I’ve had a couple of questions about how to attach adjectives, and it’s probably worth saying something about that.
Adjectives are modifiers, like adverbs are. So, the way they attach is with Adjoin. The idea is that you have an NP, like students, and you want to modify the NP with an adjective, like happy. The result should still be an NP, though, because you can put happy students in all the same places in a sentence that you can put students. The result of adjoining happy to students would look like this:
NP
/ \
AdjP NP
happy students
I wrote “P” after these because they are both maximal projections—neither has any strong features left to check, so neither will project any further. You can’t in general adjoin like this until you’ve checked all of the strong features, meaning that this type of adjunction (for adverbs and adjectives) will always occur at the XP level. This would sometimes be called “XP-adjunction.”
What might happen next, after you’ve adjoined happy to students is that the NP happy students might be Merged into an argument position (to get a θ-role), e.g., as sister of V (in a sentence like I saw happy students) or as the specifier of v (in a sentence like Happy students passed the midterm). That is, once you’ve adjoined happy to students, the NP happy students functions as an inseparable unit, an NP that can get a θ-role, or move to the specifier of TP. (For whatever reason, this might be different with all and both, which do seem possible to leave behind, as in students will all come to class).
I did get an interesting question about the relationship between this and head-adjunction, of the kind that you get when you move V to v or an auxiliary to T. Head-movement (movement of a head up to a higher head) also winds up creating an adjunction structure that looks very much like the structure of happy students above. But there are a couple of differences.
For historical reasons, it is always assumed that XPs adjoin to XPs and heads adjoin to heads—you don’t have an XP adjoining to a head, or a head adjoining to an XP. This distinction made a little bit more sense back in the days of X-bar theory, where anything you take out of the lexicon projected a structure that included a head, an intermediate projection, and a maximal projection. In our theory, however, the distinction between “head” and “maximal projection” is often quite blurry, since the very same node in the tree can be both a head and a maximal projection.
When you draw a head-adjunction, of the kind that arises when V moves to v, you draw it like this:
v
/ \
V v
Because v is a head here (unambiguously so, it projects to a v-bar, and its sister is a VP), when you adjoin V to it, you are adjoining the head V to the head v. This is why no P was written by V here. In a sense, this is partly because the head V already projects its features to a VP, lower in the structure. When you move the head away, it doesn’t get to project again, and since it doesn’t even have the possibility of projecting when adjoined to another head, we don’t label it as VP in the structure above. But, mainly, it’s just because the only thing you adjoin to a head is another head.
Another point about head-movement (adjunction of a lower head to a higher head) is that it differs from XP-adjunction in that head-movement does occur in order to check a feature. XP-adjunction doesn’t.
I sometimes draw head-movement as happening from V to v in the step before the step in which the Agent is Merged. Merging the Agent checks a (strong) selectional feature of v, and by the reasoning I’ve presented in class about this, it should be that adjunction should wait until there are no more strong features to check on the head to which you are adjoining. Since head-movement does check a feature (such as the [uV*] feature of v), the best we can do is make that the last strong feature checked (it can’t wait until there are no more strong features to check, because it has to check one of them itself). That is, perhaps the Agent should really be Merged first, before V moves to v. It doesn’t really matter either way, but for consistency perhaps I’ll start doing that.
Probably the best way to distinguish between head-adjunction and XP-adjunction would be in terms of the features that get checked, then. Head-adjunction (which will arise from moving a lower head to a higher head) happens only when the higher head has a strong feature that needs to be checked. XP-adjunction happens only when there are no features left that need checking. Practically speaking, XP-adjunction will be cases of adjunction of a modifier, and head-adjunction will be cases of adjunction of a moved head.
The term “complex head” really only refers to the latter case, the one where a head adjoins to another head due to movement. The structure for happy students given above is not considered to be a complex head because, although it does happen to be made of heads, the NP students actually serves as a maximal projection. It’s not going to project any further, it doesn’t have any strong uninterpretable features to check. In that respect it’s different from v.
It’s possible that all of this has not really made the situation any clearer, but I’m hoping that, if you were wondering about this, you have at least a little bit more to go on.