Domains, objects, elements
Explicating the position according to which ‘weather-it behaves as though it were referential, but it can have no referent’ (Chomsky 1981a: 324), Chomsky (1981a) is explicit about possible relationships between syntactic levels of representation—where ‘syntactic’ is understood in the strictest sense of the generative the- ory—and representations belonging to the interpretive side:
The latter property is not as strange as it sounds; in fact, it is not uncharacteristic of what are often considered “referential expressions.” (...) Suppose now that we make a rather conventional move, and assume that one step in the interpretation of LF is to posit a domain D of individuals that serve as values of variables and as denotata. Among these individuals are specific flaws that can appear in arguments (cf. “the same flaw appears in both arguments”), John’s lack of talent, and so on. Then we might also assume that weather-it denotes a designated member of D, and is thus “referential” in the sense required for our discussion. Note that this step in the process of interpretation is not to be confused with what might be called “real semantics,” that is, the study of the relation between language or language use and the world. Rather, it should be considered to be in effect an extension of syntax, the construction of another level of mental representation beyond LF, a level at which arguments at LF are paired with entities of mental representation, this further level then entering into “real semantic interpretation.” (Chomsky 1981a: 324)
The claim that a substantial part of formal semantics should be properly characterized as investigating syntactic properties of (elements of) mental representations, together with the demand that several notions which play crucial roles therein be rather assigned to pragmatics, is a familiar motive going through several discussions of the relationship between syntax and semantics, language and the world, in Chomsky’s writings (to take just a handful of examples, see e. g. (Chomsky 1986b: 44, 2000b: 34, 2000c: 74, 2002: 158, 2016b: 48)). Despite their seemingly having an air of paradox—semantics being a part of syntax does sound at least a little bit paradoxical, as (rhetorical) questions like ‘why shouldn’t the meaning side of language work like that: no semantics at all—that is, no reference relation-just syntactic instructions to the conceptual apparatus which then acts?’ (Chomsky 2012b: 29) do, even although they are crucially qualified by the ‘that is’ explication, just as claims that ‘natural language has no semantics...’ are immediately made precise by adding ‘. in the sense of relations between symbols and mind-independent entities. Rather, it has syntax (symbol manipulation) and pragmatics (modes of use of language).’ (Chomsky 2013a: 44)—such claims would not for the most part be particularly controversial were it not for the fact that model theoretic semantics happened to be viewed either as belonging properly to the study of formal languages, seeking a most general way to characterize their interpretation and (merely) extending the use of such tools to the study of natural language (‘I reject the contention that an important theoretical difference exists between formal and natural languages,’ as Montague (1970a: 189) famously declared), in which case they might be ‘used as a technique of descriptive semantics’ (Chomsky 2004b: 115), but it ‘does not lead very far into the frightening area of general explanatory principles’ (Chomsky 2004b: 74); or as being intimately and inextricably tied to the laws of the kingdom of philosophical analysis of natural language expressions, ‘motivated by an interest in formalizing inference, or in determining ontological commitment’ (Chomsky 1981b: 11). In either case, the difference between the generative approach and formal semantics concerns both the role assigned to the model and its ingredients and the procedure of finding representations of natural language expresssions deemed appropriate for the purpose at hand and their properties. The pursuit of the latter aim, even if not involving a radical departure from structures which may be assigned by a syntactically (in the generative sense) informed analysis—as it happens inevitably in a quest for a ‘logically perfect language’, be it following a Russellian ideal according to which it ‘will show at a glance the logical structure of the facts asserted or denied’ (Russell 1986: 176) or a Quinean regimentation suitable for ‘limning the true and ultimate structure of reality’ (Quine 1960: 221) (see recently Hylton (2013, 2016) for a discussion of similarities and differences in the ‘perfect language’ strand of analytic philosophy)—is plagued by the ‘too much and too little’ problem, the fact that syntactic analyses provide both ‘too much’ information than it is required for purposes of philosophically oriented semantics or semantically oriented philosophy and ‘too little’ information to ensure that distinctions required for specific philosophical reasons are obtained—as J. Collins (2007) puts it,
... there is a presumption that (...) the structures specified by syntactic theory mesh with or support our conception of content/linguistic meaning as grounded in our first- person understanding of our communicative speech acts. This paper will suggest that there is no such tight fit. Its claim will be that (...) syntactic structure provides both too much and too little to serve as the structural partner for content (. ) the suggestion (. ) is that the contribution from syntax is by no means straightforward and is certainly not clearly reflected in the kind of structure that is familiarly taken to constitute propositional content. On this view, the philosopher’s content, as it were, is the result of a massive cognitive interaction effect as opposed to an isomorphic map onto syntactic structure. (J. Collins 2007: 805-806)
This picture of the relationship between syntactic analyses and their transformations for a possible deployment in a philosophical analysis (on which see further King (2013) and J. Collins (2014)) conforms to the pessimistic view about fruitfulness of the interaction between the minimalist modeling of syntactic structures and their generation on the one hand, and formal approaches to their interpretive properties on the other, expressed in Chomskyan quotes above. The role commonly, if frequently tacitly, assigned to components of models on the model theoretic approach may only strengthen this pessimism.
One of the most frequently debated points of disagreement between the generative stance on the proper investigation of semantic properties of natural language expressions and the approach of formal semantics as typically practiced concerns the components of structures used therein—in particular, sets arising by applying functions D to points of evaluation—and the relationship between their elements and linguistic expressions. A realist stance on models will take such elements to be straightforwardly in the world outside—the aim of a theory properly delineating the ‘scientific picture of the world’ being to characterize reliably citizens of the domain and to exclude all its illegitimate inhabitants by providing a regimentation of natural language appropriate for this purpose; it is an irrelevant step in this respect if one makes the domain of model an internal representation with elements of the domain standing in a one-to-one relationship with external objects. A significant body of work in formal semantics adopts a stance along such lines, and it is against this property that the polemic against referentialism is directed:
In his development of the Aristotelian theory of language, Moravcsik (...) suggests that “there are no expressions that perform solely the task of referring,” which we can revise as the suggestion that the referentialist doctrine is radically false: there are no expressions that pick out objects or things that are mind-independent. That seems accurate for natural language. Many inquiries illustrate that even the simplest expressions have intricate meanings; it is doubtful that any satisfy the referentialist doctrine. The referen- tialist doctrine has a role elsewhere. In mathematics, for example (...). In the sciences, one goal is to adhere as closely as possible to the referentialist doctrine. Thus in devising technical notions like electron or phoneme, researchers hope to be identifying entities that exist in the world, and seek to adhere to the referentialist doctrine in using these notions. It is common to speak of “the language of mathematics/science,” but these constructs should not of course be confused with natural language—more technically, with the linguist’s I-language. (Chomsky 2013a: 42)
Denying that the interpretation performed in the C-I component should be understood in a realist manner is one thing; providing a way to elucidate properties of interpretive procedures occurring therein is another. The domain D, if understood as part and parcel of the machinery of internalist semantics, with the relation R linking expressions of natural language and objects belonging to D— along the lines suggested e. g. in Chomsky (2000b), viz.
Within internalist semantics, there are explanatory theories of considerable interest that are developed in terms of a relation R (read “refer”) that is postulated to hold between linguistic expressions and something else, entities drawn from some stipulated domain D (perhaps semantic values). The relation R, for example, holds between the expressions London (house, etc.) and entities of D that are assumed to have some relation to what people refer to when they use the words London (house, etc.), though that presumed relation remains obscure. As noted, I think such theories should be regarded as a variety of syntax. (Chomsky 2000b: 38-39)
—is a hopeless non-starter as a candidate for being determined by functions D; it is hopeless as a candidate for being a set at all. Restricting it and imposing on it an internal structure is a property which may be attributed to the C-I com- ponent—without there being an incentive for this proceeding nor indications of the way it should proceed on the part of narrow syntax and objects which it creates. A procedure along the lines indicated in section 3.2.3 would suffice to create sufficient structure and would admit of a sufficient variety of ways to do it, the most abstract characterization thereof belonging to ‘pure semantics’ which, in a polemic againts Quine’s objections to quantified modal logic, was invoked in Kripke (2015) as one pole of the distinction between pure and applied semantics in a way worth recalling in the present context:
As Quine himself has pointed out (...), necessity might be construed more narrowly, as validity with respect to the logic of truth functions and quantifications and perhaps classes. Or it might be construed more liberally, as say some sort of physical necessity. But, if we are dealing with a single system of modal logic, all these alternative interpretations, giving different types of applied semantics, will nevertheless yield semantical notions having a common mathematical structure; and this mathematical structure (...) will be the pure semantics of the theory. (Kripke 2015: 2)
The distinction is a familiar one, well entrenched in thinking about semantic theories, their scope and purpose(s), made popular by Plantinga (1974: 126-127) and Haack (1978), who elaborates on the difference as follows:
I distinguished (...) four aspects relevant to ones understanding of ordinary, non-modal sentence logic; the distinction applies, equally, to modal logic. One has:
(i) (ii) (iii) (iv)
syntax of the formal informal formal semantics for informal account of
language readings of (i) (i) (‘pure semantics’) (iii) (‘depraved
In the case of the sentence calculus, the formal semantics (iii) supplies a mathematical construction in which one of t, f is assigned to wffs of the calculus, and in terms of which (semantic) validity is defined and consistency and completeness results proved. For all the formal semantics tells one, however, the calculus could be a notation representing electrical circuits (...) But the claim of the calculus to be a sentence logic, to represent arguments the validity of which depends upon their molecular sentential structure, depends upon one’s understanding the formal semantics in such a way that ‘t’ represents truth and f ’ falsehood; it depends, in other words, on the informal account of the formal semantics—level (iv). (Haack 1978: 188-189)
Attributing to the C-I component the use of structures comprising sets of points of evaluation and functions assigning to each of them a domain belongs to pure semantics of the interpretive component, and may well be justified for other (sub)components of the C-I side of the derivation; neither is explicitly forced by narrow syntax as such, and various ways of assigning domains to points of evaluations reflect the impact of non-linguistic modules (note that in the case of points of evaluation, the standard construction may be tentatively assumed to be chosen for reasons of simplicity, and further refinements may be imposed by the C-I component for distinct purposes, leading also to translation of Kripkean models into models constructed differently—a case in point may be provided by possibility models as arising in a development of ideas of Humberstone (1981), studied in Benthem, Bezhanishvili, and Holliday (2016), Harrison-Trainor (2016), Holliday (2016a,b)). All this is far away from any realist understanding of points of evaluation—which may be subsequently tied to it, but not as a matter of belonging to the apparatus employed by the C-I component upon receiving objects built in narrow syntax—and thereby remains strictly within the domain of an internalist approach to the interpretive component. Objects belonging to domains cannot be so easily dismissed, though. Assuming only that there are ‘mental objects associated with formal entities of language by a relation with many of the properties of reference’ (Chomsky 1986b: 45) leaves properties of such objects underdetermined. Steering a course between Scylla of making them simply mirror a possible external domain—which, beside threatening to replicate problems arising with the realist interpretation of models, merely pushing them one step inwards, would also make interpretive procedures linking syntactic objects and objects in a domain unaccounted for, chosen arbitrarily without regard to the nature of the syntax-semantics relationship—and Charybdis of making elements of a domain dissolve entirely in operations of the interpretive component—which is what strategies of consistent intensionalization achieve, replacing in effect objects with new elements of a structure, as models incorporating Hintikka’s individuating functions would do (see Hintikka (1967, 1969a, 1970a,b, 1975, 1998); Hintikka and Sandu (1995); Hintikka and Symons (2003) and Tulenheimo (2009) on properties of such models) or as positing exclusively intensional predication would effect (as done in Belnap and Muller (2014a,b), who build upon the intensional framework of Bressan (1972) and make individual variables be so called only as a matter of convention, since they do not range over elements of a domain), one would hope to find interpretive mechanisms which seem tailor-made for interpretation of syntactic objects because narrow syntax is a guide for the C-I component in this regard, and such ways of interpretive deployment of domains of points of evaluation which give rise to different ways of conceptualization of objects without predetermining them, without identifying them with elements of domains, and without neglecting syntactic structures. Counterpart-theoretic considerations seem promising in this respect. Fitting (2004) comments on distinctive properties of the counterpart-theoretic framework as follows:
In counterpart semantics, objects are present since they are what counterpart relations connect, but the counterpart network is fundamental, and an object, at a world, is actually something like a slice across that network. (...) In counterpart semantics what, exactly, is the morning star? (...) The morning star is something more like a web of relationships, connecting Venus in our world with some (actually non-existent) objects in the world of the Babylonians, and those with still other objects in other worlds, and so on—relationships that sometimes split and sometimes merge. In counterpart semantics, the morning star is there in the network of relationships, somehow, but I find myself unable to point at it, figuratively speaking. (Fitting 2004: 178-179)
What seems troublesome for an analysis of natural language expressions which has metaphysical ambitions, may turn fruitful for the C-I component to work with: instead of importing a domain of full-fledged objects, it has merely to establish domains containing elements of which the interpretation function makes use, but whose relationship with objects anywhere outside is not even in view at this stage. Interpretive operations may then well give the C-I component opportunities to construct objects in a more worldly sense. It may do so, provided that syntactic objects are not neglected.