Table Of ContentPLURALITY AND QUANTIFICATION
Studies in Linguistics and Philosophy
Volume 69
Managing Editors
GENNARO CHIERCIDA, University ofM ilan
PAULINE JACOBSON, Brown University
FRANCIS J. PELLETIER, University ofA lberta
Editorial Board
JOHAN VAN BENTHEM, University ofA msterdam
GREGORY N. CARLSON, University ofR ochester
DAVID DOWTY, Ohio State University, Columbus
GERALD GAZDAR, University of Sussex, Brighton
IRENE HElM, M.L T., Cambridge
EWA N KLEIN, University ofE dinburgh
BILL LADUSAW, University ofC alifornia at Santa Cruz
TERRENCE PARSONS, University of California, Irvine
The titles published in this series are listed at the end oft his volume.
PLURALITY AND
QUANTIFICATION
edited by
FRITZ HAMM and ERHARD HINRICHS
University of Tiibingen, Germany
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4943-8 ISBN 978-94-017-2706-8 (e Book)
DOI 10.1007/978-94-017-2706-8
Printed on acid-free paper
All Rights Reserved
C 1998 Springer Science+Business Media Dordiecht
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint of the hardcover 1st edition 1998
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
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TABLE OF CONTENTS
Introduction 1
I
Godehard Link Ten Years of Research on Plurals-
Where Do We Stand? 19
I
Kurt Eberle The Influence of Plural NPs on
Aktionsart in D RT 55
I
Chris Fox Mass Terms and Plurals in Property Theory 113
I
Frans Zwarts Three Types of Polarity 177
I
Jaap van der Does Sums and Quantifiers 239
I
Henk Verkuyl Some Issues in the Analysis of Multiple
Quantification with Plural NPs 283
I
Christine Michaux Reducing the Coordination of
Determiners: Some Principles 321
I
Joao Peres Issues on Distributive and Collective
Readings 339
Index of Subjects 367
Index of Names 379
v
FRlTZ HAMM/ERHARD HINRJCHS
INTRODUCTION
The papers in this volume address central issues in the study of Plurality
and Quantification from three different perspectives:
• Algebraic approaches to Plurals and Quantification
• Distributivity and Collectivity: Theoretical Foundations
• Distributivity and Collectivity: Empirical Investigations
Algebraic approaches to the semantics of natural languages were in
dependently introduced for the study of generalized quantification, pred
ication, intensionality, mass terms and plurality. The most prominent
modern advocate for an algebraic theory of plurality (and mass terms)
is certainly Godehard Link. It is indicative of the Wirkungsgeschichte
of Link's work that most of the contributions in this volume take the
logic of plurals proposed by Godehard Link (Link 1983, 1987) as their
foundation or, at the very least, as their point of reference. Link's own
paper in this volume provides a concise summary of many of the central
research issues that have engaged semanticists during the last decade.
Link's paper also contains an extensive bibliography that provides an
excellent resource for scholars interested in the semantics of plurals.
Since we can refer readers to Link's paper for an excellent survey of
the subject matter of this book, we will limit our attention in this in
troduction to summarizing the individual contributions in this volume.
The book is organized into three main sections; within each section the
papers are ordered alphabetically. However, as in much of linguistic the
orizing, there is an exception: for reasons pointed out above, Godehard
Link's article appears as Chapter 1.
1. ALGEBRAIC APPROACHES TO J:>LURALS AND
QUANTIFICATION
Godehard Link's contribution "Ten Years of Research on Plurals
Where Do We Stand" surveys recent research in the semantics of plu
rals and goes on to consider three specific questions that have arisen in
algebraic approaches to plurality: (i) should groups be included in the
ontology for the semantics of noun phrases, (ii) how is the distinction be
tween collectivity and distributivity to be characterized, and (iii) where
does this distinction originate - in the semantics of verbal predicates,
1
F. Hamm and E. Hinrichts, (eds.), Plurality and Quantification, 1-18.
© 1998 Kluwer Academic Publishers.
2 F. HAMM/E. HINRICHS
iii the semantics of generalized quantifiers or is it due to the interaction
between these two classes of expressions?
The first part of Link's paper gives a short overview of some recent
research activities in plural semantics: typological studies of distributiv
ity markers which correspond roughly to English each or German je,
the general program of an algebraic semantics for natural languages,
and L0nning's {1989) work on the metatheory of a plural logic. Link's
comments on the relationship of plural theory to the most prominent
approach to anaphora resolution, viz. discourse representation theory,
are rooted in the empirical phenomenon of plural anaphora. His dis
cussion of how to structure a formal ontology of plural terms focuses
on the denotational view of definite terms like the men. Link rejects
Barry Schein's {1993) argument that such a view leads to paradox and
argues for a mereological theory of plural denotations. The first part of
his paper concludes with some brief remarks on AI-related research on
plurals.
The next section examines Landman's {1989) semantic arguments for
introducing so-called groups into the ontology. The intuitive motivation
for assuming the existence of groups, in addition to individual sums {i
sums) and ordinary individuals, derives from examples such as {1)
{1) The boys and the girls had to sleep in different dorms, met in the
morning at breakfast, and were then wearing their blue uniforms.
The NP The boys and the girls seems at the same time to be interpreted
as a uniform i-sum (when considered as argument of meet), distribute
down to the level of individuals (when considered as argument of wear
ing), and denote something in between these two levels (when considered
as argument of sleep in different dorms). In order to account for this
intermediate-level reading Landman assumes the existence of groups.
But he doesn't stop here. Given a domain of discourse M, Landman
constructs a cumulative hierarchy of groups over this domain. Link
agrees with Landman that the intermediate readings have to be taken
seriously1; nevertheless he criticizes Landman's approach for two rea
sons. The first is that the cumulative hierarchy of groups is much too
general. Convincing empirical arguments have only been given for one
intermediate level. The second reason is based on Schwarzschild's {1991)
argument against groups. According to this argument, natural language
predicates do not differentiate between levels. Schwarzschild suggests
instead that it is important to consider the way in which the operative
subsums (Schwarzschild's term) are referred to by the NPs in question.
INTRODUCTION 3
Which sums are, in fact, operative is determined by many factors, in
cluding intonation and cross-sentential deixis. Link therefore concludes
that Landman's theory of groups is a case of over-representation.
The last section of Godehard Link's contribution is devoted to the
topic of distributivity. Link introduces L0nning's standard proposal,
which says that sentences such as (2) have two readings depending on
whether the subject NP is interpreted distributively or collectively.2
(2) Four men lifted three tables.
Link discusses two arguments which have been leveled against the stan
dard proposal. The first argument says that this approach fails to ac
count for the full range of truth-conditionally relevant readings. This
type of criticism is typically based on the by now classical example of
Gillon (1987).
(3) Hammerstein, Rodgers and Hart wrote musicals.
Since none of the three composers wrote a musical all by himself, the
sentence cannot be read distributively. Furthermore, there is no musical
all three wrote together, which shows that the sentence cannot be inter
preted collectively. Hence, a third reading seems to be required. Link,
however, claims that predicates such as musical writing can be true of
single individuals as long as they show significant involvement in the
composition of a piece, even though no single individual may be the sole
author. Regardless of such empirical arguments, Link demonstrates that
the algebraic theory of plurals is, in any case, flexible enough to account
for the mixed reading as well. Link shows that this can be achieved
if one incorporates in the algebraic theory "type shifting" operators as
suggested by van der Does (1992).3 Under this strategy the collective
and the distributive readings of sentences like (2) turn out to be limiting
cases of the mixed reading.
If the distributive and. the collective readings are just limiting cases
of a third reading, then there should be no ambiguity at all.4 This obser
vation provides the basis for the second argument against the standard
proposal: since the standard approach posits an ambiguity, it fails to
capture the generalization inherent in the putative single interpretation.
(The argument from a missed generalization). Link rejects this argument
as well. For him the empirical boundary between the distributive and
the non-distributive domain does give rise to a genuine ambiguity, while
the distinction between mixed readings and strictly collective readings
is a matter of indeterminacy and not of ambiguity.
4 F. HAMM/E. HINRlCHS
The last topic Link discusses concerns the related question of where
the distributive/collective distinction originates, in the semantics of noun
phrase or of the verb phrase. Link opts for the verb phrase - a position
which van der Does (1992)5 explicitly rejects. Link defends his posi
tion by showing that non-monotone increasing determiners, which were
shown to be problematic for the VP-strategy by van der Does, can nev
ertheless be handled by this strategy if additional scope and cardinality
requirements are included.
Kurt Eberle's contribution "The Influence of Plural NPs on Ak
tionsart in DRT" studies characteristic differences among (bare) plural
NPs in the way they contribute to the compositional semantics of Ak
tionsart. It is commonly assumed (cf. Verkuyl (1972) and Dowty (1979)
for detailed discussion) that bare plural NPs, when used as arguments
of event predicates, lead to an activity reading of the sentence in the
terminology of Vendler (1967). However, citing examples from German
such as (4) and (5), Eberle notes that the Aktionsarten effect of bare
plural NPs is far from uniform.
(4) Beim Stiirmer-Training drosch Voller Balle aufs Tor.
(At the forward training, Voller kicked balls into the goal)
(5 ) Sportier brachten die olympische Fackel nach Barcelona.
(Sportsmen took the olympic torch to Barcelona)
As can easily be verified by applying standard tests for distinguishing
the Vendler classes of activities from accomplishments, events described
by sentences such as (4) are temporally homogeneous, while events de
scribed by sentences such as (5) are temporally heterogeneous. Eberle
attributes this difference of Aktionart to differences in the availability of
distributive readings for plural NPs for a given event description. For
event descriptions such as (5), the property of being shot on goal by
Voller (temporally) distributes over the members denoted by the plural
NP Balle, while such a distributive reading is dispreferred or unavailable
for the plural NPs in examples such as (4).
Eberle accounts for the impact of plural NPs on the Aktionsart of a
given sentence by significantly modifying and extending the event seman
tics proposed by Krifka (1987). Eberle formalizes his event semantics
in the framework of Discourse Representation Theory (DRT) (Kamp
1981), (Kamp/Reyle (1993)) which is suitably extended to be able to
account for plural NPs and Aktionsarten properties of event descrip
tions. Aktionsarten differences are attributed to the mutually exclusive
properties of temporal discourse-homogeneity and temporal discourse-
INTRODUCTION 5
heterogeneity. Temporal homogeneity applies to predicates that denote
non-punctual, divisible and cumulative events or to predicates that de
note iterative events.
Eberle shows that bare plural NPs as arguments of an event predicate
describe temporally homogeneous events, only if the bare plural can be
interpreted distributively with respect to the event in question. Eberle
provides a DRS construction algorithm that compositionally derives the
Aktionsarten properties of complex event descriptions. The construc
tion algorithm covers distributive, collective, and cumulative readings
of bare plurals and is illustrated by step-by-step derivations of relevant
linguistic examples.
The paper "Mass Terms and Plurals in Property Theory" contributed
by Chris Fox is concerned with three related phenomena.
• The judge-cleaner-problem: Why is it that the judge and the
cleaner may well be one and the same person, but have different in
comes?
• The part-whole-problem: Why can we say that the dirty water is
liquid and infer that parts of the dirty water are liquid, without inferring
that the dirt is liquid?
• The problem of non-denoting definites: How can we assign two
different semantic values to the definite descriptions the present king
of France and the largest prime number within a classical two-valued
theory?
In order to account for the judge-cleaner-problem, Landman (1989)
introduces a new set of individuals 'individuals under guises or roles'
which are made explicit in sentences of the following kind:
(6) a. John, as a judge, earns 20000 £.
b. John, as a cleaner, earns 2000 £.
Landman's solution to the above problem, therefore, is that the definite
description in a sentence like the The judge earns 20000 £ does not refer
to an ordinary individual, but to an intensional individual, an individual
in the role of judge, who is different from the individual in the cleaner's
role in The cleaner earns 2000 £, even if the two individuals in question
are the same ordinary individual.
Chris Fox argues for a different approach. Roughly speaking, Fox
claims that roles are not modifications of individuals, but modifications
of predications. This strategy gives rise to modified properties like earns
20000 £-as-a-judge or earns 2000 £-as-a-cleaner instead of modified
individuals such as John, as a judge etc. The major advantage of this
