4    X' theory: Functional categories

In this chapter, we extend the three-level X' schema from the lexical categories to the functional categories I(nflection), C(omplementizer), D(eterminer), and Q(uantifier). As we will see, this has considerable consequences for how we view the structure of noun phrases.

Inflection

The special status of modals in English

English has a special class of elements called modals, which include the lexical items can, could, may, might, must, shall, should, will, and would. These elements resemble ordinary verbs, but differ from them in several important respects, both morphologically and syntactically.

In contrast to ordinary verbs, modals bear no -s suffix in the third person singular of the present tense.

(1) a. Modal ok S/he { can, may } sing
b. * S/he { can-s, may-s } sing
(2) a. Ordinary verb * S/he { can, play } all day.
b. ok S/he { can-s, play-s } all day.

Modals also have no infinitive form of their own (rather, a suppletive form is used).

(3) a. Modal * to { can, may } sing
b. ok to be { able, allowed } to sing
(4) Ordinary verb ok to { can, play } all day

Related to this is the fact that modals neither require nor allow so-called do support in questions.

(5) a. Modal ok { Can, may } s/he sing?
b. * Does s/he { can, may } sing?
(6) a. Ordinary verb * { Cans, plays } s/he all day?
b. ok Does s/he { can, play } all day?

Finally, modals neither require nor allow do support in negated statements.

(7) a. Modal ok S/he { cannot, may not } sing.
b. * S/he does not { can, may } sing.
(8) a. Ordinary verb * S/he { cans, plays } not all day.
b. ok S/he does not { can, play } all day.

Because of these special properties, modals are assigned to a syntactic category of their own: I(nflection). The reason for the name is that although the English modals are independent words, they serve the same function that verbal inflections serve in many other languages. For example, the modals will and can mark future tense and possibility, both grammatical categories that in other languages are expressed by verbal endings.

Auxiliary verbs

It is worth noting that certain lexical items—namely, auxiliary be, auxiliary have, and the auxiliary do of do support itself— do not exhibit the morphological properties illustrated in (1)–(4), yet do behave like modals from a syntactic point of view, as shown in (9) and (10).

(9) a. No do support in questions ok Is s/he singing? Has s/he sung? Does s/he sing?
b. * Does s/he { be singing, have sung, do sing }?
(10) a. No do support in negative statements ok S/he { isn't singing, hasn't sung, doesn't sing }.
b. * S/he doesn't { be singing, have sung, do sing }.

For this reason, we will often group these verbs together with the modals. If we need to draw a distinction between the two classes, we will speak of true modals versus auxiliary verbs (or auxiliaries).

Surprisingly, main verb be patterns syntactically with the modals. Main verb do and have, on the other hand, behave like ordinary verbs, as one would expect given their morphology.

No do support Do support
(11) a. ok Is s/he reliable?
S/he isn't reliable. 		b. * Does s/he be reliable?
S/he doesn't be reliable.
(12) a. * Does s/he the job?
S/he doesn't the job. 		b. ok Does s/he do the job?
S/he doesn't do the job.
(13) a. * Has s/he a television set?
S/he hasn't a television set. 		b. ok Does s/he have a television set?
S/he doesn't have a television set.

Notice also that main verb do has an infinitive, whereas auxiliary do does not.

(14) a. ok They do repairs.
b. ok They claim to do repairs.
(15) a. ok They do ({ not, so }) like your brother.
b. * They claim to do ({ not, so }) like your brother.

Doublets

Finally, at least one lexical item exists as a doublet: namely, need. As a modal, it combines with a bare infinitive, but as an ordinary verb, it combines with a to infinitive.

(16) a. Modal ok Need s/he write the letter?
S/he needn't write the letter.
b. * Need s/he to write the letter?
S/he needn't to write the letter.
(17) a. Ordinary verb ok Does s/he need to write the letter?
S/he doesn't need to write the letter.
b. * Does s/he need write the letter?
S/he doesn't need write the letter.

Extending the X' schema to I

So far, we have been treating sentences as maximal projections of V. But although an approach equating sentences with VPs is successful for sentences without modals, like (18a), it breaks down for sentences containing them, like (18b), because there is no slot for the modal will within VP. (Assignment 4, Exercise 1 asks you to provide empirical and conceptual support for this assertion.)

(18) a.   The children found the toy.
b. The children will find the toy.

The solution to this problem is to extend the idea that lexical items project an X' schema from lexical categories like V to functional categories like I. This allows the modal to project the structure in (19a). Substituting an NP specifier and a VP complement then yields (19b) as the full structure for the sentence.

(19) a.       b.  

Subject movement

As usual in syntax (and in life more generally), having solved one problem, we immediately find ourselves with another on our hands. Specifically, despite the minimal difference between the sentences in (18)—they differ only in tense—they now differ quite substantially in structure, since (18a) and (18b) are now represented as a VP and an IP, respectively. Related to this is the fact that the subject occupies a different position in each sentence (Spec(VP) versus Spec(IP)), even though it is interpreted as an argument of find (= a necessary participant in the action denoted by the verb) in both cases. These categorial asymmetries, which are conceptually undesirable, are thrown into high relief by (20), which is truth-conditionally equivalent to (18a), but which must be assigned a different structure—one analogous to (19b)—due to the presence of the emphatically stressed modal.

(20)     The children did find the toy.

We will solve the problem posed by our current analysis of (18) and (20) in three steps. First, we build a core for the sentence containing only the predicate along with its arguments. Apart from the morphological form of the projecting lexical item (find versus found), this predicate-argument structure is identical for (18a,b) and (20).

(21) a.       b.  

Second, we substitute the common predicate-argument structure in (21) into the various modal treelets in (22), yielding the structures in (23). For convenience, (19a) is repeated as (22b).

(22) a.       b.       c.  
(23) a.       b.       c.  

Note that we assume the existence of a silent past tense element in (22a) and (23a). This element can be considered as a silent, semantically neutral counterpart of the overt emphatic did in (22c) and (23c). We adopt the convention of enclosing silent lexical items in square brackets. In the remainder of the course, we will encounter a fair number of such elements. As in the present case, they are motivated by a concern to represent semantic similarity in terms of structural similarity.

Finally, we must derive the correct word order of the subject with respect to the modal. In order to do this, we will simply move the subject from its post-modal position in Spec(VP) to its surface position in Spec(IP). This yields the structures in (24).

(24) a.       b.  

     c.  

A few remarks are in order about the process of movement just introduced. Movement is not intended as a psychologically real process. Rather, it is a metaphor intended to resolve the dilemma posed by the fact that a single phrase is pronounced once in a particular position, yet can satisfy more than one syntactic function in a sentence. It is in this sense that Chomsky speaks of movement (and syntax more generally) being at the interface between Phonetic Form (phonology) and Logical Form (semantics). In the case at hand, the children satisfies two distinct functions. First, it is a semantic argument—the agent, to be precise—of the predicate find. Second, it is the grammatical subject of the entire sentence. (Grammatical subjects are not always agents, as the existence of passive sentences shows.) In order to clearly express the phrase's double function, we do not simply move the phrase from one position to another. Instead, movement leaves a so-called trace in the phrase's original position, and the two positions share an index.

Note: By convention, indices for movement are represented by the same alphabetical subscripts as binding indices. For clarity, we diverge from this practice and use the natural numbers as binding indices, and the lowercase letters i, j, k, and so on as movement indices.
A constituent and any associated traces of movement (possibly none, in the absence of movement) are referred to as a chain. The elements of a chain are called its links. For instance, the tree in (24a) contains one chain with two links ([the children]i, ti) and another chain with a single link ([the toy]). Higher links in a chain are often referred to as the antecedents of lower ones. In (24a), for example, the phrase the children in Spec(IP) is the antecedent of the trace in Spec(VP). The motivation for this terminology is that traces of movement, just like reflexive pronouns, must be c-commanded by their antecedents.

Complementizers

A further example of a functional category is C(omplementizer), which corresponds to a subset of the traditional category of subordinating conjunction. Complementizers include lexical items such as if and that, the treelets for which are shown in (25).

(25) a.       b.  

As is evident, complementizers take IP complements. Their maximal projections (that is, CP) can in turn function as the complements of verbs, nouns, adjectives, and prepositions, as illustrated in (26)–(29).

(26) a. V   She asked [CP if there were any announcements ] .
b. They suspect [CP that there is a solution ] .
(27) a. N the question [CP if there are any announcements ]
b. the possibility [CP that there is a solution ]
(28) a. A It is uncertain [CP if there is a solution ] .
b. It is possible [CP that there is a solution ] .
(29) a. P They differ in [CP that they are not the same size ] .
b. the question of [CP whether there are any announcements ]

In traditional grammar, many subordinating conjunctions are held to be homophonous with prepositions, as illustrated in (30).

(30) a. Subordinating conjunction   { before, after, since } [IP the war began ]
b. Preposition   { before, after, since } [NP the war ]

Expressing this traditional analysis in the formal framework we have developed so far yields treelets for the homophonous items like those in (31).

(31) a.       b.  
Subordinating conjunction Preposition

The treelets in (31) differ from each other in two respects: in the category of the projecting lexical item (C, P), and in the category of the complement (IP, NP). But distinguishing (31a) from (31b) in terms of both of these categories is clearly redundant. As we noted earlier in our critique of phrase structure rules, redundancy in the formulation of a grammar violates conceptual parsimony, and generative grammarians strive to eliminate it. In the case at hand, it isn't reasonable to eliminate the redundancy by assigning clausal and noun phrase complements the same syntactic category. Instead, we will assign the same category to the heads. This is actually not that radical a step. After all, even in traditional grammar, all verbs share the same category, regardless of whether their complement is a noun phrase (NP), a prepositional phrase (PP) or a clause (CP). In principle, the unique category assigned to the projecting lexical item could be either C or P, but by convention, the label chosen is P, as shown in (32).

(32) a.       b.  

Do you find it confusing that the 'supercategory' encompassing both subordinating conjunctions and prepositions is assigned a label (namely, P) that is mnemonically related to one of its subcategories ('preposition' in the traditional sense)? If so, an analogy may help to convince you that the approach just described is actually nothing out of the ordinary. Think of how a very young child might experience ice, water, and steam as very different entities. After all, ice is cold and rocklike, water is liquid and has a whole range of temperatures, and steam is hot and gaseous. If you asked the child whether ice and steam are 'the same thing,' it would look at you as if you had lost your marbles. And in one sense, of course, the child is right. You can't put steamcubes in a glass of ice. But in another, more abstract sense, the child is wrong, and it is a step forward in its understanding of the world when it realizes that the three apparently distinct substances are all manifestations of a single chemical compound. We often call this chemical compound water, though if we want to be perfectly clear, we can distinguish between 'H2O' on the one hand and 'the liquid form of H2O' or 'water in the ordinary sense' on the other.

Why do we have a distinct label H2O for the supercategory that includes ice, water (in the ordinary sense), and steam, but none for the supercategory that includes subordinating conjunctions and prepositions? Presumably, this is a consequence of our more advanced scientific understanding of certain aspects of the universe (the material ones) than of others.

It is worth noting that the analyses in (31) and in (32) are both compatible with X' theory. It is further worth noting that the traditional distinction between prepositions and subordinating conjunctions can still be reconstructed straightforwardly, no matter which X' analysis we adopt, as shown in (33).

(33)     Traditional analysis X' analysis
Preposition P with NP complement
Subordinating conjunction P with IP complement (32a), or
C with IP complement (31a)

Determiners

The dialectic of cross-categorial parallelism

Recall that X' theory was originally motivated by the parallelism between sentences and noun phrases like (34) (= (1) of Chapter 3).

(34) a.   The army destroyed the city.
b. the army's destruction of the city

Before we extended X' theory to the functional categories in this chapter, this parallelism was captured by the structures in (35) (= (4) of Chapter 3).

(35) a.       b.  

But now that we have introduced the category of I(nfl) and assume that sentences are projections of I rather than V, the structure that we assign to (34a) is (36), which is no longer parallel to (35b).

(36)    

Our generalization of X' theory as it stands thus negates its original motivation, and we face the contradiction in (37).

(37) a.   Thesis: In the original formulation of X' theory, sentences and noun phrases are structurally parallel.
b. Antithesis: In (the current version of) generalized X' theory, sentences and noun phrases are no longer structurally parallel.

What we need is a synthesis that sublates the contradiction between the thesis and the antithesis (= resolves the contradiction between them without giving up any of the insights that we have gained so far).

The DP analysis of noun phrase structure

The desired synthesis comes from faithfully pursuing our path of generalizing X' theory to all syntactic categories. Note that we have not yet provided the syntactic category D(eterminer) with its own projection. This category includes what are traditionally called articles (a(n), the), demonstrative adjectives (as in this car, that house), and demonstrative pronouns (this, that). For the moment, we will also assume that D is the syntactic category of the possessive morpheme in English, realized as ’s in the singular and as ’ in the plural (this assumption is the focus of Assignment 4, Exercise 5). It is consistent with this assumption that the possessive morpheme cannot cooccur with another determiner in English. If both share the same syntactic category, they compete for the syntactic slot, and the ungrammaticality of (38a) is then simply parallel to that of (38b).

(38) a. * { John's the, John's this, John's that, John the's book, John this's book, John that's } book
b. * { the this, the that, this the, this that, that the, that this } book

Assuming that D projects to DP then allows us to represent the examples in (34) schematically as in (39). The movement of the subject from Spec(NP) to Spec(DP) in (39b) is assumed on the strength of cross-categorial parallelism.

(39) a.       b.  

As is evident, representing noun phrases as DPs restores the parallelism between sentences and noun phrases that was the original motivation for X' theory. In both cases, the entire structure under consideration (the sentence or noun phrase) consists of a core headed by a lexical category (V, N), together with a 'shell' headed by a functional category (I, D).

The structures in (39) are shown in more detail in (40).

(40) a.       b.  

It is worth stating explicitly that adopting the DP analysis of noun phrase structure commits us to uniformly representing any noun phrase, including a possessive noun phrase, as DP, rather than as NP, or some variety of NP (say, PossNP). You can verify that this has been done in (39) and (40). In this connection, it is important to distinguish carefully between pretheoretical terms like 'noun phrase' and theoretical terms like 'NP' and 'DP.' Both kinds of terms are tools that we use in our attempts to describe and understand some aspect of reality, but they differ in how close a look they afford us. Pretheoretical terms are like the pointers that people use in presentations or the famous finger pointing at the moon in Zen Buddhism. They focus our attention on something, but they aren't terribly explicit about what the internal makeup of that something is. Theoretical terms are more like microscopes or telescopes, allowing us to see aspects of the something under investigation that we wouldn't otherwise see. It is true that the label for the theoretical concept 'NP' was originally chosen to be mnemonically related to the pretheoretical term 'noun phrase.' But mnemonic convenience has no theoretical standing. Rather, if a theoretical term becomes problematic, misleading, or counterproductive, as when 'NP' makes it impossible to express the cross-categorial parallels between noun phrases and sentences, it must be redefined (as in the present case) or discarded entirely (as in the case of terms like 'ether' or 'phlogiston' in the history of science).

Further arguments in favor of the DP analysis

In addition to restoring cross-categorial parallelism between sentences and nouns, the DP analysis has several other conceptual advantages. First, it solves an anomaly that you may already have noticed. Recall that in the general X' schema in (41) (= (5) in Chapter 3), the specifier is a maximal projection.

(41)    

However, if noun phrases are represented as NPs, the category is problematic because Spec(NP) can be filled not only by a maximal projection, as in (42a), but also by a head, as in (42b).

(42) a.       b.  

But if the noun phrases are represented as DPs, as in (43), the anomaly vanishes, since there are now two separate positions, one for maximal projections and the other for heads.

(43) a.       b.  

A second, related conceptual argument in favor of the DP analysis is that it eliminates the following redundancy. As just discussed, under an NP analysis of noun phrases, nouns are systematically associated with pairs of treelets, one with a substitution site for a possessive noun phrase, as in (42a), and the other with a substitution site for a determiner, as in (42b). Assuming the DP analysis eliminates this systematic duplication of noun treelets. Rather, each noun can be associated with a single treelet of the form in (44).

(44)    

Possessive and non-possessive structures can then be derived by substituting such treelets into possessive or non-possessive treelets like those in (43). Of course, even under a DP analysis of noun phrases, some nouns (for instance, author) are associated with two treelets, one with and one without a complement. The point is simply that under an NP analysis, nouns must be associated with twice the number of treelets as under a DP analysis, and that the DP analysis is therefore preferable.

A third argument in favor of the DP analysis is that it allows us to recast the traditional distinction between articles, demonstrative adjectives, and demonstrative pronouns in terms of the single category D and the independently motivated distinction between transitive and intransitive heads. As (45) and (46) show, articles differ from demonstratives in not being able to appear in isolation.

(45) a. I'll buy { a, the } book.
b. * I'll buy { a, the } .
(46) a. I'll buy { this, that } book.
b. I'll buy { this, that } .

We can therefore say that articles are obligatorily transitive determiners, whereas demonstrative adjectives and pronouns are determiners that are associated with both transitive and intransitive treelets, as shown in (47).

(47) a.       b.       c.  

From this cross-categorial perspective, articles correspond to verbs like devour and prepositions like of, whereas demonstratives correspond to verbs like eat and prepositions like in (cf. come in the house and come in ). The question of course immediately arises whether there are obligatorily intransitive determiners corresponding to verbs like wait. It has been suggested that such determiners do indeed exist, and that the elements in question are pronouns (or more precisely, a subset of them, as the contrast between (48b) and (49b) shows).

(48) a. I, he, she, it, they
b. * I linguist, he fool, she idiot, it piece of junk, they traitors
(49) a. we, you
b. we Americans, you fool(s)

(50) illustrates the treelets needed to represent the two types of pronouns in (48) and (49).

(50) a.       b.       c.  

Further evidence for assigning pronouns to the syntactic category D comes from the impossibility of combining them with articles, as shown in (51), a fact that follows straightforwardly if pronouns and articles occupy the same structural slot.

(51)   * the he, this she, that you, a they

Quantifiers

The term 'quantifier' is used of expressions that refer to quantities, and it includes the numerals, expressions such as few and many and related comparatives and superlatives, any, every, no, and some and the compounds formed with them, and all and both. Despite their semantic similarity, however, these expressions are diverse from a syntactic point of view. For instance, as illustrated in (52) and (53), every has the distribution of a nominal modifier, but like no and some, it also appears in the determiner slot.

(52) a.   his every invention
b. his clever invention
(53) a. any useful concept, every red circle, no sane person, some well-meaning incompetent
b. this useful concept, the red circle, a sane person, that well-meaning incompetent

Not surprisingly, the compounds formed with any, every, no, and some function as noun phrases.

(54) a.   { Everyone, No-one, Someone } showed up. Anything would please her.
b. I see { everything, nothing, something } . I'll eat anything.

All and both contrast with the semantically similar every and two in being able to precede, but not follow determiners, as shown in (55) and (56).

(55) a.   all Lukas's toys, all this commotion, both Lukas's friends
b. * Lukas's all toys, this all commotion, Lukas's both friends
(56) a. * every Lukas's toy, every this commotion, (the) two Lukas's friends
b. Lukas's every toy, Lukas's two friends

The contrast between (55) and (56) suggests that when all and both are used as in (55a), they are heads that takes DP as their complement. Since quantifiers in the cases other than (55) can be assigned to already existing syntactic categories like A and D, the mnemonic label Q(uantifier) is available for the special syntactic category. Of course, in order to avoid confusion, we must carefully distinguish between the syntactic category Q and the semantic category quantifier. According to the analysis just outlined, the structures for the phrases in (55a) are as in (57) (the internal structure of NP is omitted for convenience).

(57) a.       b.       c.