by Vered Arnon
Russell’s theory of descriptions explains how sentences are understood in such a way that a person knows what the speaker or writer is trying to express. The theory uses formal logic to show the meaning of sentences by analyzing them in the form of “there is an x such that x is thus and nothing else is thus and x has such and such a property”, or in the case of negations, “there is an x such that x is thus and nothing else is thus and x does not have such and such a property”.
The first part of the analysis, “there is an x”, expresses the subject of the original sentence, making it clear to the reader or listener’s mind that x is the object being described. The second part of the analysis, which is the actual description, has two parts, “x is thus” and “x has such and such a property”. By saying “and nothing else is thus”, one is merely clarifying that the subject x alone is the object being described, to further ensure that the reader or the listener knows exactly what object is being described.
The part of the description “x is thus” is drawn from the subject of the sentence, even though it is the first part of the description. When one says, for example, “The teacher of this class”, according to Russell’s theory one is actually expressing the proposition “there is an object such that it is the teacher of the class”.
The last part of the description, “x has such and such a property”, is an analysis of the rest of the descriptive sentence. One the object that is being referred to and described has been established, its attributes can then be stated. Thus, “The teacher of this class is here” ultimately, according to Russell’s theory, expresses the proposition “there is an object such that this object is the teacher of this class, and no other object is the teacher of this class, and this object is here.” Everything in the sentence is clearly expressed in such a way that the reader or listener can know exactly what the speaker or writer is communicating.
When a sentence is in the form of a negation, the last part of the sentence is all that changes. The same rules follow and the same structure is used to understand the sentence.
When a sentence has scope ambiguities, there can be two different ways to analyze the sentence, according to Russell. One way would be like a regular negation, as explained above. The other possible way would be to analyze the sentence as explained in the first part of this paper, but modify the beginning to state “it is not the case that there is an x…”. Sentences like “The king of France is bald” introduce this kind of scope ambiguity, because there is no such object as “the king of France”.