Quine’s topic is “ontological commitment,” the conditions under which someone accepts the existence of certain things or sorts of things. His discussion of this issue is divided into three parts.

• He begins (pp. 318-325) by considering two views on the matter that he doesn’t accept. At the end of this part of the paper, he summarizes what he has said.

• Next (pp. 325-327) he offers his own account and illustrates it with the example of different views of the basic ontology of mathematics. Given what he means by “to be the value of a variable”—roughly, the range of things pronoun might refer to, but see below for a fuller explanation—his criterion for ontological commitment might seem trivial. But that’s his point: he wants to say that we aren’t committed to the existence of anything beyond what is required to make true our claims that “something is ….”

• He concludes (pp. 327-330) by discussing the grounds for accepting a given ontology. He begins by outlining a way of discussing such issues that he later called “semantic ascent,” but his main aim is to say that we commit ourselves to the existence of various sorts of things on pragmatic and empirical grounds, grounds similar to those on which we commit ourselves to various claims about these things. In particular, there is no a priori ontology built into the language we use.

Values of variables. Quine gives a brief explanation of the idea of a “value” of a “bound variable,” but a little more may help.

First, what does he mean by “variable”? I might rephrase “Something is a dog” as “Something is such that it is a dog.” In the result, the pronoun “it” has “something” as its antecedent. In the usual symbolic notation for logic, algebraic variables play the role of pronouns; and a variable that has a symbolic version of a word like “something” or “everything” as its antecedent is said to be “bound” to the latter symbol, which is known as a “quantifier”. Quantifiers function like the English phrases “something is such that” and “everything is such that,” so a sentence like “Something is a dog” would always be expressed in a form containing a symbolic pronoun. As a result, the symbolic versions of claims that things exist and generalizations about the things that exist will always involve variables bound to quantifiers. In any complete symbolic sentence, every variable must be bound to a quantifier (just as a pronoun like “it” always needs an antecedent), so, when Quine speaks simply of “variables,” he has in mind variables bound to quantifiers.

The possible “values” of variables will determine what I generalize about when I say “everything is such that …” and the range of things I look to when I say “something is such that ….” So, for the symbolic version of “Something is a dog” to be true, there must be at least one dog among the possible values of the variables. And, more generally, anything I claim to exist will be among the values of the variables. Furthermore, anything among these possible values will be among the things I generalize about when I say “everything,” so I will be committed to their existence in the sense that, in order to be true, my generalizations must be true of all these things.