# Government and Binding Theory/Binding Theory

So far, we have not seriously discussed the relationships of pronouns to their antescedents, although we have touched upon the subject slightly, such as this example:
(1a) I$_i$ introduced myself$_i$ (1b) *Myself$_i$ is so proud of me.
This phenomenon is actually part of binding theory, which explores such relationships in detail, and explains the ungrammaticality of sentences like (1b).

## Binding

In our discussion of the VP-Shell Hypothesis, we noticed that (1a) is grammatical because I c-commands myself, and (1b) is ungrammatical because me does not c-command myself.
The relationship between the two is known as binding: I binds myself. However, c-command is not the sole criterion that determines binding:
(2a) I hate homework. (2b) I hate myself.
In (2a), I c-commands homework, but obviously does not bind it. In (2b), I c-commands myself and binds it. We can explain this using the concept of indexation:
(2a) I$_i$ hate homework$_j$. (2b) I$_i$ hate myself$_i$.
* Binding
* α binds β if:
* α c-commands β
* α and β are co-indexed

## Governing categories

Binding does not appear to be a sufficient explanation for reflexives like myself, however. Refer to this:
(3a) *I$_i$ think he hates myself$_i$.
Although I c-commands myself and the two are co-indexed, (3a) is not grammatical. This suggests a locality constraint on the grammaticality of reflexives. Reflexives bound by antecedents too far away – outside of some local domain – are not grammatical. However, that is a weasel word. What exactly is a local domain?

### Clause-Mate Condition

This observation led to the Clause-Mate Condition, which, however, does not stand up to scrutiny.
* Clause-Mate Condition
* Reflexives must be bound by its antecedent in the same clause.
Exceptional case-marking (ECM) sentences, for example, are an exception:
(3b) [IP I want [IP myself to be happy]].
In (3b), myself is the subject of the lower-level IP, while I is the subject of the higher-level IP, yet the sentence is grammatical.

### Government

We can further examine using these examples:
(4a) [IP I want [IP myself to be happy]]. (4b) *[IP I think [IP myself is happy]]. (4c) *[IP I want [IP someone to love myself]].
In (4c), myself is governed by love and in (4b), myself is governed by the finite inflection of is. However, in (4a), myself is governed by want. This suggests that the local domain of a reflexive is the smallest clause containing its governor. (We do not go into the details of government here; refer back to the chapter Case Theory.)

### Subjects

Yet another example complicates the situation:
(5a) *He disapproved of the way by which [IP the government treated himself]. (5b) *He disapproved of [DP the government's treatment of himself].
(5b) is grammatical according to our previous assumption, since himself and he belong to the same clause where himself's governor on is found. Yet it is not. This suggests that the DP also limits binding. We have seen in our discussion on DPs that DP and IP structure share significant similarities. In fact, the possessor in a DP can be said to be the subject of a DP, so (5a) and (5b) are ungrammatical for similar reasons:
By incorporating the notion of subject in our definition of the local domain, we come to what is called the complete functional complex (CFC).
* Complete Functional Complex
* The complete functional complex is the smallest domain that contains
* A DP
* The governor of the DP
* A subject
Even the concept of CFCs does not fully capture all the possibilities of binding, however. Further modifications have been made, and the resulting domain is most commonly known as the governing category. We will not go into the intricacies of the governing category here, and will hereafter refer to the local domain as the governing category without regards to these intricacies.

## Exploring the four cases
### Typology of DPs

DPs can be divided into four types according to two features: [anaphoric] and [pronominal].
| [anaphoric] | [pronominal] | Symbol | Name of empty category | Corresponding overt noun type |
| - | - | t | Ā-trace | R-expression |
| - | + | pro | little Pro | pronoun |
| + | - | t | A-trace | anaphor |
| + | + | PRO | big Pro | / |
In the sections below, we will look at each type and its corresponding principle in Binding Theory.

### Anaphors and A-traces

In GB theory, anaphors refers not to pronouns in general, but to reflexives and reciprocals. In English, this includes myself, yourself, each other, one another and so on. Anaphors and Ā-traces have the features [+anaphoric], [-pronominal] and are subject to Principle A of Binding Theory:
* Principle A of Binding Theory
* Anaphors must be bound in their governing categories.
Here are some examples:
(6a) [GC I$_i$ introduced myself$_i$]. (6b) *I$_i$ think [GC he introduced myself$_i$]. (6c) [GC He$_i$ seemed t$_i$ to be unhappy]. (6d) *He$_i$ seemed [GC t$_i$ was unhappy].
We will not go into (6a) and (6b) as our explanations above were sufficient. The entirety of (6c) is a GC as a to was infinite and thus unable to govern the trace. Instead, the whole sentence was a GC with the subject he$_i$ and the governor seemed. (6d) was ungrammatical as the trace was not bound in the IP t$_i$ was unhappy, in which the finite inflection of was governs the trace.

### Pronouns and pro

In GB Theory, pronouns excludes reflexives, and includes pronouns like it and him. They act in the same way as pro, since pro appears when these pronouns are left out. Both are [-anaphoric] and [+pronominal].
* Principle B of Binding Theory
* Pronouns must be free in their governing categories.
(7a) [GC I introduced him]. (7b) *[GC He$_i$ introduced him$_i$]. (7c) Zhe-ge youxi$_i$ hen haowan, [GC wo keyi jieshao pro$_i$ gei ni]. (this-classif. game very fun, I can introduce pro to you) (This game is fun; I can introduce it to you.) (7d) *[GC Ta$_i$ jieshao-le pro$_i$] hou, women jiu kaishi chifan-le. (he introduce-asp. pro after, we then started eat-asp.) (After he introduced himself, we started eating.)
In (7a), both I and him were free. In (7b), him was bound to he, which is impermissible. In the Mandarin sentence (7c), pro referred to this game, and was free in its governing category. In (7d), pro was bound by ta in its governing category, and was thus ungrammatical.
Note, however, that (7e) is grammatical:
(7e) My$_i$ mother introduced me$_i$.
This is because my does not c-command me:
[DIAGRAM NEEDED]

### R-expressions and Ā-traces

An r-expression has no antecedent. It refers directly to something in the real world, like Wikibooks, Barack Obama, those colourless green ideas and the sandcastle I just built. Both r-expressions and Ā-traces are [-pronominal] and [-anaphor], and therefore subject to Principle C of Binding Theory:
* Principle C of Binding Theory
* R-expressions and Ā-traces must be free everywhere.
(8a) I$_i$ dare say there is absolutely not a living soul on the earth [GC who does not hate Derrick$_j$]. (8b) *I$_i$ dare say there is absolutely not a living soul on the earth [GC who does not hate Derrick$_i$]. (8c) What$_i$ do$_j$ you t$_j$ think he has done t$_i$?
Although Derrick was free in its governing category in (8b), it was not free everywhere: I still c-commands and is co-indexed with Derrick, so Derrick is bound by I and the sentence is thus ungrammatical.

### PRO

As PRO is [+anaphoric] and [+pronominal], it faces two conflicting principles regarding its governing category: It must be bound and free in its governing category at the same time. This is impossible... unless it doesn't have a governing category in the first place. [+anaphoric] and [+pronominal] explains the PRO theorem, which states that it must appear in ungoverned positions.