Reducing the Asymmetry of Theta-Assignment to Third-Factor Principles

Abstract

This study focuses on the long-standing issue of θ-assignment in the generative enterprise literature. Despite the asymmetry of θ-assignment regarding structural positions (Head–Complement/Specifier–Head) being sanctioned by the Duality of Semantics, I argue that it is possible to eliminate the asymmetry in full accordance with third-factor principles by proposing two independent frameworks. In the first framework, I propose that θ-assignment is executed by applying Minimal Search to locate the assigner and the assignee, where both the external argument and the internal argument receive the θ-role in the same way. In the second framework, which does not hinge on the assumptions or results of the first one, I propose that θ-assignment is a postsyntactical operation; thus, the Duality of Semantics, as well as concepts like θ-assignment in the syntax or θ-position, may be disregarded. For a proper θ-interpretation to be possible, the assigner and the assignee must be in the same transfer domain. Nonetheless, the empirical coverage of the Duality of Semantics is largely retained, suggesting merge can and must be simplest with respect to θ.

1. Introduction

The assignment of θ-roles has been a major topic in the generative enterprise literature. Under the standard assumption (Chomsky, 1981, and Baker, 1988, among many others), the θ-role assignment is undertaken in a representational form; that is, θ-roles are assigned to specific positions related to predicates (θ-assigners). For example, Theme/Patient is assigned to a predicate’s complement position, while Agent is assigned to a predicate’s specifier position. The fact that the nature of θ-marking is stated rather than derived may seem to be an imperfection, but in recent works such as those by Chomsky (2008, 2020) and Chomsky et al. (2023), the representational approach can be seen as a natural result of third-factor principles. The creation of θ-position is supposed to be conditioned by the Duality of Semantics:

(1)

Duality of Semantics: only External Merge creates the θ-position, and the non-θ-position is created by Internal Merge1.

According to Preservation, which is a general rule for formal systems, the interpretation of lexical items does not alter during the course of derivation. To illustrate, if an argument is Externally Merged to a non-θ-position, it must merge to another position to be θ-marked; its interpretation is doomed to be changed. By contrast, if an argument is Internally Merged to a θ-position, the newly received θ-role would definitely change its interpretation. Thus, the representational approach is not purely stipulated. However, despite the distribution of arguments with respect to θ-assigners being couched in a third-factor-compliant fashion, the mechanism of assignment entails structural asymmetry. To put this in informal terms, Theme/Patient is assigned in a sisters-of relation, whereas Agent is assigned in a specifier-of relation. Note that Merge has recently been assumed to be a pure set-formation operation (cf. Chomsky, 2013, 2015); the configuration of v*P can then be represented in a set-theoretic form:

(2)

{EA, {v* {V, IA}}}

In (2), the asymmetry referred to above is that the assigner and assignee of Theme/Patient are co-set-members, while the assigner and assignee of Agent are not. Therefore, the assignment of different θ-roles necessarily varies.

It should also be noted that the assignment of θ-role is argued to be carried out in derivational form (see Bošković & Takahashi, 1998; Hornstein, 1999; and Funakoshi, 2009). Particularly, Funakoshi (2009) introduces the concept that θ-role assignment is realized via feature agreement (θ-roles are considered formal features). Technical details aside, the Agree-based θ-role assignment of Funakoshi (2009) can be paraphrased as follows: (i) Predicates function as Probe (embedded with uninterpretable θ features); (ii) Arguments are Goal (embedded with interpretable θ features); and (iii) a head X above vP is responsible for the θ-marking of external arguments. What is crucial to us is that the asymmetry observed within representational approach disappears2:

(3)

What (3) showcases is that both arguments acquire θ-roles through an identical Agree-configuration. Since v cannot c-command EA, it would be impossible to create a Probe–Goal relation, which is reminiscent of the asymmetry issue (2) presents. Although Funakoshi’s (2009) approach successfully reduces the asymmetry of θ-assignment/interpretation to a Probe–Goal relation, ideally Agree should be dispensed because Merge should be the only narrow syntax operation (see Epstein et al., 2015 for a related discussion).3

In Shim and Epstein (2015), the asymmetry of θ-assignment presented above has been marked as a problem of non-unified θ-marking. The analysis they propose is that θ-assignment must and can be carried out in a unified Head–Complement way, and the Specifier–Head relation should be eliminated. To make this possible, according to their derivational approach, {EA, v*} and {R, IA} are constructed by External Merge separately in the Workspace. θ-assignment would be completed at this point. Upon the creation of the two sets, External Merge applies again, yielding a structure in the form of {{{EA, v*}, {v*{R, IA}}}, where v* is the intersection of the two sets {EA, v*} and {v*{R, IA}}*. Notice that the Duality of Semantics is retained, because both EA and IA are θ-marked via External Merge. However, the formation of {{{EA, v*}, {v*{R, IA}}} relies on the so-called Parallel Merge (see Citko, 2008), which is not a third-factor-principle-compliant operation. Parallel Merge necessarily exhibits a counter-cyclicity nature, which is not in line with the third-factor principle Minimal Yield (MY). MY precludes any Merge applications that create more than one new accessible item. In fact, what Shim and Epstein (2015) posit is that there are two occurrences of v* in distinct sets, namely, {EA, v*} and {v*{R, IA}}, suggesting no c-commanding relation is possible, resulting in two new accessible items, a violation of MY.4

The goal of the present work is to derive a uniform mechanism for θ-assignment in conformity with the Strong Minimalist Thesis (SMT), which is a fundamental principle for explaining human language’s basic properties.5 It will be shown in the following sections that the advantages of the feature-agreement approach can be largely retained, and in the meantime, the Duality of Semantics, the third-factor-constrained principle, remains intact. Specifically, the uniform mechanism for θ-assignment/interpretation can be entirely deduced by the simplest Merge going hand in hand with various third-factor principles. Given that there is not a unique third-factor principle defined a priori, multiple assignment models rooted in various principles are possible and will be discussed. As will be detailed, each third-factor-principle-compliant model is independent from the others.

The remainder of this paper is organized as follows: In Section 2, I will present an assignment mechanism based on distinct modes of Merge and Minimal Search after reviewing Chomsky’s (2013, 2015) argument structure regarding θ-assignment. In Section 3, I will point out an innate problem θ-assignment system poses. As a solution, θ-interpretation is argued to be a postsyntax operation, suggesting the Duality of Semantics may be disregarded. The same empirical merits can be accessed by transferring the assigner and the assignee within the same unit, where Phase Impenetrability Condition and Preservation can give rise to legit θ-interpretation. Section 4 provides a conclusion.

2. θ-Assignment Under Minimal Search

In this section, I propose that θ-assignment is executed via Minimal Search (MS), a third-factor principle that feeds information to interfaces. Technically, only the externally merged objects can be the proper search target, and MS locates them in a minimal way, yielding the intended assigner–assignee relation. As stated in Chomsky et al. (2023, p. 30), “…language must provide predicate/argument structure at CI (Conceptual–Intentional interface).” In fact, in addition to the assigner–assignee relation discussed here, there is another interpretative operation that must be implemented by optimal computation (i.e., MS): Form Copy (see Chomsky, 2021). Form Copy assigns copy-relation to identical syntactic objects via MS, as in the set {X, {Y, Z}}, where X and Z are identical items. MS first locates X, and within the second application, it locates Z, with the copy-relation established. Instead, if the set has the form of {X, {W, {Y, Z}}}, where X, W, and Z are identical items, the copy-relation between X and Z cannot be built directly, as MS locates W with less computation.

The crucial condition is that assigner and assignee must be located by MS via the shortest path, in a way akin to Form Copy. In the following, I demonstrate that, in addition to the standard framework, by adopting distinct modes of Merge, another two mutual-independent methods that can eliminate the conceptually undesirable internal pair- Merge are obtained.

2.1. Defining the Minimal Search for Theta-Assignment

Before embarking on the hypothesis that θ-assignment can be reduced to MS, an explicit definition of MS regarding how it works in terms of θ-assignment must be clarified. I will mainly adopt Ke’s (2024) proposal that MS comprises three components—Search Algorithm (SA), Search Domain (SD), and Search Target (ST). See (4) for a formal definition of MS:

(4)

MS = <SA, SD, ST>

Search Algorithm (a slightly simplified version of Ke, 2024, p. 855):

• The Search probes into an SD to find the ST (a head) the search agent wants.
• Whenever the Search hits a head, it returns it to the search agent.
• When an ST is found and returned to the search agent, the search terminates.
• If an ST is not found after a run of a search, the search saves the more embedded set(s) in memory and sees it (them) as a new SD.
• If an ST is found in the more embedded set(s), the search terminates.
• If an ST is not found in the most embedded set(s), the search terminates.

The search algorithm proposed by Ke (2024) implicitly suggests that a non-target head would also be returned. That said, MS does not ignore the non-target head and keeps going deeper. In fact, since the MS itself is not able to decide what is and is not a target, it must keep the search agent updated with every head it finds. If the returned head is not what the search agent expects, a further MS is conducted. Therefore, (4ii) should be considered a crucial subpart of the SA that initiates the subsequent runs of MS.

Notice that the SA formulated by Ke (2024) ensures that the search should be executed in parallel (not serial) breadth-first (see Branan and Erlewine (n.d.) to appear for a related discussion) and global (not modular) ways. The language system would naturally favor a parallel search because linear order does not play a vital part in narrow syntax derivation and semantic interpretation (Chomsky, 2013, p. 36). An overview of how parallel breadth-first MS works is as follows:

(5)

{γ {α 1,2}, {β 3,4}}

Suppose the SD of MS is the root set γ; then the first application of MS would find two sets: α and β. Since MS is a parallel breadth-first search, α and β should be found simultaneously. Within the second application of MS, 1, 2, 3, and 4 are all to be found at the same time. If MS is serial, it could be the case that either α or β is found first, rendering a linear order. If MS is depth-first, the members of either α or β would be found first, resulting in a situation where, say, 1 and 3 can never be found at the same time.

The SA should also be global instead of modular. Modular search simply probes into every set of the SD to find all the ST, because the parallel searches do not communicate with each other. Even if one search finds the ST, the other search would still not be terminated because it does not know the ST has already been found. Consequently, the burden of redundant computation is inevitable. By contrast, global search allows the two parallel searches to communicate, yielding the “minimality” one would expect.

The present work generally adopts the SA proposed in Ke (2024), who contends that the SA stays invariant regardless of the purpose of MS (Agree or Labeling). Thus, it is expected that the SA utilized for θ-assignment should be identical to that used for Agree and Labeling. Meanwhile, Ke (2024, p. 862) claims that the SD and ST are independently determined by the purpose of each operation. For example, the ST of Agree is a head with valued features that match the unvalued features of another c-commanding head. Conversely, the ST of Labeling is any feature or head. If MS is also responsible for θ-assignment, what are the ST and SD for MS-Theta? The proposal is as follows:

(6)

Minimal Search-based θ-assignment = def. SA+ SD+ST, where

(a)

SA = (4);

(b)

SD = a set that contains a predicate and an argument;

(c)

ST = a predicate and/or an argument6,7.

MS, a third factor, should in principle be free to be applied at any stage of a computation. However, only the MS that incorporates the SD and ST defined in (6) can yield correct θ-relations. As language must provide predicate/argument structure at CI, MS-TH(eta) must look into a domain that contains a predicate and an argument, because they are the precise targets MS-TH is searching for. A structure in the form of (7) would not be able to produce the expected output in terms of θ-assignment, as neither a proper SD nor all the STs are available:

(7)

{the, boy}

In (7), although nothing precludes MS-TH from applying, no θ-relation is returned due to the absence of a predicate. If R, the semantic root of the verb, next externally merges to the set in (7), MS-TH can then return the correct information to CI, as the set {R {the, boy}} contains two STs: a predicate and an argument, making it a proper SD.

With the establishment of an explicit definition of an algorithm that conditions the MS-based θ-assignment, I will next demonstrate that the MS-TH proposed above can generate the θ-relations that are traditionally assumed to be conducted under Spec–Head and Head–Complement configurations.

2.2. R and v* Are Introduced via Separate External Set-Merge and Aggregated Eventually: The Standard Assumption

This study adopts the assumption that Merge applies freely as long as it does not violate third-factor principles. Even Internal Merge, traditionally termed as Move, no longer requires any driving force (cf. “Last resort” in Chomsky, 1995). Thus, unless presumed otherwise, here, Merge has free application. Merge, both external and internal, has two modes: set-Merge and pair-Merge. set-Merge constructs an unordered set such as {X, Y}, and pair-Merge forms an ordered set such as <X, Y>8.

With the basic forms of Merge in mind, let us review Chomsky’s (2015) analysis for the simple transitive clause, where the semantic R(oot) of verb and the phase-head/categorizer v* are entered into the derivation via External Merge. As the pair-Merge of R and v* would by definition render v* invisible to the semantic components, erasing the provider of θ-role, the External Merge of EA should be performed earlier to that:

(8)

a. {R, IA}

b. {IA {R, IA}}

c. {v* {IA {R, IA}}}

d. {EA {v* {IA {R, IA}}}}

According to the representational approach, the θ-assignment can be reached only with recourse to the asymmetric assignment relation shown above. Regarding this issue, my proposal is that θ-assignment can be achieved by MS-TH. The question is, can the assigner and assignee be detected by MS with the least efforts? Let us review if the MS-TH formulated in (6) can cope with the derivations presented in (8).

In the case of IA, at the point where {R, IA} is formed, as in (8a), the application of MS-TH can yield the expected θ-relation. Since the set {R, IA} contains both a predicate and an argument, it suffices to be the SD of the MS-TH. Within the first application of search, R and IA (to put more precisely, the head of IA; see footnote 6) can both be found and returned to the search agent (i.e., the CI interface). By doing so, the interface could have the access to the information that these two lexical items are closely related, where I assume Theme-marking takes place. In (8b), where IA internally merges to the Spec of RP, although nothing forbids MS-TH from applying, there would be no accessible STs. If the SA, which dictates that Search returns every head it looks into, mapped out in (4) is tenable, CI would know that R and IA are already incorporated into a θ-relation. Although {IA {R, IA}} might still serve as an SD, no legit ST is available. Recall that the STs of MS-TH are defined as “a predicate and/or an argument”. While the higher copy of IA should by theory be returned by MS as well, no assigner remains available for it, since R’s role has already been discharged to the lower IA. The assumption that R inherently bears two roles and can serve as an ST twice does not help, as IA, an argument, is strictly prohibited from having more than one role by Theta Theory9. One may claim that at this derivational stage, which has not reached the phase level, Form Copy is not activated, and hence CI does not have access to the information that the two inscriptions of IA are copies. Regardless, a derivation would reach the phase level sooner or later, where Form Copy applies. If the higher copy of IA is returned as an argument assigned with a role that is distinct from that of the lower copy, the violation of Theta Theory is impending: CI will eventually recognize that they are copies10.

Then, regarding the EA and Agent-marking, let us examine (8c-d). With the External Merge of v*, as in (8c), what would happen if a run of MS-TH is activated? Assuming per Ke that MS is a free and universal operation, MS-TH should in principle be allowed to be applied at the stage of (8c). However, MS-TH cannot find all the STs that the search agent seeks. In the first run of MS-TH, v*, the predicate associated with the θ-marking of EA can be found. If MS indeed proceeds in a universal way, and the two parallel searches communicate with each other, CI would recognize that a predicate has been found within the first run of MS-TH. The right-branching search would then be devoted to the search for an argument within the set {IA {R, IA}}, which is the new SD, following the definition in (6). It is obvious that no ST is to be found. Neither the θ-discharged R nor the θ-marked IA is a good ST11. Only after the external merger of EA can MS-TH find the STs that CI seeks. In the derivation of (8d), the two parallel searches of MS-TH would find EA and v* in a way that adheres to the algorithm depicted above.

Based on the previously discussed overview of how MS-TH operates, only two forms of MS-TH may lead to the correct output, despite MS-TH being an unconstrained operation: (i) MS-TH applies when IA and R are externally merged; (ii) v* and EA are successively externally merged. In other words, only that which is newly entered into the computation can be the ST of MS-TH. Consequently, unconstrained MS coupled with the language-specific first factor (Theta Theory) is all we need to generate the θ-relation that CI intends to recognize.

The derivations that violate the Duality of Semantics are immediately ruled out under the MS-based assignment system. The attempt to assign a θ-role to the higher IA, which is at a position traditionally termed as a non-θ position, as in (8b), faces the difficulty of not being able to find eligible STs.

A case in which EA externally merges to {IA {R, IA}} (unless stipulated otherwise, nothing stops EA from externally merging into such a position) requires our attention. This EA cannot receive the Theme-role for the same reason outlined above. There seems to be a solution that the merger of v*, which has the to-be-discharged Agent-role, may be helpful: {v* {EA{IA {R, IA}}}}. Both v* and EA are newly entered into the computation; thus, MS-TH should be able to generate the relation CI seeks. As a result, EA will be assigned the Agent-role, which seems to be an apparent violation of the Duality of Semantics, as the EA gets θ-marked in a non-θ position. Notice the EA may still move further for, say, labeling, but it can no longer be targeted by the θ-assigning-MS hereafter since it has already been entered into the computation. The violation of Preservation, which is the motivation for the Duality of Semantics, should not occur12.

The MS-based θ-assignment approach also yields a natural account for the interpretative difference between EA and IA, which is that IA plays a bigger role in determining the meaning of the verb. To the best of my knowledge, Marantz (1984) was the first study to reveal this matter. As shown in (9), the verb can have various interpretations according to the meaning of the object, but not the subject.

(9)

a. He killed a whole day.

b. He killed a beer.

c. He killed a goat.

In (9), all instances of killed are interpreted differently, and it seems tenable to assume the θ-role of EA is determined by {R, IA}. In fact, Chomsky (2008) points out that the Agent is assigned by V-OBJ configurationally. I tentatively argue that the Agent-role is assigned by v* alone. Simplest Merge by definition does not integrate the information its targets carry into the set it newly creates. The output of Merge must be just a set without being encoded with a θ-role that is available for an argument. Therefore, {v* {R, IA}} may not be able to function as a proper assigner under the current theoretical framework13.

The closer connection between the verb and IA immediately follows if MS assigns the θ-roles. Note that R, the semantic root, and IA can be located by MS simultaneously, suggesting CI can always see them as a pair. By contrast, it takes much more effort for MS to locate EA and R in a derivation like (8d). Even if it does, such a search can hardly be called “Minimal”14; this may explain why EA is not as prominent as IA when deciding on the meaning of the verb. Moreover, since EA can only receive the Agent-role from v* (unless the assumption that R inherently bears Agent-role and Theme-role is adopted), which is a categorizer deprived of semantic content, under the MS-based θ-assignment system, one could only expect EA to be an entity that is somehow involved in the event centered on the verb (all instances of he did something in (5a–c)), but what he actually did is determined by {R, IA} (he was idling/drinking/butchering).

Idioms including the subject seem to suggest the Agent also plays a role in determining the idiomatic interpretation, as in “The shit hit the fan”. However, it is the closer connection between R and IA that contributes to the overall meaning:

(10)

a. When the Battle of Cannae was lost, everything started to hit the fan.

b. # When the Battle of Cannae was lost, the shit started to hit the wall.

In (10a), with the subject shit being replaced with everything, the idiomatic reading persists, while (10b) can barely be construed as an idiom if the fan is changed into something different.

The discussion above suggests that the derivation model proposed in Chomsky (2015) is readily compatible with the MS-based θ-assignment. There is, however, one conceptual issue we cannot overlook: in the standard assumption, immediately after the Merge of EA, R Internally pair-Merges with v*, rendering it invisible to interfaces. What concerns me is that pair-Merge is not a third-factor-compliant operation because (i) it changes the status of an item (i.e., R’s category is determined through derivation) during the course of derivation (also known as stability/no-tampering; see Chomsky, 2005, 2008)15; (ii) it involves counter-cyclic movement (the internal merge of R does not target a root), which should be avoided (cf. Extension Condition in Chomsky, 1993, 1995).

In the next subsection, I appeal to modes of Merge distinct from the standard assumption to minimize the conceptual issues discussed here.

2.3. R and v* Are Associated via External Merge

2.3.1. <R, v*> Are Formed via External Pair-Merge

As pointed out in 2.2, Merge, ideally the sole structure-building operation, applies freely as long as it conforms to third-factor principles. Therefore, it is only logically possible to assume External pair-Merge (EpM) to be a licit operation. Epstein et al. (2022b) employ EpM to resolve the paradox regarding the invisibility of the lower copy of R in the cases of transitive verbs and bridge verbs in Chomsky (2015), illustrated in (11a–b).

(11)

a. {EA {<R, v*> {_β IA {_α R IA}}}} (R is a transitive verb)

b. {EA {<R, v*> {_β R {_α C}}}} (R is a bridge verb)

Two lower copies of R are assumed to be different in Chomsky (2015) as to whether they are invisible. R in (11a) must be visible to CI for the labeling of α and β. As R inherits the phase-headhood in addition to agreement feature φ from v*, if R becomes invisible, the <φ, φ> labeling for β breaks down. Likewise, with IA, due to the complement of phase-head being transferred, α cannot be labeled. However, R must be invisible in (11b) for β to be labeled. Given that C does not Internally Merge to [Spec, R], <φ, φ> labeling is not accessible. Consequently, β can only be labeled by C under the assumption that R is invisible (β = α = C).

As a solution, the tenet of Epstein, Kitahara, and Seely’s work is that bridge verb constructions involve the EpM of R and v*, which cancels the phasehood of v*, resulting in (12):

(12)

{EA {_β <R, v*> {_α C}}}

The amalgam <R, v*> is formed via EpM, indicating that both the phasehood and φ on v* become invisible. Thus, the labeling of β no longer poses a problem. With this novel mode of Merge in mind, let us explore how EpM can produce a formation of θ-assignment in a strictly cyclic way.

Assume EpM forms <R, v*> amalgam in the lexicon, and the phasehood/φ on v* is canceled (i.e., invisible)16. Nonetheless, it would be undesirable to treat v* as naught to CI. For one thing, CP in (13) needs a θ-role, and the EA also needs the Agent. The question is as follows: who assigns Agent to EA? Since Epstein et al. (2022b) have not elaborated on this matter, I will take the liberty to argue that R inherits θ-to-be-assigned from v* upon the formation of <R, v*>17 to circumvent a Theta Theory violation18:

(13)

{EA {_α <R^{Agent, Theme}, v*>, IA}}

According to the structure in (13), with R equipped with Agent (inherited) and Theme (innate) roles, EA and IA will be assigned with θ-roles from a unique assigner. Beyond this, the conceptual advantage of this approach is that there are no items whose interpretation is changed during computation; <R, v*> is formed before it enters narrow syntax. Hence, the intrinsic incompatibility between pair-Merge and no-tampering/counter-cyclicity ceases to be a problem as long as pair-Merge is performed externally.

The asymmetry between EA and IA discussed in 2.2 remains properly accounted for under the MS-based approach with the External pair-Merger of R and v*. In (13), the θ-determining MS would apply as soon as <R^{Agent, Theme}, v*> and IA are entered into the system, discharging the Theme-role of the former. After EA is externally merged to {<R^{Agent, Theme}, v*>, IA}, MS applies two times locating EA and R with the Agent-role. It is exactly this more costly search that leads to the difference between EA and IA with respect to the determination of the meaning of the verb.

One significant conceptual advantage of this framework is that the so-called EA/IA asymmetry can be captured under a unified MS-based θ-assignment system instead of an assignment mechanism that can go either parallel (Head–Complement assignment) or upwards (Spec–Head assignment).

2.3.2. {R, v*} Are Formed via External Set-Merge

I now turn to another logical possibility in the application of Merge. That is, R and v* form an unordered set before they are added to the Workspace. Such a mode of Merge has been employed in the literature by, for example, Saito (2013). Japanese lexical compound verbs are implicitly suggested to be Externally set-Merged (EsM).19 In Narita and Fukui (2022), R and v* are also assumed to be introduced into the syntax via EsM, complying with strict cyclicity and no-tampering. Let us review whether an EsM-formed {R, v*} can lead to a desirable consequence.

In contrast to <R, v*>, whose formation rests on pair-Merge, I argue the phasehood of v* is not canceled (invisible) upon its merger with R in the lexicon. The proposal given in 2.2 follows Chomsky (2015) in assuming that pair-Merge of R onto v* makes the latter invisible. Though further study is required, in addition to the mover projects analysis (see Epstein, 1998), I conjecture that the fact that pair-Merge yielding an invisible element can also be reduced to the fact that pair-Merge indeed meddles in an essential structural relation—sisters-of—on which multiple essential definitions hinge. An example is the chain-formation (see Narita & Fukui, 2022, p. 76). If v* stays visible to, for example, MS, then it would be hard to determine whether v*, R, or <R, v*> is the sister-of the arguments. Inversely, set-Merge is free from such a burden, as the sister-of relation, either within or outside the set, is straightforwardly clear. Then, what will happen if {R, v*} merges with IA and EA cyclically?

(14)

{EA {{R, v*} IA}}

An immediate issue is that the phasehood of v* is not canceled, suggesting the derivation would reach phase-level as soon as {R, v*} emerges (prior to the merger of IA) in the system. If the transfer takes place at this point, R can no longer participate in any further operation given the Phase Impenetrability Condition (PIC). Consequently, IA cannot hereafter be θ-marked. There is a potential solution to this dilemma: like what has been assumed for the EpM approach formulated above, upon the merger of R and v* in the presyntactic stage, the inheritance of both phasehood and θ-role occurs. As soon as {R, v*} enters into the derivation, transfer takes place, leaving a structure in the form of (15), a one-membered set20:

(15)

{R^Agent/Theme v*}

In (15), what has been transferred is v*21. Next, IA and EA join cyclically. The structure would look like (16) after the merger of EA and IA:

(16)

{EA {{R^Agent/Theme v*}, IA}}}

The MS-TH applies as soon as {{R^Agent/Theme v*}, IA}} is constructed to find both STs, assigning IA the Theme-role. After EA is merged, MS-TH would locate the EA and the set {{R^Agent/Theme v*}, IA}}, where one more search is required to locate the assigner. The EA/IA asymmetry is again correctly captured22. An anonymous referee wonders how the framework proposed here ensures that it is the Theme-role, instead of the Agent-role, assigned to IA. By theory, the MS-TH proposed in (6) does not preclude such a possibility, as {R^Agent/Theme v*}, IA}} contains a whole set of ST. Note that one cannot simply claim that assigning Agent-role to IA leads to gibberish, especially with reversible predicates like criticize (e.g., “Some people criticized Mary”). Another referee enlightened me that there should be an ordering concerning the assignment of Agent and Theme, where R consistently discharges Theme to IA first. The critical question is as follows: how is this ordering derived? I argue that at least two approaches address this issue:

First, if IA could be marked as Agent immediately upon merging with R, it would be impossible to capture the fact that it is the object, instead of the subject, that plays a greater role in determining the meaning of the verb. For instance, if IAs like “beer” and “deer” are marked Agent in structures like {killed, ^Agenta beer} and {killed, ^Agenta deer}, the first “killed” may never have the meaning of to drink (the verb kill may be universally interpreted as an action to deprive creatures of lives, i.e., a beer killed someone). Recall my proposal in Section 2.2 that the tighter semantic link between R and IA is deductible from the minimal computational effort (fewest MS-TH runs) required to locate them, contrary to the searches looking for R and EA. Thus, MS efficiently identifies R and Agent-marked IA, whereas additional searches are needed for Theme-marked EA and R—yielding the undesirable results presented above.

Secondly, although Chomsky (2008) assumes that Agent-role is assigned by V-OBJ configurationally, this assumption is incompatible with the Simplest Merge system, where V-OBJ set cannot inherently assign roles. Alternatively, the V-OBJ assigning assumption may be couched in terms of MS-based θ-assignment, successfully blocking the illicit Agent-to-IA assignment. If v*, a categorizer, only has an unspecified θ-role that is to be specified by entering into a relation with R (whose meaning is determined by earlier MS-TH locating R and Theme-marked IA), it becomes possible to explain why He in “He broke his leg” and “He broke his words” is marked as Experiencer and Agent, respectively. Under the standard assumption, where R and v* are introduced into syntax separately, He’s assigner, namely v*, can have the role specified only after an application of MS-TH (it might have distinct STs from those responsible for constructing θ-relations) finds v* and R. In structures like (16), where R inherits v*’s unspecified role presyntactically, if IA receives this role first, its specification is delayed until MS-TH locates Theme-marked EA and R. Assigning Theme to IA first (e.g., {{^Unspec EA {R, ^Theme IA}}}) requires fewer MS runs than assigning the unspecified role to IA first (e.g., {{^Theme EA {R, ^Unspec IA}}}), as the latter necessitates an additional search to determine verb meaning. Thus, Theme-to-IA priority is computationally preferable.

One remaining issue is how my framework can block IA from being assigned the Agent-role if the IA internally merges to Spec, RP, as in (17):

(17)

{IA, {{R^Agent/Theme v*}, IA}}

Recall that I have proposed in 2.2 and 2.3 that only the assigner and assignee that are newly entered into the computation (i.e., External Merge) can yield the results the search agent expects, suggesting that undergoing Internal Merge would deactivate any θ-determining MS. This assumption is based on the general rule that one argument must have one and only one θ-role, which yields the Duality of Semantics. Thus, IA, when newly introduced into the computation, can be assigned the θ-role via MS-TH. However, IA at Spec, RP is not newly introduced into the computation but raised from a θ-position that was created a moment ago (i.e., Internal Merge). My proposal given in 2.1 can immediately be accommodated by the derivations utilizing the merge mode developed in this subsection. It is predicted that the MS-TH that is supposed to be responsible for Agent-marking of the higher copy of IA in (17) does not identify the correct argument as a part of the ST, because CI would know that the IA at Spec, RP already has a role. The prediction that IA at Spec, RP cannot be assigned the Agent-role is also in line with Preservation. If IA is assigned the Agent-role in addition to the Theme-role, Preservation would be violated.

It should again be clarified that (17) does not block object shift. IA is free to internally merge to Spec, RP; my framework only blocks the possibility of IA getting θ-marked at this position.

2.4. R and v* Stay Separate: Does MS-TH Suffice to Enable θ-Assignment While Capturing the Asymmetry?

The alternative θ-assignment conditions based on different modes of Merge and MS discussed above are instituted on the notion that R, the semantic root, and v*, the verbal categorizer, are supposed to be amalgamated when they appear in the narrow syntax. What this paper proposes is an MS-based mechanism for θ-assignment that can obtain the empirical merits of the Duality of Semantics as well as capture the asymmetry between EA and IA without the recourse to configurational difference (i.e., Spec–Head vs. Head–Complement). I next appeal to a null hypothesis that R and v* do not have to be combined, as shown in Chomsky et al. (2023, Secs. 5–6). I demonstrate θ-interpretation concomitantly follows from third-factor-compliant MS without any stipulations.

What occurs if R and v* are not merged, which is a plausible option assured by the Free Merge Application? As shown in (18), R and v* externally merge to IA and {R, IA} successively.

(18)

{EA {v* {R, IA}}}

In (18), in the case of Theme-assignment, MS-TH applies once to locate R and IA, where MS-TH returns the information that there is a pair of proper assigner and assignee (all the STs that CI seeks) that can be detected through least computation: θ-assignment occurs. Regarding Agent-assignment, within the first application of MS-TH, what has been located is EA. At this moment, CI, along with the right-branching search, recognizes a part of the ST, namely an argument, that is returned, and the next application of MS-TH aims to find a predicate with an undischarged role. The second application of MS-TH would then locate v*, the Agent-assigner. Given this, the third-factor MS, coupled with the assumption that R and v* remain separate, is able to produce the desirable output. The proposed approach in Section 2 therefore remains defensible under the argument structure design in Chomsky et al. (2023): both the assigner and assignee are located via least efforts, and the asymmetry between EA and IA comes from the different times of MS-applications.

3. θ-Assignment Under PIC and Preservation

In this section, I will explore the possibility of retaining the empirical coverage of the Duality of Semantics without assuming notions such as θ-positions and θ-assignment in narrow syntax23. My proposal is as follows: the θ-interpretation is determined by transferring the θ-relation between an argument and a predicate to CI, and such a relation cannot be interfered by phase boundaries. In fact, invalid operations such as “internally merging the IA, a θ-marked argument, to Spec, v*P, a θ-position” are blocked because they end up in different phases. The Duality of Semantics may even be disregarded because, as pointed out by an anonymous referee, assuming that θ-interpretation is absent in the narrow syntax allows such invalid mergers: internally merging IA to Spec, v*P does not change its interpretation, because there is not yet an interpretation. Therefore, this is a completely different approach from what has been proposed in Section 2. In fact, nothing is dependent on the assumptions or results of the MS-based framework.

An important motivation for this proposal is that despite the empirically tenable analysis given in Section 2, the nature of the syntactic operation Assignment seems to conflict with some grounding rules of computation in general. Although the Duality of Semantics correctly predicts the distribution of arguments in full accordance with Preservation, assigning a θ-role necessarily changes the interpretation of arguments during derivation. The picture is clear: an argument extracted from the lexicon must be θ-less; it being θ-marked in subsequent narrow syntax can only run afoul of Preservation. For example, a lexical item John does not have any θ-interpretation in the lexicon, and it can be interpreted as either Agent or Theme, according to specific sentences: John scammed Bill vs. Bill scammed John.

In the following section, I will propose an alternative that reanalyzes Assignment in terms of phasal relation, showing that θ-interpretation is subject to third-factor principles. Most importantly, no θ-roles are added to/factored out from either argument or predicate.

θ-Interpretation Is a Relation: Assigner and Assignee Are Transferred Together

In this subsection, I propose that the predicate and argument of a θ-role must be in one transfer domain for them to be detected as the assigner and assignee by CI.24 This hypothesis assumes that there would be no θ-assignment in the narrow syntax. First, I will present the correct derivations that can be obtained from it. Following that, I will show that this hypothesis is able to preclude undesirable outputs that are also rejected by the Duality of Semantics. The reasoning behind this condition is that, as stated above, assignment necessarily alters the interpretation of both predicates and arguments; a Merge-only system has no way to identify the information of θ-role. Therefore, narrow syntax only feeds a valid structure to CI to obtain the intended interpretation. This can be reviewed stepwise:

(19)

{v*{R, IA}}}

Since my proposal rests on the reference to the transfer domain, it would be crucial to determine what constitutes the initial transfer domain in (19). If we take the stance of Chomsky (2013, 2015) that R inherits both the uninterpretable φ feature and phasehood from v*, the transfer domain would be the complement set of R. θ-assignment, an operation that changes the interpretation of lexical items, is no longer a warranted operation. θ-interpretation is only retrieved in CI after transfer. For that to be possible, items carrying θ and items seeking θ must be transferred simultaneously. What (19) presents, however, fails to offer CI the correct phasal relation between R and IA. IA without R is transferred alone, and CI can only see this as an argument without a θ-role where R, the head of the phase, can only stand idling, because PIC bans the transferred object from participating in subsequent computation.25 One intuitive solution is to apply Internal Merge, raising IA to the edge of R, as illustrated in (20):

(20)

{v*{IA {R, IA}}}

Notice that the structure in (20) reaches phase level as soon as the inheritance takes place; thus, Form Copy applies to the two occurrences of IA in (20), interpreting the two inscriptions of IA as copies. A ramification is that CI can unproblematically see R and IA in the same transferred domain after the next phase CP is completed. Further, the θ-interpretation of EA naturally follows because EA and v* are innately in the same transferred domain:26

(21)

{C {EA {v* {IA, {R, IA}}}}}27

The structure in (21) seems to fall outside the regulation of the Duality of Semantics: IA in (21) is “θ-marked” in a position created by Internal Merge. It should be clarified that the approach of Section 3 not only attains the empirical merits of the Duality of Semantics, but it is also free from any conceptual conflict. Given that the notion of Assignment in syntax is dispensed with under the transfer-domain-based approach for θ-interpretation, θ-position is also no longer in my system. In effect, IA does not get interpreted as Theme at a designated position, but via its being within the same transfer domain with R. No violation of Preservation, on which the Duality of Semantics stands, or Full Interpretation is attested; therefore, my analysis is parallel to the Duality of Semantics in the sense that they are both interpretations of Preservation. Tentatively, the only difference between them is that the approach outlined in Section 3 delineates how θ-interpretation is conducted, while the Duality of Semantics dictates how arguments are introduced into the syntax. The reader may wonder—in a structure such as (21), where EA, v*, the higher copy of IA, and R seem to be in the same transfer domain—how the proposed framework can assure the correct output. An anonymous referee enlightened me (see footnote 21) that the inheritance of phasehood is more like the copying of a feature; hence, the phasehood on v* does not simply disappear after a copy of phasehood is passed down to R. If v* remains a phase-head after the inheritance, only the higher copy and R constitute the second transfer domain, separating them from EA and v*28.

Also note the difference it makes if the inheritance of phasehood does not occur. The proposal is that the optionality of such inheritance is the key to some crosslinguistic variations.29 If v* is opted to not transmit the phasehood to R, then R and IA are bound to be in the same transfer domain:

(22)

{C {EA, {v* {{R, IA}}}

IA may or may not be shifted to the edge of R, because IA and R can be identified by CI after a single application of transfer, as illustrated in (22). EA and v* are likewise fixated within one transfer domain, and they are to be detectable by CI phase-locally. Consequently, Agent and Theme are properly interpreted via the in-the-same-transfer-domain relation.

The optionality of phasehood inheritance shown above may account for obligatory/optional object shifting among various languages. Obligatory object-shifting languages like English (see Johnson, 1991; Koizumi, 1995) and Japanese (see Ochi, 2004) would consistently employ phasehood inheritance. In contrast, an optional object-shifting language like Chinese (see Qu, 1994; Shyu, 2001) is not subject to such a constraint. For languages like Japanese, as discussed in Ochi (2004, p. 65), an obligatory object shift may offer a straightforward account for the restriction of transitivity imposed on Ga-No conversions, as illustrated in (23):

(23)

a.	Hanako-ga	saihu-o	nakusi-ta	kyositu.
	Hanako-NOM	purse-ACC	lose-PAST	classroom
	“The classroom where Hanako lost her purse.”
b.	*Hanako-no	saihu-o	nakusita	kyositu.
	Hanako-GEN	purse-ACC	lose-PAST	classroom
	“The classroom where Hanako lost her purse.”

The genitive subject (no-marked) and nominative subject (ga-marked) can be found in alternation when used in prenominal relative clauses. However, as suggested in (23b), the appearance of an object causes ill-formedness. According to Ochi, it is the obligatorily raised object that intervenes with the probe from the DP in the next phase level into the genitive subject that leads to ungrammaticality.

By contrast, in Chinese, object shift is optional. Zhang (2000) argues that object shift in cases like (24b) is triggered by feature-checking requirements of the verb and the focus marker of the object:

(24)

a.	Zhangsan	mai-le	shu.
	Zhangsan	bought	book
	“Zhangsan has bought a book.”
b.	Zhangsan	shu	mai-le.
	Zhangsan	book	bought
	“Zhangsan has bought a book.”

Therefore, another conceptual advantage of my approach is that it manages to reduce the optionality of object shifting to the requirement of validating θ-interpretation, which is entirely subjugated to third-factor principles, namely PIC and Preservation.

Moreover, the asymmetry between EA and IA in determining the meaning of a verb that has been discussed in 2.2 can also be explained with my Transfer-based approach. Notice that in a derivation like (25), R and IA are assumed to be transferred simultaneously regardless of the inheritance of phasehood from v* to R:

(25)

{EA {v* {IA, {R, IA}}}}

However, EA is not in the same transfer domain as R; thus, it can hardly play a role in determining the meaning of the verb. Hence, the asymmetry between EA and IA can be reduced to either (i) different times of MS-applications, as argued in Section 2; or (ii) a different transfer domain.

Next, let us examine whether the illicit mergers of arguments that are banned by the Duality of Semantics can be properly dealt with under the Transfer-based framework. I will go through three instances of such mergers: (i) internally merge IA to Spec, v*; (ii) internally merge EA from Spec, v* to another “θ-position”; (iii) externally merge EA to a “non-θ-position”.

(26)

a. *{IA {v* {IA {R, IA }}}} > *the man sees (intended: the man sees himself)

b. *{EA{v*^matrix{EA{C {EA{v* {IA {R, IA}}}}}}}} > *Johnⁱ thinks Johnⁱ hit Mary

c. ?{v* {EA{IA {R, IA}}}}

In (26a), if the inheritance of phasehood takes place, IA should be raised to Spec, RP, as previously discussed. The introduction of v* then brings the derivation to the phase level. IA may still be able to further move to the edge of v* before transfer, but once transfer applies, the lower copy of IA and R will be transferred for θ-related interpretation. This is exactly how IA obtains a Theme-role under the Transfer-based framework. However, with the higher copy of IA showing up at the edge of v*, and with IA in (26a) and v* being transferred together, IA would again be construed as the Agent, which is an undesirable result violating the univocality (IA has two roles while EA has none).30

The same analysis could be directly applied to (26b). Although the θ-relation of EA and v* can be established since they are in the same transfer domain, the θ-relation of EA and v*^matrix cannot be obtained in CI because the lower copy of EA is already in a θ-relation. If the hypothesis that θ-interpretation is not a syntactic operation (which is Markovian) is defensible, CI would know the EA has a θ-role before it reaches Spec, v*^matrixP. Supposing that the EA and v*^matrix are transferred together and that an additional Agent-role is assigned to the EA postsyntactically is a violation of Theta Theory.

The derivation in (26c), however, poses a challenge. Recall a very similar case discussed in Section 2.2 that EA externally merging to {IA {R, IA}} seems to be sanctioned by the MS-TH-based θ-assignment framework, despite it being disallowed by the Duality of Semantics. It seems that such a derivation is also supported by the Transfer-based system. The EA in (26c) remaining in its position can be ruled out by the analysis discussed above; however, as long as there is an option for the EA to be internally merged to Spec, v* and transferred with v*, the problem disappears. Derivation like (26c) is prohibited by the Duality of Semantics because internally merging the EA to receive a θ-role necessarily changes its interpretation. However, this is no longer a reason to eliminate such derivation under my Transfer-based framework, since θ-interpretation is exclusively performed in CI, suggesting no interpretation change would happen in the syntax. At this point, I have to admit that whether this derivation may lead to overgeneration is unclear. Even though EA appearing at this position yields a form of {XP, YP}, labeling failure can be easily circumvented by moving EA away (putting EA and v* in the same transfer domain is also vital to θ-interpretation under the current framework).

In Section 3, I have reviewed the implicit deficiency of the traditional θ-assignment system. The conflict between Assignment and Preservation can be fully remedied under my transfer-domain-based (predicate and argument must be in the same transfer domain) approach. As an anonymous referee points out, the transfer-domain-based approach may ultimately prevail over the MS-based one formulated in Section 2, because a minimized architecture of syntax results (the apparent complication of Merge disappears if we leave the issue of internal pair-Merge alone). Although external pair/set-merges of R and v* are theoretically allowed, they are merges in morphological components. In my transfer-domain-based framework, merge only takes place in syntax. A non-trivial empirical consequence is that the optionality of object shifting can now be boiled down to the essential requirement that the predicate and argument must be in the same transfer domain.

4. Conclusions

This paper reviewed the nature of θ-assignment, an important aspect of argument structure. An implicit asymmetry can be observed within the traditional account. To put this in informal terms, Theme/Patient-assignment is in the form of Head–Complement (co-set members), whereas Agent-assignment is Specifier–Head (non-co-set members). The intricacy is that such asymmetry is properly conditioned by the third-factor-compliant principle, the Duality of Semantics, masking the structural asymmetry with computational legitimacy. Aiming to dissolve the asymmetry, I reduced the ordinary θ-assignment to third-factor principles without challenging the conceptually well-motivated Duality of Semantics.

Specifically, I examined the argument structures formulated in both Chomsky (2013, 2015) and Chomsky et al. (2023) and proposed that the MS-based θ-assignment framework couched in third-factor principles offers a uniform mechanism of θ-assignment. In addition, the asymmetry between EA and IA in determining the meaning of the verb is simply reduced to how minimal the relevant search is; R and IA are located by one MS application, while R and EA require more than that.

To eliminate the notion of pair-Merge, which is not a valid operation in the view of the simplest merge, I presented two logically possible modes of Merge, namely, External pair-Merge and External set-Merge, to form the amalgam of R and v* presyntactically. Consequently, the violation of no-tampering and cyclicity disappears.

In Section 3, I explored the possibility of obtaining the empirical merits of the Duality of Semantics without notions such as θ-assignment or θ-position by assuming that θ-interpretation is exclusively carried out postsyntactically. That the assigner and assignee must be in the same transfer domain is a crucial condition for CI to construct a θ-interpretation. Consequently, any merge that integrates an argument previously interpreted with respect to θ into another θ-relation is prohibited, just as the Duality of Semantics predicts.

Prior to ending this paper, we recall that the two frameworks proposed in Section 2 and Section 3 are completely independent from each other. Specifically, they involve different assumptions and rest upon different third factors. If they are truly independent of each other, one would then wonder: which one is conceptually and empirically better? The short answer is that the MS-TH-based approach is roughly on par with the transfer-domain-based one.

The reader may notice that the first approach seems to invoke more assumptions compared to the second. For example, assumptions—such as (i) the feature/phasehood inheritance can take place before syntax; or (ii) since both R and v* can be the phase-head in externally constructed {R, v*}, either R or v* can be transferred upon the first application of transfer—are integrated into the overall framework. Nevertheless, it is fair to claim that those assumptions are necessary when pursuing the elimination of the internal pair-Merge, a third-factor offending operation. Under the standard assumption that R internally pair-Merges to v*, no necessities appeal to the merge modes (external pair/set-Merge) that are only applicable to presyntax constituents; hence, the additional assumptions adopted in 2.3 can be dismissed. All that is needed is MS and Transfer in the two approaches, so they should be equal in terms of theoretical optimality.

Empirically, the two approaches seem to have identical coverage. As shown in 2.2 and Section 3 while the correct θ-relation can be reached no matter if it is accessed via MS or Transfer, unwanted output like assigning a role to the higher copy of IA in {IA, {R, IA}} is ruled out uniformly. The equivalency is further marked by the fact that both approaches allow the θ-assignment to the EA in (26c) (repeated as (27)):

(27)

?{v* {EA{IA {R, IA}}}}

In a derivation like (27), MS-TH can find v* and EA as the ST, identifying them as the participants of a θ-relation without violating the Theta Theory, because v* and the EA are externally merged into the system. By contrast, although a derivation such as (27) should be allowed if we do not assume assignment in syntax, the EA in (27) must be raised to Spec, v*P, while the MS-TH approach does not impose such an obligation on the EA. If empirically undesirable derivation results because the EA in (27) stays at this position, the transfer-domain-based approach may be the better one: the MS-TH approach can lead to the correct result, while the transfer-domain approach ensures it.

Thus, the transfer-domain-based approach may show some superiority as it also accounts for the crosslinguistic optionality of object shift. If the inheritance of phasehood occurs, the object must raise to [Spec, RP] for the sake of being in the same transfer domain with R, the predicate. If no inheritance occurs, the object would invariantly be in the same transfer domain with R, where θ-relation is immediately accessible after the first application of Transfer. By contrast, following the MS-TH-based approach, IA would receive a role immediately after the merger with R, and it may or may not be raised to [Spec, RP]. MS-TH only rejects IA at [Spec, RP] from being θ-marked.