Optional: Emily Elizabeth Constance Jones, "Mr. Russell's Objections to Frege's Analysis of Propositions", Mind 19 (1910), pp. 379-86 (JStor)
Russell is generally interested here in what he calls denoting phrases. The examples he gives are of two types: quantifier phrases, such as "a man" or "every man", and descriptive phrases, such as "the man with the yellow hat". The latter are the main focus of the paper, but it is important to understand what Russell is saying about the former in order to understand what he is saying about the latter.
Russell's central idea is "that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning" (p. 480). Russell first explains this point in connection with quantifier phrases, and he claims that "Everything is F" means: F(x) is always true (for all values of x). The contrast here is with a view, which Russell seems to have held earlier, in The Principles of Mathematics, that "Everything" names a sort of variable entity. So what Russell is saying is that quantifiers are not names of things. That is right, by our current lights, and much of the discussion on pp. 480-1 explains what is now standard fare in basic logic.
The way Russell puts this point might well be regarded as misleading, however, or even false. Some contemporary theories of quantification (which descend from Frege's) regard quantifiers like "every" as having meanings of their own without regarding them as being names of anything. I will explain this in class by presenting some of the basic ideas behind so-called generalized quantifers. For our purposes, however, the important point is that Russell is claiming that quantifiers behave very differently, from a logical point of view, from how names of things do.
Russell turns at the bottom of p. 481 to descriptive phrases. His view, as he states it, but modernizing the notation, is that a sentence of the form "The F is G" means:
∃x[Fx ∧ ∀y(Fy → x = y) ∧ Gx]
I.e.: There is one, and only one, F, and it is G. As Russell notes, this incorporates an assumption that "The F" always involves an assertion of uniqueness. This can be questioned, and not just in cases of so-called plural descriptions (such as "the books on the table"). We will see Strawson raise questions along these lines later, but it will not be of particular concern to us.
Russell's main point, however, does not concern the specific analysis displayed above (which, as Gareth Evans once quipped, simply massacres the surface structure of the sentence). The main point, rather, is that descriptions are a sort of quantifier, in this case, one might say, a "complex" quantifier. I'll explain in class, again, how this insight can be expressed in terms of generalized quantifier theory.
Russell sees the main alternative to his view as being a version of Frege's, who did indeed hold that descriptive phrases are names. So Frege thought that "the smallest prime number" referred to the number 2, but that this phrase also has a sense different, say, from "two".
Russell's first objection to Frege's theory is that, if a descriptive phrase has no denotation, then sentences containing that phrase should be meaningless. And Frege does indeed accept this consequence: He thinks, e.g., that if Homer never existed, then "Homer wrote the Iliad" is not false but without truth-value (i.e., it has no reference). But, Russell says, "The King of France is bald" is not meaningless but "plainly false".
Why does Russell think "The King of France is bald" is not meaningless but "plainly false"? Is he right? How can one tell? What is the bearing on this question of examples like "If there is a greatest prime number, then the greatest prime number is odd"?
Russell gives another argument against Frege's account on pp. 485-8. This is known as the Gray's Elegy argument, due to an example Russell uses. The argument is extremely confusing, and I would not claim to understand it. There is some good work on this, however: See, for example, this paper by William Demopoulos or this one by Berit Brogaard. But this is more an historical issue, so I do not propose to spend much time on the Gray's Elegy argument, though you should read it.
Feel free to explain the Gray's Elegy argument.
Russell's main defense of his own theory consists in his arguing that it does a good job, and a better job than Frege's (or Meinong's), of solving three puzzles that he describes on p. 485. The first of these is the puzzle about identity that we have already seen in Frege. The second is a puzzle about excluded middle: Mustn't it be the case that either "The King of France is bald" or "The King of France is not bald" is true? The third puzzle, which Russell introduces using a very confusing example, seems mostly to concern claims of non-existence. So one might put it by asking how it could be possible to say, truly, e.g., "The greatest prime number does not exist". On Frege's theory, it again looks as if this ought to be without truth-value.
Russell explains on pp. 488-91 how his view resolves the three puzzles.
In the case of identity, the key move is to deny that "Scott is the author of Waverly" really is an identity-statement. In what sense? And what, then, should Russell do about, say, "Twain is Clemens"?
In the case of excluded middle, the solution rests upon a distinction between "primary" and "secondary" occurrences of a description. Explain why this is really an observation about scope. (If you represent the different "readings" in logical notation, this will become obvious.)
The same distinction allows Russell to explain how "The greatest prime number does not exist" can be both meaningful and true. How so? And what should Russell do about "Homer did not exist"?
Russell concludes the paper by gesturing at epistemological implications of his theory. These are discussed in more detail in "Knowledge by Acquaintance and Knowledge by Description", which we shall read next.