Displacement and substitution
Application of internal merge has been frequently modelled by employing А-abstraction over the trace at the extraction site; and the use of the device has raised doubts about its legitimacy in a minimalist setting in particular, given that such a way to represent displacement involves tampering with syntactic structures and reliance on devices forbidden by the Inclusiveness Condition—indices are most commonly held not to be proper parts of strictly syntactic representations (with few dissenting voices, see Elbourne (2005) and Kural and Tsoulas (2005)), yet the structures generated by movement in a system like that of Heim and Kratzer (1998) require movement to include indices occupying their own nodes, adjoined to movement targets; even discarding indices as parts of such representations, as e. g. in Sauerland (2007), it must be assumed that А-operators are crucially present, seemingly heading their own projections, as in (13).
Although such structures are claimed to be LF-type representations, their makeup requires that there be operations—syntactic at that, given that LF’s are syntactic representations, not their counterparts on the C-I side of the derivation—which would permit not only А-operators to enter a structure, but also to appear as its constituents in their own right. Such considerations apply equally to A-movement and A-bar movement, although distinct abstraction processes may be posited to account for differing properties of two types of displacement (as e. g. in van Urk (2015), who proposes abstraction over individuals and over choice functions to model distinct properties of A- vs. A-bar movement).
Various operations specific to the route from the syntactic derivation to the interpretive component have been proposed, with quantifier-related operations being perhaps the most prominent members of the group, but they have become more and more difficult to justify theoretically within a general picture in which there is little room left for building interface-specific representations after the syntactic structure has undergone the transfer procedure; on the other hand, А-operators obviously cannot be taken to be lexical items in the sense required by the labeling algorithm of Chomsky (2013c, 2015b) and related work: they cannot be supposed to be merged either externally nor internally—there are no free-floating As in syntactic structures, nor chains of А-operators—nor could they possibly provide labels in the same sense as lexical items do; nor do they, being parts of representations as the one in (13), enter into interpretive processes as other parts thereof do: А-operators do not compose with their sisters via ^-reduction. There were good reasons for Church (1941), after all, to make them belong to the set of improper symbols of the formal language. Closely related objections may and have been raised against operations designed to convert syntactic structures into representations susceptible of an interpretation as involving variables corresponding to traces/copies of elements undergoing internal merge during syntactic derivations—the Trace Conversion Rule of Fox (2002, 2003), where ‘for the sake of accessibility the rule is stated somewhat informally using objects of the semantic theory (the “meta language”) as if they were syntactic objects (in the “object language”)’ (Fox 2003: 119 n. 53), or the Quantificational Trace Conversion of van Urk (2015):
(14) Trace Conversion (Fox 2003: 110)
a. Variable Insertion: (Det) Pred ^ (Det) [Pred Ay (y = himn)]
b. Determiner Replacement: (Det) [Pred Ay (y = himn)] ^ the [Pred Ay (y = himn)]
(15) Quantificational Copy Conversion (van Urk 2015: 39)
Quantifier Replacement: Quant Pred ^ f Pred
Such operations require not only that structure-changing processes be available on the route from narrow syntax to the C-I component, thus being crucially syntactic in nature, and not happening beyond the border of the syntax-C-I component interface; they are substitutional, which is a major problem within the current framework of assumptions about the syntactic component of the human language faculty (see Fox (2003: 111-112) on the possibility of the elimination of trace conversion as a syntactic rule, cited below in section 3.6.1). Being substitutional used not to be a problematic property—in fact, substitutions had played an essential role as a technical device from the early days of the generative theory on, suffice it to recall their extensive and substantial presence in the framework of Chomsky (1975b) and ubiquitous presence in the theoretical machinery later on: rewriting rules, transformations, projection of lexical properties—all involve substitutions, which may be either explicitly stated over strings of symbols, with A being the most conspicuous signal of the presence of substitutional operations (playing a significant theoretical role, although cautiously introduced as a ‘convention’: suppose that (for uniformity of specification of transformational
rules) we add the convention that in the categorial component, there is a rule A ^ A for each lexical category A, where A is a fixed “dummy symbol.” The rules of the categorial component will now generate Phrase-markers of strings consisting of various occurrences of A (marking the positions of lexical categories) and grammatical formatives' (Chomsky 1965: 122)), or over positions in a structure (as was the case with substitution in the GB period), reemerging in Chomsky (1993), where substitution again plays a significant role, although the ‘dummy symbol’/‘designated empty position’ is now built-in into the operation itself:
GT is a substitution operation. It targets K and substitutes K1 for 0 in K. But 0 is not drawn from the lexicon; therefore, it must have been inserted by GT itself. GT, then, targets K, adds 0, and substitutes K1 for 0, forming K*, which must satisfy X-bar theory. Note that this is a description of the inner workings of a single operation, GT. (...) We never see 0; it is subliminal, like the “first half” of the raising of an NP to subject position. Alongside the binary substitution operation GT, which maps (K, K1) to K*, we also have the singulary substitution operation Move a, which maps K to K*. Suppose that this operation works just as GT does: it targets K, adds 0, and substitutes a for 0, where a in this case is a phrase marker within the targeted phrase marker K itself. We assume further that the operation leaves behind a trace t of a and forms the chain (a, t). Again, 0 is invisible when we scan the derivation; it is part of the inner workings of an operation carrying the derivation forward one step. (Chomsky 1993: 22)
It is worth recalling details of GT’s and Move a as they were seen as late as Chomsky (1993), because, first, substitutional devices employed in this environment persist much longer—indeed, even although the displacement operation has long been reconceptualized as internal merge, and crucially not involving substitution of a distinct grammatical formative (trace) for an occurrence of a displaced object at the extraction site, substitution was well and alive as involved in a countercyclic account of EPP effects up to and including Chomsky (2013c), as well as an essential ingredient in the workings of projection and the X-bar theoretic schema
(‘SPEC is in effect a cover-term for delta as well' as Epstein, Kitahara, and Seely (2015b: 103) observe). All this is gone by now. It is gone, to be sure, as a part of the theoretical machinery—structures generated by narrow syntax may be subject to description in terms of substitutional relationships, but—as far as narrow syntax is concerned—it may be hypothesized that such operations are not part of the explanatorily relevant apparatus. This, again, is an entirely different question than the issue of availability of substitutions and related operations in the C-I component: it may be easily hypothesized that substitutions are not only available, but actually play a crucial role within the C-I component(s) as part and parcel of pattern recognition so essential for inferential processes. These are not processes occurring within the confines of the syntactic engine, though. The absence of substitutional operations from the syntactic component has already made its appearance in sections 1.3.5, 2.2.1 and 2.2.2: various operations plausibly attributed to the C-I component in general are entirely lacking in narrow syntax and may be hypothesized to be absent from the C-I component as well insofar as it is under the influence of the syntactic machine. Semantic substitution, on the other hand, used in section 2.2.1 for the interpretation of adjunction structures, and used by Fox (2003: 111-112) instead of syntactic substitution (see below), may be assumed to be in place in the C-I component as it grapples with syntactic objects delivered from narrow syntax. This view makes all processes crucial for the Dum- mettian-Brandomian line of approach to semantics belong to other, separate stages of cognitive procedures taking place in the C-I component. ‘Intellectual operations’ ‘of the highest importance, constituting one of the most fruitful methods of concept formation' as Dummett (1991: 196) announced complex predicate formation, are bound to constitute another level of cognitive activity, which is an aspect of the situation outlined in Chomsky (2009: 29) (see section 1.3.2), where the emergence of ‘an internal generative system that constructs thoughts of arbitrary richness and complexity’ is coupled with the use of ‘conceptual resources that are already available or may develop with the availability of structured expressions' Substitutional operations and complex concepts that they give rise to belong to resources which ‘develop with the availability of structured expressions.’ Just as atomic LI’s qua predicates are not patterns, fragments of sentences or whichever susbtitutional candidate may be invoked in an analysis, so complex predicates as they are constructed in narrow syntax renounce substitutional procedures and obey standard laws of syntactic computation, requiring that the C-I component proceed accordingly (see Oliver (2010) for an overview of various characterizations of the notion ‘predicate’; P. M. Sullivan (2010) on the Dummettian analysis of Frege’s procedures, and Pickel (2010, 2014) on both internal problems of the approach and an evaluation of conceptual advantages and disadvantages of different stands on complex predicates and their philosophical import). There is no way that structures like (13) could be said to be syntactic structures obtained via operations of external and internal merge and subject to the set of syntactic operations assumed in the current minimalist setting: As are not candidates for being lexical items, nor are they plausibly conceptualized as set-theoretic syntactic constructs. Given absence of a dedicated level between narrow syntax and the C-I component, it is implausible to assume that they ever appear within confines of the realm of syntax as understood in minimalist terms. This is so because, as far as effects of internal merge are concerned, the presence of As signals a property of a complex syntactic object as a whole: they are not properly understood as properties of lexical items, except for the bottommost layer of the structure—a variable binding operator at the level of a root may be reasonably taken to be a property of the latter, enabling it to be combined with an argument. Adding A-operators in narrow syntax is in conflict with minimalist tenets as much as explicit annotation of labels would be, the latter being also properties of complex syntactic objects except for atomic ones. Instead of maki ng them parts of syntactic representation, then, it would be more in accordance with their nature to take them to be to ‘assume that lambda abstraction is simply an interpretive reflex of a configuration involving a chain (Nissenbaum 2000: 544 n. 2), where ‘an interpretive reflex’ differs according to whether a direct interpretation method is chosen or an indirect one, with a translation step into a formal language, is followed (see recently Ruys (2015: 482-485) for a discussion of these options in the context of modeling semantics of minimalist syntactic structures), the latter having at least the advantage of providing an explicit picture of the relevance and import of both intrinsic and relational properties of syntactic objects, be they atomic or complex, thereby making explicit commitments of the theory to particular features as relevant and required by narrow syntax and the syntax-semantics transition (see also section 1.3.3). Making semantic substitution the proper mechanism employed in the C-I component for the interpretation of expressions for which otherwise syntactic substitution is freely available opens the way for a more correct and interpretively richer interpretation of occurrences of objects undergoing internal merge.