Definite descriptions are linguistic expressions that describes a particular definite object but does not refer to it. The theory of definite descriptions put forward by philosophers like Bertrand Russell is found as a result of considering the differences between a proper name like "Barack Obama" and a descriptive phrase like "the President of the United States". One is tempted to say that because the words 'Barack Obama' refer to a person called Barack Obama, and the words 'the President of the United States' refer to the same person, that the two are semantically equivalent - they are just a sort of 'code' to refer to the same underlying person. This would lead to an unacceptable conclusion: 'Barack Obama' and 'the President of the United States' are just referring expressions pointing to the man Barack Obama, meaning that the sentence 'Barack Obama is the President of the United States' has the logical form x = x. But the sentence does express something important about the world - it could quite possibly be that someone else is the President of the United States'. What makes the sentence 'Barack Obama is the President of the United States' true is not simply that 'Barack Obama equals Barack Obama' (a rather trivial claim of self-identity) or that 'Barack Obama does not equal Hillary Clinton' or 'Barack Obama does not equal John McCain'. What makes it true is that he - in this particular case - won the presidential election and was inaugurated as President.
The problem with this is that if we were to construct a sentence that contains a definite description of someone who does not exist, such as 'the present King of France is bald', we would have to state that the sentence constructed about him cannot have any truth value. Most people do not wish to accept this conclusion. The sentence 'the President of the United States has a law degree' can be true or false, and it seems like we would want it to be so that another sentence with a similar form could be true or false also. Bertrand Russell attempts to provide a set of formal criteria to evaluate the truth or falsity of a sentence of the form 'the F is G':
- There is at least one F.
- There is at most one F.
- All things which are F are G.
Sentences containing definite descriptions are true if all three of these conditions are true. If any one of the conditions is false, then the sentence is false. To continue our example, 'the President of the United States has a law degree' is true because there is at least one President of the United States and there is at most one President of the United States and all things which are Presidents of the United States have the property expressed by the words 'has a law degree'. The counter-example, 'the present King of France is bald' is false because there is not at least one present King of France, and of all the present Kings of France (zero), none of them are bald.
- Avrum Stroll, Twentieth Century Analytic Philosophy, 2001, Columbia University Press, ch. 2.