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Chains and their objects

Chains in Kripkean worlds

The interpretive import of chains and their relevance for processes taking place in C-I component(s) are quite restricted on most generative approaches to the syntax-semantics relationship. This is partly due to accidental properties of theoretical ways in semantic and syntactic theorizing, partly to more deeply rooted assumptions which affect understanding of chains and their role in syntactic and semantic processes. On the semantic side, it is a nonnecessary property of the Montagovian approach to adopt, together with the Kripkean possible worlds approach to modality, the take on domains of models as comprising individuals, world-independent at that (‘the widespread adoption of Montague’s practice has not been the result of much explicit argument’ as Partee and Hendriks (2011: 26 n. 20) note), much as it is not necessary to regard such domains as constituted of particulars—individual substances; nor is it inevitable to raise the type of expressions of the interpreted language so that expressions directly connected interpretive ly with objects in a domain—nominal phrases, proper names included—dissolve on the semantic side, the interpretive process relying on sets of properties, as the classical Montague grammar proceeds. That is no to say that such assumptions and proposals are unfounded or that there are no theoretical gains in proceeding these ways; the Montagovian approach to nominal phrases provided several insights into properties of nominal expressions and their semantic behaviour; such assumptions are not accidental, they are not, however, essential to the general program, being a consequence of specific theoretical choices. It is accidental, on the other hand, that several such choices were taken over by formal semantics, thereby narrowing the range of options for possible analyses of such linguistic phenomena as chains (it is another accident that Montague grammar was born well before the trace theory and the theory of chains, although—were we to perform an exercise in counterfactual history—even if the generative approach had already developed such theoretical concepts, it would presumably have had little impact on the semantic theory, given the discrepancy of methodological choices between Montague and the generative tradition, summarized in the former’s well known statement that it is crucial to ‘regard the construction of a theory of truth—or rather, of the more general notion of truth under an arbitrary interpretation—as the basic goal of serious syntax and semantics; and the developments emanating from the Massachusetts Institute of Technology offer little promise towards that end’ (Montague 1970a: 189)). With regard to objects of the domain, Montague himself was willing to consider alternative stances, if required by purposes of the analysis of natural language expressions, witness his epistolary discussion with Dana Scott concerning the draft version of Scott (1970) and partly documented in Scott (1970: 173), partly in Montague (1973a) (see also van Leeuwen (1991: 105-108)):

It is perfectly possible to construct an ontology allowing for physical objects of different sorts, objects that may coincide without being identical. The construction was sketched in a letter I wrote in June 1968 to Dana Scott, and corresponds, I believe, to Hume’s outlook. Let us for present purposes suppose that our basic objects have no temporal duration, each of them existing only for a moment; they are accordingly what we might regard as temporal slices of ‘ordinary objects’ and might include such physical slices as heaps of molecules at a moment, and possibly such additional objects as instantaneous mental states. Then ordinary objects or continuants (for instance, physical objects, persons) would be constructs obtained by ‘stringing together’ various basic objects— or, more exactly, certain functions from moments of time to basic objects. (Montague 1973a: 292-293)

The base line of this approach—analyzing entities away by construction—is familiar and employed famously by Montague himself with regard to ‘certain philosophical entities’ in order ‘to construct an exact language capable of naturally accommodating discourse about the dubious entities, and to introduce an intuitively satisfactory notion of logical consequence for sentences of that language’ (Montague 1969: 165). Such analyses, not only building on Carnap’s technical results, but also carried with the general attitude of Carnapian tolerance in mind, are prime examples of the Janus nature of Carnap’s principle:

Jeder mag seine Logik, d. h. seine Sprachform, aufbauen wie er will. Nur mufi er, wenn er mit uns diskutieren will, deutlich angeben, wie er es machen will, syntaktische Bestim- mungen geben anstatt philosophischer Erorterungen. (Carnap (1934: § 17); ‘Everyone is at liberty to build up his own logic, i.e. his own form of language, as he wishes. All that is required of him is that, if he wishes to discuss it, he must state his methods clearly, and give syntactical rules instead of philosophical arguments'; Carnap (1937: § 17))

The principle, one of the most often quoted, discussed and interpreted passages of Carnap’s works, is a statement of an attitude of which Carnap himself affirmed: ‘This neutral attitude toward the various philosophical forms of language, based on the principle that everyone is free to use the language most suited to his purpose, has remained the same throughout my life’ (Carnap 1963: 17)—quite independently of a particular context in which he arrived at its most famous formulation (see Creath (2009, 2012))—and which, still holding in the semantical period of

Carnap’s thought (Carnap 1948: § 39), is connected as much with elimination of several problems as pseudoproblems as with a project of conceptual engineering (see Richardson (1994, 2012) with further references):

Semantics—more exactly, pure semantics as here conceived—is not a branch of empirical science; it does not furnish knowledge concerning facts of nature. It is rather to be regarded as a tool, as one among the logical instruments needed for the task of getting and systematizing knowledge. (...) I am convinced that many other workers will soon recognize the value of semantics as an instrument of logical analysis, will help in developing and improving this instrument, and will then apply it to the clarification and solution of their special problems in various fields. (Carnap 1943: viii-xiv)

Montague himself is very explicit that, beside reducing ‘several dubious ontological categories to one, that of predicates’ which ‘should not be regarded as wholly dubious’ (Montague 1969: 163), his purpose is ‘to construct an exact language capable of naturally accommodating discourse about the dubious entities, and to introduce an intuitively satisfactory notion of logical consequence for sentences of that language’ and thus to make a philosophical progress— ‘by metamathematical or model-theoretic means—means available within set theory—one can “justify” a language or theory that transcends set theory, and then proceed to transact a new branch of philosophy within the new language’ (Montague 1969: 166). This is how the life of Montague’s intensional logic begins; and, on a smaller scale, what analyses analogous to the one exemplified in the quote from Montague (1973a) above are intended to achieve. Making claims as that ‘if there are individuals that are only possible but not actual, A is to contain them; but this is an issue on which it would be unethical for me as a logician (or linguist or grammarian or semanticist, for that matter) to take a stand’ (Montague 1973b: 242 n. 8), Montague remains faithful to the idea of logic as providing tools tailor-made to grapple with specific problems, but, as the preceding quotes testify sufficiently, he is also well aware that a quite specific metaontological stance comes together with an apparently purely pragmatic—in a colloquial sense—attitude towards the semantic enterprise, a stance transcending the boundaries set up by methodological choices (see also Eklund (2009, 2013, 2016) for a recent reassessment of Carnap’s metaontological commitments and Hirsch (2016) for a discussion of continuing relevance of various facets of Carnapian tolerance). It is hardly surprising in this context that alternative approaches to the characterization of the domain of objects and the relationship between the latter and their more mundane counterparts in ordinary discourse make an appearance mostly with an aim to analyze and elucidate various specific issues. It turns useful for Carlson (1977a,b) in an analysis of differences in the semantic behaviour of ‘states’ and ‘properties’ in the sense of Milsark (1974), with stages of individuals being proposed as the basic stuff of which individuals in the ordinary sense are built, and which may enter into predication. Thus, Carlson (1977a) comments on the notion of stages:

I do not see them simply as clips of film of an individual’s lifetime that are taken out and examined, with the sum of the clips of film being the individual. The individual is more than the sum of the parts, and the stages are not static sorts of things. The stages aren’t simply things that are; they are more akin to things that happen. That is, stages are conceived of as being much more closely related to events than to objects. (Carlson 1977a: 448)

The relationship between objects of the domain and individuals as the term is commonly used is understood in various ways in different proposals, as much as the concept of stages (think how happy Russell might be reading that ‘stages are more akin to things that happen—at least some of Russell’s stages, that is; it is not surprising to see the distinction offered in Carlson (1977a,b) being absorbed by the distinction relying on the introduction of the semantic type of events, see Kratzer (1995)) is variously analyzed whenever similar considerations emerge—which they do mainly outside linguistically oriented inquiries, in particular in connection with the debate over criteria of persistence, individuation and identity, suffice it to recall proposals, contemporary with Montague’s, as in the discussion in Gab- bay and Moravcsik (1973) or Kaplan (1973), the latter first contemplating the view according to which:

Individuals are taken to be specific to their moment, thus they are momentary stages of what we would call individuals. Variables and constants, when evaluated with respect to a moment t, take as values stages occurrent at t. Our individuals can be constructed from these individuals (which were sliced out of our individuals in the first place) by assembly (or, perhaps, reassembly). The assemblages of stages are used to evaluate quantification into and out of temporal operators. Although you cannot literally step in the same river twice, you can step in two stages of the same assemblage.(Kaplan 1973: 503-504)

Taking interpretive consequences of such a view into account, Kaplan (1973) considers an alternative according to which we ‘continue to think of things as before, but take the assemblages themselves as the values of the variables and constants’ (Kaplan 1973: 504). Such discussions thus offer frameworks for a philosophical analysis, either developed with a very specific issue in view or intended as an all-encompassing general proposal which admits of further refinements suited to particular needs—as Belnap and Muller (2014a,b), Belnap (2014), wherein the nature of the objects of the domain is ultimately entirely left undetermined (which it may be in virtue of the specific setup of the procedure of interpretation), and which is devised so as to allow inter alia comparisons of different views on persistence and its criteria (see Muller (2012) for such a discussion, and Muller (2014) for an application of the framework in the philosophy of science)—and examples may be easily multiplied, belonging basically more to philosophical logic than to the linguistic tradition of formal semantics, the distinction between stage-level and individual-level predication mentioned above being one of few exceptions (handled in various ways, see Diesing (1992a,b), Musan (1995, 1997, 1999), Krifka et al. (1995) and Kratzer (1995) for classical discussions). To be sure, the apparatus used to capture the difference in semantic properties of sentences built around predicates belonging to these two classes does not seem to be of much general use in the theory of the syntax-semantics relationship, involving differences in syntactic structure and/or specific principles resulting from requirements of particular predicates, not to mention the enrichment of the ontology of the model-theoretic side—all this seemed quite parochial, nothing of the sort expected if general syntactic or semantic principles were to be found or explained; in the minimalist setting, such worries may be only more pertinent and constitute more of an obstacle against incorporating such distinctions into the main theoretical machinery. Doubts gain even more force when one notes that the discussion revolves around the distinction between stages and individuals understood in temporal terms, analogous distinction in the modal (‘world-modal’) realm being at least questionable, if at all intelligible in the standard Kripkean setting, wherein it is rather the notion of transworld identification that is at stake. It is, again, accidental that the debate about transworld identity had been already abandoned by the time that the syntactic theory of chains was being developed— in contrast to the period of intense discussion concerning possibilities of identification of individuals across possible worlds, the problem by and large lost its charm by the early 80’s, and making his classical paper of 1967 (a ‘locus classicus of the views I am criticizing’’ says Kripke (1980: 45 n. 14), and Kaplan (1978) is happy to invoke this statement, concealing the identity of its author as ‘the leading modal logician of our time,’ Kaplan (1978: 88 note)) available in print, Kaplan (1978) both considered it ‘anachronistic’ and recanted his earlier views. Given both this and the original setting in which transworld identity was discussed, the notion seemed pertinent to the investigation of hyperintensional contexts, hardly to be considered basic elementary bricks to build a theory of syntax-semantics mapping, their ubiquitous presence nothwithstanding; the same goes for discussions of sortal predication in modal contexts—although involving phenomena pervading the interpretation of natural language expressions, and providing a fertile area for the inquiry into the syntax-semantics relationship (Gupta (1980) being an example of an extensive treatment of the issue without losing from view the advantage of ‘nicely enhancing the fit of the formal system with English syntax and semantics’ as Belnap and Muller (2014b: 401) put it).

 
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