[3.4.5.] Puzzle #1: Substitutivity and Propositional Attitude Reports.
Russell intended the Theory of Descriptions to solve three philosophical puzzles. (He describes them on p.38.)
The first is a puzzle about co-referring terms in reports of propositional attitudes.
propositional attitude (df.): a psychological relationship that a person can have with a proposition (e.g., believing that, knowing that, hoping that, wishing that, desiring that, fearing that...)
· Remember that, on the standard view, a report of a propositional attitude creates an intensional context, i.e., a context in which the Principle of Substitutivity fails. See lecture notes 2.8.
Russell uses the following sentence to illustrate the puzzle:
(A) “George IV wanted to know if Scott is the author of Waverley.” [true]
Scott (i.e., Sir Walter Scott) is in fact the author of the historical novel Waverley. So “Scott” and “the author of Waverley” seem to refer to the same thing.
So according to the Principle of Substitutivity the truth value of (A) should not change if we replace “the author of Waverley” with “Scott.”
But that truth value does change:
(B) “George IV wanted to know if Scott is Scott.” [false]
George IV does not want to know if Scott is Scott—he knows that Scott is Scott. So (A) is true and (B) is false. How do we explain this apparent failure of the Principle of Substitutivity?
[3.4.6.] Solving Puzzle #1.
Frege would say that words that occur in reports of propositional attitudes do not have their customary reference; rather, they have an indirect reference, which is their customary sense [see lecture notes 2.8.].
Russell will answer the question differently. On his view,
(C) “Scott was the author of Waverley.”
should be translated as follows:
(D) “One and only one entity wrote Waverley, and Scott was identical with that one.” (40)
The expression “the author of Waverley” has been analyzed away. The same will happen when we translate (A) “George IV wanted to know if Scott was the author of Waverley.”
So how should it be translated? Russell says that the sentence is ambiguous and can be translated in either of two ways:
(E1) “George IV wished to know whether one and only one man wrote Waverley and Scott was that man.” (40)
· In order for this to be true, George IV must know that there is a written work known as Waverley, and he must want to know whether Scott wrote that work.
(E2) “One and only one man wrote Waverley, and George IV wished to know whether Scott was that man.” (40) I.e., “George IV wished to know, concerning the man who in fact wrote Waverley, whether he was Scott.” (The second sentence still contains a definite description: “the man who in fact wrote Waverley”; so the first sentence is a better translation.)
· This could be true even if George IV never heard of Waverley. For example, suppose that George IV sees someone walking towards him and wonders, “Is that guy walking toward me Scott?” He could wonder this without knowing anything about writing or books, and without wondering whether Scott had written a book.
But neither of these translations contains a definite description that refers to Scott. So the problem about the Principle of Substitutivity does not arise for either of these translations.
In general, Russell’s solution is this: when the sentence is accurately translated, the words that seem to be co-referring expressions and that pose a problem for the Principle of Substitutivity disappear. Accurate translations eliminate threats to the Principle of Substitutivity.
[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.
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?
[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.”
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.”
[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.
[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 Thursday September 20. For next time (Tuesday Sept.22), read “The Subject-matter of Ethics.” YOUR SECOND RESPONSE PAPER, ON THIS READING, IS DUE AT THE BEGINNING OF THE NEXT CLASS. We will be discussing pp.439-446 (secs.1-12) on Tuesday and the remainder of this chapter next Thursday. YOUR FIRST EXAM IS SCHEDULED FOR TUESDAY OCTOBER 2.
 This is Russell’s own translation, so he must take the phrase “one entity” not to be a denoting phrase. More strictly, the sentence can be translated: “There is an x such that x wrote Waverley, and for all y, if y wrote Waverley, then y=x, and Scott=x”; or even more strictly: “It is not always false of x that x wrote Waverley, that it is always true of y that if y wrote Waverley y is identical with x, and that Scott is identical with x.” (40) These are preferable, since neither contains a denoting phrase.
 If this is what the original sentence means, then in that sentence, “the author of Waverley” has its secondary occurrence, i.e., when it is translated, the existence claim it contains is preceded by something else.
 If this is what the original sentence means, then in that sentence, “the author of Waverley” has its primary occurrence, i.e., when it is translated, the existence claim it contains is not preceded by anything else.
 But does Russell’s solution have a chance of working for cases involving co-referential proper names rather than cases involving at least one definite description? It might, if Russell construes proper names as abbreviations for definite descriptions. Some commentators say that he does exactly that, just not in “On Denoting”. Elsewhere he asserts that for a given language-user, a name (“Venus”, so forth) is associated with some or other definite description. (E.g.: “the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description” (Autobiography, 1967, p.29) So on Russell’s view, in order to solve Frege’s Puzzle About Reports of Propositional Attitudes with regard to names, it is sufficient to solve it with regard to definite descriptions-- which is just what his Theory of Descriptions is supposed to do.
 This is not what most philosophers today mean by “law of excluded middle.” The phrase “law (or principle) of excluded middle” is sometimes used to refer to a theorem of classical logic, the formula “ p Ú ~p “, sometimes to the natural language analog of that formula, “Either P or not P”. The negation operator in these formulations ( ~ or “not”) ranges over an entire sentence, whereas in Russell’s formulation, it ranges over a predicate only.
 This is especially interesting, given that contemporary philosophers would not state LEM as Russell did; they would state it as something like this:
The (Modern) Law of Excluded Middle (df.): either “p” or “not-p” must be true.
“p” is a variable standing for a declarative sentence (or proposition). Stating the principle this way makes it explicit that the “not” modifies the entire sentence, not just the predicate.
This page last updated 9/20/2012.
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