Bertrand Russell and Analysis

Bertrand Russell (1872–1970) lived to the age of ninety-eight and touched almost every area of philosophy. Born in Wales and educated at Cambridge, Russell would make major contributions to mathematics and logical analysis, for which he received much acclaim. From 1910 to 1949 he was occupied with moral, political, and social issues. One illustration of his analytical acumen was his theory of definite descriptions.

Definite Descriptions

Russell had a different approach than the logical positivists on the meaning of sentences. This is especially true of his treatment of sentences that fail to refer to reality. For instance, consider a statement like “The present king of France is bald.” Since there is no present king of France, do sentences of this sort count as false or meaningless? You end up with a problem no matter which way you decide.

To say it is meaningless goes against a person's ability to understand what the sentence is trying to convey. To say that it is false, on the other hand, implies that its contradiction — “The present king of France is not bald” — is true. But this statement about the king not being bald is no truer than the first. So how can one deal with sentences such as these that fail to refer to anything?

Russell's answer was original. He maintained that such sentences were descriptions consisting of a conjunction of separate claims. First, that there is some person who is the king of France; second, that there is just one person who is the king of France; third, that any person who is the king of France is bald. Each of these parts can be tested as true or false. But the first is false, since there is no king of France. Logically, any statement that is a conjunction of propositions is false if any one of the conjuncts is false. The conjunction is false, then.

Bertrand Russell was denied a professorial appointment at City College in the City University of New York. He was denied because it was learned that he had written Marriage and Morals, which discussed the feasibility of having an open marriage. A parent of one college student was offended and the Board of Education rejected Russell's appointment.

The German philosopher Gottlob Frege did more to originate analytic philosophy with his predicate logic. Bertrand Russell used predicate logic to reveal philosophical problems more clearly. To take one example, Russell showed how the English word is can be expressed in three different ways:

In ‘the ball is blue: the is of predication says that ‘x is P’: P (x)

In ‘there is a ball’: the is of existence says that there is an x: (x)

In ‘twelve is half of twenty-four’ the is of identity says that x is the same as y: x = Y

But Russell's theory of definite descriptions shows that it is possible to speak sensibly of things that do not exist. Since Russell, it has become a standard tool of logical analysis.

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