# Government and Binding Theory/IP and CP

In our last chapter, we discovered that auxiliaries are part of the VP, and thus reverted to this phrase structure rule for sentences:
(1a) S → NP VP
Still, this is highly problematic as it is not an X-bar rule!
You could, of course, treat NP as a head, and S as a third-level projection of VP.
(1b) VP‴ → NP V″
There are two problems with this that violate what we have learnt in the last chapter:
* Heads must be lexical categories.
* We only have two levels of projection.
We will now look for a new phrase to replace the sentence.

## Inflection as a head

There must be some mysterious lexical category that serves as the head of the sentence. What could it be? Firstly, we should look at the word to. You might be tempted to think that to is simply a specifier:
Yet there is good reason to believe that this is not the case. A specifier cannot choose its head. The behaviour of to indicates that it is pretty capable of choosing what comes after it:
(2a) to do homework (2b) *to does homework (2c) *to did homework
Recall that in our introductory book on linguistics, we learnt that inflection occurs when we mark a word with one or more grammatical categories. Clearly, to only precedes verbs without inflection. Thus we can reach this subcategorisation frame:
* Subcategorisation frame of to
* to [__ VP$_{[+bare]}$]
Since to is obviously not a specifier and can choose what comes after it, we are forced to conclude that it is a head.
Yet to applies only to non-finite clauses, i.e. clauses that are not inflected. Then what could possibly apply to finite clauses? Yep, you guessed it - the finite inflection.
To is not alone in requiring uninflected verbs after it. Modal auxiliaries are perfectly capable of doing this as well:
(3a) will do homework (3b) *will does homework (3c) *will did homework
* Subcategorisation frames of modal auxiliaries
* will [__ VP$_{[+bare]}$]
* may [__ VP$_{[+bare]}$]
* can [__ VP$_{[+bare]}$]
This gives rise to our new lexical category, inflection (INFL/I), which projects inflection phrases (IP).
* Inflection Phrase
* The sentence is not a further projection of the VP, but another phrase with the INFL (I) as the head, the VP as the complement and the subject as the specifier.
As the inflection is a functional category, this type of structure is called a functional projection, contrasted with lexical projection. Here is an example of IP:
Unlike last time, the specifier is not optional. This gave rise to a new principle:
* Extended Projection Principle
* Each clause must have a noun phrase (or, as we will soon see, a determiner phrase) in its subject position.

## Complement Clauses

In our introductory book, we mentioned complement clauses. These allow us to form sentences in a recursive manner, English examples being if, whether and for. Since we've already dealt with IPs, let's save ourselves the trouble of the trial-and-error process and form the complementiser phrase (CP) by analogy.
Complementisers can also choose the type of clause that can come after them. Consider: (4a) I think that you are a genius. (4b) *I think that you to be a genius. (5a) It is strange of you to think that I am a genius. (5b) *It is strange of you think that I am a genius.
(4b) and (5b) are wrong, which allows us to construct subcategorisation frames for complementisers:
* Subcategorisation frames of complementisers
* that [__ IP$_{[+fin]}$]
* if [__ IP$_{[+fin]}$]
* for [__ IP$_{[+inf]}$]
* of [__ IP$_{[+inf]}$]
This allows us to construct the complementiser phrase.
* Complementiser Phrase
* The complement clause is not a further projection of the IP, but another phrase with the Complementiser (C) as the head and the IP as the complement.
You may have noticed that we copied the Inflection Phrase definition above and pasted it here. This is the beauty of the X-bar theory: The same structure applies to all elements. (OK, we deleted the specifier of the complementiser phrase as we are not in a position to discuss this yet.)
Here are some examples of CP trees:
One final note on CPs: They have the semantic function of determining the illocutionary force of the CP. The complement of that must be a declarative, while that of if must be an interrogative, for example.
Speaking of recursion, there's another type of recursion that we've covered in our introductory book, but so far failed to address within the GB framework. They are adjuncts.