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Un-Fregean syntax

In a discussion of essentially unsaturated entities of the Fregean picture and their correlated syntactic incompleteness, Kaplan (2005) observes (see also Kaplan (1964: 162-163) for further dicussion of the relationship between syntactic and semantic properties of such expressions and complex expressions in which they apppear):

The syntactic operations (functions) that yield compounds from components needn’t do so by filling gaps. (...) We can, of course, make substitutions on component expressions at any level, but it isn’t a matter of gap filling. When we substitute ‘bad’ for ‘good’ in ‘Bertie made the best choice’ we get ‘Bertie made the worst choice. Where’s the gap? Frege’s incomplete expressions, formed by extraction, seem to be of his own creation. (Kaplan 2005: 954)

‘Syntactic theory doesn’t work like that’’ Kaplan (2005: 954) concludes, and as far as the generative engine is concerned, one may add that it does not generally work in the way which would accord with his own view, either: ‘We build the ‘complete’ expression by using a variable, and then adding an operator. Instead of the incomplete ‘((2 + 3_2)_)’, we construct ‘Xx((2 + 3x2)x)’’ (with the possible exception of structures involving EA’s). The point applies to the theory of narrow syntax and its immediate neighbourhood in the C-I component; the latter may later apply substitutions and replacements as the need dictates. It follows that, irrespectively of exegetic issues and internal problems arising for procedures postulated in Frege’s development of logic, there are no syntactic—in the minimalist sense—processes involving discernment of patterns across syntactic structures and replacement of their terms by other terms. This is not surprising: the generative engine does not have (counterparts of) ‘dissection’ or ‘analysis’ of complex expressions, which might result in the same ‘thought’ or ‘conceptual content’ being carved up in different ways, as when—crucially beginning with complex expressions, in the most basic case, sentences, in conformity with the ‘priority of judgment’ thesis (see Heis (2014) for a discussion of this principle in its historical context)—one takes into consideration invariance under substitution, following the lead of Frege (1964):

If in an expression (whose content need not be assertible), a simple or a complex symbol occurs in one or more places and if we imagine it as replaceable by another (but the same one each time) at all or some of these places, then we call the part of the expression that shows itself invariant a function and the replaceable part its argument. (Frege (1964:

§ 9); transl. as in Frege (1972: 127))

Changes and waverings of Frege’s own position put aside (see Heck and May (2013)), the basics of the procedure—leaving out of account Frege’s epistemological and metaphysical concerns and claims—remain constant throughout in relying on substitutional properties, recognition of features of expressions which may cause problems because they do not even allow the relevant part of an expression to be extracted without further ado, necessitating sometimes introduction of additional signs not belonging to the object language if invariant parts are to be separated, as when writing with Frege f(?)’. The importance of the procedure was stressed by Dummett (1973, 1991), who contrasts it with the Tarskian practice of building ‘the ‘complete’ expression by using a variable, and then adding an operator,’ as Kaplan (2005: 954) summarizes it:

...Tarski’s device of using open sentences—expressions like sentences except that they contain indefinitely many free variables—was unashamedly a technical device, not corresponding to any natural operation of thought. Frege, in contrast, regarded the operation of extracting the predicate from a complex sentence by omitting one or more occurrences of some one term as a linguistic reflection of an intellectual operation of the highest importance, constituting one of the most fruitful methods of concept formation. (Dummett 1991: 196)

Narrow syntax cannot be onerated with any tasks involving inference-related operations, where the notion of substitution is of so crucial importance; as Bran- dom (1994) summarizes the relevance of the procedure for Frege:

His idea is that the way in which sentences are related to one another when one results from the other by substituting one subsentential expression for another confers an indirectly inferential role on the occurrence of subsentential expressions. Roughly, subsentential expressions can be sorted into equivalence classes that can be thought of as having the same conceptual content in an extended sense. For they can be assimilated insofar as substitution of one for another does not alter some feature of the inferential role of the sentences they are substituted into—paradigmatically, insofar as such substitution does not turn any materially good inferences those sentences are involved in into materially bad inferences. It is this methodology for carving up sentences into semantically significant subsentential parts by noting inferential invariants under substitution that he elaborates into the theory of functions, which throughout his later work he takes to be one of his greatest intellectual contributions. (Brandom 1994: 281-282)

Quite clearly, the task of ‘carving up sentences into semantically significant subsentential parts by noting inferential invariants under substitution’ is not the task of narrow syntax; but beside expressing an obvious distinction between syntax and interpretive processes (obvious, that is, if we remain in the territory of formal logic), a prohibition of substitutional operations in a merge-based, label-oriented theory of syntax imposes constraints on (i) a proper characterization of objects entering the derivational space—although they may belong to equivalence classes exhibiting common properties with regard to inferential processes, and they may be so described, narrow syntax cannot be in an official way said to work on a basis of a difference between what can be ‘substituted-in’ and ‘substituted-for’ on the one hand, and substitutional frames on the other (as in the Brandomian framework); (ii) a proper understanding of syntactic processes which take part on the route to interpretive components, which should not involve replacement/substitution, either, thus questioning trace conversion rules or availability of ^-reduction if they are to be understood as part and parcel of syntax, a point to which we return in section 3.5; (iii) a proper alignment of syntactic structures and their interpretation—in particular, an answer to the question about availability and extent of substitutional processes in interpretive procedures immediately following transfer to the C-I component. For although the C-I component may make use of such devices for inferential purposes, it does not necessarily follow that they are required for interpretation as it occurs with regard to structures generated by narrow syntax as they are delivered to the interface, phase by phase; and if they are ultimately judged to be required, it remains to be established what shape they take and how far their presence extends.

Semantic substitution may be hypothesized to be a procedure apt for performing required roles during the interpretation taking place directly after transfer to the C-I component, being an effect of the influence of narrow syntax on the interpretive module (to be sure, sensitivity to alphabetic variance remains a problematic property of such interpretive procedures, whether they involve standard infinitary assignments or avail themselves of finitary ones; see recently Klein and Sternefeld (2013, 2016) for an extensive discussion of variable capture in the context of semantic analysis and Pickel and Rabern (2016) on the latter issue, building upon ideas in Tarski (1933: 43 n. 40) = Tarski (1935: 309 n. 40) = Tarski (1956: 191 n. 1)). Availability of replacement operations later on in the C-I component does not exclude availability of rules like the predicate modification rule; what is at stake is rather a minimalist mapping of syntactic objects—together with features they bear and operations insofar as they are kept in the phase level memory and remain relevant for determination of their interpretive properties—onto objects and operations belonging to the C-I component. It is with respect to this point that the basic interpretive procedure for adjunction structures delineated above seems superior to its rivals. The structural makeup of adjunction structures may be hypothesized to be mapped onto an interpretive asymmetry, in contrast both with assumptions about interpretation of such structures as NP-RRC or AP-NP, treating both components of a structure to participate in interpretation on a par, with possible differences stemming from internal syntactic complexity of constituents; and with general hypotheses about the role and interpretation of adjunction structures originating in linguistically- oriented revamping of the event theory of Davidson (1967) as relying on the neo-Davidsonian decomposition of predicates and taking as the starting point an analysis of adjuncts as ending up in a string of conjoined predicates of events (see Hunter (2011, 2015) for a recent development of this idea), extending this line of approach by taking ‘predicate-adjunct combination as the compositionally “pure” case’ (Pietroski 2005: 245) to generalize conjunction-based mechanisms of interpretation, covering also relationships between objects created by set-merge alone, as advocated in Pietroski (2006, 2010, 2011, 2012a,b, 2014a,b),

Boeckx (2008b, 2015a), Lohndal (2014) and much related work. Asymmetry of interpretation arising in structural contexts relevant for the present discussion is reminiscent of the asymmetry postulated by Keenan (1974) (the crucial difference being that the functional dependency arises at the level of interpretive operations) or introduction of specifically asymmetric interpretive operations in Chung and Ladusaw (2004, 2006); Ladusaw and Chung (2012) and holds as an essential property of the basic interpretive strategy, although several details await further clarification (including possibility of reducing interpretive options for adjectival modification to either the subsective or even to the intersective case; see further Kamp and Partee (1995), Partee (2010) and the discussion of various options in Morzycki (2016: 26-43)).

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