1.1 Head movement and the controversy surrounding it

Heads can be spelled out higher than their merge-in position. For instance, the exponent of a verb is expected to appear in the verb phrase, but in certain languages (and certain types of clauses) it appears higher, in the inflectional or the complementizer domain. Naturally, this has an effect on the word order of the clause.

Let us consider the specific examples in (1).

In English, the verb is in the vP because it follows negation and adverbs, the sign-post elements that mark the left edge of the verb phrase. In French and German, however, the exponents of the verbs appear outside of the vP. In French the verb follows the subject but precedes negation (1b), so it is in a position above NegP but still in the IP-domain. In German non-subject-initial root clauses, on the other hand, the verb is obligatorily in the second position; it precedes the canonical positions of the subject, object, and negation (1c), and so it is in the CP-domain.¹

Pre-theoretically, we can use the term head movement (HM) as the name of the operation that the transformationalist generative literature uses to model the word order difference between (1a), (1b) and (1c). There is currently great controversy over what grammatical mechanism this operation exactly corresponds to: whether it is movement or not, and if it is movement, what exactly moves (only a head or a whole phrase), where it moves, and in which component of the grammar. While both ingredients of the label “head movement” are under debate, it will serve as a useful descriptive term for the operation involved in the word order difference between (1a) to (1c) thoughout this paper.

The proposed alternatives of what HM exactly involves fall into four main groups.

The operation of HM is:

• syntactic movement

• a combination of syntactic movement and a post-syntactic operation

• post-syntactic movement

• post-syntactic and involves no movement; it falls out from the way the syntactic hierarchy is translated into linear oder

The aim of this paper is to offer a balanced discussion of these alternatives and to evalue their strengths and weaknesses.

1.2 Constraints on HM

While the exponent of a head can occur higher than the merge-in position of that head, not all logically possible types of patterns are attested. Researchers have come to the conclusion early on that the operation that is used to model the data must be subject to three constraints, or else overgeneration cannot be avoided.

The first constraint applies to morphologically complex heads. The HM operation always displaces the exponent of the head from the merge-position of the head. In some cases the displaced exponent remains morphologically unaltered. We can observe this in English matrix yes-no questions, where the preposing of the auxiliary from T to C does not change the form of the auxiliary.

In other cases, the change of the base-generated word order is also accompanied by word formation: affixation of a stem with derivational and/or inflectional suffixes (3) or incorporation of a noun into a(n inflected) verb (4b).

As first discussed in Baker (1985), the internal structure of complex words created by HM reflects the underlying syntactic structure of the given expression.

What the Mirror Principle says is that an affix that spells out a lower head will end up closer to the root than an affix that spells out a higher head.² This way the morphological make-up of words allows insights into the syntactic hierarchy of functional projections. For instance, on the basis of the morphology of the Hungarian verb in (6a) we can conclude that the syntactic hierarchy of the causative, modal, and tense heads is as in (6b).

The first constraint on the HM operation is that it cannot break up the morphologically complex heads that it creates at a later point in the derivation: there is no excorporation from complex heads. This restriction is a subcase of the Lexical Integrity Hypothesis.

The no excorporation condition amounts to saying that head movement is always “roll-up” movement and there is no successic cyclic head movement; chains of head movement are maximally two-member chains.

The second constraint on the operation is that it is strictly local: it always establishes a relation between two structurally adjacent heads. This has been formulated as the Head Movement Constraint (Travis 1984).³

In cases in which a head apparently moves to a structurally non-adjacent higher head position, e.g. when V ends up in C, we have the successive creation of separate local chains: V-to-T and then T-to-C. V ends up in C because it is pied-piped by T when T moves to C.

Thirdly, the HM operation is clause-bound, or more generally, it applies only within but not across extended projections.⁴

Importantly, these constraints do not apply to phrasal movement. Phrasal movement can skip intermediate phrasal positions; it is not the case that it has to target the next higher specifier. Phrasal movement can also be successive cyclic: phrases can touch down in intermediate positions and move further on without pied-piping any other material with them. Finally, phrasal movement can cross clausal boundaries giving rise to so-called long movement (long wh-movement, long topicalization, long focalization, etc.).

1.3 The structure of the paper

This paper is organized as follows. Section 2 discusses the GB-style syntactic adjunction analysis proposed for (1b) through (4b), as well as the theory-internal arguments that were leveled against this analysis. Approaches that maintain that data like (1b)–(4b) should be captured with a syntactic operation will be surveyed in Section 3. A model in which such data arise as a result of a syntactic movement followed by a post-syntactic operation will be discussed in Section 4. Theories that account for these data with a post-syntactic displacement operation will be the topic of Section 5. The analysis of (1b) to (4b) as positioning via syntax-phonology mapping is taken up in Section 6. I will discuss to what extent these theories can eliminate the problems posed by the adjunction analysis as well as the new problems they give rise to.⁵ In the current Minimalist framework, the most important question is whether (1b) through (4b) should be modeled by a narrow syntactic operation or not. Section 7 addresses arguments related to this issue. Section 8 concludes the paper.

3.1 Sideward movement

The first syntactic alternative to head-adjunction to be discussed here is sideward movement, i.e. movement of heads between different derivational spaces. This approach is pursued in Nunes (1995; 2001; 2004); Bobaljik & Brown (1997) and Uriagereka (1998).

3.1.1 The mechanics

Mainstream generative grammar holds that structure building proceeds in a bottom-up fashion.¹⁷ A consequence of this approach is that whenever a head merges with an internally complex specifier (or a phrase merges with an internally complex adjunct), syntax must make use of two different workspaces (aka. derivational spaces) in parallel. Consider the case in which v takes a subject NP/DP in which the noun has a modifier, e.g. three cats. Before merger of the subject and v′, we have the two syntactic objects in (17).

(17)	a.
	b.

Crucially, (17a) is internally complex and must have been built independently of (17b). So in order for the derivation to reach the stage with the two objects in (17), syntax must have used two parallel workspaces: one to construct (17a), and another, independent one to create (17b).¹⁸

Nunes (1995; 2001; 2004); Bobaljik & Brown (1997) and Uriagereka (1998) suggest that movement can take place between two parallel workspaces. They call this type of movement sideward movement, interarboreal movement or paracyclic movement, and suggest that HM also proceeds in this fashion.

The standard approach holds that a head Y can move to the next higher head, X, only after X has merged with its phrasal complement YP (see Section 2). The sideward movement analysis abandons this assumption and suggests that the order of operations is exactly the other way around. Consider the case of v-to-T movement, for instance. (The internal structure of v resulting from V-to-v is ignored for expository purposes). Once the vP is constructed, the head T is placed into a workspace separate from vP (18).

(18)	a.	workspace 1
	b.	workspace 2
		T

In the sideward movement approach, the next step is that v moves out of workspace 1 into workspace 2 and adjoins to T. This creates a complex head in workspace 2. At this stage, the two instances of v are not in a c-command relationship.

(19)	a.	workspace 1
	b.	workspace 2

Next, the trees in (19a) and (19b) are merged with each other. At this stage, we have a structure that contains two non-distinct instances of v, and (on Kayne’s definition of c-command) these instances are in a c-command configuration. Consequently, they are interpreted as forming a chain and Chain Reduction silences the lower copy at PF.

1. (20)

1. 

The final output of the sideward movement approach is the same as the output of the head-adjunction analysis discussed in Section 2.

3.2 Agree with a defective goal

In an analysis developed in Roberts (2010) and taken up in Livitz (2011); Aelbrecht & Den Dikken (2013); Walkden (2014) and Iorio (2015), among others, head-adjunction is replaced by Agree between a probing head and a head that serves as its defective goal.

3.2.1 The mechanics

In this analysis HM happens when a probe and a goal enter into a syntactic Agree relationship, and the goal’s formal features are a proper subset of the probe’s. A goal in such a relationship is called a defective goal.²¹

(21)	Defective goal
	A goal G is defective iff G’s formal features are a proper subset of those of G’s Probe P. (Roberts 2010: 62)

After Agree, all of the features of the defective goal are also present on the probe, and the goal incorporates into the probe. As a result of this mechanism, the goal’s features are pronounced at the probe.

Let us consider the case of v-to-T as a specific example.²² This movement happens when T has an interpretable Tense-feature and an uninterpretable V-feature (as well as ϕ-features to be valued by the subject), while v has an uninterpretable T-feature and an interpretable V-feature. In the trees below, the ϕ-features and the internal structure of v (after V-to-v movement) are ignored for simplicity of exposition.

(22)	Environment for Agree

The Agree relationship beween T and v exhausts the goal’s features: after Agree the label of T contains valued versions of v’s features. Crucially, originally unvalued features are assumed not to undergo deletion at the transfer of the phase. So as a result of Agree, the same set of features will be present both in v’s label and within T’s label at the final stage of the derivation. As T c-commands v, the two sets of identical V and T features will be interpreted to form a chain. This means that the output of Agree with a defective goal is formally indistinguishable from the output of Move. The resulting configuration allows v to adjoin to T in an incorporation operation. The result is a derived minimal head, a T^min rather than a T⁰.

(23)	v-to-T: valuation, incorporation

At this point the iV and uT features are present at two places, and the higher instances (in T^min) c-command the lower instances (in v). They are therefore subject to regular chain reduction when the structure is linearized. As usual, it is the head of the chain that receives phonetic form and the tail remains silent. In other words, we have “the PF effect of movement” (Roberts 2010: 61).

(24)	Chain reduction

3.3 Reprojective movement

In another recent analysis of data like (1b) through (4b), a head projects a phrase, moves up and adjoins to that phrase, and then projects another phrase with a different label. This approach is advocated, among others, in Koeneman (2000); Bury (2003); Fanselow (2004); Surányi (2005; 2008) and partly also in Biberauer & Roberts (2010) and Roberts (2010) for the verbal domain, in Donati (2006) for wh-movement in free relatives, and in Georgi & Müller (2010) for the nominal domain.

3.4 Phrasal movement

The final syntactic alternative to head-adjunction is (complete or remnant) phrasal movement. This view is advocated by Koopman & Szabolcsi (2000); Massam (2000); Rackowski & Travis (2000); Kayne & Pollock (2001); Mahajan (2003); Nilsen (2003); Müller (2004); Pollock (2006) and Bentzen (2007) for verb movement, and by Shlonsky (2004); Cinque (2005) and Cinque (2010) for noun movement, to mention just a few.

Some proponents of the phrasal movement analysis hold that syntax cannot move heads at all; data like (1b) to (4b) always involve phrasal movement (Mahajan 2003). Others allow for syntactic movement of heads under restricted circumstances, while maintaining that the majority of the relevant data are derived by phrasal movement (e.g. Koopman & Szabolcsi 2000: 41–42).

4.1 The mechanics

In Section 2 we have seen that in BPS head-adjunction violates the Chain Uniformity Condition. Some researchers suggest that this condition is too strong (or wrong), however. Matushansky (2006); Vicente (2007); Gallego (2010) and others propose that heads move to phrasal (specifier) positions rather than adjoin to higher heads. v-to-T, for instance, involves v moving to Spec, TP, as in (34) (the results of the earlier V-to-v step are not shown here).³² This step is followed by a rebracketing operation called morphological merger (m-merger). M-merger forms a complex head out of the moving head and the head whose specifier serves as the landing site (35). The output of HM to specifier followed by rebracketing is a head adjunction structure, just like in the case of the GB-style head-adjunction approach.³³

M-merger is subject to the constraints in (36). When these conditions are met, m-merger is obligatory. This means that movement of a head is always followed by m-merger.

There is some disagreement as to which grammatical component m-merger is part of. Matushansky (2006) argues that m-merger takes place post-syntactically. She suggests that syntax interfaces with the post-syntactic component after every Merge operation. This means that while movement and rebracketing take place in different components of the grammar, rebracketing can still immediately follow the movement. She argues that rebracketing returns a feature bundle, and it also involves partial spellout of the rebracketed structure, i.e. the complex head. The rebracketed and spelled out structure is then handed back to narrow syntax, where the derivation can continue.

Importantly, in this approach both the syntactic and the post-syntactic component are implicated in every individual step of HM. There are other approaches, too, in which both syntax and post-syntax have a role to play (see esp. Harizanov 2016; Gribanova 2017b and Harizanov & Gribanova accepted and the references in fn. 58). However, in these models syntax and post-syntax do not work together in any individual step of head movement: each HM step is either purely syntactic or purely post-syntactic. For instance, in these models V-to-v could be syntactic and v-to-T could be post-syntactic, but the syntactic and post-syntactic components are never both involved in V-to-v or v-to-T.

Vicente (2007) and Gallego (2010), on the other hand, argue that m-merger takes place in narrow syntax; post-syntax is not involved in the HM operation at all. Their analysis thus forms a natural class with the approaches surveyed in Section 3 in a way that Matushansky’s does not. Vicente argues that complex heads are not opaque to syntactic operations in general. For instance, parts of complex heads are accessible for binding and coreference relations (Section 2.2.2) and possibly also variable-binding (Vicente 2007: 17, fn. 11). Therefore spellout cannot be involved in m-merger. It is only movement that complex heads are opaque to. For Vicente (2007: 48), m-merger has a morpho-phonological trigger: word formation (“it happens so that two morphemes can be spelled out as a word”); and the no excorporation condition is a phonological restriction.³⁴

4.2 The pros and cons of this approach

The movement to specifier plus rebracketing analysis solves many problems raised by head-adjunction. It eliminates the problem with the Extension Condition because it involves a cyclic movement: it extends the root of the tree. This analysis does not require a cumbersome definition of c-command either, as the moved head straightforwardly c-commands its lower copy from the specifier position. Matushansky further proposes that if m-merger is taken to return a feature bundle, then we can derive the no excorporation condition, as syntax can move whole feature bundles but it cannot subextract from them.³⁵ She suggests that the Head Movement Constraint can also be derived if we assume that the movement takes place to check a c-selectional feature on the higher head by the lower head. Since c-selection is a relation between a head and (the head of) its complement, the moving head will always target the next higher, selecting head. Gallego (2010) proposes that the anti-locality problem can also be solved if after head movement both the moved head and the target head project, creating a hybrid label, e.g. after v-to-T movement, the label is the composite v-T. As the creation of this new label becomes possible only as a result of the movement, anti-locality is not violated. Movement to specifier plus rebracketing still violates the A-over-A Principle, however.

There is also an important new problem that arises with this particular approach: rebracketing does not look like a licit syntactic operation, and it also violates the Extension Condition. One answer to this problem is to relegate it to the post-syntactic component, as Matushansky does. This requires syntax to interface with the post-syntactic component at every step. Richards (2011), however, shows that this is difficult to reconcile with phase theory.³⁶

5.1 Post-syntactic movement, PF movement

According to current Minimalist ideas, syntax manipulates abstract units without phonological content. When the syntactic derivation reaches the point of Spell Out, the derivation splits into two branches. One branch ships the syntactic structure to the LF interface (LF branch), while the other branch ships the syntactic information to the PF interface (PF branch).³⁸

An explicit theory of the mapping from Spell Out to the PF interface is provided by Distributed Morphology (DM). According to DM, in the early phase of the PF branch nodes are still in the hierarchical arrangement that syntax has created. This hierarchy can be slightly modified by a few types of morphological processes (Fusion, Fission, Lowering, etc.) that happen due to language-specific morphological or morpho-phonological requirements. This is followed by Vocabulary Insertion (the pairing of abstract nodes with Vocabulary Items) and Linearization. After Linearization, phonological information is present in the representations, but hierarchy is not; morphemes are related to each other by precedence and subsequence rather than c-command or dominance. Linearization is followed by various phonological processes, e.g. the building of prosodic domains. The final product of the mapping from Spell Out to PF is Phonological Form (see Embick & Noyer 2001: Fig. 1.).

To the best of my understanding, all analyses that claim that HM is PF movement mean that HM takes place after Spell Out, in the PF branch of grammar, but before Vocabulary Insertion/Linearization. What this means is that HM applies in a part of grammar that follows narrow syntax, but which still retains the hierarchy produced by syntax. There is no analysis, as far as I understand, that claims that HM takes place after Vocabulary Insertion/Linearization, when only precedence/subsequence information is accessible to the representations. In the rest of this paper, post-syntactic movement and PF movement will be used as synonymous terms and will refer to movement that takes place after Spell Out but before Linearization.

5.2 Arguments that HM takes place after syntax

Chomsky suggests that since HM has no semantic effect, it plausibly takes place at PF and is “conditioned by the phonetically affixal character of the inflectional categories” (Chomsky 2001: 38). He observes that none of the movements that he assumes to take place at PF can iterate, and raises the possibility that lack of iteration is a property that characterizes PF operations in general.³⁹

Beyond this, he says very little about the nature of PF movements. He suggests that one of the PF movements, namely Thematization/Extraposition, adjoins the internal argument to vP in the case of rightward movement, while it substitutes the internal argument in Spec, vP in the case of leftward movement (Chomsky 2001: 23). From this, it is clear that this type of PF movement takes place in the part of the PF branch where hierarchy is still retained (i.e. before Linearization), but this is never made explicit. We can assume that heads also move in this part of the PF branch (but this is again not claimed explicity). This is consistent with his proposal that HM does not to create a chain (Chomsky 2001: 39): post-syntactic movements in DM (such as Lowering) are assumed not to leave a trace.

While the theoretical arguments for HM being a post-syntactic movement come from the lack of semantic effects, the empirical arguments mainly involve data from ellipsis constructions. Boeckx & Stjepanović (2001) argue that pseudogapping constructions support the idea that heads move at PF. Lasnik (1999) observes that in English non-elliptical sentences the verb has to raise, but in pseudogapping constructions the verb may either raise or stay put and be part of the elided constituent. In Boeckx & Stejepanović’ interpretation, this means that ellipsis can apply before HM, and since ellipsis takes place at PF, it follows that so must HM. They do not make any suggestions as to how PF movement works, however.⁴⁰

Schoorlemmer & Temmerman (2012) study verb-stranding VP-ellipsis, i.e. ellipsis that affects all arguments and adjuncts in the verb phrase but not the main verb itself. (This is attested e.g. in Portuguese, Irish and Semitic.) The literature agrees that this kind of ellipsis is regular VP-ellipsis except for the fact that the verb moved out of the ellipsis site. This kind of ellipsis, however, presents an apparent paradox. It is well known that there is a general identity requirement on elided elements: in order to be recoverable, the element in the ellipsis site and the corresponding element in the antecedent have to be identical. For verbs, for instance, this means that the antecedent and the ellipsis site must contain the same verb(al root). The apparent paradox is that in verb-stranding VP-ellipsis the verb is not elided, but (modulo inflectional affixes) it still has to be identical to the verb in the antecedent. Goldberg (2005) proposes that this is because at LF, the verb is within the ellipsis site, and this forces it to be interpreted identically to the verb in the antecedent. Schoorlemmer & Temmerman (2012) pick up on this suggestion and argue that the verb is in the ellipsis site at LF because it does not move out of the VP either in narrow syntax or at LF; the movement takes place at PF only (see also McCloskey 2017). This movement thus affects the linear order but not the interpretation (and so being in the ellipsis site at LF, the verb is subject to the identity requirement on ellipsis).⁴¹

It is interesting to note that both Boeckx & Stjepanović (2001) and Schoorlemmer & Temmerman (2012) use VP-ellipsis and verb movement to argue that (at least in certain cases) heads move at PF, however, in order for the Boeckx & Stjepanović (2001) analysis to work, ellipsis has to be able to precede HM at PF (or ellipsis and HM apply at the same time, and one has to choose between them), while for the Schoorlemmer & Temmerman (2012) analysis, HM must be able to precede ellipsis at PF.⁴²

That data from ellipsis support placing the HM operation into the PF component has been seriously challenged in the recent literature. In direct opposition to Schoorlemmer & Temmerman (2012), Gribanova (2017a) argues that the identity condition in verb-stranding ellipsis is actually an argument for HM being a narrow syntactic operation. Stripped to its essentials, her argument proceeds like this: HM influences the way parallel domains are calculated between the antecedent and the ellipsis site, therefore it feeds LF, therefore it must be syntactic. (The paper offers detailed argumentation which I cannot reproduce here for reasons of space.) Relatedly, Lipták (2017) shows that the identity condition on verbs studied by Schoorlemmer & Temmerman cannot be due to the special nature of HM. On the one hand, the same condition also holds in answers to questions that involve no ellipsis, therefore it is not an effect of ellipsis or HM out of an ellipsis site. On the other hand, an identity condition also holds of certain XPs moving out of ellipsis sites (see also Gribanova 2017a). This means that the identity requirement is independent of heads, and so it cannot be used as an argument for the special nature of the movement of heads.

Gribanova (2017b) points out, however, that authors who study ellipsis and come to contradictory conclusions about the place of the HM operation in grammar (syntax or post-syntax) are looking at different languages. She suggests that it is possible that all of them are right for the particular cases they are studying. Specifically, two different operations may have data like (1b) to (4b) as their output, and while one of these operations takes place in syntax, the other happens in the PF branch.⁴³ If this is so, then data from different languages must be looked at on a case-by-case basis, and a compelling argument from one case does not warrant definitive conclusions about the HM operation across the board.

5.3 The mechanics

In general, proponents of the PF movement analysis do not address the question of what the exact mechanism of post-syntactic HM is. As Boeckx & Stjepanović (2001: 353) acknowledge, “a full-fledged theory of PF operations remains to be worked out before the view that head movement falls outside the core computational system can be fully endorsed”. To my knowledge, the only work that addresses this issue is Harizanov & Gribanova (accepted).⁴⁴ This paper suggests that data which GB analyzed with head-adjunction can arise either as a result of a syntactic operation or as a result of a post-syntactic operation, and it offers an explicit discussion of what the post-syntactic operation consists of.

Harizanov & Gribanova suggest that heads that (for language-specific reasons) have to form a morphological word with another head are endowed with the binary morphological selection feature M. The [M:–] specification triggers adjunction to the structurally adjacent lower head. This is, in effect, a formalization of DM’s well-known Lowering operation. The [M:+] specification, on the other hand, triggers adjunction to the structurally adjacent higher head. This operation, called Raising, is basically the upward counterpart of Lowering, and its effect is that a head is spelled out higher than its syntactic merge-in position.⁴⁵

In this analysis the case of post-syntactic v-to-T, for instance, is triggered by a [M:+] feature on v (38). After Raising, v and T form a complex head as in (39). It is always the head that is amalgamated into that projects the label of the complex head, so in this case the label will be T.

After Raising (or Lowering) has taken place, the [M] feature on the moved head is erased or becomes inactive. In (39) this is reflected by the lack of [M:+] on v. Note also that in (39) there is only one instance of v. This is because Raising/Lowering does not leave a trace, and so it does not involve chain formation.

The output of Raising is very similar to the output of the head-adjunction analysis in Section 2, but the operation that produces the complex head resides in the post-syntactic component rather than in narrow syntax.

5.4 The pros and cons of this approach

In Section 2 we have seen that the GB-style head-adjunction analysis violates several syntactic principles. If the HM operation does not take place in narrow syntax, then by definition, it cannot violate any syntactic principles and can pose no problems for syntax. There is, therefore, little point in checking post-syntactic HM against our original list of problems: all of them will be eliminated.⁴⁶ In and of itself, however, this does not mean that placing the HM operation into the post-syntactic component is superior. The posited operation must fit with what we independently know about post-syntactic operations, and the theory working with it should be internally consistent and constrained, making the right empirical predictions.

In DM, all post-syntactic operations are highly local in nature. Raising fits with this view because it operates only on structurally adjacent heads. The Head Movement Constraint and the no excorporation condition are baked into the definition of Raising, so these constraints will always be obeyed. Raising also delivers the Mirror Generalization: Harizanov & Gribanova suggest that like other post-syntactic operations, Raising also proceeds bottom up, which means that lower heads will be closer to the stem than higher heads.

There are, however, some general architectural issues with DM that naturally, hold of this approach, too. The first issue is that post-syntactic operations that work on the hierarchical representation (i.e. all operations before Vocabulary Insertion) are triggered by morpho-phonological properties of Vocabulary Items, but at the point that these operations are in effect, Vocabulary Items have not yet been paired with terminals. In other words, these operations, including Raising, involve look-ahead. One might argue that Raising (and Lowering) is exempt from this problem. Harizanov & Gribanova (accepted: 22) argue that the M feature triggering post-syntactic head-adjunction is “one of the features in the feature bundle that constitutes the lexical item and … the lexical item comes specified with a value for M from the lexicon”. Therefore the derivation can simply make reference to a feature that is inherently part of the terminal; it does not have to know about properties of actual Vocabulary Items, and so no look-adhead is involved.⁴⁷ This is problematic because M is not a syntactic feature in the sense that syntax does not make reference to or manipulate it, and recent Minimalist work aims to eliminate all non-syntactic features from narrow syntax.⁴⁸ The second issue is whether post-syntactic operations are indeed indispensable, or we could make do without them and so simplify the model or grammar. Theories of syntax without post-syntactic operations are pursued both within DM (Julien 2002) and outside of DM (e.g. in Nanosyntax, see Caha 2009 and Starke 2009; 2014). Whether post-syntactic operations are well motivated is, in the end, an empirical question: they are if their properties can be shown to be systematically different from those in syntax.

5.5 Analyses that involve PF movement in name only

Some use the term “PF movement” or “phonological movement” to characterize their alternative to head-adjunction, but the operation they posit does not, in fact, involve post-syntactic movement. Here I will briefly discuss two of them, because it is important to see how they differ from the analyses surveyed earlier in this section.

Building on ideas in Hale & Keyser (2002), Harley (2004) proposes an analysis that she considers to be “a natural candidate for a Minimalist, phonological head-movement mechanism” (Harley 2004: 240). In short, the analysis works as follows. Each head in syntax is endowed with a position-of-exponence; a kind of place-holder for phonological features that will be filled in during post-syntactic Vocabulary Insertion. In line with BPS, an XP is assumed to have all the features that its head X does, including the position-of-exponence of the head. When XP is merged with a head α whose position-of-exponence is defective, a Conflation mechanism takes effect: XP’s position-of-exponence is merged into α’s position-of-exponence. As XP has the same position-of-exponence as its head, Conflation means that α acquires the position-of-exponence of X, the next head down. After conflation X’s position-of-exponence will be present in the tree both at X and at α, and as usual for elements with multiple copies, only the highest one is pronounced. This means that X will be spelled out at the next higher head, α.

It is clear that Harley’s analysis does not involve movement in the PF branch: the operation that is responsible for a head being pronounced higher than its merge position takes place during the narrow syntactic derivation. In fact, Harley claims that her analysis does not involve any movement at all (Harley 2004: fn. 5 and Harley 2013: 73).⁴⁹ Conflation can be said to be a phonological operation in the sense that only the phonology-related subpart of the head is affected by it.

Zwart (2001) argues that head movement has two subtypes: syntactic and phonological head movement. The term “phonological head movement”, however, is potentially misleading, as this type of movement, too, takes place in syntax rather than in the PF branch after Spell Out. Zwart suggests that syntactic terminals may have two types of features: all of them have F[ormal] features, and in addition, many of them also have LEX[ical] features. Agree chains always involve movement of formal features. If this is all that happens, then the movement has no phonological reflex in the phonological component, thus we get covert head movement. This is what he terms “syntactic movement”. If the highest head in an Agree chain is defective in the sense that it has no LEX-features of its own, then the LEX-features of the bottom of the chain also move along with the formal features. LEX-feature movement has a reflex in the phonological component, i.e. it yields overt head movement. Zwart calls this type of movement “phonological movement”.

It is phonological, however, only to the extent that it is “triggered by requirements of the spell-out procedure only” (Zwart 2001: 38). The movement’s target is set by syntactic mechanisms (feature-valuation), and the movement takes place in narrow syntax. LEX-movement always accompanies movement of formal features, and in this sense, ““phonological verb movements” are a subset of “syntactic verb movements”” (Zwart 2001: 60).

Harley’s and Zwart’s analyses differ in significant details. The following points, however, are shared by their proposals: 1) syntactic terminals are endowed with phonology-related features (Harley’s position-of-exponence, Zwart’s LEX-features), 2) if a higher head’s phonology-related features are defective, a lower head’s phonology-related features move up to the higher head, 3) the movement takes place in syntax, and 4) morphemes and linear order are not manipulated in the PF branch itself.

Another potentially misleading use of the term “PF” appears in Platzack (2013). The title of this paper is “Head movement as a phonological operation”, but his analysis does not involve any movement either during or after syntax. Instead, it belongs to the group of analyses discussed in Section 6.

6.1 The mechanics

In this section we first look at syntactic representations in DLTs, then discuss how these structures are mapped onto linear order. This discussion will lead to the analysis of data like (1b) to (4b) in DLTs.

In both GB-style and BPS representations, if a head has both a complement and a specifier, then the head, the intermediate projection, and the phrase are represented by separate levels of projection in the structure.

(40)	Government and Binding

(41)	Bare Phrase Structure

The Telescope principle, given in (42), states that this is not necessary: one node can represent both the head and the maximal projection even if the head has both a complement and a specifier.

Telescope allows representations like (40) and (41) to be replaced by (43). By convention, in DLT trees specifiers are represented with leftward sloping lines, while complements are represented with rightward sloping lines. In (43) the node A in and of itself represents a head, while taken together with its dependents, the specifier X and the complement B, it represents the phrasal level.

(43)	Telescopic representation

As shown by (43), the structural relationship between a selecting head and a selected head is that of immediate domination rather than c-command. The heads in a structure form one uninterrupted line; specifiers dangle from this line to the left rather than intervene between heads, as in traditional representations.

Applied to a specific example, the standard representation of (44), featuring an unergative verb, is replaced in DLTs by (45).

In both cases, the subject moves from the specifier of vP to the specifier of TP, which gives rise to a phrasal chain.

Let us now turn to the mapping rules from hierarchy to linear order. The first Direct Linearization Statement says that when mapped to a linear order, a specifier precedes its head.

The second Direct Linearization Statement regulates the linearization of the head and its complement.

The two Direct Linearization Statements in (46) and (47) yield a specifier-head-complement order, like the LCA, but the hierarchical relation that they take to be the basis for linearization is immediate dominance rather than c-command.⁵⁰

The third Linearization Statement regulates morpheme order within morphologically complex words.

A morpheme is the morphological specifier of the morpheme that it immediately precedes within a morphologically complex word. Thus in a morphological word of the form V+v+T, V is the morphological specifier of v, and v, in turn, is the morphological specifier of T. It follows from Mirror that if the exponents of a series of heads form a morphologically complex word (i.e. are involved in an affixation or incorporation relationship), then the order of the morphemes within the morphological word will be the inverse of the syntactic hierarchy. In other words, (48) ensures that the relationship between morphology and syntax obeys Baker’s Mirror Principle. As Brody points out, Mirror in Baker’s work is a generalization over the observed data. In DLTs, on the other hand, Mirror is a genuine principle; morphological structures that do not conform to it cannot be generated.⁵¹

A sample representation of V-to-T is given in (49). Here the subject John has moved from Spec, vP to Spec, TP. In order to make the exposition more transparent, I follow Bowers (1993); Hale & Keyser (1993); Arad (1996) and Den Dikken (2015), among others, and represent the object Mary as a specifier of V (hence the left-sloping line), but nothing crucial hinges on this.⁵² The heads V, v, and T have separate exponents; those of T and v have an affixal requirement.

Due to the language-specific morphological rules of English, when mapped to a linear order, the exponents of T, v and V will have to form a morphological word. By (48), the order of the morphemes within the morphological word will be the inverse of the syntactic hierarchy, that is, V + v + T = love + ∅ + s. So in the sentence John loves Mary, the morphologically complex word loves spells out all of T, v, and V.

The question that arises now is in which of the three positions loves will be pronounced. In DLT any head that a complex word spells out is a potential spell-out position for that word: in (49) all of T, v, and V are possible in principle as a spell-out position for loves. What the actual spell-out position will be is regulated by the Positioning algorithm.

Positioning says that the actual spell-out position depends on whether there is a strong head in the complement line. If so, then the spell-out position will be at the highest strong head. For graphic convenience, strong heads are marked with a diacritic in syntactic trees (@, →, or *, varying across works in the DLT family). If there is no strong head in the complement line, then the morphological word in question spells out in the lowest head.

That is, in absence of a strong head, or if the highest strong head is V, then loves spells out down in V, and (if the object stays low and the subject moves to Spec, TP, as in English), SOV order arises (51). If the highest strong head is v, then loves spells out in v, yielding the SVO word order of English (52). (By (46) the object still precedes V, but now loves spells out in a higher head, and so it precedes V and everything that V dominates). Finally, if the highest strong head is T, then loves spells out at T, delivering the SVO word order of French (53).

As shown by the examples above, when the complement line contains a strong head that is not the lowest head, as in (52) and (53), then the exponents of the heads below @ appear higher than the heads themselves. However, no real movement takes place; no chain formation is involved. The syntax of languages with “no V movement”, with “V-to-v movement” and with “V-to-T movement” is exactly the same.

It is important that (52) and (53) do not involve PF movement either. The morphemes that make up a morphologically complex word do not come together by movement under one terminal at any point; they are simply placed next to each other at Phonetic Form by the mapping rule that translates syntactic hierarchy into linear order.⁵³

Readers are also encouraged to check Platzack (2013) for a related theory. Like the DLTs in this section, Platzack’s theory uses direct linearization statements (his Spell-out Principles 1 and 2) that i) make it possible for a head to be spelled out in a higher head within its own extended projection, with the spell-out position marked with a diacritic (which he calls an EPP feature), and ii) ensure that within the morphological word, suffixes mirror the syntactic hierarchy. This approach differs from the DLTs reviewed here in two respects: it does not use Telescopic structures and it suggests that the spell-out marking diacritic is always on a head that enters into an Agree relation with a lower head.

6.2 The pros and cons of this approach

As in the case of post-syntactic movement, many considerations raised in Section 2 are not applicable to DLTs: in this approach the operation that displaces (the exponents of) heads upwards does not take place in syntax, therefore no syntactic principles are violated or syntax-internal problems arise. What needs to be considered instead is if this theory is internally consistent, if it makes the right predictions, and if it gives rise to new problems of its own.

DLTs capture Baker’s Mirror Generalization via Mirror in (48). The locality effect of the HMC and the no excorporation condition also fall out from this axiom automatically. Structures that do not conform to the HMC or which involve genuine excorporation simply cannot be generated.

The DLT approach captures the long-standing observation that the upward displacement of (the exponent of) a head is local in the sense that phrasal movement is not, and in contrast ot phrasal movement, it can only operate in a roll-up fashion (no excorporation). In DLTs, these differences arise because phrasal movement and the displacement of (the exponents of) heads are completely different mechanisms: the former takes place in syntax and gives rise to chains, while the latter does not. This view is also compatible with Grodzinsky & Finkel’s (1998) findings that aphasics treat phrasal movement and the displacement of (the exponents of) heads differently.

In DLTs heads are spelled out in positions other than their merge position as a by-product of a spell-out instruction to phonology. This makes the strong prediction that for heads, the dissociation between the position of merge and the position of exponence will never have any semantic effects and will never alter syntactic locality domains. We will see in Section 7 that there are arguments both for and against interpretive and locality-changing effects of the HM operation, and arriving at definite conclusions is not easy because the arguments are often quite involved and rely on rather subtle judgments. It is clear, however, which side of the debate DLTs come down on: similarly to the post-syntactic movement approach, they predict that such effects will not arise.

There are also some problems that arise internal to DLTs. The spell-out instruction @ is probably part of the featural content of the relevant heads, and is therefore present in the syntactic representation. But since the position of pronunciation becomes relevant only after narrow syntax, a pronunciation-related feature should have no place in narrow syntax.⁵⁴ Furthermore, whether a particular head is strong or weak still cannot be reduced to an independent property.

7.1 Semantic effects

The idea that the HM operation is not part of syntax can be entertained at all because it appears to have no semantic effects. As semantic interpretation is computed at LF, and LF has a syntactic (hierarchical) representation, if HM turns out to have semantic effects, it must be a syntactic operation and cannot be relegated to the PF branch or the translation rules between the syntactic hierarchy and linear order.

Matushansky (2006) suggests that in spite of taking place in narrow syntax, head movement often lacks a semantic effect because several cases (including verb movement) involve displacement of a non-scopal element, and so the logical possibility that movement leads to a new interpretation does not arise in the first place. In this respect, HM is similar to A-movement, which also characteristically lacks semantic effects, but it is nevertheless part of narrow syntax.

There are also several cases in which HM has been argued to have interpretive effects. The relevant empirical domains include i) the generic vs. existential interpretation of determinerless plural subjects in English and Spanish (Benedicto 1998), ii) the scope of modals relative to negation (Lechner 2006; 2007; Iatridou & Zeijlstra 2013), iii) the licensing of NPI subjects by English subject-auxiliary inversion (Roberts 2010; Matyiku 2014), iv) quantifier scope interaction between aspectual raising verbs and quantified subjects (Szabolcsi 2010: Chapter 3 and Szabolcsi 2011), v) the way parallelism domains are calculated in ellipsis (Hartman 2011; Gribanova 2017a), and vi) verb cluster formation in German long passives (Bhatt & Keine 2015; Keine & Bhatt 2016). Space prevents me from summarizing their arguments here; I refer the interested reader to the cited papers for the details.

Whether these works offer conclusive evidence for HM being a syntactic operation depends on the correctness of their basic (as well as auxiliary) assumptions and the correctness of the details of their analyses (cf. also Platzack 2013: 34, fn. 12). Hall (2015), for instance, argues in detail that the interpretive effects studied in Benedicto (1998); Lechner (2007); Roberts (2010) and Hartman (2011) can be captured my means other than movement. McCloskey (2016) reviews the arguments for semantic effects in Lechner (2007) and Iatridou & Zeijlstra (2013) and suggests that they are not conclusive, in part because the two studies need to make contradictory assumptions about the obligatoriness of reconstruction. Another case when two different proposals for semantic effects actually weaken each other is Lechner (2007) versus Roberts (2010). Both papers use the scopal interaction of negation with some other element in English to make a case for HM taking place in syntax, neither explicitly assumes more than one NegP in the language, and the position of NegP is crucial for both authors. However, while Lechner (2006; 2007) places NegP above TP, Roberts (2010) uses the opposite hierarchy.⁵⁵ As pointed out by a reviewer, the NPI-licensing effects discussed in Roberts (2010) and Matyiku (2014) are not necessarily strong either, as (at least in some dialects) English NPIs do not have to be c-commanded by their licensor (Henry 1995; Hickey 2007).

7.2 Interaction with locality

There are two different types of arguments in the literature that use locality to make a case that HM is a syntactic operation. The first type of argument is that the HM operation is licensed by and complies with syntactic locality principles. Preminger (2017) argues that the locality principle called Principle of Minimal Compliance (Richards 1998; 2001) is directly relevant for the licensing of HM. This principle states that if a certain position is involved in more than one syntactic dependency (movement or Agree relation), then only the first one has to meet locality criteria; the next dependencies targeting that position need not. The reader will recall from Section 2 that head-adjunction poses a problem for the A-over-A Principle. Preminger argues that HM happens only when a head H is either c-selected or agreed with by a higher head, and there is a second dependency between a higher head and H, too. In such a case, the first dependency, c-selection or Agree, will target HP, in compliance with the A-over-A Principle. But the Principle of Minimal Compliance allows the second dependency between the higher head and H to violate locality, therefore this second dependency can target (and move) the head in violation of the A-over-A Principle. Crucially, the Principle of Minimal Compliance is a general locality condition that also holds of phrasal movement. Therefore the fact that the HM operation also complies with it means that it must take place where general locality principles apply: in narrow syntax.⁵⁶

The second type of argument is that the operation of head movement interacts with locality in a dynamic way, specifically, it can change locality domains in syntax. While executing the details differently, Den Dikken (2007); Gallego (2010); Stepanov (2012) and Mathew (2015) share the core idea that movement of a phase head “Ph” extends the phase boundary up to the landing site (this has been called phase extension or phase sliding).⁵⁷ This movement affects locality because the specifier of PhP is on the phase edge before movement of Ph but ends up in the phase domain after the movement. Due to the Phase Impenetrability Condition, movement of Ph makes Spec, PhP inaccessible for further operations that would have been able to affect it had Ph stayed in situ. If HM can indeed shift the phase boundary and affect locality, then it must be a syntactic operation.

Similarly to the semantic effects discussed above, locality-based arguments make a case for syntactic HM only to the extent that the proposed analyses are on the right track.

7.3 Interim summary

Whether the HM operation can have semantic effects or it can interact with locality domains are crucial questions for two reasons. Firstly, debates about HM are often too focused on the theory-internal issues, and leave room for the individual’s perception of what is a more elegant or parsimonius solution to a problem. The issues brought up in this section bring empirical data into the discussion.

Secondly, if the answer to either of the above questions is a clear, unambiguous “yes”, then the PF movement approach and DLTs become non-starters. These approaches are built on the premise that HM is semantically and syntactically inert, and so they predict that it cannot have an effect on interpretation or locality. Any strong evidence to the contrary will serve as a knock-down argument against these approaches, leaving only syntactic alternatives in the competing arena.