Dissertation Live Blogging: Russell on Definite Descriptions

How are we to analyze the semantics of linguistic expressions like the following?

(1) The Queen of England is old.
(2) The prime minister of England is male.
(3) The present king of France is bald.

(1), (2) and (3) contain what are called definite descriptions (because they are descriptions beginning with the definite article "the"). At first blush, it seems like we might analyze them in the same way we do names. When it comes to names like "George W. Bush" or "Samuel Clemmens" we tend to think that all there is to the meaning of a name is what it refers to. "George W. Bush" picks out Dubya, so it means Dubya. That's all there is to it. And when it comes to definite descriptions, this solution seems appealing - 'the queen of England' just means Elizabeth II.

But there is a problem with this approach, one which becomes readily apparent when we examine sentence (3). The expression 'the present king of France' has no referent. There is no king of France at the moment. But, on the approach we are taking, that would mean that the expression 'the present king of France' is meaningless, and that seems wrong.

To get around this problem, Bertrand Russell suggested that the semantics of definite descriptions are quantificational. He gave the following analysis of (3) (using E and A as the existential and universal quantifiers, respectively):

(4) Ex(Px & Bx) & Ay(Py > x=y)

In plain English, (4) reads "There exists exactly one thing that is the king of France and it is bald."

Russell's solution is pretty effective at avoiding the problem we ran into earlier. Sentence (3) is meaningful even though it lacks a referent. And because it lacks a referent, it is false.

Russell's solution is not without it's problems, however. For example, what about sentence (5)?

(5) The cat is on the mat.

We'll look at why Russell's analysis can't handle (5) next time.