The interpretation of universally quantified DPs and singular definites in adverbially quantified
sentences
In my talk, I compare the behaviour of universally quantified DPs and singular definites in adverbially
quantified sentences. More specifically, I investigate the conditions under which the respective DPs
can be interpreted as co-varying with the situations quantified over by a Q-adverb.
In contrast to singular indefinites and bare plurals, singular definites and universally
quantified DPs do not get co-varying interpretations in adverbially quantified sentences that are
presented without any context. Consider the contrast between (1a, b), on the one hand, and (2a, b), on
the other: while (1a, b) get a QV-reading that can be paraphrased as in (1c), (2a, b) only get the
readings given in (2c, d), respectively. They are therefore odd if the predicate smart is interpreted as
an individual-level predicate. If the sentence in (2a) is embedded in a context like the one given in
(3a), however, a co-varying interpretation becomes available (furthermore, the definite DP has to
contain a focus-accent; see below): (3a) easily gets a reading according to which the piano-player
varies with the jazz-concerts attended by the speaker. Concerning (2b), on the other hand, it is not
sufficient to set up a context like the one in (3b) in order for an interpretation to become available
according to which the students vary with the classes taught by the speaker: as is evidenced by the
contrast to the perfectly fine example (3c), it is furthermore necessary that the Q-adverb occupies a
position where it c-commands the universally quantified DP overtly.
The role of the context can be explained as follows. Despite their differing semantic types (e
and <, t>, respectively), the definite determiner and the determiner every have two things in
common: they both presuppose that the sets they are applied to are non-empty (cf. Lappin and
Reinhart 1988), and they both exhaust those sets. Concerning the second point, this has the
consequence that co-variation is only possible if the sets denoted by the NP complements of the
respective determiners vary. I argue that this comes about in the following way: the NPs contain a
situation variable that gets be bound by the respective Q-adverb (see Kratzer 2004, Büring 2004,
Recanati 2005 and Elbourne 2005). This in combination with the first point from above explains the
role of the context: due to the non-emptiness presuppositions mentioned above, the respective
determiner can only be applied to the set denoted by its NP complement if it is guaranteed that each of
the situations quantified over by the Q-adverb contains a non-empty set of individuals of the required
kind (which, in the case of the definite determiner, furthermore has to be a singleton). Therefore, it
has to possible to accommodate a set of situations such that each of those situations contains a
plurality of individuals/exactly one individual of the required kind: if this is the case, the free C-
variable (ranging over situation predicates) in the restrictor of the Q-adverb (see von Fintel 1994) can
be resolved to a predicate that characterizes the respective set. I assume that in the case of (3a) and
(3c), the respective context makes available a set of suitable situations. The adverbially quantified
sentences can thus be interpreted as shown in (4a) and (4b).
Finally, the above mentioned word order contrast is explained as follows: I assume that DP-
internal situation variables are free variables that can either be resolved to a contextually salient
situation (or to w0, by default), or be turned into variables bound by a Q-adverb via the insertion of a
binding operator directly beneath that Q-adverb at LF (cf. Büring 2004). This has the consequence
that Q-adverbs can only bind DP-internal situation variables if they c-command the respective DPs at
LF. I assume now that Q-adverbs (which, after all, are adjuncts) cannot be moved from the position
where they have been inserted, and that only focal DPs can be reconstructed into their vP-internal
base positions at LF (which is evidenced independently by the contrast between (5a) and (5b)).
Furthermore, being of type e, definite DPs have to indicate their discourse status via focus-marking: if
they introduce new discourse referents, they have to be focus marked. Universally quantified DPs, on
the other hand, cannot introduce discourse referents by definition, and therefore do not have to
indicate their discourse status via focus marking. This explains the contrast in (3): as co-varying
definites introduce new discourse referents, they have to be focus-marked and can thus be
reconstructed at LF. Concerning the universally quantified DP in (3b, c), on the other hand, there is no
reason for its being focus-marked, and reconstruction is thus blocked. Accordingly, a co-varying
interpretation is only possible if the Q-adverb c-commands the universally quantified DP overtly (as
in (3c)). That this assumption is on the right track is evidenced by the fact that a co-varying
interpretation becomes available in cases like (6) and (7), where the universally quantified DP c-
commands the Q-adverb, but where there is an independent reason for focussing this DP.
(1) a. A piano-player is usually SMART. (Note: capital letters indicate focus-accents).
b. Piano-players are usually SMART.
c. Most piano-players are SMART.
(2) a. ??The piano-player is usually SMART.
b. ??Every student is usually SMART.
c. Most s [in(s, x. piano-player(x)) C(s)] [smart(s, x. piano-player(x))]
d. x [student(x) Most s [in(s, x) C(s)] [smart(s, x)]
(3) a. I love going to jazz-concerts: The PIANO-player is usually SMART (and it's nice
to talk to him after the show).
b. I love teaching classes on formal semantics at this University: ??Every student is
usually SMART.
c. I love teaching classes on formal semantics at this University: Usually, every
student is SMART.
(4) a. Most s [jazz-concert(s)] [smart(s, x. piano-player(s, x))]
b. Most s [class-on-formal-semantics(s)] [x [student(s, x) smart(s, x)]]
(5) a. Someone from New York is likely to win the LOTTERY.
Preferred reading: > likely.
"There is someone from New York such that it is likely that this person wins the
lottery."
b. Someone from NEW YORK is likely to win the lottery.
Preferred reading: likely > )
"It is likely that someone from New York (whoever he/she is) wins this lottery."
(The original example is found in Chomsky1993: 35).
(6) a. Who stands usually in the first row at a Michael Jackson concert?
b. Every kid under FOURTEEN usually stands in the first row at a Michael Jackson
concert.
(7) Death metal concerts are spooky: Every MALE musician usually wears a long lack
COAT, and every FEMALE musician usually has painted BLOOD stains all over her
face.
References:
Büring, D. (2004): Crossover Situations. Natural Language Semantics 12, 23-62.
Chomsky, N. (1993): A Minimalist Program for Linguistic Theory. In: K. Hale and S. J. Keyser
(eds.), The View from Building 20: Essays in Linguistics in Honour of Sylvain Bromberger, 1-52.
Cambridge, Mass.: MIT Press.
Elbourne, P. (2005): Situations and Individuals. Cambridge, Massachusetts: MIT Press.
Kratzer, A. (2004): Covert Quantifier Restrictions in Natural Languages. Handout of a talk given at
the Milan Meeting `Covert Variables at LF' (Palazzo Feltrinelli, Gargnano).
Lappin, S. and T. Reinhart (1988): Presuppositional Effects of Strong Determiners. Linguistics
26:1021-1037.
Recanati, F. (2004): Descriptions and Situations. In: A. Bezuidenhout and M. Reimer (eds.),
Descriptions and Beyond, 15-40. Oxford: Oxford University Press.