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Roots and their labels

Consider now how the details of featural relationships are established under the labeling algorithm: upon the introduction of a phasal head, feature inheritance occurs, and labeling takes place subsequently. The initial external merge site for IA and the root is not a site at which it may establish a direct link with its sister— the algorithm, detecting a lexical item, takes it to be the head of the syntactic object and tries to label the structure accordingly, which in the case at hand could not proceed, since the root is ‘too weak’ to serve as the label. This weakness of the root, described in terms of syntactic categorization, may be understood as type-theoretic underspecification. If the root were built around a predicate letter classified typically as a monadic one (i. e. as denoting property of objects of the domain), its type would still be undetermined as standing between (e ^ (s ^ t)), the type of verbal monadic predicates, and (e x s ^ t), the type of nominal roots; instances of higher adicities are analogous. Consider a simple case of a two-place predicate in (12).

(12)

The constituents of в in (12), the set obtained by external merge of IA and a root, do not enter into relationships relevant for label-theoretic purposes in virtue of undergoing external merge, the operation being applied freely, without need for a trigger—neither a specific one, as a selectional feature, nor a generalized one, as an edge feature, both options having been explored and later discarded in the free merge system. Thus, in Chomsky (2000a),

...when а, в merge, it is to satisfy (selectional) requirements of one (the selector) but not both. Fairly generally, furthermore, the selector is uniquely determined for a pair (а, в), as can be seen by reviewing cases. Set-Merge of (а, в) has some of the properties of Agree: a feature F of one of the merged elements (say, а) must be satisfied for the operation to take place. (Chomsky 2000a: 133-134)

S-selection is eliminated by the time of Chomsky (2004a), and edge features are introduced in Chomsky (2007), accounting for applications of the operation merge:

The property of unbounded Merge reduces to the statement that LIs have EF. The property has to be stated somehow, and this seems an optimal way. So far, then, the only syntactic properties of UG are that it contains Merge and LIs with undeletable EF, and that expressions generated must satisfy interface conditions—in a principled way, insofar as SMT holds. (Chomsky 2007: 11)

Later on, such features are dispensed with altogether: the web of assumptions in Chomsky (2013c, 2015b) does not include any conditions which would impose a limit on applications of merge, thus putting ultimately to rest

.the lingering idea, carried over from earlier work, that each operation has to be motivated by satisfying some demand. But there is no reason to retain this condition. Operations can be free, with the outcome evaluated at the phase level for transfer and interpretation at the interfaces. (Chomsky 2015b: 14)

In a way that stage was already in view in Chomsky (2007), despite the fact that edge features of lexical items might seem to resemble features participating in the derivation: as noted in Boeckx (2010b), the latter require valuation and enter into Agree-based featural interactions, whereas the former do not require that there be such a relationship between objects undergoing external merge—edge feature of an LI is merely ‘a feature that permits it to be merged’ (Chomsky 2008: 139), hence ‘a purely structural property’—the only property of lexical items in Boeckx (2015a: 28), with precedent discussion in Boeckx (2011b,c). The most recent framework gets rid of properties which were in fact used to reinstate the fact the lexical items participate in merge, and the assumption of the freedom of merge therefore may appear in its pure form.

The absence of featural interaction within в in (12), and between LI’s and their complements in general, does not lead to interpretive problems if an LI in question is specified in a way which allows a direct type assignment in the interpretive component; roots, by assumption, do not belong to this category. Feature inheritance would provide a solution, were it not the case that it is a process that occurs too late for в to be labeled. What can be labeled is y: the labeling algorithm, finding a {XP, YP} structure, accepts as satisfactory a structure with LI’s heading XP and YP standing in a feature-valuation configuration. Yet у in (12) is a different predicate than the root is:

(13)

Labeling of у may be read off as determining the functional character of the type of в, hence of ‘Xz. (Xy.P (x, y)) (z)’, and it is in itself an outcome which is obviously important for the C-I component to proceed; yet for interpretation to go smoothly, the nature of the type of ‘Xy.P (x, y)’ has to be established as well, and nothing on the part of narrow syntax is of help here—until head raising occurs, that is. The order of operations in (7) ensures that в is not transferred in its entirety at the first step; after head raising—the process to which we return in more detail in section 2.3—R enters into a configuration with v*. If it is not deprived of its featural content by feature transmission, R appears in a configuration which may be read off by the C-I component as determining its type as functional, and в may be considered acceptable for the interpretation to proceed. The situation is murky as far as syntactic analysis is concerned; Chomsky (2013c: 47 n. 47) assumes that

‘inheritance has to be understood as copying’ and ‘valued uninterpretable features’ are deleted, and the most explicit recent statement concerning the extent of feature transmission as given by Chomsky (2015b) with respect to C sticks to the requirement of deletion of unvalued features:

The natural assumption is that phasehood is inherited by T (...) along with all other inflectional/functional properties of C (^-features, tense, Q), and is activated on T when C is deleted. (...) More specifically, all inflectional/functional properties of C are inherited and the unvalued ones are deleted from C. All are activated at T when C is deleted. (Chomsky 2015b: 11)

The requirement is connected with the Chomsky-Richards deduction of phase inheritance, to which we return in section 3.4.2; another stance on the issue is to assume that such features are not harmful if made invisible by the process of head movement (see section 2.4.3), and are either invisible for the C-I component—a view adopted in Epstein, Kitahara, and Seely (2010, 2016)—or interpretable after all: when v* with its ^-features is in a configuration with R, they will be interpreted as operating on the latter and determining its type as functional; otherwise, they will be idle, much as on the approach of Epstein, Kitahara, and Seely (2010, 2016). What should be also noted is that the very notion of ‘valuation’ is rather to be considered as being equivalent to ‘being in a proper structural configuration’ (as also suggested on different grounds in Kato et al. (2014, 2016)). A label ( is therefore an instruction for the C-I component to interpret syntactic objects as a function-argument structure, with ф-features acting type-wise on the leftmost occurrence of the e-type in the type specification and possibly types other than e, if any, with the Case feature providing access to an object in the domain of a model: the head position in an argument chain is interpretively the place when it ‘enters’ the interpretation (whence the C-I component cannot take the impact of unvalued ф-features to affect more than the leftmost occurrence of e—the configuration of ф-features is related to the presence and interpretation of one chain). An analysis along such lines may be viewed as modifying and extending the main line of the proposal put forth in Gallego (2014), who hypothesizes that the property of being an argument-taker depends upon there being a categorizing head with unvalued ф-features which acts as a probe searching its complement for a goal with valued ones: updating this proposal, the relationship in question should be seen as established in compliance with minimal computation, without invoking the probe-goal mechanism, hence achievable by such processes as feature transmission and head movement, which, making the result being local structural configurations, makes room for covering label-theoretic properties and providing a tentative account of the interpretive import of the presence of such features.

It is worth noticing that it would be, on such an account, misleading to take trees as in (13) to be labeled with А-expressions or with semantic types: the label of в, if taken to be ф (рф, more precisely)—a property of R obtained as a result of head movement—is not seen by the C-I component as the type of the {R, IA} object as a whole, and it could not be, since the copy of IA is not visible to the labeling algorithm; it is, in accordance with the fact that R is an LI, a property of the head of the structure, semantically composable with the copy of IA visible as a variable provided that the head of the IA-chain is in a configuration which allows it to enter interpretively the structure; and when labeling involves a complex {XP, YP} structure, the label indicates how both constituents are compos- able type-wise. Note that the requirement that there be an additional relationship between v and R established—beyond feature transmission—follows from distinctions which are purely syntactic—between atomic lexical items and complex syntactic objects, thereby bringing out the importance of the divide denied on some accounts (contrast Chomsky (2013c: 46 with n. 42) and C. Collins (To appear 2017))—and processes which are again syntactic, C-I oriented as they are, viz. the details of the labeling procedure. Were it the case that narrow syntax satisfies requirements of the C-I component, it should be enough for R to get ф-features under feature inheritance for the syntactic object to get labeled: the type of R would be determined as a strictly functional one, thereby enabling it to take an argument; and the problem of в in (9) would not appear. If the direction of influence goes from narrow syntax to semantics, so that it is the former that gives shape to the latter, the impossibility of having properties established this way follows from the fact that being an LI prevents R from labeling в under ф-valuation with IA, a complex syntactic object. Narrow syntax is not identified with any part of the C-I component—what it does is to determine the way that the latter proceeds.

We have assumed above that roots as they appear by themselves in narrow syntax are translatable into an ancillary formal language as А-abstracts, thereby seen by the C-I component as having the capability of being interpretively com- binable with other objects at all, А-operator binding a variable in the body of the expression—a property which distinguishes concepts as available pre-linguistically and concepts qua atoms of syntactic computation. Exhibiting the property in a minimal way lets y in (13) remain free until it gets bound at the phase level—another facet of the head movement of a root to the phasal head, which simultaneously provides the C-I component with a way to read off the type specification for the sister of EA and compose both interpretively in a correct way (a speculative strengthening of this property would lead to a prohibition against the presence of free variables in interpretation at the C-I side, with structures containing free variables being possibly not interpretable, as familiar from the method relying on recursion on truth, see Mates (1972), Bostock (1997: 85-86)). If a tentative account of the mechanisms of head raising to which we turn in section 2.4 proves viable, it is a further consequence of such timing of the operations and dividing the labor between various stages of the phase building process that strictly speaking, narrow syntax as such does not have access to type-theoretic properties of the root as interpreted with respect to IA, nor does it have access to such properties with regard to the {EA, {(v*, R), ZP}}: the labeling algorithm accepts в after head raising and {EA, {(v*, R), ZP}} due to there being a head adjunction structure which does not mean that it inspects it for features and labels a structure in the same way as with {LI, XP} structures or {XP, YP} structures under feature sharing. This is in conformity with the hypothesis that thematic properties have their place in the C-I component. It is natural on this account— which preserves a syntactic property of copies left by internal merge as far as possible—to see ^-relations as belonging entirely to the realm of the interpretive component, simultaneously being dependent on the establishment of labels in narrow syntax.

 
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