The distinction between obligatory and non-obligatory control is illustrated by the following.

The non-agentive, inanimate subjects in (3) may co-refer with the embedded pro, as in (3a), or not, as in (3b). In the latter case, the embedded pro is interpreted as referring to an arbitrary individual/group who might serve as a listener in this context. Insights from Chomsky 1981, Williams 1992, Landau 2013, and Landau 2021 teach us that an inanimate interpretation for pro requires c-command by a controller, while an animate interpretation for pro does not. To reflect this difference, (3a) is called a case of obligatory control and (3b) a case of non-obligatory control.

In McFadden & Sundaresan 2018 it is argued that obligatory and non-obligatory control, despite appearances like in (3), are in complementary distribution. On that view, a better description of (3) would be that (3a) is a case of genuine control while (3b) is what happens when control cannot be established—that is, (3b) is an elsewhere construction. When the predicate of the adjunct clause is strongly biased toward an interpretation where its subject has sentience—as is the case with listen—and when there is no corresponding controller, a preference for the elsewhere construction emerges.

This view of the obligatory–non-obligatory control distinction is further motivated by the observation that obligatory control adjuncts are transparent for wh movement while non-obligatory control adjuncts are opaque (Truswell 2011):

The examples in (4) show that infinitival adjuncts can either be fully transparent for wh movement and control or fully opaque. We propose that this variable transparency of control adjuncts results from a structural ambiguity in their attachment sites.1

Following Landau 2021 and references there, we propose that the control adjuncts under discussion are attached within vP. In addition, we follow Landau in assuming that adjuncts that are ambiguous between an obligatory control interpretation and a non-obligatory control interpretation have an ambiguous position within vP. Landau suggests that the two relevant attachment positions for a control adjunct of this sort are above and below the base position of the external argument, as in (5); each choice is compatible with a different control outcome.

This proposal suggests that the variable transparency of an adjunct clause is tied to its position. An adjunct that is in the right position to participate in obligatory control is also in the right position to be transparent to wh movement. An adjunct that is in the wrong position to participate in obligatory control will conversely be opaque to wh movement. We now discuss other cases where the position of an adjunct is shown to affect its transparency for dependencies into it.

We have discussed how wh movement out of adjuncts correlates with obligatory control into them. We now observe that this correlation with control is not limited to wh movement. Parasitic gaps inside adjuncts show the same correlation. Observe in (6) that parasitic gaps are possible in obligatory control adjuncts but not in non-obligatory control adjuncts.

In section 2.1, we speculated that obligatory control adjuncts are transparent as a consequence of the position that they are merged in. Adjuncts that are adjoined in a position that makes them available for obligatory control are transparent both for control and for wh movement; the same adjunct merged in a different position will be opaque for both control and wh movement, forcing a non-obligatory control interpretation of pro. We propose to take the same basic approach to the contrast in (6).

Nissenbaum 2000 develops a theory of parasitic gap licensing that is compatible with such an approach. For independent reasons, Nissenbaum proposes that parasitic gap–containing adjuncts must merge in a particular position: immediately above the subject that controls pro and immediately below a position occupied by the wh element that licenses the parasitic gap. In other words, parasitic gap–containing adjuncts must be second specifiers of vP, as in the following schema.

According to Nissenbaum’s analysis, if the adjunct merges as a second specifier, it will be accessible to parasitic gap licensing. Since parasitic gaps are only licensed in obligatory control, not in non-obligatory control, as shown in (6), adjuncts in second specifier position must also be allowed to participate in obligatory control. Non-obligatory control adjuncts must not be in this position, since they block parasitic gap licensing. On this view, if the adjunct is in a different position, it will no longer be accessible for parasitic gap licensing or obligatory control, accounting for the correlation of these different dependencies into the adjunct clause.

We have now seen two different phenomena where control appears to correlate with another kind of dependency into an adjunct clause. On the one hand, we saw that obligatory control adjuncts permit wh extraction out of them while non-obligatory control adjuncts don’t. On the other hand, we saw that obligatory control adjuncts also tolerate parasitic gaps while non-obligatory control adjuncts don’t. In both cases, there is precedent from the literature for tracing accessibility to these dependencies to the position of the adjunct: adjuncts in a particular position are accessible to obligatory control and parasitic gaps, suggesting that adjuncts in other positions are opaque to such dependencies.

Unfortunately, though, there is a conflict. Landau proposed that it was the first specifier position that made an adjunct accessible to obligatory control, while Nissenbaum suggested that it was the second specifier position that made an adjunct accessible to parasitic gap licensing. For these two dependencies to correlate, we need to decide which position is the right one for adjuncts that are transparent to obligatory control, wh movement, and parasitic gaps. We resolve this issue in section 2.4, after discussing a third example of multiple specifier constructions with variable transparency effects.

Before moving on, we want to address an analogy that we are drawing between dependencies of different types. We follow Chomsky 1986, Larson 1988, Postal 1998, and Nissenbaum 2000 in assuming that parasitic gap constructions do not involve across-the-board wh movement out of both matrix and adjunct clauses but rather involve binding of an operator that moves adjunct-internally. Nonetheless, we consider it to be significant that parasitic gaps pattern with wh movement with respect to their relationship to obligatory control. We think their similarity in this respect supports a view of operator binding as being subject to the same locality conditions as wh movement. In sections 3 and 4, we propose a theory of locality that applies uniformly to dependencies such as parasitic gap licensing, wh movement, and control.

Müller 2010 discusses a class of exceptions to the Condition on Extraction Domains, which Müller calls melting effects. He observes that external arguments in German and Czech are typically opaque to extraction, as expected for specifiers according to the Condition on Extraction Domains. However, he shows that scrambling an object to the left of the external argument has the effect of making the external argument transparent for extraction. In other words, object scrambling obviates the Condition on Extraction Domains for transitive subjects. This is shown in (8) and (9) for German and Czech respectively. Wh extraction out of the subject is only available when the object appears to its left.2

Importantly, Müller cites evidence from Grewendorf 1989 suggesting that the subject of a psych verb like beeindrucken ‘impress’ is a regular external argument in German and not a VP-internal argument. Thus, it must be a specifier, making (8b) a true counter-example to the Condition on Extraction Domains.

What is surprising about (8) and (9) is that the exact same specifier (was für Bücher/stará žádná) can be opaque in (8/9a) but transparent in (8/9b), solely based on the position of the object. The surface position of the object presumably does not affect the specifierhood of the subject, suggesting that island effects have more to do with local context than with the complement–non-complement distinction.

Müller proposes that the contrast is due to the fact that melting examples like (8b) and (9b) involve multiple specifier constructions. A starting assumption is that object movement proceeds successive-cyclically through the edge of vP. Thus, a scrambled object must arrive in the edge of vP at some point in the derivation, in which case the (b) examples differ from the (a) examples with respect to the total number of specifiers vP has. When no scrambling takes place, the external argument is the only phrase to ever occupy the edge of vP, while in scrambling derivations, vP has two specifiers at some point in the derivation.

Müller presents a phase-based theory of the Condition on Extraction Domains, in which phases can only produce escape hatches as long as they are incomplete. The last-merged element in a phase completes the phase and blocks it from producing an escape hatch. As a result, Müller’s theory predicts that only the last-merged specifier of a phase is opaque for extraction. All earlier-merged material is transparent, including specifiers, because they merge early enough for an escape hatch to be produced. In non-scrambling contexts, the subject is the last-merged specifier of vP, while in scrambling contexts, Müller proposes that the object is the last-merged specifier of vP, making the subject transparent. In other words, his theory requires the following configuration of specifiers in vP in order to capture melting effects.

Following Moltmann 1990, Grewendorf & Sabel 1999, McGinnis 1999, and Yoshida 2001, among others—based on evidence from quantifier scope and the position of negation and adverbs—spec-vP is not the final landing site for objects scrambled to the left of subjects; a higher position is, like spec-TP. We therefore expect the object to be able to surface in a position that derives the surface word order OS, regardless of the order of specifiers of vP. Since word order, then, is not conclusive to prove the order of specifiers of vP, we need another metric.

It is sometimes argued that the second movement step in German scrambling has Ā properties (Grewendorf 1988, Webelhuth 1992, and Müller & Sternefeld 1994), in which case we might be able to diagnose the order of specifiers in vP with reconstruction tests. The results of such tests suggest ambiguity. Supposing that the first movement step may have mixed properties (as it targets spec-vP), it might be able to affect binding relations, but the second step, having Ā properties, should not; this then should provide some insight into the order of specifiers in spec-vP. As it turns out, a scrambled anaphoric object may be bound by a subject, as in (11a) (with no Condition C effect), consistent with the order of specifiers SO, while a scrambled quantificational object may bind a pronoun in the subject, as in (11b), motivating the opposite.

This divergence may indicate that specifier ordering is generally ambiguous, just as the position of adjuncts is, with the choice of position affecting extraction and binding possibilities.3

In sum, we have seen three cases in which multiple specifier constructions feed exceptions to the Condition on Extraction Domains. Adjuncts and specifiers that are normally opaque to extraction or parasitic gap licensing may become transparent if they are in a multiple specifier environment. What remains to be decided is which specifier position gets to be exceptionally transparent to such dependencies and what principles underlie this choice. We will argue, contra Müller and Landau but with Nissenbaum, that it is second specifier position that is transparent.

What follows is a discussion of the position of adjuncts that contain parasitic gaps, contrasting Landau and Nissenbaum’s approaches. The latter but not the former is consistent with the proposal that second specifier position is transparent. Readers who are willing to follow us and Nissenbaum may proceed directly to section 3.

The remainder of section 3 will describe the analysis in detail, but we first want to clarify why we chose this approach. The present article is a preliminary attempt to make use of existing probing tools to understand an unusual empirical pattern. The challenge with this kind of pattern is that it refers to specifier number in a way that syntax should not be able to do. We know that grammars are not able to “count” and as such should not be able to treat specifiers differently from each other in a way that references only their number. The present approach therefore tries to single out what is unique about the structural context of a second specifier and exploit that in the analysis. As we will lay out in section 3.3, we hypothesize that second specifiers are special due to how the feature projection algorithm labels projections that already contain a specifier. While there may be other ways to approach this locality profile, we think this one has the advantage of making nuanced predictions with existing mechanisms.

This article develops a novel theory of locality rooted in the notion of paths (Kayne 1981, Pesetsky 1982, and McFadden & Sundaresan 2019). Long distance dependencies, on this approach, must be mediated by a sequence of local dependencies:

We propose that underlying this notion of paths is a more general notion of economy in dependency formation. Paths, as we define them, allow the grammar enough information to know whether or not a search procedure, on which long distance dependencies are contingent, will succeed or fail.

Chomsky 2004 and subsequent works suggest that probing involves an operation of “Minimal Search.” Minimal, for the purposes applicable here, means that the search procedure will halt once a match has been found, the hope being that the right specification of the search procedure will capture Relativized Minimality effects (Rizzi 1990). A number of algorithms for Minimal Search have been proposed and discussed in the literature; see Branan & Erlewine 2021 for an overview and Atlamaz 2019, Ke 2019, Preminger 2019, Chow 2022, and Krivochen 2022 for more specific proposals. The basic idea is that nodes in a syntactic tree are sequentially “examined” to see if they match what the probe is specified to look for, with the sequential search algorithm only being able to move to sisters or daughters of failed matches.

Why should Search be minimal? One reason, as Chomsky suggests, might be computational efficiency. Searching the tree involves examining a number of nodes to see if they are a match for the probe. We can define a cost in terms of the number of failed examinations that take place prior to success. Examining as few nodes as possible would be desirable, given that the process of examining a node to see if it is a match bears some computational cost.

With this in mind, consider a scenario in which a probe is destined to fail because there is no corresponding goal anywhere in the structure. The probe’s failure cannot be determined, and the derivation cannot proceed to the next step, until every node in the tree is examined. In terms of computational cost, this is the worst case scenario: every node in the tree must be examined, but doing so does not produce any observable change to the structure.

We suggest that the grammar is designed to avoid costly failed searches of this type.7 In the abstract, we suggest that the grammar is endowed with a set of flags that provide (limited) information about the makeup of a constituent. For instance, in the case of a probe specified for a feature [F], the daughters of a node will only be examined by the search procedure if the node itself bears :

A desirable consequence of this is that it provides a new perspective on island effects: (some) islands, on this approach, would simply be phrases that lack a flag for the relevant sort of feature. In (23), for example, the internal components of YP, which lacks , will not be subject to Search. Probe–goal relationships for [F] will thus be impossible into YP.

Note that this entails a series of local relationships between a probe and its goal: every node in the sister of the probe that dominates the goal must bear a flag for a feature on that goal.

This proposal raises a number of questions, the most pressing of which we hope to answer. In the next sub-section, we suggest that the flags in (0) are checked selectional features—presumably an independently necessary component of the grammar.8 Checked selectional features provide a record of the derivation: the presence of a checked selectional feature on a maximal projection serves as a flag indicating that either the specifier or complement of that phrase is of a particular sort. The chief innovation here will be an algorithm for determining whether or not checked selectional features are able to project past the maximal projection of the head they originate on. Crucially, this decision is local: it creates paths of local relationships between a probe and a licit goal, in the sense of (21). We show that the theory captures the basics of the classic Condition on Extraction Domains: adjuncts and specifiers are, in the basic case, opaque for extraction, while complements are not. We show also that the theory avoids what we term the “escape hatch problem” for phase-based approaches to the Condition on Extraction Domains, a stipulation that requires adjunct islands to both be phases and consistently lack an edge feature.

As discussed in the previous sub-section, we propose that a notion of paths mediates Search. As Search underlies the establishment of long distance dependencies, paths become pre-conditions for long distance dependencies by extension. One of the consequences of a path-based approach to Search is that there are many scenarios in which Search may fail at the outset, before it has examined any nodes. For example, if the sister of a probe does not bear a flag for the relevant feature, the probe won’t bother to search its sister’s daughters at all, given that there is no path of checked selectional features leading from the probe to any of its sister’s descendant nodes in this case.

Our proposal, which we briefly outline here, is based on the following consequence of this approach. For a probe A to establish a dependency with a goal B, A must as a minimal first step be able to identify the relevant flag on its sister. An algorithm for projecting features checked by B from the head that selects B to the sister of A establishes a series of local relationships that links probe and goal. The projection algorithm thus ensures that if a feature has reached A’s sister, it must have been projected at every node between A’s sister and the goal B, thus creating a path between the two, satisfying the condition in (24). We can thus operate with a shorthand definition of path, shown in (25). Here we will discuss the predictions of the approach for dependencies involving selected elements, such as the long distance dependency in (26), where [•B•] is a selectional feature checked by B (see below). We return to the extraction of unselected elements, for example, adjuncts, in section 4.

If for some reason A’s sister does not bear a feature checked by B (i.e., because there is no local B), Search fails at the outset, without examining any nodes in the tree. Thus, Search never applies unnecessarily.

We begin by establishing some assumptions about clause construction, before showing how a modified theory of feature projection creates long distance dependencies according to (24) and (25). Adopting the notation of Müller 2010, we represent the features that drive Merge as in (27). A head that selects for a YP, for example, might bear a feature [•Y•], which is checked when that head (or a projection of it) merges with a YP. In other words, a head X with an unchecked [•Y•] feature that merges with a YP produces a projection XP bearing the checked version of that feature, [•Y•], as in (28).

As will become important later, we follow Heck & Müller 2007, Müller 2010, Longenbaugh 2019, and Newman 2024 in assuming that these features may drive any kind of Merge, thus not only External Merge but movement (Internal Merge) as well.

The checked features are inactive in the sense that they may no longer drive syntactic operations. In other words, an element that bears [•X•] does not count as an element that bears [X] and thus cannot feed X Merge. Similarly, [•X•] does not count as a selectional feature, which would require checking by an element bearing [X]. It simply indicates that X Merge has taken place. However, contra Chomsky 2000, Adger 2003, and Asudeh & Potts 2004, among others, we suggest that these checked features do not disappear from the derivation. Instead, we propose that they remain present throughout the computation to serve as a pseudo record of selection. On this view, XP provides more information to higher heads than just its own category feature. It also bears checked Merge features, which tell higher heads something about the elements inside XP, for instance that XP contains a YP in the case of (28).

So far, we have seen how checked features may be projected from a head X to its own maximal projection XP, when it merges with elements it selects for. These features are not deleted and are thus visible to whatever subsequently merges with XP. According to the conditions in (24) and (25), for YP to be accessible to anything beyond XP’s sister, [•Y•] must project past XP. Only if it does so can it ever appear on the sister to a higher probe, making YP accessible to that probe.

We propose that feature projection past a maximal projection is conditioned by the local context of that maximal projection. More specifically, maximal projections whose sisters are what we call indivisible feature bundles get to project their checked selectional features to higher nodes, making their contents accessible to later operations, as stated in (29). Indivisible feature bundles are defined in (30)—they are essentially nodes whose features locally come from a single source.

The intuition guiding this approach is that language is binary: at every step of the derivation, feature projection should only involve two bundles of features at a time. If one sister already locally projects two feature bundles, the other cannot project at all. If one sister locally projects one or fewer feature bundles, the other can project one as well.

On this view, lexical items are always indivisible feature bundles. Thus, sisters of lexical items (i.e., complements) will always be permitted to project their checked selectional features. Non-terminal nodes, by contrast, might or might not be indivisible feature bundles; that depends on whether their daughters were allowed to project their features. Thus, sisters to non-terminal nodes (specifiers/adjuncts) might or might not be allowed to project their features.

Recalling the XP maximal projection in (28), we can now calculate the predicted effects of context on whether XP gets to project its [•Y•] feature to higher nodes.

If XP is the element merged first with a head Z (otherwise known as Z’s complement), as in (31), the rule in (29) entails that XP can project its [•Y•] feature, because its sister Z is an indivisible feature bundle.

If XP is the second-merged element in ZP, that is, the first specifier of ZP, as in (32), its sister is not an indivisible feature bundle. The Z′ sister to XP projects from two daughters: the terminal node (which always projects) and its sister (complements get to project, according to (31)). Since Z′ is not an indivisible feature bundle, XP does not get to project [•Y•] in this context, rendering YP inaccessible to operations external to XP.

The theory thus accounts for basic Condition on Extraction Domains effects: complements permit sub-extraction but first specifiers do not.

The theory makes a surprising prediction for third-merged elements, however, such as the second specifier XP in (33). Here XP’s sister only locally projects from one daughter. Its sister may bear features that originally came from multiple sources, but the notion of indivisibility that we are pursuing only examines a node’s local context: whether it projects from each of its immediate daughters or not. On this view, the sister to XP in (33) only projects from one daughter because first specifiers cannot project, as we saw in (32).

The first node that dominates a first specifier is therefore an indivisible feature bundle according to (30b), and this licenses projection from a second specifier.9

This approach therefore generates an on-again-off-again profile. If some maximal projection is allowed to project, it often creates a context in which the next-merged maximal projection cannot project. If a maximal projection does not project, it often creates a context in which the next-merged maximal projection can project, and so on. Thus, we expect the time of Merge to determine transparency for higher operations, more so than the complement–specifier distinction. We will leverage this context sensitivity to explain the variable opacity of adjuncts and specifiers in different contexts.10

In sum, we propose that the distribution of checked features on nodes creates paths between probes and goals, where paths are a pre-condition for Search. A probe whose sister bears a feature checked by its goal may initiate Search for that goal, so that each successive node is examined for features checked by the goal until the goal is found. If the probe’s sister has no relevant checked features, Search fails before it starts, avoiding unnecessary and costly searches. We proposed that the distribution of checked features is controlled by the rules of feature projection outlined in (29) and (30): maximal projections may project their checked features if their sisters are indivisible feature bundles but not otherwise. Successive projection of checked features creates paths.

It is important to recall that [•Y•] is not equivalent to the YP that checked it. [•Y•] is a feature that was checked/rendered inactive by an element bearing [Y]. By contrast, YP is a phrase that can check some set of features on a probe, including [•Y•]. Thus, a probe whose sister bears [•Y•] has not “found” YP before searching, because [•Y•] can never feed syntactic operations like Y Merge and Y Agree. The probe must still search for the YP that checked the feature in order to satisfy the probe.

At this point, one might wonder why we don’t simply invoke the feature [Y] in path formation, instead of checked selectional features like [•Y•]. If we had a projection algorithm that projected instances of [Y] (i.e., the property of Y that makes it a goal for a [•Y•] probe), then the resulting paths might look like (34), in which [Y] projects to ZP and beyond.

The problem with an alternative like this comes from the literature on pied piping. If a higher head seeks [Y], minimality considerations will cause that probe to attract/agree with the highest instance of [Y] in the structure, rather than the phrase [Y] originated on. The result should therefore be a kind of pied piping: ZP, which contains the original YP, should move/agree, but the YP itself should not be available for sub-extraction, due to minimality. Thus, invoking [Y] instead of [•Y•] would produce a feature percolation type approach to pied piping and would not produce a theory that allows the intended goal to move on its own.11 We therefore need some other feature to mediate path formation, one that does not intervene for the dependency being formed. Checked selectional features do just this, without adding to the existing typology of features: they record what kinds of phrases are dominated by a certain node, without making that node an intervener for the goal of the probe.

Lastly, though the presentation here only discussed the case where one checked feature is projected, we assume that feature projection is wholesale in general. What we mean by this is that multiple checked features on a phrase get projected together as a bundle; a maximal projection cannot selectively project some of its features but not others. The following illustrates wholesaleness of projection.

Because projection is wholesale, we expect a maximal projection to be opaque or transparent to higher operations in a very general sense. The projection rules create long distance dependencies in the way illustrated in (35): if XP is selected as the complement of A, then the newly formed AP not only bears [•X•], indicating the presence of an XP inside it, but also inherits any checked features borne by XP itself, allowing whatever selects for AP to search into it for YP and BP as well.12 A transparent maximal projection is transparent for potentially multiple dependencies across itself: it projected every feature it had, so everything inside it that checked a projected feature is visible to higher heads. An opaque maximal projection is similarly opaque for every imaginable dependency: if a maximal projection projects no features past itself, there can be no paths leading into it. We will see that this all or nothing approach captures correlations between different dependencies that cross adjunct boundaries.

In section 4.2, we will clarify certain assumptions that we make about features that drive syntactic operations, assumptions that underpin much of the discussion that follows. But to foreshadow here: we assume that certain elements bear a [D] feature, which marks them as an argument of a clause. This is the same feature that allows certain elements but not others to satisfy the EPP in English; it is also similar to the Case feature of Van Urk & Richards 2015 and the ϕ feature assumed in Van Urk 2015 and Longenbaugh 2019. We use [wh] as a feature for elements that enter into Ā dependencies.

In section 2 we observed (following Müller, Nissenbaum, Landau, etc.) that violations of the Condition on Extraction Domains often occur in multiple specifier environments. We furthermore concluded with Nissenbaum, contra Landau and Müller, that second specifiers are always exceptionally transparent.

To understand this pattern, we first propose that wh movement, parasitic gap licensing, and obligatory control involve the establishment of a long distance syntactic dependency through Search. To illustrate the proposal with the wh movement–obligatory control correlation, we propose that wh movement arises when interrogative C searches its complement for a phrase bearing a [wh] feature, which is used to check a [•wh•] feature on itself. Obligatory control likewise involves syntactic dependency formation that is contingent on a successful search, with the sister of a potential binder for pro being subject to search for pro (see Ke 2019 for a similar proposal for reflexive binding). Consequently, there must be a path between pro and its controller for obligatory control to arise and a path between a wh phrase and interrogative C for movement to occur.

As proposed in section 3, such path formation is contingent on successful projection of checked selectional features from the sister of the goal to the sister of the probe. The proposed algorithm for feature projection predicts that features from first specifiers do not project to their mothers, making the contents of first specifiers opaque to higher operations. The features of second specifiers, by contrast, do project, creating paths into them. Thus, second specifiers are predicted to be transparent for dependencies like wh movement and control, accounting for the facts in section 2.

Importantly, when an adjunct/specifier projects its features, there are paths into it for every feature that it projects. As a result, when an adjunct is transparent for control, it is also transparent for other dependencies like wh movement. In what follows, we discuss the specific features we have in mind for each of these dependencies and explore some other multiple specifier contexts.

On the theory developed here, the requirement for there to be a path between two elements “linked” through Search should be seen as a way to ensure that Search will succeed. We now explain how Search interacts with movement to account for the correspondent transparency effects. Recall from section 3.3 that both Internal Merge and External Merge are licensed only when they check [•F•]s. Movement—or Internal Merge—requires an invocation of Search on the sister of the probe for some matching feature, followed by merge of the goal at the root of the tree.

Not only must there be a path of checked features between the two elements in question, but the target of Search must have checked the sort of feature that Search is looking for. In other words, a probe with a feature [•X•] must find a path of [•X•] features to its goal, not just any path of features checked by its goal.13

At this point, one might wonder which features actually establish these paths between the matrix subject and pro and between C and the wh element and how those features get checked/projected. For pro, the answer is straightforward. pro is presumably selected as the external argument of the adjunct clause. We can therefore imagine that it checks a [•D•] feature on adjunct v, which gets projected to the highest node in the adjunct clause, as in (36). We have represented pro as the highest specifier of AdjP on the assumption that pro moves to the edge of its clause (Heim & Kratzer 1998).

As long as control is mediated by a search for DPs, if the [•D•] feature projects to the sister of the matrix subject, the matrix subject may find and control pro.14

For wh elements, we propose that their visibility for wh movement is regulated by the distribution of heads bearing [•wh•]. On the assumption that all phase heads have the necessary machinery for hosting successive-cyclic wh movement, we propose (following Longenbaugh 2019 and Newman 2024) that these probes for movement are represented as Merge-inducing features specified to be checked by wh phrases: [•wh•]. If heads like v, C, and possibly D are endowed with such features, then the manner in which [•wh•] gets checked and projected as [•wh•] could be that wh phrases undergo a step of [•D•]-driven movement to the specifier of an intermediate phase head in the clause, before moving to spec-CP.15

For concreteness, consider the case in (37). Here, v bears both a [•D•] and [•wh•] feature. Internal merge to satisfy [•wh•] is not possible: the complement of v does not bear a [•wh•] feature, so it may not be searched for [wh]. The complement does, however, bear a [•D•] feature, so it may be searched for an element bearing [D], in which case the object will be found. Subsequent merge of the object in spec-vP will check both the [•D•] and the [•wh•] on v. Consequently, the [•wh•] will be able to project higher in the tree from this vP, creating a path between the wh phrase in spec-vP and higher elements in the tree.

For the sake of having a concrete analysis, we will adopt this approach here, though it may not be the only possible solution. It does, however, have the advantage that it has precedent in the literature from Canac Marquis 1994, Van Urk & Richards 2015, and Longenbaugh 2017. The first two propose that Ā movement chains involving non-subjects always involve a step of A movement within VP.

Canac Marquis suggests that English Ā movement of objects is analogous to tough movement, involving A movement of a null operator to the inner specifier of the phrase that the element undergoing Ā movement is introduced to as an outer specifier. This step of operator movement allows the moved element to be linked to its gap; the position that the moved object is itself initially merged in is presumably motivated by a need to check the [wh] feature of the relevant projection.16

van Urk & Richards propose that wh movement of objects in Dinka (Nilotic; Sudan) is parasitic on a prior step of A movement to a position low in the clause, based on facts about the exceptional absence of an internal argument in an otherwise obligatorily filled pre-verbal slot, in contexts involving Ā movement of an internal argument. The idea, presented using the feature ontology assumed throughout this article, is that movement to this pre-verbal position may in principle check both [•wh•] and [•D•] features. In the absence of an element that bears [wh], this happens solely to satisfy the needs of [•D•] on the relevant head. When an element bears both, checking of the [•wh•] feature on the head that triggers movement may take place, with the path that licenses movement involving a [•D•] feature.

Longenbaugh, like Canac Marquis, discusses a derivation like this in the context of English tough constructions, though the details of the analyses differ. On Longenbaugh’s view, tough movement involves successive-cyclic composite movement through spec-vP, which has both A and Ā properties. On the present view, this “mixed” movement is represented by the multiple checking of two different features on v: [•D•] and [•wh•].

The proposal that wh movement is mediated by DP movement raises questions about wh movement of non-DPs, such as PP arguments and adjuncts:

For adjuncts a fairly straightforward analysis would be to propose that they consistently externally merge in spec-vP, at least in cases where they undergo wh movement. For argument PPs the way forward is less obvious. One possibility is that wh PP arguments, like adjuncts, often have the option of initially merging with a functional head like vP, ensuring that the PP argument checks a wh feature (see Newman 2024 for a proposal along these lines). Another possibility is that PP arguments are required to exit the VP for independent reasons (see Stowell 1981 for such a proposal). Assuming this movement is feature-driven, subsequent merge of a PP argument with vP consequently checks v’s [•wh•] feature in cases where the PP bears [wh].

In sum: pro and wh elements must respectively check [•D•] and [•wh•] if they are to be visible for subsequent Search operations. In the case of pro, this is relatively trivial: pro checks a [•D•] when it is initially merged. In the case of wh elements, it means that the wh element must first undergo movement for independent reasons to an intermediate projection, with checking of [•wh•] on this intermediate position taking place as a side effect. Only after movement to such a position will there be a path of [•wh•] features to the wh element, rendering it visible for subsequent searches.

Before moving on, we want to address another dimension of this issue of which features to invoke in path formation. Here we have focused on the type of feature, for example whether it is of category [D] or [wh]. However, one could ask about tokens of features as well. Does the derivation track which DP a given [•D•] corresponds to?

The two possible answers make different predictions when the matrix verb is transitive. In a transitive clause, regardless of the position of the external argument within spec-vP, a [•D•] from the internal argument should project to every node within vP, including the sister of the adjunct. If path formation only cares about the presence of [•D•] on nodes and doesn’t care whether that feature was actually created by the controller, then we might expect all adjuncts that modify transitive clauses to be obligatory control adjuncts. However, non-obligatory control is available in (39), suggesting that there is a derivation available with no path to the adjunct.17

This result could teach us either of two things: maybe (i) we need checked features to be indexed with the element that checked them, with paths being sensitive to these indices, or maybe (ii) heads that select for DPs suppress existing instances of [•D•] from their sisters, breaking the chain of [•D•] until they introduce their own arguments. For concreteness, we tentatively assume the first possibility, but we are optimistic that the proposal could also work without indices.

It is worth tying up a loose end. As noted by Nissenbaum 2000, one instance of wh movement may license parasitic gaps in more than one adjunct:

As pointed out by a reviewer, an analysis like (1) for such stacked adjuncts poses a potential problem for the theory developed here: only one of the two adjuncts on such an analysis would be of the right parity (the property of being an even/odd specifier) to project its features and license the parasitic gap within.

We believe there is good reason, then, to favor an analysis like that in (42) for “stacked” adjuncts of the sort discussed here, following Chomsky 2019.

In this structure, the two adjuncts merge with each other prior to their merge with vP. Since the “combined” adjunct is an even parity specifier of vP, it will be able to project its features from this position. Furthermore, since the adjuncts that make up the combined adjunct themselves have a specifier—the null operator that gives rise to the parasitic gap—they will be able to project their features up to the “combined” projection.

This theory also accounts for Nissenbaum’s observation that parasitic gap–containing adjuncts must appear closer to the predicate they are construed with than other adjuncts:18

If Nissenbaum is right that parasitic gap–containing adjuncts are of a distinct semantic type, then they should only be able to conjoin with adjuncts of the same type (i.e., gap-containing adjuncts can conjoin with other gap-containing adjuncts).19 Given this, the adjuncts in (43) must form different specifiers of vP. The inner adjunct may be of even parity provided the Ā-moved object lands above it in vP; the outer adjunct, conversely, may not. It would have to be above both the inner adjunct and the subject but below the wh phrase to license a parasitic gap (according to Nissenbaum). From this position, however, it couldn’t project, blocking a parasitic gap. As a result, when there are two adjuncts, one with a gap and one without, the adjunct with the gap must be the inner adjunct.

What we have seen, then, is that multiple kinds of dependencies that Search plausibly underlies—control and Ā dependencies such as wh movement and binding of null operators—are allowed into adjuncts/specifiers only when those adjuncts/specifiers appear in a particular context. Moreover the theory captures the fact that one and the same adjunct/specifier may be transparent or opaque, given that such elements may merge as second specifiers or not. In section 5 we discuss further implications of the theory we’ve developed and compare it to other theories with comparable empirical coverage.

Since Cattell 1976, it has been common to treat specifiers and adjuncts as islands for extraction as a matter of definition. The Condition on Extraction Domains states that any non-complement is opaque for extraction:

The Condition on Extraction Domains raises several questions. First, many have shown that it is not exceptionless (see, e.g., Stepanov 2007 for discussion). In particular, we have discussed in this article examples of wh extraction out of adjuncts and specifiers, both of which are clear violations of (44). These counter-examples refute the generality of (44) and suggest that we need a more fine-grained metric for islandhood besides the complement–non-complement distinction. Second, existing attempts to derive (44) face a conceptual disadvantage compared to the present theory.

A popular approach to the Condition on Extraction Domains is to treat adjuncts and specifiers as subject to different rules than complements. For example, Uriagereka 1999, Johnson 2003, Sheehan 2013, and Privoznov 2021 suggest that non-complements must spell out when they merge, rendering their contents inaccessible to further operations.

This approach requires some elaboration to theories of spellout, given that complement clauses are also often proposed to spell out at particular points in the derivation. Phases (including complement clauses) are typically assumed to be opaque to operations external to them after their time of spellout. However, unlike adjuncts/specifiers, phasal complements are thought to have an escape hatch. Elements that move to that escape hatch become accessible to later operations, despite the fact that the phase has spelled out. For the contrast between adjuncts/specifiers and complements to be captured, adjuncts/specifiers must therefore lack an escape hatch.

One could imagine several ways to encode the escape hatch property on a phrase such that complements have escape hatches but adjuncts/specifiers do not. For example, we could stipulate that complementation triggers spellout of the complement of the phase head while adjunction/specifier merge triggers spellout of the entire phrase. Complements therefore have a specifier position that has not spelled out, while adjuncts/specifiers do not. Alternatively we could propose that edges of spelled-out phrases are always accessible but that only certain heads have the ability to attract elements to their edge, with adjuncts/specifiers routinely lacking these edge features, in contrast to complements.

Both of these possibilities require us to stipulate a distinction between complements and non-complements, whereas the theory outlined in this article does not. The present theory treats complements as the element merged first with a head, specifiers as the second-merged element, and so on, reducing the number of ad hoc distinctions we need between different phrases. Moreover, the present theory is able to account for variable islandhood of adjuncts and specifiers, without stipulating special properties of those adjuncts and specifiers. Instead we propose that every phrase (complement or non-complement) is subject to the projection algorithm, which yields different results depending on how many feature bundles are present on each node.

In sum, this article examined a number of exceptions to the Condition on Extraction Domains and offered a novel theory of locality designed to account for these exceptions. On the proposed approach to locality, a specifier or adjunct is rendered transparent or opaque based on the properties of its sister. This allowed us to explain why the same adjunct or specifier might be transparent in one context but opaque in another: aspects of context more subtle than specifierhood/adjuncthood determine opacity.

The proposed theory made use of a modified projection rule, which conditionally allows features to percolate higher than the maximal projection of a head. When the conditions for projection past the maximal level are met, the contents of that phrase become visible to higher probes, allowing dependencies to target them. Crucially, we proposed that probes cannot search for a goal in the absence of such a path of features (created by feature projection). Phrases whose features get suppressed by the projection rule are therefore predicted to be opaque.

Importantly, the projection rule does not reference the complement–non-complement distinction; it instead references the local feature context of a phrase, that is, the features of its sister. As a result, specifiers/adjuncts are not uniformly predicted to be opaque: only those whose local context suppresses feature projection are opaque, accounting for observed exceptions to the Condition on Extraction Domains.

This approach to locality of course raises many questions, which we have not had space to discuss fully here. For example, we have looked at the transparency/opacity of phrases in their base positions but have not yet considered what the approach should look like for phrases derived by movement. To be more specific, consider the melting cases discussed in Müller 2010. Müller shows that object scrambling licenses extraction out of in situ subjects but not those that have raised to a higher position, as diagnosed by the presence of intervening adverbs:

This kind of freezing effect raises several questions about our proposal, such as: How do copies of phrases interact with the projection rule? And in cases where movement alters the parity of a specifier, can a path of features created by projection from one position find those elements in their new positions? We hope to explore these and related questions in future research.20

While there are certainly further details to develop, the theory as developed so far already makes interesting and nuanced predictions in a traditionally tricky empirical domain and has the advantage of unifying Condition on Extraction Domains effects with other kinds of locality effects analyzed by a search procedure (e.g., intervention effects). As such, we believe it holds promise for a more unified approach to locality, grounded in the nature of the combinatorial system itself rather than the typology of adjunct/specifier phrases.