2.1 Merge and labeling

As is typical in recent work in the Minimalist Program (Chomsky 1995, etc.), the operation of Merge is a core component of POP, whereby two syntactic objects (SOs) are combined to form another SO. This operation is described below (adapted from Chomsky 2001: 3).

The need for an SO to be labeled is also a core component of POP. According to Chomsky (2015: 6), the labeling algorithm is “a special case of minimal search (like Agree).” The labeling operation of POP is summarized by Chomsky (2013: 43) as follows:

“Suppose SO = {H, XP}, H a head and XP not a head. Then LA [labeling algorithm] will select H as the label, and the usual procedures of interpretation at the interfaces can proceed.

The interesting case is SO = {XP, YP}, neither a head… Here minimal search is ambiguous, locating the heads X, Y of XP, YP, respectively. There are, then, two ways in which SO can be labeled: (A) modify SO so that there is only one visible head, or (B) X and Y are identical in a relevant respect, providing the same label, which can be taken as the label of the SO.”

When a head that is strong enough to label merges with an XP, the labeling algorithm LA finds the head and the head becomes the label. When an XP merges with a YP, the labeling algorithm “finds {X, Y}, the respective heads of XP, YP, and there is no label unless they agree (Chomsky 2015: 7).” This latter proposal does away with the notion of endocentricity, since there is no head of this {XP, YP} projection. Rather, there are two primary ways that an SO of the form {XP, YP} can be labeled. One way labeling can occur is if the SO is modified via movement of the XP or YP out of the SO.¹ For example, if XP moves out of an SO of the form {XP, YP} and merges in a higher position, then the label of the SO becomes the label of the YP, since not all instances of XP are contained within this SO. Note that movement here refers to merge of another instance of the XP in a higher position in the structure. Epstein, Kitahara, and Seely (2014) basically describe this approach as follows: given SO_k = {_A NP, {T, {_B NP, {v, VP}}}}, the highest copy/instance of the NP is in the domain of the entire SO that is labeled A, since every instance of the NP is within this domain. The lower NP instance, however, is not in the domain of B since not every instance of this NP is within this domain. Thus, the label of B is the label of {v, VP}. Another way that an SO of the form {XP, YP} can be labeled is if XP and YP share, via agreement, prominent features; prominent features discussed by Chomsky are phi-features and a Q feature, although the possibility of other features that are capable of labeling remains. So if XP and YP in an {XP, YP} structure have identical phi-features (resulting from an agreement relation), the labeling algorithm identifies these shared features as the label. The labeling operation is summarized below. A “strong head” is a head that is strong enough to label.²

Feature inheritance also plays an important role in POP. Chomsky (2013) follows Richards’ (2007a) proposal that T inherits its features from C, which accounts for the difference between finite and non-finite T. Finite T inherits its features from C, whereas non-finite T occurs without C, and thereby lacks core tense and agreement features. Chomsky (2015) suggests that feature inheritance also occurs within a v*P, so that the features of v* are inherited by a verbal root. The feature inheritance operation is summarized as follows.³

One question arises with respect to shared features: when an {XP, YP} structure is labeled via shared features, if YP is unlabeled, how does YP obtain a label? According to Chomsky (2015), lexical roots, as well as T, are too weak to label. In Figure 1a below, there is a verbal root read that merges with an object a book. Assume that when v* is merged, the uPhi (uninterpretable phi-features) of v* are inherited by read, and the uPhi agree with a book, which remerges with read. The result is that shared phi-features label the structure {a book, read a book}. But it is not clear what the label is of the structure {read, a book}. Similarly, when a subject remerges with T (present tense Tpres), uPhi of T (which are inherited from C) agree with the phi-features of the subject, so that shared phi-features label (Figure 1c). But assuming that T is too weak to label, then it isn’t clear what the label of the lower {T, XP} structure is.

Chomsky (2015) relies on strengthening to account for labeling of projections that are initially too weak. Chomsky (2015: 10) writes, “[j]ust as English T can label TP after strengthening by SPEC-T, so R [Root] can label RP after object-raising.”⁴ In Figure 1c, shared phi-features (indicated as Phi2) label the previously unlabeled SO {Tom, Tpres read a book}, thereby strengthening Tpres, so that Tpres can label the intermediary projection (see Figure 1d). Similarly, in Figure 1a, shared phi-features (Phi1) label the structure {a book, read a book}, and this results in strengthening of the root read, so that read can label the intermediary projection (see Figure 1b).

Chomsky refers to “strengthening” in this labeling process, raising the question of what exactly strengthening is. Strengthening refers to the process whereby a projection that is “unlabelable”, due to the lack of a prominent feature, becomes “labeable”. In Figure 1a and 1c, the previously unlabelable {XP, YP} projections obtain shared phi-features, thus becoming labelable (i.e., they are strengthened). In Figure 1a–b, the intermediary projection has the verbal root read as a root node, where read initially contains no prominent features that are capable of labeling. After read inherits uPhi from v* and these uPhi are checked, then read contains checked phi-features, which are capable of labeling because they are visible to the labeling algorithm; thus read is strengthened. Similarly, in Figure 1c–d, T, which is initially too weak to label, is strengthened after its inherited uPhi features are checked, so that it can label. We formulate strengthening as follows.

Figure 1

Labeling of intermediary projections via strengthening⁵ (“Tom reads a book.”).

Note that Figure 1 could also be represented as shown below in Figure 2, with the strengthened intermediary nodes labeled by the prominent features. When an intermediary projection is strengthened, the labeling algorithm finds the prominent features in the root node of that projection, and in the cases in Figures 1–2, the prominent features are phi-features. Thus, it is reasonable to assume that the labels of the intermediary projections in these cases are phi-features. However, we will use the type of representation shown in Figure 1 because it is easier to read.

Figure 2

Labeling of intermediary projections with phi-feature label (“Tom reads a book.”).

2.2 Cyclicity

In the original version of POP from Chomsky (2013), derivations are counter-cyclic. Consider the derivation of (5).

As shown in Figure 3a, v* is merged, and then features are inherited by the verbal root read. Next, shown in Figure 3b, there is an agree relation formed between the inherited uPhi of v* and a book, followed by remerge of a book. This remerge operation is necessary to enable labeling via shared phi-features. Note that remerge of the object does not occur until after v* is merged, so this operation is counter-cyclic. This violates the Extension Condition (Chomsky 1995), since it requires altering, via movement, an already constructed SO. Shared phi-features label the SO, with an {XP, YP} structure, formed from the remerged object and the verbal root, and the lower structure {read, a book} is labeled by the strengthened read, in accord with Strengthening, defined in (4) above. Figure 3c shows merge of C. At this point, the uPhi of C are inherited by Tpast, and an agree relation is established between the inherited uPhi of Tpast and the subject. As shown in Figure 3d, the subject remerges counter-cyclicly. Remerge of the subject enables v* to label – movement of Tom leaves v* as the most prominent XP in the relevant structure so that v* can label. Then due to the relation Agree(Tpast,Tom), the shared phi-features of the subject and Tpast label, and the strengthened Tpast labels.

Figure 3

“Tom read a book.” with countercyclic steps.

Chomsky (2015) proposes a non-countercyclic approach. He writes that the counter-cyclic operation of movement of a subject to T after merge of C “is problematic, as pointed out by Epstein, Kitahara, and Seely (2012), because it involves a substitution operation that is ternary, even though only narrowly so (Chomsky 2015: 13).”⁶ A cyclic derivation avoids this undesirable substitution operation.

Chomsky (2015) suggests a way in which a non-counter-cyclic derivation is possible; this proposal requires that movement precede feature inheritance. The relevant portions of the bottom-up derivation of (5), with no counter-cyclic movement operations, proceed as shown in Figure 4. After the verbal root read is merged, the object a book remerges with the unlabeled structure {read, a book}, producing another unlabeled structure (Figure 4a). After v* is merged (Figure 4b), the features of v* are inherited by read. Then the shared phi-features of read and the object label. Later in the derivation, shown in Figure 4c, the subject remerges with the Tpast structure to form an unlabeled structure. Note that movement of the subject enables v* to label, since not all copies of the subject are contained within this structure. At the last stage, shown in Figure 4d, C is merged, followed by inheritance of the uPhi of C by Tpast. Tpast agrees with the subject, and uPhi and uCase are checked. The phi-features shared between the Tpast structure and the subject label.

Figure 4

“Tom read a book.” with no countercyclic steps.

This derivation shown in Figure 4 has the advantage over the derivation shown in Figure 3 in that it is not counter-cyclic, as there is no need to alter (at least with respect to movement) an already formed SO. We adopt this non-countercyclic view.

2.3 Probing from the root node and feature unification

POP faces problems with respect to feature checking and cyclicity. As pointed out by Richards (2007b), probing in Phase Theory (Chomsky 2000; 2001; 2008, etc.) is technically only a property of root nodes (e.g., the root node T probes for and agrees with a goal subject in the specifier of the projection of v*). Probing from a non-root node is counter-cyclic, since it involves altering an already constructed syntactic object. Furthermore, limiting probing to only the root node (the top of the current structure) simplifies the derivational process, since only the root node is involved in probing. But feature inheritance implies that there can be probing from a non-root node. Consider what happens at the v* phase level, as shown in Figure 5. The uPhi of v* are inherited by the verbal root read, and read eventually agrees with the object a book. If the verbal root read probes, via its inherited uPhi features, and agrees with the object (either before or after the object has moved), then there is probing from a non-root node, since the root node is v*, not read.

Figure 5

Probing from non-root node read.

We take the position that probing is limited to root nodes, relying on the idea that feature inheritance leads to multiple unified (i.e., identical) instances of a feature in a structure, following Fong (2014) who takes a similar approach to account for multiple agreement in Chomsky (2001).⁷ When any instance of this feature is checked, then all instances are checked. This view is summarized in (6).

For example, in Figure 6, uPhi of v* are inherited by the verbal root read. Thus v* and read have unified uPhi features. The uPhi on v* also probe and agree with a book. This relation Agree(v*,a book) checks the uPhi on v*, as well as the unified uPhi on read. As a result of this feature checking relation, read now has phi-features that are shared with a book, thereby enabling labeling via shared phi-features. Crucially, only the uPhi on the root node v* probe. Thus, in a single probing operation, the uPhi on v* probe and find read (resulting in feature inheritance) and a book (resulting in feature checking).⁸

Figure 6

Probing from the root node and feature unification.

An anonymous reviewer points out that feature inheritance, whereby features pass from a root node to a non-root node in a previously constructed syntactic object, alters an already formed syntactic object, and thus, is counter-cyclic. For example in Figure 6, uFs inherited from v* are passed to read, thereby altering an already constructed SO. While this may be an imperfection of the current system, it is one that is inherited from POP, since POP requires feature inheritance. However, we think that our system is an improvement over the manner in which feature checking occurs in POP, because in our system probing is limited to a root node, whereas in POP, it appears as though probing is not limited to root nodes.

2.4 Movement

In POP, movement operations are closely connected with labeling, due to the fact that movement is required in order to produce configurations that can be labeled via shared features. The configuration in Figure 7a shows the structure necessary for shared feature labeling. Starting with a label-less structure, formed from a lexical root or head that is too weak to label and an XP complement, as shown in Figure 7b, if the XP remerges with the label-less structure (Figure 7c) and features are shared between the two structures, then labeling occurs, as shown in Figure 7d (assuming that shared phi-features label). In this case, the previously unlabeled intermediary projection is labeled as a result of strengthening, as defined in (4), after its inherited uPhi are checked. This is the type of structure that is found in object shift constructions. Another method of obtaining a label is shown in Figure 7e–f. In this case, a phrasal structure ZP, which is contained within the unlabeled SO complement of Y, remerges with the root node (i.e., undergoes internal merge). If ZP and the unlabeled SO share phi-features, then the shared features label, as shown in Figure 7f. This is the type of movement that occurs when a subject moves from the vP level to the TP level. Chomsky (2015: 9) proposes that tense in languages such as English “is too “weak” to serve as a label.” Therefore, movement of a DP to remerge with T enables labeling via shared phi-features, as in Figure 7f.⁹

Figure 7

Labeling and movement.

Assuming that derivations are cyclic, given an unlabeled structure, the closest SO to the unlabeled root node that has phi-features remerges with the root node. In Figure 7c, the closest SO with phi-features is XP, whereas in Figure 7e, the closest SO with phi-features is ZP.

Figure 7 shows instances in which movement turns a label-less structure into a labeled structure, but movement does not always result in labeling, as can be seen with respect to wh-movement. Examples (7b–c) show relevant portions of the structure of (7a).

In POP, under normal circumstances, the complement of a phase head is transferred (see section 2.5 below). In (7b), what must remerge with the embedded C projection; otherwise, when the complement of C is transferred, what will be transferred. Note that (7b) is an unlabeled {XP, YP} structure. (7c) shows the matrix clause, with an interrogative C, indicated as C_Q. If we understand correctly, according to Chomsky (2013; 2015), movement of a wh-phrase in this type of construction is required to create a structure that is labeled by a Q feature that is shared between the wh-phrase and the interrogative C. This shared Q label is needed for semantic reasons, to produce a well-formed wh-question.¹⁰

The core movement operations are summarized in (8).

If there is an unlabeled structure, movement occurs whereby the closest available SO with phi-features remerges with the root node. An SO is available if it is not within a transferred domain.^11,12 Movement also occurs in order to create a configuration in which labeling is possible for semantic reasons (8b), or as a last resort mechanism in order to prevent an unlicensed element from being transferred (8c).¹³ Note that there are instances in which other constraints may block remerge/movement of an unlicensed SO (see discussion of (14) below).¹⁴

2.5 Transfer and dephasing

Chomsky (2015) takes the position that the complement of a phase head is transferred.¹⁵ After transfer, this complement essentially becomes frozen, possibly inaccessible to higher operations. Also, when a derivation is completed, the entire structure must be transferred.¹⁶ The transfer operation is summarized in (9).

The transfer operation lightens the computational workload by setting aside already constructed SOs.

Chomsky (2015) proposes that movement of a verbal root results in dephasing of the v* structure. The Exceptional Case Marking (ECM) construction with wh-movement in (10) shows why this is necessary.

Consider (10) at the point that the matrix verbal root expect and v* have merged, as shown in (11a). The embedded subject who has raised to the matrix clause and remerged. The phase head v* merges with this structure, and after feature inheritance and feature checking, shared phi-features of the verbal root expect and the subject who label. If the complement of a phase head must be transferred, in accord with (9), then the structure labeled by shared phi-features will be transferred. However, if this structure is transferred, then who will no longer be accessible to the matrix C and the derivation cannot converge. Chomsky’s proposed solution to this problem is that the verbal root expect raises and remerges with v*, so that v* affixes onto expect, shown in (11b). Since the phase head v* is now an affix, it is invisible – invisibility results in dephasing, so that the complement of v* is not transferred. Rather, phasehood is transferred to the verbal root expect and the complement of expect (in base position) is transferred. When the matrix C is merged, it can then access who and the derivation converges successfully.

Chomsky (2015) also proposes an analysis of that-trace effects that involves dephasing, in which case T inherits phasehood, and the complement of T, rather than the complement of the phase head C, is transferred. For more on that-trace effects, see the discussions in the following sections. The dephasing operation is summarized as follows:

2.6 Wh-movement

We next turn to how the timing of labeling and transfer relates to constructions that involve extraction of a wh-phrase out of an embedded clause and the well-known that-trace effect, as in (13a–c).

First, we discuss how Chomsky (2015) accounts for examples (13a–c),¹⁷ and then we explain how we account for these constructions.

Note that we assume that a wh-phrase is headed by a Q morpheme that checks an uninterpretable Q feature on an interrogative C, following work by Cable (2010) and Hagstrom (1998), among others.¹⁸

The relevant portions of (13a) are shown in Figure 8. In (13a), after merge of C that, the features of that are inherited by Tpast, followed by feature checking and remerge of what. Then labeling (see (2)) applies. There are no labeling failures within the embedded clause; the object what and its SO complement read a book are labeled via shared phi-features within the v* phase. The root node in Figure 8a is an unlabeled {XP, YP} structure, but it will be successfully labeled after what moves to remerge with the matrix C_Q. In (13a) with a null C, Chomsky takes the position that there is deletion of that resulting in dephasing (see (12)). Specifically, phasehood is inherited by T and the complement of T is transferred. In this case, after C is merged, there is feature inheritance, feature checking and remerge of what with C. Then C is deleted, resulting in the structure in Figure 8b after labeling has occurred. Again, there are no labeling failures.

Figure 8

Chomsky’s (2015) account of “What do you think (that) John read?”

Note that in Figure 8a–b, it is necessary for what to remerge with C before transfer occurs. In Figure 8a, if what does not remerge with C before transfer of the complement of that, then what will be transferred. In Figure 8b, if what does not remerge with C¹⁹ before the complement of T (the v* projection) is transferred, then what will be transferred with the v* projection.

The that-trace effect in the ill-formed (13b) results from a labeling failure. After that is merged, there is feature inheritance, feature checking and remerge of who with the that projection. But then when the labeling algorithm applies, there is a labeling failure at the point shown in Figure 9 because not all instances of who are contained within the phase that is headed by that.

Figure 9

Chomsky’s (2015) account of “*Who do you think that read the book?”

In order to account for (13b), as shown in Figure 9, it is necessary to assume that labeling does not occur until after who remerges with that; i.e., labeling occurs at the C phase level. If labeling were to occur immediately after C that is merged, but before who remerges in a higher position, then the relevant {XP, YP} structure, formed from who and the embedded T clause “Tpast read the book”, would be successfully labeled via shared phi-features. This is because at the point at which that is merged, all instances of who are in the relevant domain, so that who should be visible to labeling. Then, after labeling, who would move out (assuming that transfer has not yet occurred), thus predicting that this example should be well-formed.

While Chomsky (2015) successfully accounts for the contrast in (13a–b), the situation regarding the well-formed (13c) is somewhat murky. In (13c) deletion of C results in dephasing, thus avoiding a labeling failure involving the subject wh-phrase. There are at least two possibilities for how this works.

The relevant portions of one possible derivation are shown in Figure 10. C is merged, followed by remerge of who, shown in Figure 10a. Then C deletes, phasehood is transferred to Tpast and the complement of Tpast is transferred, shown in Figure 10b. Note that after C deletion, a “strange” configuration arises with two instances of who at the edge of the embedded clause. In this case, the instance of who that is merged with “Tpast read the book” is not the highest instance of who. When this structure is eventually labeled, presumably at the next phase level, the question arises as to whether or not this lower who is visible to the labeling algorithm. If the lower who is not visible, then there should be a labeling failure.

Figure 10

Chomsky’s (2015) account of “Who do you think read the book?”

There is also another possible way of accounting for (13c). Simply assume that C deletes before who can remerge with C. After C is merged, there is feature inheritance, followed by deletion of C, shown in Figure 11a–b. If labeling then occurs, the {XP, YP} structure consisting of who and “read the book” should be successfully labeled.

Figure 11

Chomsky’s (2015) account of “Who do you think read the book?”

The facts regarding (13a–c) are summarized in Table 1.

To summarize, (13a) can be accounted for because there are no labeling failures regardless of whether or not C is deleted. Crucially, what must remerge with C. (13b) is accounted for as resulting from a labeling failure, but only if labeling occurs after who has moved out of the C phase. (13c) can be accounted for by assuming that deletion of C avoids a labeling failure. The latter case is complex in that it either a) results in a complex structure with two instances of who at the edge of the embedded clause (Figure 10), or b) it results from deletion of C before who remerges with C (Figure 11). The latter option in which who does not remerge with the C projection seems to be optimal, since then there are no problems for the labeling algorithm. However, the latter option raises the following question: if a wh-phrasal object must remerge with C (that) before C deletes, then why can’t a wh-phrasal subject also remerge with C? If the derivation in Figure 11 is correct, then there appears to be a wh-subject vs. wh-object remerge asymmetry that requires an explanation.

In this paper, we propose an analysis of (13a–c) that accounts for the relevant data, but that avoids these complications inherent in Chomsky (2015). We develop an analysis in which there is no requirement that labeling be delayed until after who moves out of the embedded clause as in Figure 9, and the complexities of Figures 10–11 are avoided.

The derivation of (13a), as proposed by Chomsky is unproblematic. Figure 12a shows the structure after v* has been merged. At the v* phase level, features of v* are inherited by the verbal root read. Feature checking between read and what occurs, and read remerges with v*, resulting in dephasing of v*. The structure {what, read what} is labeled by shared phi-features. Normally, at this point, the complement of v* would be transferred. However, because v* is dephased (see (12)), transfer of the complement of v* does not occur. Rather, the complement of the verbal root read is transferred, and thus the lower instance of what is transferred. Note that the higher instance of what is outside of the transferred domain, so it remains accessible to higher operations. After merge of C that, shown in Figure 12b, features of that are inherited by Tpast. Then labeling occurs. At this point, the Movement operation (8c) requires an unlicensed SO that is about to be transferred to remerge with the root node. As a result, what remerges with the root node, thereby escaping transfer. When transfer occurs, the complement of that is transferred. There are no labeling failures (the lower copy of what is in a structure that has already been labeled), and the higher copy of what remains accessible to further operations, so that it can eventually remerge with the matrix C_Q. The derivation successfully converges.

Figure 12

Extraction of an object wh-phrase from “What do you think that John read?”

Consider what happens when there is deletion of C that in (13a). After merge of v*, there is feature inheritance and labeling. Just as in Figure 12 above, the complement of v* is labeled by the shared phi-features of what and read. After merge of C, there is feature inheritance and labeling, shown in Figure 13a. Then, there is deletion of C, shown in Figure 13b. After deletion of C, phasehood is transferred to Tpast, and the complement of Tpast will be transferred. In order to avoid transfer of the unlicensed wh-phrase, the Movement operation (8c) requires what to remerge with the root node, as shown in Figure 13c. Then the complement of Tpast is transferred. Crucially, there is no labeling failure, and the higher instance of what remains accessible to further operations so that it can eventually agree and remerge with the matrix C. Note that C is deleted as soon as its features are inherited.²⁰

Figure 13

Extraction of an object wh-phrase from “What do you think John read?”

We next turn to that-trace effects. Consider how the derivation of (13b) works in POP, as discussed above in Figure 9. In the embedded clause, that is merged, followed by remerge of who to produce the structure in Figure 14a. After feature inheritance and feature checking, labeling occurs. But in this case, there is a labeling failure – the SO formed from who and the T structure is unable to label via shared phi-features because who is no longer visible – there is a higher copy of who merged with the that projection. There is also another possibility. Assume that who does not remerge with that. Instead, shown in Figure 14b, there is no labeling failure. However, when the complement of that is transferred, who becomes inaccessible to higher operations, since it is contained within this transferred complement. This derivation also crashes. Thus, POP seems to be compatible with either version, that shown in Figure 14a (in which who remerges with that) and Figure 14b (in which who remains in subject position).

Figure 14

Crash timing in “*Who do you think that read the book?”

Our model implements this latter approach, shown in Figure 14b, in which who does not remerge with the root, which we propose is required due to the following Remerge condition, given in (14). The Remerge condition prevents an SO from remerging with another SO with which it shares features. Assume that an SO Y is contained within the SO X. If these two SOs already share features, then remerge of one SO with the other will not result in a new feature sharing relation, and thus remerge is blocked.

The Remerge condition in (14) accounts for the that-trace effect as follows; a wh-phrasal object can remerge with C, but a local wh-phrasal subject cannot. In Figure 15a, uPhi-features from C are inherited by Tpast, and the uPhi are checked via agreement with the subject who.²¹ When the uPhi on C are checked, C and the subject share phi-features. As a result, the subject cannot remerge with C, or there will be a violation of (14). If C is not deleted, then who is transferred together with the complement of C, resulting in ill-formedness (the that-trace effect). In the case of extraction of an object wh-phrase, after C is merged and features are inherited from C, the wh-phrase is located within the verbal projection, so it does not share features with C (Figure 15b). Therefore, what is able to successfully remerge with C, without violating (14), bringing what outside of the transfer domain, regardless of whether or not C that deletes. This analysis thus accounts for the that-trace effect as resulting from an inability for a subject wh-phrase (but not an object wh-phrase) to remerge with a local C.

Figure 15

Remerge constraint and that-trace effects.

Deletion of C saves (13c). Consider how this works. The C head is merged, followed by feature inheritance and labeling, shown in Figure 16a. Then C is deleted, resulting in Figure 16b when labeling occurs. Since all instances of who are in the relevant labeling domain, labeling by shared phi-features proceeds, followed by transfer of the complement of Tpast. Crucially, who remains accessible to higher operations.

Figure 16

Dephasing of embedded clause in “Who do you think read the book?”

2.7 The remerge condition, labeling, and cyclicity

The remerge condition has two other primary benefits. First, it enables simplification of the labeling process, so that there is never any need to delay labeling until the phase level. Second, it provides an explanation (or at least a partial explanation) for why derivations must be cyclic.

In Chomsky (2015), if we understand correctly, labeling occurs at the phase-level, after feature inheritance and feature checking. In Figure 17, originally shown as Figure 9 above, after that is merged, uPhi from that are inherited by Tpast. Crucially, labeling does not occur until after who remerges with the root, which results in a labeling failure, because who is not visible to the labeling algorithm in the T projection, which requires shared phi-features for labeling.

Figure 17

Crash timing in “*Who do you think that read the book?”

If our analysis is correct, there is no reason to delay labeling. As a result of the Remerge condition (14), the wh-phrase who cannot remerge with the projection labeled by that in the first place. As soon as inherited features are checked and an intermediary projection becomes labelable, the labeling algorithm should apply. Therefore, in (13b), as soon as uPhi are inherited by Tpast, and the uPhi are checked, labeling should take place. We propose the following:

For example, as soon as a head that is strong enough to label (v*, C, etc) merges with a phrasal element, the head labels. As soon as an {XP, YP} structure has identical shared features (or a single shared feature) that are capable of labeling, then the shared feature(s) label, as shown in Figure 18. Labeling is not delayed until after a phase is complete. The situation in Figure 17, in which a wh-phrase moves before labeling occurs in the embedded C projection, does not arise.

Figure 18

Immediate labeling.

Consider how Immediate labeling (15) works in our model to account for (13b). As shown in Figure 19a, when C that is merged, phi-features are inherited and checked, followed by labeling, via shared phi-features, of the projection containing the subject who and the projection of Tpast, and the strengthened Tpast also labels. The situation in Figure 19b, in which who remerges with that, does not arise because who cannot remerge with that due to the Remerge condition (14). As a result, who is transferred together with the complement of C that, so that who becomes inaccessible and the derivation crashes, as desired. In this manner, we can explain this example without needing to delay labeling until the phase level, contra Chomsky (2015).

Figure 19

Derivation of “*Who do you think that read the book?”

Also note that Immediate labeling (15) does not create problems for other examples. Consider (13a), repeated below.

In (16), shown in Figure 20a, when that is merged, the uPhi-features of that are inherited by Tpast, and uPhi on that are checked via agreement with John, so that the unified uPhi on Tpast are also checked. The result is that the subject and Tpast share phi-features, so the shared phi-features, as well as the strengthened Tpast, label. Then, shown in Figure 20b, what remerges with C that. Delaying labeling until after what remerges with the root that makes no difference for this derivation, and thus seems unnecessary.

Figure 20

Immediate labeling in “What do you think that John read?”

The Remerge condition in (14) also has a very important function. It requires derivations to be cyclic, an observation that we thank an anonymous reviewer for pointing out.²² Consider how this works. In Figure 21a, assume the counter-cyclic version of POP. When v* is merged, the uPhi of v* are inherited by read, and then there is an agree relation, whereby the uPhi on v* are checked by the iPhi on a book, and the shared uPhi on read are simultaneously checked. The result is that read and a book now share phi-features. Thus, in accord with (14), a book can’t remerge with read. However, if a derivation is cyclic, shown in Figure 21b, then a book remerges with read before v* is merged. At this point, a book and read don’t share any features, so there is no violation of (14). This is followed by merge of v*, at which point feature inheritance, feature checking, and ultimately feature sharing, can occur.

Figure 21

Remerge condition and cyclicity.

The Remerge condition also provides an explanation (or at least a partial explanation) for dephasing of v*.²³ Consider (10), repeated below as (17). Chomsky proposes that dephasing of v* enables who to remain accessible to higher operations; without dephasing, who would be transferred after merge of v*.

The movement operation (8c) requires an SO that is about to be transferred to remerge with the root node if possible. If there were no dephasing of v*, then the question arises of why who couldn’t just remerge with v* and escape transfer. This is blocked by the Remerge condition, because v* and who already share features, so who cannot remerge with C. The result is that dephasing of v* is necessary.

2.8 Labeling of verbs that take clausal complements and non-finite T

In constructions with a matrix verb that takes an embedded clausal complement, issues regarding how labeling occurs arise. Consider (13c), repeated as (18a).

The matrix verbal root think is too weak to label. A transitive verbal root is labeled by sharing phi-features with a raised object. Chomsky points out that the object of think should raise and remerge with the projection labeled ε in (18b), in the same way that an object raises and remerges with a verbal root in a simple transitive clause, such as in Figure 1 above. Chomsky (2015: 13) writes:

“Prior to raising of who to matrix SPEC, the object of think, δ, should raise to SPEC of ε, with the root think then raising to v*, the ordinary raising to object analysis. But questions arise about how ε should be labeled, since the raised object in this case lacks the relevant features; there is no agreement.”

Chomsky points out that if δ remains in situ, then these problems don’t arise. However, if δ were to remain in situ, then the question arises of how the projection of think is labeled, considering that a lexical root is too weak to label.

First, we assume that a verbal root that takes a sentential complement does not merge with a typical v*. Assuming that v* comes with uPhi and also assigns case, then v* cannot be present in the matrix clause in (18a), since there is no object for v* to agree with and assign case to. But the verbal projection is accounted for if it contains an unergative v, which we refer to as vUnerg. This a verb that requires a subject, but that lacks uPhi and does not assign case.²⁴

This vUnerg does not have uPhi features that are checked, and thus it is different from v*. It does not seem to be the type of element that is capable of labeling on its own. Even if it were capable of labeling, it isn’t clear how the root verb that it takes as a complement, think in (18), would end up labeled, since vUnerg does not pass any uPhi to its complement. Thus, the question arises of how labeling occurs in a configuration with a verb that takes a clausal complement.

We rely on feature inheritance, originally presented in (3) above. To account for feature inheritance in Figure 1, it was necessary for a phase head to pass its uPhi only to the head of its complement. But assume that feature inheritance can travel farther; i.e. there can be “super-inheritance” (a term proposed by an anonymous reviewer), whereby uPhi from a phase head travel down a tree until they cannot travel any farther. According to (19), a phase head passes its uninterpretable features (uFs) to its complement X, if the complement X is unlicensed. Furthermore, X will pass these uFs down to its complement Y, if Y is unlicensed, and so on. An unlicensed complement is unlabeled.

Consider how feature inheritance works in the derivation of (18). When the matrix C_Q is merged, note that the projections of vUnerg and think are unlabeled, shown in Figure 22a. C_Q passes its uPhi features down the tree, from Tpres to vUnerg and then to think. Further feature inheritance is blocked by the labeled embedded clause.²⁵ Then there is feature checking. All of the unified uPhi are checked via agree between the uPhi on C_Q and the matching phi-features on you. Then the projections with these valued phi-features are labeled. Note that there is still one projection, consisting of an {XP, YP} structure, with who merged with the projection of think, that remains unlabeled in Figure 22b. This projection, however, is labeled after who remerges with C_Q in order to be licensed, shown in Figure 22c.

Figure 22

Super-inheritance in “Who do you think read the book?”

This analysis also extends naturally to non-finite T. Chomsky (2015) takes the position that in English, T is labeled via shared phi-features. The question then arises of what happens to non-finite T to. Consider (20) with a nonfinite T in the embedded clause. Note that there is no local C from which the non-finite T could inherit uFs.

We can account for the labeling of non-finite T, which we refer to as toT, as resulting from feature inheritance, as in Figure 22 above. When v* is merged, its uPhi are inherited by the verbal root expect, toT, and vUnerg, shown in Figure 23a. Then after the uPhi on v* agree with the subject John, the unified uPhi are checked, so that labeling occurs, whereby the relevant projections are labeled by shared phi-features or by strengthened heads, resulting in Figure 23b.²⁶

Figure 23

Labeling of non-finite T.

2.9 The halting problem

Chomsky (2015) discusses (21a), in which the issue arises of why which dog can’t raise from the embedded interrogative clause. Chomsky refers to this as “the halting problem”, following Rizzi (2013).

Initially, which dog raises to the edge of the embedded clause, and then it raises to the edge of the matrix clause. Both the matrix and embedded clauses are projections of interrogative Cs. Assume that β is labeled after the higher matrix phase is constructed. At this point, which dog has raised to the matrix clause. Therefore, the embedded clause β is labeled by the interrogative C alone. This produces a yes/no construction. The matrix clause α is then labeled by the Q feature that is shared between the matrix interrogative C and the wh-phrase which dog. This shared Q feature produces a wh-question interpretation. The result is a wh-construction that contains a yes/no construction. Chomsky proposes that (21a) is ill-formed because a wh-question containing an embedded yes/no question is semantically ill-formed, so that it crashes at the Conceptual-Intentional Interface.

2.10 Summary

We have discussed the core components of POP. We have tried to clarify the crucial algorithms that are required to construct derivations in the POP model. On the way, we have examined the primary proposals of POP and tried to clarify how these proposals can actually be implemented, and we have discussed some issues/problems and developed some solutions to these problems.