In linguistics, binding theory is any of a broad class of theories dealing with the distribution of pronominal and anaphoric elements. The idea that there should be a specialised, coherent theory dealing with this particular set of phenomena originated in work in transformational grammar in the 1970s. This work culminated in government and binding theory (a general theory of innate linguistic structure) whose version of the binding theory is still considered a reference point, though it is no longer current. Virtually all generative syntactic theories (for example, HPSG and LFG) now have a "binding theory" subcomponent.
Distribution of nominals under binding theory
In the tradition of generative syntax, it is argued that all kinds of nouns can be classified by the combination of two features, [anaphor] and [pronominal], features which are binary. The binding characteristics of a noun (or its corresponding empty category) are determined by the values of these features, either plus or minus. Thus, a noun that is [-anaphor, -pronominal] is a referential-expression R-expr, such as a common noun or proper name. One that is [-anaphor, +pronominal] is a pronoun, such as English he or they. [+anaphor, -pronominal] is a reflexive, such as himself or themselves.
The actual requirements on where a type of noun can occur are given in three conditions A, B, and C (also referred to as principles).
Condition A states that an anaphor (reflexive) must have a local ("nearby") antecedent (expression that refers to the same entity). Thus, John washed himself obeys Condition A: the antecedent of himself, which is John, is nearby, and both refer to the person "John". In contrast, *John asked Mary to wash himself is unacceptable, because the reflexive and its antecedent are too far away from each other.
Condition B states that a pronoun can have an antecedent, as long as the antecedent is not local (i.e. "far away") or doesn't c-command the pronoun. Thus, John asked Mary to wash him obeys Condition B: John is the antecedent of him, and him is sufficiently far away; on the other hand, *John washed him, where John is intended to be the antecedent of him, is unacceptable.
Condition C states that an R-expression cannot have an antecedent that c-commands it. Thus, *He asked Mary to wash John, with the interpretation that He is the antecedent of John, is unacceptable.
Binding of nominals versus operator-variable binding
Generative syntax distinguishes two kinds of binding. The first concerns nouns and the binding conditions discussed above: this is referred to as A-binding. The second concerns binding of another kind, a kind of logical binding known as operator-variable binding, or A'-binding.
In essence, operator-variable binding provides a way for an individual entity (or entities) to be picked out from a set of entities. Since this is a very abstract definition, an illustration will be helpful. Look at the two examples below. The first is a statement, and the second is a question derived from the statement.
(1) Smoltz hit Rodriguez with the baseball.
(2) Whom did Smoltz hit [e] with the baseball?
Notice in the question (2), whom, which corresponds to the object of the verb hit, appears at the left of the sentence, not in the position marked [e], which is where the object appears in the statement.
The position marked by [e] is linked to, (or bound by), the question word whom. Whom is the operator, denoting a set of individuals, and the [e] spot is the variable, while the range of the operator is, in essence, limited to those people whom Smoltz might have hit (with the baseball). Notice that, since (2) is a question, it would not be quite correct to say that whom and Rodriguez refer to the same thing, since it is also possible that John Smoltz hit other people (with the baseball) as well.
The names A-binding and A'-binding come from the idea of A-levels and A'-levels, which distinguish arguments (required elements, such as subjects, objects, etc.) from non-arguments, such as elements which may have been arguments, but have moved "beyond" to become something else in addition, such as a question word; also elements which are peripheral, such as certain kinds of modifiers.
Thus, in the example (1) above, Smoltz and Rodriguez are A-level elements, since they are arguments of the verb hit (hit requires both someone/something that does the hitting, and someone/something that was hit. A'-level elements are question word whom in (2), as well as with the baseball. Whom was once an argument of hit, but has moved to the left to satisfy a rule in English that (more-or-less) requires question words to move to the left. The element with the baseball is not an argument of anything, since removing it would still result in a grammatical sentence (in the sense of syntactic theory), whereas removing either Smoltz or Rodriguez would not.
Syntactic versus semantic binding
A node α syntactically binds a node β if
- α and β are co-indexed,
- α c-commands β,
- α is in an A-position, and
- α does not c-command any other node which is also co-indexed with β, c-commands β, and is in an A-position (p. 261).
βnsemantically binds αm if the sister of βn is the largest subtree of γ in which αm is semantically free, where
- αm is a variable occurrence in a tree γ,
- βn is a variable binder occurrence in γ (p. 262)
- Büring, D. (2005). Binding Theory. Cambridge; New York: Cambridge University Press. ISBN 0-521-01222-8.
- Heim, I., and A. Kratzer (1998). Semantics in Generative Grammar. Malden, MA: Blackwell. ISBN 0-631-19713-3.
- Hornstein, N. Nunes, J. Grohmann, K. (2005). Understanding Minimalism. Cambridge: Cambridge University Press. ISBN 978-0-521-82496-5.