8.4.1. The problem of definite descriptions

In 6.1.6, an individual term was described as an expression that refers, or purports to refer, to a single object in a definite way. The hedge or purports to refer acknowledges the fact that not all individual terms actually succeed in picking out something as their reference. In spite of notorious exceptions like the name Santa Claus, proper names can usually be relied on to refer to something. But definite descriptions succeed in referring only when there is something that fits the description they offer and that does so without real competition. Mathematicians sometimes speak of these two requirements for a definite description to make a definite reference as existence and uniqueness. Both must be met before a mathematician can speak of, say, the solution of a certain equation; there must be a solution (the solution must exist) and there must be no more than one (the solution must be unique).

At least this is so for the strictest and most explicit use of language. In most cases where a description is fulfilled by several entities, something in the context will distinguish one among them, and this one will be taken as the reference of the definite description. In such cases, the definite description functions as if the description it contains was more specific than its explicit statement suggests and the requirement of uniqueness really was satisfied. That is, we will understand, for example, the college as perhaps the college (we all know and love) and the task as perhaps the task (at hand). The philosopher David Lewis suggested that definite descriptions drew on a general contextual feature of salience. One way of using this idea is to think of the X as the (most salient) X; and, if a property of salience is implicit in any definite description, we may suppose that whenever there exists an object fitting the description it will be unique.

However, there is no easy way around the requirement of existence. We have admitted and nil reference value, and it falls in the domain of an unrestricted existential quantifier, so, in one sense, the reference value of every term exists. But we cannot assume that the reference value then always fits the description. And that is the key problem posed for theories of deductive reasoning by definite description: what can we say in general about the logical properties of a sentence containing a definite description when there may exist nothing fitting the description?