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Mapping issues

It is instructive to consider in a preliminary and very tentative way the case of binary operators and the issues arising in a proper modeling of syntactic structures to which they belong, as generated by narrow syntax and not by familiar rules of formal logical calculi, and their behaviour after the syntax-semantics transition; beside exhibiting their own peculiarities, they also reflect several general processes and properties of syntactic objects, mechanisms on which they must rely for learnability reasons indicated above. It is remarkable that syntactic structures which (appear to) involve counterparts of binary connectives pose significant problems for a minimalist treatment. The most immediate source is easily identifiable: the binary nature of syntactic Merge together with the rejection of the X-bar schema and projection-related mechanisms and properties. Binary connectives do not easily fit the current treatment of syntactic structures and operations, a situation which is clearly seen if the possible mapping between the feature-based analysis of the standard minimalist approach and the analysis required by formal semantics is taken into consideration. Binary connectives— and more generally, binary operators—require as their input two arguments: a syntactic requirement which is transparently mapped onto semantic interpretation. This demand may be met within a theory which relies on the X-bar theoretic approach to syntactic structures, with its hard-wired endocentricity and availability of establishing direct head-XP relationships beyond the first merge, as in (1).


Availability of head-complement and spec-head relations—with possibly multiple specifiers as an option—may be and used to be widely exploited for the purposes of modeling the syntax-semantics fit: symbols combining syntactically with n arguments and interpreted as n-ary relations may be taken to occupy the center of an endocentric structure, while arguments, instead of being supplied in an ordered package together, are contributed by consecutive applications of merge. The strategy is familiar from formal semantics, with an extensive use of currying and massive presence of functions which have as values other functions. Alas, this alignment of syntactic structures and semantic interpretation which X-bar theory offered has gone together with the rejection of the X-bar theoretic schema. Taking coordinating binary connective as an example, it is no longer possible to have a structure analogous to (1) and take it as granted that the connective is the head of the structure, with XP and ZP its arguments.


A structure along the lines of (2), which provides a way to introduce arguments of a single head into distinct structural positions, has been long assumed as approximating a correct representation of coordinate structures, providing an explanation of asymmetries they exhibit with regard to syntactic operations, but letting coordinated XPs be semantically on equal footing with regard to к, which does not impose asymmetric semantics by itself (details of syntactic structures assumed in particular proposals vary, one important deviation from (2) being hypotheses of adjunction structures as appropriate for coordinations, see Munn (1992, 1993), Moltmann (1992), a. o.), and main disagreements concern the status of к—which should provide a label for both a and в in (2) under standard X-bar theoretic assumptions, yet does not determine the distribution of coordinations, which rather exhibit syntactically properties characteristic of one of conjuncts (see e. g. the discussion and further references in Zhang (2009)). To be sure, the structural asymmetry between arguments arising from their being in different phrase-structural positions—a complement and a specifier—may cause qualms about the relationship between syntactic structures so generated and commutativity of conjunction and disjunction connectives; it may seem that an и-ary with n > 2 (ternary for the basic case) branching tree may be better suited to the task of providing a structural representation of such expressions, as it had been assumed before the generalization of the binary branching hypothesis and its set-theoretic counterpart, Merge restricted to the binary case; Freidin (2012: 77) goes so far as to accept n-ary Merge with n > 2 for coordinations as an exception to the general restriction on the number of arguments operated upon by an application of Merge, reverting in such cases to much earlier analyses along the lines of (3).


The structure in (3) is not a representation of any structure available under the strict conditions on the operation Merge and its outputs in the most recent incarnations of the Minimalist Program, requiring и-ary syntactic operation, for n > 2 (its mirror with internal merge instead of external merge would amount to introduction of multidimensionality, see Chomsky (2015a: 82), Chomsky (2015b: 6)). Nor is (2) such a representation, if it is intended to capture the fact that both a and в are operated upon by к—unavailability of specifiers, heralded in Chomsky (2013c) and following immediately from the abandonment of projection-based mechanisms and labels, makes it inappropriate for this purpose. The (informal) tree notation in (2) may somewhat obscure the issue, immediately visible in the official set-theoretic notation in (4).

(4) {XP, {к, ZP}}

Assume that (4) is a structure generated by merge in narrow syntax, and its interpretation, be it direct or indirect, amounts in the basic cases to either a Boolean or, in non-clausal cases, non-Boolean interpretation of familiar Л Bn. The mapping is no longer as straightforward as it was under the X-bar theoretic schema, when, to be sure, several syntactic properties diverged from the standard case with the head of the structure determining its distribution, but when the divide between syntax and semantics admitted of various syntax-internal solutions to such problems; in the more Spartan framework of Chomsky (2013c, 2015a,b), labeling as determined during operations at the phase level is understood as being an instruction for the interpretive component to proceed, while purely syntax- internal devices should be reduced to a bare minimum, eliminated in the best case. The simplest options for aligning (4) with required semantic interpretation thus do not work, since the most straightforward analytic possibilities which offer themselves as ways to handle the behaviour of к as a coordinating binary operator are, (i), an interpretation (with a detour of translation into a formal language like Montague’s IL in the case of indirect interpretation) which takes к to be mapped onto a syntactically (in the syntax of the formal language) binary connective, with (4) translated as/interpreted as encoding a syntactic relation between к and XP, ZP without further ado, and thus crucially diverges from the syntactic structure in (4)/(2) despite seemingly proceeding as with other structures generated by narrow syntax, mapping object to object, constituent to constituent; or, (ii), an interpretation which gives up the assumption that к is binary, and thus would lead to an interpretation which would be at variance with required properties of such connectives (leading ultimately perhaps to introduction of a set of unary connectives). Note that currying is not a device which is of help if mapping to the C-I component is supposed to preserve structural properties of syntactic objects—curried к remains к, a semantic relationship is still head-specifier in this case. In the informal parlance of Chomsky (2013c, 2015b) (informal, since strictly speaking, there are no such labels like ‘XP’ on the current modelling of syntactic structures), any application of Merge beyond the formation of a two- membered set necessarily creates an {XP, YP} structure—there is no merge to the head apart from the first merge, in other words. Sticking to the standard semantics of и-ary connectives, for n ^ 2, the option (i) requires that a relationship absent from (2) be introduced—one holding between XP and к directly. The issue is not merely technical in nature, for it concerns the relationship between the syntactic (generative) component and interpretive modules and the status of the hypothesis about the ‘optimal fit’ of the syntactic module and the interpretive one(s). Even taking into account the fact that optimality concerns may be variously overcome by other requirements when considered in an entire web of empirically supported properties of language-related systems, the divergence between syntactic structures—in the present case involving apparent counterparts of binary connectives—as conceived currently and their semantic interpretation would in this case threaten to become not a mismatch but a gulf, unless it can be justified independently and/or executed in a way which retains relevant properties of syntactic structure in (4) without being detrimental to semantic procedures and their outcomes. The transition from Narrow Syntax to C-I components, as well as later procedures within C-I modules, might be argued to involve processes which obliterate syntactic relations and properties and introduce properties of their own, much as the process of externalization crucially includes eliminating hierarchy-based relations; but the analogy would be misleading, externalization processes being considered secondary and mapping structures generated by narrow syntax to evolutionary earlier components related to externalization involving issues neither met with nor relevant for the syntax-semantics transition—. every theory of externalizationphonology, morphology, et cetera—violates about every principle you can think of. It violates Inclusiveness, it violates just about anything’. (Chomsky 2015a: 90)—and the general methodological requirement discussed in Chomskyan quotes above would be violated, were we to adopt the option (i). If there is no evidence for an otherwise unexpected transformation on the road to semantics, ‘there’s no way for a child, say, to say, “I’m going to invent a new principle for this structure I’ve never heard before.” That doesn’t mean anything’. (Chomsky 2015a: 82-83). The option (ii), on the other hand, does not seem promising as a way to make syntactically generated structures enter the realm of semantics—it seems to threaten the connection with reasoning and inference, hardly a welcome perspective, so that it is not surprising that the analysis in Chomsky (2013c) explicitly attempts to preserve the binary nature of к together with the semantically symmetric behaviour of coordinated expressions by tentatively assuming that coordinated phrases are initially merged together, forming a structure analogous to symmetric small clauses as analyzed in Moro (1997a,b, 2000), with one of the conjuncts undergoing a (very) local displacement from an {XP, YP} structure, as in (5).


The initial merger of XP and YP is supposed to be ‘capturing the semantic symmetry of coordination’ (Chomsky 2013c: 46); but this particular assumption, one which should make it possible to evade both option (i) and (ii) by aligning syntactic and semantic properties without abandoning general syntactic mechanisms, is not that obvious within the general picture of the label-based framework and requires more elucidation. A structure {XP, YP}, where neither XP nor YP is a lexical item, is present also in small clauses, where it is crucial that the constituents be not interpreted as symmetrically related. In both cases there would be, according to the mechanism outlined in Chomsky (2013c), movement of one of XP, YP forced by label-theoretic considerations (strictly speaking, only structures with one of XP, YP raised would pass the labeling algorithm). In both cases, then, there would be a copy—a trace in a more traditional parlance—left in the initial set which, even if it is hypothesized to be invisible for the labeling algorithm, does not disappear on the way to the interpretive module and is hence visible for interpretive purposes. If displacement is modeled as involving A-abstraction (be it under a direct interpretation, as a reflex of the structural configuration, or under an indirect one, via translation into a formal language), the presence of the variable bound by a А-operator at the movement site ensures that the displaced element will be interpretively connected with it, be it by a syntactically understood ^-reduction (effectively undoing displacement before interpretation even begins) or operations corresponding to it more or less closely, but taking place during interpretation and affecting interpretive properties of structures involving displacement (section 3.6 returns to the issue); in any case, the base position remains accessible and, in the case of small clauses, is essential for a predicative interpretation, XP and YP not being interpreted alike, but one being a predicate and the other one its subject, despite the initial {XP, YP}-formation with an apparent symmetry between its members. A comparison between small clause structures and hypothetical underlying coordination structures in (5) does not straightforwardly support the idea that ‘the semantic symmetry of coordination’ may be so captured without further ado; this requires going beyond both properties of merge as a set forming operation and properties of the labeling algorithm, neither of which secures the behaviour expected on the part of conjuncts at the semantic level. The labeling procedure as outlined in Chomsky (2013c) for (5) results in conjuncts providing labels for complex objects of which they are constituents (every occurrence of an object has to be a term of an object for which it might provide a label, hence XP labels only the entire expression), к remaining invisible for this purpose.


The structure in (6) would thus exhibit properties of the first conjunct, XP determining the label of the whole structure. That leaves questions about instructions for the interpretive component with regard to в' although the analysis assumes that neither к nor в are available as labels, both should receive an interpretation. The fact that the structure passes the labeling test is consistent with the conceptualization of the labeling algorithm as not literally attributing labels, but rather checking the structure for the presence of configurations relevant for unambiguous establishment of interpretive properties; it stands to reason that the absence of a label need not be indicative of uninterpretability provided that other properties which are sufficient for interpretive procedures are present—unlabeled in this sense does not mean ‘unlabeable’.

Suppose that instead of (6) and beginning with a small clause-like structure, coordination starts rather with merging an LI and YP, only then merging with XP. If there is a culprit for the behaviour exhibited by such structures both in narrow syntax and in the C-I interpretation, it should be, as on the analysis in Chomsky (2013c), the LI in question, к itself; its properties should ultimately ensure required interpretive properties without its being merged in a structure like (3). A coordinating lexical item may be hypothesized to belong to a class of lexical items which behave for the purposes of the labeling algorithm in a special way, being ‘defective, thus sharing partly syntactic properties with roots and T’s, likewise being unable to provide a label for a structure which they head. The crucial difference is that, although ‘it must still be visible for determining the structure’ (Chomsky 2013c: 46 n. 40)—for otherwise the structure effectively collapses for labeling purposes to {XP, YP} again, while properties of both XP and YP do not lead to feature valuation, whence (F, F) labeling is not available—it does not enter into relationships familiar from the case of roots and T’s: it does not head a complement of a phase head, hence no feature inheritance is possible; it does not enter into (ф, ф) labeling, as roots and T’s do, nor does XP in (5), which remains active for such purposes despite its being absolutely immobile once it has been merged with {к, YP}. It seems that it is label-theoretic deficiency that has to be inspected closer in the search for a proper elucidation of the syntax-semantics mapping in this case. It will involve going a somewhat circuitous way, not surprisingly given differences in properties of distinct types of ‘weak’ LI’s and the involvement of various general properties of the computational process as it takes place in narrow syntax. Beginning with labeling issues in section 1.3.1, leading through properties of roots and the roles of (formal) features in sections 1.3.2—

1.3.3 and details of labeling together with the issue of thematic interpretation in sections 1.3.4-1.3.5, it will end with general considerations about ‘weakness’ of LI’s and its interpretive consequences in section 1.3.6, with as little commitment to specific technical choices with regard to modeling the interpretive apparatus as possible.

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