Review --  Russell’s Theory of Descriptions is as follows:

1.      Denoting phrases have meaning only within the context of a sentence.

2.      The meaning of a denoting phrase in the context of a sentence is not what it appears to be.

3.      The real meaning of a denoting phrase (in a sentence) is given by a Russellian translation.

4.      The real meaning of a sentence containing a definite description involves an existence claim, a uniqueness claim, and a predication of a property.

 

 

 

[2.3.4.7.] Puzzle #2: Non-Referring Terms and the Law of Excluded Middle.

 

Law of Excluded Middle (df.): either “A is B” is true or “A is not B” is true.[1]

 

Sentences with non-existent subjects seem to be exceptions to the law of excluded middle (LEM), e.g.,

 

1. “The present king of France is bald.” (this has the form “A is B”)

 

There is no such person as the present king of France, so it is not true that the present king of France is bald. So if LEM is correct, the following must be true:

 

2. “The present king of France is not bald.” (this has the form: “A is not B”)

 

But it is not true that the present King of France is not bald, since there is no such person as the present king of France. So it appears as if we must reject LEM.

 

But to many people that principle seems to be correct. The puzzle is: is there some way we can avoid giving up LEM?

 

 

[2.3.4.8 ] Solving the Second Puzzle.

 

Frege held that sentences with non-referring terms (e.g., “Odysseus was set ashore at Ithaca while sound asleep”) are neither true nor false. So Frege would say that “The present king of France is bald” is neither true nor false, and that “The present king of France is not bald” is neither true nor false. In other words, Frege’s way of dealing with non-referring expressions gives up LEM.

 

It also gives up the principle of bivalence, which is subtly different from LEM:

 

Principle of Bivalence (df.): every declarative sentence is either true or else false.

 

Russell’s answer is different.

 

He argues that “The present king of France is bald” (which has the form “A is B”) is false. On his theory of descriptions, it should be translated as follows:

 

1. “There is one and only one entity which is now King of France, and that entity is bald.” [false -- since there no entity which is now king of France.]

 

But what about the opposite sentence...

 

2.  “The present king of France is not bald” (“A is not B”)

 

Russell says that it is ambiguous; it is unclear whether the “not” is supposed to modify just the predicate “is bald” or the entire sentence:

 

If “not” modifies the predicate only, then the sentence means:

 

2a. “There is one and only one entity which is now a king of France, and it is not bald.” [false]

·         On Russell’s view, this is not the way it should be interpreted.

 

If “not” modifies the entire sentence, then the sentence means:

 

2b. “It is not the case that there is one and only one entity which is now a king of France and which is bald.” [true]

·         On Russell’s view, this is the way it should be interpreted.

·         And since this sentence is true, then “The present king of France is bald” no longer threatens the Law of Excluded Middle:

 

 

“A is B”	“A is not B”
“The present king of France is bald.”	“The present king of France is not bald.”
“There is one and only one entity that is now a king of France, and that entity is bald.”	“It is not the case that there is one and only one entity that is now a king of France, and that entity is bald.”
false	true

 

 

So Russell’s attempt to save the law of excluded middle requires not only that we adopt his analysis of non-referring terms like “the present king of France”; it also requires that the second sentence in that law (“A is not B”) be interpreted so that the “not” modifies the entire sentence “A is B”, not just the predicate “is B.”[2]

 

 

[2.3.4.9.] Puzzle #3: Non-Referring Terms in True Sentences.

 

Russell states the puzzle as follows: “how can a non-entity be the subject of a proposition?” (p.36) In other words, how are true (and therefore meaningful) sentences with non-referring terms possible? For example:

 

“The round square does not exist.”

 

It is true, and therefore meaningful. But since it is true, the round square does not exist, and the sentence therefore has no subject. There is nothing that the sentence is about. So it is very mysterious how it can be meaningful.

 

 

 

[2.3.4.10.] Solving Puzzle #3.

 

Frege would have to say: since “the round square” has no reference, the entire sentence in which it occurs has no reference, and so that sentence is neither true nor false. But this seems incorrect—the sentence certainly seems to be true.

 

Russell’s explanation of how his theory of descriptions solves this puzzle is not very explicit— what follows is my best attempt to trace the consequences of this theory to see how it can solve the puzzle.

 

The troublesome subject term “the round square” is a denoting phrase (although it is one which doesn’t denote anything), and so it will disappear in a Russellian translation:

 

It is not the case that there is one and only one entity which is round and square. [true]

 

Notice that the correct translation cannot be:

 

There is one and only one entity which is round and square, and that entity does not exist. [false]

 

This is contradictory, since it both asserts and denies the existence of an entity which is round and square. So it is false—and Russell maintains that “The round square does not exist” is true.

 

**

 

The next article in your textbook, “On Referring” by Peter Strawson (pp.41-54), is a criticism of Russell’s theory of denoting. Russell wrote a response to Strawson’s criticisms, which began:

 

I may say, to begin with, that I am totally unable to see any validity whatever in any of Mr. Strawson’s arguments. Whether this inability is due to senility on my part, or to some other cause, I must leave to readers to judge. (“Mr Strawson on Referring,” Mind 66 (263) July 1957, 385-9, p.385. This article is available online through JSTOR.)

 

 

Stopping point for Friday February 6. For next time:

·         read pp.14-15 of textbook (part of Jacquette’s intro to phil language);

·         read the excerpt from the Tractatus that is on electronic reserve, paragraphs 1 through 2.225.

·         Come to class prepared to answer this question:

Explain Wittgenstein’s picture theory of meaning, citing specific passages from your reading to support your explanation. The passages that are especially relevant to this exercise begin at 2.14.