A bound variable pronoun (also called a bound variable anaphor or BVA) is a pronoun that has a quantified determiner phrase (DP) – such as every, some, or who – as its antecedent.
An example of a bound variable pronoun in English is given in (1). (1) Each manager exploits the secretary who works for him. (Reinhart, 1983: 55 (19a))
In (1), the quantified DP is each manager, and the bound variable pronoun is him. It is a bound variable pronoun because it does not refer to one single entity in the world. Rather, its reference varies depending on which entities are encompassed by the phrase each manager. For example, if each manager encompasses both John and Adam, then him will refer variably to both John and Adam. The meaning of this sentence in this case would then be:
(2) John1 exploits the secretary who works for him1, and Adam2 exploits the secretary who works for him2. (Adapted from Reinhart, 1983: 55 (19a))
where him first refers to John, and then to Adam.
In linguistics, the occurrence of bound variable pronouns is important for the study of the syntax and semantics of pronouns. Semantic analyses focus on the interpretation of the quantifiers. Syntactic analyses focus on issues relating to co-indexation, binding domain, and c-command.
Semantics: quantifier interpretation
Semantics is the branch of linguistics that examines the meaning of natural language, the notion of reference and denotation, and the concept of possible worlds. One concept used in the study of semantics is predicate logic, which is a system that uses symbols and alphabet letters to represent the overall meaning of a sentence. Quantifiers in semantics – such as the quantifier in the antecedent of a bound variable pronoun – can be expressed in two ways. There is an existential quantifier, ∃, meaning some. There is also a universal quantifier, ∀, meaning every, each, or all. Ambiguity arises when there are multiple quantifiers in one sentence.
An example of the use of quantifiers is shown in (3). (3) Every man thinks he is intelligent. = ∀x(man(x)): x thinks x is intelligent. (bound) = For every man x, x thinks x is intelligent. ≠ Every man thinks every man is intelligent. (Carminati, 2002: 2(3a))
In this example, the quantified determiner phrase every man can be expressed in predicate logic as a universal quantifier. Because of this, he refers universally and variably to each man, rather than to a single specific man.
Syntax
Syntax is the branch of linguistics that deals with the formation and structure of a sentence in natural language. It is descriptive, meaning it is concerned with how language is actually used, spoken, or written by its users, unlike prescriptive grammar/prescription which is concerned with teaching people the "correct way" to speak.
There are three main aspects of syntax that are important to the study of bound variable pronouns. These are: Co-indexation of a pronoun and its antecedent C-command relationship between the antecedent and the pronoun Binding domain of the pronoun
Co-indexation
According to the indexing theory, each phrase in a sentence can be given a unique index, which is a number (or letter) that identifies that phrase as picking out a particular entity in the world. It is possible to modify the indexes on these phrases so that two or more phrases have the same index. This is called co-indexation. If co-indexation occurs, the phrases with the same-numbered index will all refer to the same entity. This phenomenon is called co-reference.
An example of co-indexation and co-reference is shown in (4).
(4) (a) *[Mary]i likes [herself]j
(b) [Mary]i likes [herself]i
(adapted from Sportiche et al., 2014: 161 (8a))
In (4a), the determiner phrases – Mary and herself – are each given a unique index. In (4b), co-indexing takes place, and herself changes its index to be the same as the one that Mary has. Because of this, Mary and herself now refer to the same entity in this sentence.
C-command
If a pronoun has a quantified expression as antecedent, the pronoun must be c-commanded by this antecedent. An antecedent c-commands a pronoun if, when observing the structure of the sentence, a sister of the antecedent dominates the pronoun.
The c-command relationship can be shown by drawing a tree for the sentence. Take, for instance, the following tree diagram for example (4b).
Here, Mary is the antecedent, and herself is the pronoun. The sister of Mary is the T' node, and this node dominates herself. So Mary c-commands herself in this instance.