A multi-dimensional derivation model under the free-MERGE system: labor division between syntax and the C-I interface

2.1 Derivational dimensions

The original notion of Pair-Merge is defined as an alternate Merge that produces an ordered pair ⟨α, β⟩ instead of an unordered set {α, β} (see Chomsky 2000, 2004, 2008). This operation is specially proposed for adjuncts. The core idea of Pair-Merge is the introduction of a “separate plane”, which is subsumed under a syntactic object in the main panel of derivation, such as the AdjP young under the NP man in the NP young man, formally represented as ⟨_NP {_AdjP young}, {_NP man}⟩. The idea of separate planes reflects the assumption that there exists more than one derivational dimension in human language (see Chomsky 2020b). This assumption is based on the fact that stacked modifiers could each link to the same modifiee independently, such as in happy young man; we will refer to this parallel interpretation of multiple modifiers as the Markovian reading (see Irurtzun and Gallego 2007).

We now turn to the ontology of dimensions. The assumption that multi-dimension is an inherent property of human language will be a fundamental assumption for our analysis. Obviously, “dimension” here does not refer to the physical notion, because the physical parameters such as length or height do not concern syntax. Derivational dimensions are actually abstract panels for syntactic computation. In this article we treat the derivational dimension as a domain-specific property of human language, an inherent aspect in any syntactic derivation.

A note is due regarding the relation between derivational dimension and MERGE as a set-theoretical operation. It is important to distinguish between the abstraction of language and language itself. MERGE as a set-theoretical operation is a powerful abstract representation of the mechanisms in the faculty of language, which is expected, because the set-forming binary operation, being the logically simplest operation, should properly describe MERGE’s function at a certain level. However, this abstraction does not cover everything. The real items in the language activities are more complex than their abstractions, and these complications would have effects on the language activities. Dimension is such an example. The existence of Markovian reading already constitutes the argument in support of derivational dimension as a valid property of items in language. MERGE as defined in set theory does not cover dimension, and dimension does not hinder the abstraction using set theory either. We will not modify the definition of MERGE, because the issue of dimension is not a prominent matter unless relevant problems in coordination and adjunction are involved.

The question then falls on the relations between dimension, workspace, and phase, which all mark the boundaries of the derivation course in some sense. First, derivational dimension is not workspace. Under Chomsky’s (2019, 2020b) model, workspace hosts the two merged syntactic objects. The number of workspaces resulted from each MERGE can only be one. MERGE works on workspace and keeps the workspace from expanding: External MERGE always reduces the workspace by one, and Internal MERGE keeps the workspace the same. By contrast, there is no limits on the number of derivational dimensions. In fact, derivational dimension and workspace are two independent components of human language, although they do interact one with the other. A given workspace may contain more than one dimension, and the syntactic objects in each dimension can be merged from multiple workspaces.^[3] Second, derivational dimension is not phase. Different from phase, which is linked to the limited working memory of human brain, derivational dimension is not limited in such a way. Quite on the contrary, derivational dimension is capable of tracing multiple syntactic derivations, and therefore, it does not reflect the limitation of working memory.^[4] Concrete case studies will be presented in Sections 3 and 4.

2.2 Set-MERGE and Pair-MERGE under the multi-dimensional approach

With the notion of derivational dimension established as an entity independent of workspace and phase, the division between Pair-MERGE and Set-MEREGE is only a natural result. In our model, there is only one type of MERGE, and MERGE can either keep the two merge-mates in the same dimension, or, send them into two different dimensions, as this is taken as an inherent property of MERGE. The former case corresponds to Set-MERGE, and the latter Pair-MERGE. Very importantly, Set-MERGE and Pair-MERGE are not two different operations under our model. Operation-wise, Pair-MERGE does not do more than Set-MERGE given that they only differ in one aspect: the two merge-mates are in the same dimension or in different dimensions. In this sense, Pair-MERGE is just as primitive as Set-MERGE.^[5]

On the other hand, Labeling Algorithm (LA) is assumed to be limited to one dimension, and each dimension has its own LA. The LA inside one dimension ignores syntactic objects merged from other dimensions. This assumption naturally solves the labeling problem for adjuncts. When XP and YP are merged, instead of Set-MERGE, XP can be pair-merged to YP from a different dimension. Each dimension has its own labeling, so inside the dimension where YP (but not XP) is located, LA will ignore XP and label the structure as YP, producing ⟨_YP XP, YP⟩. Likewise, the LA inside XP’s dimension will produce ⟨_XP XP, YP⟩. Different labeling possibilities will give rise to different interpretation possibilities at the C-I interface. When the resulting multi-dimensional structure is transferred to C-I, C-I will judge the competition of different labels, ruling in the label that cues an appropriate interpretation and ruling out the label that cues gibberish. For instance, if C-I can only interpret XP as the modifier of YP but not the opposite, then the structure with the labeling ⟨_XP XP, YP⟩ will be filtered, the same way as C-I filters uninterpretable deviant structures (see Figure 1).^[6]

Figure 1:

Labeling and multi-dimension.

Take the Pair-MERGE of young and man, ⟨{_AdjP young}, {_NP man}⟩, as an example. From the point of view of C-I, when it sees that young and man are located in different dimensions, it will try to interpret their relation with modification relation. Then, C-I sees that two possible labels are assigned to the resulting structure ⟨{_AdjP young}, {_NP man}⟩: NP and AdjP. When the structure is labeled as ⟨_NP {_AdjP young}, {_NP man}⟩ inside the dimension where man is located, it is young that modifies man, whereas when the structure is labeled as ⟨_AdjP {_AdjP young}, {_NP man}⟩ inside the dimension where young is located, it is man that modifies young. C-I will see that only the former way of modification gives rise to a correct interpretation. As a result, the latter labeling ⟨_AdjP {_AdjP young}, {_NP man}⟩ is then filtered. Set-MERGE works in a similar way. Take the Set-MERGE of {_VP eat, {_DP an apple}} as an example. When C-I sees that eat and an apple are located inside the same dimension, and that the label of the resulting structure is VP, it will interpret the structure as (partial) argumental relation: an apple being the patient of eat.^[7]

Note that the existence of Pair-MERGE is not dictated by the need of resolving labeling problems, so Pair-MERGE is NOT a last-resort to the labeling problem. Contrary to the common assumption that Pair-MERGE exists to solve the labeling problem of adjunction, in our analysis, Pair-MERGE and Set-MERGE are both primitive. Pair-MERGE feeds labeling only by contingency (‘nature’s grace’), because dimensionality exists independently of labeling. Relatedly, there is no absolute “stem” or “main” dimension during the syntactic derivation, because at syntax each dimension is independent and equal. The assignment of ‘stem dimension’ is not done until C-I.

2.3 Labor division between syntax and the C-I interface

Although MERGE is free, there are filters on the output of the operation. Same as what has been proposed for Set-MERGE, there are at least two conditions that the output of Pair-MERGE must satisfy. The first one is the Full Interpretation Condition. The output that feeds the interface system can only contain interpretable features, but not any uninterpretable features. The second filter is the Legibility Condition. The C-I system filters out the outputs that are incomprehensible.

This paper also proposes a strict mapping from syntax to semantics, at a rather fundamental level. A necessary assumption here is that the type of MERGE indicates how C-I interprets the structure. Syntactic objects (SO) resulted from Pair-MERGE will be interpreted in terms of modification relation or coordination relation. Concretely, when the pair-merged SO are of different categories, modification relation is assigned; by contrast, when the pair-merged SO are of the same category, coordination relation is assigned. We will further argue that coordination is an unstable relation assigned by C-I, and that under certain circumstances, it can be discarded in favor of other possible relations, such as modification, as will be demonstrated in detail in Section 6.

It is not hard to see that Set-MERGE only accepts certain types of interpretation relations as well: a set-merged structure is either interpreted as an argument structure or as conveying discourse functions, which introduces scopal relations, but a set-merged syntactic object is never interpreted as modification relation.^[8] For a quick demonstration, the external argument (EA) DP-the student, when merged with the vP-bought a book, could resort to Pair-MERGE, which is a sound syntactic possibility, as shown in (1).

However, this derivational option is problematic at C-I, because C-I cannot interpret the EA the student as the modifier of the vP-bought a book. C-I will thus reject the possibility to pair-merge the EA. In this regard, a tight connection exists between LA and MERGE. The connection is the C-I system. Both MERGE and LA contributes to the interpretation at the C-I interface, which is in accordance with the Strong Minimalist Thesis, and satisfies the Legibility Condition. However, Pair-MERGE and LA make different contributions to C-I. Pair-MERGE indicates to C-I that the type of relation between the two merged syntactic objects, located in different dimensions, is modification. Labeling indicates to C-I which one of two merged syntactic objects is interpreted as the modifier, and which one is interpreted as the modifiee. Finally, it is up to C-I to decide which labeling gives rise to a correct interpretation.

3.1 Simple adjunction

Start with the simplest scenario, where a “stem” syntactic object is modified by one adjunct. Two cases will be discussed: manner adverbs and gapless relative clauses.

3.1.1 Manner adverbs

Sentences in (2a, b) illustrate three possible positions where a manner adverbial adjunct can appear. These sentences are adopted from Chomsky (2021) examples.

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a.	The mechanic who fixed the car carefully packed his tools.
b.	?? Carefully, the mechanic who fixed the car packed his tools.

Sentence (2a) is ambiguous. The mechanic could have packed his tools carefully, or could have fixed the car carefully. The former reading has the modification on the matrix verb level, the latter on the embedded verb level. (2b) on the other hand has the modification unambiguously on the matrix verb level. We now examine the derivation of these three cases.

1. Embedded verb level:

The modifier carefully is pair-merged with the embedded VP from a different dimension, and as a result, Labeling Algorithm in VP’s dimension will ignore carefully, and the resulting structure α will still be labeled as VP. Given that carefully is pair-merged with the VP, C-I will interpret it as the modifier of the verb. If α is labeled as VP, (2a) will be interpreted successfully as modification on the embedded VP. This option is illustrated in (3a, b). In (3b), the two derivational dimensions are separated by the dotted line, and the dimension where an adjunct is located is indicated in gray.

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Given our assumption that Labeling Algorithm is limited to one derivational dimension, labeling across different dimensions is impossible. Each derivational dimension has its own labeling. Accordingly, the LA in the dimension where carefully is located will label α as AdvP, as illustrated in (4a, b). This labeling will result in a structure that will be filtered by C-I, given the Legibility Condition, because C-I will have no way to interpret the VP as a modifier of the AdvP. This resulting structure is then uninterpretable.

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1. Matrix clause level:

Carefully is pair-merged with the matrix VP from a different dimension, and the resulting structure β will be directly labeled as VP, because the modifier dimension is ignored for LA. This option will give rise to the reading where the modification is on the matrix VP.

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1. Left-Peripheral level:

To derive (2b), carefully must be pair-merged with the TP (i.e., ⟨ϕ, ϕ⟩) from another dimension. The resulting structure is not perfectly acceptable. C-I cannot interpret a manner adverb, such as carefully, as a modifier of an entire TP. For the speakers who accept it, carefully is still read as a modifier of the matrix verb observed. Note that at the surface level, the apparent position that carefully occupies can be analyzed as a topic position; however, a manner adverb cannot be interpreted as a topic by C-I either.

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Different from carefully, the adverb slowly can be either a VP-level manner adverb, as in (7a) or a sentential adverb meaning “gradually”, as in (7b). Importantly, modification must be local, which is reflected in syntax. Given that modification relation is local, C-I will interpret slowly in (7a) as a modifier of the verb write. Slowly in (7b) is traditionally analyzed as an adjunct of the entire TP, which gives rise to a syntactically possible derivation. This means that (7b) involves no topicalization structures.

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3.1.2 Nouns with complex modifiers

Nouns with complex modifiers including clausal modifiers are very productive in languages such as Japanese, Korean and Chinese (see Keenan and Comrie 1977; Kuno 1973; Matsumoto 1997; Matthews and Yip 2017; Zhang 2008). (8) Shows two examples from Japanese and Chinese.

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The modifier clause, TP in Japanese, and CP (headed by de) in Chinese, will be pair-merged to the NP from another dimension, and the resulting structure will be labeled as NP by the Labeling Algorithm inside the dimension where this NP is located. The relevant structure is also referred to as gapless relative clause in Chinese as there is no gap which corresponds to the antecedent NP. At the C-I interface, the CP will be interpreted as the modifier of the NP. Note that gapless relative clauses should be crucially differentiated from complement clauses of noun, as in (9).

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In (9), the clause CP is the complement of the head noun, which is derived by set-merging the CP with the N head. Given that N is the head, the resulting structure is labeled as NP. Note that both CP and N are located in the same dimension. C-I will thus interpret the relation between the CP and the N as complementation rather than modification.^[9]

3.2 Multiple adjuncts

This section examines more complex cases involving multiple modifiers.

3.2.1 Deriving the Markovian reading

The so-called Markovian reading refers to cases where the multiple modifiers are interpreted in parallel (see Irurtzun and Gallego 2007). In (10), each modifier is located in a separate dimension.

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The AdjP-young cannot be set-merged with the NP-man because the resulting structure, {_?? {_AdjP young}, {_NP man}}, in unlabelable. Instead, young will be pair-merged with the NP-man from another dimension and the resulting structure, {_NP {_AdjP young}, {_NP man}}, is labeled as NP given that the Labeling Algorithm in the dimension where the NP man is located will ignore young. Equally, the LA in the dimension where young is located will ignore man by labeling the resulting structure, {_AdjP {_AdjP young}, {_NP man}}, as AdjP. However, C-I can only interpret young as a modifier of man but not the other way around, and as a result, only {_NP {_AdjP young}, {_NP man}} gives rise to the correct interpretation. Next, in a similar way, the AdjP-happy will be pair-merged with the NP-(young) man resulting in a structure labeled as NP. Note that happy and young are located in different dimensions, and both of them are invisible to the LA in the dimension where man is located. Importantly, happy and young are in different dimensions as well, and there is no relation between these two dimensions, as can be seen in (10c) and Figure 2. As a result, there are three dimensions involved in final output. This derivation gives rise to the Markovian reading, where the two modifiers are parallel.

Figure 2:

Markovian reading.

3.2.2 Deriving the non-Markovian reading

Examine the derivation of the non-Markovian reading in (11), where the adverb extremely modifies the adverb fast.

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In (11), the AdvP-extremely seeks to set-merge with the AdvP-fast, and the resulting structure is unlabelable given the {XP, YP} pattern. Alternatively, these two are pair-merged. In the dimension where extremely is located, the Labeling Algorithm will label the structure as AdvP-degree-extremely by ignoring fast. However, this labeling will be filtered by C-I as fast cannot be a modifier of extremely. By contrast, in the dimension where fast is located, the LA will label the structure as AdvP-fast by ignoring the degree adverb extremely, and C-I will interpret the latter as the modifier of the former. Next, the resulting structure will be pair-merged with the VP-runs. The LA in the dimension where runs is located will label the structure as VP by ignoring the AdvP-(extremely) fast, and C-I will interpret extremely fast as the modifier of runs. Similarly, the LA in the dimension where the AdvP-(extremely) fast is located will label the structure as AdvP; however, this labeling will be filtered by C-I as the VP-runs cannot be the modifier of the AdvP-(extremely) fast. See also Figure 3.

Figure 3:

Non-Markovian reading.

4.1 Case (I): both labelings are interpretable at the C-I interface

This case can be easily evidenced by Chinese compound words (see Chao 1968; Li and Thompson 1981). In (12), the NP-xuě ‘snow’ and the AdjP-bái ‘white’ cannot be set-merged, but can only be pair-merged. In the dimension where bái ‘white’ is located, the NP-xuě ‘snow’ is pair-merged to bái ‘white’, and the resulting structure is labeled as AdjP meaning “white as snow”, as illustrated in (12a). By contrast, in the dimension where xuě ‘snow’ is located, the AdjP-bái ‘white’ is pair-merged to the NP-xuě ‘snow’, and the resulting structure is labeled as NP meaning “white snow”, as shown in (12b). Both labelings are interpretable at C-I.

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Similar effects are also observed with the serial verb constructions (see Li and Thompson 1981) for the description of this type of structures). The sentence in (13) contains two VPs, yòng kuàizi ‘use chopsticks’ and chī fàn ‘eat food’.

The two VPs are externally set-merged, and the resulting structure α is unlabelable given the {XP, YP} pattern.

VP1-use chopsticks is pair-merged to VP2-eat food from another dimension, and is thus invisible to the LA in the dimension where VP2 is located. Consequently, the resulting structure α is labeled as VP2. C-I will interpret VP1-use chopsticks as a modifier of VP2-eat food, which gives rise to the meaning “eat with chopsticks”.

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Turn to another possibility, as shown in (16).

VP2-eat food is pair-merged to VP1-use chopsticks from another dimension, and is thus invisible to the Labeling Algorithm in the dimension where VP1 is located. Consequently, the resulting structure is labeled as VP1. C-I will interpret VP2-eat food as a modifier (i.e., adverbial) of VP1-use chopsticks, which gives rise to the meaning “use chopsticks while eating”.

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As we have observed in this section, a structure resulted from Pair-MERGE can be labeled in different ways, which give rise to different modification possibilities. As long as these possibilities make sense to C-I in a given language, C-I will assign appropriate interpretations to them. We will examine in the following sections cases where C-I fails to assign interpretations to all the possible labelings.

4.2 Case (II): only one of the two labelings is interpretable at the C-I interface

Recall (2a), where the AdvP-carefully and the VP-conducted the experiment are merged. Only the labeling by VP, i.e., with carefully modifying VP, feeds the correct interpretation, as shown in (18a), but not the other way around, as shown in (18b).

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Examine a more complicated case. The Mandarin case in (19) can have two readings: the AdvP-very quickly either modifies VP1-take the knife or modifies VP2-cut the vegetables. In both readings, VP1 is analyzed as an adjunct to VP2.

The analysis of the first reading is illustrated in (20), where very quickly directly modifies VP2 cut vegetables, which gives rise to the Markovian reading.

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First, VP1-take the knife will be pair-merged with VP2-cut vegetables from a different dimension, and the resulting structure α will be labeled as VP2 by the Labeling Algorithm inside the dimension where VP2 is located. Next, the AdvP-very quickly will be pair-merged with α (i.e., VP2), and the resulting structure β will also be labeled as VP2 as the LA in the dimension where VP2 is located will ignore the AdvP-very quickly. In this derivation, the two modifiers, VP1-take the knife and AdvP-very quickly, are located in different dimensions, and there is no connection between them. Also note that the AdvP-hěn kuài-de ‘very quickly’ results from a Pair-MERGE of the degree AdvP-hěn ‘very’ with the AdvP-kuài-de ‘quickly’, and the resulting structure is labeled by quickly. As a result, very and quickly are located in separated dimensions, as illustrated in (20b).

The second reading, which is non-Markovian, is illustrated in (21), where very quickly modifies VP1-take the knife.

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First, the AdvP-very quickly will be pair-merged with VP1-take the knife from a different dimension, and the resulting structure α will be labeled as VP1 inside the dimension where VP1 is located. Next, α (i.e., VP1) will be pair-merged with VP2-cut vegetables from a different dimension, and the resulting structure β will be labeled as VP2 inside the dimension where VP2 is located.

4.3 Case (III): neither labeling is interpretable at the C-I interface

In (22a), the AdjP-small set-merges with the VP-eat an apple, resulting in an unlabelable structure α. Alternatively, small will pair-merge with the VP from another dimension. Inside the dimension where the VP is located, α is labeled as VP (cf. 22b), which is uninterpretable for C-I. Inside the dimension where small is located, α is labeled as AdjP (cf. 22c), which is also uninterpretable for C-I. Therefore, both labelings give rise to uninterpretable structures.

5.1 Internal Pair-MERGE is filtered by C-I

One important question is whether Internal Pair-MERGE is possible during the derivation. Examine the example in (23).

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As shown in (23), carefully is firstly pair-merged with the embedded VP-conducted her experiment, and then is internally pair-merged with the matrix VP-observed that […]. Even if such a movement is allowed at syntax, the resulting structure will still be filtered by the C-I interface. Carefully is associated with two different verbs, and the C-I interface has no way to interpret such a dual modification relation. In other words, under this analysis the sentence fails at C-I, but not at syntax.

One might wonder whether a syntactic analysis is possible, e.g., assuming that cross-dimensional MERGE is generally banned. This assumption implies the question of whether a dimension constitutes an island for any movement. As will be discussed immediately below, the answer is no, given that cross-dimensional Internal Set-MERGE is possible. Consequently, the impossibility of Internal Pair-MERGE is not driven by syntax.

For now, examine more complex cases in (24).

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In (24), how ₁ is firstly pair-merged with the embedded VP-laughed. As Internal Pair-MERGE is not an option, the chain [how ₂ …how ₁] cannot be derived. The chain [how ₃… how ₂…how ₁] thus cannot be formed either. As a result, a legitimate chain is either [how ₃ …how ₁] or [how ₃ …how ₂], both formed by Set-MERGE. This is further evidenced by the fact that there is no answer to the question in (24), because a potential answer would simultaneously cover the two questions, “how you know?”, and “how John laughed?”.

In (25a), this month is firstly set-merged with forgetting as its complement, and then is pair-merged with prefers as its modifier. However, this month cannot be interpreted as an argument and a modifier at the same time (also see Figure 4). The failure is at C-I, but not at syntax.

Figure 4:

Illicit movement from complement to adjunct.

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5.2 Derivational dimensions do not block Internal Set-MERGE

5.2.2 Adjunct island

As discussed above, a dimension is not inherently an island, which can be evidenced by cross-dimensional internal Set-MERGE, as shown in (28a). Then, a mysterious question is why adjunct still constitutes an island for movement. (28b, c) illustrate a classical adjunct island case: who cannot be extracted from the CP because-clause.

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It seems that movement is not blocked if the entire adjunct is cross-dimensionally moved; by contrast, the movement of a subpart of an adjunct is blocked. We can assume that adjunct is constructed in an independent workspace, which is in accordance with the view on workspace in Chomsky (2019). Then, why in (28a) and the CP because-clause in (28b, c) are independently merged in a separate workspace before being pair-merged with the VP (i.e., α). Consequently, a contrast is established: the maximum item in a workspace can be moved freely as a lexical item across dimensions, but smaller syntactic objects inside the adjunct workspace cannot, which is why who inside the adjunct CP cannot be moved alone (see Figure 5).

Figure 5:

Adjunct island.

Based on this contrast, we propose a new understanding of adjunct island:

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An adjunct island is the biggest syntactic object located in a different dimension.

Along this line, an adjunct island is constructed under two conditions: 1) an adjunct is the biggest SO located in an independent workspace, and 2) this workspace hosting the adjunct is located in a dimension different from the dimension hosting the stem.

Concretely, the causal clause CP in (28b, c) is the biggest SO located in a dimension different from the one where the VP-go to Japan is located. Although neither the workspace containing the adjunct SO nor the dimension containing this workspace works alone as an island, somehow when they work together, they constitute an island. Thus, adjunct island is accounted for in terms of a general ban on the cross-dimensional internal MERGE of a non-biggest SO in the workspace.^[11] This account is schematically illustrated in (30–31), where a and b are set-merged in a separate workspace, noted as [{a, b}], before being pair-merged with X. As an entire workspace, [{a, b}] can undergo cross-dimensional internal Set-MERGE, as shown in (30). By contrast, neither a nor b alone can be cross-dimensionally internally pair-merged with X, as shown in (31).

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{[{a, b}], ⟨X, [{a, b}]⟩}

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*{b, ⟨X, [{a, b}]⟩}

5.3 Multiple interpretative possibilities at C-I resulted from Internal Set-MERGE

The labor division between syntax and C-I assumed in the current model presupposes a strict mapping from syntax to semantics.^[12] Set-MERGE and Pair-MERGE feed interpretation relations that are in complementary distributions. Table 1 summarizes combinations of different types of interpretation relations. Note that these are not combinations of derived syntactic positions that usually host the relevant interpretations.

Let us briefly summarize these possibilities one after another.

1. Adding a new argumental relation to an argumental relation is filtered under the considerations related to theta criterion. In (32), John receives two theta roles when moving from the complement position of likes to the subject position.

1. Adding a new argumental relation to a scopal relation is filtered by C-I, as in (33).

The verb wonder selects an interrogative clause as its complement, and therefore, the intermediate C has an interrogative force which is represented by the Q-feature. When who ₂ is internally set-merged with the CP, the resulting structure is labeled by the shared Q-feature between who ₂ and the intermediate C. Note that who ₂ is assigned an interpretation at the specifier of the intermediate CP, which is a criterial position in the sense of Rizzi (2007, 2015. Moving who ₂ to a higher Spec of TP will have problems related to theta relations. Chomsky (2013) also notes that if who ₂ moves away, then the remaining Q feature on the embedded C will make the CP a yes-no question, which is gibberish at C-I.

1. Adding a new argumental relation to a modification relation yields an uninterpretable structure at C-I. In (34), yesterday is firstly merged as an adjunct, and then it is moved to the subject position.

1. Adding a new scopal relation to an argumental relation is perfectly interpretable. This is standard A′-movement, as shown in (35).

1. Adding a new scopal relation to a scopal relation is generally possible only if the original scope position is not a criterial position. This corresponds to an ordinary cyclic A′-movement, from a lower (non-criterial) position to a higher (criterial) position. Note that C-I will have a full record of each copy of the wh-phrase so that it can assign them an interpretation.

The sentence in (36), cited from Sportiche (2006), is ambiguous in three ways. The reciprocal each other could refer to you, they, or we. Since a reciprocal requires a local binding relation, this three-way ambiguity suggests that the wh-element has an interpretation at each intermediate Spec of CP. Thus, the successive cyclic movement is an instance of the addition of a scopal relation to another scopal relation.

1. Adding a new scopal relation to a modification relation is possible. This corresponds to wh-adjunct movement, as in (37).

1. Adding a new modification relation to an argumental relation is filtered by C-I, as in (38). Also see Section 5.1 for the relevant discussion.

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1. Adding a new modification relation to a scopal relation is filtered by C-I, as in (39).

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In (39), why ₁ is the adjunct of the verb leave, and then it is moved to the Spec of CP (i.e., why ₂), before moving to the adjunct position of the matrix verb wonder (i.e., why ₃). Such a movement gives rise to an uninterpretable structure at C-I.

1. Adding a new modification relation to a modification relation is ruled out by C-I, as in (40). Also see Section 5.1 for the relevant discussion.

Patterns of different combinations are clear. If the interpretation acquired after the movement features an argumental or modification relation, then this addition of interpretation will not be available. On the other hand, scopal (operator-variable) relation is freely available for all interpretation relations to acquire as an additional interpretation. The explanation is likely to draw on the distinction between the left periphery and the non-peripheral positions.^[13]