Next I take up modification, a relation that has posed major difficulties for theories of constituent structure. It will be shown that the relational theory developed in the preceding chapters is sufficient to account for the fundamental properties of modification without introducing any new primitives. I consider first adverbial modifiers and then show that the same basic ideas can be extended to postnominal adjectival modifiers. I then turn to the question of prenominal adjectival modifiers, arguing that a different approach altogether is required to explain their properties—one that involves an extension of the notion of selection. I conclude by showing that the same approach is needed—somewhat surprisingly—in order to describe correctly the properties of adverbial modifiers of adjectives and adverbs.
3.1 Adverbial Modification
To see the problem that adverbial modification poses for theories of constituent structure, consider the two expressions walk slowly and eat lunch. Both are phrases consisting of two words and both are projections of the verb, hence standardly assumed to form a VP constituent. Yet the relation between the words in the two cases is entirely different. Traditional grammars typically describe the difference in intuitive terms by saying that whereas lunch is an argument of eat, slowly is a modifier of walk. An attempt to account for the difference in more formal terms was made in X-bar theory by permitting a node Xi of bar-level i to project a node of the same bar-level Xi rather than projecting a node of the next higher bar level Xi+1. The relation between such a node and its sister was defined as adjunction and it was assumed that this notion was sufficient to provide a formal characterization of the various kinds of modification relations found in natural language. That idea, however, has turned out to be problematic for many reasons. Thus VP-adjuncts, to mention only one, are incorrectly predicted to c-command all the arguments within VP (Pesetsky Reference Pesetsky1995, Bowers Reference Bowers2010).
If anything, the problem becomes even more acute in the minimalist framework. In Chomsky (Reference Chomsky, Martin, Michaels and Uriagereka2000: 133), the Merge operation is said to form unordered sets of elements when driven by selection (set-Merge), but to form ordered pairs in the case of modification (pair-Merge). Essentially, this approach deals with modification by introducing a new primitive operation into syntactic theory, with the result that syntactic representations become a mixture of sets and ordered pairs. Such representations are far more complex than representations in terms of either sets alone or relations alone, and are far more difficult to interpret at either PHON or SEM.Footnote 1 This idea is also conceptually quite strange, because it is clear, thinking in terms of relations, that the simplest way to account for the difference between eat slowly and eat lunch is to represent the latter as a relation between eat and lunch and the former as a relation between slowly and eat. In other words, in eat lunch, the verb eat is the head of a binary relation <eat,lunch> and lunch is the dependent, whereas in eat slowly, the adverb slowly is the head of a binary relation <slowly,eat> and eat is the dependent.Footnote 2 Given the notion of an ordered pair, there is no simpler way of representing the difference between selection and modification than this.
A strong argument in support of this approach derives from the fact that adverbs are naturally classified in terms of the kind of head they are required to modify (Bowers Reference Bowers1993, Reference Bowers2001a, Reference Bowers2002, Reference Bowers2010, Cinque Reference Cinque1999). I therefore propose, following Bowers (Reference Bowers1993, Reference Bowers2001a, Reference Bowers2002, Reference Bowers2010), that just as verbs contain features indicating the category of LI they select, so adverbs contain selection features specifying the category of LI they modify. Thus a manner adverb such as perfectly has the selector [_V], indicating that in an ordered pair of the form <perfectly,α>, it must be the case that α belongs to the category V. An adverb such as probably, in contrast, has the selector [_T], while an adverb such as reluctantly has the selector [_v]. Notice that this immediately accounts for the otherwise puzzling fact that adverbial modifiers are always optional. Whether or not an adverb occurs in a given sentence simply depends on whether or not it is present in LA. If it is, then it occurs; if not, not. The relational theory thus accounts in the simplest possible way for the difference between modification and selection, while at the same time accounting for the fact that modifiers are always optional.
Next we must ensure that the notion of a modifier can be formally defined within a relational theory solely in terms of the inherent properties of heads and their selectors. Recall that in Chapter 1 an argument was defined as a selected head that has no unsatisfied selectors, while a lexical projection was defined as a selected head that does have unsatisfied selectors. It was tacitly assumed, however, that both arguments and lexical projections are heads that are themselves selected by other heads. This leaves open the possibility of a third type of head, namely, one that has unsatisfied selectors but which is not itself selected as an argument by any other head.Footnote 3 It is precisely a head with these properties that I shall define as a modifier. Following traditional terminology, we may further define a modifier that selects a head of category v as an adverbial modifier and one that selects a head of category n as an adjectival modifier. Note that I have not excluded the possibility of a modifier itself being selected as a lexical projection. This is essential, since modifiers, like all syntactic expressions, are projected from roots. Indeed, if we were to exclude the possibility of a modifier being selected as a lexical projection, only bare roots would ever be capable of being modifiers.
Recalling now the tree representation of relational derivations proposed in Chapter 1, I propose as a first approximation (to be modified shortly, however: cf. §3.1.1.1) to integrate modifiers into such structures in the following manner:
(1)

As indicated in the diagram, the arrow connecting the modifier vmod to the lexical projection vy is directed downward and to the left, parallel to argument selection, though the two relations differ in that a modifier selects a lexical projection rather than being selected by it.
3.1.1 Manner Adverbs
To be more concrete, let’s consider next the empirical properties of various classes of adverbs,Footnote 4 starting with the type of adverb generally referred to in the literature as a manner adverb. As discussed in Chapter 2, every type of projection must have a minimal category. Let us designate the minimal adverbial modifier as amod, in order to distinguish it from the minimal adjectival projection aprop.Footnote 5 Noting that adverbial modifiers are regularly derived from adjectival roots by adding the suffix -ly, let us also assume that amod may be lexically realized as the bound morpheme -ly, whose phonetic form combines at PHON with the phonological form of an adjectival root. To illustrate, if the adverbial category amod is selected by the root √slow, then a phrase such as he walk slowly would be derived as follows:
(2)

I assume, anticipating the discussion of transitivity in Chapter 4, that all sentences project the category vtrFootnote 6 and that manner adverbs are modifiers of vtr in both transitive and intransitive sentences. Since walktr is the dependent and slowly the head, the former will be correctly linearized before the latter: he-walk-walk-√walk-slow+ly-√slow. The derivation of a transitive sentence such as He ate dinner slowly is derived similarly, except that the vtr head modified by slowly, being transitive in this case, also selects the vth-argument dinner:
(3)

As indicated in diagram (3), the principles of linearization established in Chapter 2 produce the correct linear order he-eat-dinner-slowly.
3.1.1.1 Linearization of Manner Adverbs
At this point, it is necessary to come to grips with the fundamental fact that manner adverbs are not restricted to clause final position, but may also occur to the left of a variety of non-core arguments such as vgoal, vben, vinstr, etc. (cf. Bowers Reference Bowers1993, Reference Bowers2001a, Reference Bowers2002, Reference Bowers2010 for discussion):
(4) He kicked the ball (perfectly) into the goal (perfectly).
In fact, it is true quite generally of -ly adverbs that they can occur either in some clause-internal position or at the right edge of a clause (Bowers Reference Bowers1993, Reference Bowers2001a):
a. He (inadvertently) kicked the ball into the goal (inadvertently).
b. He will (probably) kick the ball into the goal (probably).
c. He (unfortunately) must have kicked the ball into his own goal (unfortunately).
d. (Frankly,) he is not a first rate footballer(, frankly).
How is it possible to explain this systematic variability in the linear ordering of adverbial modifiers and the heads they modify? It seems that there must be some fundamental difference between modifiers and arguments that is in need of further explanation.
The solution to this problem lies in the fact that adverbial modification is essentially independent of argument selection and lexical projection. In diagram (1) the modification relation was simply added to a two-dimensional graph representing the relations of projection and argument, but I will argue now that such a representation is misleading. Suppose instead we interpret the graph notation quite literally as a two-dimensional space in which the vertical dimension represents the relation of lexical projection and the horizontal dimension represents the relation of argument selection. If that is the right way of thinking about these graphs, then the modification relation cannot simply be added to the plane representing lexical projection and selection. Rather, we must imagine that modifiers are represented in a third dimension orthogonal to the plane containing the heads they modify.Footnote 7 The modification relation may then be represented by a directed arrow connecting a modifier in this third dimension to a head in either the lexical projection dimension or the selection dimension. Visualizing the modification relation in this way provides a graphic representation of the fact that modifiers are fundamentally independent of the heads they modify. Thinking in terms of derivation, this implies that a modifier projection, like an argument projection, is first built from an independent subarray and then integrated into sentential structure by selecting a head in the projection/argument dimension and forming a modification relation with it.
Let us consider next how the linearization properties of modification discussed earlier can be accounted for. Suppose that the basic Spell-out algorithm proposed in Chapter 1 applies to modification in exactly the same way that it does to projection and argument selection, except that it leaves the direction of linearization free, rather than specifying (in the unmarked case) a fixed direction. One reason for thinking this might be the case is that lexical projections and arguments are obligatory, whereas modifiers are always optional. Hence it makes sense to suppose that there is a fixed direction of selection for the former but not the latter. If the direction of linearization of modifiers is simply left unspecified by the Spell-out algorithm, it follows that the phonetic form of a modifier is free to be ordered either to the left or the right of the phonetic form of the head it modifies. Once a modifier selects a head and forms a relation with it, their respective phonetic forms must of course be arranged in some linear order, since phonetic forms are only legible to the SM systems if they are linearized. If the approach proposed here is correct, the choice of direction is simply free, reflecting at the level of PHON the fundamental fact that the relation between a modifier and the head it modifies is independent of the argument selection and projection properties of the latter.
There is, however, a possible alternative to free ordering of modifiers, namely, language-specific parameterization, arbitrarily imposing a fixed ordering between a modifier and the head it modifies. Such language-specific parameters can be quite general, applying uniformly to all modification relations in a given language, or they can vary idiosyncratically from one type of modifier to another. A language can also combine free ordering of some modifiers with parameterization of others. Empirically, all of these possibilities are found in the world’s languages. In this chapter, I focus mainly on what I take to be the unmarked case, namely, free ordering, leaving for Chapter 4 some discussion of the range of parameterization found cross-linguistically.
To illustrate free ordering, consider first what happens if the modifier perfectly in example (4) is ordered to the right of the phonetic form of vtr at step 6 of the derivation:Footnote 8
1
<√kick,vgoal> kick-kick 2
<vgoal,into> into-the-goal-kick-kick 3
<vgoal,vth> kick- into-the-goal-kick-kick 4
<vth,the> the-ball- kick-into-the-goal-kick-kick 5
<vth,vtr> kick-the-ball-kick-into-the-goal-kick-kick 6
<perfectly,vtr> kick-the-ball-kick-into-the-goal-kick-kick-perfectly 7
<vtr,the> the-ball-kick-the-ball-kick-into-the-goal-kick-kick-perfectly 8
<vtr,vpred> kick-the-ball-kick-the-ball-kick-into-the-goal-kick-kick-perfectly 9
<vpred,he> he-kick-the-ball-kick-the-ball-kick-into-the-goal-kick-kick-perfectly
The phonetic form of vtr after step 5 is the string kick-the-ball-kick-into-the-goal-kick-√kick. If at the point where perfectly selects vtr, the phonetic form of the adverb is ordered to the right of the phonetic form of vtr, it will end up at the end of the entire sentence.
Consider, in contrast, what happens if the phonetic form of perfectly is ordered to the left of the phonetic form of vtr at step 6:
6′
<perfectly,vtr> perfectly-kick-the-ball-kick-into-the-goal-kick-kick 7′
<vtr,the> the-ball-perfectly-kick-the-ball-kick-into-the-goal-kick-√kick 8′
<vtr,vpred> kick-the-ball-kick-perfectly-the-ball-kick-into-the-goal-kick-√kick 9′
<vpred,he> he-kick-the-ball-kick-perfectly-the-ball-kick-into-the-goal-kick-√kick
The result is that the phonetic form of the adverbial modifier perfectly ends up between the object the ball and the vgoal argument into the goal.
Notice, however, that it is crucial that perfectly forms a relation with vtr before the argument selection feature of the latter is satisfied. If the relation <vtr,the> at step 7′ of derivation (7) was formed first, followed by the formation of the relation <perfectly,vtr>, i.e. if the order of steps 6′ and 7′ were reversed, the result would be *he kicked perfectly the ball into the goal, which, as is well known, is robustly ungrammatical in English. This leads to the conclusion that a modifier may only select a head none of whose selectors have been satisfied. In other words, modifiers may only select completely unsaturated heads. This constraint is not arbitrary but reflects a fundamental property of the modification relation, namely, that the content of a modifier is combined with that of the head it modifies, irrespective of whatever arguments or lexical projections the latter may be required to select. In other words, the relation between a modifier and the head it modifies is not dependent in any way on satisfaction of the selection properties of the latter.
The next step is to show that this constraint can be derived from the selection properties of modification, together with the general principles of the theory. Recall that IG states that the selection features of a head must be satisfied immediately. It follows from IG that given two unsaturated heads α and β, where β selects α, the selection features of β must be satisfied first. Otherwise, it would never be possible for β to satisfy IG. In the case of projection, IG thus ensures that projection starts from the lowest possible head and proceeds upward, rather than permitting a derivation to start somewhere in the middle. In the case of modification, IG implies that the selection feature of a modifier head must be satisfied as soon as a head of the required kind is projected in another subarray. In the case at hand, for example, a manner adverb such as perfectly must form a relation with vtr as soon as the latter is projected, i.e. before any of the projection and selection features of vtr itself are satisfied. If vtr projected another head before the selection feature of perfectly was satisfied, that head in turn would have to project a further head, which would itself be required to satisfy IG, and so forth, making it impossible for the selection feature of the modifier to be satisfied immediately, hence violating IG. More generally, it follows from IG that a selected head must either be fully unsaturated or the maximal fully saturated head in a projection. This prevents argument selection features from being satisfied by selecting an intermediate saturated head in some projection. At the same time, it prevents both projection features and modifier selection features from being satisfied by selecting anything but a fully unsaturated head. Notice, however, that nothing prevents a modifier from having projection and selection features of its own, quite independent of its modifier selection feature, that are required to satisfy IG within the modifier subarray.
It is important to stress that the hypothesis that modifier heads are represented in a separate “dimension” from argument heads and lexical projection heads is not mere stipulation. Rather, it is forced by the special formal properties of the modifier relation itself, together with IG.Footnote 9 Likewise, the fact that the modification relation is linearized differently from other relations—being basically free, unless parameterized—is also a reflection of its special formal properties. There have been other attempts in the literature to account for the distinctive linearization properties of modifiers, such as Keyser’s (Reference Keyser1968) suggestion that adverbs bear a feature [+transportable] that allows them to precede or follow their sister. Such an approach, even if descriptively adequate, clearly fails at the level of explanatory adequacy since the transportability property is simply stipulated ad hoc without being derived in any way from fundamental principles. Other approaches suggested in the literature, such as the Government–Binding notion that modifiers are not “visible” to certain operations by virtue of being added at a later stage of derivation, though somewhat less ad hoc than positing a feature [+transportable], are nevertheless not derivable in any way from the basic properties of adjuncts but simply mandated. In addition, there are empirical problems with the notion of an adjunct, as mentioned earlier (cf. also §3.1.7).
In order to incorporate modification into the canonical tree notation introduced in the preceding chapters in a manner that accurately reflects these properties, I propose now to place a modifier vertically above the head it modifies, intending by this to represent graphically the fact that the modifier is actually in a third dimension relative to the plane of selection and projection. At the same time, since the modifier occurs neither to the left nor to the right of the head it modifies, this notation will serve to indicate that there is no fixed linear ordering between the two, leaving it to be freely assigned or specified by language-specific parameters. Abstractly, relational trees will thus have the following canonical form:
(8)

Here xi is a lexical projection which is selected by xi−1 and which selects xi+1, yarg is an argument selected by xi, and zmod is a modifier of xi. As indicated in the diagram, the only possible order in which these relations may be formed is as follows: 1 <xi−1,xi>; 2 <zmod,xi>; 3 <xi,yarg>; 4 <xi,xi+1>.
3.1.2 Modifiers of vpred
Having established some of the fundamental properties of modifiers, I consider next three classes of adverbs all of which are modifiers of vpred. The well-known case of subject-oriented adverbs is discussed first, followed by a consideration of two other classes of adverbs that arguably also modify vpred. A problem much discussed in the recent literature (cf. Ernst Reference Ernst2001) is posed by the fact that these modifiers can co-occur with one another in different orders with concomitant differences of scope. It is shown that this problem can be solved by permitting vpred to project another instance of vpred, thereby making it recursive.Footnote 10 I conclude by showing that frequentative adverbs such as twice, often, etc. are ambiguous depending on whether they modify vpred or vtr.
3.1.2.1 Subject-oriented Adverbs
Consider first the class of subject-oriented adverbs, which includes inadvertently, intentionally, eagerly, willingly, unintentionally, accidentally, etc. These adverbs occur most felicitously either immediately preceding the main verb or at the right edge of the clause:
(9) He (??inadvertently) might (inadvertently) offend (*inadvertently) Mary (inadvertently).
As has frequently been observed, these adverbs are predicated of the subject, independent of its argument relation to the verb, as is shown by the difference in meaning between pairs such as the following:
a. The doctor unwillingly examined Mary.
b. Mary was unwillingly examined by the doctor.
The property of doing something against one’s will is predicated of the doctor in (10a), whereas it is predicated of Mary in (10b).Footnote 11 This observation is explained under the assumptions outlined earlier if adverbs of this class are modifiers of the vpred projection, since the meaning of the adverbial modifier must be composed with the meaning of the verb prior to selection by vpred of whatever argument is the subject. Hence (9) is derived as follows:
(11)

Obviously, if the phonetic form of inadvertently is ordered to the left of the phonetic form of offendpred before the latter selects the subject argument him, then (the phonetic form of) inadvertently will be placed immediately to the left of offend, producing the sentence He might inadvertently offend Mary. If, on the other hand, PF(inadvertently) is ordered after PF(offendpred), then the phonetic form of the adverb will be linearized at the right edge of the clause, as in He might offend Mary inadvertently. Note that there is no possible way of linearizing these relations that can result in a vpred adverb being ordered between the verb and the object. It was shown earlier that there is no way for manner adverbs to be linearized between a verb and its object either. Hence there is no type of adverb that may be ordered between a verb and its object, deriving the well-known generalization of English syntax that adverbs are prohibited between the verb and the direct object.
There is independent evidence in support of this analysis. Recalling the discussion of the minimal vpred complement in English (i.e. the so-called “bare infinitive” complement) in Chapter 2, it is predicted, first, that agent-oriented adverbs should be able to occur in such complements, second, that they should only be able to follow the subject, not precede it, and third, that they should also be able to occur at the right edge of the complement. All three predictions are correct, as the following examples show:
a. I saw (*inadvertently) him (inadvertently) score an own goal (inadvertently).
b. The coach had (*deliberately) him (deliberately) foul the goalkeeper (deliberately).
This data argues strongly against Cinque’s (Reference Cinque1999) view that each adverb class is generated in the specifier of a dedicated head. The nearest equivalent of Cinque’s theory in the relational framework would be to posit a special v-projection for each adverb class which would then select the adverb itself. Suppose, for example, we assume a projection vint for subject-oriented adverbs such as intentionally, deliberately, etc. If vint is projected above vtr but below vpred, then the adverb will incorrectly be linearized between the phonetic form of the verb and the object:
(13)

If, on the other hand, vint is projected above vpred, then the adverb will be correctly linearized after the subject in finite clauses and infinitival complements, but only by virtue of the fact that the subject is subsequently selected by vinf or vtns, causing its pronunciation to be displaced leftward. In bare infinitival complements such as those in (12), however, it will be impossible for the adverb to be correctly placed between the subject and the verb:
(14)

Depending on whether pronunciation of the root offend is or is not displaced to vint, either *I saw deliberately offend him Mary or *I saw deliberately him offend Mary will be produced, both of which are totally unacceptable. In short, positing a separate vint head makes it impossible to place the adverb in the correct position between the agent of a minimal vpred head and the verb. In contrast, if agent-oriented adverbs modify vpred, then exactly the right results are predicted.Footnote 12
This analysis makes another prediction. Consider a sentence containing both a manner adverb and an agent-oriented adverb. If both adverbs are linearized to the right, then the manner adverb is correctly predicted to precede the agent-oriented adverb at the right edge, since the former modifies a head lower in the v-projection than that of the latter:
a. John might kick the ball into the net perfectly (quite) inadvertently.
b. *John might kick the ball into the net inadvertently perfectly.
Furthermore, it should be infelicitous to exchange the positions of a manner adverb and an agent-oriented adverb in a sentence containing both:
a. John might inadvertently kick the ball into the net perfectly.
b. *John might perfectly kick the ball into the net inadvertently.
c. John might inadvertently kick the ball perfectly into the net.
d. *John might perfectly kick the ball inadvertently into the net.
This prediction also appears to be correct, lending further support to the hypothesis that pure manner adverbs such as perfectly select vtr, whereas agent-oriented adverbs such as inadvertently select vpred.
3.1.2.2 Prospective Aspectual Adverbs
Consider next the class of aspectual adverbs containing almost, nearly, practically, just about, etc. These adverbs are very similar to subject-oriented adverbs in that they may occur either immediately before the main verb or at the end of the clause:
(17) John almost/nearly/just about hit him(, almost/nearly/just about).
A problem is posed by the fact that they may co-occur with subject-oriented adverbs in either order with a concomitant difference in scope:Footnote 13
a. John nearly/almost deliberately hit him.= ‘John came close to deliberately hitting him.’
b. John deliberately nearly/almost hit him.= ‘John deliberately came close to hitting him.’
Data of this sort is clearly incompatible with Cinque’s (Reference Cinque1999) theory that adverb classes are introduced in strict hierarchical order, but the question remains how these different possible orders can be produced.
The simplest solution to this problem is to assume that certain heads such as vpred may project another head of the same category, thereby making them recursive.Footnote 14 If both subject-oriented adverbs and prospective aspectual adverbs modify vpred, this will immediately permit derivations such as (19) and (20):
(19)

(20)

Given the principles governing linearization of modifiers proposed earlier, derivation (19) will produce examples such as (18a), while derivation (20) will produce examples such as (18b). In addition, examples such as the following will be produced, along with the correct interpretations:
a. John hit him deliberately, almost.= ‘John came close to deliberately hitting him.’
b. John hit him almost, deliberately.= ‘John deliberately came close to hitting him.’
Notice that in order to produce the correct word order in English, it must be assumed that the higher vpred head projects a null ∅pred head and that both heads have an athematic argument selection feature. Evidence in support of both assumptions comes from bare infinitival complements such as the following:
a. I saw (*almost) John (*hit) (almost) deliberately *(hit) him.
b. I saw (*deliberately) John (*hit) (deliberately) almost *(hit) him.
It is predicted, however, that languages in which the main verb and/or the subject has greater freedom of occurrence will exhibit a wider range of variation than is found in English.
So far it has been assumed that the two adverb classes under discussion only modify vpred, but the following data suggests that they may have other selection possibilities:
a. John might deliberately have (nearly) hit him.
b. John might nearly have (deliberately) hit him.
c. ??John might deliberately nearly have hit him.
d. ??John might nearly deliberately have hit him.
Though it seems quite awkward to order both types of adverb (in either order) before the perfect auxiliary have, either one can appear by itself in that position with or without an adverb of the other type ordered after the perfect auxiliary. This pattern of data can be accounted for under the following assumptions: (i) both subject-oriented adverbs and prospective aspectual adverbs have the option of modifying either vperf or vpred; (ii) vperf, in contrast to vpred, is not recursive. Clearly, assumption (ii) is correct, since there can be no more than one perfect auxiliary per clause in English. Hence we may conclude that it is possible for a given type of adverb to select more than one projection in a clause.
3.1.2.3 Frequentative Adverbs
Still another class of adverbs that behave like typical modifiers of vpred are frequentative adverbs such as twice, many/few/etc. times, often, rarely, frequently, etc.:
(24) John (twice/many times/often) fouled the keeper (twice/many times/often).
Moreover, these adverbs can be ordered differently with respect to subject-oriented adverbs with accompanying differences in scope:
a. John twice intentionally fouled the keeper.
b. John intentionally twice fouled the keeper.
c. John fouled the keeper intentionally twice.
d. John fouled the keeper twice, intentionally.
Examples (25a) and (25c) refer to two different occasions on which John intentionally fouled the keeper, whereas (25b) and (25d) refer to John’s intentionally engineering two events of fouling the keeper. Such data is easily accounted for under the assumption that both frequentative adverbs and subject-oriented adverbs are vpred modifiers and that vpred, as proposed in the preceding section, §3.1.2.2, is recursive. Furthermore, frequentative, subject-oriented, and prospective aspectual adverbs can all be combined in varying orders (with varying degrees of naturalness) with concomitant differences of interpretation:
a. John almost twice intentionally fouled the keeper.
b. John twice almost intentionally fouled the keeper.
c. John intentionally twice almost fouled the keeper.
etc.
Thus (26a) means that John came close on two occasions to intentionally fouling the keeper, (26b) means that John on two occasions came close to intentionally fouling the keeper, (26c) means that John intentionally engineered two occasions on which he came close to fouling the keeper, and so forth.
Further complications ensue from the fact (cf. Cinque Reference Cinque1999: 25–27, following Andrews Reference Andrews1982), that frequentative adverbs such as twice, three times, etc. may have either a “high” or a “low” interpretation, as shown by the fact that the two may co-occur:
(27) John twice (often/rarely/ …) knocked twice (three times/ …) on the door twice (three times/ …).
The frequentative adverbs on the left quantify unambiguously over events, whereas those on the right refer to repetitive action, but there is no contradiction between having, for example, two separate events of repeating a knock three times. On the other hand, if a frequentative adverb occurs alone on the right edge it is ambiguous between the two interpretations:
(28) John knocked on the door twice (three times/often/rarely/ …).
All of these facts fall into place if it is assumed that adverbs such as twice, three times, etc. may modify either vpred or vtr. In the first case, they are interpreted as quantifying over events, in the second as referring to repetitive action. Assuming that vtr, in contrast to vpred, is not recursive, then we predict correctly that it should be degraded to combine adverbs such as well and hard, which are unambiguously manner adverbs, with low frequentative adverbs, producing contrasts such as the following:
a. John hit the ball well twice. (=John twice hit the ball well.)
b. ??John three times hit the ball twice well.
a. John knocked (hard) on the door (hard) twice. (=John twice knocked hard on the door.)
b. ??John three times knocked twice (hard) on the door (hard).
c. ??John knocked hard twice on the door.
Though judgments are necessarily delicate, given the possibility of parenthetical interpolation, it seems clear that (29a) is most naturally interpreted as referring to two occasions on which John hit the ball well, rather than a single occasion on which John performed an action both repetitively and hard. This is reinforced by the fact that examples such as (29b) with frequentative adverbs both to the left and to the right of the main verb, plus a manner adverb, seem quite degraded.
3.1.3 Epistemic Adverbs and the vΣ-projection
Consider next the class of epistemic adverbs that includes probably, certainly, possibly, etc. Note first that these adverbs occur most felicitously between a modal verb and the main verb, or at the right edge of the clause, making them look superficially just like agent-oriented adverbs:
a. John will probably kick (*probably) the ball (*probably) into the net (probably).
They cannot, however, be vpred modifiers because they cannot be felicitously interchanged with any of the vpred modifying adverbs just discussed:
a. He will probably inadvertently/almost/twice foul the keeper.
b. *He will inadvertently/almost/twice probably offend Mary.
Further evidence that these adverbs modify some projection higher than vpred derives from the fact they are excluded from bare infinitive complements:
a. *I will see him probably/certainly/possibly score a goal.
b. *The coach will make/have him probably/certainly/possibly score a goal.
The following data suggests that the head modified by epistemic adverbs must be at least as high as vperf:
a. He might possibly have (??possibly) offended Mary.
b. He might possibly have inadvertently offended Mary.
c. *He might inadvertently have possibly offended Mary.
a. He will probably have (??probably) left by now.
b. He will probably have deliberately snubbed Mary by now.
c. *He will deliberately have probably snubbed Mary by now.
But since the vperf head is optional, there must be some other head that epistemic adverbs can select. One obvious possibility is vtns. However, that would predict the adverb to occur to the left of an auxiliary element in vtns:
a. John probably will have left by now.
b. John possibly could inadvertently have offended Mary(, though I doubt it).
In fact, this does seem to be a possible position for epistemic adverbs (cf. §3.1.6 for further discussion), but the optimal position of these adverbs after an auxiliary in vtns is still not accounted for.
A clue to the correct analysis is provided by the fact that epistemic adverbs are robustly confined to a position to the left of negation:
a. John will (probably) not (*probably) have left yet.
b. John has (certainly) not (*certainly) left yet.
To account for this data, as well as for the fact that epistemic adverbs optimally follow an auxiliary element, I propose to adapt Laka’s (Reference Laka1990) analysis of polarity to the relational framework by assuming an obligatory projection vΣ below vtns but above vperf. The projection vΣ has a polarity feature with two values [pos] and [neg]. In English, if vΣ has the value [neg], it is realized phonetically as the overt negative element not, whereas if it is [pos], it is null.Footnote 15 Examples (36a) and (37a) can then be derived as follows:
(38)

3.1.4 Structure of Infinitive Complements
To round out this discussion of v-projections in the middle field of English, it is necessary to consider the position of the infinitival marker to. The standard analysis is that infinitival to is generated in T along with modal auxiliaries and present or past tense features, thereby explaining the complementary distribution between these elements. This account is incorrect, however, for a number of reasons.
First, the unmarked position of negation (and certain adverbs) in infinitive complements shows that to is not in T but in some head position below T:
a. John (*not) will/did (not) leave (*not).
b. John left (*not).
a. I persuaded John (not) to (?not) leave.
b. For (*not) John (not) to (?not) leave would upset Mary.
The obvious suggestion is that there must be another head position between T and v/Pr containing to, which I shall label “Inf(initive)”:
(41)

Importantly, this structure still leaves room for “focus” or “constituent” negation between Inf and v/Pr in “split” infinitives:
a. I persuaded John to NOT be polite.
b. For John to NOT be polite would upset Mary.
That both kinds of negation are necessary is demonstrated by the existence of “double negatives” in both finite and non-finite clauses:
a. John can’t NOT be polite. (= ‘John is incapable of not being polite.’)
b. I persuaded John not to NOT be polite. (= ‘I persuaded John that he should not fail to be polite.’)
Second, there are at least two modal elements in English that obligatorily co-occur with the infinitival marker to:
a. He ought to eat.
b. He is/was to leave tomorrow.
The nominative Case-marking of the subject shows that these clauses are finite, while the position of negation after ought and be shows that the modal elements ought and be are in T:
a. He (*not) ought (not) to leave.
b. He (*not) is (not) to leave tomorrow.
As we would predict, double negatives are also perfectly possible in these constructions:
a. He oughtn’t/ought not to NOT be polite.
b. He is not/isn’t to NOT leave.
Third, neither ought nor modal be can be main verbs, because they cannot co-occur with other T elements such as the regular modal auxiliaries:
a. *He can/will/didn’t ought to leave.
b. *He can/must/didn’t be to leave.
On the other hand, auxiliary elements such as perfect have are free to occur with these modals:
a. You ought to have been there.
b. He was to have been there by now.
Most modal auxiliaries in T in English require that Inf have the null phonetic realization ∅, but ought and modal be require that Inf must be lexically realized as to, showing that both T and Inf are necessary.
Finally, note that in many languages infinitival forms are marked with a morphological suffix, e.g. Fr. all-er ‘to go,’ Ger. geh-en ‘to go,’ etc. I will assume that in such languages the verbal root raises to Inf. That this is correct is shown by the position of negative element pas, which, as is well known, must precede the infinitive (cf. Pollock Reference Pollock1989):
(49) Ne pas manger (*pas) le diner, c’est criminale. ‘Not to eat dinner, that’s criminal.’
Incorporating this analysis of infinitive complements into the relational theory proposed here is straightforward. We may simply assume that there is another category vinf in v-projections which is above vpred but below vtns and vΣ. An example such as he ought (not) to eat will then be derived as follows:Footnote 16
(50)

In contrast, if v[+fin] is realized as must, then vinf must be realized phonetically as ∅:
(51)

Similarly, v[−fin] in standard English is obligatorily realized as ∅, as in I want him ∅ (not) to leave.Footnote 17
This analysis predicts correctly that subject-oriented adverbs optimally appear to the right of infinitival to, whereas epistemic adverbs appear to its left:
a. I wouldn’t want (??inadvertently) to (inadvertently) offend Mary.
b. I can’t persuade John (??intentionally) to (intentionally) insult his best friend.
c. For him (possibly) to (??possibly) unintentionally insult Bill would be unthinkable.
d. *For him unintentionally to possibly insult Bill is unthinkable.
Furthermore, it seems that the preferred position for the adverbs yet and ever is either immediately to the left of to or in clause-final position:
a. He (*yet) will (*yet) not (yet) have (??yet) left (yet).
b. He (*ever) will (*ever) not (ever) leave the house (ever).
c. For him (*yet) not (yet) to (??yet) have (??yet) left the house (yet) is crazy.
d. For him (*ever) not (ever) to (??ever) leave the house (ever) would be absurd.
Hence it may be concluded that these adverbs are modifiers of vinf, providing evidence for yet another adverb class.
3.1.5 Evaluative Adverbs
Consider next adverbs such as (un)fortunately, (un)luckily, (un)happily, etc. If these adverbs are treated as modifiers of vtns, we predict correctly that they can appear either to the left of a modal or auxiliary verb or at the right edge of a root clause and that they can co-occur with epistemic adverbs, which are modifiers of vΣ:
a. United (unfortunately) will not win the Manchester derby (unfortunately).
b. United unfortunately will probably not win the Manchester derby.
However, when used alone both epistemic and evaluative adverbs can appear either to the left or to the right of an element in vtns, indicating that both can select either vtns or vΣ:
a. United (unfortunately) will (unfortunately) lose the Manchester derby.
b. United (probably) will (probably) lose the Manchester derby.
This in turn predicts that exchanging the positions of the evaluative and epistemic adverbs in (54b) should be possible, though in fact such examples seem somewhat degraded:
(56) ?United probably will unfortunately not win the Manchester derby.
This may be a purely semantic scope effect, however, as suggested by the fact that a similar contrast can be produced by embedding the corresponding adjectives in opposite orders:
a. It is unfortunate that it is probable that United will not win the Manchester derby.
b. ?It is probable that it is unfortunate that United will not win the Manchester derby.
Finally, if it is assumed, as seems reasonable, that neither vtns nor vΣ are recursive nodes, then sentences with both types of adverb in either pre- or post-vtns position are correctly predicted to be degraded:Footnote 18
3.1.6 Pragmatic Adverbs
The last class of adverbs that will be considered here is that of pragmatic adverbs such as frankly, sincerely, honestly, etc., which normally (i.e. except when parenthetical) occur either at the beginning or the end of a root clause:
a. Frankly, I don’t like him(, frankly).
b. Quite honestly, he is nothing but a windbag(, quite honestly).
This distribution is nicely accounted for under the assumption that pragmatic adverbs are modifiers of ∅comp[D]:
(60)

Support for this analysis is provided by the fact, noted by Cinque (Reference Cinque1999: 12), that pragmatic adverbs cannot change positions with evaluative adverbs:
a. Frankly, I unfortunately don’t like him much.
b. *Unfortunately, I frankly don’t like him much.
The same is true of epistemic adverbs:
3.1.7 Conclusion: Modification is Neither Adjunction Nor v-projection
At this point, it is useful to summarize and draw some preliminary conclusions. Let us start by comparing modification, as defined here, with adjunction, as defined in X-bar theory. Adjunction structures are recursive, since any adjunct can always project another adjunct with no upper bound: [XP YPn [XP YPn−1 … [XP YP1 XP] …]]. Modifiers, in contrast, have only a single selection feature, hence are not inherently recursive. In the case of adverbs, the empirical facts clearly support a theory of modification rather than a theory of adjunction, because in general there can only be one adverb of a given type (e.g. manner adverbs) per clause. The problem with adjunction is that it wildly over-generates, incorrectly predicting that there can be any number of adjuncts of a given type, arranged in any possible order.
Based on this observation, it might be proposed instead, following Cinque (Reference Cinque1999), that each type of adverb is restricted to one and only one specifier position in a fixed hierarchy of adverbial heads in the extended projection of the verb. The problem with this theory is that it is too rigid, failing to account for a certain degree of variability in the ordering of adverb types that is empirically observable in natural language. There are at least three sources of variability identified earlier.
First, it has been shown that some adverb classes may select more than one v-projection, permitting them to occur in more than one position in PHON. In some cases, this arises from the fact that the same root may project adverbs of different types. Thus the adverb honestly is a pragmatic adverb in (62a), but a manner adverb in a sentence such He deals with people honestly. The adverb honestly is thus simply lexically ambiguous, since it may either select ∅comp[D] or vtr, with accompanying differences of interpretation. This type of variation is common to both Cinque (Reference Cinque1999) and the theory proposed here. However, we have seen that there are also cases where an adverb of a given type is simply able to select more than one head in the v-projection with no discernible difference in interpretation, thereby enabling it to appear in more than one position at PHON. Variation of this type can only be dealt with in Cinque’s theory by insisting that there is nevertheless some subtle difference of interpretation associated with the two positions. However, it is very difficult to discern any significant differences of interpretation between pairs such as John probably will win/John will probably win, he could unintentionally have offended Mary/he could have unintentionally offended Mary, etc.
Second, we have seen that adverbs quite generally can occur either in some clause internal position or at the right edge of a clause. The only way to account for this type of variation in a Cinque-style theory is to assume a fairly elaborate set of displacement operations, for which there is little, if any, independent motivation. In the relational theory proposed here, in contrast, variation of this kind arises simply from the fact that Spell-out (in the unmarked case) does not assign a fixed linear order to adverbs. This in turn is a consequence of the fundamental formal properties that distinguish modifiers from arguments and lexical projections.
Third, it was shown in §3.1.3 that certain v-projections such as vpred are, for independent reasons, recursive, thereby permitting a potentially indefinite number of different kinds of vpred-selecting modifiers to co-occur in different orders with concomitant differences in scope. Of the three types of variation, this is the most devastating for a theory such as Cinque’s, as has been pointed out by critics such as Ernst (Reference Ernst2001), who argue that adverb order must be semantically determined, at least in part. In the relation-based theory proposed here, however, there is a well-motivated syntactic explanation for such cases, making it unnecessary to abandon the autonomy of syntax.
In conclusion, a relational theory of syntax along the lines proposed here provides just the right degree of freedom needed to account for the empirically observed range of variation found in natural language systems of modification without massively over-generating, on the one hand, or being forced to resort to semantic explanations, on the other.
3.1.8 Degree Projections of Adverbs
To complete this discussion of adverbial modification, it is necessary to consider whether adverbs can have lexical projections of their own. In fact, it is widely assumed (cf. Abney Reference Abney1987, Bowers 1987, Reference Bowers2001a, Corver Reference Corver1990, Reference Corver1991, Reference Corver1997) that the degree words that typically occur with adverbs and adjectives are lexical projections of the category a in much the same way that determiners are lexical projections of the category n. Examples of degree constructions are the following:
a. John walked so slowly (that we got impatient with him).
b. John walked too quickly (for us to keep up with him).
c. John walked slowly enough (for us to keep up with him).
d. John walked more slowly (than he needed to).
e. John walked as slowly (as he could).
Ignoring for the moment the fact that degree modifiers may have an associated clause, let us see how they can be integrated into the structures proposed so far by adding the degree projection too to the derivation in (64):
(64)

Assuming that adeg is a lexical projection of amod, the adverbial projection in (64) will be linearized as too-slowly-slow. Note, however, that it is still the adverb slowly that selects vtr to modify, even though it projects a further category vdeg, because modifier selection is, by hypothesis, a property of particular lexical roots.
One might wonder how such a derivation is possible. It was shown in Chapter 2 that an argument may only be integrated with a v-projection when it has no lexical projection features left to satisfy, but in this case the process of integrating the modifier projection with the v-projection it modifies, effected when slowmod satisfies its modifier feature by selecting eattr, evidently must take place right in the middle of both an a-projection and a v-projection. These requirements are not contradictory, however, for the simple reason that slowlymod has two different types of selection feature, a projection feature [_adeg] and a modifier selection feature [_vtr]. Because they are different types of selection feature, they satisfy IG separately. The first satisfies IG within the subarray that produces the projection of the modifier slowly; the second satisfies IG at the point where the modifier projection is integrated into the v-projection of √eat. In fact, given these assumptions, IG dictates that this is the only derivation possible. With respect to linearization, no adverse consequences result, as the following derivation demonstrates:
a.
1 <√eat,eatth> eat-√eat 2 <eatth,dinner> dinner- eat-√eat 3 <eatth,eattr> eat-dinner-eat-√eat 4 <slowlymod,eattr> too-slowly-√slow-eat-dinner-eat-√eat 6 <eattr,dinner> dinner-too-slowly-√slow-eat-dinner-eat-√eat 7 <eattr,eatpred> eat-dinner-too-slowly-√slow-eat-dinner-eat-√eat 8 <eatpred,he> he-eat-dinner-too-slowly-√slow-eat-dinner-eat-√eat 9 <eatpred,will> will-he-eat-dinner-too-slowly-√slow-eat-dinner-eat-√eat 10 <will,he> he-will-he-eat-dinner-too-slowly-√slow-eat-dinner-eat-√eat b.
1′ <√slow,slowlymod> slowly-√slow 2′ <slowlymod,toodeg> too-slowly-√slow
Within the modifier subarray, which gives rise to the derivation shown in (65b), IG is satisfied by projecting first slowlymod and then toodeg. Within the main clause subarray, which produces the derivation in (65a), the selection feature of the modifier slowlymod is satisfied by forming a relation with eattr, after which the remaining selection properties of vtr are satisfied. Thus a degree word will always be linearized immediately to the left of an adverbial modifier that projects it, despite the fact that the latter is required to integrate with the head it modifies as part of the derivation of a projection within another subdomain.
Consider finally the clauses that may optionally be associated with degree words. It is generally assumed that there is a close dependency between the degree word and the associated clause, as evidenced by the fact that the form of the clause is determined by the degree word. Thus so requires an associated finite that-clause, too requires a non-finite infinitive, -er/more requires a finite clause headed by than, etc. However, it has always been somewhat of a puzzle why degree clauses obligatorily appear to the right of the adverbs they modify while the degree word must appear to its left. In a theory based on constituent structure there is no way to express the dependency between degree heads and their associated sentences without assuming an extra unmotivated movement operation that moves the sentence into its correct position in PHON after the adverb:
(66)

To solve this problem, we need to think a bit more about the nature of degree words and their associated clauses.
It has been assumed so far that degree words are simply lexical realizations of the category adeg. There are, however, two reasons for thinking that this might be incorrect. First, there are two cases in English in which the degree element is not a word but a morpheme:
a. John ran fast+er than Bill did.
b. John ran fast enough to catch Bill.
In (67a) the comparative is realized as a morpheme -er attached to the adverb root, while in (67b) the degree word enough is apparently cliticized to the right of the adverb root rather than appearing to its left. In order to account for these cases, it must be assumed that the phonetic form of the adverb root is pronounced at the position of the degree head in order to avoid morphological ill-formedness at PHON. Supposing, then, that adeg in English is an illegible category, it follows that the adverb root must be pronounced there in order for adeg to be interpretable at PHON. This in turn entails that morphologically simplex degree words such as so, too, as, more, etc. must actually be arguments of a special sort selected by adeg, in which case they must themselves be projections of some category. What category could that be? An indication is provided by the fact that at least two degree words in English, namely, too and more, can themselves be modified by number expressions such as much, a bit, a lot, a good deal, etc.:
a. John ran much/a bit/a good deal too fast for me to catch him.
b. John ran much/a bit/a lot more slowly than Bill did.
These quantifiers are associated with the n#-projection and modify mass nouns such as milk, water, discussion, etc., e.g. much milk, a lot of water, a bit of cash, a good deal of discussion, etc., suggesting that degree words are highly specialized “small nominal” projections selected by adeg. Which degree word is selected, we may assume, is determined by features such as [comp(arative)], [equ(ative)], etc. in the degree head.
Returning now to the clauses associated with degree words, it is generally assumed, for the reasons noted earlier, that there is a close dependency between the degree word and the associated clause. Let us assume that degree clauses are in fact modifiers of the vdeg head, as is suggested by the fact that they are always optional:
(69)

It is immediately apparent that the linearization principles for modification correctly predict the following possible order of elements:
(70) so-slowly-slow-√slow-that …
The degree word so precedes slowly because it is selected by slowlydeg, whereas the phonetic form of the degree clause may follow the sequence of elements so-slowly-slow-√slow because it is a modifier of slowlydeg. The correct ordering thus follows automatically from general principles in the relational theory proposed here without having to posit an additional unmotivated displacement operation.
There is, however, one problem. If, as I have argued, the linear ordering of modifiers is generally free in English, that would seem to predict, contrary to fact, that the degree clause should also be able to appear to the left of the degree word:
(71) *that … -so-slowly
As it happens, this is just the order that tends to occur in postpositional languages (Greenberg Reference Greenberg and Greenberg1963: 89). Clearly, what we are dealing with here is just a case of language-specific parameterization. In English, sentential modifiers of a degree head may only be linearized rightward, whereas in other languages it is the reverse. As noted earlier, this is part of the much larger problem of explaining syntactic variation, which will be addressed in Chapter 4.
3.2 Adjectival Modification
Perhaps the most immediately striking property of adjectival modification of nominals is the often noted difference between prenominal and postnominal adjectives. While the latter can be full APs with degree heads and complements, the former are sharply restricted, being unable to occur with either. However, prenominal adjectives, though unable to occur with degree words, may nevertheless be modified by certain -ly adverbial modifiers. These generalizations are illustrated as follows:Footnote 19
a. that student so smart (that everybody is jealous of him)
b. *that so smart student (that everybody is jealous of him)
c. *that so smart that everybody is jealous of him student
d. that (remarkably) smart student
To these observations we may add the fact that in many languages (e.g. Dutch and German), prenominal modifiers agree in number, gender, and Case with the head noun, whereas postnominal AP modifiers do not. If AP modifiers were simply NP-adjuncts that could occur on either a left branch or a right branch, as is often assumed in the literature, none of these differences could be explained systematically.
3.2.1 Postnominal Adjectival Modifiers
To account for the fact that full AP modifiers of nominals occur on the right edge of the nominal expression, let us assume that aprop may be a modifier of nnom. Thus a phrase such as a student of physics so proud of his theory would be derived as follows:
(73)

Since the entire phrase so proud of his theory is a modifier of nnom, it must follow the phonetic form of studentnom, producing the correct linear order a-student-of-physics-so-proud-of-his-theory. Notice, however, that because modifiers in general either proceed or follow the head they modify, we should also be able to produce the incorrect order: a-so-proud-of-his-theory-student-of-physics. Once again, we are up against the brute fact of syntactic variation: in some languages complex adjectival modifiers must appear to the right of the noun they modify and may not appear to the left, whereas in other languages it is just the opposite. Exactly the same problem arises with relative clauses, which may also be analyzed as modifiers of nnom. In some languages, such as English, relative clauses must follow the phonetic form of nnom, e.g. the student of physics that I know, and may not precede it: *the that I know student of physics. In other languages it is the opposite. I put aside for the time being the problem of accounting for syntactic variation of this sort, returning to it in Chapter 4.
3.2.2 Prenominal Adjectival Modifiers
Turning now to prenominal adjectives, let us consider whether a relational theory can shed light on their special properties. An important insight is provided by Emonds (Reference Emonds and Torrego2012), who argues that prenominal adjectives are actually derived nominals formed by combining an adjective with the φ-features of gender and number (and in some languages Case as well). Thus he proposes the following structure for a phrase such as a smart student:
(74)

Emonds argues persuasively that this analysis explains a whole series of differences between prenominal and postnominal adjectives that correlate with agreement on the former and lack of agreement on the latter. What is distinctive about English, he claims, is that despite the fact that prenominal adjectives have lost all overt agreement morphology, they nevertheless behave exactly like the inflected prenominal adjectives of languages such as Dutch and German.
There is, however, one difficulty with Emonds’ proposal, namely, the fact mentioned earlier that prenominal adjectives, though they cannot project degree heads or select arguments, can be modified by -ly adverbs:
(75) an extremely smart, surprisingly nice student
This is a problem for Emonds’ analysis because prenominal adjectives are nouns and nouns can never be modified by -ly adverbs:
(76) *a surprisingly house
I therefore propose to modify Emonds’ theory, at the same time recasting it in relational terms, in the following way. Let us assume, first, that nnom may optionally project a nominal head with φ-features that I will designate nφ. Now let us assume that nφ may either project ndet or another nφ, making it possible to project an unbounded number of nφ heads, ordered to the left of the nominal root pronounced in nnom. The category nφ is thus recursive in much the same way as vpred. Second, let us assume that each nφ projection, though itself phonetically null, selects as an argument a “small adjective” argument aprop whose φ-features match those of nφ. Given these assumptions, a phrase such as the nice little old house can then be derived as follows:Footnote 20
(77)

Assuming that the entire n-projection, including nnom and ndet, has nominal φ-features and that the values of these features must be uniform for any given projection, this will ensure that prenominal adjectives agree in number and gender (and in some languages in Case as well). As far as I can see, this relational version of Emonds’ hypothesis has all the desirable features he adduces in its favor with the added attraction of allowing prenominal adjectives to be modified by adverbs, since they are adjectives rather than nouns.
This analysis, if correct, makes the claim that prenominal adjectives bear quite a different syntactic relation to the noun they modify than do postnominal adjectives, providing support for the view first expressed by Abney (Reference Abney1987) that prenominal and postnominal adjectives are not mere positional variants of one another. Specifically, whereas postnominal adjectives are modifiers, prenominal adjectives are n-projections of a special sort that select a restricted kind of adjectival argument. This analysis explains the fact that prenominal adjectives in English differ markedly from adverbs in that the direction of selection can only be uniformly leftward.Footnote 21
Notice also that the constraints on the form of prenominal adjectives that are particular to English, i.e. lack of degree elements and complements, can easily be built into the selection conditions of nominal projections. Thus nφ in English may only select a minimal aprop projection, ruling out examples such as *a so tall student and *a proud of his work student, whereas in a language such as German prenominal adjectives are not so restricted.
Finally, it is worth considering briefly how the semantics of predication is derivable from structures in which prenominal adjectives do not modify nouns directly, but rather are selected by a nominal head which is itself a projection of the noun in question. Let us assume that the denotation of mannom is a property, hence ⟦mannom⟧= λx man(x), of type <e,t>. Assume now that selecting a new nφ projection simply adds a new property whose denotation is associated with the a-projection selected by nφ. To be more specific, suppose that the denotation of ⟦nφ⟧ = λfλgλx[f(x) ∧ g(x)], of type <<e,t>,<e,t>>. Applied first to the property λx man(x), then to the property λx[tall(x)], this reduces, by λ-conversion, to the expression λx[man(x) ∧ tall(x)]. Thus each new nφ-projection combines a new property with the property of the noun itself to form, in effect, a compound permanent property, whose individual variable x will eventually be bound by an operator such as ι, ∃, or the generic operator Gen.
3.2.3 Adverbial Modifiers of Prenominal Adjectives
Turning now to -ly modifiers of adjectives and adverbs, let us try to determine precisely what their nature is. One thought is that they are simply a kind of degree word that happens to lack an associated sentence. This cannot be correct, however, since they may co-occur with degree words:
a. John ran so incredibly fast that nobody could keep up with him.
b. Mary is even more amazingly generous than Sue is.
c. Bill is too annoyingly condescending to put up with.
Another important property of these adverbs is that, unlike the sentence adverbs discussed earlier, they only occur to the left of the adjective or adverb they modify, never to the right:
a. John ran (incredibly) fast (*incredibly).
b. Mary is (amazingly) generous (*amazingly).
c. Bill is an (annoyingly) condescending (*annoyingly) person.
These two properties of these adverbs, combined with the fact discussed in §3.2.2 that they can modify both prenominal and postnominal adjectives, suggest that rather than being modifiers of the adjectives and adverbs they are associated with, they must be projected by them. Under this view the relation between a -ly adverb and the adjective or adverb it modifies is very similar to the relation between a prenominal adjective and the noun it modifies. In support of this idea, notice that there are different types of adverbial modifiers, as is revealed by the appropriate paraphrases:
a. Extent: extremely condescending = ‘condescending to an extreme extent’
b. Psychological: annoyingly condescending = ‘condescending in a way that is annoying (to someone)’
c. Intentional: deliberately condescending = ‘condescending in a deliberate manner’
d. Possibility: improbably condescending = ‘condescending in a way that seems improbable’
e. Evaluative: absurdly condescending = ‘condescending to the point of absurdity’
Furthermore, more than one type of adverb can modify the same adjective or adverb:
a. He is extremely, annoyingly condescending.
b. He was deliberately, annoyingly condescending.
c. He was extremely, improbably condescending.
d. He was improbably, deliberately, annoyingly condescending.
Thus pre-adjectival and pre-adverbial -ly modifiers can be iterated in much the same way as prenominal adjectives.
To be more concrete, let us assume that aprop can project a null head that I shall call aqual with some feature such as [psych]. This aqual can in turn select another null aqual with a different feature such as [int], thereby permitting an indefinite number of -ly qualifiers to be projected, exactly parallel to the case of prenominal adjectives. Each of these aqual heads is itself required to select an amod head projected from a root with the appropriate feature, thereby generating a projection such as the following:
(82)

In short, the relation between -ly adverbial qualifiers of adjectives and adverbs is quite different from the relation between sentential -ly adverbs and the heads they modify, in a way that parallels the difference between prenominal and postnominal adjectives.
3.3 Conclusion
It was shown in the first two chapters that the two most fundamental relations between words in natural language syntax are argument selection and lexical projection. If the speculations advanced in this chapter are anywhere near the mark, there is one additional fundamental relation between words found in natural language, to which I have given the traditional name modification. Modification is quite different from selection and projection in a number of ways, all of which stem ultimately from the fact that a modifier is never, by definition, selected as an argument, hence operates orthogonally to the selection/projection plane of the head it modifies. First, modifiers only select unsaturated heads, hence do not interact in any way with the selection and projection properties of the modified head. Second, the Spell-out algorithm does not specify, in the unmarked case, the direction of selection of modification. Hence they are free to be linearized either to the right or to the left of the heads they modify unless restricted by a language-specific parameter. Third, modifiers are always optional because they are unselected. Despite these special properties of the modification relation, its existence is entirely predictable, given the primitives that underpin the relational theory proposed here. Finally, we have seen that not all elements traditionally described as modifiers, in a broad sense, are necessarily instances of the modification relation. In particular, prenominal adjectival modifiers, as well as adverbial qualifiers of both adjectives and adverbs, arise through an entirely different mechanism which is basically an extension of projection and selection, as is evidenced by the fact that their empirical properties are distinct in many ways from those of free modifiers.



















