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Degrees of weakness

The case of C-T relationship differs from the v-R case with regard to obligatoriness of head movement, absent in the T-C case; it should be expected that this behaviour finds its ground in how properties of T are mapped onto its type- theoretic behaviour. In contrast to the character of roots, neutral by themselves with regard to the mapping to the functional or product type, T heads may be taken to have modal operators as their interpretive counterparts, standing syntactically in need of establishing their (t, t) pre-types to become full-fledged en- dotypical functors at the C-I side of the derivation. The analysis of Chomsky (2015b) may be recast in type-theoretic terms as demanding that there be a possibility of a parametric difference between languages resulting from having in the lexicon a relevant LI which is seen by the C-I component as one with (t ^ t) already specified, hence not in need of featural interactions, or having one which is seen as merely (t, t)-specified. The former is fully interpretable as combining with its sister without further ado, and if internal merge of EA to the so-called Spec-TP position occurs and feature inheritance takes place, the structure is correctly labeled and interpretable as an instance of ^(Лх.Д^) (Tr (EA))n, inherited ^-features not being harmful for typing which results from internal merge; if no internal merge occurs and feature inheritance takes place, ^-features would be idle entirely. The latter, on the other hand, needs a presence of an e-type due to internal merge of EA for ^-features to be interpreted as acting upon the entire type, but it does not need further head raising as roots do: its type specification will be read off in the C-I component correctly already due to feature inheritance and labeling under feature sharing. It may be thus seen as less defective in this respect than roots are. The label-theoretic defectiveness of roots, their inability to provide by themselves a label for a syntactic structure in which they occur and the requirement that they undergo raising for reasons of categorization, may be analyzed as having a type-theoretic counterpart at the C-I side: they need type- theoretic disambiguation between inhabiting a functional type or a product one in order for instructions for the C-I component to be unequivocal, with a crucial ingredient being label-theoretic—syntactic, in other words—property of inability of labeling an {LI, XP} under feature sharing, with the result that the rise of structures available for such labeling requires further head raising for type-theoretic disambiguation. The defectiveness of a T head, on the other hand, does not require interpretation-wise as many applications of ^-features, and the LI itself does not involve any e-type specification at all, whence the need for head raising does not arise. The difference in label-theoretic weakness translates in these cases directly into the interpretive behaviour—without reduction of the former to the latter, given priority of narrow syntax.

The behaviour suggested by considerations in Chomsky (2013c) to be in the nature of coordination structures should follow from properties of к in such structures; in particular, from its label-theoretic weakness which, following the gist of the analysis in Chomsky (2013c), is stronger even than in the case of roots: it prevents it from entering feature-based dependencies and makes both к itself and the structure in which it appears as a structurally determinable source of the label unavailable for labeling, although acceptable for the labeling test.

(17)

What is visible for the labeling algorithm as a real source of label in (17) is the left conjunct exclusively: к not only is unavailable as a label, but also makes в unavailable as a label, thereby precluding labeling by YP as well. The invisibility of в, a complex structure, together with its being acceptable for the labeling test before transfer, is a behaviour typically exhibited by adjuncts, captured on analyses like Munn (1992, 1993) or Moltmann (1992); on the assumptions of Chomsky (2013c) it should be rather attributed to the defectiveness of к itself than to structural properties of such syntactic objects, but the intuition behind such proposals seems to point to a correct characterization of their label-theoretic properties. The defectiveness in question should be due to inherent properties of an LI, which manifest themselves in the C-I component as type-theoretic properties: in the case of coordinating LI’s it may be understood as their being undetermined along the Boolean-non-Boolean dimension. The high degree of interpretive flexibility correlates with a high degree of label-theoretic defectiveness: the ultimate determination of semantic properties of к happens only in the C-I component, and it is its extreme—extreme to the extent that narrow syntax permits—inactivity for the labeling procedure that allows it. Properties of coordinating LI’s, involving their label-theoretic invisibility and invisibility of the structure in which they appear as heads, giving rise to establishment of relations partly reminiscent of adjuncts, partly—with regard to the leftmost conjunct, interpreted as an argument of the entire в—reminiscent of the relationship of the external argument to the complex head of the verbal phrase, but still differing importantly from both, are responsible for their interpretive characteristics, resulting from their being special as far as label-theoretic deficiency is concerned, narrow syntax influencing thereby the C-I component in a systematic way and label-theoretic properties being intimately tied to the interpretive behaviour at the semantics side. Different degrees of weakness with respect to the labeling algorithm are reflected at the C-I side as different type-theoretical properties; given that labels are now conceptualized as relevant and required for interpretive processes and not for the application of syntactic operations, their doing so remains consistent with general theoretical assumptions. In accordance with minimalist guidelines, syntactic properties are not explained by or reduced to C-I properties; the former are however expected to find correlates in the latter. Label-theoretic weakness is one of properties which should not be treated as purely syntax-internal quirks of the generative machine, making its appearance in a wide range of cases, ranging from structures along the lines of (17) and adjunction structures (to which we turn in chapter 2) to parts of discontinuous syntactic objects, viz. chains (to which we turn in chapter 3). In the interpretive process at the C-I side we would encounter a class of C-I interpretive counterparts of j8’s: binary connectives would be properly said to emerge as equivalence classes under substitution of C-I counterparts of structures like (17). Adopting type-theoretic polymorphism as a descriptive device obscures to some extent the fact that the associative nature of such interpretive operations as conjunction may enter the scene only at further stages of C-I processes, due to availability of substitution in the C-I component on the one hand and label- theoretic deficiency of a certain class of LI’s on the other.

 
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