7.1.2. Pronouns and quantifier phrases

When a logically complex predicate is applied to an individual term, the result can be restated as a compound of simple predications. We used this as basis for our analyses in truth-functional logic. The first example of that in §2.1.1 was to analyze That bear is large and edgy into That bear is large and That bear is edgy. However, when a sentence is formed from a complex predicate by applying a quantifier phrase to this predicate, no such simplification need be possible. The sentence Some company is such that it does business in Tokyo and Terre Haute cannot be restated as the conjunction of Some company does business in Tokyo and Some company does business in Terre Haute since, although all these sentences are true, the last two require only that each of these cities has some company operating while the first implies some international business.

The reason for the difference in the two examples is a different relation between the logical form of the complex predicate and the logical form of the sentence as a whole depending on whether the predicate is applied to an individual term or has a quantifier phrase applied to it. The logical form of a complex predicate—as it would be displayed were we to analyze the body of a predicate abstract—reflects the form of any sentence that results from predicating it of a term. So every predication of this predicate has the same sort of structure. For example, the predicate [ _ does business in Tokyo and Terre Haute] can be analyzed as

so, if we apply it to a term—Sony say—

we will be asserting a conjunction because the body of the predicate is a conjunction, so the predication in reduced form

will also be a conjunction.

On the other hand, when we apply a quantifier phrase to a complex predicate, we make a claim about the population of the predicate’s extension. And there is no reason to think that the form of this claim will reflect the logical form of the predicate’s claims about individual objects. In the example at hand, Some company is such that it does business in Tokyo and Terre Haute says that the extension of [ _ does business in Tokyo and Terre Haute] contains at least one company. To say this is to say something about the way in which the extensions of [ _ does business in Tokyo] and [ _ does business in Terre Haute] overlap, and this sort of relation between their extensions cannot be expressed by a truth functional compound of claims made about the two extensions individually. This is one instance of a general point: few interesting relations between things can be restated as truth-functional compounds of claims made about the things individually. For example, try restating the claim John Stuart Mill was the son of James Mill as a truth-functional compound of claims each of which refers to only one of the two men.

This difference between individual terms and quantifier phrases has an impact on the significance of pronouns whose antecedents are quantifier phrases. A pronoun that has an individual term as an antecedent is a device for avoiding repetition, and it can be eliminated if we are willing to tolerate the repetition. That is why nothing like pronouns was introduced into our symbolic notation for truth-functional logic. We are able to restate Jack built the house and sold it so that the pronoun it is replaced by a second occurrence of the house, giving us a compound of two independent components. When we use abstracts, we are able to represent pronouns could analyze this sentence as [Jack built x and sold x]_x the house. The possibility of replacing pronouns by their antecedents means that this expanded form can be restated in reduced form by replacing the variable x by the term the house. But this sort of restatement or reduction is not possible with Jack built a house and sold it—since Jack built a house and sold a house can be true without him having sold a house he built—so we cannot eliminate the pronoun.

Something similar can happen with compounded predicates and other compounded phrases. We can restate the sentence The Titanic ran into an iceberg and sank so that and joins clauses rather than predicates if we repeat the phrase the Titanic. But A ship ran into an iceberg and sank cannot be restated as a conjunction of clauses by repeating the phrase a ship. Since we regard conjunction only as an operator on sentences, a restatement as a conjunction of clauses is necessary if we are to subject the predicate [ _ ran into an iceberg and sank] to further analysis. And, because we cannot repeat a ship without changing the meaning, we must introduce a pronoun with a ship as its antecedent. So not only are we often prevented from eliminating pronouns with quantifier phrase antecedents, we are often forced to introduce such pronouns in order to analyze sentences. Because of this abstracts will play a central role in the analysis of quantifier phrases: often sentences containing quantifier phrases can be analyzed only by identifying a complex predicate and subjecting it to analysis.