The index 1 corresponds to the“lifted”quantifier in the standard logical expression; it is placed in accordance with its
logical scope in the sentence. The index 5 corresponds to the bound variable. Thus we end up again with referential
dependencies that do not strictly mirror embedding in syntax.^216
The issue for linguistic theory is then whether either syntax or the descriptive tier needs to encode the“lifted”
quantifier, the bound variable, and/or relative quantifier scope. The standard approach in generative grammar (the
theory of LF) is that they do. But this assumption is based on the syntactocentric architecture, in which all differences
in meaninghaveto stem from differences in syntax. Under the present architecture, withthe possibilityof mismatches
among tiers, we can explore the possibility that relative quantifier scope is (at least often) a matter of enriched
composition, unexpressed in syntax. Given that I have elsewhere (Jackendoff 1997a: ch. 3) offered arguments against
the very possibility of constructing a theory of LF that incorporates quantifier scope, my own preferences ought to be
clear. But here I will officially leave the question open.^217
A moregeneral setofquestionswouldconcern the“operators”thatcreateframes. First,howmanydifferentoperators
are needed? The practicein formal semantics has been to try to cut them to a bare minimum; however our experience
with ontological categories (section 10.8) might indicate that a somewhat greater degree of profligacy is worth
considering. Second, how do we elaborate the semantic values of these operators so they can drive inferences? Third,
we have seen such operators coming from illocutionary force (question), sentence operators (negation, future tense,
may), adjectives and verbs (possible and want), conjunctions (if), and quantifiers (every). Why should referential
dependencies be affected by so many different grammatical factors? Fourth, what are the overall principles for
mapping between the descriptive and the referential tier?
More generally, the theories of quantification, negation, and modality are among the most richly explored areas of
formal semantics. It is a major challenge to see if this tradition of research can be recast in terms of the referentialtier.
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(^216) The reversalofthenormal referentialdependence (1 above4 in(51))explainsthecloseparaphrasewith a conditional:If someone is in this room, (s)he speaks two languages. I leave
it to the reader to work out the structure of this latter sentence, using the model of (48), and to observ e the similarity.
(^217) See Jackendoff (1996c) for one proposal about ho w distributed quantification show s u p in the descriptivetier. It is worth mentioning that Csuri (1996) derives certain
constraints on long-distance dependencies fro mreferential tier structure; Erteschik-Shir and Lappin (1979) offer related results. Thus certainevidence for syntactic
movement vanishes in favor of independently motivated constraints on referential dependency.