Government and Binding Theory/Trace Theory

Refer to the following sentence:

(1a) Who do you think [IP went to the cinema]?

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:

(5a)            he could not have done what (5b)      could he       not have done what (5c) what could he       not have done (5d) *what could he have not      done

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) Whomi didj you tj see ti 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 ti, apparently violating the Theta Criterion. The solution is to see the antecedent and traces to be part of a chain, i.e. < Whomi, ti>. We then rewrite the Theta Criterion thus:

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) Wheni willj you tj go to school i?

Formal definition of chains
< x1, ... xn> is a chain iff xi is the local binder of xi+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) Ii introduced myselfi (2b) *Myselfi is so proud of me.

I binds myself, but me does not bind myself here. We will also define local binders as follows:

α is the local binder of β iff α binds β and there is no γ such that γ binds β but not α.