• The distinction in §I between examples (1) and (2) at extremes, with (3)-(5) between them, is central to the whole paper, so spend some time thinking about these examples. And be ready to come back to these and other numbered examples and look at them again when Kaplan refers to them—I can’t emphasize enough the necessity of doing this if you are to follow his discussion.

The basis for the distinction lies in feasibility of operations of substitution and existential generalization. The first is related to the idea of interchangeability salva veritate that Quine noted in “Two Dogmas.” The language used in (1) is “extensional” in the sense Quine used there while that in (3)-(5) is not. The problem raised by (2) is even worse: think about the result of replacing the sequence of four letters ‘nine’ in it by ‘9’ or ‘ix’.

Existential generalization is the operation that takes us from a claim about a particular object to the less specific (and thus more general) claim that “something” has the such a property—e.g., from ‘Nine is greater than five’ to ‘Something is greater than five’. When the singular term referring to the particular object is buried deeply in a sentence, we may need to express the result using a pronoun, and this device can be used even when it is not needed. So we can express two ways of existentially generalizing from (1) as ‘Something is such that it is greater than five’ and ‘Something is such that nine is greater than it’. When symbols are used to express some of the logical structure of sentences (as Kaplan will beginning in §IV), we could restate these two claims as ‘∃x [x is greater than five]’ and ‘∃x [nine is greater than x]’, respectively, where ‘x’ functions as a symbolic pronoun and ‘∃x […]’ can be read as ‘something, x, is such that …’.

To see why (3)-(5) are problematic, you can exploit an example that Kaplan mentions in a different context later—try substituting ‘5+4’ on the one hand and ‘the number of positions on a baseball team’ on the other for ‘nine’ in each of them. One substitution will preserve truth while the will not (or might not in the case of (4), depending on your views about what is essential to baseball). Quine argued against existential generalization on this basis—if the truth of a claim depends on the way something is referred to, how, he asked, can we say there is some thing that has the corresponding property? What thing is it? If it is 5+4, it seems to have these properties, but then it is also the number of positions on a baseball team, which doesn’t seem to have them.

• The ideas in §II parallel Quine’s example in “Speaking of Objects” (pp. 16–17) of Tom’s confusion about the name ‘Tully’. The difference between examples (6)-(8) of §II and the earlier (3)-(5) appeared there as the difference between the two uses of ‘Tom believes that Tully wrote the Ars Magna’. The use in which the sentence is false could be expressed as in a way analogous to (6)–(8) as ‘Tully is such that Tom believes that he wrote the Ars Magna’, something which, if true, would be equally true if stated using the name ‘Cicero’ instead of ‘Tully’. Further, example (10) is parallel to Quine’s suggestion that we might say ‘There is someone whom Tom believes to have written the Ars Magna’.

• You can regard §III as an introduction to §IV, and you’ll find its content neatly summarized in its concluding paragraph. Section IV itself suggests how Frege would explain, by analogy with the case of quotation, quantifying into what Quine would regard as “opaque” contexts. Kaplan’s discussion of (12) is really an in-joke since Quine had used precisely this notation in the same way. (Indeed, the symbols ‘⌜’ and ‘⌝’ are standardly referred to as “Quine corners.”) Example (14) is intended merely as an example of quantifying into another sort of opaque context, but Kaplan has probably chosen this example because the difference between ‘a kicked b’ and ‘b was kicked by a’ is one that Frege held not to affect the sense expressed.

• Section V completes Kaplan’s comparison of Quine’s and Frege’s accounts of (4)–(5) and (7)–(8). (Examples (3) and (6) have dropped out of consideration and were proabably included only for the sake of the comparison of (6) and (7) on p. 181, but the idea of “standard names” that is mentioned there will reappear later.) The two philosophers’ treatments of (4) and (5)—namely, (15) and (19) for (4) and (16) and (20) for (5)—are essentially the same (for reasons mentioned after (20), and can be read as

In the case of (7) and (8), the two accounts differ; Quine employs new expressions ‘Nec’ and ‘Bel’, which must be understood independently of ‘N’ and ‘B’ while Frege employs the latter. For (7), Quine’s account is (17), which Kaplan tells you how to read, while Frege’s is (24), which might be read as ‘There is some expression which denotes nine and which is such that the sentence formed by writing it before “is greater than five” is necessarily true’. The point is that Quine uses the idea of ‘necessarily true of’ while Frege makes do with ‘necessarily true’. Quine’s account of (8) is (18), and it may be read as ‘Hegel believed “x is greater than five” of nine’. Frege’s account is (25) and may be read ‘There is some expression which denotes nine and which is such that Hegel believed the sentence formed by writing it before “is greater than five”’.

The existential quantification (i.e., the ‘there is’ talk) in Frege’s accounts did not appear in the original (7) and (8), and you might wonder why Kaplan didn’t choose to generalize universally about expressions denoting nine (i.e., referring to every expression denoting nine rather than just some expression denoting nine). In fact, that is one way of posing a problem that Kaplan will discuss in the next few sections.