Shifting sets, hidden atoms
the semantics of distributivity,
plurality and animacy
The research reported here was supported by NWO VICI grant no. 277-80-002
to Yoad Winter.
Cover illustration: Margriet Smits, collage, 50x65. Reprinted with permission
from RIBW Arnhem & Veluwe Vallei.
Copyright c 2015 by Hanna de Vries. All rights reserved.
Shifting sets, hidden atoms
the semantics of distributivity,
plurality and animacy
Vermomde verzamelingen en
ogenschijnlijke atomen
de semantiek van distributiviteit,
meervoud en bezieldheid
(met een samenvatting in het Nederlands)
Proefschrift
ter verkrijging van de graad van doctor aan de Universiteit Utrecht
op gezag van de rector magnificus, prof. dr. G.J. van der Zwaan,
ingevolge het besluit van het college voor promoties
in het openbaar te verdedigen op
vrijdag 13 maart 2015 des middags te 2.30 uur
door
Hannah de Vries
geboren 24 december 1984
te Waalwijk
Promotoren: Prof. dr. Y. S. Winter
Prof. dr. M. B. H. Everaert
Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
1.1 Structure of the dissertation . . . . . . . . . . . . . . . . . . . . 4
2 Laying the groundwork 9
2.1 Plurality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Sets versus lattices . . . . . . . . . . . . . . . . . . . . . 12
2.2 Distributivity and collectivity . . . . . . . . . . . . . . . . . . . 13
2.2.1 Winter’s classification: atom and set predicates . . . . . 15
2.3 Impure atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Impure atoms and different ‘roles’ . . . . . . . . . . . . 18
2.3.2 Previous works on the impure atom mapping . . . . . . 19
2.4 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . 23
3 P- and Q-distributivity 25
3.1 P-distributivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Q-distributivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 VP disjunction . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 Interaction of ¦ with other quantifiers . . . . . . . . . . 32
3.2.3 Anaphora . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Distributivity effects with group NPs . . . . . . . . . . . . . . . 36
3.3.1 Groups as atoms . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Distributivity behaviour of group nouns . . . . . . . . . 40
3.3.3 Two more Q-distributivity tests . . . . . . . . . . . . . 42
3.3.4 P-distributivity with groups; conclusion . . . . . . . . . 45
vi
3.4 Embedding P-distributivity in our formal framework . . . . . . 46
3.4.1 A pseudo-formalisation of P-distributive inferences . . . 46
3.4.2 Tying up another loose end: collectivity . . . . . . . . . 48
3.5 Remarks on the syntax of Q-distributivity . . . . . . . . . . . . 49
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Polyadic P-distributivity and indefinites as properties 57
4.1 Distributivity effects with group nouns and indefinites . . . . . 59
4.2 Analysis: P-distributivity beyond unary predicates . . . . . . . 60
4.2.1 Additional evidence for a property analysis . . . . . . . 65
4.3 Alternatives to the P-distributivity analysis . . . . . . . . . . . 68
4.3.1 Group credit . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.2 Quantification over kinds . . . . . . . . . . . . . . . . . 70
4.4 Remaining issues . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.1 P-distributivity and implicature . . . . . . . . . . . . . 73
4.4.2 Stubborn distributivity and weigh-predicates . . . . . . 74
4.4.3 A remark on modified numerals . . . . . . . . . . . . . . 76
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5 Q-distributivity and morphosyntactic number 81
5.1 Q-distributivity with British English group NPs . . . . . . . . . 83
5.1.1 A related contrast: reciprocity . . . . . . . . . . . . . . 87
5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Comparison with alternative analyses of group NPs . . . . . . . . 91
5.3.1 Defining ‘group noun’ . . . . . . . . . . . . . . . . . . . 92
5.3.2 Alternatives to impure atom formation: ‘fission’ or ambiguity
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.3 A note on Winter’s analysis of group nouns as atom
predicates . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4 Tying up some loose ends . . . . . . . . . . . . . . . . . . . . . 102
5.4.1 Multiple groups with the same members . . . . . . . . . 102
5.4.2 Morphosyntactically plural group NPs . . . . . . . . . . 103
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6 Animacy and plurality 107
6.1 Group NPs as sets in other languages than British English: some
evidence from Dutch . . . . . . . . . . . . . . . . . . . . . . . . 110
6.1.1 Pearson’s ‘half of’-test . . . . . . . . . . . . . . . . . . . . 111
vii
6.1.2 The ‘half of’-test in Dutch . . . . . . . . . . . . . . . . . 112
6.1.3 The influence of animacy . . . . . . . . . . . . . . . . . 113
6.2 Q-distributivity and animacy in Afrikaans . . . . . . . . . . . . 115
6.3 More on impure atoms: the Ò mapping and group-level predicates117
6.3.1 A problem with the impure atom mapping . . . . . . . 118
6.3.2 Group-level predicates with inanimate, animate and human
subjects . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3.3 Intermediate conclusions . . . . . . . . . . . . . . . . . . 123
6.4 Discussion: animacy and semantic number . . . . . . . . . . . . 123
6.4.1 Number agreement and the Animacy Hierarchy . . . . . 124
6.4.2 Back to the impure atom mapping . . . . . . . . . . . . 126
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7 Conclusions 131
Appendix A British English Q-distributivity questionnaire 135
A.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.1.1 Test items . . . . . . . . . . . . . . . . . . . . . . . . . . 137
A.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Appendix B Dutch half-of questionnaire 143
B.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.1.1 Test items . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Appendix C Afrikaans Q-distributivity questionnaire 149
C.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.1.1 Test items . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.3 Group nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Appendix D Dutch group-level predicates questionnaire 157
D.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D.1.1 Test items . . . . . . . . . . . . . . . . . . . . . . . . . . 158
D.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Samenvatting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
viii
Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Acknowledgements
In the introduction to his ‘Jerusalem Lectures’ on events and plurality, Fred
Landman (whom I will spend some parts of this dissertation agreeing with, but
nowhere as strongly as here) writes:
If you do not have the enviable temperament for writing a Book a
Coherent and Comprehensive Account of a Certain Topic, and
you find yourself writing a book instead, you have to find a way
of tricking yourself into actually getting it done. This is because
the Book is always hovering over the horizon: you are swimming in
an ocean of topics that cannot possibly be left out, and literature
which obviously needs to be not just mentioned but analyzed and
discussed thoroughly, and it’s just impossible. And while the book
takes shape, these problems actually increase, and with them the
threat of paralysis.
In getting me to abandon my pursuit of the elusive Book in favour of a much
more attainable book, no one has been more helpful than my supervisor (and later,
deservedly, first promotor), Yoad Winter. Without him, this dissertation would
probably have been twice as long, infinitely more rambling, and undoubtedly
very silly at points, and I’m extremely grateful for the many hours he has
put in reading, rereading, rerereading and occasionally even rererereading its
chapters at their various stages of development. I’ve learned an incredible
lot from working with Yoad, and he has been instrumental in not just my
development into a better semanticist, but into a better and more grown-up
person in general.
x
My second promotor, Martin Everaert, was not as involved in the contents
of my project as Yoad was, but I’m very grateful to him for always making
me feel like I could count on his support whenever I needed it, and providing
many helpful comments and suggestions along the way. The same goes for the
members of my support committee, Alexis Dimitriadis, Joost Zwarts, Remko
Scha, and Roger Schwarzschild, who have all helped me out at some point
or another by commenting on drafts or functioning as consultants on areas
of linguistics I wasn’t very familiar with. Thank you all very much! Many
thanks also to my assessment committee, consisting of Henri¨ette de Swart, Eric
Reuland, Bart Geurts, Ede Zimmermann, and (again) Roger Schwarzschild, for
taking the time to read and comment on the final draft.
The very short and unofficial visit I paid to NYU and Rutgers in October
2012 marked a turning point in my PhD career in many ways. Realising that
my work was taken seriously by people outside of Utrecht boosted my academic
confidence and gave me the energy to keep going. Thank you, Anna Szabolcsi,
Lucas Champollion, Chris Barker, (again!) Roger Schwarzschild, and Veneeta
Dayal, for taking the time to discuss my work with me, providing me with a
small but significant platform to present it, and for being so incredibly nice,
inspiring and brilliant.
I came to Utrecht in 2008 to become a computational linguist (the summer
previous, I had taken an ESSLLI course taught by Michael Moortgat, understood
next to nothing of it, and considered this an interesting challenge). But it didn’t
take me a long time to realise that I’d much rather do semantics - and that I
had accidentally managed to end up in the very best place for it. Over the years,
my fellow semanticists here at UiL OTS have taught me a great deal, and I’ve
enjoyed collaborating with them on various research projects, teaching, and
the organisation of talks, workshops and conferences. When I was working on
my MA degree in Utrecht, many people contributed to my semantic education
and/or supervised parts of my work: thank you, Min Que, Henri¨ette de Swart,
Rick Nouwen, Joost Zwarts, Marijana Marelj (whose lessons in rigidly thinking
through the implications of a theory - and general amazingness - I still treasure),
Eddy Ruys, and Herman Hendriks. Thanks also to my fellow PhD students,
in particular my paranymph Eva Poortman, Assaf Toledo, Anja Goldschmidt,
Maartje Schulpen, Stavroula Alexandropoulou, Dominique Blok, Lisa Bylinina,
and Anna Chernilovskaya (also: Lena Karvovskaya from Leiden University and
Matthijs Westera from ILLC/University of Amsterdam) - you were all a joy to
xi
work with (and also a joy to drink, chat, change the world, gossip, & exchange
languages and/or favourite Harry Potter fanfiction with). Thanks also to the
other members of Yoad’s research group: Marijn Struiksma, Sophia Katrenko,
Choonkyu Lee, and all the MA students who helped out at one point or another
(in particular Sophie Chesney).
And of course, I also got to know some people I did not actually work with although
not as many as I might have, had I bothered to arrive at the office
in time for lunch more often. Liquan Liu deserves special mention for being
particularly gravity-defying. Others I’d like to mention are my other paranymph
(or paranymph-and-a-half!) Marjolein van Egmond, and then Arno Bastenhof,
Hans Rutger Bosker, Desiree Capel, Marta Castella, Jakub Dotlaˇcil, Heimir
Freyr van der Feest-ViDarsson, Nadya Goldberg, Mirjam Hachem, Sander van
der Harst, Carolien van den Hazelkamp, Marko Hladnik (and S¸irin Tu˘gbay),
Brigitta Keij, Heidi Klockmann, Bert Le Bruyn, Anne van Leeuwen, Xin Li,
Zenghui Lui, Sophia Manika, Sandrien van Ommen, Liv Persson, Anne-France
Pinget, Erin Pretorius, Anna Sara Romøren, Marieke Schouwstra, Marko Simonovi´c,
and Anna Volkova. There are some of you I wish I’d gotten to know
much better than I actually did - maybe we’ll get another chance someday!
Now to the really important parts. As a little girl, I possessed enough common
sense to realise that my dad probably wasn’t the strongest man in the world;
still, I was pretty sure that he was the cleverest. Accordingly, I spent much of
my life trying to become as learned as my dad (I guess I have surpassed him
now!). But even though it’s easy to point to my father as my main scientific
influence, I recently realised that it was actually my mum who taught me
the basics of Aristotelian logic when I was ten (I remember all the confusions
of material implication, and the thrill of discovering the fallacy in an invalid
syllogism). It was also my mum who instilled in me her love of language(s). I
don’t think I’d have managed to end up where I am now without my parents - is
it weird to say that I’m proud of them? Anyway, thank you. Many thanks also
to my parents-in-law, who have been almost equally supportive and all-around
wonderful; to my brilliant, funny, charismatic and always impeccably dressed
brothers Homme and Evert, and to all remaining (extended) family, friends,
roommates, neighbours & everyone else who has been part of my life in the
past couple of years.
Clich´e has it that life is what happens to you when you’re busy making other
plans, and so, in the year that was supposed to be all about dissertation-writing,
xii
I suddenly found myself embarking on an entirely different adventure. Baby
Roanne, you don’t really produce any useful linguistic data yet so I don’t have
much to thank you for, but I do think you’re pretty amazing.
Finally, Klaas, for continuing to put up with a logistically challenged nerd
who has no problem leaving shoes and dirty laundry all over the house but
gets hysterical when anyone messes up the order of her books - thank you. You
make my world an infinitely more wonderful place.
A final note about something else that is quite important to me.
I wrote part of this dissertation in the wee hours of night while volunteering
as a night watch at an Utrecht homeless shelter. Being surrounded by people
who have absolutely nothing - not even the legal right to be where they are
- made me realise how incredibly privileged I am to be able to earn a living
pondering the application of set theory to natural language meaning. It also
made me realise (again) that science should not exist to build ivory towers for
a select few, but to make the world a better and more just place for everyone.
Even if we’re not directly saving lives, there are many small things we can
do, like freely sharing our knowledge instead of hiding it behind paywalls,
promoting equal opportunities for women and minorities, spending taxpayers’
money fairly and with integrity, keeping our ecological footprints small, or even
just acknowledging the presence of the cleaning lady. To the reader of this
dissertation and everyone else, I promise I will try my best.
CHAPTER 1
Introduction
When it comes to the interpretation of morphosyntactically singular and plural
referential noun phrases, it seems natural to assume a corresponding difference
between semantically singular and plural individuals, and associate morphosyntactically
singular NPs with the former and morphosyntactically plural NPs
with the latter. In a set-theoretical version of such a system, for example, the
singular NPs in (1a) could be associated with entities (‘atoms’) and the plural
NPs in (1b) with sets of entities:
(1) a. Singular NP: Referent (for example):
Mary mary
the girl mary
our guinea pig bert
b. Plural NP: Referent (for example):
Mary and Sue {mary, sue}
the girls {mary, sue, jane}
our guinea pigs {bert, ernie}
However, there are several reasons why this one-to-one correspondence between
morphosyntactic and semantic number may turn out to be too simple. For
example, there are NPs that are morphosyntactically singular but refer to
collections of individuals, displaying all kinds of ‘plural’ behaviour like the
2 Chapter 1
ability to bind plural pronouns, compatibility with predicates that normally
require a plural argument, and (in some languages) the ability to occur with
a morphosyntactically plural VP ((2-4), respectively). And in predicative position,
they can function as predicates over plural individuals despite being
morphosyntactically singular themselves ((5)):
(2) Every team loves their tough guys and thinks the other teams’ are idiot
thugs.1
(3)
$
'&
'%
*Mary
The girls
The committee
,
/.
/gathered
/ met / split up.
(4) My family are early risers. (British English)
(5) John and Mary are a happy couple.
Because of behaviour like this, group NPs like the committee or my family have
been analysed as semantically plural in some of the literature (e.g. Bennett
1974; Pearson 2011; Magri 2012), which results in a system in which morphosyntactic
and semantic number do not always match. Others (e.g. Barker 1992;
Schwarzschild 1996) claim that these NPs, in spite of appearing ‘plural’ in
some respects, nevertheless denote singular individuals (that just happen to
have a very salient conceptual part-whole structure). This means that we need
additional ways to map singular individuals into plural ones or vice versa, in
order to be able to account for mixed predication structures like (5): if nouns
like couple range over singular individuals but NPs like John and Mary denote
plural ones, the former should not be able to function as a predicate over the
latter unless our semantics is equipped with a mechanism that either maps the
predicate into a predicate over sets, or the argument into a singular entity. So,
regardless of whether we analyse group NPs as semantically plural or singular,
their existence complicates the clear singular/plural split as pictured in (1).
Group NPs are not the only reason why the relation between morphosyntactic
and semantic number may well turn out not to be a one-to-one mapping. Many
researchers have proposed, for various reasons, that morphosyntactically plural
NPs like the ones in (6b) may be interpreted as a kind of ‘group entity’, which
is semantically singular (e.g. Link 1984; Landman 1989; McNally 1993; Winter
1Sentence (2) was found via Google (search term ‘team loves their’).
Introduction 3
2001a). In many cases the motivation for this claim is at least partly theoryinternal,
but here is one that is more intuitive (based on data in Mador-Haim
& Winter 2012):
(6) a. Mary kissed the boys
ô Mary kissed boy1 and Mary kissed boy2 and... Mary kissed boyn.
b. The mouse is hiding in the apples
ø The mouse is hiding in apple1 and the mouse is hiding in apple2
and... the mouse is hiding in applen
While we interpret (6a) to mean that the kiss-relation holds between Mary and
each of the boys, the same does not hold for (6b): the most salient interpretation
of sentence (6b) is one under which the apples means something like ‘the heap
of apples’. Under this interpretation, the sentence does not require the mouse
to actually have made its way into any individual apple, let alone each of them:
it is sufficient for the mouse to be sitting among the apples, as long as the
apples form a coherent whole together that makes it easy to perceive them
as a single, complex ‘heap entity’ (it does not work if the apples are strewn
randomly across the floor). The in-relation, then, does not hold between the
mouse and any individual apples, but between the mouse and a ‘heap entity’
that incorporates both the apples and the spaces in between the apples. Thus,
sentences like (6) suggest that morphosyntactically plural NPs can, at least
under the right circumstances, behave like semantically singular entities. Again,
this gives us a mismatch between morphosyntactic and semantic number that
complicates the simple picture in (1).
The aim of this dissertation, then, is to investigate the relationship between
morphosyntactic and semantic number of both NPs and VPs - in particular,
whether a fully functioning account of semantic number needs to allow for the
kind of mismatches between morphosyntax and semantics as described above. I
will argue that it does: in order to account for all the relevant data, our system
should allow both singular NPs to be associated with sets, and plural NPs to be
associated with entities. I will propose that this semantic flexibility is regulated
by two different mechanisms. The first is the need to avoid type mismatches
between subject and predicate: semantically plural NPs must be shifted into
semantically singular ones when they are combined with a semantically singular
predicate. The second factor that determines whether a given NP is interpreted
as semantically singular or plural is the degree of animacy of its referent: the
4 1.1. Structure of the dissertation
more animate an NP, the more likely it is to be interpreted as semantically
plural, and the more inanimate, the more likely it is to be interpreted as semantically
singular - regardless of its morphosyntactic number. I will suggest
that this is related to individuation (cf. Corbett 2000; Grimm 2012): the more
we care about the individual members of the collection to which a given NP
refers, the higher the likelihood that the NP will be interpreted as semantically
plural; if, on the other hand, distinguishing the individual members is not very
important (as with the heap of apples above), the NP in question is more likely
to be interpreted as a singular complex ‘group entity’, that does not formally
distinguish its member parts.
1.1 Structure of the dissertation
The argument is built up as follows.
I will start out by presenting, in chapter 2, a basic theoretical framework for
the semantics of number, containing various formal tools that we can use to
analyse the data presented in subsequent chapters.
In chapter 3 (and, partly, chapter 4), I will develop a range of tests to determine
whether a given NP is interpreted as semantically singular or plural, based on
the availability of distributive interpretations in various contexts. A predicate
P is distributive if it follows from P’s being true of a group of individuals that
P is true of each of the individual members of that group. For example, it is
possible to infer (7b) on the basis of (7a):
(7) a. The cats (which are called Fluffy and Mittens) are purring.
b. Fluffy is purring and Mittens is purring.
There are essentially two competing theories on the origin of such distributive
interpretations. The first and most widely adopted one, which originated in
Link (1983), treats it as a kind of universal quantification over the members of
the plural individual associated with the sentence subject - in the case of (7a),
the set consisting of fluffy and mittens. According to this theory, distributive
inferences like the one from (7a) to (7b) can only occur when the subject is
semantically plural, because singular individuals do not have members that can
Introduction 5
be quantified over. If this is correct, the availability of distributivity would be
a good diagnostic for the semantic number of an NP.
However, another possible theory of distributivity does not link its availability
to semantic number - Scha (1981), for example, proposes that distributivity
has nothing to do with the formal properties of plural predication, but that it
is a non-logical inference that follows from reasoning about the lexical meaning
of the predicate in a particular context. If it turns out that a lexical theory like
Scha’s does a better job of accounting for the relevant data, we cannot use the
availability of distributivity as a diagnostic for semantic plurality.
A third option is to combine the two theories and assume that both formal
and lexical mechanisms can underlie distributivity: while some kind of quantificational
operator is necessary to account for all the data, many distributive
inferences can in principle be analysed without such a quantificational mechanism,
in terms of lexical properties of the predicates involved. This is the
approach that I will argue for in chapter 3 (building on earlier proposals by e.g.
Dowty 1987, Hoeksema 1988; Winter 1997, 2000; Champollion 2010). I will show
that neither lexical nor quantificational distributivity is, on its own, sufficient
in order to account for all the relevant data, and that a fully functional theory
of distributivity need both mechanisms. The point is exemplified by contrasts
like the following:
(8) a. The committee laughed
ô Each of the committee members laughed.
b. The committee is hiding somewhere
ø Each of the committee members is hiding somewhere.
I will show that all distributive inferences that could, in principle, be explained
in terms of lexical reasoning, are available when the subject is a group NP like
committee in (8a). However, distributive inferences that cannot be derived without
some kind of quantification over individuals are systematically unavailable
with group subjects. The two statements in (8b) are not equivalent because only
the second one is compatible with a situation in which each committee member
is hiding in a different location, an interpretation that cannot be derived unless
somewhere is outscoped by a quantifier over individual committee members.
The fact that the group-subject sentence lacks this interpretation indicates that
such distributive quantification is unavailable.
The contrast in (8) supports an analysis of group NPs as semantically singular
(and hence impossible to quantify over), as well as the need to assume
6 1.1. Structure of the dissertation
two different possible sources for distributive inferences: one quantificational
(which, as (8b) shows, is unavailable with group subjects), one lexical (which,
as (8a) shows, is available with group subjects). Thus, the contrast in (8) shows
that it is possible to use the availability of certain inferences, but not of others,
as a diagnostic for semantic number. Structural phenomena like the appearance
of an overt quantifier (somewhere in (8b)) provide a context that enables
us to distinguish the two types of distributivity: if a distributive inference is
supported in such a context, it has to be quantificational in nature. I will call
these contexts Q-distributivity tests (‘Q’ for ‘quantificational’) and introduce
a whole range of them in chapter 3. Because quantificational distributivity is
only available with semantically plural subjects, these Q-distributivity tests all
function as a diagnostic for semantic plurality.
Chapter 4 addresses an apparent problem with the previous chapter’s claim
that group NPs are incompatible with Q-distributivity. In sentences like (9),
assuming that the indefinite a blue shirt denotes an existential quantifier, we
expect it to take scope over the entire sentence, resulting in an interpretation
according to which the entire team is squeezed, improbably, into a single blue
shirt (compare (8b)):
(9) The team is wearing a blue shirt.
However, the most salient interpretation of (9) is one according to which each
team member is wearing his or her own blue shirt. From this one might conclude
that it is possible to quantify over individual team members after all
and that group NPs should be analysed as sets rather than atoms (cf. Magri
2012); however, this goes against the general pattern identified in chapter 3.
I therefore propose that the indefinite a blue shirt in (9) does not denote an
existential quantifier but an (individual correlate of a) property, following many
other examples of property analyses of indefinites in the literature (e.g. Milsark
1974; McNally 1992; Zimmermann 1996; Mador-Haim & Winter 2007). The
distributive interpretation of (9) can then be analysed in terms of ‘Scha-style’
lexical distributivity over multiple arguments of the same predicate.
Chapter 5 takes us back to the main issue of the relation between morphosyntactic
and semantic number. Because the Q-distributivity tests from chapter
3 enable us to distinguish predication over sets from predication over atoms,
we can now start investigating which factors influence the interpretation of
Introduction 7
predicates and their arguments as singular or plural. In chapter 5, we will look
at the role of number marking on the VP; in chapter 6, at the role of animacy.
Based on data from British English, I will argue that quantificational (but
not lexical) distributivity has to be licensed by plural number marking on the
VP. Since Q-distributivity requires a semantically plural subject, it also requires
a semantically plural predicate (i.e., a predicate over sets) to match; I claim
that only morphosyntactically plural VPs are able to denote such semantically
plural predicates. This claim is supported by the behaviour of British English
sentences with a group NP subject. As it turns out, the claim from chapter 3
that group NPs do not allow Q-distributivity does not capture the behaviour of
group NPs completely: in British English, where singular animate group NPs
can take either a singular or a plural VP, group NPs are only incompatible with
Q-distributivity if they appear with a morphosyntactically singular VP. If they
occur with a plural VP, the sentence can be interpreted Q-distributively. Since
Q-distributivity functions as a diagnostic for semantic number, this means that
morphosyntactically singular group NPs are associated with atoms when the
VP is singular, but with sets when the VP is plural.
To capture this mixed atom/set behaviour of group NPs, I propose that
they originate as sets, but are forced to shift into an atomic ‘group entity’ if
the VP is morphosyntactically singular. The reasoning is as follows. If only
morphosyntactically plural VPs are able to denote semantically plural predicates,
and morphosyntactically singular VPs can therefore only be interpreted
as semantically singular, combining a group NP with a singular VP leads to a
type mismatch: since the latter denotes a predicate over singular individuals,
it cannot be applied to a semantically plural argument. In order to repair this
type mismatch and enable the predicate to apply to its argument, the group
NP has to be interpreted as semantically singular; as a result, Q-distributivity
is unavailable. On the other hand, if the VP is morphosyntactically plural, Qdistributivity
is licensed and no typeshifts are necessary. This analysis explains
both the pattern in chapter 3 and the behaviour of British English group NPs
in a way that follows directly from the basic assumptions about the semantics
of number that were made in chapter 2.
Finally, in chapter 6, I explore the relationship between semantic number and
animacy by means of three different case studies of Dutch and Afrikaans. The
animacy connection came up implicitly in chapter 5: according to the analysis
presented there, the group NPs that are associated with sets rather than atomic
8 1.1. Structure of the dissertation
entities are precisely those NPs that allow a plural VP in British English, which
animate (in particularly human) group NPs do, but inanimate ones do not. This
suggests that there is a link between semantic plurality and animacy that holds
more or less independently of an NP’s morphosyntactic number. In this final
chapter, I claim that the opposite also holds: inanimate NPs are quite likely to
be interpreted as semantically singular, even if they are morphosyntactically
plural.
The first case study (of partitive NPs in Dutch, inspired by data from
Pearson 2011) provides support for an analysis of group NPs as basically setdenoting
even in languages where they never take a plural VP, suggesting
that there is nothing unique about the semantics of British English group NPs:
rather, the set-like behaviour of British English group NPs appears to be a
universal property of these NPs brought out by the fact that British English
grammar allows this particular agreement mismatch between a singular group
NP and a plural VP. In addition, it shows that inanimate NPs tend to be
interpreted as atom-denoting, regardless of their morphosyntactic number.
The second case study applies several of the Q-distributivity tests from
chapter 3 to Afrikaans (which does not mark number on the VP). The results
show that sentences with plural human subjects are more likely to be interpreted
Q-distributively than sentences with plural non-human and inanimate subjects,
which, under the assumptions made in this dissertation, means that the former
are more likely to be interpreted as set-denoting than the latter (despite their
morphosyntactic plurality).
For the third study, which again looks at Dutch, I paired both plural and
collective NPs of varying animacy with ‘group-level’ atom predicates like be
constituted and have x members and obtained grammaticality judgements for
the resulting sentences. While human and non-human animate plural subjects
are extremely degraded with these predicates (an observation often made in
the literature), the sentences with inanimate plural subjects turned out to be
relatively acceptable, suggesting that the former cannot easily be shifted into a
group entity but the latter can.
The chapter ends with a discussion of the questionnaire results in light of
the abundant typological literature on the relationship between animacy and
morphosyntactic number (as summarised by Corbett 2000), offering several
directions for further research.
Chapter 7 concludes this dissertation.
CHAPTER 2
Laying the groundwork
In this chapter, I present the various assumptions on plurality, distributivity
and other related topics that I will be building on in this dissertation, and
put together a ‘formal toolbox’ that I will use to analyse the semantic data
presented in chapters 3-6. It will contain several very common assumptions
distilled from four decades of semantic literature on plurality (which I will
present without much discussion or argument) and a few more controversial or
unusual assumptions, to which I will pay a bit more attention.
Section 2.1 discusses the basic mechanisms of pluralisation of (both nominal
and verbal) predicates. Section 2.2 introduces the traditional distinction between
collectivity and distributivity; we will formalise this distinction in set-theoretical
terms, starting from the assumption that predicates in their uninflected form
range either over atoms or over sets of atoms (following several earlier proposals
and in particular Winter 2002). Section 2.3 introduces the notion of ‘impure’
atomicity, and adds a mapping from sets to impure atoms to our formal toolbox.
Finally, section 2.4 concludes this chapter.
2.1 Plurality
If singular noun phrases like Mary or the girl are associated with entities in a
model (via generalised quantifiers over the domain of entities), it intuitively
10 2.1. Plurality
makes sense to treat plural noun phrases like Mary and Sue or the girls as sets of
entities, and accordingly, to analyse plural predication in terms of membership
of a set of sets. This is exemplified in (10):
(1) a. Mary is a linguist and Sue is a linguist and Jane is a linguist.
m € linguist and s € linguist and j € linguist
b. Mary, Sue and Jane are linguists.
tmary, sue, janeu € linguists
To capture the entailment between (1a) and (1b), the denotation of linguists
needs to be derived in a systematic way from the denotation of linguist: the
latter denotes the set of all linguists, so the former should denote the set of all
possible combinations of those linguists, which we can compute by taking the
powerset of linguist and removing the empty set (cf. Bartsch 1973; Bennett
1974; Hoeksema 1983; Link 1983, and many others afterwards). We will call
this operation pluralisation of the predicate, and use the notation ¦ (from Link
1983, although we will not use Link’s definition):
(2) Predicate pluralisation
¦P : ℘pPq¡tr}
The way ¦ is defined guarantees both the entailment from (2a) to (2b) and vice
versa. The first entailment captures a property of plural predication known as
cumulativity: if mary, sue and jane are all in the extension of the singular
predicate linguist, then any set containing one or more of these individuals
will be in the extension of the plural predicate ¦linguist. So if (2a) is true,
(2b) must also be, as are the ‘intermediate’ statements ‘‘Mary and Sue are
linguists’’, ‘‘Mary and Jane are linguists’’, and ‘‘Sue and Jane are linguists’’. The
second entailment - from (2b) to (2a) - captures the property of distributivity:
if the set {mary, sue, jane} is a member of plural ¦linguist, then so are all
of its subsets; also, it follows that the entities mary and sue and jane are
all members of singular linguist. So if (2b) is true, so is (2a), and so are all
intermediate statements.
Since a single operation, ¦, is responsible for both directions of the equivalence
between (2a) and (2b), semantic plurality and distributivity are inextricably
tied up: we cannot turn a predicate over singular individuals into a predicate
over plural individuals without, in the process, endowing it with the property
of distributivity.
In function notation, we can represent ¦ by means of universal quantification,
as follows:
Laying the groundwork 11
(3) ¦petqpetqt : λPetλXet.dx € XrPpxqs
So, p¦PqpXq = 1 if and only if Ppxq = 1 for all x € X; this directly captures the
entailments from (1a) to (1b) and vice versa. It also follows from this definition
that if p¦PqpXq = 1, then p¦PqpY q = 1 for all subsets Y of X; this captures
the intermediate entailments.
Although I will adopt a set-theoretical rather than a functional perspective
throughout most of this dissertation (unless otherwise stated), the fact that ¦
introduces a universal quantifier will be central to the argument, and is useful
to keep in mind.1
We have seen that pluralisation with ¦ turns any set-denoting predicate into a
set of sets. As to how the correct denotation for the coordinated subject NP is
derived, I will just assume without going into too much detail that coordination
of multiple entity-denoting expressions (e.g. Mary and Sue) gives us the set of
those entities (e.g. {mary, sue}), and coordination of multiple set-denoting
expressions (e.g. The girls and the boys) gives us the union of those sets (e.g.
{mary, sue, paul, george}; cf. Schwarzschild 1996). For extensive discussion
of NP coordination, see Hoeksema (1988); Krifka (1990); Schwarzschild (1996);
Winter (2001b), among others.
I will not be talking much about coordinated NPs in this dissertation; rather,
the kind of plural NP I will be using for most examples are plural definites,
like the girls. For singular definites, we can interpret the as the iota operator,
that picks out the unique member of a set if such a unique member exists. For
plural noun denotations, we want the(¦N) to be defined even if ¦N has more
than one member (which it will have in nearly all cases), so we cannot translate
plural the as ι. Rather, what plural the should do is pick out the largest set in
1In representing pluralisation by universal quantification, I am abstracting away from the
well-observed fact that plural predication usually leaves room for exceptions (i.e. members
of the subject set for which the predicate does not hold). Thus, the sentence ‘‘The girls are
linguists’’ (unlike the universal paraphrase ‘‘All the girls are linguists’’) can be true even if
some of the girls are not linguists, especially if we are talking about a large number of girls.
This particular kind of vagueness is known as non-maximality (Dowty 1987; Brisson 1998).
There are three general strategies for dealing with non-maximality: it can be built into the
semantics of ¦ (e.g. Schwarzschild 1996; Brisson 2003); it can be treated as a property of
predication over impure atoms (cf. section 2.3; Landman 1989; Winter 2002), in which case
non-maximality is more or less a direct consequence of not involving ¦; or it can be treated
as a specific instance of a more general phenomenon of ‘pragmatic slack’ (Lasersohn 1999).
Since I will not address the issue of non-maximality in this dissertation, I will simply treat
distributivity as more or less paraphraseable by universal quantification.
12 2.1. Plurality
¦N, such that in effect, the denotation of the girls in a model is just the set of
girls in that model. This ‘largest set’, in more general terms, is the maximum:
the smallest element in an ordered set such that it is greater than or equal to
all elements in that set.
(4) Plural the
theppetqtqet(¦N) := max(¦N)
In fact, the same definition can be extended to cover singular the (Sharvy 1980;
Link 1983). If a set has just a single member, the maximum operator reduces to
iota: the unique element in a singleton set is trivially greater than or equal to
all elements of that set (since it is always equal to itself), so the applied to that
set will return that member. For unordered sets with more than one member,
the maximum will be undefined; for example, in (5b), the set corresponding to
singular girl contains no element that is greater than or equal to all elements in
that set, and this will be the case for all unordered sets of entities that contain
two or more distinct members.
(5) Denotations for the girl and the girls in different models, derived using
the maximum operator:
a. M1: girl = {mary}
the(girl) = mary
the(¦girl) = {mary}
b. M2: girl = {mary,sue}
the(girl) = undefined
the(¦girl) = max({{mary}, {sue}, {mary, sue}}) = {mary, sue}
So, we will use the following generalised definition for the:
(6) Generalised the
thepσtqσ(Nσt) := max(N) (where σ represents any type)
2.1.1 Sets versus lattices
In the literature, semantic theories of plurality are generally formalised using
either set theory (a tradition starting with Bartsch 1973; Bennett 1974; Hausser
1974) or lattice theory (an alternative approach proposed by Link 1983). Both
are associated with their own advantages and disadvantages (see Champollion
2010, for an overview). An important difference is the way the domain of
Laying the groundwork 13
singular and plural individuals is structured. In set-theoretical approaches to
plurality, singular and plural individuals are usually of different types (e and
et, respectively)2
. In a lattice-theoretical approach, both singular and plural
individuals are of type e; the domain of singular and plural entities (‘atoms’
and ‘sums’) has the structure of a complete join semilattice (fig. 1). Lattice
Figure 2.1: The complete join semilattice built on three atomic entities a, b and c.
theory is often used by semanticists who want to emphasise the link between
different kinds of part-whole structures in natural language, including those
that lack atomic minimal parts, like mass terms and degree scales (e.g Link
1983; Champollion 2010). However, for the domain of count nouns - which I will
be concerned with in this dissertation - the relevant semilattices are isomorphic
to a power set structure with the empty set removed (Landman 1989), which
means that for the present purposes it does not really matter which formalism
we pick. I will continue to use a set-theoretical implementation of the various
ideas I will propose in this dissertation, mainly because many of them capitalise
on certain semantic differences between singular and plural individuals, which I
feel are expressed more clearly in set-theoretical terms.
2.2 Distributivity and collectivity
The intuitive approach to predicate pluralisation presented in section 2.1,
according to which plural predicates denote sets of sets and pluralisation and
distributivity are two sides of the same coin, lies at the basis of many early
theories of plurality (e.g. Bennett 1974; Hoeksema 1983; Link 1983). However,
2An exception is Scha (1981), in which singular individuals denote singleton sets while
plural individuals denote non-singletons.
14 2.2. Distributivity and collectivity
not all plural predicates are distributive. For example, in (7a-b), we cannot
analyse the plural predicates gathered and are a good team as sets of sets
derived from their singular equivalents by ¦, because that would result in the
unwanted distributive entailment that each of the cats gathered on the roof
and each of the girls is a good team.
(7) a. The cats gathered on the roof.
b. The girls are a good team.
Predicates like gather and be a good team are traditionally called collective.
Unlike distributive predicates like be a linguist and smile, they are ‘inherently’
plural; in our framework, we will analyse them as predicates whose set-of-sets
denotation is basic rather than derived by ¦.
In addition to distributive and collective predicates, the traditional classification
also includes ‘mixed predicates’, that can behave like either. For example,
in (8), the predicate won can be interpreted either distributively (in (8a)) or
collectively (in (8b)):
(8) a. Five boy/girl pairs played a game of chess against each other. (Each
of) the girls won.
b. Five girls played a football match against five boys. (*Each of) the
girls won.
Predicates like win are often formalised as predicates that include in their
extension both singular individuals (the individual girls from (8a)) and plural
ones (the girl team from (8b)). Link (1987) proposes a special operator, D,
to deal with the distributive interpretation of mixed predicates; D is like ¦,
but applies only to the atoms in the predicate’s extension. With the addition
of D to the system, distributivity is essentially divorced from pluralisation
and treated as a more or less independent phenomenon (Link describes D as
a ‘quantificational adverb’). There is also the additional problem of trying
to implement mixed predicates and D in the set-theoretical system we have
adopted here, as it assigns different types to singular and plural individuals (e
and et, respectively).
However, there is nothing inevitable about the notion of ‘mixed predicate’
as a formally distinct class of predicates - there are at least two different
frameworks that explicitly do without them. One is the framework developed by
Landman (2000), in which all uninflected predicates - collective, distributive, or
‘mixed’ - range over atoms (corresponding to either individual entities or ‘group
Laying the groundwork 15
entities’ - for more on the latter, see section 2.3). The other, which I will adopt
in this dissertation (with some minor alterations) is that of Winter (2002), who
proposes a two-way classification of predicates that cross-cuts the traditional
three-way collective/distributive/mixed typology. Adopting this system allows
us to analyse all predicates (including those like win) in a way that preserves
the direct relation between pluralisation and distributivity, and can easily be
formalised in set-theoretical terms.
2.2.1 Winter’s classification: atom and set predicates
Winter (2002) distinguishes two classes of predicates, which he calls atom
predicates and set predicates and which roughly (but not entirely) correspond
to the traditional distributive/collective distinction. Class membership is decided
by a truth-conditional criterion, as follows:
(9) a.
$
'''&
'''%
All the
No
At least two
Many
,
///.
///girls
PRED
b.
$
'''&
'''%
Every
No
More than one
Many a
,
///.
///girl
PRED
(10) Atom predicates
If ((9)a) is truth-conditionally equivalent to ((9)b), or if both of them
are ungrammatical/anomalous, then PRED is classified as an atom
predicate
Set predicates
If ((9)a) has different truth conditions from ((9)b), or if one of them
is ungrammatical/anomalous, PRED is classified as a set predicate.
(11) a. All the cats purred.
b. Every cat purred.
(12) a. All the cats gathered on the roof.
b. *Every cat gathered on the roof.
(13) a. All the girls won the match.
16 2.2. Distributivity and collectivity
b. Every girl won the match.
(14) a. All the committees are good teams.
b. Every committee is a good team.
Sentences (11a) and (11b) are truth-conditionally equivalent, which means that
purr is categorised as an atom predicate. On the other hand, gather is classified
as a set predicate, since (12a) and (12b) are not equally grammatical. The
sentences in (13) show that the traditionally ‘mixed’ predicate win the match
counts as an atom predicate by Winter’s criteria. Finally, the sentences in (14),
which are truth-conditionally equivalent, show that the traditionally collective
predicate be a good team is classified as an atom predicate.
The distinction between atom predicates and set predicates is primarily
intended descriptively, but the terminology is not accidental: Winter assumes
that atom predicates, in their basic (uninflected) denotation, range over atomic
entities (i.e. are of type et), while uninflected set predicates range over sets
of entities (i.e. are of type (et)t). While this distinction is familiar from our
earlier discussion, Winter expands on it a bit by developing an explicit theory
of the interpretation of morphosyntactic number. In addition to the atom/set
distinction, he also assumes that morphologically singular predicates all range
over atoms, and morphologically plural predicates all range over sets. In order
to achieve this, we need both a pluralisation operation for atom predicates
and a singularisation operation for set predicates. We have already seen the
pluralisation operator ¦ at work. The singularisation operation Winter proposes
takes just the singleton sets in the predicate’s original extension and returns
the set of all the entities in the union of these singletons. This enables him to
analyse singular set predication over group NPs such as the committee:
(15) a. If meet weekly = {{mary, jane, bill},{comm 1, comm 2},
{comm 2}}
then meet weeklysg = {comm 2}
b. Committee 2 meets weekly.
= comm 2 € meet weeklysg
I will not be using this version of the singularisation operation, because (as we
will see) it does not work very well within the theory of group nouns that I
will develop in chapter 5. Instead, I will adopt another operation from Winter
(2001a) that also has the effect of singularising a set predicate, albeit in a
somewhat different way:
Laying the groundwork 17
(16) Predicate singularisation3
òPet,t : tpÒPqe | Pet € Pu
Here, Ò is a function that takes a set and maps it to the corresponding impure
atom (see section 2.3), which we can think of as a set ‘grouped into’ a single
conceptually complex but semantically singular entity. Thus, the singularisation
operator ò takes a set of sets and returns the set of all impure atoms
corresponding to those sets; the result is a singularised predicate of type et.
Here are some examples of predicates with different number features and
their formal analysis:
(17) a. The boys are smiling.
rrare smilingss = ¦smile
b. The cricket team is smiling.
rris smilingss = smile
(18) a. The councillors meet weekly.
rrmeetss = meet
b. The city council meets weekly.
rrmeetsss = òmeet
In the next section, we will have a closer look at the impure atom mapping.
2.3 Impure atoms
As already mentioned, the final tool in our set-theoretical toolbox will be a
type-shifting operation that maps sets into their corresponding ‘impure’ atoms
(cf. Link 1984; Landman 1989; Winter 2002), which we will write as Ò (following
Landman 1989).
3This is a generalised version of the Ó operation from Winter (2001a:243), which Winter
proposes (together with some additional meaning postulates) in order to deal with predication
structures like (i) and entailments like the one in (ii):
(i) The students are a good team.
(ii) The math department has a car. ñ The members of the math department have a car.
Unlike Winter’s Ó mapping, that is stipulated to apply only to nominal predicates, the
singularisation operation proposed here applies more generally to all set predicates. (Note that
Winter’s use of the Ò and Ó notation is quite different from Landman’s (1989); notationally
I am following the latter, associating Ò with a mapping from sets to atoms and Ó with a
mapping from atoms to sets.)
18 2.3. Impure atoms
(19) Impure atom formation
If Xet is the denotation of a referential NP, pÒXqe is the impure atom
corresponding to X.
The notion of impure atomicity captures the intuition that we sometimes
conceptualise a collection of entities as an entity in itself - we can talk about a
collection of things without really knowing or caring which individual entities
make up the collection (this observation is often made about group nouns like
council or family, but it holds for ‘ordinary’ plurals just the same). However, the
main reason I will be adopting impure atom formation here is not its conceptual
value or psychological realism - which we can debate - but its usefulness as a
formal tool (which will mainly become apparent in chapter 5).
I will assume that the impure atom typeshift is freely available for referential
plural NPs (but see chapter 6 for a nuancing of this position), and sometimes
required for type-matching reasons (see chapter 5 and section 3.5 of chapter 3).
The reverse operation, Ó (which maps conceptually complex entities into the
corresponding set of individual members of that entity, and is often invoked in
the literature on group nouns (cf. chapter 5)), will not be part of our toolbox.
2.3.1 Impure atoms and different ‘roles’
The definition in (19) defines impure atom formation as a one-to-one mapping,
with a single impure atom corresponding to each set. However, we might wonder
whether it would not be more accurate to describe the relationship between sets
of individuals and group entities built from those sets as a one-to-many relation
instead. It is possible, for example, for two distinct committees A and B to
consist of precisely the same members (Landman 1989; Barker 1992), which
suggests that sets should be able to correspond to more than one impure atom.
Otherwise, it seems difficult to account for the fact that (20a) and (20b) do not
entail each other:
(20) a. Committee A paid an official visit to South Africa.(From Landman
1989)
b. Committee B paid an official visit to South Africa.
However, as Landman (1989) shows, this non-substitution problem also arises
with other referential NPs, including non-group singulars like the judge or the
hangman, which means that it cannot be accounted for in terms of some property
of the relation between sets and impure atoms. For example, (21a) and (21b)
Laying the groundwork 19
do not entail each other even if the judge and the hangman are necessarily the
same person; if this person is John, I can utter the sentence in (22) without
contradicting myself.
(21) a. The judge is on strike.
b. The hangman is on strike.
(22) John is on strike and John is not on strike.
The key here seems to be the observation that the same individuals - whether
they be judges, a committee, or John - can have many different roles or functions,
and have different properties in each role. Thus, just as John-as-a-judge can be
on strike while John-as-a-hangman is executing people as usual, the same group
of people can be on an official visit to South Africa in their role as Committee
A, but not be on an official visit to South Africa in their role as Committee B.
Any formal system that incorporates this notion of different roles (for example,
the intensional system developed for this purpose by Landman 1989) can in
principle account for the nonentailments in (21) and (20) in precisely the same
way; there is no need to turn our Ò mapping into a one-to-many relation in
order to deal with the latter. (I will briefly return to this point in section 5.4.1.)
2.3.2 Previous works on the impure atom mapping
Impure atoms were introduced in Link (1984) as a way of dealing with the
interpretation of complex NPs such as the one in (23):
(23) a. The cards below 7 and the cards from 7 up were separated.
b. The cards below 10 and the cards from 10 up were separated.
Without impure atoms, our system assigns precisely the same denotation to the
cards below 7 and the cards from 7 up and the cards below 10 and the cards
from 10 up, since both coordinated NPs together refer to the exact same set of
cards. However, the sentences in (23) do not have the same interpretation: the
way the cards are separated into two piles according to (23a) is clearly different
from the way the cards are separated according to (23b). For Link (1984) and
Landman (1989), this is evidence that the two subject NPs in (23) have different
semantic structures. Rather than denoting the entire set of cards, they both
denote a distinct set of impure atoms that correspond to the particular groups
of cards expressed by the NP coordinates:
20 2.3. Impure atoms
(24) a. rrThe cards below 7 and the cards from 7 upss 
tÒt2, 3, 4, 5, 6u, Òt7, 8, 9, 10, J, Q, K, Auu
b. rrThe cards below 10 and the cards from 10 upss 
tÒt2, 3, 4, 5, 6, 7, 8, 9u, Òt10, J, Q, K, Auu
However, Schwarzschild (1991, 1996) argues extensively against the need for
impure atomicity, claiming that the different interpretations of the subject NP
in (23) do not exist as separate readings but are rather determined pragmatically.
Also, Schwarzschild argues, assuming a freely available impure atom mapping
overgenerates, as it predicts the acceptability of sentences that are in fact
ungrammatical or anomalous:
(25) a. Part of the car / the whole car was made in Italy.
b. *Part of the boys / the whole boys were in Italy.
(26) a. The board of advisors is composed of two lawyers and an ethicist.
b. # The advisors are composed of two lawyers and an ethicist.
As (25a) shows, the expressions part of X and the whole X are fine when X
refers to an atomic entity; if the boys were able to refer to an atomic entity,
then, we would expect the sentences in (25b) to be just as good.4
Similarly, if
predicates like composed of lawyers and ethicists are acceptable with impure
atoms (as (26a) shows) and plural NPs were able to denote impure atoms, there
is no reason why (26b) should be out.5
As Winter (2001a) points out, however, a system that lacks a way to formally
relate the set denotation of the advisors to the atomic denotation of the board
runs into trouble when faced with sentences like those in (27):
(27) a. These four people are our board of advisors.
b. Mary and Sue are a happy couple.
The fact that these predication structures are grammatical and interpretable
indicates that there must be a denotation available for an NP like these four
people that has the appropriate semantic type for a member of the predicate
are our board of advisors. So either we should be able to analyse predicates like
4See section 6.1 for a related discussion on British English data from Pearson (2011) and
some new Dutch data, where the judgements are a bit different from what Schwarzschild
claims here.
5I return to the issue of ‘group-level’ predicates in chapter 6 as well, in particular section
6.3.
Laying the groundwork 21
our board of advisors and happy couple as predicates that range over sets, or
we should be able to analyse NPs like these four people and Mary and Sue as
atoms. By rejecting the latter option, Schwarzschild is forced to adopt the first
(which he does in a footnote, stipulating a mapping from atoms to sets whose
availability is restricted to just NPs in predicative position). The upshot is
that some kind of mapping between atoms and sets cannot be avoided; anyone
who adopts a mapping from sets to impure atoms will have to find a way
to account for contrasts like those in (25-26), while anyone who adopts the
opposite mapping from atoms to sets will need to explain why its application is
restricted in the way it is without resorting to ad hoc stipulations. (In chapter
5, I will argue that group nouns like board and couple range over sets, enabling
an analysis of the predication structures in (27) without requiring a typeshift
of the subject; however, as I will show, this analysis of group nouns is made
possible precisely because we have included a mapping to impure atoms in our
formal toolbox.)
Regardless of the above considerations, impure atoms have proven to be a
handy tool for the analysis of many natural language phenomena. I will include
a short overview here of several semantic phenomena that have been analysed
using impure atoms, since the impure atom mapping is probably the most
controversial of the various background assumptions discussed here, as well as
the least well-documented.
McNally (1993) proposes that so-called ‘comitative’ NPs in Russian and
Polish - a special kind of coordinated NP - should be analysed as impure atoms,
since unlike ordinary NP coordinations they do not allow distribution of the
VP over the coordinates. For example, while the Russian sentence in (28a)
is true in a situation in which Anna and Masha won 1000 rubles each, the
sentence in (28b), which involves comitative coordination, can only receive a
collective interpretation according to which Anna and Masha won the 1000
rubles together.
(28) a. Anna i Maˇsa vyigrali 1000 rublej.
Anna-Nom and Maˇsa-Nom won-Pl 1000 rubles
‘Anna and Maˇsa won 1000 rubles’
b. Anna s Maˇsej vyigrali 1000 rublej.
Anna-Nom with Maˇsa-Instr won-Pl 1000 rubles
‘Anna and Maˇsa won 1000 rubles’
22 2.3. Impure atoms
For a reply to McNally that explains the comitative data in terms of pragmatics
rather than the semantic structure of the NP, see Dalrymple et al. (1998).
Kwak (2003) and Joh (2008) make use of impure atoms to account for
certain semantic differences between two types of plural NPs in Korean, one of
which is formed using a plural suffix -tul, the other of which is an uninflected
noun that can be interpreted as either singular or plural depending on the
context. While the tul-plural behaves just like a definite plural in English,
the ‘bare-formed’ plural (as Kwak and Joh call it) behaves semantically like
an atomic individual rather than a set. For example, unlike tul-plurals, it is
incompatible with distributive particles like kakca ‘each’:
(29) a. Haksayng-tul-i kakca sensayngnim-kkey cilmwun-ul ha-yss-ta.
Student-Pl-Nom each teacher-Dat question-Acc do-Past-Decl
‘Students each asked questions to a teacher’
b. #Haksayng-r-i kakca sensayngnim-kkey cilmwun-ul ha-yss-ta.
Student-Nom each teacher-Dat question-Acc do-Past-Decl
‘Students each asked questions to a teacher’
Based on this and similar data, Kwak and Joh argue that Korean tul-plurals
denote sets, while bare-formed plurals denote impure atoms corresponding to
those sets.
A third example of the use of impure atoms in recent semantic theories is
Mador-Haim and Winter (2012), who appeal to impure atomicity to account for
the interpretation of English locative PPs with a definite plural complement.
In the situation depicted in fig. 2.2, sentence (30) is true even though all the
individual utility poles are located further than 10 meters from the house, which
we would not expect if the spatial location of ‘the utility poles’ is just the union
of the locations of the individual poles.
(30) The house is exactly 10 meters away from the utility poles.
Figure 2.2: A house and a row of utility poles.
However, if we group the utility poles together into a single entity (which is a
natural thing to do considering their function and neat linear configuration),
Laying the groundwork 23
the resulting entity - to which we might refer as ‘the row of utility poles’ - is
located at exactly 10 meters from the house, which would account for the fact
that (30) is true in such a situation.
To sum up, impure atoms are evidently useful in describing and formalising
natural language phenomena, and as such they will be playing a central role in
this dissertation. As we will see, mapping from sets to impure atoms will be a
key part of the various semantic analyses presented in chapters 3 and 5, which
will provide additional empirical justification for the idea; in chapter 6, I will
address (among other things) Schwarzschild’s objection that such a mapping
overgenerates.
2.4 Summary and conclusions
In this chapter, I have put together the basic toolbox that I will be using
to formalise the plurality- and distributivity-related phenomena that will be
studied in this dissertation. I outlined a basic set-theoretical approach to the
pluralisation of atom predicates, which emphasises the close relationship between
semantic plurality and distributivity as two sides of the same coin (in this it
is very close in spirit to the work of Fred Landman, although many details
differ). As a side-effect of this, I rejected the notion of ‘mixed predicates’ as a
separate formally distinct class of predicates: instead, I adopted the two-way
classification of Winter (2002), which takes the additional step of relating
semantic and morphosyntactic number in a systematic way. Finally, I returned
some flexibility to the system by assuming a freely available typeshift from sets
to atomic denotations for referential plural NPs.
CHAPTER 3
P- and Q-distributivity
In the previous chapter, we have been treating distributivity as an inevitable
property of pluralised atom predicates, inseparable from the process of pluralisation
itself: the pluralisation operator and the distributivity operator are one and
the same. In this chapter, I argue that this cannot be the whole story, and that
distributivity effects are actually a bit more varied. In particular, I claim that
distributivity effects can also occur with singular predication as a consequence
of lexical reasoning about the meaning of the predicate (cf. Scha 1981; Roberts
1987; Hoeksema 1988; Winter 1997; Champollion 2010). The main evidence for
this will be the availability of (limited) distributivity effects with group NPs
like the team, which are generally taken to be semantically singular, and in fact
are shown to be incompatible with ¦-based distributivity. Following Winter’s
(1997) terminology, I will refer to ¦-based distributivity as Q-distributivity, and
to lexical distributivity as P-distributivity. The two kinds of distributivity can
be distinguished using a couple of tests that I will develop in this chapter. In our
set-theoretical framework, P-distributivity is formalised in terms of predication
over impure atoms.
The chapter is structured as follows. In section 3.1, I discuss the notion of
P-distributivity in more detail, including a couple of conceptual arguments both
for and against. In section 3.2, I use the observation made in section 2.1 that ¦
26 3.1. P-distributivity
essentially functions like a quantifier to identify a series of contexts in which the
observed distributivity effect have to be explained in terms of Q-distributivity,
showing that P-distributivity alone cannot account for the full range of distributivity
data. In section 3.3, I show that Q-distributivity is unavailable in
these contexts if the subject is a group NP, but that certain distributive effects
are still available with group NPs, showing that Q-distributivity alone cannot
account for the full range of distributivity data either. Section 3.4 contains
a formalisation of the notion of P-distributivity in terms of predication over
impure atoms. Finally, section 3.5 offers some speculation about the syntax
of Q-distributivity; I argue based on data from Dutch that coordination of a
collective and a Q-distributive VP is not possible, which provides some support
for the assumption that predicate pluralisation is not a lexical but a structural
process, in which ¦ occupies a separate syntactic projection of its own. Section
3.6 concludes the chapter.
3.1 P-distributivity
In chapter 2, we have treated distributivity as the direct consequence of applying
the ¦ operator to a predicate, which is essentially a quantificational process:
because of the way ¦ is defined, a set is in the extension of a pluralised predicate if
and only if every individual member of that set is in the extension of the original
non-pluralised predicate. This view of distributivity is due to Link (1983). But
there is a possible alternative way to derive distributivity effects, as argued
for by Scha (1981): in Scha’s theory of plurality, collectivity and distributivity
inferences with referential expressions are not triggered by the compositional
semantics of the sentences in question, but by lexical information. Thus, there
is no formal difference between the derivation of the distributive sentence in
(1a) and the collective sentence in (1b): both involve direct application of the
predicate to the plurality expressed by the children. (In Scha’s system, there
is no structural difference between singular and plural predication because he
treats both singular and plural NPs as set-denoting; hence, all VPs denote
sets of sets, and already include plural individuals in their extension from the
beginning.)
(1) a. The children laughed.
laughed(the children)
b. The children gathered in the garden.
gathered in the garden(the children)
P- and Q-distributivity 27
The process underlying the distributive inference in (1a) and the collective
inference in (1b) is the same in both cases: we draw conclusions about the
way the individual members participate in the expressed event by using our
knowledge of the world and of the predicate’s lexical meaning. We know that
in order to be able to laugh one needs lungs and a vocal apparatus, and we
know that individuals have this but groups or collections do not; hence, we
interpret ‘‘The children laughed’’ as a statement about individual children.
Similarly, we know that gathering cannot be done by single individuals but
only by groups, and hence we interpret ‘‘The children gathered’’ as a statement
about a collection of children. Thus, according to Scha’s analysis, distributivity
is not a direct consequence of the semantic pluralisation of a predicate (which
does not exist in his system), but purely a lexical property of certain verbs.
Many authors have incorporated Scha’s idea of lexical distributivity into
a Linkian framework, arguing that distributivity effects can be either lexical
or structural (i.e. due to ¦). For example, Roberts (1987) writes that ‘‘the fact
that a particular lexical item is a group predicate or a distributive predicate
doesn’t really need to be specified independently: it follows from the sense
of the predicate itself. (...) What is it to be a pop star or to walk or to die?
The actions or states denoted by these verbs can generally only be performed
or endured by an individual with a single will and consciousness. It is for
this reason that we think of them as distributive’’ (p. 124). This intuition
was built into the theory more explicitly by Winter (1997), who distinguishes
Q-distributivity (for ‘quantificational distributivity’) and P-distributivity (for
‘predicate distributivity’); the first is our familiar ¦-based distributivity, while
the second is Scha’s lexical distributivity. A similar distinction is adopted by
Hoeksema (1988) and Champollion (2010).1
These more mixed approaches to distributivity agree with the observation
made by various authors (Dowty 1987; Verkuyl and van der Does 1996; Verkuyl
1994) that the line between collectivity and distributivity is not as clear-cut as
suggested by the way we have set up our formal system so far. Dowty (1987)
notes that even many collective predicates enable certain inferences about
individuals; he calls these inferences subentailments. For example, while we
1Bartsch (1973) is an early example of an account of plurality in which distributivity is
sometimes made explicit in the formal semantics, and sometimes left to lexical inferencing,
but she is not very explicit about this aspect of her theory. In Kroch (1974), plural predication
introduces a universal quantifier, but an additional interpretation rule ensures that distributive
readings generated in this way come out as anomalous if they are incompatible with the
lexical semantics of the predicate.
28 3.1. P-distributivity
cannot infer (2b) from (2a), we can infer (2c):
(2) a. The children gathered in the garden.
b. *Each child gathered in the garden.
c. Each child was in the garden.
If the inference from (2a) to (2c) were enabled by some ¦-like operator, such
an operator would need to be able to break up the lexical meaning of gather
and distribute only part of it to the individual children. There is no way to
do this in standard model-theoretic semantics, and even if there were, every
subentailing predicate would need its own corresponding operator to ensure
the distribution of only the intended meaning parts. Considering this, it is
reasonable to assume that the inference from (2a) to (2c) is enabled not by a
covert quantificational mechanism but by the lexical properties of the predicate
to gather. But then, if the distributive inference from (2a) to (2c) can be lexically
based, without actual quantification over individual children, the same should
hold for the distributive inference from ‘‘The children laughed’’ to ‘‘Each child
laughed’’. Put differently, if part of a predicate meaning can be distributed over
members of a plurality by a lexical process, there is no reason why the same
process couldn’t be responsible for the lexical distributivity of entire predicate
meanings. There seems to be little conceptual sense in a theory that allows for
subentailment but not for complete P-distributivity.
A counterargument to this kind of reasoning, however, is brought up by
Landman (1996, 2000) (who, as far as I am aware, is the only author who
has explicitly argued against the possibility that at least some distributive
interpretations could be due to lexical inferences). Landman’s point is based
on argument structure: whatever saturates the argument position of laugh in
the sentence ‘‘The children laughed’’ is not just there to give the sentence a
grammatical subject so it may end up as an expression of type t, it also receives
the thematic agent role from the verb, which according to Landman plays a
crucial role in our interpretation of the sentence. If the subject argument of a
distributive predicate could be an entire plurality, Landman argues, this entire
plurality would end up with the role of agent; but that would render the whole
notion of ‘agent’ both meaningless and useless, since the plurality itself is not
in fact the agent of the expressed event (it’s the individual children that are
the laughing agents, not the group of children as a whole). So according to
Landman, we really do need a quantificational mechanism that allows us to
interpret ‘‘The children laughed’’ as expressing a whole series of laughing events,
P- and Q-distributivity 29
each with their own individual agent. On the other hand, with a collective verb
like gather, the subject plurality as a whole should receive the agent role; the
fact that there are certain subentailments to individuals does not change the
fact that the agent of the gathering event is still the plurality as a whole.
Since what this gives us is two conceptual arguments with completely
opposite conclusions, it seems clear that we will not be able to decide on purely
conceptual grounds whether we should make room for P-distributivity in our
formal framework. What, then, about empirical grounds - can we demonstrate
empirically whether we need something like P-distributivity as part of our
theory?
Winter (1997), who introduced the term ‘P-distributivity’, does not make an
explicit empirical case for it, although it is possible to make such a case on the
basis of the data in Winter (2000). In the same vein, Champollion (2010) argues
(following observations by Lasersohn 1989, 1995; Schwarzschild 1996, and others)
that P-distributivity freely allows intermediate or non-atomic interpretations
when these are supported by the lexical semantics of the predicate, while Qdistributivity
only allows a nonatomic interpretation if this is made sufficiently
salient by context. In both cases, P-distributivity accounts for distributive
interpretations that, under Winter’s and Champollion’s assumptions, cannot be
explained in terms of covert quantification. In this chapter I provide some new
empirical evidence along the same lines. First, however, we need to set up the
stage for this argument by taking a closer look at Q-distributivity.
3.2 Q-distributivity
So far, our discussion of Q-distributivity has been rather abstract and technical.
In this section, we will take a more linguistic look at Q-distributivity. Our earlier
observation that Q-distributivity is essentially a quantificational phenomenon
will become more concrete as we study the way it interacts with several other
natural language phenomena and identify several contexts in which the observed
distributivity effects can only be accounted for in terms of ¦. As a result, we will
end up with a list of tests that we can use to distinguish Q- from P-distributivity,
which will prove useful in the remainder of this chapter and in chapters 5 and
6.
As several people have pointed out in response to Scha (e.g. Winter 1997; Brisson
1998), distributivity effects cannot be reduced completely to P-distributivity.
30 3.2. Q-distributivity
In the following subsections, I will discuss a couple of examples of distributive
interpretations in different linguistic contexts that need the kind of covert
quantificational mechanism provided by ¦. In this section, I will discuss VP
disjunction (3.2.1), interaction with other quantifiers (3.2.2), and anaphora
(3.2.3). (In section 4, I will discuss two additional cases of Q-distributivity that
only become obvious when we contrast plurals with group NPs: VP conjunction
and Dutch proportionality adverbs (3.3.3).) In all cases, I will be contrasting
‘distributive’ and ‘collective’ interpretations, which I will for the present purposes
define as follows:
(3) Distributive and collective interpretations
Suppose we have a sentence S of the form X Pred, where X is a plural,
conjunction or group NP, and Pred is a predicate. An interpretation of
S is distributive if we infer that Pred holds for every member x of X ;
otherwise2
it is collective.
This means that in sentences like ‘‘The children are singing or dancing’’ (which
we will look at shortly), the crucial factor in deciding which interpretations are
available is the interpretation of the entire predicate are singing or dancing, not
just the individual verbs. According to the above definition, this sentence can be
interpreted distributively just in case the entire disjunction singing or dancing
can hold for each individual child; whether the coordinated verbs themselves
express properties of individuals or collections is irrelevant here. As we will
see, formulating the definition in this way will help us to separate Q- from
P-distributivity since it takes into account the VP with all its internal structure,
and not just verb semantics.
3.2.1 VP disjunction
As shown in (4), analysing predicate disjunction by set union is mathematically
equivalent to analysing it as a predicate formed by lambda abstraction and
sentential disjunction. We can see this equivalence playing out in natural
language in entailments like (5):
(4) x € pP ‰Qq ô Ppxq•Qpxq
2For now, I am ignoring cases of ‘intermediate distributivity’, as in Rodgers, Hammerstein
& Hart wrote musicals (Gillon 1987), which is true not because each wrote musicals of their own
or because the three of them wrote musicals together, but because Rodgers and Hammerstein
collaborated to write musicals and so did Rodgers and Hart. The definition in (3)can be
straightforwardly extended to accommodate such cases.
P- and Q-distributivity 31
(5) Sue is singing or dancing.
ô Sue is singing or Sue is dancing.
When we replace Sue in (5) with a plural definite, the entailment pattern
gets a bit more complicated, however. A disjunctive sentence like (6) can be
interpreted in two different ways:
(6) The children are singing or dancing.
a. ð The children are singing or the children are dancing. (CI)3
b. ð For every child y, y is singing or y is dancing. (DI)
We see that there are two ways to analyse (6), each of them corresponding
to a possible interpretation of the sentence. According to the first analysis,
the disjunction singing or dancing holds of the group of children as a whole;
this makes it equivalent in meaning to (6a). No quantification over individual
children is needed in order to derive this interpretation. According to the second
analysis, the disjunction singing or dancing holds not of the group as a whole
but of each of the individual children, which makes it equivalent to (6b). In
order to derive the second analysis, we need to access the individual children
by quantifying over the plurality denoted by the subject. Under our current
assumptions, this can be done using ¦, as follows:
(7) rrthe childrenss € ¦psing ‰danceq
ô dy € rrthe childrenss : y € sing ‰dance
ô dy € rrthe childrenss : y € sing or y € dance
The logical form in (7) is a clear example of Q-distributivity: it can only be
derived assuming the quantificational mechanism provided (in our framework)
by the ¦ operator. Since the interpretation it represents is truth-conditionally
distinct from the collective interpretation in (6a) (the former, but not the latter,
is true in a situation in which part of the children are singing while the rest
are dancing), sentences like (6) provide us with a truth-conditional test for the
availability of Q-distributivity. If a sentence of the form X Pred1 or Pred2 can
be interpreted as true in a ‘mixed’ situation (in which Pred1 is true of one
part of X and Pred2 of the other), it must have a Q-distributive interpretation.
Conversely, if it cannot be true in that situation, it cannot have a Q-distributive
interpretation.
3Here, ‘CI’ and ‘DI’ are shorthand for ‘collective interpretation’ and ‘distributive interpretation’
as defined in (3).
32 3.2. Q-distributivity
3.2.2 Interaction of ¦ with other quantifiers
For this and the remainder of the Q-distributivity tests in this section and
section 4, I will not make the formal derivation as explicit as in the previous
section; this is partly because they involve semantic phenomena for which there
are a lot of different analyses around that I do not want to choose from, and
partly because the idea should be clear by now: the Q-distributive mechanism
provided by ¦ enables quantification over the individual members of the subject
plurality, which makes an interpretation available that direct predication
(without ¦) cannot provide.
The data in this section all involve the interpretation of sentences that contain
some overt quantificational element. Since the ¦ operator essentially introduces
a universal quantifier into the semantics, we expect it to be able to take scope
over any other quantifiers in the sentence; this produces an interpretation that
is truth-conditionally distinct from readings where ¦ takes narrow scope or is
absent. If a particular sentence has such an interpretation, then, it is evidence
for the presence of the ¦-operator.
The entailments in (8) provide a concrete example of this reasoning:
(8) The children admire someone famous.
a. ð There is a famous person x such that the children admire x. (CI)
b. ð For every child y, there is a famous person x such that y admires
x. (DI)
If we analyse the NP someone famous as an existential quantifier, an analysis
in terms of direct predication would result in the object’s taking scope over the
entire plurality of children:
(9) hx [famous person(x) ” admire(the children,x)]
However, this only accounts for the entailment in (8a), according to which there
exists one particular famous person that the entire group of children admires.
The second possible interpretation of (8), that corresponds to the entailment in
(8b), cannot be derived in this way, since it requires the existential quantifier to
take scope below the children. And the only way to allow the children to have
wider scope than someone famous is to introduce another quantifier, as in (10):
(10) dy € the children [ hx [famous person(x) ” admire(y, x) ] ]
P- and Q-distributivity 33
We have already seen that this kind of quantification over individual children
is precisely what ¦ provides when it is applied to the predicate.
The following examples work in a similar way: they, too, involve quantifiers
(a comparative quantifier in (11), and a numerical quantifier in 12); and all
examples are similarly ambiguous between two interpretations. The examples
were chosen in such a way that the DI does not entail the CI; hence, it is
possible to imagine a situation that verifies the DI but falsifies the CI. This
means that if we can accept a sentence as true in such a situation, we have to
be able to derive the DI as a separate reading. It can be shown for each of the
cases below that this is only possible by assuming covert quantification over
the members of the subject plurality.
Example (11) shows a comparative construction that can be interpreted
both collectively and distributively:
(11) The cows won fewer prizes at the fair than the pig.
a. ð The cows together won fewer prizes than the pig. (CI)
b. ð Every cow won fewer prizes than the pig. (DI)
Figure 3.1: Cows, pigs and prizes
As a context for (11), imagine a country fair at which prizes are awarded to
animals in various categories. One farmer brought three of his cows and his
very best pig, and all four animals ended up winning a number of prizes. One
possible distribution of prizes is depicted below in Figure 3.1; sentence (11)
34 3.2. Q-distributivity
is true in this situation under its first, distributive, interpretation, since the
cows each have two prizes while the pig has three. However, it is false under its
collective interpretation, since the cows together have six prizes, which is more
than the pig has. Direct predication only gives us the CI: without quantification
over individual cows, the quantifier fewer prizes than the pig necessarily takes
scope over the entire subject plurality. Again, we need to assume some covert
quantification mechanism in order to derive the distributive interpretation.
The reasoning is similar for the next example:
(12) These artists dress in black one day a week.
ð For every artist x, there is one day a week y such that x dresses in
black on y. (DI)
ð There is one day a week y such that every artist dresses in black on y.
(CI)
Without quantification over individual artists, the only interpretation that can
be derived is the collective one, according to which all the artists dress in black
on the same day of the week.
A final note is in order here. In the preceding list of Q-distributivity tests, I
deliberately have not used the example sentences involving an indefinite object
that are usually invoked against Scha’s theory of distributivity (cf. Winter 1997;
Brisson 1998, 2003):
(13) The boys are eating a pizza.
a. ð There is a pizza that the boys are eating. (CI)
b. ð For every boy x, there is a pizza that x is eating. (DI )
The reasoning here is again the same: if a pizza is given a quantificational
analysis, and there are no other quantificational elements in the sentence (as in
Scha’s lexical theory of distributivity), a pizza will necessarily take widest scope
and the only interpretation we will end up with is (13a). However, this reasoning
depends on the indefinite a pizza being analysed as quantificational, and in
chapter 4 I will argue that this is not the only possibility and that a-indefinites
may also receive a property analysis in contexts like (13). As we will see, this
enables us to derive a P-distributive interpretation for sentence like (13), which
means that they cannot be used as a reliable test for Q-distributivity.
P- and Q-distributivity 35
3.2.3 Anaphora
Our third class of examples involves pronoun binding. When a pronoun or
reflexive is bound by a plural subject, it can be interpreted as either referring back
to the entire plurality, or to each of the members of the plurality individually
(as when the pronoun is bound by a universal quantifier). The availability of
the latter interpretation points to the presence of a covert quantifier in the
derivation. I will provide Dutch examples here, to avoid the complications posed
by dependent plurality in English, among other reasons.4
(14) Deze jongens worden woedend als je hun moeder beledigt.
These boys become furious when you their mother insult
‘These boys get furious when you insult their mother(s)’
a. ð These boys get furious when you insult their mum (the boys are
brothers). (CI)
b. ð For every boy x, x gets furious when you insult x’s mum. (DI)
Because the NP hun moeder ‘their mother’ is singular here, we would not
expect the distributive interpretation (in a situation in which the boys are not
siblings, which means that we are talking about more than one mother) unless
the NP is interpreted in the scope of a quantifier. Hence, the fact that we can
interpret (14) as true in such a situation provides another piece of evidence for
the presence of a covert quantifier in the semantics of (14).
Dutch is also the source of the next example, which involves a reflexive
anaphor. Unlike English, the Dutch third person reflexive pronoun zichzelf is
not inflected for either number or gender; as (15) demonstrates, zichzelf can be
interpreted as ‘himself’, ‘herself’, ‘itself’ or ‘themselves’. This will make Dutch
4Winter (2000) provides an English example along the following lines:
(i) The boys will be glad when their mothers arrive.
ð For every boy x, x will be glad when x’s mother arrives.
However, most varieties of English really need the dependent plural mothers here to bring
out the distributive interpretation, which means it is hard to tell whether the DI here is really
due to covert quantification and not just a special case of the collective interpretation (for
‘‘The boys will be glad when the mothers of the boys arrive’’ to be true, it is only necessary
for the boys to be glad when the mothers arrive, a condition that is satisfied when each boy
is happy to see his own mother). When the singular their mother is used, most speakers are
only able to get a collective interpretation in which the boys are all children of the same
mother. In contrast, Dutch (sometimes) allows dependent plurality but does not require it,
so the Dutch equivalent of ‘‘The boys will be glad when their mother arrives’’ can easily be
interpreted both collectively and distributively.
36 3.3. Distributivity effects with group NPs
reflexive predication particularly useful when we will compare the behaviour of
plurals with that of group nouns in section 3.3.
(15)
#
Jantje vindt
De kinderen vinden
+
zichzelf nogal slim.
Johnny considers / the children consider SELF.3sg/pl rather clever
‘Johnny considers / the children consider himself/themselves rather clever’
When the subject is a plural definite like the children, two different interpretations
arise, depending on whether we take the antecedent of zichzelf to be the
entire group denoted by the subject, or each of the members of that group in
turn:
(16) De kinderen vinden zichzelf nogal slim.
‘The children consider themselves rather clever’
a. ð The children consider the children rather clever (as a group). (CI)
b. ð For every child x, x considers itself rather clever. (DI)
In a situation in which each child considers itself clever but thinks the other
children are stupid, (16) is false on its collective interpretation but true on its
distributive one. This interpretation cannot be derived if only the plurality de
kinderen ‘the children’ as a whole may function as the antecedent of zichzelf,
but it can be derived if we allow zichzelf to be bound by a quantifier over
individual children.
To conclude: while simple distributive sentences like ‘‘The children laughed’’
might well be analysed in terms of P-distributivity, the above examples all
show that Scha’s theory of plurality is unable to account for the full range of
distributivity data. The truth conditions of more complex sentences involving
phenomena like scope interactions and binding cannot be adequately captured
without assuming covert quantification by ¦ (or, more generally, some kind of
distributivity operator).
3.3 Distributivity effects with group NPs
We have been interpreting Q-distributivity in terms of semantic plurality: the
same operator ¦that pluralises atom predicates is responsible for Q-distributivity.
Q-distributivity occurs ‘automatically’ when a starred predicate applies to a
P- and Q-distributivity 37
semantically plural argument. From this it follows that Q-distributivity is only
available when the subject denotation is semantically plural: if the subject
denotation is semantically singular (i.e. of type e), the predicate cannot be
starred, and Q-distributivity is out. Or, to put it differently, since ¦ is essentially
a quantifier and only sets can be quantified over, we predict that Q-distributivity
is only possible when the subject denotes a set.
Why is this relevant? As it turns out, there is a class of noun phrases that
intuitively seem to refer to the same collections5
as the plural definites we have
been looking at so far, yet are generally taken to have an atomic denotation:
singular definites formed with group nouns like team, committee, set, or pile. If
it is true that these NPs are atomic, we expect them to ‘fail’ the Q-distributivity
tests from the previous section. As we will see, this turns out to be the case: in
this section I will show that none of the relevant sentences has a Q-distributive
interpretation when the subject is a group NP rather than a plural. In addition,
I will use this contrast between plurals and group nouns to identify two more Qdistributivity
tests. This result supports both the validity of our Q-distributivity
tests and the atomic analysis of group NPs. Finally, I will show that group
NPs, despite their incompatibility with Q-distributivity, do show distributivity
effects; this confirms the need for a theory of P-distributivity, without which
we would be unable to account for these observations.
3.3.1 Groups as atoms
Group nouns are singular nouns that refer to a seemingly plural entity, such as
committee, team, collection, set, council or group itself. In many contexts, they
can be used interchangeably with a plural noun phrase that refers to the same
collection of entities:
(17) a. The
#
choir
members of the choir
+
sang beautifully.
b. The
#
council
councillors
+
voted on the issue today.
c. The
#
bouquet
flowers
+
has/have wilted.
Group nouns behave like plurals in other respects: they may appear as the
argument of a collective predicate (18), and function as the antecedent of both
5I’m using the word collection in a pretheoretical, descriptive sense here to refer to any
conceptually plural referent, i.e. plural as well as group denotations.
38 3.3. Distributivity effects with group NPs
discourse and bound plural anaphors ((19b-c) were found through Google along
with many similar examples):6
(18) The committee gathered in the meeting room.
(19) a. The committee debated for two hours before they could agree on a
solution.
b. HUD will continue to enforce the Fair Housing Act to ensure that
no family has their housing options limited because of their race.
c. The crew was obviously enjoying themselves and having fun with
the script.
In some varieties of English, most notably British English, they may also take
a plural VP:7
(20) This art collective are always dressed in black.
Considerations like these led Bennett (1974) to treat group nouns as pluralities,
denoting the set of the group’s members; however, most researchers afterwards
have argued that groups are not reducible to the set of their members, but are
entities in their own right (Link 1984; Landman 1989; Barker 1992; Schwarzschild
1996, but see Pearson 2011 and Magri 2012 for a different account in
the spirit of Bennett). This is intuitively reasonable: groups have identities,
purposes and histories that may be independent of any properties of the group’s
members. In line with this, (21) shows that while plurals and proper name
conjunctions inherit the properties shared by their members and vice versa
(Link 1983), this does not always happen with groups:
(21) Supposing the women are, and the committee consists of, Mary and Sue:
a. Mary is old and Sue is old ô Mary and Sue are old ô The women
are old.
b. but: Mary is old and Sue is old ø The committee is old.
6An elicitation study by Bock et al. (2006) found that British and American speakers are
equally likely to follow up a group antecedent with a plural pronoun, regardless of whether
the pronoun is bound by the antecedent or not. Examples (18b) and (18c) were both found
on US websites reporting on local news. Since the ability of group NPs to function as the
antecedent of plural pronouns is not limited to a particular dialect of English, it appears to
be unrelated to their ability (in some varieties of the language) to occur with a plural VP.
7According to Corbett (2000), the same phenomenon is attested in various other languages,
like Spanish, Old Church Slavonic, Samoan, the Brazilian language Paumar´ı and the Caucasian
language Kumaxov.
P- and Q-distributivity 39
There are several other examples that show that a group noun denotation can be
in the extension of a certain predicate while the plurality formed by conjoining
the group’s members is not, or vice versa; Barker (1992) lists many of them.
(22) a. The committee has two members.
b. *The women/Mary and Sue have two members.
(23) The women/Mary and Sue are members of the committee ÷ The committee
is a member of the committee.
Data like these suggest that group nouns (like the committee) do not have the
same denotation as the corresponding pluralities (like Mary and Sue or the
members of the committee).
On independent grounds, Schwarzschild (1996) argues that their denotations
must be atomic. His argument is based on contrasts like the following:
(24) a. Each of the boys is from Texas.
b. *Each of the car was manufactured in the Czech Republic.
c. *Each of the group is from Texas.
(25) a. *Part of the boys is/are from Texas.
b. Part of the car was manufactured in the Czech Republic.
c. Part of the group is from Texas.
In both of these cases, group nouns pattern with singular entities (the car),
not with pluralities (the boys). For various other empirical arguments that
support an analysis of groups as atoms, see Barker (1992), Schwarzschild (1996),
Chierchia (1998); Krifka (2003).8
Link, Barker, Schwarzschild and (up to a point) Landman all conclude
that group noun denotations are atomic: they lack internal structure, their
individual members are inaccessible to the compositional semantics. I will adopt
this conclusion; as we will see, the data discussed in the next section are in line
with it, adding more support to the groups-as-atoms analysis.
8Krifka (2003), citing Barker (1992) and Kleiber (1989), mentions that group nouns seem
to be incompatible with cardinality predicates such as be numerous or be few, suggesting that
groups do not have countable members, but not everyone seems to agree with this judgement
(cf. Champollion (2010:189)).
40 3.3. Distributivity effects with group NPs
3.3.2 Distributivity behaviour of group nouns
Of the examples of Q-distributivity listed in section 3.2, all are unavailable with
group NPs. Below, I repeat the examples, this time with group rather than
plural subjects:
(26) The team is singing or dancing.
a. ô The team members are singing or the team members are dancing.
(CI)
b. ö For every team member x, x is singing or x is dancing. (DI)
Recall from the data in (6) that both a distributive and a collective interpretation
are available if the subject is a plural definite; the former, but not the latter,
is true in a mixed situation in which part of the team members are singing
while the others are dancing. Its group-subject counterpart in (26), however,
cannot be interpreted as true in such a situation, which shows that it only
has a collective interpretation. According to this interpretation (paraphrased
in (26a)), the disjunction singing or dancing applies to the team as a whole:
either they are all walking, or they are all cycling. In section 3.2.1, I have shown
that only this interpretation can be analysed in terms of direct predication; the
other, distributive interpretation can only be derived by means of ¦. The data
in (26) suggest that this option is unavailable with a group NP subject.
Our next examples also run parallel to our earlier data in section 3.2, and
show a similar contrast between plurals and group nouns:
(27) The class admires someone famous.
a. ô There is a famous person x such that the pupils admire x. (CI)
b. ö For every pupil y, there is a famous person x such that y admires
x. (DI)
(28) The trio of cows won fewer prizes at the fair than the pig.
a. ô The cows together won fewer prizes than the pig. (CI)
b. ö For every cow x, x won fewer prizes than the pig. (DI)
(29) This art collective dresses in black one day a week.
a. ô There is one day a week y such that every artist dresses in black
on y. (CI)
P- and Q-distributivity 41
b. ö For every artist x, there is one day a week y such that x dresses
in black on y. (DI)
(30) Deze groep wordt woedend als je hun moeder beledigt.
‘This group gets furious if you insult their mother’
a. ô The group members have the same mother and get furious if you
insult her. (CI)
b. ö For every group member x, x gets furious if you insult x’s mum.
(DI)
(31) De klas vindt zichzelf nogal slim.
‘The class considers SELF.3sg/pl rather clever’
a. ô The class considers the class rather clever (as a group). (CI)
b. ö For every pupil x, x considers itself rather clever (DI)
In each of these cases, the only available interpretation is the CI (hence, the
original sentence and the CI entail each other); distribution over individual
group members is ruled out. As a consequence, sentence (27) requires that the
same famous person be admired by all children in the class; sentence (28) can
only be false in the situation depicted in fig. 3.1; sentence (29) must mean
that all artists in the collective dress in black on the same day of the week;
in sentence (30), the members of the group all have to be children of one and
the same mother; and finally, sentence (31) requires that the pupils in the
class collectively feel that they are clever as a group, regardless of what each
individual pupil thinks about his or her own cleverness. (Since the third person
reflexive pronoun zichzelf is not marked for number, and can be bound by
singular as well as plural NPs, the contrast between (31) on the one hand
and (16) on the other cannot be due to any morphosyntactic properties of the
anaphor that might make either a singular or a plural antecedent more salient.)
The generalisation that emerges is that sentences with group noun subjects
systematically lack a distributive interpretation that their plural-subject counterparts
do have. As already suggested in the introduction to this section, this
generalisation can be accounted for in terms of the atomicity of the subject
denotation. If a group NP denotation lacks internal structure, it has no individual
members that can be quantified over, hence Q-distributivity is out. The
contrast between the data in sections 3.2.1 to 3.2.3 on the one hand and (24-29)
on the other thus supports an analysis of groups as atoms.
42 3.3. Distributivity effects with group NPs
3.3.3 Two more Q-distributivity tests
The Q-distributivity tests from section 3.2 were based on theory - given standard
assumptions about disjunction, scope, and binding, we expect not to be able to
derive distributive interpretations for the sentences involved unless distributivity
involves covert quantification. Now that we have established that we can
diagnose Q-distributivity by checking whether it is available when the sentence
subject is a group NP, we can in turn use this observation to identify additional
Q-distributivity tests involving linguistic phenomena that different theories
have different predictions about, and perhaps use the results to decide between
competing theories (just as our original Q-distributivity tests provided support
for an atomic, rather than set-based, analysis of group NPs). In this section, I
will mention two of these, and briefly discuss the theoretical implications.
Proportionality modifiers. The first of these examples is from Dutch, where
the adverb gedeeltelijk ‘partly’ modifies the telic predicate kaalgeschoren ‘shaved
bald’ to indicate that the shaving-bald event was only partly completed:
(32) De studenten zijn gedeeltelijk kaalgeschoren. (Dutch)
The students are partly bald.shaven
‘The students were partly shaved bald’
a. ð Part of the students have been shaven bald. (CI)
b. ð Every student has been shaven partly bald. (DI)
If we take the group of students as a whole to be the incremental theme of the
shaving-bald event, and this event was only partially completed, we get the
collective interpretation according to which a part of the students were shaven
bald. If we quantify over individual students, we get a partially completed
shaving-bald event for each of them, resulting in the distributive interpretation
according to which every student is now partly bald.
There is a possible objection to this, however. Perhaps the DI simply entails
the CI in this case: a situation in which every student is shaved partly bald
might be interpreted as a partially completed shaving-bald event involving the
entire group, so the collective interpretation of sentence (32) would be verified
in such a situation. However, when we compare the entailment pattern in (32)
to that of its group-subject counterpart, we see that this cannot be the case:
(33) Het dispuut is gedeeltelijk kaalgeschoren. (Dutch)
The fraternity is partly bald.shaven
P- and Q-distributivity 43
‘The fraternity was partly shaved bald’
a. ô Part of the students have been shaven bald. (CI)
b. ö Every student has been shaven partly bald. (DI)
If the collective interpretation - a partially completed shaving-bald event with
the entire fraternity as its theme - could be verified by a distributive situation
in which each of the students has been partly shaved, we would expect (33) to
have precisely the same range of interpretations as (32). However, in the case
of (33), a distributive interpretation is clearly out: unlike (32), it is false in the
described situation.9
This shows that (a) we do need to derive the DI in (32b)
as a separate (Q-distributive) reading, and (b) however we analyse adverbs like
‘partially’, we should take into account the fact that its behaviour depends on
the semantic number of the sentence subject.
VP conjunction. Another Q-distributivity test that I have not discussed
in section 3.2 is VP conjunction, which shows a contrast between plural and
group subjects that is very similar to the disjunction data:
(34) a. The women are short and tall.
b. # The committee is short and tall.
While (34a) is acceptable to many speakers, and is interpreted as equivalent
to ‘part of the women are short, the other part of the women are tall’, this
non-Boolean interpretation seems to be out for (34b). The only interpretation
available for (34b) is an intersective one according to which each member of
the committee is (impossibly) both short and tall, which makes the sentence
anomalous.
The issue of non-Boolean VP conjunction has received some attention in
the literature (e.g. Krifka 1990; Winter 2001b; Poortman 2014). The contrast
between plural and group subjects, however, seems to have gone unnoticed so
far. It is unexpected under Krifka’s account, which is explicitly designed to
capture both (34a) and the non-Boolean interpretation of (35) with a single
analysis:
(35) The flag is green and white.
9I have checked this with several native speakers of Dutch, who all shared my intuitions
about these sentences.
44 3.3. Distributivity effects with group NPs
Krifka posits an interpretation rule according to which sentences like (34a)
and (35) are true if the subject denotation can be partitioned in such a way
that the first predicate holds of one partition and the second predicate holds
of the other one. Since the rule must be able to account for (35), it needs to
be defined for both plural and singular entities. This predicts that the atomic
entity corresponding to the committee should be able to be similarly partitioned
into a short part and a tall part, which means that (34b) should be completely
equivalent to (34a). However, we have seen that this is not the case.
The account in Winter (2001b) is better equipped to deal with the plural/group
contrast, since it only works on pluralities (Winter analyses singular
predicate conjunctions like (35) as an independent phenomenon, following Lasersohn
1995). Under this account, the strong, Boolean meaning of (34a) is basic,
but it is weakened under the influence of lexical knowledge that tells us that
being short and being tall are mutually exclusive. The actual interpretation,
then, will be the strongest interpretation compatible with this lexical knowledge
- i.e., an interpretation according to which each of the women is either short or
tall.10
As a Q-distributivity test, the VP conjunction test functions much the same
as the disjunction test: since the non-Boolean interpretation can only be derived
when the subject is a plurality, (34a), but not (34b), is true in a situation where
part of the women is short while the rest is tall.
10Essentially, we can view plural predication as expressing a relation between two sets - a
set of entities and a set of properties - where the Boolean interpretation can be expressed by
universal quantification over both of these sets, as follows:
(ii) rrThe women are short and tallss = 1 iff dxx, Py € woman ¢tshort, tallu : Ppxq
In order to derive the non-Boolean interpretation, we can ‘chip away’ at the Cartesian product
of woman and {short,tall} by removing ordered pairs until it is compatible with our lexical
knowledge - for example, this weakened relation may contain either the pair xw1, shorty or
the pair xw1, tally, but not both. The result is a set of new, weakened relations with the
mutual exclusivity of short and tall taken into account; the ‘Extended Strongest Meaning
Hypothesis’ states that the strongest of these relations (i.e. the maximal subsets of woman
¢ {short,tall} that are still compatible with our lexical knowledge) are used in evaluating
the truth of the sentence.
For our purposes, the precise workings of the ESMH are not important - the important
thing is that the above procedure is only defined for predication over pluralities, not for
singular predication. This means that the same mechanism cannot be applied to derive a
non-Boolean interpretation for (34b).
P- and Q-distributivity 45
3.3.4 P-distributivity with groups; conclusion
As we have seen, the availability of Q-distributivity can be used as a diagnostic
for semantic number, with the result that group NPs like the team and my
family are not semantically plural. However - and now we are finally back
to the question of empirical support for P-distributivity - group NPs are not
generally incompatible with distributive interpretations. We have already seen
some examples in (17). Here are a few others:
(36) a. The team smiled.
b. My family has blue eyes.
c. The jury got up and left the room.
The predicates in these sentences are all interpreted distributively according to
the definition in (3): all sentences in (36) can be accurately paraphrased by means
of (near-)universal quantification over the members of the collection expressed
by the subject. We interpret smiled in (36a) as something the individual team
members did, has blue eyes in (36b) as an individual characteristic of my
relatives, and got up and left the room as actions of individual jurors.
I conclude (contra Landman) that collections are fine as the subject of a
distributive predicate even if they are not semantically plural (so if we accept
Landman’s reasoning, this might imply that we have to rethink our conception
of the ‘agent’ role). This means that the data in (36) show that we cannot do
without the concept of P-distributivity: since we cannot explain distributivity
effects with groups in terms of ¦, we need to assume that distributive inferences
can also occur with semantically singular predicates, if the lexical semantics of
the predicate supports them. The data in this chapter thus show that we can
neither do without Q-distributivity, nor without P-distributivity: in order to
account for the full range of distributivity data, we need both as part of our
toolbox.
In the remainder of this chapter, I will tie up some loose ends considering the
formal implementation of P-distributivity (section 3.4) and the syntax of ¦
(section 3.5).
46 3.4. Embedding P-distributivity in our formal framework
3.4 Embedding P-distributivity in our formal
framework
Within the set-theoretical framework introduced in chapter 2, we will formalise
P-distributivity in terms of (singular) predication over impure atoms. (In fact,
by assuming a typeshift to impure atoms in chapter 2, I have already built
the necessity for something like P-distributivity into the system, since impure
atoms cannot really take part in meaningful predication structures otherwise.)
We will assume that uninflected atom predicates11
may range over both
pure and impure atoms, where an impure atom ÒX is in the extension of a
predicate P just in case the individual members of X are in the extension of P
(exactly how many individual members of X have to be members of P depends
on the lexical meaning of P and various other factors; cf. footnote 1, chapter 2).
I will further assume that, in order to receive an atomic interpretation, plural
NPs have to be mapped into impure atoms with Ò, while group NPs denote
impure atoms to begin with (this is a temporary assumption, just for present
purposes: in chapter 5 I will adopt a different analysis of group denotations
according to which they also start out as sets). This gives us the following
options:
(37) Possible logical forms underlying a P-distributive interpretation:
a. rrThe group is tallss = tall(the group)
b. rrThe boys are tallss = tall(Òthe boys)
3.4.1 A pseudo-formalisation of P-distributive inferences
All this does not actually tell us how P-distributive interpretations are derived
- merely what the compositional semantics of P-distributive sentences should
look like in order for said interpretation to be derivable. In Scha (1981), the
derivation of distributive and collective interpretations is governed by meaning
postulates on the predicate, for example:
11At least verbal and adjectival atom predicates. Many nominal predicates are not compatible
with group subjects in their singular form, which would mean under our current
assumptions that they do not include impure atoms in their extension. For example:
(iii) a. *This family is my guest.
b. *This couple is a dentist.
I do not know where this difference between verbal and adjectival predicates on the one hand
and nominal predicates on the other should come from.
P- and Q-distributivity 47
(38) walkpÒXq is interpreted as dx € Xrwalkpxqs12
A more recent version of Scha’s meaning postulates approach can be found in
Winter and Scha (to appear). Winter and Scha propose a pseudo-formalisation
of P-distributivity using pseudo-equivalences, which are non-logical and contextsensitive
equivalences (written with a squiggly arrow ú) between pairs of
statements, designed to capture the lexical semantics of certain expressions.
Just as the sentence pairs in (39a) and (39b) are pseudo-equivalent, so are the
pairs in (40):
(39) a. The table is white. úEvery part of the table is white.
b. The machine is broken. úSome part of the machine is broken.
(40) a. The boys are tall. úEvery boy is tall.
b. The books touch the ceiling. úSome book touches the ceiling.
What about predicates that are not necessarily interpreted distributively? As
is well-known, sentences can be vague between a collective and distributive
interpretation, or - given the right pragmatic context - fall somewhere in between
(the sentences in (41) are repeated from chapter 2; (42) is due to Schwarzschild
1996):
(41) a. Five boy/girl pairs played a game of chess against each other. (Each
of) the girls won.
b. Five girls played a football match against five boys. (*Each of) the
girls won.
(42) The shoes cost 50 dollars.
a. ð All the shoes together cost 50 dollars. (CI)
b. ð Each shoe costs 50 dollars. (DI)
c. ð Each pair of shoes costs 50 dollars. (intermediate)
According to Roberts (1987) and Hoeksema (1988), the existence of predicates
like win and cost 50 dollars poses a problem for an approach based on
meaning postulates, because this would force the meaning postulates (or pseudoequivalences)
to be optional. Winter and Scha do not explicitly address this, but
12I have adapted Scha’s formalisation to fit our particular semantic framework; in Scha’s
own analysis both singular and plural individuals are of type et and there is nothing like our
impure atom mapping, so his original formalisations look a bit different.
48 3.4. Embedding P-distributivity in our formal framework
it seems to me that the above interpretations could all follow from a meaning
postulate like (43) if we allow for different contextually salient granularities in
deciding what the ‘parts’ of an impure atom are (cf. Verkuyl and van der Does
1996).
(43) cost 50 dollarspxq údx1
rx1
is a salient part of x Ñ cost 50 dollarspx1
qs
(where x is an impure atom)
In an ordinary clothing shop, where shoes are priced and sold in pairs, a
partitioning of ‘the shoes’ into pairs of shoes might be the most contextually
salient; but if the shop went out of business and is selling its entire inventory in
bulk, the most contextually salient partitioning of ‘the shoes’ might be one in
which it has just a single part, namely the entire collection of shoes. By allowing
an impure atom to count as a part of itself, the collective interpretation of (42)
could be captured by the context-sensitive application of the meaning postulate
in (43).
If treating the collective interpretation of a predication over an impure
atom13
as a special case of distributivity in this way makes us feel uncomfortable,
it is possible to generalise our pseudo-equivalences in a way that captures both
collective and distributive interpretations without subsuming the former under
the latter:
(44) Ppxq údx1
rx1
is a proper part of x Ñ x1
participates in the event or
state associated with Ps
Context and additional lexical knowledge can fill in what it means to ‘participate
in the event or state associated with P’ for any given P. In the case of win, for
example, we know that there are two distinct ways to take part in a winning
event: either you defeat an opponent yourself, or a team that you are member
of defeats its opponent. In both cases, the pseudo-equivalence in (44) comes out
true, even though the right-hand statement does not allow an impure atom to
count as a part of itself.
3.4.2 Tying up another loose end: collectivity
The reasoning that lay at the basis of our adopting the notion of P-distributivity
- atom predicates are compatible with, and can be interpreted distributively with,
atom-denoting subjects - does not just hold for atom predicates. As evidenced
13This is the kind of collectivity that I will call ‘atom collectivity’ in section 3.4.2.
P- and Q-distributivity 49
by examples like (18), group NPs are also compatible with set predicates. This
means that set predicates should also be able to range over impure atoms, and
that collectivity effects may also be derived in two different ways:
(45) a. rrThe group gatheredss ògather(the group)
b. rrThe boys gatheredss = gather(the boys)
In both (45a) and (45b), we conclude that the gathering was done by the boys
or group members collectively, but the underlying logical forms are different.
In (45b), the collective inference is supported by the formal semantics of set
predication: plural, non-distributive predication over a set of entities. In (45a),
however, the formal structure of the predication is singular predication over
an impure atom, which, as we have seen, does not in itself support any kind of
inference about the individual involvement of group members: we need to rely
on the lexical meaning of the predicate gather to tell us that the sentence is a
statement about a collectively performed action rather than a distributive one
(cf. Scha’s analysis of collectivity inferences). This means that singular predication
over an impure atom is vague with respect to collectivity/distributivity
inferences: we are free to interpret it either collectively or P-distributively or
something in between, depending on the lexical semantics of the predicate and
our world knowledge.
I will call the two collectivity options in (45) ‘atom collectivity’ and ‘set
collectivity’, respectively (we could also think of them as ‘Scha-style’ and ‘Linkstyle’
collectivity, to emphasise the parallel with our discussion of the two
different ways to derive distributivity effects); the distinction is relevant to the
discussion in the next section.
(46) Possible predication forms and their interpretation
a. ¦PetpXetq: Q-distributive
b. Petpxeq, with x an impure atom: vague between P-distributive and
atom-collective
c. PpetqtpXetq: set-collective
3.5 Remarks on the syntax of Q-distributivity
In his original 1983 paper, Link conceived of pluralisation as a lexical phenomenon,
in which starred predicates entered the derivation directly from the
50 3.5. Remarks on the syntax of Q-distributivity
lexicon. An alternative view (which I will refer to as the ‘structural’ view) is
to regard the operator ¦ as a separate lexical item that combines with the
predicate compositionally. For example, in Sternefeld (1998); Beck (2001); Beck
and von Stechow (2007), ¦ has its own syntactic projection with the VP as its
complement; Sternefeld (1998) and Joh (2008) argue explicitly that ¦ is the
semantic translation of plural verbal morphology. See also Kratzer (2008) for
an overview of and comparison between both positions (Kratzer herself argues
for an analysis that incorporates both lexical and structural pluralisation).
It is easy to confuse the debate on where ¦ applies with the P- and Qdistributivity
distinction presented in this chapter, but it is not the same. In
the semantic framework I have developed in chapter 2 and the current chapter,
Q-distributivity is an unavoidable consequence of pluralisation with ¦ (and
therefore an inherent property of plural atom predication), while P-distributivity
is an optional, context-sensitive property of singular predication (so explicitly
not due to ¦). Seen in this way, any debate about where and how ¦ applies to
predicates is a debate about the nature of Q-distributivity, with no bearing on
P-distributivity.
That said, the distinctions between P- and Q-distributivity on the one
hand and between lexical and structural Q-distributivity on the other, while
technically independent, are not unrelated. As it turns out, many if not all the
Q-distributivity tests presented in section 3.2 of this chapter can also be used
as arguments in favour of a structural view of ¦ (and many of the arguments
in favour of lexical ¦ that Kratzer puts forward could also be accounted for in
terms of P-distributivity). Take for example the Q-distributivity test of VP
disjunction (section 3.2.1). As (47) shows, assuming that the denotations of
sang and danced are ‘born’ pluralised predicts that the sentence will be false in
a ‘mixed’ situation in which Sue and Jane sang and Mary danced, but in fact
we understand it as true in such a case.
(47) a. The girls sang or danced.
b. if rrsang or dancedss  rrsangss‰rrdancedss  ¦sing ‰¦dance,
then rrsang or dancedss  ttsueu, tjaneu, tsue, janeuu‰ttmaryuu
 ttsueu, tjaneu, tsue, janeu, tmaryuu
which means that tmary, sue, janeu ‚ rrsang or dancedss
Compare this to the derivation in (7), where ¦ applies to the entire coordinated
VP sang or danced: unlike the derivation in (47b), this derives the right truth
conditions for (47a). The fact that (47a) is true in a mixed situation thus
P- and Q-distributivity 51
supports an analysis in which predicates are ‘born’ singular and pluralised
somewhere in the course of the derivation, rather than one in which they enter
the derivation already pluralised. Moreover, it suggests that ¦ applies relatively
late in the derivation, at a level higher than VP.
In this section, I will provide some additional support for the latter conjecture,
based on the observation that VP coordination of a set predicate and a
Q-distributive atom predicate does not seem to be possible.
Dowty (1987) observes that it is possible to coordinate collective and distributive
predicates, as in (48) (the same point was made independently by Roberts 1987
and Lasersohn 1989):
(48) The students closed their notebooks, left the room and then gathered in
the hallway after class.
Dowty, who takes for granted that all distributive inferences are operator-based,
argues that this shows that the distributivity operator applies to individual
predicates, rather than to the subject NP (a third option, which he does not
consider but is also ruled out by this reasoning, is that it applies to the entire
VP coordination at once). However, this reasoning crucially depends on the
assumption that we cannot have distributivity without ¦, an assumption that
I have shown to be incorrect in this chapter. If closed their notebooks and
left the room are P-distributive, the intended interpretation can be derived
without needing a distributivity operator anywhere, by treating all coordinated
predicates as semantically singular and the subject as an impure atom. In
short, the coordination in (48) is not guaranteed to tell us anything about
the properties of ¦. The real question, therefore, is whether coordination of a
collective and a Q-distributive predicate is possible (or, to be even more precise,
coordination of a set predicate and a Q-distributive atom predicate).14
According to my own judgements15
, this does not actually seem to be the
case. Let us have a look at a couple of examples (‘DI’ and ‘CI’ here refer to the
interpretation of the second conjunct).
14The example often cited in later literature is Lasersohn’s (1989) ‘‘John and Mary met in
the bar and had a beer’’, which is compatible with a distributive interpretation of had a beer.
In the next chapter, I will argue why this, too, is not necessarily Q-distributivity despite the
involvement of an indefinite object. See also the final part of section 3.2.2.
15I have not done any systematic data-gathering here, although I have asked a couple of
other Dutch native speakers for their judgements and they mostly agreed with me. Still, it
would be worthwile to test this more systematically and in more languages.
52 3.5. Remarks on the syntax of Q-distributivity
(49) The guests are surrounding the happy couple and singing or dancing.
a. ô The guests are surrounding the happy couple and singing or the
guests are surrounding the happy couple and dancing. (CI)
b. ö The guests are surrounding the happy couple and for each guest
x, x is singing or x is dancing. (DI)
(50) John and Mary will meet in a bar and spot someone famous.
a. ô There exists a famous person x such that John and Mary will
meet in a bar and spot x. (CI)
b. ö John and Mary will meet in a bar and for each of them, there
exists a famous person x such that s/he will spot x. (DI)
(51) Jan en Marie moeten zonder ruzie uit elkaar gaan en goed voor hun kind
zorgen. (Dutch)
Jan and Marie must without fight from each.other go and well of their
child take.care
‘John and Mary should separate without fighting and take good care of
their child.’
a. ô John and Mary should separate without fighting and take good
care of the child they have together. (CI)
b. ö John and Mary should separate without fighting and each take
good care of their own child. (DI)
Comparing these examples and the available interpretations to the data in
(6), (8) and (14), we see that the Q-distributive interpretation systematically
disappears when the predicate is coordinated with a set predicate. In (49), all
the guests have to be either singing or dancing; there is no ‘mixed’ interpretation.
In (50), someone famous necessarily takes scope over John and Mary. And in
(51), hun kind ‘their child’ needs to refer to one child who is the child of both
John and Mary.
One way to interpret these data is as support for an analysis in which (some
appropriate version of) the distributivity operator applies to NPs, so that a
single NP cannot be semantically compatible with both a set and an atom
predicate (cf. Bennett 1974 and more recently Ouwayda 2011, 2014). But since
this would require an extensive revision of our background assumptions, we will
not explore this further here.
P- and Q-distributivity 53
Instead, I propose to account for this in terms of a third option not mentioned
by Dowty: ¦ applies not at the level of the VP itself, but higher, at the functional
level where verb inflection is located (IP) (cf. Roberts 1987). Another way of
putting this is that ¦ always has to be licensed by plural morphology - it is not a
freely available operation, like singularisation or impure atom formation. (This
idea also fits in nicely with our general approach of treating Q-distributivity as
a ‘side-effect’ of pluralisation.) So, if we have multiple coordinated VPs headed
by a single IP, there are only two options: either ¦ applies to its complement,
i.e. the intersection of all coordinated predicates, or it does not. When both
coordinated predicates are atom predicates, the result of applying ¦ to their
intersection is indistinguishable from taking the intersection of two starred
predicates:
(52) rrare singing and dancingss  ¦psing ˆdanceq
: ℘psing ˆdanceq¡tru
 p℘psingqˆ℘pdanceqq¡tru
 p℘psingq¡truqˆp℘pdanceq¡truq
=: ¦psingqˆ¦pdanceq
However, when one of the coordinated predicates is a set predicate, things
change. Since uninflected atom predicates range of atoms and uninflected set
predicates range over sets, they do not have the same type, and hence cannot
be coordinated (and even if we do allow for the coordination of differently-typed
predicates, their intersection will be empty). So the only way to interpret a
coordinated atom and set predicate when ¦ is not available at VP level is to
singularise the set predicate first. The result will be a set consisting of just the
impure atoms that are members of both predicates:
(53) rrgathering in a circle and dancingss 
gatherpetqt ˆdanceet type mismatch
pògatherqet ˆdanceet type mismatch resolved
ô tx ÒX | X € gather and x € danceu
So, from our assumptions in chapter 2 plus the stipulation that ¦ applies at IP
level, the only possible denotation of a coordination like gathered in a circle and
danced (if we rule out type mismatches) is a set of impure atoms. At this point
we could apply ¦; this would result in a predicate over sets of impure atoms,
appropriate for the denotation of a plural group NP (e.g. the committees).16
As
16For more on the semantics of group NPs, see chapter 5.
54 3.5. Remarks on the syntax of Q-distributivity
predicted, such a predication will be true iff each of the committees is gathering
in a circle and dancing (54). Alternatively, we could not apply ¦17
and end up
with a predicate over impure atoms, which could then be applied to any plural
subject, provided this gets mapped into an impure atom first (55).
(54) (¦ppògatherqˆdanceqqpthe committeesq
= 1 iff dx € the committees : x €ògather and x € dance
(55) ppògatherqˆdanceqqpÒthe girlsq
= 1 iff Òthe girls €ògather and Òthe girls € dance
ô the girls € gather and Òthe girls € dance
As we have seen, predications over impure atoms are vague between a Pdistributive
and an atom-collective interpretation; in the above case, the lexical
semantics of gather supports an atom-collective inference, and the lexical
semantics of dance a P-distributive one.
It should now already become clear how this analysis may account for
the lack of a Q-distributive interpretation of the second conjunct in predicate
coordinations like are surrounding the happy couple and [singing or dancing]:
because the denotation of such a coordination is necessarily a set of impure
atoms, the contribution of singing or dancing to that set are precisely those
impure atoms that are either members of sing or of dance. An impure atom
corresponding to a certain set X will be a member of a predicate P just in
case the members of X are also members of P. So singing or dancing only
contributes groups of singers and groups of dancers, not mixed groups consisting
of some singers and some dancers. This is the case regardless of whether or not
we apply ¦ to the set corresponding to are surrounding the happy couple and
[singing or dancing]. Formally:
(56) rrsurrounding the happy couple and [singing or dancing]ss 
surroundpetqt ˆpsinget ‰danceetq type mismatch
pòsurroundqet ˆpsinget ‰danceetq type mismatch resolved
 tx ÒX | X € surround and x € dance or x € singu
17I have been implicitly assuming that ¦ is optional, even for syntactically plural atom
predicates. The precise link between plural morphology and ¦ is something that any ‘structural’
theory of pluralisation will have to solve: to make the theory work, we need to assume that ¦
is licensed by plural morphology but not denoted by it. How to implement this formally is a
really interesting question that I will not however address here, because it seems to me that
the solution will require a considerable syntactic component that is beyond the scope of this
dissertation.
P- and Q-distributivity 55
So the observation that the Q-distributive interpretation of singing or dancing
seems to disappear when it is coordinated with a set predicate is accounted for
by our theory of plurality together with the assumption that ¦ may only apply
at the IP level.
Let’s sum up this section. The Dutch and English coordination data suggest
that VP coordination of a set-collective and a Q-distributive predicate is not
possible, which does not fit with a theory of pluralisation according to which
the ¦ operator applies to predicates at the level of the VP itself (either because
VPs are ‘born plural’, as in lexical theories of pluralisation, or because they
are pluralised in syntax immediately after entering the derivation). Instead, it
suggests that pluralisation happens at a syntactic level higher than VP; I have
proposed that it applies at IP, where it is licensed by the presence of plural
inflection. The upshot of this is that semantic pluralisation is closely related to
the presence of plural morphology; in chapter 5, I will provide more evidence
for this idea.
3.6 Conclusions
In this chapter, I have argued that distributivity effects can be derived in
two different ways: either by world knowlegde-based reasoning about parts
and wholes in relation to a predicate meaning (P-distributivity), or by covert
quantification over members of a collection, which is a direct effect of predicate
pluralisation with ¦ (Q-distributivity). P-distributivity is available with both
morphosyntactically plural NPs and with group NPs, but in both cases the
formal analysis is the same: singular predication over an impure atom. Qdistributivity
is available with plural NPs but not with group NPs, a contrast
that supports an analysis of groups as atomic entities.
In addition, I have presented some support for a structural, clausal analysis
of ¦, according to which it is not part of the VP itself but applies at a separate
syntactic level higher up in the derivation, where it is licensed by the presence
of plural number inflection.
CHAPTER 4
Polyadic P-distributivity and indefinites as properties
This chapter will be devoted to an issue that briefly came up in the previous
one: the analysis of distributivity in sentences with an indefinite object.
(1) The boys ate a pizza.
Sentences like (1), which have a distributive interpretation according to which
the boys ate a pizza each, have been used by e.g. Winter (1997); Brisson (1998) in
support of a quantificational, ¦-based account of distributivity. If the indefinite a
pizza is analysed as a quantifier and there are no other quantificational elements
in the sentence, a pizza will necessarily take scope over the entire sentence. This
results in a collective interpretation of (1) according to which a pizza was eaten
by the boys together, but it does not account for the distributive interpretation:
for this, Winter and Brisson reason, we need an additional quantifier over
individual boys that can take scope over a pizza. The pluralisation operator ¦
provides such a quantifier.
In chapter 3, we have analysed group NPs as atom-denoting, and argued
that this accounts for the fact that Q-distributivity is unavailable in sentences
with a group subject. Sentences like (1), however, provide a problem for this
account. If we replace the boys from (1) with a group NP, it would follow
from our analysis in chapter 3 plus the above reasoning that the distributive
interpretation should disappear. However, it does not: sentence (2) is just as
58 Chapter 4
ambiguous as sentence (1).
(2) The team ate a pizza.
a. ð There is a pizza x such that the team ate x. (CI)
b. ð For each team member y, there is a pizza x such that y te x. (DI)
The lack of contrast between (1) and (2) thus seems to provide a counterargument
for the atomic analysis of group NPs as argued for in chapter 3. Since this
particular analysis was an essential component of the empirical argument presented
in that chapter (according to which we need both P- and Q-distributivity
as part of our semantic toolbox), we may wonder how these data affect the
validity of this conclusion.
In this chapter, I will argue that it will not be necessary to revise our
particular analysis of group NPs and P-distributivity; rather, the claim that
sentences like (1) cannot be analysed without Q-distributivity is wrong. I claim
that the indefinite in (1) and (2) may be analysed as (an individual correlate
of) a property rather than a quantifier, which enables direct predication over
the indefinite and, by that means, P-distributivity over the instances of the
property it denotes. This means that the distributive interpretation of sentence
(2) (and possibly also (1)) can be regarded as a case of two-place P-distributivity,
comparable to the analysis of codistributivity cases in Scha (1981) and Winter
(2000).
The chapter is structured as follows. In section 4.1, I will take a closer look at the
relevant data and their possible implications for our theory of group NPs and
P-distributivity as presented in chapter 3. In section 4.2, I will account for these
data in terms of a property analysis of indefinites. In section 4.3 I will explore
two alternative accounts of the data, and show that none of them accounts
for the data as fully as the property analysis does. Finally, in section 4.4 I will
address some remaining issues, looking (among other things) at the interaction
of P-distributivity and number implicatures, so-called ‘stubbornly distributive’
predicates that lack expected P-distributive interpretations, and the problem
of assigning a property denotation to non-upward-entailing modified numerals.
Section 4.5 concludes this chapter.
Polyadic P-distributivity and indefinites as properties 59
4.1 Distributivity effects with group nouns and
indefinites
The truth-value judgements for (1) and (2) are complicated by the fact that
many English speakers cannot get a distributive interpretation for either of
these sentences unless the object is a dependent plural (‘‘The boys ate pizzas’’).
However, all of my informants who accept a singular in the case of (1) also
accept one in the case of (2). And in Dutch, where dependent plurality is
optional but the singular is preferred, the equivalent of (2) is unproblematic
(from this point on, I will not explicitly paraphrase the available interpretations
every time, but simply use ‘CI’ and ‘DI’ to indicate whether they are available):
(3) a. De jongens aten een pizza. (CI/DI)
The boys ate-pl a pizza
‘The boys ate a pizza’
b. Het team draagt een blauw shirt. (CI/DI)
The team wears a blue shirt
‘The team is wearing a blue shirt’
The apparent Q-distributivity over group nouns also happens with numerical
indefinites; examples like (4) seem to be fine in all varieties of English I have
encountered:
(4) This batallion received four insignia. (CI/DI)
Finally, group distributivity is available with both direct and indirect indefinite
objects:
(5) The children in Group A and Group B each made an origami animal.
Group A gave the animal to a teacher, Group B gave it to a parent.
(CI/DI)
How to account for this apparent exception to the generalisation established
in section 3.3.2? In principle, we have two ways out. The first is to reconsider
the analysis of groups as atoms and claim that in cases like the above, the
individual group members are accessible to the semantics, perhaps because
group denotations can shift into sets under certain circumstances. Such a shift the
opposite of our impure atom mapping Ò - is proposed by Landman (1989)
60 4.2. Analysis: P-distributivity beyond unary predicates
for independent reasons.1
This line is pursued by Magri (2012), who mentions
the distributive interpretation of sentences like (3-5) in support of his claim that
group NPs denote sets rather than atoms. While this solution would account
for the above data, it would also render the general pattern (as identified in
chapter 3) inexplicable, so going down this road creates more problems than it
solves.
The second way out is to claim that there is something special about
numerical and a-indefinites. It is this approach that I will develop here.
4.2 Analysis: P-distributivity beyond unary pre-
dicates
In this section, I propose that the group distributivity cases with indefinite
objects can all be accounted for if we analyse them as cases of P-distributivity.
While the examples of P-distributivity we have seen so far all involved intransitive
predicates, with distribution over a single argument, there is no a priori
reason that would limit P-distributivity to only one argument. Just as we can
analyse sentence (6a) in terms of direct predication over an impure atom (as
in (6b)), we can analyse a sentence like (6c) as a relation between two impure
atoms (as in (6d); cf. Scha 1981). And just as (6b) is vague with respect to
the involvement of particular individuals, (6d) is vague with respect to the
particular relations: we cannot tell if all the boys and all the girls were involved
1Landman proposes an operator Óthat shifts group noun denotations to their corresponding
pluralities (the set of the group’s members). According to Landman, we need this operator to
account for data like (i):
(i) The Talking Heads are pop stars.
In Landman’s analysis, the predicate are pop stars is a predicate over plural entities, which
would lead to a mismatch with the group-denoting The Talking Heads unless the latter is
able to shift into a set. But note that this only works (at least in American English) if the
group name is morphologically plural:
(ii) a. ??The Cure are pop stars.
b. *The committee are good managers.
The contrast between (i) and (ii) suggests that only groups with a morphologically plural
name may denote pluralities. But in that case, we cannot be sure that we are actually dealing
with groups: The Talking Heads might be an ordinary plural definite that denotes a plurality
of entities, each of them a Talking Head. So there seems to be little reason to enrich our
semantics with an operation that shifts atoms to their corresponding sets.
In any case, the Ó-operator does not seem central to Landman’s account of group semantics,
which is otherwise compatible with an atomic approach to groups.
Polyadic P-distributivity and indefinites as properties 61
in the kissing, how many boys were kissed by each of the girls or how many
girls kissed each of the boys, but we do know that individual boys were kissed
by individual girls.
(6) a. The girls laughed.
b. laugh(Òthe girls)
c. The girls kissed the boys.
d. kiss(Òthe girls,Òthe boys)
In order to be able to extend this analysis to cases of group distributivity with
indefinite objects, we cannot analyse the indefinite as a generalised quantifier
with existential force. Because there is no quantifier over group members,
an existential quantifier introduced by the indefinite would necessarily take
scope over the whole group, yielding (for example) (7b) as the only possible
interpretation of (7a):
(7) a. The First Aid team is wearing an orange vest.
b. There is an orange vest such that the First Aid team is wearing it.
(CI)
I propose that the indefinite in (7a) and similar sentences denotes a property,
which I view here as something very similar to a group - a higher-order entity
that allows P-distributivity over its individual instantiations. Thus, just as the
verb in (6c) denotes a relation between two pluralities, it denotes a relation
between a property and a group in (7a); and just as with (6c), any inferences
about individual members of the group or individual instances of the property
are due to P-distributivity, not based on quantification.
Neither the idea of property-denoting indefinites nor the idea of polyadic
P-distributivity is new. The latter was already assumed in Scha (1981) and
empirically motivated (although not very explicitly) in Winter (2000); the
former are the subject of a growing body of semantic literature. While classical
Montagovian semantics treats indefinite noun phrases as generalised quantifiers
with existential force, non-quantificational analyses of indefinites have been
proposed at least since Carlson (1977) and Milsark (1974), in which they can
denote kinds or properties, and the work of Kamp (1981) and Heim (1982),
in which they denote free variables. McNally (1992) and Zimmermann (1993)
propose that indefinites may also be interpreted as properties (of type xe, ty)
even outside of the predicate position, and this idea has subsequently been used
to account for a wide range of semantic phenomena.
62 4.2. Analysis: P-distributivity beyond unary predicates
McNally (1992) discusses property-type indefinites in relation to theresentences,
arguing that the traditional distinction between weak and strong
NPs of Milsark (1974) can be reduced to the distinction between propertytype
and quantificational NPs. de Hoop (1996) makes use of property-type
indefinites in her analysis of light verb constructions like take a walk or have
a drink. Zimmermann (1993, 2006) proposes that opaque verbs like seek take
property-type arguments. Van Geenhoven (1998) links the property analysis
of indefinites to the syntactic phenomenon of noun incorporation, proposing a
semantic counterpart of this operation that is also argued for in Farkas and
de Swart (2003) and Chung and Ladusaw (2004), among others. Assuming that
indefinite PP complements denote properties, Mador-Haim and Winter (2007,
2012) argue that a puzzling contrast between the interpretations of certain PPs
follows naturally.2
There are several definitions of what precisely counts as a property-type
indefinite; I follow e.g. Chierchia (1998) in defining them as those indefinites
that are allowed in predicative position. Thus, the NPs in (8a-b) count as
properties, the ones in (8c) do not:
(8) a. John is
#
a doctor.
a friend of mine.
+
b. John, Mary and Sue are
#
doctors.
three friends of mine.
+
c. John is
$
'&
'%
*some doctor.
*some friend of mine.
??a doctor I met at a conference ages ago.
,
/.
/-
3
A recurring question in the literature on property indefinites in argument
position is how they compose with the predicate. After all, unless the relevant
predicates are systematically ambiguous, there is a type mismatch between the
argument (which is of type xe, ty) and the predicate function (which wants an
entity). In principle, there are two ways to go about this: there might be some
special operation that composes verbs and property-type arguments (e.g. Chung
& Ladusaw’s Restrict or Van Geenhoven’s Semantic Incorporation), or the
2See also section 4.3.2.
3The third sentence is not ungrammatical per se, but it is much more likely to be
interpreted as an identity statement: an answer to the question ‘Who is John?’ rather than
‘What is John?’, where a doctor I met at a conference ages ago is an argument and not a
predicate.
Polyadic P-distributivity and indefinites as properties 63
property might shift into its entity correlate (cf. Chierchia 1984, 1985; McNally
1992; Mueller-Reichau 2006; McNally 2009). I think the second approach is the
most appropriate in this case: we have been talking about P-distributivity as
involving reasoning about entities with a salient part-whole structure, and an
individual correlate of a property seems just this kind of thing.
What, then, is an individual correlate of a property? Chierchia (1984, 1985),
following a much earlier observation by Frege, notes that we can attribute
properties to entities but also to other properties, suggesting that properties
can function both as predicates and as arguments:
(9) a. The sky is blue.
b. (Being) blue is beautiful.
He proposes a typeshift X
that turns properties (type xe, ty)4
into their entity
correlates (type e), such that (9a-b) can be analysed as follows:
(10) a. blue(the sky)
b. beautiful(X
blue)
The semantics of our polyadically P-distributive sentence The team is wearing
an orange vest, then, can be derived according to the following steps:
(11) Let
rrthe teamss = the team (type e)
rran orange vestss = rrorange vestss = orange vest (type xe, ty)
rris wearingss = λxλy[(wear(x))(y)] (type xe, ety)
X
= a function of type xet, ey
Then:
(i) λxλy[(wear(x))(y)](orange vest) (type mismatch)
Following the common assumption that a type mismatch may trigger a typeshift
(if an appropriate typeshift is available in the grammar), we apply X
and the
derivation proceeds as follows:
(12) (ii) λxλy[(wear(x))(y)](X
orange vest)
(iii) λy[(wear(X
orange vest))(y)]
(iv) λy[(wear(X
orange vest))(y)](the team)
(v) (wear(X
orange vest))(the team)
4Or actually type (type xsxetyy) - Chierchia analyses properties as intensional functions.
For simplification, I will follow the example of Partee (1987) and McNally (2009) and
misrepresent X as an extensional typeshift from sets of entities to entities.
64 4.2. Analysis: P-distributivity beyond unary predicates
Chierchia’s X
operator is very similar to our impure atom typeshift Ò- both turn a
set into an entity that, while being semantically singular, has a salient conceptual
part-whole structure reflecting its close relationship with its corresponding set.
The impure atom the team is semantically singular, but conceptually it still
refers to a collection of individuals; similarly, the property X
orange vest is
semantically singular, but conceptually the parts that ‘make up’ this property
entity are individual orange vests. I will refer to this kind of semantically singular
but conceptually plural entities as higher-order entities. I will not conflate the
two different operations that produce them (Ò and X
), however, since completely
eliminating the formal difference between impure atoms and properties leads to
problems when trying to capture the interpretation of verbs like wear using
the kind of pseudo-equivalences we have seen at work in chapter 3 (section
3.4.1). In (13), we see how a pseudo-equivalence can be used to interpret a
wear-relation between an impure atom and a property5
:
(13) For every impure atom x and property X
y:
wearpx,X
yq údx1
rx1
is a part of x Ñ hy1
€ yrwearpx1
, y1
qss
Note that this postulate has nothing to say about the orange vests that are
not worn by a member of the team; the only thing that is required (with
the room for vagueness and context-dependency that is characteristic of these
pseudo-equivalences) is that each team member is wearing a vest. But this is
not the interpretation that wear(x,y) receives if y is a higher-order individual
associated with a referential NP like the orange vests or the 2014 summer
collection in (14):
(14) The team is wearing
#
the orange vests
the 2014 summer collection
+
.
For this sentence to be true, it is not enough that every team member is wearing
an orange vest or an item from the summer collection: it must also be true
that each of the orange vests or items from the collection is worn by a member
of the team. So, incorporating the pseudo-equivalence in (13) into the lexical
5In the rest of this chapter, I will often simply talk about ‘properties’ as a shorthand for
‘individual correlates of properties’, not just to save time and space but also because ultimately
it does not really matter what implementation we choose. I have chosen to formalise the
property-based account of polyadic P-distributivity in terms of entity correlates just to make
the semantics more explicit, but if future work should show that there is actually some kind of
Semantic Incorporation at work here, the idea behind this analysis would not be invalidated.
The important point is that the indefinites in question denote properties, and it is this point
that I will stress in the remainder of this chapter.
Polyadic P-distributivity and indefinites as properties 65
semantics of wear is not enough. We also need the postulate in (15) (cf. Scha
1981):
(15) For all impure atoms x and y:
wearpx, yq údx1
rx1
is a part of x Ñ phy1
ry1
is a part of y”wearpx1
, y1
qsqs”
dy1
ry1
is a part of y Ñ phx1
rx1
is a part of x ”wearpx1
, y1
qsqs
To sum up, since higher-order entities corresponding to referential NPs are
interpreted differently when it comes to two-place P-distributive relations than
higher-order entities corresponding to properties, I will keep the two apart in
our notation: Ò derives the former, X
the latter.
4.2.1 Additional evidence for a property analysis
Co-argumenthood
The polyadic P-distributivity approach predicts that in order to get P-distributivity
with both a group and a property, they have to be arguments of the same
predicate (see Sauerland 1994; Winter 2000, for a similar point in a different
context). This is because P-distributivity is a lexical phenomenon: it is rooted
in the relationship between a predicate and its (higher-order) arguments, as
captured by pseudo-equivalences like the ones in (14) and (15). And as (16b)
shows, sentences with a group subject where the indefinite does not directly
compose with the predicate seem to lack a DI (the judgements are admittedly
subtle):
(16) a. The children will get upset if a drawing is taken off the wall.
ð For every child x, there is a drawing y such that x will be upset
if y is taken off the wall. (DI)
ð For every child x, x will be upset if there is a drawing y such that
y is taken off the wall. (CI)
b. The class will get upset if a drawing is taken off the wall.
ö For every child x, there is a drawing y such that x will be upset
if y is taken off the wall. (DI)
ð For every child x, x will be upset if there is a drawing y such that
y is taken off the wall. (CI)
Consider the following situation. Ms Smith, an art teacher, has picked one
drawing from each of the pupils in her class to put up on the wall of her
classroom. But over time, wall space has become limited and Ms Smith fears
66 4.2. Analysis: P-distributivity beyond unary predicates
she’ll have to remove some of the drawings. Now, imagine that Ms Smith’s class
is a very close-knit group, and Ms Smith knows that if she removes any of their
drawings, the entire class will be upset. In this situation, both (16a) and (16b)
are true.
We might also imagine that the children in Ms Smith’s class are not so close
to each other, but they are quite insecure about their own talents. Ms Smith
knows that they will not care much if the drawing of one of their classmates
is taken off the wall, but each of them will be quite upset if his or her own
drawing gets removed. Now, (16a) is true but (16b) is not.
This is what the polyadic P-distributivity approach predicts: since the
indefinite a drawing is not an argument of the predicate get upset, it cannot be
related to the class or the children by P-distributivity. In the case of (16a), the
DI can still be the result of Q-distributivity, but that option is unavailable for
(16b), which has a group noun subject. Thus, the contrast between (16a) and
(16b) follows.
This coargument requirement is similar in spirit to the way indefinite objects
are treated in the semantic incorporation literature, in which predicate and
indefinite object are often analysed more like a complex intransitive predicate
than like a predicate with one argument saturated. Both the coargument
requirement on P-distributivity and the ‘incorporation’ accounts of propertytype
objects emphasise the lexical character of this close bond between predicate
and object (cf. Carlson 2006).
Underspecification versus ambiguity6
In the present analysis, binary P-distributivity is analysed as a relation between
two higher-order entities that is underspecified with respect to the relations
that hold between particular members or instantiations of these entities. This
also means (as already argued in section 3.1) that the difference between
P-distributivity and atom collectivity is a matter of vagueness, not ambiguity.
Now that I have hypothesised that P-distributivity is not limited to oneplace
predicates, we can put this hypothesis to the test by using a well-known
ambiguity test: VP ellipsis. The examples in (17) show how VP ellipsis can
distinguish underspecification from ambiguity:
(17) a. The floor is clean and John’s scalpel is, too.
6Thanks to Lucas Champollion (p.c.) for pointing out this issue and the VP-ellipsis test
to me.
Polyadic P-distributivity and indefinites as properties 67
b. An American flag was hanging in front of every building, and a
Dutch flag was, too.
Sentence (17a) can be true even if the notion of cleanliness is quite different for
a scalpel than it is for a floor: clean is underspecified with regard to the level of
cleanliness required, and nothing stops both conjuncts from being specified in
different ways (the floor is clean because there’s no visible dirt on it; the scalpel
is clean because it is completely sterile). In (17b), on the other hand, it is not
possible to assign different interpretations to both conjuncts: if we interpret
the first conjunct with surface scope, we have to interpret the second conjunct
with surface scope as well, and the same goes for the inverse scope reading.
Assuming that VP ellipsis is only possible if the second conjuncts semantically
parallels the first, this means that scope ambiguities should be reflected in the
logical form of a sentence, while levels of cleanliness should not.
If the distinction between P-distributivity and collectivity is like the distinction
between sterile and not visibly dirty, we expect to be able to assign different
interpretations to the conjuncts of a VP ellipsis structure. If, on the other hand,
the distinction is a matter of ambiguity, we expect that both conjuncts should
receive the same interpretation: either both collective, or both distributive. The
example in (18) suggests that the first option is the right one:
(18) The adults had a pizza and the children did too. Only the children had
to share a pizza with each other, while the adults each got their own.
The judgement is a bit subtle here, but I believe that the second sentence in
(18) does not contradict the first; most of my English-speaking informants also
agreed that there is no contradiction. This suggests that the difference between
P-distributivity and collectivity is a matter of vagueness: there is nothing in
the formal semantics of the sentence that enforces a particular pizza-to-people
ratio (Kratzer 2008, makes a very similar point).
A caveat is needed at this point: not all cases of vagueness are well-behaved
with respect to the VP-ellipsis test. For example, in sentence (19), it is very
hard (if not impossible) to interpret the overt VP as ‘start-to-cook’ and the
elided one as ‘start-to-eat’:
(19) John started dinner, and Mary did, too. ??Only John started cooking his
dinner and Mary started eating hers.
Still, we probably would not want to claim that start x should be ambiguous
68 4.3. Alternatives to the P-distributivity analysis
between ‘start to cook x’ and ‘start to eat x’ (and, presumably, ‘start to read
x’, ‘start to write x’, ‘start to sing x’, ‘start to smoke x’ and dozens more).
Similarly, mixed collective/P-distributive interpretations are not always as
acceptable as (18) suggests. For example, it is not very easy to get a mixed
interpretation in the following case:
(20) The red team carried a piano upstairs and the blue team did, too. ?Only
the members of the red team carried a piano together and the members
of the blue team each carried one individually.
Thus, it seems that the VP ellipsis test is mainly useful for distinguishing
a subset of the vagueness cases from the rest of the vagueness cases plus
ambiguity: if different interpretations are possible, we are definitely dealing
with underspecification, if they are not, it could be either underspecification
or ambiguity. While cases of ambiguity fail the VP-ellipsis test for semantic
reasons, the reason that some cases of vagueness fail may be more pragmatic:
the use of a VP ellipsis construction implicates that we are talking about very
similar situations (if not, we would probably have given more information),
and starting to cook and starting to eat (or, carrying a piano singlehandedly
and being one of many carriers) may simply not be ‘similar’ enough to merit this.
Even if mixed collective/P-distributive interpretations of VP ellipsis constructions
are not always fully acceptable, the fact that mixed interpretations are
possible in at least some cases shows that they are not ruled out by the semantics.
They might be marginal for pragmatic reasons, but so are other cases of
VP-ellipsis with underspecified predicates (like start). All in all, the VP-ellipsis
test gives us reason to assume that an account of the distinction between
collectivity and P-distributivity in terms of vagueness is on the right track.
4.3 Alternatives to the P-distributivity analysis
In this section, I will discuss two alternative analyses of the group distributivity
data that do not involve property-type indefinites: group credit and quantification
over kinds. I argue that neither of these alternative approaches is able to
fully account for the data.
Polyadic P-distributivity and indefinites as properties 69
4.3.1 Group credit7
One might argue that we could analyse group distributivity as a special case
of a ‘group credit’ interpretation, which in turn is a special case of collectivity.
Consider the following sentence:
(21) The team is holding up a trophy.
Sentence (21) can be true if only one of the team members (say, the captain) is
actually holding a trophy: because the captain represents his team in doing so,
the entire team ‘takes credit’ for the trophy-holding and (21) can be considered
true on its collective interpretation. Similarly, we might say that if some
representative proportion of the team is wearing a blue shirt, the team as a
whole is wearing a blue shirt, and therefore the collective sentence The team
is wearing a blue shirt can be true in a ‘distributive’ situation where each
individual team member is wearing their own shirt.
If group distributivity is a special case of group credit, it should behave in a
similar way. In particular, we expect the group-distributive reading to persist
under an existential paraphrase, just as happens with the group credit-reading
of our trophy sentence: both (21) and its existential paraphrase in (22a) are
verified by a situation in which some representative member of the team (and
no one else) is holding up the trophy. However, the same relation does not hold
between the group-subject sentences in (22b-c):
(22) a. There is a trophy that the team is holding up.
b. The team is wearing a blue shirt.
c. There is a blue shirt that the team is wearing.
Unlike (22b), sentence (22c) cannot be interpreted distributively - it is false in a
situation in which every team member is wearing his or her own blue shirt (unless
we read a blue shirt as ‘a kind of blue shirt’). So while group credit interpretations
persist under an existential paraphrase, group-distributive interpretations do
not. This contrast between group credit and group distributivity cannot be
explained under an analysis that treats them as essentially the same phenomenon.
I therefore conclude that this kind of analysis cannot fully account for the group
distributivity data.
7This alternative analysis was suggested to me by Roger Schwarzschild (p.c.)
70 4.3. Alternatives to the P-distributivity analysis
4.3.2 Quantification over kinds
The second alternative analysis is based on the aforementioned observation
that sentence (22b) is compatible with every individual team member wearing
their own shirt if we interpret a shirt as ‘a kind of shirt’. From this, we might
conclude that the group distributivity effect in The team is wearing a blue shirt
is a matter of quantification over kinds as well: the noun shirt does not denote
a set of ordinary objects but a set of kinds (each of them a subkind of shirt),
and The team is wearing a blue shirt is interpreted as the assertion that there is
a subkind of shirt (say, the polo shirt) of which the team members are wearing
instantiations. Again, this assertion is compatible with a situation in which
every team member is wearing their own shirt.
Quantification over kinds may be able to explain part of our group distributivity
data - it is hard, if not impossible, to prove that it is not involved but
it does not explain all of it. In particular, there is a contrast between aand
some-indefinites that would remain quite mysterious under this analysis.
Consider the following data:
(23) a. A rare owl was sighted in this forest recently.
b. Some rare owl was sighted in this forest recently.
(24) a. The team is wearing a blue shirt.
b. The team is wearing some blue shirt.
The pair of sentences in (23) shows that some-indefinites can quantify over
kinds as easily as a-indefinites can: (23a) and (23b) are both grammatically
correct, and truth-conditionally equivalent. However, this is not the case for
the sentences in (24), which are both grammatical but do not have equivalent
meanings. Sentence (24b) requires that every team member is wearing the
same kind of blue shirt; if half of the team is wearing a polo shirt and the
other half a button-down shirt, the sentence is false. This follows when we
analyse the sentence in terms of existential quantification over kinds. However,
(24a) can be true in such a situation, which cannot be explained under a
quantification-over-kinds analysis.
Here is another way to capture the difference between the data with a and
some. While (24a) is truth-conditionally equivalent to its existential paraphrase,
this does not hold for (24b), as shown here:
(25) a. The team is wearing some blue shirt
ô There is some blue shirt that the team is wearing.
Polyadic P-distributivity and indefinites as properties 71
b. The team is wearing a blue shirt
÷ð There is a blue shirt that the team is wearing.
Under a fully quantificational analysis, we expect all the sentences in (25) to
be equivalent. However, this is only the case for the pair in (25a). The pair of
sentences in (25b) is not truth-conditionally equivalent because the first allows
for a multiple-kinds-of-shirt interpretation while the second, like its counterpart
with some, does not. It follows that the truth conditions of the first sentence
are not fully captured by a quantificational analysis of the indefinite.
Concludingly, while quantification over kinds is able to account for certain
distributivity effects with groups in the case of some-indefinites, it fails to fully
account for the data involving a-indefinites.
Under the P-distributivity analysis, the difference between a and some can be
accounted for in terms of their ability to form property-denoting NPs: while
a-indefinites can easily be analysed as properties, some-indefinites are nearly
always quantificational. We find this difference between a and some with
nearly all of the previously-mentioned phenomena that have been argued in the
literature to involve property-type indefinites (the judgements below are my
own, not the original authors’):
(26) Be-predicates:
a. John is a linguist.
b. John is #some linguist. (on the intended interpretation)
In (26a), it is predicated of John that he is a linguist - a linguist is of type xe, ty
and the sentence is entirely on a par with, for example, a sentence like John is
tall. In contrast, (26b) cannot express such a simple predication. Its most readily
available interpretation is a taxonomic one that may be paraphrased as ‘John is
a (specific or nonspecific) kind of linguist’; in addition, it has an (albeit slightly
strange) identity reading with is as a full verb, paraphraseable as ‘There is
some linguist and this person is John’. Neither reading involves a predicate
linguist of type xe, ty, suggesting that this is not a possible denotation for the
indefinite some linguist. Similarly:
(27) Opaque verbs (Zimmermann 1993, 2006):
a. John is looking for a secretary.
b. John is looking for some secretary.
72 4.3. Alternatives to the P-distributivity analysis
On its opaque reading, (27a) is interpreted to mean that John is looking for any
secretary, not a particular one; it also has a transparent reading according to
which there is a particular secretary that John is looking for. In contrast, I am
unable to get the opaque reading for (27b): it only has the transparent reading
(in addition to a ‘some kind of’-reading comparable to the one in (27b)). If we
claim, with Zimmermann, that opaque readings result when the verb takes a
property-type complement, this again suggests that property denotations are
unavailable for some-indefinites.
(28) Eigenspace semantics (Mador-Haim and Winter 2007):
a. We’re far from a gas station.
b. We’re far from some gas station.
The same pattern again appears in (28a-b). Sentence (28a), despite the fact
that it involves an indefinite object, has a prominent ‘universal’ interpretation
according to which we are far from all gas stations. This can be accounted for
under the assumption that a gas station denotes a property. According to the
spatial semantics adopted by Mador-Haim and Winter, the location function
associated with the preposition, when applied to a property, returns the location
or ‘eigenspace’ of the entire set of gas stations, rather than that of a particular
individual gas station. Being far from a collection of elements entails being far
from each element in the collection, hence the universal interpretation. Again,
this interpretation does not seem to be available with the some-indefinite in
(28b).
Finally, there are light verb constructions like have a smoke, take a walk
or make a fuss, where the verb is semantically (nearly) empty and all content
is provided by the indefinite noun (such that the aforementioned examples
may be paraphrased by a verb - to smoke, to walk, to fuss - without loss of
information):
(29) Light verbs (cf. de Hoop 1996):
a. John took a walk.
b. John took some walk.
Unlike the light verb reading of (29a), (29b) cannot be paraphrased as ‘John
walked’ without loss of information, because unlike (29a) it asserts that there
exists a particular walking route that John took. In contrast, the a-indefinite
in (29a) shows all the signs of property denotation: it is nonspecific, number
Polyadic P-distributivity and indefinites as properties 73
neutral, and scopes with the verb. Again, the some-indefinite only seems to
have a quantificational interpretation, while the a-indefinite can denote either
a quantified expression or a property.8
All in all, if we take the claims made in the literature about the kind of
linguistic phenomena that rely on property-type indefinites at face value, the
above contrasts suggest that property denotations are not available, or at least
much less readily so, for some-indefinites than they are for a-indefinites. Since
the P-distributivity approach attributes certain group distributivity effects
to the involvement of property-type indefinites, it predicts (correctly, as we
have seen earlier in this section) that these effects will be easily available with
a-indefinites, but not with some.
4.4 Remaining issues
In the next two sections, we take a look at two cases that show that the
available interpretations of a predication over an impure atom are not always
fully determined by world knowledge or reasoning about parts and wholes. In
this section, I argue that P-distributivity also involves the relativisation of
number implicatures to individual group members, which puts a limit on the
number of interpretations a group-distributive sentence may have. Section 4.4.2
discusses cases where P-distributivity is completely unavailable.
4.4.1 P-distributivity and implicature
Consider the following data:
(30) a. #The team is wearing a blue sock.
b. The team is wearing two blue socks / a blue and a green sock.
Sentence (30b) is fine in a situation where every team member is wearing two
socks; (30a), though, is very odd. This number sensitivity is unexpected if we
analyse (30a) as expressing a relation wear between the group the team and
the property X
blue sock. World knowledge tells us that socks tend to be worn
in pairs, so if the pseudo-equivalences governing our interpretation of predicates
like wear are really as context-sensitive as I have claimed (following Winter and
8With existential there-sentences (which (McNally 1992) argues involve property-type
NPs), the contrast is less clear - There is some cat in the garden is fine, and although a
taxonomic kind reading (‘some kind of cat’) seems the most readily available, it also has a
reading on which its meaning is identical to that of There is a cat in the garden.
74 4.4. Remaining issues
Scha to appear) in sections 3.4.1 and 4.2, there might well be a P-distributive
interpretation of such a relation that links single team members with pairs
of socks. And yet this interpretation is out. If wear(the team,X
blue sock)
is vague with respect to the particular relationships that hold between team
members and blue socks, why does (30a) only seem to mean that the team
members are each wearing just a single sock?
The fact that the statement in (30a) seems more odd than false suggests
that the manifested number sensitivity is pragmatic in nature. Compare the
oddness of (31) (uttered while I am perfectly aware that I own two guinea pigs):
(31) #I have a guinea pig.
While (31) is strictly speaking true in a world in which I have two guinea pigs,
it is infelicitous because the use of a singular indefinite triggers the implicature
that I have only one - after all, if I did have more than one guinea pig, I could
just as easily have made the stronger claim I have two guinea pigs. Similarly,
sentence (30a) is infelicitous because it implicates that the team members are
wearing just a single sock.
Support for the claim that the number sensitivity in (30a) is an implicature
comes from the fact that, like other implicatures, it can be cancelled:
(32) The team is wearing a blue sock. In fact they’re wearing two of them.
The number implicature triggered by the use of a singular indefinite - ‘not more
than one sock’ - is relativised to individual group members (the situation as a
whole may well involve many more socks than one). From this, we can conclude
that P-distributivity does not just link the semantic content of a predicate to
individual members of a higher-order entity: any implicatures associated with
the predicate are carried along to the individuals as well.
4.4.2 Stubborn distributivity and weigh-predicates
In discussing P-distributivity, I have so far been talking about ‘lexical semantics’
and ‘world knowledge’ in a rather loose way, as if the former is merely a way of
capturing the latter a bit more formally. But I do not want to suggest that this
is the case. Of course, the two are closely related; however, the lexical semantics
of a word may impose restrictions on its meaning that do not seem to have
anything to do with our understanding of how the world works. Some predicates
do not seem to be vague between a collective and a P-distributive interpretation,
even though this might very well be possible according to our knowledge of the
Polyadic P-distributivity and indefinites as properties 75
world. For example, according to Schwarzschild (2009), sentence (33a) has no
interpretation under which it means the same as (33b), and vice versa:
(33) a. The boxes are large.
b. The collection of boxes is large.
According to Schwarzschild’s judgements, sentence (33b) can only mean that
the collection itself is large, not that the boxes that make up the collection are.
Sentence (33a) has the opposite meaning: it can only be used to express that
the individual boxes are large, not that the boxes together are (compare The
boxes take up a lot of space, which means roughly the same but does have a
collective interpretation in addition to a distributive one). World knowledge
tells us that largeness can be a property of individuals as well as collections,
so why are not both of the sentences in (33) vague between two interpretations?
Schwarzschild (2009) suggests that predicates like large, which he calls
‘stubbornly distributive’, can only apply to single-participant events, which
rules out a collective interpretation for (33a) (the boxes together are large). In
principle, this approach is not incompatible with the current one - stubborn
distributivity is still a lexical property of the predicate and could easily be
captured in the form of a pseudo-equivalence. Still, cases like these tell us that
delegating semantic tasks to ‘world knowledge’ or ‘context-sensitivity’ easily
leads to overgeneration if we do not carefully define what we mean by this.
In addition to the stubbornly distributive predicates, there are other predicates
that seem to lack a distributive interpretation when they occur with a
group subject. An example is weigh:
(34) a. These athletes weigh 60 kilos.
b. This team of athletes weighs 60 kilos.
Weigh 60 kilos is not stubbornly distributive: sentence (34a) is vague between a
distributive and a collective interpretation. However, (34b) seems unambiguously
collective. Again, it is not clear why the P-distributive interpretation is
unavailable in the latter case, as nothing in our world knowledge would rule it
out (in fact, it is a much more likely interpretation than the collective one).
I do not see an immediate explanation for these facts, but I would like to
leave open the possibility that the ‘missing’ P-distributive interpretation of
The team is large and The group weighs 60 kilos are not actually blocked, but
(for some reason) need to be made extremely salient by context before they
become acceptable. (Of course, this would in itself require an explanation.) For
76 4.4. Remaining issues
example, I am not so sure that The group weighs 60 kilos cannot be interpreted
distributively in the following context:
(35) The contestants in this boxing match have been divided into three different
weight classes. Watch them enter the arena in groups corresponding to
their weight class! The first group weighs up to 80 kilos, the second group
weighs 80-100 kilos, and the third group weighs 100 kilos and up.
And similarly for large:
(36) A family of four, all renowned hamburger-eating champions, wants to
book seats for tonight’s performance of Hamlet. We’d better bring in some
plus-size chairs, because this family is large.
If this were true, and we could bring out the ‘missing’ distributive interpretations
in the right context, the only thing that would be left to explain would be the
lack of collectivity effects with stubbornly distributive sentences like The boxes
are large. As this issue is independent of the present analysis, I will leave it for
further research (see Schwarzschild 2009 for an event-based analysis of stubborn
distributivity).
4.4.3 A remark on modified numerals
A case of binary P-distributivity I have not mentioned so far involves modified
numerical indefinites:
(37) The battalion received
$
'&
'%
exactly one medal.
less than four medals.
at most two medals.
,
/.
/(37)
is true if every member of the battalion received the number of medals
mentioned, so under our analysis of group distributivity, the indefinites in (37)
should be able to denote properties. Modified numerals may also appear in de
dicto readings with opaque predicates (38a), there-sentences (38b) and with
be-predication (38c):
(38) a. Lily wants to adopt exactly four orphans.
b. There are less than four cats in the garden.
c. These are exactly / at most 20 dots.
According to the latter fact, they count as property indefinites under our definition;
considering their analyses of de dicto readings and existential sentences,
Polyadic P-distributivity and indefinites as properties 77
Figure 4.1: An array of dots (cf. sentence (38c))
respectively, Zimmermann and McNally also need to claim that they denote
properties.
However, a property analysis of these modified numerals is problematic
(McNally 1992). Because they are not upward entailing, exactly n, less than
n or at most n exhaustively cover a domain: (38a) is incompatible with Lily
wanting to adopt more than four orphans, and (38b) is incompatible with
there being more than three cats in the garden. In other words, stating that a
predicate P holds for exactly n or at most n entities also amounts to stating
that P does not hold for the rest of the entities in the domain. This contrasts
with unmodified numerical indefinites like four orphans or two cats, which are
monotone increasing and hence compatible with the existence of more orphans
or more cats of which the expressed property holds.
All this means that it is unclear how the truth conditions associated with
the nonincreasing modified numerals in (37) and (38) could be derived without
quantification over the domain of medals, orphans or cats; and yet, their
appearance in sentences like (37) and (38) seems to call for a non-quantificational
analysis.
McNally (1992) proposes to solve the problem by assuming that exactly and
at most do not modify the indefinites themselves; rather, they should be treated
as adverbial modifiers comparable to only or even. Evidence for this claim is
the fact that exactly and at most can appear in other positions in the sentence
without changing its semantics:
(39) a. At most, there were four cats in the garden.
b. Lily wants to adopt four orphans exactly.
78 4.5. Conclusions
In McNally’s analysis, exactly and at most are applied to propositions associated
with ordered alternative sets; essentially, rrat mostssppq or rrexactlyssppq means
that there are no true propositions in this alternative set that are ranked higher
than p. Thus, rrat mostssprrthere were four cats in the gardenssq would be false
if the alternative proposition There were five cats in the garden were true, since
the latter (a semantically stronger statement) is ranked higher than the former.
Although this analysis technically solves the problem for at most and exactly,
it leaves less than unaccounted for - we would not want to claim that less than
is a propositional modifier. It seems that a truly satisfying property analysis
of non-upward entailing modified numerals, that does not result in the wrong
truth conditions, has yet to be given. I will not attempt to do so here, but leave
it as an open question.
4.5 Conclusions
We started out this chapter with an apparent counterexample to the analysis
of group NPs (and, consequently, to our empirical argument in favour of Pdistributivity)
that was presented in chapter 3. However, I argued that this
apparent case of Q-distributivity with group nouns - sentences with an indefinite
object like The team is wearing an orange vest - can be analysed in terms of
P-distributivity if we assume a property analysis of the a-indefinite, following
much recent literature. Additional evidence for this idea comes from VP ellipsis,
which supports the claim that the difference between P-distributivity
and collectivity can be a matter of vagueness rather than ambiguity, and the
requirement that the subject and the indefinite be co-arguments of the same
predicate. Further, I discussed two quantificational alternatives to the polyadic
P-distributivity analysis - ‘group credit’ as a special case of the collective interpretation,
and quantification over kinds - and concluded that they can not
account for the full range of distributivity data with groups. The chapter ended
with a couple of additional and unresolved issues, and suggestions for further
research.
The ‘moral’ of this chapter and the previous one can be summed up as follows:
wherever we find higher-order entities with a clear part-whole structure, there
will be distributivity - not because of any formal semantic operation, but
because of the way we reason about parts, wholes and predicate meanings.
Since distributivity is not a unified phenomenon, we should be careful to draw
Polyadic P-distributivity and indefinites as properties 79
conclusions about the formal semantic analysis of sentences involving pluralities
or higher-order entities based on distributivity effects: not all distributivity
involves semantic plurality or quantification. In order to make sure that our
data actually have something to say about the particular formal theory we
need evidence (or counterevidence) for, we need to pay close attention to the
linguistic context and use it to bring out the empirical distinction between Pand
Q-distributivity.
CHAPTER 5
Q-distributivity and morphosyntactic number: a study
of group nouns in British English
In the previous chapters, we have developed the idea that the distinction between
P- and Q-distributivity can be used as a diagnostic for semantic number:
P-distributivity is available with arguments that have a clear part-whole structure
regardless of semantic number, but Q-distributivity is a quantificational
mechanism and as such only available with semantically plural arguments. We
have used this diagnostic to show that singular group NPs behave like atoms
in Dutch and American English: while P-distributivity is available with group
subjects, comparing the (a) and (b) sentences in (1) shows that Q-distributivity
is not.
(1) a. The baseball players are singing or dancing.
ð Every member of the baseball team is singing or dancing.
b. The baseball team is singing or dancing.
ö Every member of the baseball team is singing or dancing.
This conclusion may have been a bit too simple, though, because the comparison
here is not just between group NPs and definite plurals. The morphosyntactic
number of the VP is also different: in the (a) sentences, that feature a plural
subject, the VP is plural as well; in the (b) sentences the VP is singular. So
82 Chapter 5
the most we can actually say about the (un)availability of Q-distributivity
with plural and group subjects based on the data we have seen so far, is that
it is available with the former if the VP is morphosyntactically plural and
unavailable with the latter if the VP is morphosyntactically singular. This raises
the question of the role of VP number in the availability of Q-distributivity.
Would Q-distributivity still be available with definite plural subjects if the VP
were morphosyntactically singular? And, conversely, would it still be unavailable
with group subjects if the VP were plural?
In chapter 3 (section 3.5), I have already suggested that the predicate
pluralisation operator ¦ might have to be licensed by the presence of plural
morphology on the VP. This hypothesis ties in with the questions above, since
it suggests that the morphosyntactic number of the VP plays an important role
in the availability of Q-distributivity.
Of course, it is difficult to investigate the role of VP number separately from
the group/plural contrast, since English has obligatory subject-verb agreement
that links NP and VP number. In some varieties of English, however (most
notably British English), singular group NPs are allowed to appear with a plural
VP: both (2a) and (2b) are grammatical in British English.
(2) a. The cricket team is laughing.
b. The cricket team are laughing.
In this chapter, I will make use of this fact to investigate the availability of
Q-distributivity with group subjects with either a singular or a plural VP, by
means of a small questionnaire study of six native speakers of British English.
As we will see, the study shows that group NPs in British English behave like
sets (allowing Q-distributivity) when they occur with a plural VP, but not when
they occur with a singular VP. I will argue that the behaviour of British English
group NPs is best accounted for by assuming that they underlyingly denote
sets, but that they have to be shifted into impure atoms in sentences like (1b)
and (2a) to avoid a type mismatch with the morphosyntactically singular VP.
While the effect is the same here (a lack of Q-distributivity), this makes the
story of group nouns a bit more complicated than we have been assuming so
far; it also shows the need for a more in-depth investigation of the link between
morphosyntactic number and Q-distributivity, some suggestions for which I
will offer in the final sections of this chapter.
Q-distributivity and morphosyntactic number 83
Section 5.1 presents the main data of this chapter: the results of the questionnaire
study. In section 5.2, I show that the British English facts can be analysed
straightforwardly within the formal system I have set up in chapter 2, if we
assume that group nouns range over sets. This analysis allows us to account for
the behaviour of British English group NPs in very general terms, without the
need for any language-specific assumptions or special type-shifting mechanisms,
which gives it an advantage over earlier analyses (such as Landman 1989; Barker
1992; Schwarzschild 1996; Sauerland 2004). I will compare the proposed analysis
with some of these earlier ones in section 5.3; in this section I also present some
English data that suggest that the availability of Q-distributivity depends on
the number of the VP not just if the subject is a group NP, but also if the
subject is an ‘ordinary’ plural - something that is expected under the advocated
analysis but not under the aforementioned alternatives. Once again, section
5.4 is devoted to tying up some loose ends, especially in the formal part of the
analysis. Section 5.5 concludes this chapter.
5.1 Q-distributivity with British English group
NPs
In chapter 3 (section 3.2), I have identified a couple of contexts where the
distributive interpretation cannot be reduced to any lexical properties of the
main predicate (P-distributivity); I have shown that distributivity in these
contexts has to be derived by assuming some kind of covert quantificational
mechanism (Q-distributivity). As expected, these contexts all show a contrast
between definite plural and group subjects: Q-distributivity is available with
the former but not with the latter.
Of the Q-distributivity tests I discussed in chapter 3, the anaphora and
proportionality tests were only defined for Dutch, but the remaining three tests
- VP disjunction, VP conjunction, and other quantifiers - are suitable for testing
for the availability of Q-distributive interpretations in British English. The
judgements in this section were obtained from a small group of 6 native speakers
of British English; for methodology, a list of test items and a quantitative
summary of the results see appendix A.
VP disjunction. (For a more elaborate discussion of this Q-distributivity
test, see section 3.2.1.)
84 5.1. Q-distributivity with British English group NPs
(3) a. The children are sleeping or drawing.
ð The children are sleeping or the children are drawing. (CI)
ð For every child x, x is sleeping or x is drawing. (DI)
b. The class is sleeping or drawing. (only CI)
As we have seen in chapter 3, the plural-subject sentence in (3a) can be
interpreted in two ways, only one of which (the distributive interpretation) is
compatible with a ‘mixed’ situation in which part of the children are drawing and
the others are sleeping. So, if a sentence with two disjunctively coordinated VPs
can be interpreted as true in the situation depicted in fig. 5.1, Q-distributivity
must be available for that sentence. This means that sentence (3a) can be
true in the depicted situation; on the other hand, (3b) cannot. Both of these
observations hold for British English as well. However, (4), with a group subject
Figure 5.1: ‘‘The children / the class is/are sleeping or drawing.’’
and a plural VP, behaves like (3a) and not like (3b): according to my informants,
it can be interpreted as true in the mixed situation.1
(4) The class are sleeping or drawing. (CI/DI)
1This contrast was first pointed out to me by Michelle Sheehan and Hazel Pearson (p.c.),
whose observations first motivated me to pursue this particular line of inquiry.
Q-distributivity and morphosyntactic number 85
Following our earlier reasoning in chapter 3, this means that the denotation of
the class in (4) should be analysed as semantically plural.
VP conjunction. (For a more elaborate discussion of this Q-distributivity
test, see section 3.3.3.) The same pattern appears with conjunctive coordination.
As we have seen in chapter 3, this is necessarily interpreted with its strongest
possible (Boolean) meaning when the subject is a group noun and the VP is
singular, even though a weakened, non-anomalous meaning is readily available
when the subject is plural (I have put ‘DI’ in quotes here, since even though the
general entailment pattern is similar, the interpretation itself does not precisely
fit our definition of a ‘distributive’ interpretation):
(5) a. The cricket players are underweight and obese.
ð #The cricket players are underweight and the cricket players are
obese. (CI)
ð For every cricket player x, x is underweight or x is obese. (‘DI’)
b. #The cricket team is underweight and obese. (only CI)
This means that (5a) but not (5b) can be interpreted as true in the situation
depicted in fig. 5.2; sentence (5b) only has the anomalous interpretation according
to which each of the cricket players is both underweight and obese at the
same time. Again, British English behaves in the familiar way for plural-subject
sentences and group-subject sentences with a singular VP, but the group-subject
sentences with a plural VP pattern with the former in allowing a non-Boolean
interpretation: (6), like (5a), can be interpreted as true in the situation depicted
in fig. 5.2.
(6) The cricket team are underweight and obese. (CI/‘DI’)
If it is only possible to derive the non-Boolean interpretation when the subject
is semantically plural - as in the approach of Winter (2001b), which as I argued
in chapter 3 is justified by the group/plural contrast in (5) - this means that
the group NP the cricket team in (6) cannot denote an atomic entity. Again,
we see a group NP behaving like a set rather than an atom when it occurs with
a plural VP.
Other quantifiers. (For a more elaborate discussion of this Q-distributivity
test, see section 3.2.2.) Since the pluralisation operator ¦ introduces, in effect, a
quantifier over individual members of a plurality, we expect this quantifier to be
86 5.1. Q-distributivity with British English group NPs
Figure 5.2: ‘‘The cricket team / cricket players is/are underweight and obese.’’
able to take scope over other quantificational elements in the sentence. On the
other hand, in the case of singular predication (without ¦), any quantificational
elements in the sentence end up scoping over the subject NP. In accordance with
this, we see that a quantificational wide-scope interpretation for the children
is available in (7a), while the class in (7b) as an entity that is scopeless with
respect to the adverb somewhere:
(7) a. The children are hiding somewhere.
ð There is a place x such that the children are hiding in x. (CI)
ð For every child y, there is a place x such that y is hiding in x.
(DI)
b. The class is hiding somewhere. (only CI)
In (7a), the quantificational wide scope interpretation of the children results
in a distributive interpretation according to which each child is hiding in a
potentially different location, which is true in the situation depicted in fig. 5.3.
In American as well as British English, the DI is unavailable in the case of (7b),
which means that (7b) is false in the depicted situation. But in British English,
Q-distributivity and morphosyntactic number 87
Figure 5.3: ‘‘The children / the class is/are hiding somewhere.’’
when the subject is a group NP and the VP is plural, it behaves like (7a) and
not like (7b): sentence (8) can be interpreted as true in the situation depicted
in fig. 5.3.
(8) The class are hiding somewhere. (CI/DI)
The picture that emerges from these observations, then, is that British English
group sentences pattern with their American and Dutch counterparts if the VP
is singular: they are unable to receive a Q-distributive interpretation. However,
if the VP is plural, British English group sentences pattern with plural-subject
sentences in generally allowing Q-distributivity.
5.1.1 A related contrast: reciprocity
The observed pattern is also found with reciprocal predication in British English,
which should not come as a surprise given that reciprocity, like Q-distributivity,
is usually analysed as a form of quantification (cf. Dalrymple et al. 1998) and
hence requires a semantically plural argument. It has been noted in the literature
that reciprocal expressions are fine with plurals, but at best marginal with
group nouns (Schwarzschild 1996; Lønning 2011):
88 5.2. Analysis
(9) a. The cricket players are friends / usually coach each other.
b. *The cricket team is friends / usually coaches each other.
However, Schwarzschild hypothesises that reciprocal predication over a group
subject may be grammatical with British English when the VP is plural, a
suggestion supported by the data in (10) (from Pearson 2011). Many examples
of these sentences ‘in the wild’ can be found with Google (11a-d)2
:
(10) The family can’t stand each other.
(11) a. The Team are friends on track as well as off track, and are as much
family as we are friends.
b. Can a scientific program really change the way the Diaz family love
each other?
c. It is puzzling when medical staff disagree with each other.
d. Remember that your group are neighbours who have to get along
outside the group as well as within it.
Like the Q-distributivity data, these reciprocity data are in line with the idea
that the semantic number of a morphosyntactically singular group NP depends
on the number of the VP it agrees with: since Q-distributivity (and by the same
reasoning also reciprocity) can function as a diagnostic for semantic number,
we can conclude that group NPs behave like atomic entities when the VP is
singular, but like sets when the VP is plural.
5.2 Analysis
The way I have formulated the above generalisation - group NPs behave like
atoms with a singular VP and like sets with a plural VP - already suggests
the first part of an analysis: I have stressed throughout this dissertation that
Q-distributivity is an automatic consequence of the semantic pluralisation of
atom predicates, and also suggested that this semantic pluralisation needs to be
licensed by the presence of plural morphology (section 3.5). This suggests that
the morphosyntactic difference between singular and plural VPs in our group
noun data is also reflected in the semantics: when a group NP occurs with a
singular VP, the VP denotes an unstarred predicate (hence, no Q-distributivity),
2Search terms used: ‘team are friends’, ‘family love each other’, ‘staff disagree with each
other’, ‘group are neighbours’, respectively.
Q-distributivity and morphosyntactic number 89
but when it occurs with a plural VP, the VP denotes a starred predicate and
we get a Q-distributive interpretation.
But this is only half of an analysis, since it does not yet account for the
observation that group NPs are sometimes interpreted as atoms and sometimes
as sets. Are they ambiguous between the two? Is there a typeshift that maps
one to the other? Are group NPs interpreted as atoms (sets) because they occur
with a singular (plural) VP, or is the VP singular (plural) because the group
NP denotes an atom (set)?
In this section I will propose that group nouns, in their basic form, range
over sets and that the atomic interpretation is the result of a typeshift to avoid
a type mismatch with the morphosyntactically and semantically singular VP.
As it turns out, once we assume that group NPs are set-denoting, the rest of
the analysis follows almost automatically from the general assumptions about
number we made in chapter 2, and we can account for the behaviour of group
nouns in both British and American English without any further assumptions
or language-specific semantic mechanisms.
With the assumption that group nouns range over sets, we have built a problem
into our system that every language will have to solve in some way: because
we now have a class of nouns that are semantically plural but syntactically
singular, we cannot combine these nouns with a predicate without ending up
with either a type or an agreement mismatch. With matching agreement (a
syntactically singular VP to match the syntactically singular group NP), we end
up with a type mismatch as both the NP and the VP will be of type et. With
matching typing (a pluralised VP to match the set-denoting NP), we end up
with mismatched number inflection, as semantic pluralisation of the predicate
needs to be licensed by plural number morphology. So, either a language will
have to allow mismatched agreement, or it will have to shift the group to its
corresponding impure atom. The plural agreement option in British English
exemplifies the first option, while American English exemplifies the second.
Schematically:
(12) tall[sg],et
(the group[sg],et
) : matching agreement but mismatched types
a. The American strategy (always available):
rrThe group is tallss = tall[sg],et
(Ò the group[sg],e
)
b. The British strategy (only available if the grammar allows it):
rrThe group are tallss = ¦tall[pl],petqt
(the group[sg],et
)
90 5.2. Analysis
I am assuming that the ‘American’ strategy is always available because (1)
to my knowledge, there are no languages that require singular group NPs to
take a plural VP3
, and (2) the typeshift involved is the impure atom mapping
from chapter 2, which I have been assuming is freely available anyway4
. The
availability of the ‘British’ strategy, on the other hand, depends on the syntax
of the language in question: if the combination of a singular group noun and a
plural VP is ungrammatical, it obviously cannot be used as a solution to the
mismatch problem.
It follows that group NPs must behave like atoms when they occur with a
singular VP, but can behave like sets when they occur with a plural VP: as
can be seen in (12), the NP denotes an atomic entity (type e) in (12a), and a
set (type et) in (12b). To illustrate how this accounts for the observed pattern
with Q-distributivity, let us look at the derivations of the sentences ‘‘The class
is sleeping or drawing’’ (in (13)) and ‘‘The class are sleeping or drawing’’ (in
(14)):
(13) Ò(the class) € sleep ‰draw
ô Ò(the class) € sleep or Ò(the class) € draw
(Ò(the classet))e (sleep ‰ draw)et
sleepet
or drawet
Because the union of sleep and draw is not pluralised in (13), is sleeping or
drawing denotes just the set of entities that are either sleeping or drawing. For
the sentence The class is sleeping or drawing to be true, then, the impure atom
corresponding to the class must be one of these entities, which is true if it
is either a member of sleep or of draw. By P-distributivity over this impure
atom, we infer that the individual group members are either sleeping or drawing,
but a split interpretation is impossible in this derivation.
3Corbett (2000) mentions Spanish, Old Church Slavonic, Samoan, the Brazilian language
Paumar´ı and the Caucasian language Kumaxov as other languages that (sometimes) allow
group NPs to appear with a plural VP, but he does not mention any languages for which this
is obligatory.
4But see chapter 6 for a more nuanced version of this claim
Q-distributivity and morphosyntactic number 91
(14) the class € ¦psleep ‰drawq
ô dx € the class: x € sleep or x € draw
the classet ¦psleep ‰drawqet,t
¦ (sing ‰ draw)et
sleepet
or drawet
In (14), on the other hand, the class is interpreted as a set, and the pluralised
predicate are sleeping or drawing denotes the set of all sets whose members
are either sleeping or drawing. This means that the class is a member of
¦psleep ‰drawq just in case each of the group’s members is either a member
of sleep or a member of draw. This is also true in a split situation where part
of the group is sleeping and the rest is drawing.
Because the proposed analysis treats the observed semantic differences between
languages as a direct consequence of differences in morphosyntax, it is able to
account for the behaviour of group nouns in both British and American English
without any language-specific semantic assumptions, and without the need for
any semantic machinery that is specifically tailored to group NPs (like the Ó
typeshift - the opposite of Ò - that is used by e.g. Landman 1989; Barker 1992;
Sauerland 2004 to handle the semantics of group nouns). In the next section, I
will compare the present analysis to several of its possible alternatives, and see
whether there are any empirical reasons to favour one over the others.
5.3 Comparison with alternative analyses of group
NPs
Broadly speaking, there are two possible alternative analyses to the one that I
have proposed. The first is to do everything the opposite way around - according
to this alternative analysis, group NPs denote atoms but if the VP is plural these
atom are broken up by a ‘fission’ operation Ó (see Barker 1992; Schwarzschild
1996; Sauerland 2004, for proposals in this vein). The second is to assume that
British English group nouns, unlike their American counterparts, are ambiguous
between a predicate that ranges over sets and one that ranges over atoms (cf.
92 5.3. Comparison with alternative analyses of group NPs
Schwarzschild 1996:9). I will discuss these approaches in section 5.3.2. But first,
I want to take a step back and look at the different ways the class of ‘group
nouns’ has been defined in the literature, since the definition I have been using
more or less implicitly in this chapter (just those collective nouns that can take
a plural VP in British English) is by no means universal and rather narrow by
comparison, something which we have to keep in mind when comparing the
current approach to ‘group nouns’ with earlier ones.
5.3.1 Defining ‘group noun’
The Oxford English Dictionary defines what it calls a collective noun as ‘‘a
substantive which (in the singular) denotes a collection or number of individuals’’.
In his Modern English Grammar on Historical Principles, Jespersen (1927)
adopts this definition, citing nouns like train (a collection of carriages), library
(a collection of books), forest (a collection of trees), and army (a collection of
soldiers) as examples.
The problem with this definition is that it is not always clear what counts
as an individual. Is puzzle a collective noun because it denotes a collection of
individual puzzle pieces? Is book a collective noun because it denotes a collection
of individual pages? Most entities in the world have parts of some sort, but a
semantic theory that classifies every noun that ranges over these entities as a
‘group noun’ probably would not be very helpful in accounting for the properties
that, intuitively, set nouns like army and family apart from other nouns.
To delimit the relevant class of nouns, Barker (1992) proposes to define
them in syntactic terms: a group noun is a noun that can take a plural but not
a singular of-complement, as in (15):
(15) a. A committee of women / *woman
b. An army of children / *child
c. A stack of cups / *cup
According to this definition, puzzle, book, and piece are not group nouns. They
cannot take a plural of-complement ((16a-c)), and/or they are grammatical
with a singular complement ((16c)):
(16) a. *A puzzle of pieces
b. *A book of pages
c. *A piece of cookie / *cookies
Q-distributivity and morphosyntactic number 93
Furthermore, although Barker’s definition does not explicitly mention this, his
use of examples like (17) makes clear that he also rules out nouns that are
compatible with mass noun of-complements: ocean, although it is compatible
with the plural complement of tears, does not count as a group noun according
to Barker because it can also take a mass noun complement of water.
(17) An ocean of tears / water
Barker’s definition is also adopted by Schwarzschild (1996) and Champollion
(2010), although the latter modifies it a bit: instead of ruling out nouns that
can take a mass of-complement, Champollion rules out ‘container’ nouns like
box by postulating that if a noun X can take a plural of-complement, the
resulting interpretation must entail the presence of an actual X for X to count
as a group noun. So, because we can talk about a box of sweets on a measure
reading that does not entail the presence of an actual box (for example, if I say
I ate an entire box of sweets I do not mean to say that I ate a box, just that I
ate a certain quantity of sweets), box does not count as a group noun under
Champollion’s modified definition. In practice, both definitions seem to rule
out the same nouns, albeit for different reasons: Barker would rule out box as
a group noun because it can take a mass noun of-complement (box of cardboard).
However, does Barker’s syntactic definition really rule out the nouns that he
wants to rule out? If we choose our examples somewhat differently, we see that
nouns like puzzle or book, which Barker claims are not group nouns, are not
always incompatible with plural of-complements:
(18) a. A book of pictures / poems
b. A puzzle of one hundred (strangely shaped) pieces
It seems that the reason these nouns are incompatible with the plural ofcomplements
in (16), is that these complements are redundant or trivial: a
book necessarily consists of pages, and a puzzle necessarily consists of pieces. In
contrast, (18) shows that book and puzzle have no problem taking a non-trivial
plural of-complement. Consider also (19):
(19) A committee of *(six (perpetually arguing)) members
According to Barker, the group noun committee should be compatible with
a plural of-complement; however, if that complement is trivial (a committee
of members), the result is just as unacceptable as *a book of pages. Adding a
94 5.3. Comparison with alternative analyses of group NPs
modifier (like six or perpetually arguing) results in a construction that is once
again grammatical, showing that the problem is not with the noun members
per se.
It seems that the nouns that Barker classifies as group nouns are not
actually distinguished from his non-group nouns by their ability to take plural
of-complements. What about their compatibility with mass noun complements?
Here, too, the line between Barker’s group nouns and non-group nouns seems
rather blurry upon closer inspection. Consider the following data:
(20) a. A jury of flesh and blood
b. A forest of oak
c. A pile of gold
According to Barker, jury, forest and army are group nouns, but according
to his definition, group nouns should not be compatible with mass noun ofcomplements.
So not only does it turn out that certain nouns that Barker does
not consider group nouns should count as such by his definition, there are also
nouns that Barker does consider group nouns that do not count as such by his
definition.
With respect to the data in (20), Champollion’s more semantic definition fares
better: all three nouns in (20) are still considered group nouns under his account.
His definition also leads to a classification that seems to be in line with a third,
independent attempt to define the notion of ‘group noun’: that of Pearson
(2011), to which we will turn next.
Pearson’s definition of group nouns is the narrowest so far: under her account,
the relevant class of nouns (which she calls ‘committee nouns’) include only
those nouns that denote groups consisting of humans, like team and committee.
Other ‘group nouns’, like bunch and pile, are treated as count nouns like any
other (Pearson calls them ‘collection nouns’, and according to Champollion
(2010), they seem to coincide with those nouns whose group noun status is
dubious under his definition because they have very salient measure readings).
Pearson’s paper includes a number of tests to distinguish committee nouns
from collection nouns. Here are a few of them:
(21) Compatibility with collective predicates:
Q-distributivity and morphosyntactic number 95
a. The couple
$
'&
'%
is similar.
is a good match.
looks cute together.
,
/.
/b.
*The bunch of flowers
$
'&
'%
is similar.
is a good match.
looks cute together.
,
/.
/(22)
Compatibility with plural agreement in British and Canadian English:
a. The staff are friendly.
b. *The list of party guests are long.
(23) Number of verifying situations for partitive constructions:5
a. Half of the committee had been painted yellow.
false if half of every committee member had been painted yellow
b. Half of the bunch of flowers had been painted yellow.
true if half of every flower had been painted yellow
According to Pearson, committee nouns consistently pass all the tests, while
collection nouns consistently fail them.
However, just looking at the three tests illustrated above, it is already
possible to find exceptions: there are committee nouns that do not pass them
all, and there are collection nouns that do not fail them all. For example,
some collective predicates (even those that Pearson explicitly argues are only
compatible with committee nouns, like gather and come together) can take
arguments that fail the plural agreement test:
(24) a. ??The herd of cows are hungry.
b. The herd of cows piled up near the gate / dispersed.
(25) a. *That pile of dead skin cells are a disgusting sight.
b. A small pile of dead skin cells has gathered in the sink.
And others are marginal even with arguments that pass the plural agreement
test:
(26) a. The orchestra are based in London.
b. ??The orchestra is similar / numerous.
5For a more elaborate discussion of this particular criterion, see chapter 6, section 6.1.
96 5.3. Comparison with alternative analyses of group NPs
Throughout this dissertation, the ‘group NPs’ I have been using in my examples
have all been NPs that, in British English, are compatible with a plural VP,
which means they correspond to Pearson’s committee nouns (albeit based on
a single criterion, rather than several). With Pearson, I believe that these
nouns should be treated as a separate subclass within the class of ‘collective
nouns’ as defined by the OED. This means that the observations presented
in this chapter do not invalidate Barker’s and Schwarzschild’s insights about
the atomic nature of many collective NPs, and that the present analysis of
group NPs as set-denoting should be seen as a supplement to rather than a full
replacement of the Barker-Schwarzschild-Champollion approach to collective
nouns: I do not want to claim that all nouns that are classified as group nouns
by these authors should be analysed as ranging over sets.
The obvious disadvantage of using ‘the ability to take a plural VP in British
English’ as the defining criterion for the class of NPs that our analysis applies
to, is that it has only limited use beyond English. If we want to know whether
an analysis of group NPs as sets is empirically justified for other languages as
well, we need a more universal way to delimit the relevant class of nouns. I
have argued above that Pearson’s other, less language-specific criteria are not
always consistent with the plural-VP criterion, even within English itself, so
they are not immediately useful for this purpose.
However, the well-known observation (already made in Jespersen 1927)
that the ability to take a plural VP in British English is limited to animate
(and in particular human) collective nouns provides us with both a universally
usable definition, and - together with the analysis of British English group
nouns as proposed in this chapter - a hypothetical cross-linguistic generalisation.
Following Jespersen’s observation on animacy, I will define ‘group nouns’, as I
use the term in this dissertation, as just those collective nouns (as defined by
the OED) that refer to collections of animate entities. I have analysed these
nouns as ranging over sets based on their behaviour in British English; we can
now hypothesise that this property does not just apply to a particular class of
British English nouns, but to animate collective nouns in general, regardless of
the language. In chapter 6, I will provide some evidence that this hypothetical
generalisation is correct, and that animate collective NPs - unlike inanimate
ones like Pearson’s collection NPs - behave like semantic pluralities in other
languages than British English as well.
Q-distributivity and morphosyntactic number 97
5.3.2 Alternatives to impure atom formation: ‘fission’ or
ambiguity
As mentioned in the introduction to this section, there are two possible alternative
analysis to the present impure atom-based approach. The first is to do
everything the opposite way around - according to this analysis, group NPs
denote atoms but if the VP is plural these atom are broken up by a ‘fission’
operation (cf. Barker 1992; Schwarzschild 1996; Sauerland 2004). The second is
to assume that British English group nouns, unlike their American counterparts,
are ambiguous between a predicate that ranges over sets and one that ranges
over atoms (cf. Schwarzschild 1996:9).
The fission approach seems logically indistinguishable from the present one,
since it only reverses directions: instead of a typeshift from sets to atoms forced
by a type mismatch with a singular VP, it assumes a typeshift from atoms to
sets forced by a type mismatch with a plural VP. However, there are at least
two reasons why I think it fares worse than the present analysis. The first is
related to animacy. As I have argued, the class of NPs that behave like sets
when they occur with a plural VP are just those NPs that are associated with
collections of animate/human entities. Under the present impure atom-based
analysis, this requirement follows from the fact that both animacy and semantic
type are lexical properties that happen to coincide in the relevant class of
nouns6
: if animacy is a lexical property of all the nominal predicates that range
over sets, and singular nouns are compatible with plural agreement only if they
denote such predicates, it follows that the only singular NPs compatible with
plural agreement are animate NPs. On the other hand, it is unclear how the
animacy requirement (and the resulting effects on the interpretation of the NP)
might be enforced if group nouns are semantically indistinguishable from other
nouns, as they are under a fission-based approach. Such an approach would
need to restrict the application of the atom-to-set mapping to just those NPs
that refer to animate entities (Barker (1992) acknowledges this, but Sauerland
(2004) does not). This means that animacy has to be analysed as not just a
lexical property of certain nominal predicates, but as a formal feature, that
influences the compositional semantics of the entire NP; furthermore, we have
to stipulate that the atom-to-set typeshift is sensitive to the value of this feature
6In chapter 6, I will argue that this coincidence is not accidental, and that animacy and
semantic plurality are inherently related in the conceptual system.
98 5.3. Comparison with alternative analyses of group NPs
and formally enforce this sensitivity in some way. An analysis that takes the
atomic denotation to be basic and the set denotation to be derived is incomplete
without a formally explicit account of the role of animacy, but to my knowledge,
no such account has been given.
A second reason to prefer the impure atom-based approach over the fission
approach is that the latter is tailored to group nouns in particular, while the
former has a much wider use in a theory of plurality. I believe that the more
general implications of the impure atom-based analysis are empirically justified:
the ability to switch between a set and an atom denotation is a property of plural
NPs in general, not just of group nouns (I have provided some evidence for this
in section 3.5, and will provide more evidence for it in chapter 6). Impure atom
formation captures this because it can apply to all set-denoting NPs. Fission
does not, since it only explains the mixed atom/set behaviour of group NPs,
and nothing else. The same reasoning applies to the ambiguity approach: while
this is hard to rule out as such, it cannot be the whole story because it only
captures the mixed behaviour of group nouns and not of set-denoting NPs in
general. (An additional, more conceptual problem with the ambiguity account
is that it declares a whole class of nouns systematically ambiguous, which is of
course technically possible, but not very elegant.)
This second point is related to the double question I started out this chapter
with. First, would Q-distributivity still be available with definite plural subjects
if the VP were morphosyntactically singular? And, conversely, would it still
be unavailable with group subjects if the VP were plural? In this chapter, we
have looked only at the second question; I have shown that Q-distributivity is
available when the VP is plural regardless of whether the subject is a plural
or a group NP. However, the analysis I have proposed in order to account
for this also predicts a particular answer to the first question. If the presence
of ¦ has to be licensed by plural morphology, so that it is impossible for
morphosyntactically singular VPs to denote a pluralised predicate, we expect
Q-distributivity to be unavailable with plural subjects if they occur with a
singular VP for the same reason that it is unavailable with group subjects under
these circumstances. So, if it turns out to be the case that Q-distributivity is
unavailable with plural subjects if the VP is singular, the proposed analysis
accounts for that straightforwardly, while the fission-based and ambiguity-based
approaches would have to find an independent solution for it.
In colloquial English, speakers occasionally allow a plural subject to occur
Q-distributivity and morphosyntactic number 99
with a singular VP. For example, Kratzer (2008) notes that conjoined mass
nouns are often judged acceptable with a singular VP in some varieties of
English and her own dialect of German (see (27), the Dutch equivalent of which
sounds fine to me as well):
(27) The moss on the rocks and the moss on the trees is blighted.
This observation gives us an opportunity to test the availability of Q-distributivity
with such conjoined subjects, depending on the number of the VP (the entailments
given in (28) represent my own judgements):
(28) a. Good hygiene and regular exercise are more effective than antibiotics.
ð A combination of good hygiene and regular exercise is more
effective than antibiotics. (CI)
ðGood hygiene is more effective than antibiotics and regular exercise
is more effective than antibiotics. (DI)
b. Good hygiene and regular exercise is more effective than antibiotics.
ô A combination of good hygiene and regular exercise is more
effective than antibiotics. (CI)
öGood hygiene is more effective than antibiotics and regular exercise
is more effective than antibiotics. (DI)
This kind of Q-distributivity test is more difficult when the subject involves
conjoined count definites, since these sentences are more degraded than their
mass noun counterparts. However, when I asked some of my Dutch- and Englishspeaking
informants to compare the sentences in (29), they all felt that (29d)
was much worse than (29b):
(29) a. The credit crunch and his company’s bankruptcy have evaporated
John’s savings and given him an ulcer.
b. ??The credit crunch and his company’s bankruptcy has evaporated
John’s savings and given him an ulcer.
c. The credit crunch and the Occupy movement have evaporated John’s
savings and given him some hope for the future.
d. #??The credit crunch and the Occupy movement has evaporated
John’s savings and given him some hope for the future.
While neither (29b) nor (29d) are quite grammatical, (29d) is also problematic
because it suggests that the credit crunch has given John hope (in addition
100 5.3. Comparison with alternative analyses of group NPs
to evaporating his savings) and the Occupy movement has evaporated his
savings (in addition to giving him hope), both of which are quite contrary to
the properties we generally associate with the credit crunch and the Occupy
movement. In other words, the non-Boolean interpretation of the VP that allows
each of the VP conjuncts to apply to just a part of the subject denotation
seems to be unavailable in (29d), which leads to an anomalous interpretation.
In (29b), the absence of a non-Boolean interpretation does not result in such an
anomaly, since both VP conjuncts can apply naturally to both credit crunches
and bankruptcies. The judgements are admittedly subtle because of the interference
of grammatical and pragmatic factors, but there does seem to be a real
difference between (29b) and (29d), which would follow from the analysis of
VP number and Q-distributivity presented in this chapter.
A second example of the influence of VP number on the availability of Qdistributivity
can be found with there-sentences. In colloquial English, many
speakers accept there-sentences with mismatched agreement, as in (30b):
(30) a. There are four semanticists singing or dancing in my garden.
b. There’s four semanticists singing or dancing in my garden.
Under the proposed analysis, we expect the Q-distributive interpretation (which
is compatible with a scenario in which some of the semanticists are singing while
the others are dancing) to be present in (30a) but absent in (30b), as the latter
features a morphosyntactically singular VP which I have claimed cannot denote
a starred predicate. And according to most of my English-speaking informants
(not all of them accepted (30b) as grammatical), these sentences do show a
contrast similar to the British English Q-distributivity cases: while (30a) can be
interpreted as true in the described ‘mixed’ situation, (30b) cannot.7
Again, this
observation follows straightforwardly from the way I have analysed the mixed
atom/set behaviour of group NPs, but would require additional explanation
had we adopted either a fission-based or an ambiguity-based approach to the
group noun data.
7Unfortunately, I have not been able to gather substantial quantificational data on the
availability of Q-distributivity in there-sentences beyond the handful of judgements regarding
(30); I will leave this for further research.
Q-distributivity and morphosyntactic number 101
5.3.3 A note on Winter’s analysis of group nouns as atom
predicates
While I have presented the groups-as-sets analysis as a reasonably straightforward
extension of the framework in Winter (2002), at one point they seem
incompatible: based on the data in (31), Winter categorises group nominal
predicates like team and committee as atom predicates.
(31) a. *All the students are a good team.
b. *Every student is a good team.
Since (31a) and (31b) are equally ungrammatical, (be a) good team is classified
as an atom predicate (see chapter 2, section 2.2).
I see two possible ways to reconcile Winter’s judgement with the analysis
presented in this chapter. The first is that there is something special about bepredication
that blocks the set-of-sets interpretation of good team, for example
by an obligatory type-shift (this solution is essentially the mirror image of an
idea suggested by Schwarzschild (1996:9) to deal with ‘mismatched’ predication
structures like My guests are a couple). In addition to its ad hoc nature, this
solution is problematic because it predicts that sentences like (31a) are always
ungrammatical, which in fact does not seem to be the case. For example, the
all-sentences in (32) and (33) are judged fine by all native speakers of English
and Dutch that I consulted (although some comment that they would be even
better with together):
(32) Context: I want to divide my students into three project groups, which
I do by telling them the following. ‘‘All the redheads are a team. All the
students over 21 are a team. And the third team consists of everyone
else.’’
(33) ‘‘Alle roodharigen zijn een groep. Alle brildragers zijn een groep. En de
laatste groep bestaat uit iedereen die dan nog over is.’’ (Dutch)
‘All redheads are a group. All glasses-wearers are a group. And the last
group consists of everyone who remains’
And here are some examples found with Google (emphases mine):8
(34) a. Alle moslims zijn een grote familie. (Dutch)
‘All muslims are a big family’
8Search terms used: ‘alle * zijn een grote familie’, ‘all the * are one big family’, ‘all * are
a lovely bunch’, ‘all the * are a close-knit group’, ‘all * are a hate group’, respectively.
102 5.4. Tying up some loose ends
b. I enjoy living here at Broadway Plaza, all the people are one big
family.
c. It’s a great way to meet new people and have a real fun day out at
the races, all our members are a lovely bunch of people who love the
sport and the craic of being involved with the horses, trainers and
jockeys.
d. All the seniors are a close-knit group and a lot of us came in together.
e. I have always gone to pains to differentiate myself from the idea that
all atheists are a hate group.
So, while the seeming contradiction between the results of Winter’s atom/set
test and the groups-as-sets analysis presented in this chapter is somewhat
troubling, it is hard to tell precisely how contradictory they are because the
atom/set test results are not very conclusive. At this point, I do not think that
Winter’s data provide enough counterevidence to reject an analysis in which
group nouns range over sets.
5.4 Tying up some loose ends
5.4.1 Multiple groups with the same members
In chapter 2, I observed (following Landman 1989 and Barker 1992) that it
is possible for two groups to consist of precisely the same members and be
distinct nonetheless - for example, even though the same group of people might
make up both the Programme Committee and the Committee in Charge of
Flower Arrangements, that does not make them the same committee. Under
an atomic analysis of group NPs, this is easy to account for: the two NPs are
simply associated with different entities, both of which are included in the
extension of committee (as in (35a)). Under the current analysis however,
in which group NPs denote the set of the group’s members (say, {mary, sue,
bill}), the Programme Committee and the Flower Committee have the same
denotation (as in (35b)). So, under an atomic analysis of group NPs, a predicate
like committee has as many members as there are different committees; under
a set-based analysis, it has as many members as there are different groups of
people that form committees:
(35) a. committeeet = { programme comm, flower comm }
Q-distributivity and morphosyntactic number 103
b. committeeet,t = { {mary, sue, bill} }
Since the impure atom mapping Ò was defined as a one-to-one mapping in
chapter 2, according to which each set is associated with a unique impure atom,
there is no way in the current system in which the Programme Committee can
be made to refer to a different individual than the Flower Committee: they are
associated with the same individual at both the set and the impure atom level.
As argued in section 2.3.1, however, this is not necessarily problematic as long
as we also equip our formal system with a way to distinguish between different
‘roles’ or functions that a single individual might have (such as the intensional
system from Landman 1989). Just as John-as-a-judge can be on strike while
John-as-a-hangman is not, it is possible for the plural individual {mary, sue,
bill} to habitually meet on Tuesdays in their role as the Programme Committee,
while never meeting on Tuesdays in their role as the Committee in Charge of
Flower Arrangements. The former does not require us to associate the proper
name John with several different entities; neither does the latter force us to
assume that the Programme Committee and the Flower Committee have to refer
to different sets, or that the result of applying the Ò mapping to the set {mary,
sue, bill} should be different depending on which of the two committees we
are talking about.
5.4.2 Morphosyntactically plural group NPs
In chapter 2, we have seen that it is possible to analyse the denotation of the
as the maximum operator regardless of whether it is applied to a singular or a
plural noun: if we apply the to an ordered set, it returns the maximal element
in that set; if we apply it to a singleton set it returns the unique member of that
set (i.e. it reduces to iota); and if we apply it to a set with no unique maximum
(including the empty set), the result will be undefined. Unfortunately, this
unified analysis of the is untenable under the current approach. An example
will illustrate this. Imagine a model in which the extension of rrcommitteess
equals the set {{a},{b},{a,b}}, so the denotation of committee happens to
coincide with ¦ta, bu. Then the committee would denote the maximal set {a,b}
in this model, even though we want it to be undefined: because there are three
committees in our model, uniqueness is not satisfied and the committee should
fail to denote.
This means that I will assume after all that the is ambiguous between
thesingular and theplural: the former an untyped function that picks out the
104 5.5. Conclusions
unique member (set or entity) from a singleton set, the latter a function that
picks out the maximum from a set of sets. This ambiguity is not necessarily
problematic - many languages have different words for thesingular and theplural
(and English itself has this/that versus these/those).
The next question is what exactly a morphosyntactically plural group NP like
the committees denotes. In chapter 2 we have seen that the denotation of a
plural NP like the girls is just the denotation of girl - that is, the set containing
all girls in the model - because of the way theplural is defined. In a similar
way, we could analyse rrthe committeesss as equivalent to rrcommitteess, if we
take theplural to be an untyped function that can operate on sets of sets (type
ppetqtqet) and sets of sets of sets (type pppetqtqtqppetqtq) alike. But this results in
a classic problem: if we allow NPs of type petqt, we would also need to be able
to lift predicates into a type ppetqtqt. This introduces a lot of ambiguity and
complexity into the system for which we do not really have an empirical basis.
Instead, I propose that theplural only ever has type ppetqtqet, and that
rrcommitteesss is the result of applying ¦ to the singularised version of com-
mittee9
:
(36) rrcommitteessspetqt = ¦pòpcommitteepetqtqetq
So, the committees then denotes the maximal set of committee-atoms just as
the girls denotes the maximal set of girls. In this way, we do not add any
unnecessary complexity to the system by adding a third type of referential NP
and all the additional type lifting that this would require, while still being able
to account for all the relevant data (as far as I can tell).
5.5 Conclusions
I have shown that morphologically singular group NPs in British English
behave like atoms when they occur with a singular VP, but like sets when they
occur with a plural VP: in the former case, they do not allow Q-distributivity
and reciprocity, but in the latter case they do. If we assume that group NPs
are basically set-denoting, their behaviour with both singular and plural VPs
follows from our general assumptions about the semantics of plurality. Either
the language allows a mismatch in number agreement so the group NP can
9The singularisation operator ò was introduced in chapter 2, section 2.2.1, and functions
to turn predicates over sets into predicates over impure atoms.
Q-distributivity and morphosyntactic number 105
participate in semantically plural predication, or the NP has to be shifted into
its corresponding impure atom to avoid a type mismatch with the, similarly
set-denoting, singular VP.
The advantage of this proposal is that it reduces crosslinguistic variations
in interpretation to morphosyntactic differences between languages, allowing
us to maintain a uniform semantics for group nouns. It also has the empirical
advantage of being applicable to a wider range of semantic phenomena than
just group nouns, because it is based on the mapping from sets to impure atoms
that I have assumed is generally available to all set-denoting referential NPs.
Our next step, therefore, should be to look beyond English and see whether we
see the same pattern - set-denoting NPs shifting into impure atoms to resolve a
type mismatch - pop up when ‘ordinary’ plurals occur with a singular VP, as
the present analysis predicts it should.
A topic that came up briefly in this chapter is animacy: I have argued that
this is the property that sets apart what I have called ‘group nouns’ (that range
over sets according to the proposed analysis) from other collective nouns like
pile or bunch (that the present analysis is not concerned with). In the next
chapter, we will take a closer look at the relationship between animacy and
semantic number.
CHAPTER 6
Animacy and plurality
In the previous chapter, I have developed an analysis of the mixed atom/set
behaviour of British English singular definite group NPs by proposing that they
denote sets, but have to be shifted into impure atoms because a morphologically
singular VP is necessarily also semantically singular. One of the advantages of
this approach is its crosslinguistic applicability: it does not explain the behaviour
of group NPs in British English as some kind of isolated ‘special case’, but
analyses it as part of a general theory of semantic number from which the
behaviour of group NPs in American English and other languages follows just
the same. I have suggested that group nouns range over sets not just in British
English but in language in general, and placed the burden of their varying
behaviour fully on morphosyntax: in a language where group NPs obligatorily
take a singular VP they will always be forced into their atomic guise, but in a
language that allows them to appear with a plural VP (like British English) they
are free to behave according to their underlying set nature. So far, however, we
have not seen any empirical evidence for this supposed underlying set nature of
group NPs in other languages than British English. One of the aims of this final
chapter, therefore, is to investigate whether there are any empirical reasons to
analyse group NPs as sets even in languages where they always take a singular
VP, or whether it might be more accurate to allow for some variation in the
denotation of group nouns across languages.
108 Chapter 6
The second question I want to address in this chapter has to do with my
assumption, back in chapter 2, that the Ò mapping from sets to impure atoms
is freely available for all set-denoting referential NPs. Like the assumption that
group nouns uniformly range over sets, I have not backed this one up empirically;
and in fact, it can be shown that this assumption leads to predictions that are
not always borne out. For example, it predicts that referential plural NPs will
always be able to receive an impure atom denotation, which means (at least
within our current framework) that they should be able to do anything group
NPs can do. As it turns out, however, this is not the case: atom predicates like
founded in the 16th century or composed of experts, that denote properties of
groups, are compatible with group subjects but not with plurals.
(1) a. The board is composed of experts.
b. # The board members are composed of experts.
If the NP the board members were able to receive an impure atom interpretation,
we would expect sentence (1b) to be unproblematic: it could receive a semantics
equivalent to that of (1a) and be interpreted in precisely the same way. The
fact that (1b) is anomalous suggests that such a semantics is unavailable for
(1b), which in turn suggests that plural NPs like the board members cannot
always be shifted into an impure atom. It appears we should constrain our Ò
mapping in some way; the question is how.
At first glance, these two issues appear to be independent; however, I believe
that they are actually closely related. Both cases involve (potential) discrepancies
between morphosyntactic number on the one hand and semantic number
on the other: in the first case, the question is whether or not certain morphosyntactically
singular NPs should denote a semantically plural individual,
and in the second case, whether or not certain morphosyntactically plural NPs
should be able to denote a semantically singular individual. The way I will
approach the answer to these questions is very similar, too: I will argue that
whether any referential NP (whether morphoyntactically singular or plural) is
interpreted as atom- or set-denoting is strongly influenced by the animacy of
the referent. Based on several kinds of data from Dutch and Afrikaans, I will
show that inanimate NPs are much more likely to be interpreted as atomic than
animate (and especially human) NPs, regardless of morphosyntactic number;
and conversely, that animate (and especially human) NPs are much more likely
Animacy and plurality 109
to be interpreted as sets than inanimates, again regardless of morphosyntactic
number. The latter observation makes it plausible that group nouns range
over sets across languages (and not just in British English) because they are
by definition animate. The former observation suggests that the impure atom
mapping is not completely free, but licensed (or even triggered) by certain
properties of the NP including, but perhaps not limited to, a lack of animacy.
The chapter is structured as follows. In section 6.1 I address the question of
group noun denotations in other languages than British English, using a test
inspired by Pearson (2011) to determine the semantic number of embedded
group and plural NPs in Dutch. I will show that according to this test, Dutch
group nouns pattern with (animate) plurals rather than with singular inanimate
‘collection nouns’ such as pile or set, lending support to the idea that referential
group NPs also denote sets in languages (like Dutch) in which they obligatorily
appear with a singular VP. Additionally, the test shows that the behaviour
of plural NPs is not uniform either: while animate plural NPs show behaviour
characteristic of semantically plural individals, inanimate plural NPs pattern
with the singular collection nouns in behaving like atoms.
In section 6.2, I further explore the animacy connection by applying our
familiar Q-distributivity tests to Afrikaans, which marks number on the subject
NP but not on the VP. As it turns out, in the absence of morphological clues
that tell us whether we are dealing with singular or plural predication, there
is a correlation between animacy and the availability of Q-distributivity: in
Afrikaans, sentences with human subjects are more likely to be interpreted
Q-distributively than sentences with a non-human or inanimate subject. Since
Q-distributivity is a diagnostic for semantic plurality, this study confirms the
relation between animacy and semantic number that we also saw in Dutch.
In section 6.3, I return to Dutch in order to address the question of the
impure atom shift. By testing the acceptability of sentences like (1b) with
human, animate non-human and inanimate subjects, I show that the contrast
between group or collection nouns (like the board in (1a)) and plurals (the board
members in (1b)) is much smaller if these nouns refer to inanimate collections:
unlike animate plurals, inanimate plurals are relatively acceptable as the subject
of a predicate like composed of. This suggests that many speakers are able to
get an atomic interpretation of the latter, but not the former.
Section 6.4 interprets and discusses the findings of these three studies. I
introduce the so-called ‘Animacy Hierarchy’ and its relation to morphosyntactic
110
6.1. Group NPs as sets in other languages than British English: some evidence
from Dutch
number and agreement (Corbett 2000), and suggest that this relation might
reflect an underlying difference in semantic number between referents high and
low on the hierarchy. Finally I use the insights gained from our Dutch and
Afrikaans data to reflect on the two main issues from the beginning of this
introduction. Section 6.4 concludes the chapter.
This chapter is not an exhaustive investigation of the relationship between
animacy and semantic number, nor does it provide a definitive answer to the
two questions we started out with. However, the three small case studies I
discuss will provide us with both a window into this relationship and a direction
in which to look for our answers, and as such may be a good starting point for
future research.
6.1 Group NPs as sets in other languages than
British English: some evidence from Dutch
While the analysis of group NPs presented in chapter 5 allows us to treat them
uniformly across languages - i.e. as underlyingly set-denoting, even in languages
like Dutch and American English where they are not ‘outed’ as such by an
ability to occur with a plural VP - this is not the only option. In theory, we
could account for the behaviour of group nouns in other languages than British
English with a much more straightforward atomic analysis and get precisely
the same results. The downside of this simplification would be the return of
language-specific assumptions (some languages have nouns that range over sets,
others do not).
From a theory-driven point of view, the existence of nominal set predicates
should be the null hypothesis; after all, verbal and adjectival predicates also
come in both atom and set varieties. However, this does not mean that this role
should be universally played by group nouns - relational nouns like sister(s)
and neighbour(s) can also be analysed as set predicates (Winter 2002). So the
question boils down to an empirical one: is there a way to tell whether singular
group NPs underlyingly denote sets, even in languages like Dutch or American
English where they obligatorily take a singular VP?
In order to answer this question, we need a semantic environment that distinguishes
between set-denoting and atom-denoting NPs, without forcing the
Animacy and plurality 111
former to shift into the latter for type-matching reasons. In this section I suggest
one such ‘sethood test’ (based on an observation on partitives made in Pearson
(2011)) which may be applied to group nouns irrespectively of the agreement
rules of the language in question. I show that the ‘half of -test’ (as I will call
it) diagnoses Dutch singular group NPs as semantically plural; as we will see,
the Dutch data also suggest that it is animacy, rather than morphosyntactic
number, that primarily determines whether a given NP denotes a set or an atom.
This means that the results of the half of -test not only lend support to the idea
that group nouns range over sets in languages where group NPs obligatorily
take a singular VP, but also provide us with the start of an explanation, as we
have defined group nouns as precisely those nouns that, in the singular, refer to
collections of animate individuals (section 5.3.1).
6.1.1 Pearson’s ‘half of’-test
According to Pearson (2011), proportional expressions like half of the N are
sensitive to the distinction between atoms and sets. Syntactically, they are
compatible with both singular and plural Ns (as (2) shows), but the sentences
in (2a-b) have different truth conditions even if the wall refers to exactly the
same physical stuff as the bricks in the wall does:
(2) a. Half of the wall had been painted yellow.
b. Half of the bricks in the wall had been painted yellow.
According to Pearson, it does not matter for the truth of (2a) whether half
of the bricks has been painted completely yellow, half of each brick has been
painted yellow, or some bricks have been painted completely and others only
partly - (2a) is true as long as half of the stuff that makes up the wall has
been painted yellow. However, (2b) is only true in the first situation. Pearson
accounts for this contrasts as follows. She assumes (following Barker 1998)
that expressions like half of the N denote quantifiers over atomic proper parts
of N. If N denotes a set, as in (2b), those atomic proper parts are precisely
the entities that this set consists of (individual bricks in the case of (2b)). On
the other hand, if N denotes an atom as in (2a), embedding it in a partitive
NP yields a mass interpretation, which is underdetermined with respect to its
atomic proper parts (Chierchia 2010). The result is that any situation in which
half of the ‘wall-stuff’ has been painted yellow may satisfy the truth conditions
of (2a), which means that (2a) can be construed as true in more situations than
(2b).
112
6.1. Group NPs as sets in other languages than British English: some evidence
from Dutch
Pearson then goes on to apply this test to group nouns, and concludes that
they behave like (2b) rather than like (2a): sentence (3) is false in a situation
in which each committee member has been painted yellow up to the waist.
(3) Half of the committee had been painted yellow.
This means that the atomic proper parts of rrthe committeess are the individual
members of the committee, not just any partition of the committee into bits
of ‘committee-stuff’: the committee does not behave like the wall, but like the
bricks in the wall. This means that the committee, just like the bricks in the
wall, denotes a set and not an atom.
Since Pearson is herself a native speaker of (British) English and seems
to have based her judgements on introspection, we cannot simply extend the
results of her half of -test to other languages. But the test itself does extend to
other languages: since it features group NPs in embedded positions (where they
do not enter into an agreement relation with the VP), it works regardless of the
agreement requirements that the particular grammar imposes on group NPs.
More concretely, whether or not the partitive NP as a whole is shifted into
an impure atom does not make a difference: any interpretational differences
resulting from embedding either an atom or a set are preserved. This means
that Pearson’s half of -test provides us with a way to test the hypothesis that
group nouns also range over sets in other languages than British English.
6.1.2 The ‘half of’-test in Dutch
To test whether I could replicate Pearson’s results in another language than
(British) English, I gathered judgements from 15 native speakers of Dutch (for
a full description of the method and results of this small questionnaire, see
Appendix B). In Dutch, proportional partitives like half of the N always take
a singular VP, regardless of the morphosyntactic number of N. This makes
Dutch particularly suitable for the purposes of the half of -test, since there is
nothing in the syntax that might disambiguate between semantically singular
and semantically plural partitive NPs. Any interpretational difference between
the sentences in (4) must therefore be due to the semantics.
(4) a. Driekwart van de stapel tentamens is al nagekeken.
Three quarters of the pile exams is already graded
‘Three quarters of the pile of exams has already been graded’
Animacy and plurality 113
b. De helft van de meisjes is met modder bedekt.
The half of the girls is with mud covered
‘Half of the girls are covered in mud’
c. De helft van het bestuur staat op de foto.
The half of the board stands on the photograph
‘Half of the board is pictured’
If Pearson’s judgements carry over to Dutch, we expect (4a) to be true in a
situation in which three quarters of each exam has been graded, but (4b) and
(4c) to be false in situations in which half of each girl is covered in mud and
half of each board member appears in the picture, respectively. Assuming that
the Barker/Chierchia/Pearson analysis of partitives is correct, this would mean
that collection nouns (Pearson’s term for inanimate collective nouns like pile
(of exams)) range over atomic entities, while plurals and group nouns (like girls
and board) range over sets. If, on the other hand, Dutch group NPs pattern
with the collection NPs and not with the plurals, we can infer that they denote
atoms in Dutch.
According to my informants, there does turn out to be a difference in
interpretation between sentences with a partitive subject depending on whether
the embedded NP is a collection NP or a group NP: while the former are
generally judged true in ‘distributive’ situations like the ones described above,
the latter are mostly judged false. According to the above reasoning, this
confirms Pearson’s intuitions and provide support for the idea that group NPs
denote sets even in languages where they require plural agreement.
However, contrary to Pearson’s intuitions for (2), my informants’ judgements
did not show a similarly large difference between plurals and collection NPs:
while sentences with an embedded plural NP were, on average, rated ‘less
true’ than sentences with a collection NP, they were not rated as badly as the
sentences with an embedded group NP. We might therefore wonder whether
the half of -test really works as intended. If it really functions as a diagnostic
for semantic plurality, why do plural definites come out as ‘less plural’ than
group NPs?
6.1.3 The influence of animacy
In chapter 5, I defined the class of ‘group nouns’, as I use the term in this
dissertation, as those collective nouns (as defined by the OED) that refer to
collections of animate individuals. In contrast, Pearson’s ‘collection nouns’
114
6.1. Group NPs as sets in other languages than British English: some evidence
from Dutch
can be defined as those collective nouns that refer to collections of inanimate
individuals. This means that the only difference between group nouns and
collection nouns, from a conceptual point of view, is animacy. As to formal
differences between the two classes, I have argued that group nouns range over
sets; this claim is supported (for English and Dutch) by the results of the half
of -test, which also shows that collection nouns range over atoms. In short, the
difference between group nouns and collection nouns is that the former are
animate and range over sets, while the latter are inanimate and range over
atoms. The co-occurrence of animacy and semantic plurality suggests that these
properties might be connected. But if this is true, there is no a priori reason why
this connection should be limited to singular collective nouns: perhaps animate
NPs tend to be interpreted as sets and inanimate NPs tend to be interpreted as
atoms regardless of their morphosyntactic number.
As it turns out, closer inspection of my informants’ judgements appears to
confirm this hypothesis. Of the four sentences with an embedded plural NP
that I presented to my informants, two were animate and two were inanimate.
Looking at these sentences individually reveals that the two sentences with an
animate plural subject (e.g. half of the girls) were generally judged false by
my informants, just like the sentences that contained a group NP. In contrast,
the two sentences with an inanimate plural subject (e.g. half of the exams)
were generally judged true, just like the sentences with an embedded collection
NP. Thus, the test’s diagnosis of plural definites both as ‘more atomic’ than
group NPs and as ‘less atomic’ than collection NPs only holds on average: when
we separate them into animates and inanimates, we see that plural definites
clearly behave either like atoms (patterning with the collection NPs) or like
sets (patterning with the group NPs).
The entailments in (5) and (6) exemplify these results:
(5) a. Inanimate collective (‘collection’) NP: Driekwart van de stapel tentamens
is al nagekeken.
‘Three quarters of the pile of exams has already been graded’
ð Three quarters of each exam has been graded.
b. Inanimate plural NP: Driekwart van de tentamens is al nagekeken.
‘Three quarters of the exams have already been graded’
ð Three quarters of each exam has been graded.
(6) a. Animate collective (‘group’) NP: De helft van de klas is met modder
bedekt.
Animacy and plurality 115
‘Half of the class is covered with mud’
ö Each of the pupils is half covered with mud.
b. Animate plural NP: De helft van de meisjes is met modder bedekt.
‘Half of the girls are covered in mud’
ö Each of the girls is half covered with mud.
In short, the results of the Dutch half of -test, when split up according to
animacy, suggest that animate NPs that refer to collections of individuals
are interpreted as sets regardless of morphosyntactic number, and inanimate
NPs that refer to collections of things are interpreted as atoms regardless of
morphosyntactic number. This means that these findings not only support the
hypothesis that group nouns range over sets in Dutch, but also provide us with
a direction in which to look for an explanation of this: if it is true that sethood
is primarily determined by animacy, and group nouns are animate by definition,
it becomes plausible to assume that they range over sets universally and not
just in British English. In section 6.4 I offer a bit of additional speculation on
this issue.
6.2 Q-distributivity and animacy in Afrikaans
In this section, I further explore the animacy connection by applying several of
our familiar Q-distributivity tests to Afrikaans. Afrikaans is quite similar to
Dutch but does not mark any agreement features on the VP, including number:
(7) a. Die kat/katte slaap in die tuin.
The cat/cats sleep in the garden
‘The cat is / cats are sleeping in the garden’
b. Die koffiekoppie/koffiekoppies is rooi.
The coffee cup / coffee cups is red
‘The coffee cup is / coffee cups are red’
Since the VP could be either singular or plural and, accordingly, could denote
either a starred or an unstarred predicate, it should be compatible with both
atomic and set-denoting arguments. Unlike in English and Dutch, there is nothing
about the morphosyntax of the VP that could influence whether the subject
is interpreted as an atom or a set. We therefore expect the semantic number
of the subject NP (and, consequently, the availability of Q-distributivity) to
depend completely on the properties of the NP itself - like animacy. This means
116 6.2. Q-distributivity and animacy in Afrikaans
that Afrikaans - like the Dutch partitives discussed in the previous section
- provides us with a good environment to test the influence of animacy on
semantic number without the possible interference of VP morphosyntax.
I asked seven native speakers of Afrikaans for their judgements regarding the
Q-distributive interpretation of different sentences with inanimate, non-human
animate and human plural subjects, using several of the Q-distributivity tests
from chapter 3 (for a full description of the questionnaire and the obtained
data, see Appendix C). The results confirm our hypothesis that animacy and
semantic plurality are related: even though my informants generally seemed to
be able to accept the Q-distributive interpretation regardless of the animacy of
the subject, their judgements indicate that they got this interpretation more
easily when the subject was animate, and most easily when it was human. These
results are exemplified by the entailments in (8), where each arrow indicates
how easy it was for my informants to accept that particular entailment:
(8) a. Inanimate subject: Die koffiekoppies is rooi of wit.
‘The coffee cups are red or white’
hardest
ð For every coffee cup x, x is red or x is white.
b. Animate subject: Die honde hardloop deur die tuin of slaap.
‘The dogs are running through the garden or sleeping’
medium
ð For every dog x, x is running through the garden or x is
sleeping.
c. Human subject: Die meisies sing of dans.
‘The girls are singing or dancing’
easiest
ð For every girl x, x is singing or x is dancing.
Since the availability of a Q-distributive interpretation reflects the semantic
plurality of the subject NP, this means that plural NPs denoting a collection of
humans are interpreted as sets more easily than plural NPs denoting nonhuman
collections, and non-human animates are in turn more likely to be interpreted
as set-denoting than inanimates. This is in line with the results from Dutch
described in section 6.1.
Animacy and plurality 117
6.3 More on impure atoms: the Ò mapping and
group-level predicates
In the two previous sections, we have seen evidence suggesting that inanimate
NPs tend to be interpreted as atoms even if they are morphosyntactically plural.
I should perhaps emphasise that this does not mean that they are interpreted as if
they were morphosyntactically singular. The atomic entity denoted by a singular
(non-collective) NP like the coffee cup corresponds to a conceptually singular
individual (a single coffee cup), but the atomic entity denoted by an inanimate
plural NP like the coffee cups corresponds to a collection of individuals. These
semantically singular but conceptually plural entities have to be derived from
the basic noun denotation in some way. Under our current assumptions, this
can be done straightforwardly (and compositionally) by semantically pluralising
the noun, applying the maximum operator the, and then shifting the resulting
set of entities into the corresponding impure atom by means of Ò:
(9) the coffee cups :
Òpthep¦pcoffee cupqqqe
r : Ò the coffee cups :
thep¦pcoffee cupqqet
the : thepl coffee cups :
¦pcoffee cupqet,t
-s : ¦ coffee cup :
coffee cupet
We cannot do without either pluralisation or an impure atom mapping here: the
first is needed because we need the coffee cups to refer to an entire collection
of coffee cups, not to a single coffee cup; the second is needed because the
behaviour of inanimate NPs like the coffee cups in Dutch and Afrikaans shows
that they are often interpreted as semantically singular in spite of referring
to multiple coffee cups. Thus, our observations on Dutch and Afrikaans not
only suggest that semantic number is related to animacy, they also support the
need for a notion of impure atomicity and a way to derive impure atoms from
corresponding sets.
118 6.3. More on impure atoms: the Ò mapping and group-level predicates
The Dutch and Afrikaans data suggest that the impure atom shift is triggered
by a lack of animacy (although probably not obligatorily, at least not in
Afrikaans, where inanimate plurals are still more likely to be interpreted as
sets than collection nouns1
. Moreover, the Dutch half of -data suggest that
animates are very unlikely to receive an atomic interpretation even if this could
‘save’ an otherwise false sentence. Both of these observations could help us deal
with a specific problem posed by the assumption of a freely available impure
atom mapping: the overgeneration problem already briefly mentioned in the
introduction to this chapter. In the following sections, I will introduce the
problem in more detail and discuss some new data that I gathered from a large
group of Dutch native speakers, which confirm that the overgeneration problem
is much less of a problem if we assume an animacy-based restriction on the
application of the impure atom shift.
6.3.1 A problem with the impure atom mapping
In previous chapters, I have been assuming that the Ò shift from sets to impure
atoms is more or less freely available for the denotation of referential NPs.
While it is sometimes required for type-matching reasons - when a group subject
occurs with a singular VP (chapter 5), or in the case of VP coordination of
a set and an atom predicate (chapter 3, section 3.5) - it is not just a ‘last
resort’ strategy. For example, it is not possible to claim (as I have done) that
simple predication structures like ‘‘The girls smiled’’ may be analysed in terms
of P-distributivity if the impure atom shift only applies as a last resort, since
mapping the set denoted by the girls into an impure atom is not necessary for
type reasons: the sentence can be analysed with a starred predicate and a set
denotation for the girls just fine.
The assumption that the impure atom mapping is freely available, however,
is not unproblematic. It predicts that any predicate that is compatible with a
group subject should also be compatible with a plural subject, since the latter is
always able to shift into an impure atom. But, as (10) shows, this is not the case:
while the group-subject sentences in (10a) are grammatical, their plural-subject
counterparts in (10b) are not (see also Schwarzschild 1996; Winter 2001a; Magri
2012).
1See the final section of Appendix C. While the Q-distributive interpretation was not
easily available for sentences with an inanimate plural subject, my informants were unable to
get this interpretation at all when the subject was a collection NP like stapeltjie ‘stack’ or
se”elversameling ‘stamp collection’.
Animacy and plurality 119
(10) a. The council
$
'&
'%
was constituted in 2001
has five members
consists of lawyers and archaeologists
,
/.
/-
.
b. *The councillors
$
'&
'%
were constituted in 2001
have five members
consist of lawyers and archaeologists
,
/.
/-
.
Other predicates are compatible with both plural and group subjects but give
rise to a different range of available interpretations with each, as can be seen
by comparing (11a) and (11b):
(11) a. The committee is old.
ð The committee’s members are old.
ð The committee is an old institution.
b. The committee members are old.
ô The committee’s members are old.
ö The committee is an old institution.
In a system that lacks a freely available mapping from sets to impure atoms,
the data in (10) and (11) can easily be accounted for. Without such a mapping,
the semantics of sentences like those in (10b) and (11b) - which both contain
plural atom predicates - must be derived by applying a starred predicate to the
set denoted by the subject. As we have seen, this requires that each individual
member of the set of councillors or committee members be in the extension
of (unstarred) constituted in 2001 and old, respectively: ‘‘The committee
members are old’’ is true just in case the individual committee members are
old, and ‘‘The councillors were constituted in 2001’’ is true just in case the
individual councillors were constituted last year. In other words, without a
freely available impure atom mapping, these sentences receive an obligatory
Q-distributive interpretation. Since this interpretation is anomalous in the case
of (10b) and incompatible with the ‘old institution’ interpretation of (11b), the
contrasts between the (a) and (b) sentences above are accounted for.
On the other hand, in a system that allows for an atomic interpretation
of NPs like the committee members, the differences between the (a) and (b)
sentences in (10) and (11) are unexpected, since any semantics that can be
derived for the group-subject sentences in (10a) and (11a) should be available for
the plural-subject sentences in (10b) and (11b) as well. With a freely available
impure atom mapping, there is nothing in our current system that would block
the logical forms in (12b) and (13b):
120 6.3. More on impure atoms: the Ò mapping and group-level predicates
(12) a. constituted in 2001(Òthe committee)
b. constituted in 2001(Òthe committee members) (unavailable)
(13) a. old(Òthe committee)
b. old(Òthe committee members) (unavailable)
Yet, the fact that the ‘group-level’ interpretations of old and constituted are
incompatible with plural subjects suggests that these logical forms are not
available. The assumption that the impure atom mapping is freely available
thus leads to an overgeneration problem, in which non-existent interpretations
are predicted to exist.2
2In an observation related to the present one, Pollard and Sag (1994) mention that
group-level predicates like be constituted are ungrammatical with plural agreement in British
English:
(i) *A new committee have been constituted.
Similarly, Barker (1992) notes that (ii.b) (in which the group noun appears with a plural
VP) can only mean that the members of the committee are old, unlike (ii.a) which can also
mean that the committee is an old institution. (Barker also claims that (ii.a) does not have
the ‘old members’ interpretation, but this appears to be too strong a claim: according to my
informants, sentence (ii.a) can have both interpretations, just as it does in other varieties of
English.)
(ii) a. The committee is old.
b. The committee are old.
Under the analysis of group NPs as developed in chapter 5, these observations can be accounted
for just like the contrasts in (10) and (11): in (i) and (ii.b), the morphosyntactically plural
atom predicate is analysed as semantically plural and the subject is analysed as a set, and the
sentence is necessarily interpreted Q-distributively. In this case, we might get away with the
apparent unavailability of an impure atom interpretation of the committee when it occurs
with a plural VP by adopting some sort of ‘blocking’ account: since there is already a more
economical way to express a predication over an impure atom using a group subject - namely,
by using a singular VP, as in (10a) and (ii.a) - the existence of this possibility would then block
the same interpretation for the more marked (cf. Corbett 2000) plural sentences in (i) and
(ii.b). While such a blocking mechanism is not implausible, it only solves the overgeneration
problem for group subjects, not for plurals: since the latter can only occur with a plural VP,
there are no ‘competing’ forms that can end up with different meanings through a blocking
process. This means that the observed contrasts in (10) and (11) still form a challenge for
any semantic framework that includes a freely available impure atom shift.
Animacy and plurality 121
6.3.2 Group-level predicates with inanimate, animate and
human subjects
The examples above, most of which I adapted from earlier literature, all involve
human subjects. Considering the connection between animacy and semantic
plurality that we have uncovered in this chapter, it makes sense to wonder
whether the humanness of these plural NPs has something to do with their
inability to occur with a group-level predicate. If group-level predicates like
constituted and consist of behave the way they do because they are atom
predicates whose extension is restricted to impure atoms, and animate NPs are
less likely to receive an atomic interpretation than inanimate ones, we might
expect group-level predicates to be more acceptable with plural subjects if those
subjects are non-human or inanimate. According to my own judgement, the
sentences in (14) certainly sound much better than those in (10)b:
(14) a. The stolen items consist of six pearl necklaces and five gold watches.
b. These campaign ideas were compiled by our interns.
Similarly, with predicates like old and new, that can be interpreted on either an
individual or a collective level, we see a contrast between (11)b and (15). The
sentence ‘‘The matchboxes are new’’ sounds quite natural to me in the context
of (15a), in which the group-level interpretation is made salient; note that (15a)
can be true even if Susie’s matchbox collection consists mostly of antiques, as
long as the collection itself was put together recently. This suggests that the
group-level interpretation of new is available in (15b), unlike the group-level
interpretation of old in (11).
(15) a. Susie has always loved to collect things - mainly Star Wars merchandise
and matchboxes. She started her Star Wars collection ten years
ago, but the matchboxes are new.
b. The matchboxes are new.
ð The matchboxes in the collection are new.
ð The matchbox collection is new.
To further test the hypothesis that the less animate a plural NP, the more
acceptable it is with a group-level predicate, I asked 41 native speakers of Dutch
for their grammaticality/acceptability judgements on 18 different sentences,
each featuring a group-level predicate and either an inanimate, non-human
animate or human subject. (For a full discussion of the methods and results
122 6.3. More on impure atoms: the Ò mapping and group-level predicates
of this study, see Appendix D.) On the whole, my informants’ judgements
confirmed the observations from the literature: while group-level predicates are
perfectly grammatical with collective subjects of all levels of animacy, they are
at best marginal and at worst extremely degraded with plural subjects. But
the judgements also showed a clear animacy distinction: while my informants
consistently disapproved of the sentences with plural animate subjects (both
human and non-human), they were relatively happy with the inanimate ones
(even though these are still not quite as acceptable with group-level predicates
as their collection NP equivalents).
The examples in (16) summarise the link between the animacy of an NP
and its acceptability as the subject of a group-level predicate in Dutch:
(16) Inanimate subject:
a. Collective: De tiplijst is door onze eigen dj’s samengesteld.
The tip-list is by our own djs compiled
‘The list of tips was put together by our own djs’
b. Plural: ?De tips zijn door onze eigen dj’s samengesteld.
The tips are by our own djs assembled
‘The tips were put together by our own djs’
(17) Animate subject:
a. Collective: Het nestje bestaat uit twee katertjes en een poesje.
The litter consists of two male.cats and a female.cat
‘The litter consists of two males and a female’
b. Plural: *De kittens bestaan uit twee katertjes en een poesje.
The kittens consist of two male.cats and a female.cat
‘The kittens consist of two males and a female’
(18) Human subject:
a. Collective: De onderzoeksgroep is in 2010 in het leven geroepen.
The research-group is in 2010 into the life called
‘The research group was established in 2010’
b. Plural: *De onderzoekers zijn in 2010 in het leven geroepen.
The researchers are in 2010 into the life called
‘The researchers were established in 2010’
Animacy and plurality 123
Given that (according to the assumptions of the present theory) an NP should
be acceptable with a group-level predicate if it can be interpreted as an impure
atom, these data again confirm that the sets associated with inanimate plural
NPs can be shifted into impure atoms much more easily than those associated
with animate NPs.
6.3.3 Intermediate conclusions
All this means that we can no longer claim that the impure atom mapping is
freely available - but neither is it true that it only applies as a last resort to
resolve type mismatches. Rather, whenever shifting a set into an impure atom
is not necessary for type-matching reasons, it may be mapped into an impure
atom anyway but only if the NP associated with it has the right properties.
This chapter has demonstrated that a lack of animacy is one of these properties,
but there might well be more (see section 6.4.1).
Let me give a schematic overview of the picture that has emerged so far.
(19) Impure atom formation (extended version)
If Xet is the denotation of a referential NP, pÒXqe is the impure atom
corresponding to X.
X must be typeshifted to ÒX if X is:
a. the argument of an unstarred atom predicate (cf. sections 3.3.4, 5.2,
5.3.2) or a singularised set predicate (cf. section 3.4.2);
b. the argument of a complex predicate derived by intersecting or
unioning the extensions of an unstarred atom and a singularised set
predicate (cf. section 3.5).
X may be typeshifted to ÒX if:
c. the NP corresponding to X is sufficiently inanimate, where what
counts as ‘sufficiently inanimate’ might depend on the language.
In the next section, we will look at (c) in more detail.
6.4 Discussion: animacy and semantic number
The relation between animacy and morphosyntactic number has been studied
at length in the typological literature, and a great overview can be found in
124 6.4. Discussion: animacy and semantic number
Corbett (2000). Corbett demonstrates that animate NPs are crosslinguistically
more likely to be marked for number and to trigger number agreement on other
elements (like adjectives and VPs). In this section, I briefly summarise his main
points and discuss how the semantic observations made in this chapter might
tie in with Corbett’s more morphosyntactic approach. Then, armed with the
technical knowledge of Corbett’s ‘Animacy Hierarchy’, we will go back to our
three questionnaire studies in more detail to see to what extent we can define
the conditions on the impure atom mapping. Even though I will not be able
to provide any definitive conclusions, I hope to end this chapter with a better
idea of the kind of questions we still have to answer when it comes to atomic
interpretations of plural NPs, and the kind of data we have to study in order
to answer them.
6.4.1 Number agreement and the Animacy Hierarchy
In his typological overview of number and number agreement, Corbett (2000)
shows that whether or not a language expresses plural marking on a noun often
depends on animacy. For example, in the West Chadic language Miya plural
number is obligatorily marked on nouns denoting humans, domesticated animals
and large wild animals, but only optionally on inanimates (Schuh 1998):
(20) a. t`@vam ts`@r / * ’´am ts`@r (Miya)
woman.pl two / woman.sg two
‘two women’
b. z`@kiy´ay`aw vaatl@/ z`@kiy vaatl@
stone.pl five / stone.sg five
‘five stones’
In many other languages, the level of animacy of the NP determines whether
it triggers plural agreement. In the Austronesian language Muna, plural human
nouns and pronouns obligatorily take plural predicates, plural inanimates
obligatorily take singular predicates, and non-human animates may take either
(data from van den Berg 1989):
(21) a. ihintu-umu o-kala-amu / *o-kala (Muna)
2-pl 2-go-pl / 2-go.sg
‘you (plural) go’
b. bara-hi-no no-hali / *do-hali
good-pl-his 3.sg.realis-expensive / 3.pl.realis-expensive
‘his goods are expensive’
Animacy and plurality 125
c. o kadadi-hi no-rato-mo / do-rato-mo
the animal-pl 3.sg.realis-arrive-pfv / 3.pl.realis-arrive-pfv
‘the animals arrived’
We find many languages like Miya and Muna that distinguish number for
animates but not for inanimates, but the opposite pattern is unattested: there
are no known languages that express plural number on inanimate nouns but not
on animate ones, or languages where plural number agreement between an NP
and VP is optional for humans but obligatory for nonhumans. Generally, the
‘more animate’ a plural noun is, the more likely it is to be marked for number
and trigger agreement. By observing where different languages draw the line
between nouns that distinguish number and nouns that do not, it is possible to
arrive at a universal ‘Animacy Hierarchy’; Corbett’s eventual proposal (based
on an earlier version by Smith-Stark 1974) is given in (22). The constraint in
(23) expresses the above generalisation that number distinctions always affect a
top segment of the hierarchy: if a language distinguishes number for a particular
class of nouns but not for another, the former must rank higher on the Animacy
Hierarchy than the latter.
(22) The Animacy Hierarchy (Corbett, p. 56)
1st person ¡¡ 2nd person ¡¡ 3rd person ¡¡ kin ¡¡ human ¡¡ animate
¡¡ inanimate
(23) General constraint of the Animacy Hierarchy on number differentiation
(Corbett, p. 70)
As we move rightwards along the Animacy Hierarchy, the likelihood of
number being distinguished will decrease monotonically (that is, with no
intervening increase).
Corbett describes the relation between number agreement and the Animacy
Hierarchy in purely morphosyntactic terms: the higher on the hierarchy a plural
expression is, the higher the chance that other expressions will overtly agree
with it in number. The observations in this chapter suggest that we are not just
dealing with a purely morphosyntactic phenomenon, though. They show that the
Animacy Hierarchy and the associated constraint play a role even in languages
in which animacy has no influence on the morphosyntactic expression of number
at all: neither Dutch nor Afrikaans has any morphosyntactic phenomena that
depend on animacy3
, but animacy still influences semantic number in both
3Although according to van Bergen et al. (2011), animacy or at least humanness is relevant
in certain nonstandard Dutch pronoun systems.
126 6.4. Discussion: animacy and semantic number
of these languages. And it does so in a way that, as far as I can tell, obeys
the same general constraint that governs morphosyntactic number distinctions:
the likelihood that a given NP is interpreted as semantically plural decreases
monotonically as we move down the Animacy Hierarchy.
It seems unlikely to me that these two manifestations - morphosyntactic
and semantic - of the influence of animacy on number are independent. Rather,
the morphosyntactic facts that Corbett reports might be a reflection of the
underlying semantics; that is, if a predicate does not show number agreement
with its plural subject, this might be not ‘just’ because the subject carries some
syntactic feature [-animate], but because the subject is actually semantically
singular. When it comes to number agreement, languages will have to seek a
balance between faithfulness to morphosyntax and faithfulness to semantics.
In languages like American English or Dutch, VP number is fully determined
by the morphosyntactic number of the subject, regardless of whether it is semantically
singular or plural; in British English, VP number sometimes reflects
semantic rather than morphosyntactic number (resulting in plural agreement
with singular group NPs); in languages like Muna, VP agreement mostly reflects
the semantic number of the NP.
Another observation from Corbett that is important to mention here is that
agreement is influenced by other factors than just animacy - notably, highcardinality
numerical NPs are less likely to trigger plural agreement on the
VP than low-cardinality ones, as Corbett demonstrates using data from twelve
different Slavic languages (p. 215). He speculates that the influence of animacy
is really a special instance of a more general phenomenon, namely individuation:
the more we care about the individual members of the collection to which a
plural NP refers, the higher the likelihood that the NP will be marked for number
and/or trigger plural agreement. We are more likely to individuate humans than
inanimate objects; we are also more likely to individuate the members of small
collections than the members of large ones. From our semantic perspective, it is
precisely the possibility to individuate that distinguishes sets from impure atoms:
while both may refer to collections of individuals, only the former preserves
those individuals in the semantics.
6.4.2 Back to the impure atom mapping
We are now in a position to take a closer look at the influence of animacy on the
impure atom mapping, using our knowledge of the way the Animacy Hierarchy
Animacy and plurality 127
is manifested in morphosyntax to identify some relevant questions and enable
an educated guess as to their answers - anything beyond the level of educated
guess I will leave for future research.
Cut-off points. As we have seen, languages in which animacy influences
morphosyntactic number carve up the Animacy Hierarchy in different ways:
while number distinctions always affect a top segment of the hierarchy, some
languages might only distinguish plural number on first and second person
pronouns, while others might distinguish it on everything except inanimates,
and so on. We might expect this to be different when it comes to the influence
of animacy on semantic number: not only is semantics often taken to be more
‘universal’ than syntax, but the difference between sets and impure atoms is
pretty much invisible in everyday language use (we have to coax it out using
carefully designed Q-distributivity and half of -tests), so it is hard to see how a
cut-off point on the Animacy Hierarchy above which plural NPs denote sets
and below which they are likely to denote impure atoms could be learnable if it
were a language-specific part of the grammar.
Even so, this does not mean that the relation between animacy and semantic
number could not involve such cut-off points, nor that it should manifest itself in
the same way across languages. For example, if animacy is morphosyntactically
relevant elsewhere in the language’s grammar, and this involves carving up
the Animacy Hierarchy in some specific way, this same cut-off point might
govern the relation between animacy and semantic number. Another option is
that languages might have different cut-off points as a reflection of cultural
differences - it is likely, for example, that different cultures have different
views of non-human animals that may influence their position on the Animacy
Hierarchy4
. In short, further research should determine (1) whether the relation
between animacy and semantic number is a gradual one (the less animate
the NP, the more likely it is to receive an atomic interpretation) or one that
involves sharp distinctions or cut-off points between different animacy classes;
(2) whether this is language-specific or universal; and (3) how the cut-off point
(if any) is determined.
Optionality. In languages where number marking is influenced by animacy,
this is not always a matter of marking plurality above a certain point on the
4For example, Corbett mentions the Athabaskan language Slave, in which dogs (and only
dogs) ‘count as’ humans for the purposes of number marking.
128 6.4. Discussion: animacy and semantic number
hierarchy and not marking it below that: as the examples from Miya and
Muna show, sometimes the distinction is between obligatory and optional (non)marking.
We have seen that Dutch and Afrikaans inanimate plurals are more
likely to receive an atomic interpretation than human/animate plurals, but is
there a way to tell from the results if this atomic interpretation is obligatory or
merely optional?
The best way to answer this question is to compare the behaviour of
inanimate plurals with that of collection nouns; being both morphosyntactically
singular and inanimate, collection NPs can only denote atoms (as evidenced
by their near-total incompatibility with Q-distributivity in Afrikaans). Thus,
they can function as a ‘baseline’ of atomicity. If inanimate plurals pattern
with collection NPs in our various tests, we have to conclude that inanimacy
inevitably leads to atomicity. If, on the other hand, the behaviour of inanimate
plurals falls somewhere in between that of collection NPs and that of animate
plurals, we should conclude that they can denote either a set or an impure
atom, even if the latter is more likely.
Unfortunately, the results of our three studies are not consistent when it
comes to this question. The first study (the half of -test in Dutch) showed no
difference between plural and collective inanimates, which suggests that they
are equally likely to receive an impure atom interpretation. However, according
to both the second and the third study, collection nouns are still much more
likely to receive an atomic interpretation than inanimate plurals, suggesting
that the latter may still be interpreted as sets. More research is therefore needed
before we can answer this question.
Atomic interpretations of animates. A question related to the previous
point is whether the impure atom mapping is completely unavailable for animates
(unless, of course, they are involved in one of the phenomena described in (20ab)),
or merely a bit difficult. The results of the first and third questionnaire
studies suggest that it is simply unavailable - in both cases, the animates scored
close to zero, where they would have scored quite a bit higher had they been able
to receive an atomic interpretation. However, if the relation between animacy
and plurality is a special instance of a more general relation between plurality
and individuation, we expect animates to be able to shift into impure atoms
if there are other factors that reduce individuation, for example if they refer
to very large groups. It might also be possible to add contextual factors that
downplay the distinction between individual group members and emphasise
Animacy and plurality 129
the group as a single unit. For example, recall the following example from
Mador-Haim and Winter (2012) that was discussed in chapter 2:
(24) The house is exactly 10 meters away from the utility poles.
Figure 6.1: A house and a row of utility poles.
Here, the fact that sentence (24) can be interpreted as true in the depicted
situation shows that it must be possible to interpret ‘the utility poles’ as a single,
row-shaped unit, rather than a set of points. The impure atom interpretation
is natural here because we know that the utility poles are both neatly lined
up and part of a single functional system. We can invent a similar situation
involving an animate NP, for example:
(25) John is exactly 10 meters away from the ticket inspectors.
Figure 6.2: John and a row of ticket inspectors.
Here, the ticket inspectors are lined up in such a way that each of them will
end up near a door when the train arrives, ready to inspect the tickets of every
emerging passenger. If we emphasise their functioning as a single unit in this
way, my judgement is that (25) is perfectly true in the depicted situation, which
indicates (if we accept Mador-Haim & Winter’s reasoning) that I am able to
assign an atomic interpretation to the ticket inspectors despite the fact that it
refers to a collection of humans.5
5This is reminiscent of a point made in Grimm (2012), who discusses the role of individuation
in number systems. Languages like Welsh and Maltese possess a class of nouns that
refer to collections of individuals in their morphosyntactically unmarked form, and to single
130 6.5. Conclusions
6.5 Conclusions
I started out this chapter with two related questions. First, is the claim that morphosyntactically
singular group nouns range over semantically plural individuals
crosslinguistically applicable? And second, can morphosyntactically plural NPs
freely receive a semantically singular interpretation or is this restricted in some
way? I have suggested that the answers to both of these questions lie in the
observation that the higher the position of an NP on the Animacy Hierarchy,
the more likely it is to be interpreted as a set and the less likely it is to be
interpreted as an atom. This makes it plausible that group NPs - which are, by
definition, (human) animate - denote sets universally and not just in British
English, a hypothesis that was confirmed for Dutch by using the half of -test
from Pearson (2011), which should be easy to apply to other languages as well.
The observed link between animacy and semantic plurality also suggests that
the mapping Ò from sets to impure atoms that was introduced in chapter 2 is
restricted rather than completely free in its application: when it is not necessary
as a last resort operation to resolve type mismatches, it has to be licensed by
inanimacy, or more generally a lack of individuation.
individuals in their marked form:
(i) a. Ile mae ’r adar? (Welsh, from Grimm 2012)
Where is the bird
‘Where are the birds?’
b. Ile mae ’r ader-yn?
Where is the bird-sg
‘Where is the bird?’
As is often observed, these ‘aggregate nouns’ all refer to entities that tend to cluster together in
space - small animals that move in swarms or flocks, plants that grow together in patches, or
substances like grains of sand or specks of dust. Grimm argues that the unmarked (collective)
form should not be analysed on a par with plural count nouns, but as a separate kind
of individual that falls somewhere in between count and mass on a countability scale. He
also argues that this countability scale directly reflects the degree of individuation of the
noun referent: the higher the degree of individuation, the ‘more countable’ the noun will be.
According to this reasoning, languages like Welsh and Maltese show that spatial coherence is
much like animacy - both influence the degree of individuation of a noun referent, and this
influence may be reflected in a language’s number system. And just as animacy influences
the interpretation of NPs as semantically singular or plural even in languages without
grammaticalised animacy distinctions, examples like (25) suggest that spatial coherence is
relevant to the interpretation of NPs also in languages that do not recognise a separate
morphosyntactic class of aggregate nouns.
CHAPTER 7
Conclusions
The contents of this dissertation may be separated into two distinct but closely
related parts. In the first part, consisting of chapters 2 to 4, I investigated
the different sources of distributive interpretations. Its central claim is that
distributivity effects can occur with both plural and singular predication, but
through different mechanisms. In the first case, distributivity is a ‘side effect’ of
semantic pluralisation: the operation that turns a predicate over atomic entities
into a predicate over sets results in a predicate that is distributive by definition.
In the second case, distributivity is the result of reasoning about the lexical
semantics of the predicate in relation to the part-whole structure of the entity it
applies to: given the lexical meaning of P, and knowing that P holds of an entity
x with a salient part-whole structure, what can be concluded about the relation
that holds between P and the individual parts of x? Following the terminology
of Winter (1997), I called the first kind of distributivity Q-distributivity and
the second kind P-distributivity. Q-distributivity is necessarily a property of
plural predication, that requires the application of a pluralised predicate to a
semantically plural (set-denoting) argument. P-distributivity does not require a
semantically plural argument: it can occur with any singular individual with
a salient conceptual part-whole structure. The upshot of this is that only the
availability of Q-distributivity, and not the presence of distributivity effects
in general, can be used as a diagnostic for semantic plurality. To this purpose,
132 Chapter 7
several tests were developed in chapters 3 and 4 to distinguish P- from Q-
distributivity.
The second part of the dissertation, consisting of chapters 5 and 6, built on
the P/Q-distinction to ‘diagnose’ the semantic number of group NPs (chapter
5) and plural NPs with varying levels of animacy (chapter 6). The overarching
claim of this second part is that the morphosyntactic number of an NP is not a
reliable indicator of its semantic number: I argued that some morphosyntactically
singular NPs are interpreted as semantically plural (animate group NPs), and
some morphosyntactically plural NPs tend to be interpreted as semantically
singular (inanimate NPs). In addition to this, type mismatches between a plural
subject and a singular predicate can force the former to shift into an atomic
entity; I argued that this is what happens to group NPs if they occur with
a singular VP, which explains why they behave like atomic entities in most
languages.
Taken together, the two parts of this dissertation show that, once we have
determined which kind of distributivity effects are indicative of semantically
plural predication and which are not (part 1), we can use distributivity judgements
to determine whether a given NP denotes a singular or a plural individual
(part 2); the latter process both uncovers a clear relationship between semantic
plurality and animacy (or, more generally, individuation), and provides support
for a ‘flexible’ system of semantic number in which a typeshifting mechanism
systematically relates singular and plural individuals.
The main aim of this dissertation was to investigate the relationship between
morphosyntactic and semantic number of both NPs and VPs. Let me give
a schematic overview of the answers I have proposed to both parts of this
question.
Morphosyntactic and semantic number of NPs. I have argued in chapters
3, 5 and 6 that singular group NPs are able to denote sets and plural
NPs are able to denote atoms. The picture is not completely symmetrical, however:
while singular group nouns originate as predicates over sets, the atomic
denotation of plural NPs is derived from their set denotation by a typeshift.
This asymmetry - represented schematically in table 7.1 - makes sense from
a conceptual point of view: singular group nouns like team are conceptually
plural by definition, while ‘ordinary’ nouns like cat first need to be pluralised
before they can refer to a collection of individuals. It also allows us to maintain
Conclusions 133
basic predicate pure atom set of atoms impure atom
team : teamet,t n/a the team :
thepl(team)
the team :
Òpthepl(team))
cat : catet
the cat :
thesg(cat)
the cats :
thesgp¦(cat))
the cats :
Òpthesgp¦(cat)))
Table 7.1: Reference to singular and plural individuals with group and non-group
NPs
a formal system in which it is possible to derive both set and impure atom
denotations for singular group NPs as well as plural non-group NPs with only
a single typeshifting mechanism. Given this picture, it is possible to account for
both ‘mixed’ predication structures like ‘‘John and Mary are a happy couple’’
(the group noun happy couple ranges over plural individuals), and for various
entailments from group-subject sentences to plural-subject sentences and vice
versa (the NPs the team and the team members are associated with the same
set of entities, and the impure atom mapping preserves the set’s membership
structure as part of the conceptual meaning of the associated impure atom).
I observed in chapter 6 that it is much easier to shift the denotation of
an inanimate plural NPs into an impure atom than it is for animate (and in
particular human) NPs, which helps to account for the various cases in which
group-subject sentences do not entail the corresponding plural-subject sentence.
For example, ‘‘The committee is old’’ does not entail ‘‘The committee members
are old’’ because the ‘old institution’ interpretation requires the subject to
denote an impure atom, which it does in the first case because the VP is
singular, but not in the second case because the subject is human.
Morphosyntactic and semantic number of VPs. The morphosyntactic
licensing of Q-distributivity was mainly addressed in chapters 3 and 5. Based
on the notion of Q-distributivity as a diagnostic of semantic plurality, and given
the observation that British English allows Q-distributive interpretations with
group subjects when the VP is plural but not when it is singular, I argued that
only morphosyntactically plural VPs are able to denote starred predicates. This
is in line with the earlier suggestion (from chapter 3) that the pluralisation
operator ¦ does not apply at the level of the predicate itself, but at IP level,
the location of plural number morphology. This supports an analysis of ¦ as
the semantic correlate of plural number inflection. The question of the precise
syntactic or semantic mechanism by which the presence of plural number
134 Chapter 7
basic predicate singular VP plural VP
laugh : laughet
is laughing :
laugh
are laughing :
¦laugh
OR are laughing :
laugh
gather : gatheret,t
is gathering :
ògather
are gathering :
gather
OR are gathering :
ògather
Table 7.2: Reference to predicates over atoms and predicates over sets.
morphology on atom predicates licenses ¦ was left for future research.
The table in 7.2 shows the various relations between the morphosyntactic
and semantic number of VPs as proposed in this dissertation. I have argued
that plural morphology is required to license semantic pluralisation, but that
morphosyntactically plural atom predicates are not obligatorily pluralised.
This assumption is a necessary consequence of allowing morphosyntactically
plural NPs to be associated with impure atoms in languages with obligatory
subject-verb number agreement: the morphosyntactically plural NP requires
a morphosyntactically plural VP, while the semantically singular individual
associated with it requires a semantically singular predicate.
Further, while the semantic pluralisation of atom predicates has to be licensed
by plural morphology, I have assumed that semantic singularisation
of set predicates is freely available. This asymmetry enables us to derive a
semantics for coordinated atom and set predicates, which have to be of the same
type before they can be coordinated. Apart from this technically motivated
point, the relation - or lack thereof - between verbal number morphology and
the singularisation operator ò has fallen outside the scope of this dissertation.
One of the open questions is whether we should assume that morphosyntactically
singular set predicates are obigatorily singularised, or whether it is more
empirically accurate to treat ò, like ¦, as optional (i.e., should is gathering be
able to denote a predicate over sets gather despite being morphosyntactically
singular?).
APPENDIX A
British English Q-distributivity questionnaire1
A.1 Method
The judgements used in investigating the availability of Q-distributive interpretations
with British English group nouns were obtained from 6 native speakers
of British English (5 from England, 1 from Wales, all with a background in
linguistics), by means of a pen-and-paper truth value judgement task. Each test
item consisted of a sentence and a picture of a situation that was compatible
with a distributive interpretation of that sentence, but incompatible with a
collective one; subjects were asked to judge whether or not the sentence could
be true in the depicted situation.
There were 18 test items in total: three Q-distributivity tests were used
(disjunction, conjunction and other quantifiers), with two different pictures in
each test category, and each picture being accompanied by one of three different
test sentences. This led to six different ‘item clusters’ (a pictured situation with
its associated test sentences), which are all given at the end of this section.
The test items were supplemented with 8 control items (an example is given
in fig. A.1) to check whether subjects accepted group-subject sentences with
different kinds of agreement in the first place, and 13 fillers (an example is given
1I would like to thank Sophie Chesney, whose native speaker intuitions have been of great
help to me in developing this questionnaire.
136 A.1. Method
in fig. A.2). The items were then distributed semi-randomly across two versions
Figure A.1: Control item: ‘‘The Evans family is/are tall.’’
Figure A.2: Filler: ‘‘The cows are chewing on a daisy.’’
of the questionnaire. Each of the two versions contained 4 of the control items,
all of the 13 fillers, and 2 of the test items from each of the 6 item clusters:
the plural-subject item and one of the group-subject items, in such a way that
each questionnaire version contained 3 group-subject items with a singular VP
and 3 with a plural VP. A few days after filling out the first questionnaire, the
informants were asked to fill out the second version, which contained all test
and control items missing from the first one, and also had the order of these
British English Q-distributivity questionnaire 137
items reversed. The goal of all this was to rule out both sloppy answering (from
seeing the same picture too many times with near-identical test sentences) and
a possible effect of order (people might like the group-subject sentence less
when they have already seen the same situation described by a plural-subject
sentence earlier).
If the availability of Q-distributivity depends only on the number of the subject
NP and not on the number of the VP, we expect all British English group
noun sentences to behave like their Dutch and American English counterparts,
disallowing Q-distributive interpretations regardless of VP number. However,
if the availability of Q-distributivity depends on the number of the VP, we
expect British English group sentences to disallow Q-distributivity when the
VP is singular (like their American and Dutch counterparts), but to pattern
with plural-subject sentences when the VP is plural. For all test items, it holds
that the given sentence is true in the depicted situation only if it receives a Qdistributive
interpretation; thus, the number of ‘true’ responses directly indicates
the availability of a Q-distributive interpretation for every test sentence in the
questionnaire.
A.1.1 Test items
Subject type Q-distributivity test / item cluster
& VP number Disjunction 1
Plural; plural The Joneses are sleeping or watching TV.
Group; plural The Jones family are sleeping or watching TV.
Group; singular The Jones family is sleeping or watching TV.
138 A.1. Method
Subject type Q-distributivity test / item cluster
& VP number Disjunction 2
Plural; plural The reading group members are very short or very tall.
Group; plural The reading group are very short or very tall.
Group; singular The reading group members are very short or very tall.
Subject type Q-distributivity test / item cluster
& VP number Conjunction 1
Plural; plural The children are drawing and sleeping.
Group; plural The class are drawing and sleeping.
Group; singular The class is drawing and sleeping.
British English Q-distributivity questionnaire 139
Subject type Q-distributivity test / item cluster
& VP number Conjunction 2
Plural; plural The cricket players are underweight and obese
Group; plural The cricket team are underweight and obese
Group; singular The cricket team is underweight and obese
Subject type Q-distributivity test / item cluster
& VP number Quantifier 1
Plural; plural The children are hiding somewhere.
Group; plural The class are hiding somewhere.
Group; singular The class is hiding somewhere.
140 A.2. Results
Subject type Q-distributivity test / item cluster
& VP number Quantifier 2
Plural; plural The Andersons dress in black once a week.
Group; plural The Anderson family dress in black once a week.
Group; singular The Anderson family dresses in black once a week.
A.2 Results
All 8 control items were judged to be true by all informants. While this does not
strictly indicate that the informants considered both matched and mismatched
agreement equally grammatical with group subjects (they were asked for a
truth-value judgement, not a grammaticality one), it does indicate that the
informants’ truth-value judgements are not affected by potential grammaticality
differences. This means that we may also expect the judgements on the test
items to reflect the semantic differences we are interested in, rather than any
differences in grammaticality.
Fig. A.3 shows the percentage of ‘true’ judgements for each of the 18 test
British English Q-distributivity questionnaire 141
items (each triplet of bars corresponds to one of the item clusters from section
A.1.1). In total, 23% of the singular-VP group-subject sentences was judged
true, against 61% of their plural-VP counterparts and 83% of the sentences
with a plural subject. As expected, most plural-subject sentences scored close
to 100%, with the exception of two particular item clusters (Conjunction 2 and
Quantifier 2) where they only scored 10% and 50%, respectively. This might
indicate that some unexpected aspect of these sentences interfered with their
ability to be interpreted Q-distributively, which means that these sentences are
less suitable as Q-distributivity tests. If we remove the test items from those
two clusters from our calculation of the total score, the total score becomes
92% ‘true’ for the plural-subject sentences, 74% for the plural group-subject
sentences and 33% for the singular group-subject sentences (see fig. A.4).
Figure A.3: Percentage of ‘true’-judgements for each of the 18 test items.
Figure A.4: Total percentage of ‘true’-judgements for each sentence type.
APPENDIX B
Dutch half-of questionnaire
B.1 Method
I did a small questionnaire study with 15 native speakers of Dutch (recruited
from my Facebook friends, and of varying ages, backgrounds and levels of
education) to test whether I could replicate the contrast between collection
NPs on the one hand and group and plural NPs on the other reported in
Pearson (2011) for English. The questionnaire consisted of 10 items, which
in turn consisted of a situation description and a sentence pertaining to that
situation (all test items are listed at the end of this section; they appeared in
the questionnaire in random order). Of the 10 test items, four of the sentences
contained a collection noun (Pearson’s term for inanimate group-like nouns like
wall or pile of exams), four a plural NP, and two a group NP. Informants were
asked to rate the truth of each sentence on a 1-5 scale from clearly false to
clearly true.
The situations were designed in such a way that they verified the sentence
under an atomic interpretation of the embedded NP, but not under a set
interpretation (assuming Pearson’s analysis of partitives is correct). So, in
theory, we expect high scores for the collection nouns and low scores for the
plurals; the group nouns will pattern with the former if they range over atoms
144 B.1. Method
in Dutch, and with the latter if they range over sets.
B.1.1 Test items
NP type: +plural, +animate (animate plural definite)
Situation
(translated)
A group of girls has been playing football in the mud. Each of
the girls is half covered in mud.
Sentence De helft van de meisjes is met modder bedekt.
‘Half of the girls is covered with mud’
Situation
(translated)
A father is not yet sure where he stands on the issue of Black
Pete (beloved folk figure or racist caricature?). As a compromise,
he has decided to paint only half of himself black this year, an
example followed by his wife and seven children.
Sentence De helft van de gezinsleden is zwart geschminkt.
‘Half of the family members is painted black’
NP type: +plural, -animate (inanimate plural definite)
Situation
(translated)
I used to have a strange chess set whose pieces each consisted of
two halves: a ‘foot’ that was the same for all pieces, and a click-on
‘head’ that had to be attached to the foot. Unfortunately I lost
the box containing the heads, so only the feet are left.
Sentence De helft van mijn schaakstukken is kwijt.
‘Half of my chess pieces is lost’
Situation
(translated)
Yesterday, professor Johnson’s students made an exam that consisted
of 4 questions. Prof. Johnson graded questions 1, 3 and 4
from each exam, but then she didn’t feel like doing the rest, so
she put the entire pile of exams on her grad student’s desk.
Sentence Driekwart van de tentames is al nagekeken.
‘Three quarters of the exams has been graded already’
Dutch half-of questionnaire 145
NP type: -plural, +animate (group NP)
Situation
(translated)
The board of a fraternity has had portraits made of its individual
members for inclusion in the yearbook. When developing the
pictures, they discover that the camera had a defect, and the
right half of each picture is completely black.
Sentence De helft van het bestuur staat op de foto.
‘Half of the board is pictured’
Situation
(translated)
A school class just had a custard fight. Each child is three-quarters
covered in custard.
Sentence Driekwart van de klas is met vla bedekt.
‘Three quarters of the class is covered with custard’
NP type: -plural, -animate (collection NP)
Situation
(translated)
I used to have a strange chess set whose pieces each consisted of
two halves: a ‘foot’ that was the same for all pieces, and a click-on
‘head’ that had to be attached to the foot. Unfortunately I lost
the box containing the heads, so only the feet are left.
Sentence De helft van mijn schaakspel is kwijt.
‘Half of my chess set is lost’
Situation
(translated)
The board of a fraternity has had portraits made of its individual
members for inclusion in the yearbook. When developing the
pictures, they discover that the camera had a defect, and the
right half of each picture is completely black.
Sentence De helft van de portretserie is zwart.
‘Half of the portrait series is black’
Situation
(translated)
A journalist has obtained a list of members of a local youth gang,
but unfortunately he spilled coffee on it, and now either the
first or the last name of each of the gang members has become
unreadable.
Sentence De helft van de lijst is onleesbaar.
‘Half of the list is unreadable’
Situation
(translated)
Yesterday, professor Johnson’s students made an exam that consisted
of 4 questions. Prof. Johnson graded questions 1, 3 and 4
from each exam, but then she didn’t feel like doing the rest, so
she put the entire pile of exams on her grad student’s desk.
146 B.2. Results
Sentence Driekwart van de stapel is al nagekeken.
‘Three quarters of the pile has been graded already’
B.2 Results
As the graph in fig. B.1 shows, the half of -test initially does not seem to
work entirely like Pearson claims it does: with an average grade of 2.2 for the
plurals and 2.8 for the collection nouns, their behaviour when embedded in a
proportional NP does not actually seem very different. At an average grade
of 1.7, the group nouns even score a bit lower than the plurals. According
to the reasoning above, these low scores would confirm our hypothesis that
group nouns range over sets in Dutch. However, the general pattern does not
really show the large difference between collection NPs and plurals that Pearson
claims for English.
Figure B.1: Average judgements on the Dutch half of-sentences, split according
to morphosyntactic number.
Something interesting happens, however, when we split up the results according
to animacy rather than according to morphosyntactic number, as figure B.2
shows.1
When we group the inanimate plurals with the collection nouns and the
animate plurals with the group nouns, the results clearly fall into two categories:
the animates score an 1.6 on average, the inanimates a 2.8. This suggests that
1Luckily, the test items with a plural subject happened to be pretty evenly divided among
the two animacy categories even though I did not design the questionnaire with animacy in
mind.
Dutch half-of questionnaire 147
(1) animates are more likely to denote sets and inanimates are more likely to
denote atoms, and (2) this is the case regardless of the morphosyntactic number
of the NP.2
Figure B.2: Average judgements on the Dutch half of-sentences, split according
to animacy of the NP referent.
2One might wonder why, if the singular collection NPs and the inanimate plurals are all
interpreted as atomic, they do not score much higher than a 2.8 on an 1-5 scale. Pearson’s
theory and judgements for English predict that these sentences can all be interpreted as true
in the relevant situations, so we might expect them to score much closer to a 5. Looking at
the individual results, there is still a relatively large number of informants who reject these
sentences in the given contexts. If we accept the theory behind the half of -test (according
to which mass individuals are underdetermined with regard to their atomic proper parts),
this might indicate that many people have a strong preference to construe the atomic proper
parts of collection nouns as the things that make up the collection (e.g. the individual exam
papers in the case of the pile in (25)), rather than anything smaller (e.g. the individual exam
questions). The fact that it is not formally determined what the atomic proper parts of a mass
individual are does not mean that some possibilities might not be more salient than others.
What matters is that on the whole, the results show that many people are able to construe
the atomic proper parts in a different way for the inanimate nouns when such a partitioning
is made salient by the context, while for the animates such alternative partitionings are
systematically unavailable.
APPENDIX C
Afrikaans Q-distributivity questionnaire1
C.1 Method
For this questionnaire, I used several of the Q-distributivity tests from chapter 3:
VP disjunction and three different quantificational constructions. Each test item
consisted of a description of a situation (in English) and a sentence (in Afrikaans);
informants were asked to rate the truth of the sentence in the given situation
on a scale from 0 (clearly false) to 4 (clearly true). All sentences contained
a definite plural subject that was either inanimate, non-human animate, or
human. A list of all test items is given at the end of this section.
In total, the questionnaire contained 15 test items and 5 fillers, in random
order. In order to rule out possible ordering effects, I made a second version
that contained all items in reverse order. Seven native speakers of Afrikaans, all
with some background in linguistics or language studies and fluent in English,
filled out a version of the questionnaire.
1I would like to thank Christine Barkhuizen Le Roux for translating all test sentences
into Afrikaans for me, and Erin Pretorius for helping me out with some follow-up questions.
150 C.1. Method
Situation There are two cows standing in a field: a red one and a blackand-white
one. There are two birds sitting on top of the red cow
and there’s one bird sitting on top of the black-and-white cow.
All the birds are taking a nap.
Sentence Op al die beeste sit ’n vo¨el en slaap.
On all the cows sit a bird and sleep
‘On top of all the cows, a sleeping bird is sitting’
Table C.1: An example of a filler item.
Similarly to the British English Q-distributivity questionnaire (Appendix A),
the test items were all designed in such a way that the sentences could only be
true in the given context under a Q-distributive interpretation. So, a high truth
value rating reflects easy availability of a Q-distributive interpretation. Given
our approach to Q-distributivity as a diagnostic for semantic plurality, this
means that the higher the truth value rating of a sentence, the more easily its
subject is interpreted as semantically plural. If it is true that semantic number
is influenced by animacy, we therefore expect sentences with human subjects to
receive higher scores than sentences with non-human or inanimate subjects.
C.1.1 Test items
Subject type Q-distributivity test: VP disjunction
Inanimate 1 Situation: My neighbour has a lot of guests coming over and
wants to borrow my coffee cups. I have five red coffee cups and
five white ones. Since I’m busy and can’t get them myself, I tell
my neighbour to just take the ten cups from my cupboard. To
make sure she’ll get the right ones, I tell her:
Sentence: Die koffiekoppies is rooi of wit.
‘The coffee cups are red or white’
Inanimate 2 Situation: There’s a very old and uninhabited house in my street
that’s slowly falling apart. Half of the house’s windows are broken.
The other half are still whole but someone has sprayed paint on
them.
Sentence: Die rame is gebreek of met verf bemors.
‘The windows are broken or soiled with paint’
Afrikaans Q-distributivity questionnaire 151
Animate 1 Situation: I’m watching my neighbour’s dogs, who are out in
the garden. Several of the dogs are asleep under a tree, the others
are running around.
Sentence: Die honde hardloop deur die tuin of slaap.
‘The dogs are running through the garden or sleeping’
Animate 2 Situation: I work in an animal rescue. Recently people have been
bringing in a lot of seabirds. Currently we are taking care of ten
birds. Half of them have broken legs. The other half are covered
in oil from an oil spill.
Sentence: Die vo¨els het olie op hulle vere of gebreekte pootjies.
‘The birds have oil on their feathers or broken legs’
Human 1 Situation: A group of girls is practicing for a musical. Half of
them are singing; the others are dancing.
Sentence: Die meisies sing of dans.
‘The girls are singing or dancing.’
Human 2 Situation: During a boring board meeting, several of the managers
present are trying to kill time by doodling stick figures
in the margins of their paperwork. The rest have simply fallen
asleep.
Sentence: Die bestuurders slaap of sit en figuurtjies teken.
‘The managers are sleeping or doodling’
Subject type Q-distributivity test: Quantificational object
Inanimate Situation: A couple of years ago oil was discovered in a small
local desert area. Three different companies each drilled an oil
well there. The three wells yielded so much oil that the directors
of all companies got incredibly rich.
Sentence: Die oliebronne het iemand baie ryk gemaak.
‘The oil wells have made someone very rich’
Animate Situation: My office is currently home to two mice, a large brown
one and a small grey one. This week two unsuspecting visitors
foolishly left their lunch lying out in the open. First the brown
mouse came out and ate the first visitor’s lunch. Then, the grey
mouse appeared and ate the second visitor’s lunch.
Sentence: Die muise het iemand se kos opge¨eet.
‘The mice have eaten someone’s food’
152 C.1. Method
Human Situation: Three criminals escaped from prison recently. They’ve
since split up and are hiding out in different cities; yesterday,
each of them mugged someone there.
Sentence: Die boewe het iemand beroof.
‘The criminals have mugged someone’
Subject type Q-distributivity test: Quantificational adverb
Inanimate Situation: I own three bicycles. One of them is parked in my
shed. One of them is parked at the train station in the city where
I work. The third, which I use for cycling trips in the national
park near where my parents live, is parked at my parents’ place.
Sentence: My fietse is ˆerens geparkeer.
‘My bicycles are parked somewhere’
Animate Situation: My neighbour owns a small number of cows, which
he keeps in several different fields a couple of miles apart. One
day, in a rather mysterious event, the cows decided to break out
simultaneously: despite being miles apart, they broke through
the fencing around their fields and wandered off. In total, seven
different fences got wrecked.
Sentence: Die beeste het ˆerens deur ’n hek gebreek.
‘The cows have broken through a fence somewhere’
Human Situation: Three scientists, John, Mary and Sue, each went to a
different foreign country to do various kinds of fieldwork. John
went to Russia to study a couple of minority languages. Mary
went to the Amazon to collect plant samples. Sue went to Japan
to do an anthropological study of teenage gamer culture.
Sentence: Die wetenskaplikes het ˆerens veldwerk gedoen.
‘The scientists have done fieldwork somewhere’
Afrikaans Q-distributivity questionnaire 153
Subject type Q-distributivity test: Comparative quantification
Inanimate Situation: I’m at a party with a friend. In the span of half an
hour, I finish one bottle of beer, while my friend finishes three
cocktails. I’m worried that she might not be able to drive home,
but my friend tells me not to worry: she has calculated that each
of the cocktails contained only 8 ml of alcohol. On the other hand,
I might want to worry about my beer, since it’s a Belgian triple
that contains 20 ml of alcohol! My friend claims:
Sentence: Die cocktails bevat minder alkohol as die bier.
‘The cocktails contain less alcohol than the beer’
Animate Situation: Two cats and one owl went mouse-hunting. The cats
each caught three mice. The owl caught five mice.
Sentence: Die katte het minder muise as die uil gevang.
‘The cats have caught fewer mice than the owl’
Human Situation: Last week Mary went to the country fair with her
three brothers. They played a lot of games and each of the children
won several prizes. Mary won a total of four prizes, and her three
brothers won two prizes each.
Sentence: Die seuns het minder pryse as Marie gekry.
‘The boys have won fewer prizes than Mary’
C.2 Results
On average, the sentences with an inanimate subject scored an 1.86 on a 0-4
scale. The nonhuman animates scored slightly higher at 1.97, and the human
subjects scored the highest with an average of 2.57. The results can be seen
in fig. C.1 and C.2.2
As fig. C.1 shows, the human-subject sentences receive
the highest truth value ratings in each of the four Q-distributivity tests used
(although in one case, they tie with the inanimates). In three of the four tests,
the inanimates score the lowest. Although the differences are not extremely
large, they are mostly consistent, supporting the conclusion that Q-distributive
interpretations are more easily available for sentences with human subjects than
for sentences with nonhuman subjects, and least easily of all for sentences with
2One informant was consistently unable to get the distributive interpretation anywhere,
as evidenced by her awarding a score of zero to each of the test items. When her results are
discounted, the averages become 2.17, 2.31 and 3.00, respectively; the relative pattern stays
the same.
154 C.3. Group nouns
Figure C.1: Mean truth value judgements for each Q-distributivity test, split
according to the degree of animacy of the sentence subject. (Each bar corresponds
to the average score for a single test item, except the three leftmost ones
(‘Disjunction’), which each show the average score of two items.)
inanimate subjects. As noted above, since the availability of a Q-distributive
interpretation reflects the semantic plurality of the subject NP, this means that
plural NPs denoting a collection of humans are interpreted as sets more easily
than plural NPs denoting nonhuman or inanimate collections.
C.3 Group nouns
While this questionnaire did not focus on the interpretation of group nouns, I
later sent the participants a small follow-up questionnaire containing four test
sentences (along with some fillers): two had a (human) group NP subject, two
an (inanimate) collection NP.
Subject type Q-distributivity test: VP disjunction
Collection NP Situation: My neighbour has a lot of guests coming over and
wants to borrow my coffee cups. I have five red coffee cups and
five white ones and they’re all stacked up in a single stack in my
cupboard. I tell my neighbour to just take the entire stack from
my cupboard. To make sure she’ll get the right cups, I add:
Sentence: Die stapeltjie is rooi of wit.
‘The stack is red or white’
Afrikaans Q-distributivity questionnaire 155
Group NP Situation: A local primary school organises a summer camp
for the oldest kids every year. It traditionally ends with a big
game where the children, divided into a boy team and a girl team,
compete against each other on various subchallenges. The children
take this event very seriously and, on the day of the match, are
seen preparing for it in various ways. The girls are mostly doing
stretching exercises. The boys on the boy team have different
strategies: half of them are running around to warm up, the other
half are taking a last-minute nap.
Sentence: Die seunspan hardloop of slaap.
‘The boy team is running or sleeping’
Subject type Q-distributivity test: Quantificational adjunct
Collection NP Situation: After my grandfather’s death, the family had to decide
what to do with his huge and valuable stamp collection. In the
end the albums were distributed among many different friends
and family members all over the world, so the stamps are now
stored in many different places.
Sentence: Die se¨elversameling is ˆerens gestoor.
‘The stamp collection is stored somewhere’
Group NP Situation: Our local chess club mostly consists of amateurs who
just play for fun, with the exception of John, Mary and Bill (locally
known as ‘the trio’): not only are they very close friends who are
often seen together, they are also extremely good professional chess
players who regularly compete in international tournaments. Last
weekend, John played an important chess match in Amsterdam,
Mary played a match in Tokyo, and Bill played one in Cape
Town.
Sentence: Die trio het ˆerens ’n wedstryd gespeel.
‘The trio has played a match somewhere’
Five informants filled out the follow-up questionnaire, with inconclusive
results. The group-subject sentence containing a VP disjunction received an
average score of 2.80, which is comparable to the scores the animate pluralsubject
sentences from the main questionnaire received. This would support
the idea that group nouns range over sets in Afrikaans. However, the other
group-subject sentence (involving the quantificational adjunct ˆerens) showed
a sharp decline in the mean rating compared to the plural-subject sentences:
156 C.3. Group nouns
Figure C.2: Mean truth value judgements for all Q-distributivity tests together.
only one of the informants gave it a full score of 4, the others all gave it a zero
rating (an average score of only 0.80). This suggests that this particular group
NP (die trio) is interpreted as an atom by the majority of speakers.
At an average score of 0.70, the two sentences with a collection subject
(stapeltjie ‘stack’ and se¨elversameling ‘stamp collection’) scored quite a bit
lower than their inanimate plural counterparts from the main questionnaire.
This would fit with an analysis in which collection NPs are atomic from the
start - a set interpretation is just not available to them. In contrast, inanimate
plural NPs have to be shifted into atoms from their original set denotation. The
contrast between collection NPs and inanimate plurals suggests that while this
shift is made more easy or likely by a lack of animacy, it is still optional: unlike
inanimate singulars, inanimate plurals can still receive a set interpretation.
Since the results here are based on very little data, and (with regard to the
group nouns) inconclusive to boot, it is unfortunately impossible to use them
as the basis of anything more than tentative suggestions. I hope to be able to
address the interpretation of Afrikaans group NPs in future research.
APPENDIX D
Dutch group-level predicates questionnaire
D.1 Method
Unlike the questionnaire studies described in the previous three appendices,
this one involved grammaticality ratings rather than truth-value judgements. I
used three different group-level predicates (predicates that, based on my own
judgements, were grammatical with collective subjects of all animacy types, but
ungrammatical/anomalous with similar plural subjects), and combined each
of them in a sentence with collective as well as plural versions of inanimate,
non-human animate and human subjects. This resulted in 18 test items (3
predicates ¢ 3 animacy categories ¢ 2 number categories), to which I added
15 fillers. Two example fillers can be seen below; a list of all test items can be
found at the end of this section. I added a bit of context to each sentence so
the informants wouldn’t give them a low grade simply because they did not
fully understand what the sentence was ‘about’.
To avoid having a very long questionnaire with a lot of near-identical items
that might provoke sloppy answering or betray the purpose of the study, I
made two questionnaires, each containing 9 of the test items and all 15 fillers in
random order. Each questionnaire contained either the plural or the collective
version of each test sentence. 41 native speakers of Dutch of varying ages,
158 D.1. Method
Context (translated): A baby has built a block tower.
Sentence: De toren is uit blokken opgestapeld.
‘The tower is piled up from blocks’
Context (translated): The library in our village is so small that over
the years I’ve read all the books in it.
Sentence: Ik heb de bibliotheek ´e´en voor ´e´en gelezen.
‘I’ve read the library one by one’
Table D.1: Two examples of filler items; most of the fillers contained either a
collective predicate or a collective NP, so they would not stand out too much
from the test items, but they did not contain group-level predicates and, if they
were ungrammatical, they were not ungrammatical in the same way as the test
items might be.
backgrounds and levels of education (recruited via Facebook), filled out one of
the questionnaires, rating the acceptability of each sentence on a scale from 0
(‘you can’t say that at all!’) through 2 (‘I wouldn’t say this but someone else
might’) to 4 (‘perfectly fine’).
D.1.1 Test items
Subj. type Predicate: samengesteld ‘assembled’
Inanimate Context: A radio station publishes a list of ‘tips’ every week,
consisting of the station’s djs favourite new songs.
Stc.:
#
De lijst is
De tips zijn
+
door onze eigen dj’s samengesteld.
‘The list is / the tips are assembled by our own DJs’
Animate Context: A zoo has started a new breeding programme for giraffes
and put together a herd with giraffes from all over Europe.
Stc.:
#
De kudde is
De giraffes zijn
+
in overleg met een geneticus
samengesteld.
‘The herd was / the giraffes were assembled in consultation
with a geneticist’
Dutch group-level predicates questionnaire 159
Human Context: Two football experts have put together the hypothetical
‘best football team of all times’.
Stc.:
#
Het team is
De voetballers zijn
+
door twee voetbalexperts samen-
gesteld.
‘The team was / the football players were assembled by two
experts’
Subj. type Predicate: in het leven geroepen ‘established’ (lit. ‘called into
life’)
Inanimate Context: Ten years ago, my great uncle started collecting and
catalogueing all sorts of family memorabilia, for the benefit of
future generations.
Stc.:
#
De familieverzameling is
De familie-memorabilia zijn
+
door mijn oudoom in het
leven geroepen.
‘The family collection was / the family memorabilia were established
by my great uncle’
Animate Context: Since the 80s, geneticists have been carefully breeding
the offspring of the genetically modified stallion Kevin in order
to study how the altered gene manifests itself throughout the
generations.
Stc.:
#
De bloedlijn is
De paarden zijn
+
in de jaren ’80 in het leven geroepen.
‘The bloodline was / the horses were established in the 80s’
Human Context: The university established a special interdisciplinary
‘Social Media’ research group, consisting of several anthropologists,
psychologists and computer scientists, among others.
Stc.:
#
De onderzoeksgroep is
De onderzoekers zijn
+
in 2010 in het leven geroepen.
‘The research group was / the researchers were established in
2010’
Subj. type Predicate: bestaan uit ‘consist of’
160 D.2. Results
Inanimate Context: A jewelry shop was robbed.
Stc.:
#
De buit bestaat uit
De buitgemaakte voorwerpen bestaan uit
+
vijf parelkettingen
en zes horloges.
‘The loot consists of / the stolen items consist of 5 pearl
necklaces and 6 watches’
Animate Context: A litter of three kittens.
Stc.:
#
Het nestje bestaat uit
De kittens bestaan uit
+
twee katertjes en ´e´en poesje.
‘The litter consists of / the kittens consist of two males and
one female’
Human Context: An advisory committee with five members.
Stc.:
#
De commissie bestaat uit
De adviseurs bestaan uit
+
twee juristen en drie bedrijfs-
kundigen.
‘The committee consists of / the advisors consist of two
lawyers and three business administrators’
D.2 Results
As the graph in fig. D.1 shows, the general pattern confirms the observations
from Schwarzschild (1996), Winter (2001a) and Magri (2012): while the used
predicates are fine with collective nouns1
, they are quite degraded with plurals.
While the sentences with a collective subject score a 3.4 on average, those
with plural subjects score only a 1.1. This supports an analysis of group-level
predicates as predicates over impure atoms, which leads to an anomaly when
they are are applied to a set of pure atoms.
The second thing to note about the graph is that plural inanimate NPs, even
though they are not quite as acceptable with group-level predicates as their
collection NP equivalents, nevertheless receive much higher ratings than plural
human and non-human animate NPs. The latter two received an average score
of 0.7, while the sentences with an inanimate plural subject scored an 1.7, nearly
1The graph also shows that non-human animates score a bit lower than the group nouns
and the collection nouns; the average is dragged down by one particular sentence whose subject
(bloedlijn ‘bloodline’, intended to refer to a group of related horses) might, in retrospect, be a
bit too abstract to qualify as a real collective noun. I think that this relatively low average
score reflects this somewhat unfortunate choice of test item, rather than any fundamental
property of non-human animate collectives that somehow sets them apart from human and
inanimate ones.
Dutch group-level predicates questionnaire 161
Figure D.1: Mean grammaticality judgements for Dutch sentences with group-level
predicates, split according to animacy and morphosyntactic number of the sentence
subject.
2.5 times as high. This confirms our hypothesis that the sets associated with
inanimate plural NPs can be shifted into impure atoms much more easily than
those associated with animate NPs, a result in line with our earlier observations
on both Dutch (the half of -test, see Appendix B) and Afrikaans (Q-distributivity,
see Appendix C).
The third thing the graph suggests is that the relation between animacy and
the ability to shift into an impure atom in Dutch seems to involve an abrupt
‘cutoff point’ rather than a gradual increase in grammaticality as we move down
the animacy hierarchy. However, because of the small number of test items
involved, we cannot draw anything more than a very tentative conclusion from
this at this point.
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Samenvatting
Deze dissertatie gaat over de formele interpretatie van enkelvoudige en meervoudige
naamwoordsgroepen zoals Marietje of mijn cavia’s. De formele semantiek
houdt zich niet zo bezig met de betekenis van individuele woorden,
maar met de rol die een woord of zinsdeel speelt bij het ‘berekenen’ van de
betekenis van de zin als geheel. Dit betekent dat ik niet zozeer genteresseerd
ben in de eigenschappen van Marietje of de vraag wat een cavia tot een cavia
maakt, maar in de wiskundige objecten waarmee we kunnen modelleren wat zo’n
enkelvoudige of meervoudige naamwoordsgroep bijdraagt aan deze berekening.
Een intu¨ıtieve suggestie is om gebruik te maken van de verzamelingenleer,
waarbij we de betekenis van een enkelvoudige naamwoordsgroep (zoals Marietje
of mijn cavia) associ¨eren met een entiteit (‘atoom’), en de betekenis van een
meervoudige naamwoordsgroep (zoals Marietje en Jantje of mijn cavia’s) met
een verzameling entiteiten. Met andere woorden: morfosyntactisch getal (of de
vorm van het woord of zinsdeel enkelvoudig of meervoudig is) komt overeen
met semantisch getal (of het woord of zinsdeel verwijst naar een atoom of naar
een verzameling).
Er zijn echter een paar redenen waarom zo’n ´e´en-op-´e´en-relatie tussen
morfosyntactisch en semantisch getal waarschijnlijk een te simpele voorstelling
van zaken is. Er zijn bijvoorbeeld naamwoordsgroepen (vanaf nu ‘NP’s’, voor
noun phrase) die weliswaar een enkelvoudige vorm hebben, maar waarvan de
betekenis meervoudig lijkt: de rol die ze spelen in het grotere geheel van de zin
of het discourse lijkt meer op die van mijn cavia’s dan op die van Marietje. Ze
kunnen bijvoorbeeld voorkomen met elementen die normaal bij meervouden
horen, zoals een meervoudig voornaamwoord (hun in (1a)) of een meervoudig
werkwoord (zoals in de Brits Engelse zin in (1b)):
172 Samenvatting
(1) Elk gastgezin heeft hun eigen begeleider.1
(2) My family are early risers.
‘Mijn familie zijn vroege vogels’
En ze zijn vaak grammaticaal in zinnen waar ‘normale’ enkelvoudige NPs dat
niet zijn (maar meervoudige NPs wel):
(3) a. *Marietje verzamelde zich / kwam bijeen / ging uit elkaar
b. De meisjes verzamelden zich / kwamen bijeen / gingen uit elkaar
a. De commissie verzamelde zich / kwam bijeen / ging uit elkaar
(4) a. *Jantje en Marietje zijn een cavia.
b. Jantje en Marietje zijn een cavia en een konijn.
c. Jantje en Marietje zijn een gelukkig echtpaar.
Andersom nemen sommige semantici aan dat morfosyntactisch meervoudige
NPs kunnen worden ge¨ınterpreteerd als semantisch enkelvoudig. De motivatie
voor deze aanname is vaak nogal technisch, maar hier is een wat meer intu¨ıtieve
reden (gebaseerd op data in Mador-Haim & Winter 2012; de pijltjes geven aan
of en hoe de verschillende statements uit elkaar volgen):
(5) a. Marietje kuste de jongens.
ô Marietje kuste jongen1 & Marietje kuste jongen2 &... Marietje
kuste jongenzoveel.
b. De muis zit in de aardappels.
ø De muis zit in aardappel1 & de muis zit in aardappel2 &... de
muis zit in aardappelzoveel
De zin in (5a) betekent dat Marietje in een ‘kus’-relatie staat tot elk van de
jongens (de interpretatie rechts van de pijl). Maar de vergelijkbare zin in (5b)
interpreteren we niet op deze manier: (5b) betekent niet dat de muis in een
‘in’-relatie staat tot elk van de aardappels (of zelfs maar ´e´en van de aardappels),
maar dat er sprake is van een ‘in’-relatie tussen de muis en zoiets als ‘de berg
aardappels’. Zin (5b) is waar als de muis tussen de aardappels in zit, zolang
de aardappels samen maar een samenhangend geheel vormen waardoor we ze
als ´e´en enkele complexe entiteit kunnen zien. Bovenstaande zinnen suggereren
dus dat morfosyntactisch meervoudige NPs onder bepaalde omstandigheden
kunnen worden ge¨ınterpreteerd als semantisch enkelvoudig.
1Gevonden via Google op adopteereenhond.com.
Samenvatting 173
Het doel van deze dissertatie is om de relatie tussen morfosyntactisch en
semantisch getal nader te onderzoeken - met name de vraag of een formele
theorie van semantisch getal volledig kan functioneren zonder ‘mismatches’
tussen morfosyntax en semantiek (zoals bovenstaande) toe te staan. Mijn conclusie
is dat dit niet mogelijk is: om alle relevante data uit verschillende talen
te kunnen modelleren, moet ons semantisch systeem zowel in staat zijn om
enkelvoudige NPs te interpreteren als verzamelingen, als om meervoudige NPs
te interpreteren als atomen. Ik stel voor dat deze semantische flexibiliteit gereguleerd
wordt door twee verschillende mechanismen. Het eerste is het vermijden
van zogenaamde ‘type-mismatches’ tussen onderwerp en predikaat. Het onderwerp
en predikaat dienen hetzelfde semantische getal te hebben, anders loopt
de semantische ‘berekening’ spaak; wanneer een predikaat enkelvoudig is en
het onderwerp meervoudig kan het laatste een ‘type-verschuiving’ (typeshift)
ondergaan naar een semantisch enkelvoudige interpretatie. De tweede factor
die bepaalt of een gegeven NP geassocieerd wordt met een atoom danwel een
verzameling is de mate van bezieldheid (animacy) van de referent: hoe ‘bezielder’
het individu (of de individu¨en) waarnaar de NP verwijst, hoe groter de kans
dat deze ge¨ınterpreteerd wordt als een verzameling, en hoe minder bezield, hoe
groter de kans dat deze ge¨ınterpreteerd wordt als een atoom - ongeacht het
morfosyntactisch getal van de NP. (Bezieldheid is van invloed op grammaticale
fenomenen in veel verschillende talen en kent een universele hi¨erarchie, grofweg:
mensen zijn het meest bezield, dieren minder, levenloze voorwerpen het allerminst.)
Ik stel voor dat de invloed van bezieling op semantisch getal te maken
heeft met ‘individuatie’ (Corbett 2000, Grimm 2012): hoe meer we geneigd zijn
de leden van een groep waarnaar een bepaalde NP verwijst als zelfstandige
individuen te zien, hoe groter de kans dat we deze zelfstandige individuen ook
terugzien in de verzamelingtheoretische structuur van de NP-semantiek. En
andersom: als het onderscheiden van individuele groepsleden van minder belang
is (zoals in het geval van de berg aardappels hierboven) is de kans groot dat de
NP ge¨ınterpreteerd wordt als een enkelvoudig complex ‘groepsatoom’.
In hoofdstuk 2 presenteer ik een basaal theoretisch kader voor de semantiek van
getal, met daarin diverse ‘formele gereedschappen’ die we kunnen gebruiken
om de in deze dissertatie besproken taaldata te analyseren.
In hoofdstuk 3 (en voor een deel hoofdstuk 4) ontwikkel ik een serie testjes
waarmee we kunnen bepalen of een gegeven NP in de semantiek met een verzameling
of met een atoom geassocieerd wordt. De testjes zijn gebaseerd op de
174 Samenvatting
aanwezigheid van een zogenaamde distributieve interpretatie in bepaalde contexten.
Een predikaat P geldt als distributief als P, wanneer het van toepassing
is op een groep individuen, daarmee ook van toepassing is op ieder individu in
die groep. We kunnen op basis van (6a) bijvoorbeeld afleiden dat (6b) waar
moet zijn:
(6) a. De cavia’s (Jantje en Marietje) fluiten.
b. Jantje fluit en Marietje fluit.
Er zijn twee manieren waarop we dit soort distributieve interpretaties kunnen
benaderen. De eerste benadering (terug te voeren op Link 1983) is om de interpretatie
van meervoudige distributieve predikaten zoals fluiten te modelleren
met behulp van een soort verborgen universele kwantor over leden van de verzameling
die geassocieerd is met het zinsonderwerp - de verzameling bestaande uit
de entiteiten jantje en marietje in het geval van (6a). Volgens deze theorie
heeft zin (6a) min of meer dezelfde formele structuur als de zin ‘‘Elk van de
cavia’s fluit’’, alleen is de ‘elk’ niet hoorbaar. Kwantificatie werkt alleen als het
onderwerp een verzameling is; een kwantor als ‘elk’ kan niet worden toegepast
op een atoom. Als deze theorie klopt, kan de beschikbaarheid van een distributieve
interpretatie dus fungeren als lakmoesproef voor het semantisch getal van
het zinsonderwerp, omdat deze interpretatie alleen kan worden afgeleid als het
onderwerp semantisch meervoudig is.
Het is echter ook mogelijk om distributiviteit te benaderen op een manier die
geen relatie veronderstelt tussen distributiviteit en semantisch getal. Scha (1981)
stelt bijvoorbeeld voor dat distributieve gevolgtrekkingen zoals die van (6a)
naar (6b) niet-formele gevolgtrekkingen zijn die ontstaan doordat we redeneren
over de lexicale betekenis van het betreffende predikaat in een bepaalde context.
Als bij bestudering van de data blijkt dat een lexicale theorie zoals die van Scha
beter in staat is de relevante data te verklaren, kunnen we distributiviteit dus
niet gebruiken om conclusies over semantisch getal op te baseren.
Een derde mogelijkheid is de twee benaderingen te combineren en aan
te nemen dat zowel formele als lexicale mechanismen ten grondslag kunnen
liggen aan distributiviteit: sommige distributieve gevolgtrekkingen zijn alleen
te verklaren als we een kwantificationele operatie aannemen, andere zijn juist
alleen te verklaren met behulp van lexicale mechanismen. Voortbouwend op
o.m. Dowty 1987; Hoeksema 1988; Winter 1997, 2000; en Champollion 2010
betoog ik dat dit de best werkende benadering is. Het belangrijkste argument
voor deze conclusie is het gedrag van groeps-NPs zoals de eerdergenoemde mijn
Samenvatting 175
familie en de commissie. Deze staan niet alle distributieve gevolgtrekkingen
toe, zoals het contrast in (7) laat zien:
(7) a. De commissie grinnikte
ô Elk van de commissieleden grinnikte.
b. Het dispuut is voor de helft kaalgeschoren.
ø Elk van de dispuutsleden is voor de helft kaalgeschoren
Ik laat zien dat alle distributieve gevolgtrekkingen die in principe verklaard
kunnen worden in termen van lexicale processen ook beschikbaar zijn als het
zinsonderwerp een groeps-NP is (dit geldt bijvoorbeeld voor (7a)). Distributieve
gevolgtrekkingen die alleen kunnen worden afgeleid door middel van kwantificatie
over individuele groepsleden zijn echter systematisch afwezig als het
onderwerp een groeps-NP is: zo kan (7b) alleen betekenen dat de helft van de
dispuutsleden helemaal kaalgeschoren is, niet dat ieder van de dispuutsleden half
kaalgeschoren is. Het contrast tussen (7a) en (7b) laat twee dingen zien. Ten
eerste ondersteunt het een analyse van groeps-NPs als semantisch enkelvoudig
(ondanks hun ogenschijnlijke ‘meervoudigheid’ in zinnen als (1-4)). Ten tweede
toont het aan dat we twee verschillende distributiviteitsmechanismen nodig
hebben: ´e´en die wel beschikbaar is in zinnen met groepsonderwerpen (en dus
onafhankelijk is van semantisch getal), en ´e´en die niet beschikbaar is in zinnen
met groepsonderwerpen (en dus een semantisch meervoudig onderwerp vereist).
In navolging van Winter (1997) noem ik deze twee vormen respectievelijk
P-distributiviteit (‘P’ van ‘predikaat’) en Q-distributiviteit (‘Q’ van ‘quantification’).
Zinnen als (7b) stellen ons in staat de twee vormen van elkaar te
onderscheiden: als een dergelijke zin een distributieve interpretatie heeft, kan dat
alleen Q-distributiviteit zijn en is het onderwerp dus semantisch meervoudig. In
hoofdstuk 3 introduceer ik een hele serie van dit soort ‘Q-distributiviteitstestjes’,
die fungeren als lakmoesproef voor het semantisch getal van het zinsonderwerp.
Hoofdstuk 4 gaat in op een verschijnsel dat een probleem lijkt te vormen voor
de claim dat groeps-NPs geen Q-distributiviteit toestaan. In zinnen zoals (8)
kan het predikaat draagt een blauw shirt distributief ge¨ınterpreteerd worden
(iedere voetballer draagt haar eigen blauwe shirt), terwijl we op basis van de
theorie in hoofdstuk 3 verwachten dat de zin alleen kan betekenen dat het hele
team zich in ´e´en en hetzelfde shirt heeft gewrongen.
(8) Het voetbalteam draagt een blauw shirt.
176 Samenvatting
Vanwege zinnen zoals (8) stelt bijvoorbeeld Magri (2012) voor om groeps-NPs
wel degelijk te analyseren als semantisch meervoudig, en de distributieve interpretatie
van dergelijke zinnen dus als Q-distributiviteit. Dit gaat echter
voorbij aan het feit dat de beschikbaarheid van een distributieve interpretatie
van dit soort zinnen (met een groeps-NP als onderwerp en een onbepaalde
NP als lijdend voorwerp) een uitzondering is op de regel: volgens alle andere
Q-distributiviteitstesten uit hoofdstuk 3 gedragen groeps-NPs zich als atomen,
niet als verzamelingen. Ik stel daarom voor om de onbepaalde NP een blauw
shirt in zin (8) niet te analyseren als een existenti¨ele kwantor (waardoor we
genoodzaakt zouden zijn om een Q-distributieve analyse aan te nemen voor (8)),
maar als een zogenaamd (individueel correlaat van een) eigenschap, in navolging
van vele vergelijkbare analyses van onbepaalde NPs in de literatuur (e.g. Milsark
1974; McNally 1992; Zimmermann 1996; Mador-Haim & Winter 2007). Een
individueel correlaat van een eigenschap lijkt qua structuur op een groeps-atoom:
semantisch enkelvoudig, maar met een duidelijke conceptuele deelstructuur die
het mogelijk maakt te beredeneren wat het feit dat zo’n complexe entiteit in
(bijvoorbeeld) een ‘draag’-relatie staat tot een andere complexe entiteit precies
betekent voor de betrokkenheid van de delen (individuele voetballers en blauwe
shirts) waaruit deze entiteiten conceptueel zijn opgebouwd. We kunnen de
distributieve interpretatie van zinnen als (8) dus analyseren in de stijl van Scha,
in termen van lexicale distributiviteit over (in dit geval) meerdere argumenten
van hetzelfde werkwoord.
Na het uitstapje in hoofdstuk 4 brengt hoofdstuk 5 ons terug bij de hoofdvraag
van deze dissertatie: de relatie tussen morfosyntactisch en semantisch getal. Met
behulp van de Q-distributiviteitstests uit hoofdstuk 3, die het mogelijk maken
om predikatie over verzamelingen te onderscheiden van predikatie over atomen,
kunnen we onderzoeken van welke factoren de interpretatie van predikaten en
hun argumenten als semantisch enkelvoudig of meervoudig allemaal afhangt.
Hoofdstuk 5 neemt de rol van getalsmarkering op het werkwoord onder de loep.
Op basis van data uit het Brits Engels laat ik zien dat kwantificationele
distributiviteit (in tegenstelling tot lexicale) ‘gelicenseerd’ moet worden door
meervoudige getalsmarkering op het werkwoord (e.g. de -en in ‘‘De cavia’s
fluiten’’) - met andere woorden, alleen zinnen met een morfosyntactisch meervoudig
predikaat kunnen Q-distributief worden ge¨ınterpreteerd. In hoofdstuk
3 zagen we dat zinnen met een groeps-NP als onderwerp niet Q-distributief
kunnen worden ge¨ınterpreteerd. Dit blijkt iets genuanceerder te liggen: als we
Samenvatting 177
de Q-distributiviteitstests uit hoofdstuk 3 toepassen op het Brits Engels blijkt
dat Britse groepszinnen een Q-distributieve interpretatie kunnen krijgen, mits
het werkwoord morfosyntactisch meervoudig is (zoals in (9b)).
(9) a. The class is sleeping or drawing.
‘De klas zit te slapen of te tekenen’
Geen Q-distributieve interpretatie mogelijk: de disjunctie ‘slapen
of tekenen’ is van toepassing op de h´ele klas, alle kinderen doen
hetzelfde.
b. The class are sleeping or drawing.
‘De klas zitten te slapen of te tekenen’
Wel een Q-distributieve interpretatie mogelijk: de disjunctie ‘slapen
of tekenen’ is van toepassing op elk kind afzonderlijk, het is mogelijk
dat niet alle kinderen hetzelfde doen.
Omdat de beschikbaarheid van Q-distributiviteit een lakmoesproef is voor
semantisch getal, kunnen we uit bovenstaand contrast concluderen dat morfosyntactisch
enkelvoudige groeps-NPs (in elk geval in het Brits Engels) met
atomen geassocieerd zijn als het werkwoord morfologisch enkelvoudig is, maar
met verzamelingen als het werkwoord meervoudig is.
Om dit dubbele gedrag te verklaren stel ik voor dat groeps-NPs in de semantiek
beginnen als verzamelingen, maar dat ze verplicht een type-verschuiving
naar een atomaire ‘groepsentiteit’ ondergaan als het predikaat morfosyntactisch
enkelvoudig is. Onderwerp en predikaat moeten ‘matchen’ qua verzamelingtheoretische
structuur: een semantisch meervoudig onderwerp vraagt om semantisch
meervoudige predikatie, en een semantisch enkelvoudig onderwerp om semantisch
enkelvoudige predikatie. Matchen ze niet, dan kan er geen zinsbetekenis
berekend worden. Als we nu aannemen dat alleen morfosyntactisch meervoudige
werkwoorden in de semantiek geassocieerd kunnen worden met een meervoudig
predikaat, dan leidt de combinatie van een groeps-NP met een enkelvoudig
werkwoord dus automatisch tot zo’n mismatch: het onderwerp is semantisch
meervoudig, maar het predikaat semantisch enkelvoudig. Om deze mismatch te
kunnen oplossen moet de verzameling die geassocieerd is met de groeps-NP als
het ware worden aaneengesmeed tot een complex groepsatoom; het resultaat is
semantisch enkelvoudig en staat dus geen Q-distributiviteit meer toe. In een
taal als het Brits Engels daarentegen, die de combinatie van een groeps-NP met
een morfosyntactisch meervoudig werkwoord toestaat, is geen sprake van een
mismatch op semantisch niveau; de groeps-NP kan daardoor zijn oorspronkelijke
178 Samenvatting
semantisch meervoudige betekenis behouden, en Q-distributiviteit is mogelijk.
Deze analyse verklaart zowel de generalisatie over groeps-NPs uit hoofdstuk 3
als het specifieke gedrag van groeps-NPs in het Brits Engels op een manier die
direct volgt uit onze basale aannames over de semantiek van getal.
Hoofdstuk 6, tenslotte, is een verkenning van de relatie tussen bezieldheid
en semantisch getal in de vorm van drie verschillende case studies van het
Nederlands en het Afrikaans. De link met bezieldheid dook voor het eerst
impliciet op in hoofdstuk 5: volgens de daarin voorgestelde analyse komt de
klasse van morfologisch enkelvoudige NPs die op semantisch niveau geassocieerd
zijn met verzamelingen in plaats van atomen precies overeen met de klasse van
NPs die in het Brits Engels kunnen voorkomen met een meervoudig werkwoord;
een al heel oude observatie is dat dit alleen mogelijk is voor bezielde (en met name
menselijke) groeps-NPs, niet voor onbezielde (een zin als *The stack of plates are
dirty’’ ‘‘de stapel borden zijn vuil’’ is ook in het Brits Engels ongrammaticaal).
Dit suggereert dat er een verband is tussen semantisch meervoud en bezield-zijn
dat min of meer onafhankelijk is van het morfosyntactische getal van een NP. In
dit laatste hoofdstuk beweer ik dat het omgekeerde ook het geval is: onbezielde
NPs worden eerder ge¨ınterpreteerd als semantisch enkelvoudig, zelfs als ze
morfosyntactisch meervoudig zijn.
De eerste studie gaat in op zogenaamde partitieve NPs in het Nederlands
(NPs als de helft van de meisjes of driekwart van de groep). De interpretatie van
dergelijke NPs - getest bij moedertaalsprekers met behulp van een vragenlijst suggereert
dat morfosyntactisch enkelvoudige groeps-NPs ook in het Nederlands
geassocieerd zijn met semantisch meervoudige individuen (en dat dit dus geen
unieke eigenschap van het Brits Engels is). Hiernaast laat dit onderzoek zien dat
mensen geneigd zijn om onbezielde NPs te interpreteren als atomen, ongeacht
hun morfosyntactisch getal.
In de tweede studie pas ik, wederom met hulp van een groepje moedertaalsprekers,
verscheidene van de Q-distributiviteitstests uit hoofdstuk 3 toe op het
Afrikaans (dat geen getalsmarkering op het werkwoord kent). De resultaten
laten zien dat zinnen met meervoudige menselijke onderwerpen eerder als Qdistributief
ge¨ınterpreteerd worden dan zinnen met niet-menselijke en onbezielde
onderwerpen. Volgens de inmiddels bekende aanname dat Q-distributiviteit een
lakmoesproef is voor semantisch meervoud betekent dit dat menselijke onderwerpen
een grotere kans hebben om als verzameling te worden ge¨ınterpreteerd
dan niet-menselijke, zelfs als het in alle gevallen gaat om morfosyntactisch
Samenvatting 179
meervoudige NPs.
De derde studie gaat weer over het Nederlands. Zoals regelmatig is opgemerkt
in de literatuur zijn predikaten als samengesteld zijn, bestaan uit 5 leden en
opgericht zijn in 1999 wel grammaticaal als het onderwerp een groeps-NP is,
maar niet als het een meervoud is (vergelijk (10a) met (10b)). We kunnen dit
verklaren door aan te nemen dat dergelijke predikaten alleen groepsatomen als
argument toestaan:
(10) a. De commissie bestaat uit 5 experts.
b. *De commissieleden bestaan uit 5 experts.
Door een heleboel van dergelijke zinnen op te stellen en aan moedertaalsprekers
voor te leggen laat ik zien dat de mate waarin sprekers zinnen met een meervoudig
onderwerp als ongrammaticaal ervaren sterk afhangt van de mate van
bezieldheid van het onderwerp: een zin als (11b), met een onbezield onderwerp,
klinkt volgens mijn informanten best OK.
(11) a. De buit bestaat uit 5 horloges en 4 parelkettingen.
b. ?De buitgemaakte voorwerpen bestaan uit 5 horloges en 4 parelket-
tingen.
Dit suggereert dat bezielde meervoudige NPs in de semantiek niet (of in elk geval
niet makkelijk) geassocieerd kunnen worden met het soort atoom dat geschikt
is als argument voor een predikaat als bestaan uit..., terwijl een dergelijke
atomaire interpretatie voor een niet-bezielde NP veel makkelijker is.
Aan het slot van hoofdstuk 6 bespreek ik de gedane ontdekkingen in het licht
van de overvloedige taaltypologische literatuur over de relatie tussen bezieldheid
en morfosyntactisch getal (zoals samengevat in Corbett 2000), inclusief een
lijstje suggesties voor verder onderzoek.
Hoofdstuk 7 vat tot besluit alle conclusies van deze dissertatie nog eens samen.
Curriculum Vitae
Hanna de Vries was born on December 24, 1984, in Waalwijk in the Netherlands.
After obtaining her gymnasium diploma in 2002, she obtained a propedeuse
degree in Psychology and Cultural Anthropology from Leiden University before
switching to linguistics. In 2008, she graduated with a BA in Linguistics from
Leiden University, and in 2010 she obtained her MA degree from Utrecht
University (cum laude). In the same year, she started as a PhD researcher
within the NWO-funded project ‘Between Logic and Common Sense: the formal
semantics of words’. This dissertation is the result of four years of research on
this project.
Hanna currently works at Utrecht University as a lecturer in Linguistics
and Artificial Intelligence.