Quine's main aim in this paper is to exhibit conceptual difficulties associated with range of concepts including modalities such as necessity or possibility and propositional attitudes such as belief. In the first two sections, he focuses on the latter sort of example though the former is his eventual target.

• In §1 Quine introduces two related distinctions, between occurrences of names that are or are not purely designative (p. 114) and the corresponding distinction between contexts in which the occurrences of names are of one or the other sort (p. 115). In later work, Quine used the term "referential" as he uses "designative" here and spoke of the two sorts of contexts as referentially transparent and referentially opaque, respectively. So contexts in which names are purely designative are referentially transparent (i.e., one "sees through" the name to what it designates), and those in which names are not purely designative (or are, as he often says here, "indesignative") are referentially opaque. In the opaque context of quotation, for example, one "sees" the name itself rather than seeing though it to what it designates. The best way to come to understand these ideas is to think about the points Quine makes with his examples, and we will approach them in class by talking through some of the examples of this section.

• In §2, he notes that the opaque contexts identified in §1 also interfere with inferences by existential generalization (pp. 116-117)--i.e., inferences from sentences of the form "... t ..." (for some proper name or definite description t) to sentences of the form "something is such that ... it ...." Notice that Quine's point is not merely that the inference could lead us from a true premise to a false conclusion in such cases; indeed, the conclusion will often be plain nonsense. Since, as he notes on p. 118, no similar problem occurs when the whole clause "something is such that ... it ... ." is within the opaque context, people came to refer to this as the problem of "quantifying in." (See below for this sense of "quantify.") Quine later formulated the point he makes at the end of this section as the slogan "To be is to be the value of a variable."

The points that Quine makes in these sections are of interest to us largely because of the analogous points about necessity that he goes on to make later in the paper. We won't follow him in this since he mixes in other issues, too, but you should think through the following examples, which draw on some of his examples from §§3-4. (I will use Quine's numbers for the examples; examples numbered up to and including (13) are in your assignment.) We may suppose that the following analogues to examples (6) and (7) are true:

(18) 9 is necessarily greater than 7

(20) Necessarily, if there is life on the Evening Star then there is life on the Evening Star

But even though 9 is the number of planets (setting aside recent controversies) and the Evening Star is the Morning Star (since both are the planet Venus), the following are false

(23) The number of planets is necessarily greater than 7

(24) Necessarily, if there is life on the Evening Star then there is life on the Morning Star

because the statements that result when we drop "necessarily" from each are true only as a matter of contingent fact. Analogous to example (13) are the statements

Something is such that it is necessarily greater than 7 (or: There is something that is necessarily greater than 7--see the top of p. 124)

Something is such that, necessarily, if there is life on the Evening Star then there is life on it

Quine would ask about each, as he does about (13), "What is this object?" If we answer "9" in the first case, he'll respond, "I.e., the number of planets?," and if we answer "The Evening Star" in the second case, he'll respond, "I.e., the Morning Star?"

The statements above are different from the following statements:

Necessarily, something is greater than 7
(i.e., Necessarily, ∃x (x is greater than 7))

Necessarily, something is such that if there is life on the Evening Star then there is life on it
(i.e., Necessarily, ∃x (if there is life on the Evening Star then there is life on x))

These are analogous to the example at the top of p. 118 except that both are true--as is "Philip believes something is in Nicaragua," i.e., "Philip believes ∃x (x is in Nicaragua)."

Quine uses a little logical notation, some of which may be unfamiliar even if you've seen logical notation before. Here's a glossary:

The use of the two quantifiers is what Quine refers to as "quantification." Notice that the form "~ (x) ~ ...x..." amounts to "not everything, x, fails to be such that ...x...." and is therefore another way of stating the existential claim "∃x ...x...." He uses this form in the symbolic example at the bottom of p. 123 whose restatement at the top of p. 124 is mentioned above.