Bertrand Russell's Theory of Descriptions

A negative existential statement is a statement about a nonexistent object, person, or concept, in other words, a statement about something that does not exist. Initially, making such a statement seems quite easy and straightforward. There are many things that we intuitively accept as having no existence, such as mythical creatures (like unicorns and flying horses), fictional characters (such as the Greek gods, Jane Eyre, or the Terminator), and scientifically impossible phenomena (such as the fountain of youth or the secret to turning lead into gold). However, some philosophers have said that a statement that a particular person or object does not exist (for example, "the fountain of youth does not exist") is inherently contradictory or even logically impossible. As Bertrand Russell notes in his essay "Descriptions," "[t]he question of 'unreality' . . . is a very important one. Misled by grammar, the great majority of those logicians who have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what differences in grammatical form are important." We must analyze some examples of negative existential statements more closely in order to see why some scholars find them so problematic.

A negative existential statement is generally expressed in a sentence in the form "X does not exist." Negative existential statements can be singular, referring to a specific individual object or person that does not exist. An example of a singular negative existential statement is "Apollo does not exist." In other words, the individual person or god known as "Apollo" does not exist. Negative existential statements can also be general, referring to a category or a group sharing similar characteristics. An example of a general negative existential statement is "unicorns do not exist." This general negative existential statement goes beyond saying that a specific, individual unicorn does not exist. Rather, it intends to convey that unicorns in general do not exist; there exist in the world no objects or beings with the characteristics that define "unicorns."

Through the theory of description, Russell avoids the philosophical conundrum of having to accept the existence of something before concluding that it does not exist. The necessity of presuming the existence of an object before declaring its non-existence means, essentially, that there is no way to rationally, logically, and accurately declare that a given object or person does not exist. Thus, negative existential statements such as "Apollo does not exist" or "unicorns do not exist" would be rendered meaningless, even nonsensical. However, such an interpretation of negative existential statements not only clashes with our intuitive understanding of the world but would also make it impossible to discuss the nature of existence in any meaningful way.

The problem with negative existential statements is that they raise the question of how one can even discuss something that does not exist. How can someone or something that does not exist have any characteristics capable of description or identification-even if one of those characteristics is non-existence? How can we begin to think rationally, logically, and knowingly of an object or person that does not exist? If Apollo does not exist, then how can a person say of Apollo that he does not exist? If unicorns do not exist, then how have we been able, in the first place, to construct a definition of a unicorn-a rare, mystical horse-like mammal, with a single horn protruding from its head? How can a non-existent person or object be described when it has no existence and thus no relationship to any of the concepts and terms used to understand it? Such questions undermine the presumed validity of the negative existential statements themselves, seeming to lead to the conclusion that the statements cannot be true. However, if the statement "Apollo does not exist" is not true, then we are left in the quandary of having to accept that Apollo does exist. The result is an irrational paradox which requires us to assume Apollo's existence before we can establish that he does not exist. Such a reasoning process is inherently contradictory. Russell summed up the problem of making statements about non-existent entities as follows: "It is argued [by some logicians] that we can speak about 'the golden mountain,' 'the round square,' and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless."

Bertrand Russell attempts to resolve this puzzle of the negative existential statements through his theory of descriptions. Russell starts with a simple analysis of "denoting phrases." A denoting phrase is any word or phrase that purports to point to or represent an object, person or entity. In essence, the denoting phrase takes on the "meaning" of the object, person or entity that it refers to. In his essay "On Denoting," Russell defined denoting phrases as follows: "By a 'denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the round the earth." Russell further clarified that "a phrase is denoting solely in virtue of its form."In addition, he specified three types of denoting phrases: "(1) A phrase may be denoting, and yet not denote anything; e.g., 'the present King of France.' (2) A phrase may denote one definite object; e.g. 'the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g., 'a man' denotes not many men, but an ambiguous man.".

A fundamental principle of Russell's theory is that "denoting phrases never have any meaning in themselves, but . . . every proposition in whose verbal expression they occur has a meaning." At the same time, there are denoting phrases that denote objects, persons, or entities whose existence can be proven but with which we have "no immediate acquaintance." An example would be "the centre of mass of the solar system at the first instant of the twentieth century." Through scientific measurement and analysis, we can "know" at what point the center of mass of the solar system was located at the beginning of the twentieth century. However, we are not "acquainted" with that specific physical location in that we have never seen it or been there physically. According to Russell, we "know" this location even though we are not acquainted with it, and we "know" it only through "description."

Russell explains that "[t]he distinction between acquaintance and knowledge about is the distinction between the things we have presentations of and the things we only reach by means of denoting phrases." In other words, there are some things we know because we have "immediate acquaintance" with them through physical contact and evidence of the senses or through some other form of direct experience; and there are other things that we know solely through descriptions that build upon and derive their sense from those things with which we are acquainted. As an example, Russell points out that we are not acquainted with the minds, thoughts, and perceptions of other people. But, because we are acquainted with how our own minds work and have the experience of our own thoughts and perceptions, we have some knowledge of how other human beings think and perceive the world. Thus, although we are not acquainted with the minds of others, we have some knowledge of them and can offer descriptions of them based on our acquaintance with our own minds. As Russell asserts, "All thinking has to start from acquaintance; but it succeeds in thinking about many things with which we have no acquaintance."

Russell proposes two kinds of descriptions: "definite descriptions," which address specific, known objects and entities, and "indefinite descriptions," which address objects and entities whose identities are ambiguous. A definite description has the form "The X" and an indefinite description has the form "An X." Thus, "The man" would be an example of a definite description, and "A man" would be an example of an indefinite description. The definite description tells us more because it tells us that a specific, unique man exists. On the other hand, the indefinite description refers to "a man" whose identity cannot be ascertained. Likewise, we glean more knowledge from an existential statement containing a definite description than from an existential statement containing an indefinite description. For instance, the statement "the man is bald" tells us 1) that there is a specific unique man; 2) that this specific unique man is bald; and 3) that baldness is a universal or constant characteristic of this specific unique man at the time the description is made. The statement "a man is bald" tells us only that some man is bald but does not inform us of the man's specific identity.

If we accept that a unicorn is, as Russell describes it, "a fabulous monster," in other words, a creature that does not exist in reality, we then immediately assume the assertion "I met a unicorn" to be false. However, Russell argues that "I met a unicorn" is nonetheless "a perfectly significant assertion, if we know what it would be to be a unicorn." Thus, statements referring to "unicorns" have meaning as long as we can describe the "concept" of a unicorn. As Russell explains, "it is only what we may call the concept that enters into the proposition. In the case of 'unicorn' for example, there is only the concept: there is not also, somewhere among the shades, something unreal which may be called 'a unicorn.' Therefore, since it is significant (though false) to say 'I met a unicorn,' it is clear that this proposition, rightly analysed does not contain a constituent 'a unicorn,' though it does contain the concept 'unicorn'." Thus, Russell's theory depends upon distinguishing between the "concept" of a unicorn and an "actual" unicorn. By making this distinction, Russell is able ultimately to explain how statements about "unicorns" without having to assume the existence of a non-existent entity.

Russell accomplishes this by introducing "propositional functions" which he believes provide the solution to the conundrum of negative existential statements. Russell states that "[f]or want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects." In defining propositions, Russell makes a distinction between denoting phrases considered as "descriptions" and denoting phrases considered as stand-ins for their referents, i.e., the actual object or entity to which they refer. Russell believes it is an error to treat a denoting phrase as representing an actual object or entity: "This theory regards any grammatically correct denoting phrase as standing for an object. Thus 'the present King of France,' 'the round square, etc.' are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects." For Russell, on the other hand, "a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account."

Furthermore, the constituents of a proposition are not referents or actual objects but rather descriptions. When one uses propositions containing descriptions of non-existent entities, it becomes possible to make statements about those non-existent entities without assuming the existence of unreal objects. As Russell explains, "propositions verbally about 'so-and-so' are found to contain no constituent represented by this phrase. And that is why such propositions can be significant even when there is no such thing as a so-and-so." In addition, Russell treated propositions as variables, such that, in analyzing the meaning of a statement, "Apollo," for instance, could be represented by the variable "x".

Russell believed that we can learn about and thus "know" about things that have existence in the "real world" even when we are not directly acquainted with them by building on definite descriptions that accurately describe the world. In this way, he could understand statements about non-existent objects and entities as being constituted by or made up from elements of these accurate definite descriptions. Thus a statement about a non-existent object would not require a presumption that the non-existent object actually existed; instead, a statement about a non-existent object, because it would be based on definite descriptions, could derive its meaning from the objects described in the definite descriptions whose existence is not debated. Thus, Russell was able to construe a statement about a non-existent entity as meaningful without having to make the ontologically troublesome concession that the non-existent entity actually existed.

Again using the example of the unicorn, Russell wrote: "To say that unicorns have an existence in heraldry, or in literature, or in imagination, is a most pitiful and paltry evasion. What exists in heraldry is not an animal, made of flesh and blood, moving and breathing of its own initiative. What exists is a picture, or a description in words." Thus, for Russell, statements about non-existent entities, such as negative existential statements, have meaning because they refer to "descriptions" rather than entities. When one makes the general negative existential statement that "Unicorns do no exist," one is making a statement not about actual unicorns but rather about a "description" that encompasses the characteristics that are associated with the concept of unicorns. Russell would solve the puzzle of the negative existentialist statement "Unicorns do not exist" by treating the denoting phrase "unicorns" not as a referent to an entity known as a "unicorn" but as a description which encompasses the characteristic of being a unicorn. He would analyze such a statement as follows: There are no x's, such that 'x is a unicorn' is true.'

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."