Bertrand Russell’s Theory of Descriptions

Russell would perform a similar analysis of a singular negative existential statement such as “Apollo does not exist.”  “Apollo does not exist” appears, at first, to present more of a problem for Russell’s theory of description than does the statement “Unicorns do not exist.”  The negative existentialist statement “Unicorns do not exist” is a general statement; “unicorns” is an indefinite descriptor and an ambiguous denoting phrase—it does not single out or identify any specific unicorn.  Thus, it is not difficult to accept as true the proposition that there exists in the “real” world no entity with the characteristics that describe a “unicorn.”

However, Apollo is a proper name, and a proper name refers to an identifiable individual.  It seems paradoxical for an person to be simultaneously identifiable and non-existent.  Thus, when considering the negative existential statement “Apollo does not exist,” we must consider whether the name “Apollo” must refer to someone or something in order for the statement to have logical meaning.  However, if the name “Apollo” does refer to someone or something, then the statement “Apollo does not exist” is, arguably, false.  Russell solves this problem in much the same way that he clarified the difference between an “actual” unicorn and the description of one, as discussed above.  In this instance, “Apollo” appears to be a proper name, but Russell points out that “Apollo” is actually a “disguised definite description.”  In other words, we have a concept of “Apollo”, e.g. as a “sun-god,” just as we have a concept of a “unicorn.”  “Apollo” is a description that encompasses the qualities and characteristics that are associated with concept of the fictional character that is named Apollo.  Again, it is not necessary to assume that Apollo actually exists in objective reality in order to make a meaningful statement about Apollo.  “Apollo” is a construct of readers’ imaginations, thoughts, and feelings. 

By using descriptions in this way, Russell shows that it is not necessary for denoting phrases to have referents in the “real” world in order for a proposition to make sense and be meaningful.  Russell solves the problem of a negative existential statement such as “Apollo does not exist” by concluding that, although there is not referent for “Apollo” in the real world, the statement and the denoting phrase “Apollo” still have meaning because “Apollo” as a definite description has descriptive significance.  In addition, he treats a negative existentialist statement as the negation of a positive existentialist statement. Russell would analyze the statement “Apollo does not exist” as follows: “It is not the case that: at least and at most one thing is Apollo” or “It is not the case that: at least and at most one thing has the characteristic of being Apollo.”