insane.

If this analysis of the reporter's assertion were correct, then since Jones is innocent, we should take her to mean what the discoverer of Smith's body meant, that whoever murdered Smith is insane. We should then take her observation of Jones talking to himself to be irrelevant to the truth of her assertion. This clearly misses her point.

Thus the same sentence, "Smith's murderer is insane," can be used to mean quite different things in different contexts. There are, accordingly, contexts in which "The present King of France is not bald" is false because no one is the present King of France, and contexts in which it is a sentence referring to a person whom the speaker takes to be the present King of France, true or false according to the scalp of this impostor.

References:

• Donnellan, Keith, "Reference and Definite Descriptions," in Philosophical Review 75 (1966): 281-304.
• Russell, Bertrand, "On Denoting," in Mind 14 (1905): 479-493.
• Strawson, P. F., "On Referring," in Mind 59 (1950): 320-344.

See also philosophy of language and definite descriptions.

Note: A lot of this needs to be moved to a separate page on definite descriptions. Much of the stuff about Strawson and Donnellan does not belong here.