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Interpreting adjunctions

Composing predicates

Proposing the ordered pair theory of adjunction structures, Chomsky (2004a) justifies the very existence of adjunction with the recourse to requirements imposed on the output of narrow syntactic operations by external components, the C-I component in this case:

Possibly richness of expressive power requires an operation of predicate composition: that is not provided by set-merge, which yields the duality of interpretation discussed earlier: argument structure and edge properties. But it is the essential semantic contribution of pair-merge. If the C-I-system imposes this condition, then the existence of a device to yield predicate composition would conform to SMT—a promissory note, given the limitations of understanding of C-I, but not unreasonable. (Chomsky 2004a: 118)

The background assumption behind this approach is that narrow syntax responds to the needs of the C-I component, being in this respect ‘an optimal solution to legibility conditions’ (Chomsky 2000a: 96) as the Strong Minimalist Thesis claims it to be: ‘if language is optimally designed, it will provide structures appropriate for semantic-pragmatic interpretation (Chomsky 2013c: 41). ‘The duality of interpretation’ is thus on this picture a requirement imposed by the interpretive component, an interface condition that narrow syntax must satisfy if it is ‘optimal’; and yet, as Hinzen (2006) observes,

...even if the external systems cared about different kinds of information, and this explained a distinction between a base component and a transformational component in some sense, this would not say anything about what is cause here and what is effect: maybe the ‘discourse-related’ functions are what they are because there are syntactic transformations generating certain kinds of structures, arising as a kind of side-effect from them. (Hinzen 2006: 214)

Instead of framing the account of adjunction in terms of interface conditions, and sticking to the metaphor of narrow syntax ‘fulfilling’ the needs of interpretive components, ‘responding’ appropriately to their needs, it might be better to turn turn the tables, as it were, and contemplate seriously the picture on which narrow syntax formats the C-I component—having operations and constructing syntactic objects which it constructs makes the C-I component utilize them in a systematic way, opening a space of various semantic possibilities, and apply to adjunction the conclusion that Hinzen (2006) advocates for displacement: that ‘there are certain operations that the structure of our nervous system, perhaps by virtue of deeper principles of a mathematical and physical nature that it instantiates, makes available; and that these lend themselves to certain uses’ (Hinzen 2006: 214). It is not because richness of expressive power requires that there be a syntactic operation interpreted as predicate composition that adjunction appears in syntax; rather, it would be the case that because there is adjunction in narrow syntax that semantic operations corresponding to predicate composition come to be exploited by the C-I component. On a kind of analysis outlined above, adjunction structures are freely available once merge is, and the issue is not how to justify their existence, but rather how the C-I component might cope with them in an efficient and non-stipulative way. The representation of adjunction as an ordered pair does not provide an anchor for the C-I component to apply independently available mechanisms; it is rather the case that an object with properties different from outputs of set-merge is interpreted in a manner different than they are—as it happens, the latter are by assumption coupled with the function-argument semantics, hence the C-I component, by hypothesis in need of ‘predicate composition,’ utilizes the former to this end. A paragon case of predicate composition, coming under the name of predicate modification (Heim and Kratzer 1998: 65), exemplifies the stipulative nature of this mapping perfectly: it must be assumed either to be an interpretive operation which takes place during a direct interpretation after the boundary of the C-I component is crossed or a translation rule into an intermediate formal language, with the effect of variable identification—originally conceived so as to apply to variables of the individual type e, but applicable to variables of the /-type (type of eventualities) as well:

(5) If a branching node a has as its daughters в and y, and [[8]] and [[y]] are either both of type (e, t) or both of type (l, t), then [[a]] = XX. [[в]] (X) Л [[y]](X), where X is an individual or an event (whichever would be defined). (Morzycki 2016: 214)

Such rules, be they purely interpretive or translation-oriented, when generalized, cover not only effects of adjunction of AP to NP or CPre/ to NP, but are also used to account for the semantic integration of a v0 head with the clausal spine (as Event Identification of Kratzer (1996)) and introduction of ‘extra arguments’ (as a modified version of Kratzer’s rule in Hole (2005, 2006)) and came to be generalized in McClure (1999), Solt (2009) as a Rule of Variable Identification:

  • (6) Two functions whose first argument is of the same semantic type may compose via conjunction:
  • (Aa .../(a))(Aa ... g(a)) = ... Aa.f (a) Л g(a), where the ellipses (...) reflect the possibility of additional arguments. (Solt 2009: 96)

Variations on predicate modification as widely adopted after Heim and Kratzer (1998) all have in common that—beside requiring additional care when stated in full detail, since accidental variable capture during translation (or its equivalent under direct interpretation) must be avoided, as already noted by Thomason (Montague 1974: 261 n. 12) in a comment on the Rule T3 of Montague (1973b)— they seem to be tailor-made for adjunction and they do not seem to follow from properties of syntactic structures proposed for adjunction. ‘The last temptation is the greatest treason: To do the right deed for the wrong reason' as Eliot’s Becket well knew.

In the case of structures {{a}, 8} with {a} the result of self-merge of a, an aspect which might direct the interpretive procedure performed in the C-I component is the presence of an object created by internal merge of the self-merge kind, invisible for the purposes of labeling and not entering into a featural relationship with its sister. If it looks like a copy, swims like a copy, and quacks like a copy, then it is probably a copy, and its interpretive import should come to the import of other types of copies as close as possible—without being entirely identical, for the C-I component cannot be blind to the absence of a head of such a putative chain. In a basic case, a copy—visible for the C-I interface as a variable

  • 2.2 Interpreting adjunctions
  • 67
  • (or translated as a variable, if the indirect method is followed)—signals the place in the structure at which the interpretation of the head of the chain influences the interpretation of the main structural spine; thus, taking an extremely local chain in (7), it is at the level of the copy that the interpretation of DP is combined interpretively with that of Z.

(7)

Disregarding for the purpose at hand various possibilities arising in modal contexts, absent in (7), and ignoring the complications arising from the availability of counterpart relations, which are irrelevant for establishing the parallel with adjuncts, the latter being only solitary copies, hence not interpreted via a counterpart relation, which we introduce in chapter 3 and which would require presence of a higher occurrence, the basic mechanism for interpretation of such structures in simple structures MK = {{W, R, D), Г) with the help of an assignment function gis to make Z be interpreted with respect to a modified assignment function g which takes care of the denotation of DP; thus, if we take a to be "Xx.f1, being true for в in (7) in MK with respect to the assignment function g means being true for ф in MK with respect to an assignment function g which agrees with g on all variables except possibly on x, for which g(x) = I*g(Tr (DP)), so that if I*g(Tr(DP)) = a, ф is evaluated with respect to g[x ]. The standard treatment of a copy involves ‘internalization’ thereof—as in the case of variables bound by a А-operator, their contribution to the meaning becoming part and parcel of the assignment function (on the most plausible modeling of the process, see section 3.6). Take (4) to involve adjunction in a nominal structure, as in (8), with AP adjoined to NP.

(8)

Assume that Tr(NP) = Ах.ф and Tr(AP) = Ay.f (mixing metalinguistic and object language variables without Quine corners for legibility); an operation of composition as typically assumed would lead to formation of a complex А-term Аг.ф[г/х]

Л f[z/y], where z is a variable not occurring in either ф or f. This operation is thus a substitute for an operation freely available in A-calculus (and one of its most important virtues)—formation of complex A-terms by connecting open formulas with the same free variable(s), beginning with ф and f to get ф Л f and only then closing them by prefixing A-operator(s) binding such variable(s) to obtain Ах.ф Л f . As an operation belonging to the syntactic level, neither should be adopted on minimalist grounds as the interpretive procedure applied immediately after crossing the C-I border to the output of syntactic operations: the latter would involve translating/interpreting constituents of an adjunction structure as expressions with the same variable free in both and simultaneously bound by a A-operator at the level of the whole structure, a treatment clearly available for a formal language, but without support in the syntactic structure together with operations kept in the phase level memory. On the other hand, as an interpretive operation, the operation of ‘composition’ treats both elements on a par, equally contributing to the meaning of the whole, thereby still deviating from the syntactic structure as delivered by narrow syntax to the interface. Suppose instead that the interpretive procedure takes the host NP and subjects its translation to the combined working of the interpretation function I and assignment function g modifying the latter so that the

host is interpreted as denoting the set {d: M,w = (j)[z / y] [^ g [ gly) iv ]] }, where d?e {d : M,w = ig[z/x][g[d]]}. Suppose further that the interpretive procedure makes in such cases rather use of a modified interpretation function I to incorporate semantic substitution in a familiar way; then the host is interpreted as denoting

the set {d : M, I[ z/y], w= g [ gXy) dyJ] }, where dwe{d: M, Wwl= ?igVd ]]}. In

contrast to more conventional treatments, the procedure does not involve syntactic substitution, neither as a part of the narrow syntax—where substitutional operations may be hypothesized to be unavailable, a property which made its appearance already in section 1.3.5 and to which we return again and again—nor in a possible translation into a formal language as a step preceding interpretation proper.

 
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