In his essay “On Denoting” Bertrand Russell describes three puzzles that he feels a theory of denoting ought to be able to solve and, not surprisingly, he feels that his theory solves them. The first puzzle introduces a problem with two expressions that denote the same thing (36). In Russell’s example, “Scott” and “the author of Waverley” both have the same denotation: a certain man. Since the expressions are equivalent in denotation it seems logical that one should be able to substitute one for the other in a sentence without changing the information that the sentence communicates (notice here that I do not want to use the expression “the meaning” of the sentence because to do so would cause confusion given the precise way in which Russell will use this term.) But when we try to test this in an example we see that substituting “Scott” for “the author of Waverley” does change what the sentence communicates. Here is Russell’s example:

1. George IV wished to know whether Scott was the author of Waverley.
2. “Scott” = “the author of Waverley”
3. George IV wished to know whether Scott was Scott.

But

Statement 1 ≠ Statement 3

Russell concludes that while “Scott” and “the author of Waverley” denote the same object, namely a certain individual, they differ in their meaning.

Russell’s second puzzle concerns the law of excluded middle. Either “a is b” or “a is not b” must be true. But if we pick a phrase that does not refer to anything that exists (like “the present king of France” or “a unicorn,” for example) and then attempt to apply the law, we get the following: either “the present king of France is bald” or “the present king of France is not bald” must be true. Yet if we were to compile a list of things that are bald and things that are not bald we would find that “the present king of France” is not on either list. Russell claims to resolve this dilemma with his distinction between primary occurrence and secondary occurrence (38). I admit that I find the way in which Russell explains the difference between these two notions somewhat confusing. I think it is most clear in the example that he gives. Take these two propositions:

1. One and only one man wrote Waverley) and George IV wished to know [whether Scott was that man.]
2. George IV wished to know [whether one and only one man wrote Waverley] and (Scott was that man.)

Here I have put in brackets what George IV wanted to know in each case and I have put in prentices what I will call (for lack of a better term) the purely factual statement in each sentence. Now, in his example Russell asks the reader to attend to the role of the phrase “the author of Waverley” (also stated as “one and only one man wrote Waverley”) in each of the two sentences. In the first sentence this phrase has primary occurrence and in the second it has secondary occurrence. So, where the phrase is the stated fact it has primary occurrence and where the phrase is what is in question (in this case what George IV wanted to know) it has secondary occurrence. (I hope I got this right!)

The third puzzle that Russell puts forth concerns his belief that a non-entity cannot be the subject of a proposition. Here it seems that Russell is making an argument similar (if I am remembering correctly) to the one that Kant uses to refute the argument that existence is a property. Whenever we make something the subject of a proposition we are in a way saying that it exists, so it is self contradictory to say “x does not exist” because this statement really means “x exists and x does not exist.”

So, Russell thinks that a non-entity cannot be the subject of a proposition. How then does “the present king of France is bald” express a proposition? Russell says that we can construct a proposition out of any denoting phrase. The resulting proposition will denote an entity if the proposition is true but it will not denote anything if the proposition is false (39). So “the present king of France” is a denoting phrase (in terms of structure) that does not actually denote anything. Russell goes on to flesh out this idea (bad pun intended) using another denoting phrase (I guess I am assuming that a single word or name is also a denoting phrase according to Russell’s definition) that does not denote anything, “Apollo.” Russell goes back to his distinction between primary occurrence and secondary occurrence. If “Apollo” has primary occurrence in a proposition, then it is false. If “Apollo” has secondary occurrence then the proposition is true. Russell gives the following example:

1. The present king of France is bald.
2. The present king of France is not bald.

The first of these statements is always false. The second of these statements can be true or false depending on what it means.

True: 2a)It is false that there is an entity which is {now the king of France} and is bald.

False: 2b)There is an entity which is {now the king of France} and is not bald.

Where “now the king of France” is primary (2b) the statement is false. Where “now the king of France” is secondary (2a) the statement is true. I guess the best way that I can think of to explain the difference is to say that where the phrase is secondary it belongs to the part of the sentence that is in question (not assumed to be true.)

Using the same type of model we can distinguish between two senses of the statement “Quine believed that Ralph Ortcutt was the shortest spy.” Compare:

1. (One and only one man wrote Waverley) and George IV wished to know [whether Scott was that man.]
2. George IV wished to know [whether one and only one man wrote Waverley] and (Scott was that man.)

AND

1. (There was a shortest spy) and Quine believed that [the spy was Ralph Ortcutt.]
2. Quine believed that [there was a shortest spy] and (the spy was Ralph Ortcutt.)

In the first statement “there was a shortest spy” is primary. In the second statement “there was a shortest spy is secondary. There is also a third way that the sentence “Quine believed that Ralph Ortcutt was the shortest spy” can be interpreted although this is not really relevant to the discussion at hand: Quine believed that [there was a shortest spy and the spy was Ralph Ortcutt.]

Quine can only believe the second sense without knowing that there is anyone named Ralph Ortcutt.

-- AnnieS - 12 Sep 2005