Definite descriptions
In this section we consider an important application of logical principles to the analysis of natural language, the theory of definite descriptions proposed by Bertrand Russell (1905), one of the originators of the logical formalism introduced in this chapter. Definite descriptions are noun phrases like those in (106):
Definite descriptions are singular terms: they refer to a single, specific individual. (In this they contrast to what Russell (1949: 214) called ambiguous descriptions, which contain the indefinite article and do not refer to a single specific individual: a President of Iraq, a Chancellor of Germany.) Since Frege, the need for a formal logical analysis of definite descriptions had been keenly felt. Frege himself treated definite descriptions as referring expressions, and distinguished between the referent of a definite description and its sense (see Chapter 3). Thus, the definite descriptions in (107) all have a sense, but they do not have any reference, since there is no individual which they pick out:
Russell proposed a different treatment. According to him, definite descriptions like those in (106) and (107) are not actually understood as referring expressions at all: in fact, their logical structure is quantificational. Russell treated any sentence containing a definite description as equivalent to a quantificational sentence. For example, the sentence The King of France is bald is interpreted in the following way:
(109) reads as follows: ‘there is an x, such that x is the King of France, and for all ys, if y is the King of France, then y is x, and x is bald’. In the formula, ‘( x) (K(x) . . . ’ asserts the existence of an individual, the King of France. This is what we can call the existence clause. ‘( y) (K(y) ) y = x)’ says that every individual who is the King of France is x: in other words, there is only one King of France; this is the uniqueness clause. The last section, B(x), adds the information that the King of France is bald.
As another example, consider the representation of the proposition the Chancellor of Germany is a woman:
Russell’s analysis explains how definite descriptions can be understood even when we do not know the identity of their referent. As long as we understand the meaning of the predicates involved, we can understand the definite description, even if, as in (108), there is not, in fact, any individual to whom the examples refer.
QUESTION Give equivalent analyses of the following expressions:
The emperor of China is a child.
The only house in Mosman is for sale.
The law is an ass.
Russell’s analysis of definite descriptions has been highly influential and has stimulated wide debate. One of the most influential criticisms is due to P. F. Strawson (1950), who argued against both the existence and uniqueness clauses of Russell’s analysis. According to Strawson, a speaker’s use of a definite description does not assert that anything exists, as it does in Russell’s analysis; rather, it presupposes (Strawson actually uses the term ‘implies’) this existence. Thus, if I utter a statement like ‘The King of France is angry’, I am not explicitly committing myself to the existence of an individual, the King of France; I am simply taking his existence for granted, and not putting it forward as a matter of discussion. Strawson also criticized the uniqueness clause: to say ‘the table is covered with books’, for example, is certainly not to claim that there is one and only one table. (Russell might reply, of course, that the table is in fact unique within the universe of dis course in question: if uttered, for example, in a room with only one table; if it were not, it would be necessary to specify which table was meant.)
