# Government and Binding Theory/Trace Theory

Refer to the following sentence:
(1a) Who do you think [IP went to the cinema]?
[DIAGRAM NEEDED]
Here, who was moved to an Ā-position, and is no longer present in the original IP. Thus the original IP appears to violated the Extended Projection Principle. Since (1a) is grammatical, we can propose that there is a subject in the IP, just not phonetically realised. Do you remember it? Yes, we've seen this in the introduction to our introductory book on linguistics!

## Evidence for trace theory

Apart from the Extended Projection Principle, other pieces of evidence point to traces too.

### Plurality

Refer to the following:
(2a) They compliment one another. (2b) *I compliment one another. (2c) It seems that they always compliment one another. (2d) They seem [IP to compliment one another]. (2e) Who do you suppose [IP always compliment one another]?
As we can see from (2a) and (2b), the reciprocal pronoun one another only appears in the complement position of a verb when the subject is plural. To account for the grammaticality of (2d) and (2e), a null subject is needed.
Here is another example if you are not thoroughly convinced:
(3a) He always compliments himself. (3b) *They always compliment himself. (3c) He always seems to compliment himself.

### Predicative APs

A predicative adjective modifies the subject, but is the complement of the verb:
(4a) I am growing old. (4b) The joke is growing old. (4c) I seem [IP to be growing old]. (4d) Who do you think [IP is growing old]?
In (4a), old modifies I. In (4b), old modifies the joke. How about (4c)? How is it possible that we have a predicative adjective, and yet there is no phonetically realised subject? This is another piece of evidence supporting the existence of traces.

### Impossibility of replacement

It is not possible for an element to move into a position left behind by a moved element. Take, for example:
As (5d) is ungrammatical, have could not have just moved into the blank I position left by could. There must have been something there blocking this movement.

## Chains

The existence of traces poses a problem for theta theory, as demonstrated below:
(6a) Whom$_i$ did$_j$ you t$_j$ see t$_i$ at school?
According to the Theta Criterion, the relationship between theta roles and arguments must be bijective. However, the theme role is assigned to both whom and t$_i$, apparently violating the Theta Criterion. The solution is to see the antecedent and traces to be part of a chain, i.e. <Whom$_i$, t$_i$>. We then rewrite the Theta Criterion thus:
* Theta Criterion
* Each argument chain bears one and only one θ-role, and each θ-role is assigned to one and only one argument chain.
Note that antecedents are always found in θ′-positions, while the foot of the chain, or the base position, is always found in a θ-position.
Note that adjunct wh-elements, while not subject to the Theta Criterion, also leave traces:
(6b) When$_i$ will$_j$ you t$_j$ go to school $_i$?

### Formal definition of chains

* Chain
* <x$_1$, ... x$_n$> is a chain iff x$_i$ is the local binder of x$_{i+1}$ for all i between 1 and n inclusive.
The definition of binding will be discussed in detail later. For now, we will say that it is a structural relationship based on c-command, as we have seen in our discussion of VP shells:
(2a) I$_i$ introduced myself$_i$ (2b) *Myself$_i$ is so proud of me.
I binds myself, but me does not bind myself here. We will also define local binders as follows:
* Local Binder
* α is the local binder of β iff α binds β and there is no γ such that γ binds β but not α.