Question(s):
a) Describe Russell’s three “puzzles,” why they pose a problem for the referential theory of meaning, and Russell’s account aims to solve them.
b) Does Russell successfully solve the puzzles? What problems does his account face?

The referential theory of meaning is “a theory of language that claims that the meaning of a word or expression lies in what it points out in the world”. In his work, On Denoting, Russell sets out to further support this theory with his own theory of denoting phrases. His theory analyzes sentences containing definite descriptions, rather than the descriptions themselves, as he firmly believes that denoting phrases don’t have any meaning in themselves but rather in the sentences in which they appear. Throughout his work, Russell sets out to make sense of what he claims to be a “wrong analysis of propositions”, and offers a contextual definition for definite descriptions. He presents three “puzzles” which can be seen as objections to the referential theory of meaning. In this essay, I shall analyze these three puzzles and explain the techniques Russell uses to solve them. Furthermore, I shall provide an objection to Russell’s claim about definite descriptions.

The first puzzle presented in On Denoting is that of substitutivity. If the referential theory of meaning holds, substitutivity allows one to substitute co-referential terms in a sentence, while preserving its truth value. To convey this idea, Russell provides the following example:

1. George IV wished to know whether Scott was the author of Waverly 2. Scott = the author of Waverly
∴ 3. George IV wished to know whether Scott was Scott

Here, “the author of Waverly” is replaced by the name “Scott”. As these terms appear to be co-referential, substitutivity allows for the substitution of one for the other. However, this is clearly an invalid argument, as the first and third statements disagree in truth value. This appears to be a major flaw in the referential theory of meaning because this example violates the principles of substitutivity in that the first and third statements should be equivalent. However, this is where Russell makes the clear distinction between a proper name and a definite description. He states that names (such as Scott) refer to objects, while definite descriptions (such as the author of Waverly) are not referential expressions. Therefore, since “the author of Waverly” and “Scott” are not in fact co-referential, it is impossible for them to replace one another. While both terms function grammatically in the same way, which is why one would assume that they can co-refer, the logical form of a sentence containing a definite description vastly differs from its grammatical form. Russell shows this using first order logic. The second alleged “identity statement”, isn’t in fact an identity statement when translated logically. “Scott is the author of Waverly”, translates to “There is one and only one x, who wrote

Waverly and that x is Scott” (∃x (Ax∧∀y (Ay → y = x)∧x = s)), where there is only one term (s) that refers or “picks out” x, and one that describes it (Ax). Therefore, there is no longer anything that can successfully be substituted for “Scott” in the first statement, and the principles of substitutivity can be preserved.

The second puzzle addressed by Russell is that of the “excluded middle”. The law of excluded middle is a logical principle that states that for any proposition, either it must be true or its negation must be true. Russell, presents an example which appears to violate this law; “Either the Present King of France is bald, or the Present King of France is not bald”. According to the law of excluded middle, one disjunct must be true, while other false. If the statement “The Present King of France is bald” is false, one would conclude that the statement “The Present King of France is not bald” is true. However, Russell points out that neither proposition is true, as there is no “present King of France”. To then still preserve the law of excluded middle, he introduces the idea of primary and secondary occurrences otherwise known as wide and narrow scopes in first order logic. The statement; “The present King of France is not bald”, contains a negation that takes narrow scope or as Russell would say, the description occurs primarily. That is, to say “The present King of France is not bald” is to say, in logical terms, “There is an x who is uniquely King of France at present, and x is not bald” (∃x (x is king∧∀y (y is king → y = x) ∧ ¬(x is bald))). This translation makes the statement false, as there is nothing to deny the presence of the “present King of France”, which is the problem at hand. For this reason, “The present King of France is not bald” is not in fact the negation of the statement “The Present King of France is bald”. Rather, as Russell points out, the true negation of this statement which makes the law of excluded middle hold, is (in logical terms) “It is not the case that there is an x who is uniquely King of France at present, and x is bald” (¬∃x (x is king ∧ ∀y (y is king → y = x) ∧ (x is bald))). By changing the scope of the negation so that it takes a wide scope, he changes the truth value of the statement, so that the original statement remains false, while the second (its negation) becomes true (as there is no present King of France), thus preserving the law of excluded middle. In solving this puzzle, he concludes that the falsehood of a proposition is dependent on the occurrence of its description, or scope of its negation.

The third and last puzzle mentioned in Russell’s piece is that of negative existentials which he approaches similarly to that of the excluded middle. It appears to be self-contradictory to deny the existence of anything. That is, in order to say that something does not exist, one must use a phrase that denotes it. In doing so, one is able to “pick it out”, validating it’s existence, according to the referential theory of meaning. For this reason, to say that something does not exist in a denoting phrase, is a contradiction. For example, the problem with a statement such as “Santa does not exist” lies in its exact logical translation; “For all x, x is not Santa” (∀x (x ​≠ ​s)). Here, the statement makes the generalization that for all x’s, there exists an x and it is not Santa, which as Russell points out, is self-contradictory, unless the scope of is negation is made wider and used in conjunction with an existential quantifier. In doing so, the statement’s new translation becomes; “It is not the case that there exists an x, for which x is Santa” (¬∃x (x = s)). In making this change, the statement no longer presents a contradiction, as the existence of x is denied initially, and its truth value can be preserved. Thus, Russell proves that by changing the occurrence of a description in a sentence, one can not only preserve the law of excluded middle, but that of negative existentials as well.

Russell’s analysis of the referential theory of meaning and respected contributions to analytic philosophy, as shown by his evaluation of the three puzzles, has suffered some criticisms by other philosophers. An example of this is offered by Donnellan, as he questions and argues Russell’s assumption that if a person who uses a definite description, presupposes that something fits that description, and that presupposition happens to be false, the truth value of their statement is affected. While Russell’s attempt is to show how descriptions contribute to the meanings of sentences, he fails to account for how the meaning of these sentences may vary based on the uses of their definite descriptions. Russell assumes that any utterance of a sentence of the form “The F is G”, is false if there is no thing which is F. However what Donnellan wishes to point out is that there are two distinct uses of definite descriptions, one which does not require that anything satisfy the description “the F” for the sentence to be true. For example, Russell claims that the sentence “the present King of France is bald” is false because “the present King of France” is nonexistent. However, he assumes that the literal sense of the phrase picks out a man who is King of France at present, and fails to account for the possibility that it could be denoting any bald man simply taking the name “the present King of France”. For this reason, the sentence “the present King of France is bald” which Russell determines to be be false in virtue of the presupposed literal denotation of the phrase, could in fact be true if “the present King of France” is taken to be a name for the person being described. This proves that definite descriptions can successfully refer even if nothing satisfies their description. Russell may argue that a statement’s truth value solely depends on the literal meaning of words, but both uses of definite descriptions successfully refer to individual objects, which is the only necessary condition for definite descriptions. Thus, Donnellan’s take on definite descriptions, puts into question the law of excluded middle and hence, Russell’s theory of denotation.

Based on: Russell, Bertrand. On Denoting, 1905.