The Case of Bare Plurals and Plural Definites. - Institut für Linguistik ...

Quantification over Events: 

The Case of Bare Plurals and Plural Definites. 

Cornelia Endriss 

endriss@rz.uni-potsdam.de 

Stefan Hinterwimmer 

stefan.hinterwimmer@rz.hu-berlin.de 

SFB 632 

Institut für Linguistik 

Universität Potsdam 

SFB 632 

Institut für dt. Sprache und Linguistik 

Humboldt-Universität zu Berlin 

Indefinites and Weak Quantifiers, Brussels 2005

Claims 

• Quantificational variability (QV)-readings available 

in adverbially quantified sentences with singular 

indefinites as well as with bare plurals and plural 

definites. 

• Q-adverbs exclusively quantify over (sets of) 

eventualities. 

• There are constraints for the availability of QVreadings 

with plural definites and singular 

indefinites. 

• These come about because eventualities need to 

be located in a salient time interval. 

• There is a pragmatic strategy by which this interval 

is determined: the Interval Resolution Strategy 

(IRS). 

• No such constraints for the availability of QVreadings 

with bare plurals. 


Outline 

• Data 

• QV-strategies: 

- With Singular Indefinites 

- With Bare Plurals 

- With Plural Definites 

• Constraints for the Availability of QV-Readings: 

- Tense Agreement ⇒ Interval Resolution Strategy 

(IRS): 

- For Singular Indefinites 

- For Plural Definites 

- Coincidence Constraint: 


• Explanation for Non-Restriction of QV with 

Bare Plurals 


Data: Quantificational Variability 

• Not only singular indefinites and bare plurals, but also 

plural definites get QV-readings: 

(1) A biologist is usually open-minded. 

(Most biologist are open-minded.) 

(2) Biologists are usually open-minded. 

(Most biologist are open-minded.) 

(3) The biologists that lectured on kangaroos at the 

conference last summer were usually open-minded. 

(Most biologists that lectured on kangaroos at the 

conference last summer are open-minded.) 

(4) *The biologists (over there) are usually open-minded. 


Data: Singular Indefinites 

• In sentences with singular indefinites, the tense 

markings of the relative clause verbs and the matrix 

verbs have to agree: 

(5) 

?? 

A car that was bought in the eighties is usually blue. 

(6) A car that was bought in the eighties was usually blue. 

(7) Most cars that were bought in the eighties are blue. 

• If Q-adverbs were unselective binders, the 

acceptability difference between (5) and (6) as well as 

between (5) and (7) cannot be accounted for. 

• Q-adverbs unambiguously quantify over eventuality 

variables. 


Data: Plural Definites 

• Also with plural definites, the tense markings 

of the relative clause verbs and the matrix 

verbs have to agree : 

(3) The biologists that lectured on kangaroos at 

the conference last summer were usually 

open-minded. 

(8) *The biologists that lectured on kangaroos at 

the conference last summer are usually openminded. 


Data: Plural Definites 

• Additional constraint in case of plural definites: 

(9) *The biologists that listened to Peter’s talk on 

kangaroo tails at the conference last summer were 

usually open-minded. 

(10) The people Peter met yesterday were usually friendly. 

• (9) is out though the tense marking of the relative 

clause verb and the matrix verb agree. 

• In (9), all atomic listening events necessarily 

temporally coincide (on Peter‘s lecture). 

• (10) only gets a QV-reading in a situation where Peter 

met the respective people one by one at different 

situations and not all at once. 


Data: Bare Plurals 

• No constraints for sentences with bare 

plurals: 

(11) Biologists that lectured on kangaroos in the 

eighties are usually open-minded. 


Outline 

• Data 

• QV-strategies: 






(IRS): 








QV with Singular Indefinites 

• Q-adverbs quantify over sets of 

eventualities/situations (cf. Berman (1989), 

de Swart (1993), von Fintel (1994), 

Herburger (2000)). 

• Indefinites are interpreted as Generalized 

Quantifiers with existential force. 

• Non-focal/topical material is mapped onto the 

restriction of Q-adverbs (cf. Rooth (1985), 

Chierchia (1995), Krifka (1995), Partee 

(1995)). 

→ Indefinite DPs are mapped onto the 

restriction of Q-adverbs if they are deaccented. 


QV with Singular Indefinites 

• QV comes about because the Q-adverb binds 

(minimal) situations that contain just one 

individual of the relevant sort (cf. Berman 

(1989), de Swart (1993), von Fintel (1994), 

Herburger (2000)). 

• Accordingly, (1) is interpreted as in (12): 

(1) A biologist is usually open-minded. 

(12) Most e [∃x. arg(e,x) ∧ biologist(x)] 

[open_minded(e)] 


QV with Bare Plurals 

• Bare plurals in English denote kinds (Carlson (1977), 

Krifka et al. (1995), Chierchia (1998), Dayal (2003)). 

• Kinds are nothing but sum individuals of a special sort 

(Chierchia (1998), Dayal (2003)): 

• A covert version of the σ-operator (Link (1983)) is 

applied to a set that contains (atomic as well as 

plural) individuals that fulfil the respective predicate 

not only in the actual world, but also in other 

possible worlds. 

• If bare plurals are combined with non-kind-level 

predicates, existential quantification over instances of 

the respective kind (realizations, cf. Krifka et al. 

(1995)) is triggered. 

• The instances picked out by the existential quantifier 

vary with the eventualities quantified over by the Q- 

adverb (as in the sentences with singular indefinites). 


The Use of Bare Plurals: English 

• The possibility to use a bare plural seems to 

depend not only on intensionality (as in Dayal 

(2003)), but also on the temporal specificity 

of the respective predicate 

• If the interval is “too specific”, the definite 

article has to be chosen: 

(13) (*The) biologists that lecture on kangaroos are 


(14) *(The) biologists that lectured on kangaroos at 

the conference last summer were usually openminded. 


The Use of Bare Plurals: German 

• In German, a plural definite as well as a bare 

plural may be used to express the meaning of 

(13) (see (15)), whereas the definite article is 

obligatory if the intervals are specific (see 

(16)): 

(15) (Die) Biologen, die Vorlesungen über Kängurus 

geben, sind meistens aufgeschlossen. 

(16) *(Die) Biologen, die auf der Konferenz im letzten 

Sommer einen Vortrag über Kängurus gehalten 

haben, waren meistens aufgeschlossen. 


The Use of Bare Plurals 

Assuming that kinds are sum individuals that exist not only 

during a specific time interval, it follows: 

• For English: 

• Bare Plural: respective NP denotes a temporally nonspecific 

set ⇒ kind denoting 

• Plural Definite: respective NP denotes a temporally 

specific set ⇒ not kind denoting 

• German: 

(17) (*The) Dinosaurs are extinct. 

• Bare Plural: respective NP denotes a temporally nonspecific 

set ⇒ kind denoting 

• Plural Definite: respective NP denotes a temporally 

specific or non-specific set ⇒ kind denoting or not 

(18) (Die) Dinosaurier sind ausgestorben. 


The Use of Bare Plurals 

• In the default case, in English, definite DPs denote the 

maximal sum individuals that fulfil the respective 

predicate at the time of utterance or at another 

contextually salient time interval: 

(19) The members of this club usually vote for the 

democrats. 

(20) Members of this club usually vote for the democrats. 

• The definite DP in (19) only denotes the members of 

the club at the speech time, while the bare plural in 

(20) denotes the plural individual consisting of the 

current members plus past and future members (cf. 

Lenci & Bertinetto (1999)). 


QV with Plural Definites 

• How does sentence (3) get its QV-reading, if Q- 

adverbs are not unselective binders? 



• How can co-variation with the eventualities be 

achieved in the case of plural definites? 

• Problematic because the definite article is not 

allowed to pick out different individuals from one 

and the same set (cf. Link (1983)). 

• It denotes the maximal sum individual in the set 

it is applied to. 


Plural Definites: Co-variation with Eventualities 

• Co-variation can come about because the set 

denoted by the respective NP-complement of the 

definite article varies itself. 

(21) The people in Peter’s class are usually French. 

(22) *The people in Peter’s current class are usually 

French. 

• In (21), the NP people in Peter’s class varies 

with the school years. 

• The NP class contains a silent eventuality 

variable that is bound by the Q-adverb. 

• An eventuality predicate λe.school-year(e) is 

inferred on the basis of clause internal 

information. (see appendix for details) 



• In (22), the adjective current fixes the 

denotation of class to a single eventuality: 

(22) *The people in Peter’s current class are 

usually French. 

• In effect, the set people in Peter’s current class 

is also fixed. 

• Each of the eventualities quantified over has to 

include the same sum individual. 

• (22) then is bad for the same reason as: 

(23) *Peter is usually French. 


Plural Definites: Distribution over Sum 

Eventuality Parts 

• Acceptability of (3) cannot be explained by co-variation 

with the eventualities. 



• No element like class inside the NP that may contain a 

varying eventuality variable. 

• QV-reading has to come about in a different manner. 

• Q-adverb quantifies over the atomic parts of the 

respective maximal sum eventuality. 

• If the verbal predicate is interpreted distributively, each 

atomic part of the sum eventuality contains an atomic 

part of the sum individual (cf. Nakanishi and Romero’s 

(2004) analysis of for the most part). 


Plural Definites: Distribution over Sum 

Eventuality Parts 



Most e [e ∈ Atom(σ{e’: arg* (e’, the_biologists e’’ 

)})] 

[e ∈ Atom(σ{e’: open_minded(e’)})] 

• Where the_biologists e’’ 

is the maximal sum individual 

of the biologists who participated in the relative clause 

event e’’ (lecturing) at the conference last summer. 

(see appendix for details) 


Outline 

• Data 

• QV-strategies 

strategies: 






(IRS): 








QV with Indefinites 

(5) ?? A car that was bought in the 80s is usually blue. 

(6) A car that was bought in the 80s was usually blue. 

• Every quantification comes with a domain 

restriction (cf. von Fintel (1994), Stanley 

(2000), Marti (2003)) 

• Domain restriction for events means to locate 

them in time (Lenci and Bertinetto (1999)). 

• The respective interval is determined by the 

pragmatic IRS (cf. Endriss and Hinterwimmer 

(to appear)). 

• Acceptability differences can be explained via 

(conflicting) tense information. 


Technical Assumptions 


Most e. [∃x [arg(e, x) ∧ car (x) ∧ ∃e’ [buy(e’) ∧ 

theme(e’, x) ∧ past(e’) ∧ in_80s(e’) ∧ e’ @ i’] ∧ 

C’’(x) ∧ e @ i] [blue (e) ∧ pres(e)] 

• C(e) is of the form e @ i 

• e @ i := τ(e) ⊆ i e , whereτ(e) denotes the 

running time of e 

• pres(e) := now ∈τ(e) 

past(e) := τ(e) < now 

• Interval i is determined by the IRS 


Interval Resolution Strategy (Sketch) 

• How to find the salient time interval? 

- Take overt information if available. 

- Take contextual information, i.e. the running 

time of another salient event, if available (cf. 

Partee, 1973). 




theme(e’, x) ∧ past(e’) ∧ in_80s(e’) ∧ e’ @ i’] ∧ 

C’’(x) ∧ e @ i] [blue (e) ∧ pres(e)] 


Acceptability differences explained 

• (5) is out due to the IRS: 



theme(e’, x) ∧ past(e’) ∧ in_80s(e’) ∧ e’ @ 80s] ∧ 

C’’(x) ∧ e @ τ(e’)] [blue (e) ∧ pres(e)] 

• Restrictor: eventualities take place before speech time. 

• Nucleus: eventualities include speech time. 

• Necessarily yields an empty intersection. 

• The sentence is out. 


Acceptability differences explained 

• On the other hand, (6) is predicted to be 

acceptable: 

(6) A car that was bought in the 80s was usually blue. 


theme(e’, x) ∧ past(e’) ∧ in_80s(e’) ∧ e’ @ 80s] ∧ 

C’’(x) ∧ e @ τ(e’)] [blue (e) ∧ past(e)] 


Plural Definites: Acceptability of (3) 



Most e [e ∈ Atom(σ{e’: arg*(e’, the_biologists e’’ )}) 

∧ e @ τ(e’’)] 

[e ∈ Atom(σ{e’: open_m(e’) ∧ past(e’)})] 



Plural Definites: Unacceptability of (8) 

(8) *The biologists that lectured on kangaroos at the conference 

last summer are usually open-minded. 


∧ e @ τ(e’’)] 

[e ∈ Atom(σ{e’: open_m(e’) ∧ pres(e’)})] 








(9) *The biologists that listened to Peter’s talk on kangaroo tails 

at the conference last summer were usually open-minded. 


∧ e @ τ(e’’)] 

[e ∈ Atom(σ{e’: open_m(e’) ∧ pres(e’)})] 


• Explanation for oddity of (9) has nothing to do with conflicting 

tense information. 

• Coincidence Constraint explains the oddity by restricting the 

co-occurences of the involved eventualities. 


Coincidence Constraint 

• Coincidence Constraint (cf. Lasersohn (1995) and 

Zimmermann (2003) for related constraints): QV 

only possible if atomic events allow for temporal 

variation (see appendix for details). 

• In (9), all atomic listening events necessarily 

temporally coincide (on Peter‘s lecture) which 

somehow turns the sentence uninterpretable. 

• Seems to suggest that Q-adverbs actually operate 

on the temporal component of eventualties. 

• Compare to adverbs operating on the local 

component: 

(24) A horse is loved everywhere. 


Coincidence Constraint: Unacceptability of (4) 

• The Coincidence Constraint also explains the oddity of 

(4) and (22) as well as the non-availability of a QVreading 

of (10) and (19): 

(4) *The biologists (over there) are usually open-minded. 

• As argued above, a definite DP denotes the maximal 

sum individual that fulfills the respective predicate at 

the time of utterance or at another contextually salient 

time interval. 

• In (4), the Coincidence Constraint is violated as all the 

eventualities then temporally coincide (to the time of 

utterance). 

• Compare this to: 

(25) My Maths teachers were usually open-minded. 


Outline 

• Data 

• QV-strategies 

strategies: 




• Constraints for the Availability of QV-Readings 

Readings: 


(IRS): 








Bare Plurals: Acceptability of (11) 

• Q-adverb directly quantifies over eventualities each of which 

contains an individual that realizes the kind denoted by the 

bare plural at that eventuality. 

• The denotation of the bare plural is not accessible in the 

restriction. 

• The plural eventuality introduced by the relative clause does 

not influence the choice of the eventualities quantified over. 

(11) Biologists that lectured on kangaroos in the eighties are 


Most e [∃x. real(x, biologists_tlokite, e) ∧ 

arg(e, x) ∧ e @ t world 

)] 

[open_m(e) ∧ pres(e)] 

(where real means realizes). 


Bare Plurals: Acceptability of (11) 

• Q-adverb directly quantifies over eventualities each of which 

contains an individual that realizes the kind denoted by the 

bare plural at that eventuality. 

• The denotation of the bare plural is not accessible in the 

restriction. 

• The plural eventuality introduced by the relative clause does 

not influence the choice of the eventualities quantified over. 

(11) Biologists that lectured on kangaroos in the eighties are 


Most e [∃x. real(x, biologists_tlokite, e) ∧ 

arg(e, x) ∧ e @ t world 

)] 

[open_m(e) ∧ pres(e)] 

(where real means realizes). 

• Note that existential quantification over instances is only 

possible with plural individuals the defining property of which 

is temporally not “too specific”. 


Summary 

• Q-adverbs are not unselective, but quantify 

solely over eventualities. 

• Interval Resolution Strategy (IRS) accounts 

for (un-)acceptability judgements on base of 

time information of the eventualities involved. 

• Works for singular indefinites as well as plural 

definites. 

• QV readings with bare plurals are not 

constrained by the IRS. 


References 

• Berman, Steve (1987): Situation-Based Semantics for 

Adverbs of Quantification, University of Massachusetts 

Occasional Papers 12. 

• Chierchia, Gennaro (1995): Individual Level Predicates as 

Inherent Generics. In: G. Carlson and F. J. Pelletier (eds.), 

The Generic Book, 176-223, University of Chicago Press, 

Chicago. 

• Chierchia, Gennaro (1998): Reference to Kinds across 

Languages, 

in: Natural Language Semantics 6-4, 339-405. 

• Carlson, Greg (1977): Reference to kinds in English. 

Amherst: University 

of Massachusetts dissertation. 

• Dayal, Veneta (2004): Number Marking and 

(In)definiteness in Kind Terms, in: Linguistics and 

Philosophy 27-4, 393-450. 


References 

• Endriss, Cornelia and Stefan Hinterwimmer (to appear): The 

influence of tense on quantificational variability effects. In: J. 

Doelling and T. Heyde-Zybatow (eds.), Event Structures in 

Linguistic Form and Interpretation. 

• von Fintel, Kai (1994): Restrictions on Quantifier Domains, 

PhD thesis, University of Massachusetts. 

• Herburger, Elena (2000): What Counts. Cambridge, 

Massachusetts. 

• Krifka, Manfred (1995): Focus and the Interpretation of 

Generic Sentences. In G. Carlson, F. J. Pelletier, eds., The 

Generic Book, 238-264, University of Chicago Press, Chicago. 

• Lasersohn, Peter (1995). Plurality, Conjunction and Events, 

Kluwer, Dordrecht. 

• Lenci, Alessandro and P. M. Bertinetto (1999): Aspect, 

Adverbs, and Events: Habituality vs. Perfectivity. In: F. 

Pianesi, J. Higginbotham and A. C. Varzi (eds.), Speaking of 

Events, 245-287. Oxford University Press, Oxford/New York. 


References 

• Link, Godehard (1983): The logical analysis of plurals and 

mass terms: A lattice-theoretical approach. In: R. Bäuerle 

et al. (eds.), Meaning, Use and Interpretation of Language, 

302-323. 

• Marti, Luisa (2003): Contextual Variables. PhD thesis, 

University of Connecticut. 

• Nakanishi, Kimiko and Maribel Romero (2004): Two 

construcions with Most and their SemanticProperties, 

Proceedings of NELS 34. 

• Partee, (1995): Quantificational Structures and 

Compositionality. In: A. Kratzer, E. Bach, E. Jelinek and B. 

Partee (eds.), Quantification in Natural Languages, 541- 

602, Kluwer, Dordrecht. 

• Partee, B. (1973): Some Structural Analogies Between 

Tenses and Pronouns in English. The Journal of Philosophy, 

70, no. 18, 601-609. 


References 

• Rooth, Mats (1985): Indefinites, Adverbs of Quantification 

and Focus Semantics. In: G. Carlson and F. J. Pelletier 

(eds.), The Generic Book, 265-299, University of Chicago 

Press. 

• Stanley, Jason (2002): Nominal Restriction. In: G. Peters 

and G. Preyer (eds.), Logical Form and Language, 365-388, 

Oxford University Press. 

• De Swart (1993): Adverbs of Quantification. A Generalized 

Quantifier Approach. Garland, New York. 

• Zimmermann, Malte (2003): Pluractionality and Complex 

Quantifier Formation. In: Natural Language Semantics 

11:3, 249-287. 


Appendix: 


(21) The people in Peter’s class are usually French. 

Most e. [school year (e)] [∃e’ ≤ e [arg*(e’, 

σ{X: people in Peter’s class e *(X)}) ∧ french*(e’)] 

Where σ({X: P*(X)}) = def 

(cf. Link (1983)) 

ιX(P*(X) ∧ 

∀Y[P*(Y) → Y ≤ X]) 


Appendix: 

Plural Definites: Distribution over Sum Eventuality Parts 



Most e. [e ∈ Atom (σ{e’: arg*(e’, σ{X: people* (X) ∧ 

∃e’’ [ agent(e’’, X) ∧ lecture*(e’’) ]})})] 

[e ∈ Atom (σ{e’: open_minded(e’)})] 

Where Atom is the function which maps a sum 

eventuality to the set of its atomic parts. 

(cf. Link (1983)). 


Appendix: 

Interval Resolution Strategy 

• How to find the salient time interval? 

1. Take overt information 

2. If not available: Take local contextual 

information from the same domain 

(restrictor vs. nucleus), i.e. the 

running time of another salient event 

3. If not available: Take contextual 

information from the other domain or 

take the default time interval which 

denotes the whole time axis t world 


Appendix: 

Plural Definites: Acceptability of (3) 



Most e. [e ∈ Atom (σ{e’: arg*(e’, σ{X: people*(X) ∧ 

∃e’’ [ agent (e’’, X) ∧ lecture*(e’’) ∧ 

past(e’’) ]})}) ∧ e @ τ(e’’)] 

[e ∈ Atom (σ{e’: open_minded(e’) ∧ past(e’)})] 


Appendix: 


(8) *The biologists that lectured on kangaroos at the conference 

last summer are usually open-minded. 


∃e’’ [ agent(e’’, X) ∧ lecture*(e’’) ∧ 

past(e’’)]})}) ∧ e @ τ(e’’)] 

[e ∈ Atom (σ{e’: open_minded(e’) ∧ pres(e’)})] 






Appendix: 


• Running time of a plural eventuality e*: 

τ(e*) = def ιt. ∀e’ ∈ Atom(e*) [τ(e’) ⊆ t ∧ 

∀t’ [∀e’ ∈ Atom(e*) [τ(e’) ⊆ t’] → t ⊆ t’ ]] 

• The running time of a plural eventuality e* contains the 

running time of an atomic eventuality e’: 

τ(e’) ⊆τ(e*) def 

∃e’’∈ Atom(e*) [τ(e’) ⊆τ(e’’)] 

• Coincidence Constraint: 

A set of eventualities E fulfills the coincidence constraint 

iff 

¬ [∀e, e’ ∈ E [τ(e) = τ(e’)]] 


Appendix: 


(9) *The biologists that listened to Peter’s talk on kangaroo 

tails at the conference last summer were usually openminded. 


∃e’’ [ agent(e’’, X) ∧ listen*(e’’) ∧ 

past(e’’)]})}) ∧ e @ τ(e’’)] 

[e ∈ Atom (σ{e’: open_minded(e’) ∧ past(e’)})] 

• Due to IRS, the running time of each e has to be 

included in (e’’). 

• Ergo, for each e there has to be a corresponding atom 

e’ in e’’ such that (e) ⊆ (e’). 

• Running times of all atomic eventualities in e’’ coincide. 

• Therefore, the eventualities e all coincide temporally. 

• The coincidence constraint is violated.

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