Chains in all their glory
It is the persistence of the conviction that—of any effects which arguably fall in the province of semantics—only ^-properties and scopal ones are to be determined by narrow syntax, and the restriction of the latter class to those scopal effects which involve scoping over an expression from which displacement took place, that non-trivial chains like those in (16) might be treated as semantically insignificant, if not vacuous. They do cross various elements which may be treated as counterparts of modal operators. The Carnapian solution mentioned above, together with the widespread use of Kripkean semantics and frequent appearance of proper names, treated as designating rigidly an object in the domain—the very same object in different worlds—conspired to make this conviction seem justified. Once individual constants in general are treated with due suspicion as elements of the object language (given that they would arise at the stage of translation into a formalized language or during a direct interpretation procedure, for there cannot be any atomic expressions of this sort directly in the language of narrow syntax, for syntax-internal reasons already—the labeltng algorithm would fail miserably—much as there cannot be atomic expressions corresponding to variables, the tradition of taking pronouns as sufficiently close counterparts thereof notwithstanding, see Chomsky (2013c: 46) with n. 43; their apparent atomicity is thus a property of standard formalization, and their interpretive behaviour results from the complex of properties arising due to interpretation of their internal structure—see e. g. Hinzen and Sheehan (2013); Martin and Hinzen (2014); Sheehan and Hinzen (2011) for a dicussion of the issue which takes a particularly structural stance on the problem, rejecting predicativism with regard to proper names at length in Hinzen (2016)—and properties of use, see A. Sullivan (2014)), the expectation of semantic effects arising from every application of internal merge crossing an element corresponding to a modal operator—al- though possibly obscured by other factors—does not seem bizarre. Depending upon the type of displacement—in particular, upon the size of the phasal unit which is affected by displacement—movement may happen to cross even more than one operator of the same kind in one step. This is typically not supposed to happen with basic temporal or modal operators for (ill-understood) reasons of subcategorization—the fixed hierarchy of the syntactic skeleton does not allow their iteration, in contrast to logics which make use thereof. Consider cases of A-movement on a standard analysis, as exemplified in (1), repeated here for convenience with relevant details supplied.
DP-raising in such cases is a notorious case of displacement across ‘weak’ units of syntactic computation: nonfinite complements of raising verbs are standardly supposed to be TPs, hence lacking a phase-inducing C-head, as complements of ECM-verbs also do (a heritage of GB analyses, adopted in most treatments of these structures, with refinements, allowing the size of the structure to vary but crucially never achieving the level of th CP-phase, as in Wurmbrand (2001, 2014a,b); see Ormazabal (1995) for an analysis requiring CP layer in ECM structures), whereas raising verbs themselves enter into relationship with ‘weak’ light v’s which do not force transfer of their complements. The intermediate landing site for the DP undergoing internal merge—the so-called Spec-TP position—is required by the EPP, not by phasal properties of intervening heads. Adopting such analysis, one would have displacement crossing one relevant operator at each step (taking into account the structure fully would generalize to a multimodal case, but the basic property would remain). Importantly for an analysis of such structures, a labeling-oriented perspective on the derivation, in a manner of Chomsky (2015b), casts doubts on the presence of the Spec-TP position in such cases: it would require noting more and nothing less than the EPP as a separate principle—which is what is eliminated by Chomsky (2015b), EPP effects being due to the interaction of labeling requirements and computation by phase—and an assumption that such structures require TPs, i. e. truncated clausal structures, to be present, much as on the standard analysis. Suppose instead that such structures are CPs, except that the C-head is not activated with regard to its ^-features—at least as far as the syntactic computation is concerned, the labeling algorithm in particular. An option for structures headed by such defective C-T complexes to pass the labeling test would be for C-head to be deprived of its phasal status (via T-to-C raising or via external pair-merge of T to C, in either case creating a complex with C adjoined to T; see section 2.4.3 on both analytical options and for more discussion), thereby obliterating the phasal status of the C-head. There would be no subsequent labeling operations at this point of the derivation, then, and a structure does not need the so-called Spec- TP, as per Chomsky (2015b). The label-based analysis would be thus compatible with elimination of the EPP-position in raising structures, there being no source for the label of a in (19), eliminating thereby EPP as an independent syntactic principle and intermediate landing sites in raising structures simultaneously (see Epstein, Pires, and Seely (2005); Epstein and Seely (2006) for an extensive argument in favour of elimination of EPP).
When the phasal status is deactivated, though, there is no a to be labeled, while the base position of the DP in (19) is free to undergo internal merge higher in the structure, being available for such operations due to de-phasing of the C-head.
Yet grammatici certant et adhuc sub iudice lis est, and it would be premature to assume with further qualifications that together with the elimination of the EPP as a self-standing principle the intermediate positions of long-distance A- movement should be eliminated as well (see Boskovic (2002) for a discussion of phenomena which might be taken as evidence for intermediate landing sites in such cases, as well as Boeckx (2001) on notoriously murky reconstruction effects in A-chains); in particular, the intermediate landing sites—evacuated during the derivation—would be in any case invisible for the labeling algorithm, so that they would not cause a problem during the ultimate labeling process—they would be problem-atic were they final landing sites for a DP (see also section 2.4.3). Since the label-based perspective does not forbid structures as in (18), nor does it force structures as in (20), it is possible that both are made available by narrow syntax. The derivational process may be tentatively assumed, first, to create structures with chains of A-movement consisting not only of tails and heads, but also having intermediate positions (despite there being no phasal boundaries along the path of A-movement), and to let the C-I component be given structures in which a single link of an A-chain crosses more than one modal operator, independently of any possible constraints on their co-occurrence in a single CP/TP-structure. The C-I component should be thus able to cope with structures as in (21), whether proceeding bottom-up or top-down, whether A- or A-bar movement is in question, whether interpretation occurs dynamically by phases (as assumed in current minimalism) or awaits construction of an entire expression (as in the GB framework with the LF level of representation).
Depending upon particular decisions with regard to the syntax-semantics transition, there are various problems specific to different choices, but the most general picture, as in (21), displays already points of important difference with languages of formal modal logic and their standard interpretations. To cut a long story short: internal merge is hypothesized to involve cyclic behaviour, proceeding from the base position via intermediate occurrences at edges of cyclic nodes (a.k.a. phase heads) and ending at a final landing site. This way of seeing the displacement—as having a cyclic nature and having intermediate stages at designated positions only—has been a hallmark of mainstream generative analyses from the very birth of movement as a syntactic operation and remains the standard minimalist approach to the phenomenon, thus distinguishing it from analyses which adopt a ‘uniform path’ stand on displacement, effected via some variant of slash percolation of Gazdar (1981) (and subsequent development of the GPSG/HPSG strand; see Koster (2003, 2007, 2015) and Neeleman and van de Koot (2010) for different proposals to incorporate this approach into the minimalist theory) or by reducing the size of cyclic domains—the ‘every phrase is a phase’ analysis of cyclicity as proposed in Epstein and Seely (2002) and adopted e. g. in Boskovic (2007) or Muller (2011), would lead to analogous effects as the percolation-based approach, making cyclicity-relevant domains shrink so as to make them comparable to uniform path domains (causing ‘quasi-uniform’ path effects in the terminology of Abels (2003, 2012); see further Abels and Bentzen (2009, 2012) for a discussion of empirical prospects for evaluating differences between competing approaches and Boeckx (2008c) for a general overview). The difference important for the issue of interpretation of structures akin to (21) in the C-I component does not consist in there being cyclic displacement in natural language as opposed to formal languages; this dissimilarity, resulting from cyclicity of syntactic operations which is absent from formal language setup, has been stressed frequently enough, and is closely connected to the fact that formal languages have their rules of formation stated with the extensional characterization of the set of well-formed formulae in mind—weak generative capacity in short (see section 2.2.3 for some further remarks), and a close relationship between devices used in formal languages and in narrow syntax noticed e. g. in Chomsky (2012b)—
Suppose that you’re inventing a formal language. It has no discourse-related properties. So you just use external Merge. You put a constraint on systems—in effect, not to use internal Merge. And then you get, effectively, just argument structure. (...) Formal languages don’t have internal Merge; but they have got to have something that is going to be interpreted as scope. So you use the same device you do in natural language: you put it on the outside with the restricted variables, and so on. (Chomsky 2012b: 17)
—is understood as not only restricted to dependencies involving establishment of scope, but also, even in this case, restricted further to the head and the tail of a chain, intermediate occurrences again being disregarded for C-I purposes. Letting narrow syntax give shape to interpretive procedures requires, though, that chains be interpreted without ignoring such occurrences, and demands therefore that the C-I component use interpretive procedure appropriate for this task.