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Roots and their categories

Recruiting independently available relation concepts for the purposes of narrow syntax is not, despite what the traditional stance assumed, an easy task. A proper analysis of relations and their adequate formalization have been long a matter of dispute; from the perspective imposed by minimalist considerations, it is not the most important point whether relations may be ontologically reduced to nonrelational monadic properties of objects, as held by philosophers from Aristotle to (later) Brentano (see recently Marmodoro (2014) for a refined account of the Aristotelian stance, and Brower (2016) for a dicussion of later Aritotelian influence), grounded on non-relational properties, as the Ockhamist-Meinongian line of approach would have it, or whether a Russellian approach is to be followed, with relations analyzed as external to their relata. It is not to be expected that the minimalist theory of language may simultaneously fulfill the aims of a theory of the human language and the aims of a philosophical analysis of language in the old-fashioned analytical tradition—it is an enquiry into properties of the human language faculty, not a search for philosopher’s stone; the relationship between models which the C-I component deploys in the process of interpretation and models of the external world may be safely assumed to be intricate and indirect. The relevant constraints are the methodological requirement to ‘assume that the external systems are impoverished—a natural extension of minimalist intuitions to the language faculty more broadly, including the systems (possibly dedicated to language) at the “other side” of the interface’ (Chomsky 1995: 358); and the requirements imposed by considerations related to Darwin’s Problem: introducing specifically linguistic objects, properties and operations should be reduced to a bare minimum, given the short evolutionary window for the appearance of the human language faculty. It is not therefore providing an ontological grounding for relations (in the traditional sense of ontology as the study of what-there-is) that is sought after in the theory of lexicalization, but, rather, merely investigating how relational concepts behave during the transition and which properties should be attributed to the C-I component, with as little new apparatus devised specifically for this purpose as possible.

A minimal starting assumption about pre-linguistic concepts might be that they are not relational concepts specified with respect direction and order independently of their other properties, but rather concepts of relations neutral in the sense of Fine (2000), determined further by equivalence classes with respect to relata they relate—the gist of the proposal of Fine (2000), debatable as an assumption of a philosophical theory of relations, which is however not at stake in the context of characterizing the language faculty and components it is connected to (see Fine (2007), MacBride (2007, 2011, 2013), Gaskin and Hill (2012) for discussion and further references). If roots interpreted as denoting relational properties are to have a determinate relational meaning, it would not do to invoke structural relations ‘being first-merged with X’ and ‘being merged with a set immediately containing X', since, although they do indeed differentiate one argument from another, they are not themselves able to distinguish sufficiently relations themselves—the direction (or sense, to use Russell’s term), in other words, cannot be encoded in such terms. Given that not all relational concepts are Л-representable in the sense of Humberstone (1984) (see further the discussion in Humberstone (2011: 505-507 and 729-738)), a merely conjunctional interpretation would not work, whence the direction of relation requires that there be an additional way for syntax to encode it and the C-I component to proceed in accordance with such instructions, thematic predicates actually performing this task on most analyses, a move which either leads to an enrichment of primitive syntactic concepts or to an enrichment of the C-I component with operations affecting the direct interpretation of syntactic structures without having a counterpart on the syntactic side (not to mention a possibility of incurring additional ontological commitments if proposals of Orilia (2000, 2009, 2011, 2014), Paoletti (2016) were incorporated into semantic theory). Interpretive properties of concepts qua roots thus become intimately tied to their categorization and syntactic behaviour which they exhibit as a consequence.

The way chosen in the classical Montagovian tradition to ensure that nominal and verbal structures, despite their being built so that both kinds of structures contain open places—signalled by variables—and therefore seemingly admit of being saturated, differ with respect to the latter property, is to let the distinction be encoded in syntactic categories which appear in well-formedness conditions: the syntactic categories t/e and tile, both having the same semantic type, viz. (e, t), are distinguished only at the level of their syntactic properties—the former, with a single slash corresponding to the fraction bar of Ajdukiewicz (1936), is the category of intransitive verbs, taking a nominal argument to give a truth-evaluable sentential expression; the latter, with a double slash, is the category of common nouns, denoting sets of objects; for this to happen, their e-slot cannot be saturated by an argument. The notation is arbitrary, but the distinction itself is crucial: explaining this innovation, Montague (1973b) notes:

We shall regard the categories A/B and A//B as playing the same semantical but different syntactical roles. An expression of either category is to be such that when it is combined (in some as yet unspecified way, and indeed in different ways for the two categories) with an expression of category B, an expression of category A is produced. (The precise character of the categories A/B and A//B is unimportant; we require only two different kinds of ordered pair.) (Montague 1973b: 222-223),

adding in a footnote: ‘It was perhaps the failure to pursue the possibility of syntactically splitting categories originally conceived in semantic terms that accounts for the fact that Ajdukiewiczs proposals have not previously led to a successful syntax’

(Montague 1973b: 241, n. 4). The slash notation, once so enriched, permits introducing e and t as the basic syntactic categories without losing the distinction between nominal and verbal expressions (and may be, of course, further exploited to mark analogous distinctions in other domains). Suppose that the labeling procedure is seen as checking the structure with respect to such properties of syntactic obt ects as syntactic categories and proper configurations of syntactic objects they are categories of (the procedure itself does not ‘categorize’ objects in this sense, for it is only a process inspecting the structure, not changing it or affecting it otherwise, except for forbidding it to be transferred to the C-I component)—not categories in the traditional sense, but in the Montagovian one (note that the labeling algorithm does not seem to make use of traditional syntactic categories altogether, and they may be thus considered eliminable from the theoretical landscape). In a standard setting, a type like (e, (e, t)), understood as a functional type, expressions assigned such a type being interpreted as denoting functions from individuals to functions from individuals to truth values, is equivalent to (e x e, t) —it is a general property of equivalence between functions (AB)C and ABxC. Currying is widely exploited in formal semantics to provide a smooth transition between polyadic properties of relation symbols and syntactic structure building—in connection with a multisorted type theory, it enables mapping syntactic structures formed by binary merge, thus introducing one argument at a time, and semantic representations in which several argumen- tal slots are filled in the body of the expression without structural differences between them being neither required nor, indeed, allowed. Or, rather, it used to enable such a smooth transition, since the elimination of X-bar theoretic notions has changed the landscape and the road to semantics ceased to be so easy. A direct relation between a lexical item, corresponding to a functor (possibly consisting, in a translation into a formal language, of several symbols, but nevertheless acting together as a function-denoting expression), and an argument is provided by the operation merge in the framework of Chomsky (2013c, 2015b) only as a result of the first merge of a functor and an argument. In stark contrast with possibilities open in the X-bar theoretic format, not only are there no multiple specifiers, which might host consecutive arguments—there are no specifiers at all. Beside such worries, note furthermore that the syntactic behaviour of terms assigned ultimately a functional type (p ^ (a ^ t)) will differ from the behaviour of a term assigned a Cartesian product type (p x a ^ t) if types of such terms cannot undergo currying—this is forbidden by a syntactic category assignment on the Montagovian approach if such terms are assigned to a different category slash-wise. If the C-I component ‘follows the path that narrow syntax carved’—or, better, if the latter provides instructions for the former to proceed not to be overcome or changed at will during the process of interpretation immediately after crossing the syntax-C-I border—we should expect a syntactic (in the minimalist sense) way to elucidate ‘double shlashes’ that Montague’s syntactic categories bear, so that the distinction on the semantic side mirrors directly properties of syntactic objects.

Suppose that the lexicalization process, turning concepts into syntactically manipulable objects, prespecifies their properties as far as the number and order of their open places is concerned, without necessarily following combinatory properties of concepts themselves, thus being active in a manner analogous to Pietroski’s proposal. It need not, however, turn them uniformly into monadic predicates; putting it in terms of the C-I component, it may assign them a pretype—e. g. (e, s, t)—which needs to be disambiguated for the C-I component to proceed. The disambiguation process cannot be conceptualized as mapping from traditional syntactic categories onto syntactic categories in the Montagovi- an sense any more—the former are by hypothesis idle, if not entirely superfluous; the latter require a reconceptualization in other syntactic terms so as to become grounded in syntactic properties of objects generated in narrow syntax. The possibility of reversing the direction of explanation—viewing narrow syntax as influencing the C-I component instead of as responding to its needs—suggests that syntactic properties should not be easily dismissed away as irrelevant for the C-I component, the current view on the place and function of the labeling providing further support for the relevance of seemingly purely syntactic properties for the very shape of the interpretive process. It is within such context that both feature transmission and head movement, leading to configurations acceptable for the labeling test, may be seen as ‘disambiguating’ a type-theoretic specification.

The extensive use of features in current syntactic theorizing, together with the fact that the theory of features is so far quite underdeveloped (see e. g. Adger (2010, 2013); Adger and Svenonius (2011) for much discussion of the issue)— a problem which becomes only more acute in a label-based theory, in which categorial syntactic labels cease to play any role in determination of labels and feature-valuation is crucial for providing the C-I component with instructions for interpretation—has caused severe doubts as to its explanatory power, given that features in the technical sense assumed in the syntactic theory have been frequently posited without sufficiently delineated constraints regarding their presence and syntactic/semantic import. Boeckx (2015a), arguing against a large-scale use of features, considers the recourse to properties of lexical items a device precluding explanatory investigation into syntactic phenomena; rejecting the criticisms leveled against minimalism with regard to the ‘move to the interfaces,’ which considerably lessens the burden of evolutionary and acquisition-related explanation of emergence and properties of narrow syntax, Boeckx (2015a) sees a major flaw elsewhere:

I think that minimalist syntacticians commit an even bigger mistake—one that is rarely if ever highlighted (perhaps because it’s shared across frameworks and also because it’s so deeply intuitive)—by coding virtually everything they should explain as lexical traits, better known as features. (...) I think that a lot of what makes minimalist analyses unconvincing, and certainly what makes them fall short of going beyond explanatory adequacy, is that by the time such analyses begin, all the action has already taken place, as it were. It has been carefully pre-packaged (pre-merged) into lexical entries. (...) It is clear that minimalism suffers from featuritis (to borrow a term from computer science that nicely conveys the ad hoc character of feature-creation), and often syntacticians hide away all the interesting problems by convincing themselves that (as the saying goes) it’s not a bug (an imperfection), it’s a feature. These days, we have features for everything (...). The problem is clear: in the absence of any realistic, grounded, cognitively sound, biologically plausible theory of what counts as a possible feature, it is too easy to come up with a feature that will do the job. But it should be clear that features and the way we manipulate them syntactically are the problem, not the solution. (Boeckx 2015a: 5-7)

Charges against an all too easy invocation of features and making derivations work as they should via coding the expected syntactic behaviour as the featural content of lexical items are certainly justified; it does not follow, though, that the distinction between features and syntactic objects—lexical items included— has to be entirely thrown away. The current theoretical landscape in minimalism, with its gradual elimination of assumptions taken over from earlier phases of the development of the generative inquiry, requires rather that the class of features and their behaviour, both within the bounds of syntax and outside, in interpretive components, be established, and the label-oriented framework offers an opportunity to do so—provided that temptations to introduce new features every time the analysis does not work properly are not succumbed to. In particular, it allows one to delineate more precisely the class of features which participate in labeling, thereby being active during syntactic computation, and which simultaneously provide the C-I component with instructions for the interpretive work to be performed. The investigation is much at a preliminary stage in this respect, beside case-studies of particular structures and programmatic statements—which, remaining valuable as methodological principles, still leave the details to be filled in—that ‘only certain features can serve as labels’ (Chomsky 2013c: 45). Already when feature checking of early minimalism was replaced by feature valuation, a significant step towards elimination of the look-ahead, in which ‘all the action has already taken place, as it were,’ was made; but the most important change was presumably the ultimate elimination of projection and adoption of the free merge, external and internal, hypothesis. Instead of entirely eliminating features as having explanatory roles to play, it may be advisable to take their formal and abstract nature seriously and, admitting only those that are justified on strictly syntactic grounds, to see interpretive counterparts of abstract ^-features or abstract Case as providing instructions for the C-I component, in accordance with the role they play in labeling, their lacking object-level meaning being only expected in this case.

An intuitive explication of the interpretive import of unvalued ^-features seems intuitively to be connected with the property of unsaturatedness—the need to take an argument of an appropriate kind, one to which expressions with valued ^-features belong, to result in an interpretively complete expression, along familiar Fregean lines, although without grounding the property ‘deep in the nature of things’ (Frege 1984: 156). Their interpretive import would thus be of an operator-like nature: the whole class of uninterpretable features would comprise properties which are interpretable at the C-I side if seen as/translated as operators specifying metalinguistic properties—in the case of ^-features, their import would thus be to dictate the C-I component to interpret the expression they operate upon as having a functional type, (e ^ (s ^ t)) in the case of monadic predicates, where the type s would be possibly understood as having as its denotation domain the set of pairs of assignment functions and points of evaluation, and not merely the set of the latter or of the pairs of distinct kinds of evaluation points (contrast in this regard the stance of Montague (1970b) and Montague (1973b)), thereby incorporating assignment functions type-theoretically (without making them full-fledged parts of models; see Kobele (2010b) for an approach which does so)—a property relevant for a full compositional treatment of semantic phenomena along the lines indicated in Henkin, Monk, and Tarski (1971, 1985). Nominal structures, on the other hand, seen as belonging to the class of (p x a ^ r)-typed expressions in which the ordered pair consists of types inhabited by potential arguments (left projection) and elements not belonging to the object language (right projection), would not exhibit syntactic ‘unsaturatedness,’ their apparent ‘arguments’ being merged exclusively by adj unction, and would require that there be an element or a property to be understood as/trans- lated as an operator providing an access to objects which constitute domains for interpretation functions when the structure is interpretively combined with the function-type expression—a place for the abstract Case feature to play a role, taking care of the a-type, most plausibly a type inhabited at least by assignment functions (with Li’s occupying D-head translated as familiar б/7-operators; see also section 3.4.3 for some further ramifications of this way of understanding the nature of formal features). ‘Original’ concepts are then seen related to new ones which are not determined with respect to their adicities by their sources, but also, crucially, their combinatorial capacities are not specific enough to make them combinable without further ado. Even more carefully, and more appropriately in the present context: properties which are seen by the C-I component include properties which are treated as/translated as (depending upon the choice of direct vs. indirect method of interpretation) type-theoretic properties; they need to be established unambiguously before reaching the point of transfer. What lexi- calization does is to offer distinct ‘perspectives’ on the content of original concepts without yet determining which one will be or should be used for specific purposes; what narrow syntax is bound to do is to make a choice and make it known to the C-I component. On this picture, there is no ‘turning’ a predicate into a noun (or vice-versa) at the point of categorization of a root by a v/n head: roots do not enter syntax with a determined ability to be combined with an ar- gument/arguments, although they do exhibit specification with regard to adic- ity; their properties are ultimately determined during the derivational process, their label-theoretic properties taking over the role of syntactic categories in the Montagovian sense, mapped onto type-theoretic properties at the C-I side of the derivational process.

 
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