ABSTRACT
Title of dissertation: DISTRIBUTIVITY AND PLURAL ANAPHORA
Christopher LaTerza, Doctor of Philosophy, 2014
Dissertation directed by: Professor Paul Pietroski
Department of Linguistics
This dissertation is an investigation of the semantics of sentences exhibiting plural
referential dependencies. I will pursue two main lines of thought, each with consequences
for the notion of distributivity as it is understood to apply to certain linguistic phenomena.
First I consider the empirical scope of an event-based theory of distributivity, and argue
that this approach can provide a simple and empirically adequate semantics for plural
anaphoric relations such as reciprocity, reflexivity, and distance distributivity. The second
part focuses on plural referential dependencies in attitude reports; in particular I address
issues about distributivity and plurality that arise in cases of plural De Se ascription.
DISTRIBUTIVITY AND PLURAL ANAPHORA
by
Christopher LaTerza
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2014
Advisory Committee:
Professor Paul Pietroski, Chair
Professor Norbert Hornstein
Associate Professor Valentine Hacquard
Assistant Professor Alexander Williams
Associate Professor Jimmy Lin
c⃝ Copyright by
Christopher LaTerza
2014
Acknowledgments
I would first like to thank my advisor Paul Pietroski, whose influence should be
obvious in what follows. I would also like to thank my other committee members Valen-
tine Hacquard, Norbert Hornstein, and Alexander Williams, for all their years of help.
I thank all the other faculty members and students of Maryland who I have been for-
tunate enough to interact with; especially my teachers Peggy Antonisse, Tonia Bleam,
Howard Lasnik, Jeff Lidz, Colin Phillips, and Juan Uriagereka. This dissertation also
benefitted from discussions with Pranav Anand, Alex Drummond, Lucas Champollion,
John Collins, Kenshi Funakoshi, Michaël Gagnon, Sayaka Goto, Irene Heim, Yuki Ito,
Chris Kennedy, Ruth Kramer, Dave Kush, Peter Lasersohn, Brad Larson, Terje Lohndal,
Darryl McAdams, Eric McCready, Barbara Partee, Hazel Pearson, Orin Percus, Carolina
Petersen, Kyle Rawlins, Barry Schein, Zoe Schlueter, Roger Schwarzschild, Yael Sharvit,
Chris Tancredi, and Alexis Wellwood. I thank my informants for their patience and help
with the data. I owe much thanks to the linguistics community at Stony Brook University
for getting me started and continuing to be a great place to visit; especially Yukiko Asano,
my first linguistics teacher, and Richard Larson, the person responsible for me wanting to
be a semanticist. I thank my parents for their constant love and support. And most of all
I thank Ivana, for all of the above and more. What we have together is all the motivation
I need.
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Table of Contents
1 Overview 1
2 Plurality and Events 7
2.1 Thematic roles and argumenthood . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Thematic decomposition . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2 Thematic Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Degrees of separation and compositionality . . . . . . . . . . . . 17
2.1.3.1 Classic event analyses of verbs . . . . . . . . . . . . . 19
2.1.3.2 Partial separation . . . . . . . . . . . . . . . . . . . . 22
2.1.3.3 Total separation . . . . . . . . . . . . . . . . . . . . . 24
2.1.4 Ditransitives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.5 Section Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Events and the semantics of plurality . . . . . . . . . . . . . . . . . . . . 33
2.2.1 Plurality in natural language and nonfirstorderizability . . . . . . 33
2.2.2 Ontological commitments . . . . . . . . . . . . . . . . . . . . . 37
2.2.3 Interpreting the open-class lexical categories . . . . . . . . . . . 39
2.2.3.1 Nominal categories: N and Adj . . . . . . . . . . . . . 40
2.2.3.2 Clausal categories: V and Adv . . . . . . . . . . . . . 45
2.2.4 (In)definiteness . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.5 Cumulativity of thematic relations . . . . . . . . . . . . . . . . . 49
2.2.6 Distributive and collective interpretations . . . . . . . . . . . . . 51
2.2.6.1 Distributivity in event semantics . . . . . . . . . . . . 53
2.3 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Distance Distributivity 60
3.1 An overview of distance distributivity . . . . . . . . . . . . . . . . . . . 60
3.1.1 Floating each . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.2 Binominal each . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 Extending the Taylor-Schein approach . . . . . . . . . . . . . . . . . . . 70
3.2.1 The distance composition of the Taylor-Schein distributor . . . . 71
3.2.2 The distance restrictor . . . . . . . . . . . . . . . . . . . . . . . 76
3.2.2.1 The semantic value of the restrictor . . . . . . . . . . . 76
iii
3.2.2.2 Locating the thematic role of each . . . . . . . . . . . 81
3.3 Binominal each in a variety of argument positions . . . . . . . . . . . . . 83
3.3.1 Antecedence in ditransitives . . . . . . . . . . . . . . . . . . . . 84
3.3.2 Scope differences between floating and binominal each . . . . . . 88
3.3.2.1 Comparison with Champollion 2012 . . . . . . . . . . 94
3.4 Leakage revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Reciprocity 103
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2 Issues in the semantics of bipartite argument reciprocals . . . . . . . . . . 104
4.2.1 The polysemy problem . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.2 The composition problem . . . . . . . . . . . . . . . . . . . . . 109
4.2.2.1 Primitive polyadic quantification . . . . . . . . . . . . 110
4.2.2.2 Compositional complexity . . . . . . . . . . . . . . . . 113
4.2.3 The syntactic distribution of BARs . . . . . . . . . . . . . . . . . 116
4.3 Decomposing bipartite reciprocals . . . . . . . . . . . . . . . . . . . . . 118
4.3.1 Article distribution . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Preposition placement . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.3 Case distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.4 Cross-sentential anaphora . . . . . . . . . . . . . . . . . . . . . 125
4.4 Reciprocals as distance distributivity phenomena . . . . . . . . . . . . . 128
4.4.1 The semantics of the Differentiator host . . . . . . . . . . . . . . 128
4.4.2 Prepositions and Thematic Roles within BARs . . . . . . . . . . 133
4.5 Accounting for polysemy . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.5.1 Typicality preferences are extra-semantic . . . . . . . . . . . . . 137
4.5.2 Inclusive Alternative Ordering . . . . . . . . . . . . . . . . . . . 139
4.6 Beyond elementary reciprocal sentences . . . . . . . . . . . . . . . . . . 144
4.6.1 BARs as indirect objects . . . . . . . . . . . . . . . . . . . . . . 145
4.6.1.1 The Williams paradigm . . . . . . . . . . . . . . . . . 146
4.6.1.2 Nominal BARs with nominal antecedents . . . . . . . . 149
4.6.1.3 Possessor BARs . . . . . . . . . . . . . . . . . . . . . 152
4.6.1.4 BARs in picture-NPs . . . . . . . . . . . . . . . . . . 154
4.7 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5 Plural Reflexives 159
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2 Essentially distributive plural reflexives . . . . . . . . . . . . . . . . . . 160
5.2.1 The long and short of plural reflexives . . . . . . . . . . . . . . . 162
5.2.2 Purely reciprocal situations . . . . . . . . . . . . . . . . . . . . . 163
5.2.3 Purely collective situations . . . . . . . . . . . . . . . . . . . . . 166
5.3 Heim and Kratzer (1998) on reflexives . . . . . . . . . . . . . . . . . . . 167
5.4 A Taylor-Schein analysis of long-form reflexives . . . . . . . . . . . . . 169
5.4.1 A scope argument for a local D operator . . . . . . . . . . . . . . 172
5.4.2 An antecedence argument for a local D operator . . . . . . . . . 173
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5.4.3 Advantages over polyadic quantification approaches to reflexives . 174
5.4.4 A unified analysis of local plural anaphora . . . . . . . . . . . . . 176
6 Plurality and De Se reports 179
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.2 Empirical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.3 Arguments for plural De Se pronouns . . . . . . . . . . . . . . . . . . . 186
6.3.1 Cumulativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.3.1.1 Against non-lexical approach to cumulativity . . . . . . 191
6.3.2 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.3.2.1 Against scopal theories of reciprocals . . . . . . . . . . 195
6.3.3 Section summary . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.4 Theoretical background on neo-Kaplanian De Se semantics . . . . . . . . 198
6.5 A context-based semantics for plural De Se reports . . . . . . . . . . . . 203
6.5.1 Embedded clause interpretation . . . . . . . . . . . . . . . . . . 205
6.5.2 Attitude verb interpretation . . . . . . . . . . . . . . . . . . . . . 207
6.5.2.1 Pluralized accessibility relations . . . . . . . . . . . . 207
6.5.2.2 Generalizing the Hintikkan approach . . . . . . . . . . 209
6.5.3 Plural De Se pronouns . . . . . . . . . . . . . . . . . . . . . . . 211
6.5.3.1 Thematic roles strike again . . . . . . . . . . . . . . . 211
6.5.3.2 A new semantics for De Se pronouns . . . . . . . . . . 214
6.5.4 The truth conditions of plural De Se reports . . . . . . . . . . . . 217
6.5.4.1 The range of interpretations of plural De Se reports . . 220
6.5.4.2 Reciprocity as an argument for the thematic approach . 223
6.5.5 Plural ascription of predicates of personal taste . . . . . . . . . . 226
6.5.6 Severing the arguments of attitude verbs . . . . . . . . . . . . . . 227
6.6 A separationist account of De Se reports . . . . . . . . . . . . . . . . . . 229
6.6.1 The task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.6.2 The internal argument of attitude verbs . . . . . . . . . . . . . . 230
6.6.3 Intenstionality, attitudes De Se, and separation . . . . . . . . . . 233
6.7 Some remarks about optional De Se reports . . . . . . . . . . . . . . . . 238
6.8 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
7 Concluding Remarks 243
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Chapter 1: Overview
The goal of this dissertation is to provide a theory of meaning for sentences ex-
pressing certain plural referential dependencies. The issue of referential dependencies in
general has been an important topic in linguistic theorizing, both in the areas of syntax
and semantics. Likewise, plural expressions have provided a wealth of puzzles that have
ramifications for foundational areas of natural language semantics such as clause meaning
and the composition of arguments and adjuncts. My main task is to show how phenomena
that lie at the intersection of these two domains can be treated with a particular version of
neo-Davidsonian event semantics that I will argue is superior to competing analyses.
The anaphoric dependencies that I examine throughout share one main property:
the anaphor’s reference is determined by some antecedent noun phrase in the syntax. In
particular, I look at four types of anaphoric elements that meet this criterion.
(1.1) i Reflexive anaphors
ex: They saw themselves
ii. Reciprocal anaphors
ex: They saw each other
1
iii. Distance each
ex: They saw two movies each
iv. De Se pronouns
ex: They want PRO to see a movie
I investigate examples like these which have another important property: the anaphors are
anteceded by a plural noun phrase. Two of these anaphors are licensed only when their
antecedents are plural: reciprocals and distance each. The other two type of anaphors,
reflexives and De Se pronouns can have either singular or plural antecedents, though I
focus primarily on the plural cases and the puzzles that arise there.
The semantic framework that I use to analyze these phenomena draws on ideas
from event semantics. In particular, I build on those varieties of event semantics that
make use of thematic roles, often called neo-Davidsonian event semantics. At first blush,
one might wonder at the benefit of using events and thematic roles in theories of plural-
ity, as these fundamental ideas in event semantics were originally put to use to explain
the composition of verbs with arguments and adjuncts. As many authors have shown, a
complete picture of the semantics of arguments and adjuncts can only be attained when
the particular issues raised by plural arguments and adjuncts are addressed. Sentences
with multiple plural expressions exhibit a range of interpretations that is not present with
their simpler singular counterparts, and this range of interpretations is influenced by the
syntactic configuration of the plural expressions and their interactions with other elements
such as quantification and negation. For the past twenty to thirty years, event-based theo-
ries have been rather successful in providing robust and elegant explanations for a wealth
2
of plurality phenomena. It is my hope to extend the empirical coverage of this general
approach to plural anaphora.
At the heart of all these phenomena that I consider is the notion of distributivity.
Distributivity is an aspect of meaning that provides information about parts of the collec-
tions of individuals referred to by plural noun phrases. Distributivity may be expressed
overtly, in the form of a distributivity morpheme like each in English. This morpheme
may surface as a determiner-like element, or may appear separated from the plurality
which it quantifies over. We also see an element of this form in the English recipro-
cal anaphor each other. A natural question to ask is whether these are the same lexical
items with the same lexical semantics. It is one of my goals to argue that it is indeed
the case that these elements can be given a univocal analysis that is made possible by the
neo-Davidsonian system I advocate here. In Chapter 6, I will consider the issue of dis-
tributivity in attitude reports, particularly those involving the ascription of De Se attitudes
to a plurality of individuals. Previous accounts of attitude reports put distributivity to use
in a certain way, both in the semantics of attitude verbs and in the interpretation of the
pronouns in De Se reports. I will argue that distributivity is still crucial to these reports,
though not in the way that is usually assumed.
For the remainder of this chapter, I will provide a brief outline of the rest of the
dissertation. The dissertation can be divided into three parts: the first part provides an
introduction to the event-based theory of plurality I use throughout. The second and
longest part consists of three chapters devoted to local plural anaphors and how a unified
theory of distributivity can be put to work to explain the semantic properties associated
with these anaphors. The final section of content consists of the penultimate chapter,
3
which focuses on the issue of plurality in De Se reports. I now give a brief description of
each chapter.
In Chapter 2, I develop the core components of the formal system used throughout
the dissertation. I will introduce the basic tenets of events semantics, and then turn to
the idea of neo-Davidsonianism and what sets this apart from alternative approaches to
verb meaning and argumenthood. The variety of neo-Davidson semantics that I pursue
is one that has all of the verbs arguments separated, or severed; in other words, verbs are
interpreted simply as monadic predicates of events. This sets up a neo-Davidsonian view
of distributivity first discussed by Barry Taylor and Barry Schein; in what I call Taylor-
Schein Distributivity. I then move on to define a distributivity morpheme based on Taylor
and Schein’s insights, focusing here on its role as a determiner. This lays the groundwork
for the following three chapters where I use the same distributivity operator to account
for local plural dependencies; in particular distance distributivity, reciprocity, and plural
reflexivity.
In Chapter 3, I focus on two phenomena which together are called distance dis-
tributivity —floating each and binominal each. The goal is to show how the distributivity
operator defined in Chapter 2 can be used in the semantics of sentences with distance
distributivity. I introduce previously undiscussed data involving distance distributivity
items in ditransitive sentences, for which the proposed account is argued to be superior
to competitors. The reason for discussing distance distributivity first is that the canonical
local anaphors, reciprocals and reflexives, which I spend the next two chapters discussing,
are argued to be two special cases of distance distributivity involving the Taylor-Schein
distributivity morpheme.
4
In Chapter 4, reciprocals anaphors are given a neo-Davidsonian decomposition re-
lying on the notion of distributivity developed previously. I provide two problems that
any theory of reciprocal semantics must take into account: first, the observation that re-
ciprocal sentences can be true in a constrained variety of different types of situations, and
second, the ability for reciprocals to appear in a wide range of argument positions. The
first issue is one of the most discussed aspects of reciprocal meaning in the literature,
while the second issue has received very little attention. I propose that there is a simple
answer to the first issue, namely that there is a single semantic meaning for reciprocals
given by the Taylor-Schein distributivity operator in conjunction with a morpheme like
other. Furthermore, I show that the Taylor-Schein approach, together with some other
neo-Davidsonian ideas, accounts for the composition of reciprocals in more argument
positions than is accomplished in previous accounts.
In Chapter 5, I provide an analysis of plural reflexives in languages like English. As
others have noticed, English plural reflexives often are associated with a certain distribu-
tive interpretation. I argue that this is again Taylor-Schein distributivity at work. This
particular analysis, like in earlier chapters, is strengthened by considering the behavior of
reflexives beyond simple transitive constructions. I end this chapter with some discussion
of the duality of reciprocals and reflexives, and how the well-known local properties of
these anaphors are related to the local properties of the canonical distance distributivity
constructions discussed in Chapter 3.
In Chapter 6, I address the issue of plural De Se reports. There have been previous
accounts of De Se reports, and previous accounts of plurality in attitude reports, but very
little are these two things discussed in the same breath. After introducing some basic facts
5
from these areas, I argue for the semantic plurality of De Se pronouns that are anteceded
by plural noun phrases. I review the reasons for why the majority of the literature have
thought such pronouns to be semantically singular, and then I use reciprocity and cumula-
tivity phenomena to argue for semantic plurality. Building on these results, I show that the
standard Hintikkan approach to the semantics of attitude reports is ill-suited to the case
of plural De Se reports. I then modify existing context based accounts by incorporating
ideas from plural events semantics to account for these cases.
Chapter 7 concludes the dissertation and reviews the main points argued for through-
out.
6
Chapter 2: Plurality and Events
Any attempt to give a comprehensive history of the central ideas in contemporary
natural language semantics is sure to mention two papers by Donald Davidson written in
1967. First, we were given a general claim in Davidson (1967a) that a Tarskian system
can be used to give a recursive definition of the truth conditions of sentences in natural
language. In the second paper, Davidson (1967b) made some specific proposals about this
program; in particular, he argued that the truth conditions of natural language sentences
can be given in a logical language that includes variables that range over events.
This second paper marked the beginning of event-based theories of natural language
semantics. Davidson’s original arguments were the first of many, which all seem to point
to the conclusion that event analyses provide elegant and empirically robust accounts for
a large range of semantic phenomena. In what follows I review some of the main pro-
posals from this research program, with a particular emphasis on its utility for giving the
semantics of sentences that express plurality. I will start with Davidson’s argument from
adverbial modifiers, not only for its historical significance, but also because the argument
is centered on a core empirical domain of meaning, namely entailment properties that are
related to the presence of arguments and modifiers, an issue that will surface in several
more places throughout this dissertation.
7
Davidson (1967b) argued that the logical form, or truth conditions, of action sen-
tences like (2.1a) involves existential quantification over events. In the Tarskian (T-
Schema) approach that Davidson (1967a) was pursuing, we can say that English sen-
tence (2.1a) is true iff the existential generalization given in a logical language (2.1b) is
true. I will notate predicate names with small caps and individual terms with lowercase
letters for now; assume both proper names and definite descriptions pick out individual
constants.
(2.1) a. Antonin cooked hollandaise sauce in the kitchen with a double-boiler
b. ∃e[COOK(e, a, h) & IN(e, k) & WITH(e, d)]
Transitive verbs were traditionally regimented as two place relations, but Davidson sug-
gested that verbs are somehow associated with an event variable not corresponding to any
of the overt arguments, but is instead existentially closed.
Davidson argued that the entailment relations between (2.1) and similar sentences
(2.2)-(2.4) are best understood in terms of a silent event argument which adverbials mod-
ify. He notes that sentences like (2.1) entail sentences which differ from (2.1) only in that
they have the adverbs removed. Thus, (2.1a) entails (2.2), (2.3), and (2.4); and likewise,
both (2.2) and (2.3) entail (2.4). The nonentailments are also noteworthy: an upward-
entailing sentence with less adverbs does not entail one with more adverbs (e.g., (2.2)
does not entail (2.1a)).
(2.2) Antonin cooked hollandaise sauce in the kitchen
(2.3) Antonin cooked hollandaise sauce with a double-boiler
8
(2.4) Antonin cooked hollandaise sauce
As a point of comparison, consider a non-event approach where the verb is treated
as a four-place relation. Under this view, the logical form of (2.1) is given as (2.5).
(2.5) COOK(a, h, k, d)
(2.5) does not have a logical form that accounts for (2.1a)’s entailments. At best, the en-
tailments could be contributed to lexical idiosyncrasies of the verb cook. But this would
require positing a lexicon that has numerous versions of cook, each with its own fixed
number of arguments and specific entailment properties. Furthermore, the stipulated en-
tailment properties of the verb must be such that they explain both the entailments and
nonentailments.
For the event analysis the entailment relations are explained as conjunction reduc-
tion, a familiar inference pattern from standard logic. A formula such as ∃x[P (x) &Q(x)]
implies ∃x[P (x)] in first-order logic given the syntax/semantics of the connective &.
Since adverbial modifiers are treated as conjoined predicates of events in logical form, we
have an explanation for why sentences with adverbs entail sentences that differ minimally
by not having these adverbs. Below I give the Davidsonian logical forms for (2.2)-(2.4);
which differ from (2.1b) by missing one or more conjuncts.
(2.6) ∃e[COOK(e, a, h) & IN(e, k)]
(2.7) ∃e[COOK(e, a, h) & WITH(e, d)]
(2.8) ∃e[COOK(e, a, h)]
9
Treating adverbs as conjoined predicates of events also provides an explanation for
the nonentailments, again relying on the logic of conjunction. Conjunction introduction
is not a valid inference pattern; that is ∃x[P (x)] does not entail ∃x[P (x) & Q(x)]. The
sentences in (2.2)-(2.3) do not entail (2.1b) since the logical form of the latter has more
conjoined predicates of events than the former. The direction of entailment we observed
in these sentences falls out naturally from the logic of conjunction once we accept that
natural language expressions like verbs and adverbs can be associated with predicates
of events. Davidson’s approach thus provides an elegant treatment of sentences with
adverbial modifiers, and the entailment relations among them, without increasing the size
of the lexicon.
Davidson’s adverbial argument was the first among many that converge on the idea
that not only are silent event arguments a reasonable possibility, but they often provide
better accounts of the syntax and semantics of natural language than analyses that are
events-free. I do not review all of these arguments here for reasons of space. However, I
will consider some plurality specific arguments later in this chapter.
Before moving on, some terminological remarks about events are in order. Often in
past literature it has been useful to distinguish between events and states. I will not explore
this distinction here; and I will use the term “events” loosely to talk about both events
and states1. Also important to a comprehensive eventive theory is the granularity of the
objects that serve as values to Davidsonian event variables. This issue seems to be more
metaphysical than linguistic, and it is often suggested that the values of such variables
1Essentially, I use “event” to refer to what Bach (1986) called eventualities, an ontological class which
contains both events and states.
10
as they are used in linguistic semantics may not correspond to the the metaphysicist’s
notion of event. I will remain neutral on this issue, though there will be a few points
throughout where it will be useful to consider what counts as “an event” when discussing
mereological versions of event semantics.
While it may remain unclear what specifically counts as an event value, there is still
much that can be done in giving a compositional event semantics for natural language.
There is no agreed upon definition for “individual” or “entity”, but this has not stopped
the field of model-theoretic semantics from using models with domains that consist of
such things. I will make the same concession with events.
For the remainder of this chapter, I will review the main tenets of the event literature,
in particular those that have been put to use in developing theories of sentences expressing
plurality. I first introduce one of the most profound modifications to Davidson’s original
view: the introduction of thematic roles into event semantics. In this section I will discuss
several views of the semantics of noun phrases, verbs, and their composition. I will
settle on a neo-Davidsonian approach to argumenthood that I will use throughout the
dissertation. I then turn to the details of the semantics of plurality, and how this fits
into the event-based program. This will lead to the introduction of a neo-Davidsonian
approach to distributivity, which will be fundamental in addressing anaphora phenomena
in later chapters.
11
2.1 Thematic roles and argumenthood
2.1.1 Thematic decomposition
Very shortly after Davidson introduced his event analysis, Castañeda (1967) sug-
gested incorporating the idea of thematic roles that have been suggested by Gruber (1965)
and Fillmore (1968). Part of Davidson’s analysis implies that verbs correspond to rela-
tional predicates in logical form, which have an extra event argument in addition to what
was traditionally assumed; e.g., the verb cook for Davidson would determine the relation
COOK(e, x, y) in logical form. Casteñeda argued that the logical correspondence of the
verb be a predicated only of the event argument; the traditional arguments are associated
with thematic relations in logical form that predicate of the same2 event as the verbal
monadic predicate.
(2.9) a. Antonin cooked hollandaise sauce in the kitchen with a double-boiler
b. ∃e[AGENT(e, a) & COOK(e) & THEME(e, h) & IN(e, k) & WITH(e, d)]
The traditional arguments of the verb are treated in the same fashion as Davidson treated
PP modifiers; with thematic relations that hold of an event and an individual. For the
modifiers, the choice of thematic relation used is determined in some manner from the
preposition appearing in construction with the noun phrase3. While there are not any ap-
2“Same event” may require qualifications. Authors like Parsons (1990) analyze transitive sentences as
causatives, each with two events: a causing event performed by the agent, and the caused event affecting the
theme. This analysis will not be pursued here. Furthermore, the notion of distributivity I will develop later
in this chapter and throughout the dissertation will make reference to sub-events, such that some sentences
express that some individual participates in several events, and another participates in sub-events of those
events.
3This is not to commit to the proposal that the choice of preposition is the only relevant factor in de-
termining the thematic role of such items. There is of course the issue of disentangling whether some
12
parent prepositions for the subject and object arguments in (2.9a), Casteñeda remarks that
the meaning (2.9a) can be paraphrased using a gerundive nominalization (2.10), where
the noun phrases corresponding to the agent and theme are marked with prepositions. In
§2.1.3, I will consider some different accounts of the composition of subject and object
arguments in a system with thematic relations.
(2.10) There was a cooking of hollandaise by Antonin in the kitchen with a
double-boiler
The issue of the precise inventory of thematic roles has been a source of constant
debate in the literature. The range of suggestions goes from two roles to dozens of roles;
see for example Dowty (1989) and Dowty (1991). As with many previous studies, the
exact inventory does not matter for the problems at hand in this dissertation. What mat-
ters is that there are thematic roles and that they play a role in the interpretation of noun
prepositions are homophonous with others, or if there is an underlying lexical semantics in such cases.
There are several of such puzzling cases. For example, instrumental versus comitative with in English and
other languages. Schein (2002) assumes that they share a common semantic core, a plausible hypothesis
given the similar type of actions associated with comitative and instrumental thematic roles. Though it
must surely be relevant that the majority of the languages surveyed by WALS use phonologically distinct
prepositions to represent these roles. Another problem along these lines is the case of by in English. On
the one hand, it seems that homophony is involved since we know that there are agentive uses and loca-
tive/directional uses, and these share no obvious connection as was the case with with. But does this mean
we have two morphemes here? In the case of agentive by, is it the same morpheme that appears both
clausally and nominally; (i)-(ii)?
i. The Boston butt was barbecued by Bob
ii. The barbecuing of the Boston butt by Bob was breathtaking
What about path versus proximal by; (iii)?
iii. Adam kicked the ball by the goalie
(either He kicked the ball past the goalie or He kicked the ball while near the goalie)
This is another case where there appears to be some (albeit vague) common locational concept that these
roles could fall under, though as we saw above, this does not guarantee that we are dealing with a single mor-
pheme. The arguments for differentmorphemes are strengthened by the fact that these homophonousprepo-
sitions can co-occur; given the property of thematic uniqueness discussed in the main text, co-occurrence
means that these prepositions express distinct thematic roles rather than a single all-encompassing role.
13
phrases, particularly by associating each role with a thematic relation in an event-based
semantics. I will make use of familiar roles such as Agent, Theme/Patient, Goal, Instru-
ment, Location, etc. I will also recognize that there are thematic roles expressed in noun
phrases; an idea which I will argue for when giving the semantics of anaphors contained
within noun phrases. While clausal thematic relations relate an individual and an event,
nominal thematic relations relate one individual to another individual; such as locational
roles like IN(x, y) and ABOVE(x, y). An example of a nominal thematic role which I will
reference in later chapters is the Possessor role. What I mean by “possessor” is the role
associated with the “apostrophe-s” type of possessor, which has been pointed out to be a
rather vague sort of thematic role. NPs in this position can be interpreted in a wide variety
of roles, and not all of them have to do with possession in the strictest sense. For example,
possessors seem to express the agent and theme roles respectively in the following pair of
sentences.
(2.11) a. Rome’s destruction of Carthage
b. Rome’s destruction by the Gauls
I will label the possessor role as POSS, which like the π role in the thematic analysis
of possession in Barker (1991), corresponds to the thematic relation that holds of two
individuals if the first stands in that vague, underspecified relation to the second.
Thematic roles have been somewhat of a mysterious technical notion in the litera-
ture. While many authors disagree as to which thematic roles there are, and even how a
single role such as Agent should be defined, there has still been fruitful work in develop-
ing both syntactic and semantic theories assuming thematic roles. As authors like Carlson
14
stress, it is of course possible to devise theories of syntax and semantics without thematic
roles; though theories with them have shown to be quite successful. I take thematic roles
not to be merely an ad hoc technical device, but rather a central discovery uncovered by
linguists that calls for deeper investigation. In the next section, I will review some of the
core properties of thematic roles in general, and for sections and chapters following that,
I will argue that their place in event semantics can lead to new and interesting theories of
plurality and anaphora.
2.1.2 Thematic Uniqueness
Thematic Uniqueness has been a important topic in the neo-Davidsonian literature.
For a given clause, Uniqueness requires that if one argument in that clause has thematic
role X , then no other argument can. Carlson (1984) remarks that some initial motivation
for Uniqueness comes from hypothetical verbal meanings that do not appear to be real-
ized in natural language. He notes that there are no verbs like skick, which are used in
sentences like (2.12a) that express the same meaning as (2.12b).
(2.12) a. John skicked the ball Bill
b. John and Bill kicked the ball
The Uniqueness principle rules out (2.12a) since there are two separate noun phrases,
John and Bill, which are intended to be tied to agentivity. Sentence (2.12b) does not vio-
late this rule because there is a single argument noun phrase that bears the agent thematic
role; namely, John and Bill. This assumes that the conjunction of two noun phrases is
also a noun phrase, and also suggests that Uniqueness be defined as an A-over-A rule
15
(see Chomsky (1964) for discussion of A-over-A rules). For more on the intricacies
of noun phrase conjunction, see Lasersohn (1995), Schwarzschild (1996), and Schein
(forthcoming).
Landman (2000) offers an interesting idea implementing Thematic Uniqueness (which
he calls the Unique Roll Requirement). So far we have been viewing the logical form
constituent corresponding to thematic roles as a relation; e.g. AGENT(e, x). Landman
suggests that thematic roles can be viewed as functions from events to individuals; e.g.,
AGENT(e) = x. Since functions definitionally assign a single value to each argument, we
have an reason for why each event value has a single individual value that is the agent
of that event, for example. For (2.12a), each argument would be associated with its own
function: John with AGENT(e) = j and Bill with AGENT(e) = b. But since AGENT is a
function, it cannot assign a different value to the same argument e. On the other hand,
in (2.12b), the conjunction is associated with a plural value, the plurality associated with
John and Bill, and this plurality is the sole value of the AGENT function when applied to
e; see §2.2 for details on plural values. I will still continue to represent thematic roles as
relations in logical form, though I leave open the possibility that Landmanesque functions
are at work and this is where Uniqueness comes from.
We will return to the proper formulation of Thematic teUniqueness in the next chap-
ter when distance distributivity is discussed. There I will suggest that it is possible for
two (apparent) noun phrases to bear the same thematic role, but this happens in situations
where the semantic value of both noun phrases are tied to the same plurality of individu-
als.
16
2.1.3 Degrees of separation and compositionality
Following Davidson (1967a), Montague (1973), and others, let us assume that a
declarative sentence of natural language has truth conditions that are determined by the
semantic values of particular lexical items contained in the sentence and the way the
lexical items are arranged syntactically. Giving a full theory of this sort is of course still
a work in progress; in this dissertation I will present fragments of a theory focusing on a
subset of constructions in natural language. Let us start with a simple case, the semantics
of simple unembedded sentences in English.
(2.13) Abe slept
(2.14) Bill saw Carl
(2.15) Abe introduced Bill to Carl
In the Montague tradition, building on insights from Frege (1879), the truth condi-
tions of (2.13)-(2.15) are given by a type-driven interpretation. The range of permissible
types are given by the usual recursive definition:
(2.16) Basic Frege-Montague type system
a. Basic types:
a. e (entities/individuals)
b. t (truth values)
17
b. Function types
If α is a type and β is a type, then ⟨α, β⟩ is a type; the type for functions from
objects of type α to objects of type β.
With this type system, declarative sentences are assigned values of type t, proper names
(and referential noun phrases in general) are assigned values of type e, and verbs like
those in (2.13)-(2.15) are assigned function values; functions that take entities values as
arguments and ultimately return truth values4. Other types produced in this system will
be discussed later in connection to quantification and local anaphora; for now I will limit
the discussion to the function types associated with what Davidson called “action verbs”.
Consider the composition of a sentence with a transitive verb; e.g., (2.14). For this
discussion I will assume that the proper names Bill and Carl are assigned type e semantic
values: the entities b and c, respectively. Below I give a standard lexical axiom for !saw",
which is indicative of a schema that can be used with all simple transitive verbs (TVs).
(2.17) Frege-Montague approach to TVs
!saw" = λye.λxe.SEE(x, y)
The verb saw is interpreted as a Curried/Schönfinkelized function from two entities to a
truth value; the value True is assigned if those entities stand in the SEE relation to one
another, specifically with x seeing y.
This approach to composition assumes that branching nodes are interpreted by the
phrasal axiom of Function Application5.
4There are several more sophisticated approaches to type-driven interpretation that will have to go un-
mentioned here; such as systems with type-raising, type-theoretic approaches to quantification and quanti-
fier scope, etc.
5I ignore for now any parameters on the interpretation function; assignments and contexts will be dis-
cussed in later sections.
18
(2.18) Function Application
If γ is a branching node with daughters α and β, and !α" is a function whose
domain contains !β", then !γ" = !α"(!β").
The tree below illustrates the type-theoretic composition of a simple transitive sentence.
(2.19) t
e ⟨e, t⟩
⟨e, ⟨e, t⟩⟩ e
Essentially, the Frege-Montague approach, which represents the current standard
in formal semantic research (cf., Heim and Kratzer (1998)), treats the truth conditions of
simple transitive sentences as a dyadic predication, and these truth conditions are deter-
mined largely by interpreting the verb as a Curried function from two entities to a truth
value.
2.1.3.1 Classic event analyses of verbs
The classic Davidsonian approach can be seen as making one small change to the
Frege-Montague approach, the addition of an extra argument: the event argument.
(2.20) Classic Davidsonian approach to TVs
!saw" = λye.λxe.λev.SEE(e, x, y)
Some remarks are in order about the event argument. If events can be semantic values,
then there must be some semantic type they fall under. While it might be plausible to
19
consider an event to be some sort of entity, and thus treat it as type e, several authors have
instead suggested that there is a separate ontological category for events that is distinct
from the type of entities. I will adopt this sorted-domain approach here, which essentially
amounts to adding a third basic type to the definition in (2.16). Unfortunately the letter e
is already used for the type of entities, so I will use v as the label for the type of events;
even though I will still use “e” as a variable for events in the metalanguage.
Davidson’s suggestion was that the truth conditions of natural language sentences
are existential generalizations of events, and event values serve as domain of quantifica-
tion for such event quantifiers. To implement Davidson’s event quantifier, I will assume
that there is a covert existential event quantifier in the object language, to which I assign
the following lexical axiom (this will be changed when intensionality is introduced in
Chapter 6.)
(2.21) !∃e" = λP⟨v,t⟩.∃e[P (e)]
The event quantifier will compose with a monadic predicate of events which is of type
⟨v, t⟩; e.g., the type of a transitive verb composed with its first two arguments given
lexical axioms like (2.26). The result of the composition is a truth value; True if there is
an event e of x seeing y, and False otherwise6.
6There have been several alternatives to Davidson’s existential event quantifier approach. These alterna-
tives still hold on to the idea that sentence meanings are intimately tied to event values of some sort, but not
necessarily existential quantification over them. For example, some sentences could be seen as referring to
a specific event, or plurality of events, instead of merely making an existential generalization. Some authors
pursuing event analyses of plurality have suggested sentences denote a plurality of events instead of a truth
value; and the plurality denoted are those events that satisfy an event predicate; essentially the predicate that
serves as the first argument to the event quantifier in 2.21). I will not try to determine which approach to
sentence meaning is the correct one; instead I will adopt the existential event quantifier approach for most
of the dissertation since it serves as a familiar benchmark in event semantics, and from this it should be
obvious for those interested in alternatives how to modify what I say here to fit such frameworks. Having
said that, I will raise issues and make revisions about this approach when considering intensionality.
20
The introduction of thematic roles to the system opens up several new options for
the lexical semantics of transitive verbs. Below I discuss the three main varieties, dis-
tinguished by the degree to which they eliminate argument places given in the Classic
Davidsonian approach.
This first neo-Davidsonian alternative derives fromCasteñeda’s suggestion for mod-
ifying Davidson’s system with thematic roles, an approach further pursued by Parsons
(1990) and others. This is implemented in the type system by having transitive verbs
keep the same semantic type that they have in the Classic Davidsonian approach, but the
functions associated with TVs do different things with their arguments than in the classic
approach; specifically, the entity values serve as argument to thematic predicates.
(2.22) Classic neo-Davidsonian approach to TVs
!saw" = λye.λxe.λev.AGENT(e, x) & SEE(e) & THEME(e, y)
To reiterate what was said in previously, this approach differs from Davidson’s in the way
the argument values factor into the truth conditions. In both approaches, the verb deter-
mines some lexical predicate used in logical form; in this case SEE. In the Davidsonian
approach, this predicate is a ternary relation, with one event argument and two entity argu-
ments. In the neo-Davidsonian approach this predicate is a monadic predicate of events,
and the entity arguments are related to this predicate indirectly by thematic predicates
which share the same event variable as the monadic verbal predicate.
Since the verbal predicate in logical form is just a monadic predicate of events
in the neo-Davidsonian approach, it is natural to ask if it is necessary to treat TVs as
having functional types that require type e arguments at all. Put differently, the question
21
is whether the thematic relations we see in logical forms like (2.26) are there because of
the lexical semantics of verbs, or something else.
The classic Davidsonian and classic neo-Davidsonian approaches to TVs corre-
spond to the claim that TVs are interpreted as three-place Curried functions in the type-
driven semantics assumed here. More radical versions of neo-Davidsonianism claim that
there are benefits for treating such functions as having a lower adicity.
2.1.3.2 Partial separation
Kratzer (1996) presents a theory where agent arguments are introduced by functional
heads and are thus not semantic arguments of the verb. I label this approach as “partial
separation”, since only external arguments (i.e., subjects) do not compose as semantics
arguments of the verb. For Kratzer, the internal argument, typically associated with the
Theme or Patient thematic role, is not separated. Furthermore, this argument is not even
represented via a thematic relation: the lexical relation determined by the verb is a dyadic
relation between an event and an individual. Put differently, Kratzer does not believe
there is a place for a Theme/Patient thematic role as it relates to direct objects7.
(2.23) !see" = λx.λe.SEE(e, x)
Kratzer’s argument for such a decomposition follows an observation from Marantz (1984)
about idioms. Abstracting away from particular details, the observation is that while cer-
7I will not address Kratzer’s reasons for not severing internal arguments. We will see shortly Schein’s
argument for separation of internal argument, which is considered as a viable alternative even by Kratzer
herself in later work: Kratzer (2000). See also Williams (2009), who argues that Kratzer’s arguments
against the Theme relation are unsound.
22
tain Verb+D.Object combinations trigger idiomatic interpretations, it appears that there
are few if not any cases of Subject+Verb idioms. Kratzer correlates this observation with
argumenthood: semantic arguments of the verb can lead to Verb+NP idioms while non-
argument cannot, and since there are virtually no idioms involving Subject-Verb combi-
nations, subjects must be introduced into the derivation by some other means than Func-
tional Application of the VP predicate to the subject’s denotation; see Williams (in press)
for discussion.
Following authors such as Larson (1988), Baker (1988), Hale and Keyser (1993),
Kratzer assumes that there is a functional head v which introduces subject NPs and is
responsible for them having an agent thematic role. She treats agents v as having the
meaning in (2.24) and posits the operation Event Identification for the composition of v
with the VP consisting of the verb and direct object.
(2.24) !v" = λx.λe.AGENT(e, x)
(2.25) Event Identification
If v′ is a branching node with daughters v and VP, then
!v′" = λx.λe.[!v"(x)(e) & !VP"(e)]
As we will see shortly, Event Identification will not be needed as an operation once
the more general operation of Predicate Conjunction is in place as a means of composing
NP meanings that are not semantic arguments of the verb. Though I follow Kratzer in the
general idea that subjects are not semantic arguments of the verb.
As for not severing the internal argument of verbs, Kratzer argues that such argu-
ments are “more tightly linked to their verbs”, and that they “lack the conceptual inde-
23
pendence of agents”. I refer the reader to Williams (2009) who presents both conceptual
and empirical counterarguments to Kratzer’s claims about themes. The conclusion of this
argument is that there is good reason for going one step further than Kratzer; if agents
are separated, then perhaps there is a reason for going one step further: NPs never act as
semantic arguments to verbs. This option is explored in the next section.
2.1.3.3 Total separation
The most radical form of neo-Davidsonianism holds that the event argument is the only
argument of a verb, transitive or otherwise. In other words, verbs are interpreted simply
as monadic predicts of events.
(2.26) Total separation neo-Davidsonian approach to TVs
!saw" = λev.SEE(e)
This view was first articulated in modern8 formal semantic research by Krifka (1992)
and Schein (1993), and has received support from numerous researchers since. One of
the areas where total separation has been argued to be advantageous is in the domain of
plurality phenomena. There is a wide variety of convincing arguments for total separation,
too many to be discussed here; though see Lohndal (2012) and Williams (in press) for
discussion and references. However, I will provide one argument from Schein in §2.2.6.1
8The idea of localizing thematic information on noun phrases, and not verbs, can be argued to be present
in Pa¯n. ini’s As. t.a¯dhya¯yi¯, where for him the verbal root (dha¯tu) denotes actions (kriya¯), i.e., events, and nom-
inal stems (pra¯tipadika) denote factors (ka¯raka), things which have a certain role in the action. There are
six factors that Pa¯n. ini uses in his grammar, agent (karta¯), patient (karman), source (apa¯da¯na), beneficiary
(sam˙prada¯na), means (karan. a), and locus (adhikaran. a). See Gillon (2007) for an excellent overview of
these issues and other aspects of the As. t.a¯dhya¯yi¯.
24
that is relevant for the discussion of distributivity in later chapters; and in those chapters
I will argue that the total separation approach opens the way for new theories of certain
anaphoric phenomena.
If the thematic predicates in logical form are not contributed by the verb, then where
do they come from? One option is that NPs in some way determine which thematic
predicate to use; see Krifka (1992) and Schein (1993). If this is the case, a further question
arises: what rules of phrasal composition are used for the semantics of transitive sentence
involving what are traditionally referred to as argument NPs? I will start by addressing
this second question.
Aside from Function Application, some theories make use of Predicate Conjunction
as another rule of phrasal composition, such as Heim and Kratzer (1998).
(2.27) Predicate Conjunction
If γ is a branching node with daughters α and β, and !α" and !β" are both type
⟨b, t⟩, where b is one of the basic types e or v; then !γ" = λxb.!α"(x) & !β"(x).
The definition for Predicate Conjunction is given in such a way that it will work for
the composition of both predicates of entities and predicates of events. The semantics
of certain adjective/noun combinations have been treated as Predicate Conjunction of
predicates of entities (Heim and Kratzer (1998) and others); and the semantics of verb
(phrases) composed with VP-adverbs is treated as Predicate Conjunction of predicates of
events.
(2.28) !savoryAdj pieN" = λxe.!savory"(x) & !pie"(x)
(2.29) !boilV quicklyAdv" = λev.!boil"(e) & !quickly"(e)
25
Some approaches make use of both Function Application and Predicate Conjunction as
semantic rules; such as Heim and Kratzer (1998), who use Function Application for the
composition of arguments and Predicate Conjunction for the composition of adjuncts
(adjectives and adverbs). Pietroski (2005) explores the hypothesis that Predicate Con-
junction is the only rule of phrasal composition. Just as verbs and adverbs are interpreted
as monadic predicates of events, Pietroski argues that NP/PP arguments are treated in
the same way; specifically, arguments are interpreted as thematic predicates. While I
will still make use of Function Application during several parts of the dissertation, I will
adopt Pietroski’s insight of using Predicate Conjunction for the composition of at least
non-quantificational argument NPs. I will now discuss several options for implementing
Pietroski’s idea.
Let us assume for now that NP arguments are somehow “theta-marked” in the object
language, so that an NP has some characteristic that determines which thematic predicate
to present in logical form; represented schematically below.
(2.30) !JohnAG" = λe.AGENT(e, j)
By treating NPs as monadic predicates of events, they can compose with other monadic
predicates of events such as intransitive verb meanings by PC9.
(2.31) !JohnAG walked" = λe.AGENT(e, j) & WALK(e)
Below I illustrate the type-theoretic composition of a transitive sentence where verbs and
their arguments are treated as monadic predicates of events.
9I will ignore tense here and throughout the dissertation.
26
(2.32) ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
The monadic predicate of events at the root node in (2.31) will then serve as the argument
to the existential event quantifier as defined in (2.21).
(2.33) t
∃e :: ⟨⟨v, t⟩, t⟩ ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
There are two questions that arise for this approach to the semantics of NP argu-
ments: how exactly is the NP theta-marked, and how exactly does theta-marking deter-
mine a thematic predicate; i.e, what semantic rule is responsible for (2.30).
As for the theta-marking, one option is essentially a reinterpretation of Chomsky
(1981) idea that thematic roles are formal syntactic features on NPs. These features can
be assigned by the verb, they could be assigned to the NP and then checked by the verb
(by Agreement), or they could be assigned based purely on the structural position of the
NP (e.g., being a specifier versus a complement; see Baker (1988) and others). Let us
collectively refer to these options as the Feature Approach since in each case the NP has
27
a thematic feature that plays a role in its interpretation10. A Feature Approach has been
explored for neo-Davidsonian systems by Hornstein (2002). Under this view a new rule
of interpretation is needed that interprets an NP with a theta feature as the appropriate
monadic thematic predicate. I give such a rule below, where the theta feature is repre-
sented as subscript on the NP.
(2.34) Theta Rule
!NPΘ" = λe.Θ(e, !NP")
Another way of implementing the idea that NPs are interpreted as monadic pred-
icates of events is to assume all NPs compose with an adposition which is the locus of
thematic information. This assumes that even in cases where NPs do not appear with an
overt adposition (e.g., subjects and direct objects), there is still a silent preposition that
does the work of turning an NP meaning into a predicate of events. Below I provide a
schema for appositions that compose with type e NPs.
(2.35) !PΘ" = λxe.λev.Θ(e, x)
For the adposition theory, it is not the NP per se which determines the thematic
relation, but a preposition that composes with the NP. This approach is motivated by
modifier PPs in sentences like (2.36).
(2.36) Colonel Mustard killed Professor Plum [with a candlestick] [in the kitchen]
As discussed above, modifiers are represented in logical form by instrumental and loca-
tive thematic predicates; INST(e, c) and LOC(e, k). This rule assumes that it is not just the
10Note that there is no contradiction in the claim that verbs are semantically monadic while syntactically
they still assign thematic features to NP arguments in the sense of Chomsky. In other words, subject and
objects NPs need not be semantic arguments of the verb in order to be syntactic arguments.
28
form (i.e., phonology) of a preposition that specifies its corresponding thematic relation,
but instead that the preposition itself has a “theta feature” that is responsible for the choice
of thematic relation. A benefit of the adposition theory is that particular thematic relations
can be attributed to the lexical semantics of adpositions without introducing a new rule of
composition (e.g., the Theta Rule). On the other hand, the preposition theory still relies on
something like a theta feature specification in order to account for homophonous preposi-
tions. So the issues seem to be not whether theta features are necessary, but whether they
are situated on Ps and PPs, or on NPs (or Ds/DPs). For present purposes both approaches
could be used, though I will stick to the adposition theory since it does not rely on an
additional rule for phrasal composition.
Note that PPs may appear inside of NPs, in which case the adposition will have a
lexical entry where the second argument is also of type e, and not v.
(2.37) !PΘ" = λxe.λye.Θ(y, x)
Let me conclude by pointing out that total separation does not necessitate Predi-
cate Conjunction, possibly together with the Theta Rule or a definition of adpositions,
as the rules for composition of a verb with its arguments (and other instances of argu-
ment composition). If a verb is interpreted as type ⟨v, t⟩ function, then another option not
considered yet is that an NP is interpreted as a higher-order function that takes a ⟨v, t⟩
argument. For example, an intransitive sentence would have the subject NP interpreted
as a ⟨⟨v, t⟩, t⟩ function. However, we could not treat the direct object as having this type,
because we do not want verb-object combinations to be type t. So different types are
required for different arguments under this view. While this approach might be possible
29
and would only require Functional Application as a rule of composition, I will not explore
it here. I assume that Predicate Conjunction is one of the possible rules, and as argued for
by Pietroski, it is used for the composition of NPs and PPs, regardless if they are adjuncts
or arguments
2.1.4 Ditransitives
At several points in the dissertation, I will address ditransitive constructions. I
follow Larson’s (1988) VP-shell hypothesis for the syntax of ditransitive sentences. Under
this view, there are two VP projections in the clause; the most deeply embedded VP is
where direct and indirect objects are projected, and the higher VP hosts the base position
for subjects; the latter often given the category vP. At least in languages like English,
there is head movement from the lower V position to the higher one, which account for
the verb before objects word order.
(2.38) S
NP1 VP1
NP1 V′1
V1 VP2
NP2 V′2
V2 NP3
30
In standard treatments where FA composes a verb with its arguments, one way of
representing the LF of a ditransitive sentence is as follows; the verb is interpreted in its
base position, not the higher V position which its head moves to.
(2.39) t
e ⟨e, t⟩
e ⟨e, ⟨e, t⟩⟩
⟨e, ⟨e, ⟨e, t⟩⟩⟩ e
For the neo-Davidsonian view adopted here, the type-theoretic composition is as
follows up until the introduction of the event quantifier. Every node is a monadic predicate
of events; every branching node is composed of two predicates of events. Notice that this
view of argumenthood does not require any special stipulations for the interpretation of
the verb in ditransitive sentences; since the verb is a conjoinable predicate of events, not a
function seeking arguments in a certain order, it is possible for the verb to be interpreted
either in its base or derived V position11.
11I put aside certain event-based semantics of causativity, where the higher VP is associated with a
different event value than the lower VP; see Parson (1990) and others.
31
(2.40) ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
⟨v, t⟩ ⟨v, t⟩
2.1.5 Section Summary
In this section I have presented the central components for the event semantics that
I will pursue throughout this dissertation. At the heart of the system are the basic tenets
of neo-Davidsonian semantics: the truth conditions of natural language sentences are ex-
istential generalizations of events, comprised of monadic and dyadic thematic predicates
of events12.
I will use two rules for phrasal composition throughout the dissertation: Function
Application, Predicate Conjunction. I put aside the Theta Rule, and assume that adposi-
tons are defined as functions from NP meanings to monadic thematic predicates. While
Predicate Conjunction will be used for the composition of arguments, Function Appli-
cation will still be used for the composition of some lexical items such as adpositions,
quantifiers and also an initial exposition of attitude verbs that will appear in later chap-
12Up until now, the only type of dyadic predicates in the system are thematic predicates. Pietroski
(forthcoming) presents a semantics where the only non-monadic predicates are thematic predicates. This
hypothesis greatly reduced the range of permissible types in the semantics. Recall from the standard recur-
sive definitions (2.16) that the number of permissible types is in principle infinitely large; though it seems
unlikely that natural language makes use of all of these types. Pietroski’s proposal is that there are only two
types, monadic predicates and dyadic predicates; and the dyadic predicates are constrained to only thematic
predicates.
32
ters. For the extensional fragment presented, clauses are treated as type t as usual, and
this is given by the semantics of the covert event quantifier (2.21).
As for lexical rules, all open class categories considered here will be treated as
monadic predicates; either predicates of individuals (for nouns and adjectives) or pred-
icates of events (for verbs and adverbs). In the next section, I will show how to give
suitable plural entries for these categories. I will follow the total separation view of com-
position, so all non-embedding verbs will be interpreted as monadic predicates of events.
2.2 Events and the semantics of plurality
2.2.1 Plurality in natural language and nonfirstorderizability
It has become common in the study of natural language semantics to use first-order
predicate logic in developing formal theories. Famously though, Frege’s original exposi-
tion of predicate logic was higher order and as such was susceptible to Russell’s Paradox.
Logicians like Tarski took a step back from Frege’s logic, and developed a first-order frag-
ment that was free from this flaw. The first-order predicate calculus became the “standard”
in modern logic, a fact that is undoubtedly tied to the ubiquity of first-order treatments of
natural language semantics.
In the latter half of the twentieth century, both logicians and linguistics began to dis-
cover that certain natural language meanings cannot be stated in the language of first-order
logic. At the heart of all these problematic cases are expressions of plurality; expressions
used to talk about many individuals as such. Consider first the simple case of conjoined
NPs.
33
(2.41) Adam and Eve are happy
The question now is, can this sentence be regimented in a first-order language. For the
particular example, this turns out to be the case: a first-order logical form that represents
the meaning of (2.41) can be given as the conjunction of two simpler sentences.
(2.42) HAPPY(a) & HAPPY(e)
Consider now an example that differs minimally from (2.42) by having a different predi-
cate.
(2.43) Adam and Eve are a good couple
Following the strategy used in the previous example, the logical form assigned to (2.43)
is unsatisfactory.
(2.44) GOOD-COUPLE(a) & GOOD-COUPLE(e)
The problem seems to lie in the meaning of the predicate be a good couple; in particular
it is not a predicate that can hold of just one individual. There are many such predicates
in natural language: gathered, clustered, are roommates, sang a duet, etc., which are
often called essentially plural predicates. This is just one of many examples of natural
language sentences whose meanings cannot be represented in a first-order language; see
for example Boolos (1984), Pietroski (2005). Such examples call for a revision in order
to give a proper treatment of plural expressions in natural language.
There are two main approaches to modifying first-order treatments to account for
plurality. Each proposes to eliminate one of the following tenets of first-order logic, while
preserving the other.
34
(2.45) Two first-order dogmas
i. The domain of individuals is populated solely by concrete entities.
ii. Each term (individual, constant or variable) is assigned exactly one value
from the domain of individuals.
The plural individual approach abandons dogma (i). In addition to concrete indi-
viduals like Aristotle, a ball-point pen, and Chicago, this approach allows domains of
discourse that also include collections of such individuals, which I will call pluralities.
Returning to our problematic case above, these theories have it that the predicate good-
couple while not holding of any atomic individual, can hold of a plurality. In a mereolo-
gial system the plurality of Adam and Eve is represented with a sum operator; I put aside
formal definitions until §2.2.2.
(2.46) GOOD-COUPLE(a⊕ e)
Within this approach, there are two ways of formally implementing pluralities; both
coming from important sub-disciplines of mathematical logic. Historically, the first the-
ories of plurality in natural languages drew from the field of mereology; most notably in
Link’s (1983) seminal work, with antecedents in Cartwright (1975). For this approach,
the semantic value of plural noun phrases like conjunctions and plural definite descrip-
tions are mereological sums of atomic individuals. Some authors (Scha (1984), Gillon
(1987), Lasersohn (1995), and Schwarzschild (1996), for example) argued instead that
sets should serve as the value of such plural noun phrases; for example, the semantic
value of Adam and Eve being the set containing the individuals Adam and Eve as its only
35
members. Despite some technical and conceptual differences between these approaches,
they share the feature that the domain of discourse contains more than just the basic in-
dividuals assumed in first-order logic: whether the additional plural individuals be sums
or sets. Correlatively, both approaches maintain dogma (ii): terms are assigned a single
value, whether that value be a singular/atomic value or a plurality value.
George Boolos developed a logic that deviated from the standard first-order by
abandoning dogma (ii) thoughmaintaining (i). While this approach has been less common
in natural language semantics, it has many attractive features. Perhaps most importantly
is that it does not commit one to the existence of ontologically dubious entities like plural-
ities, whether they be sets or sums. Only the most necessary ontological objects are used;
i.e., just the ones assumed a first-order ontology. With sets or sums, the logic becomes
susceptible to Russell’s Paradox, see especially Schein (1993) for arguments against this
concerning natural language. So instead of positing pluralities, Boolos’s plural logic mod-
ified the way that values are assigned to variables. Standardly, values are assigned via an
assignment function, which pairs each index (or variable letter) with exactly one value
from the domain of discourse. Boolos’s suggestion was to essentially abandon the idea
that there is an assignment function, and instead suggested the more general notion of an
assignment relation13. Functions by definition pair each argument (in this case an index
or variable letter) with exactly one value. By adopting the more general notion, each vari-
able may be associated with more than one value; so that in some cases a single argument
13One-place functions like the assignment function can be represented as a set of ordered pairs of the
form ⟨index, value⟩, where the second member of each pair is a value that is unique to that specific index.
In other words, the set of ordered pairs associated with some assignment function will never contain both
pairs ⟨x, Adam⟩ and ⟨x, Eve⟩. For a Boolos-style assignment relation, such a set containing both pairs is
possible.
36
position may be assigned multiple values.
I will not attempt here to distinguish among these competing theories. For the
purposes of this dissertation, I believe any of these approaches would work. That is not
to say that there are not larger conceptual reasons at stake; just not ones that will be
addressed in this dissertation. For the purposes of implementing formal details though, I
will have to settle on one. I chose to present the theories offered in a mereological system,
primarily because of its familiarity.
For the remainder of this section I will spell out the details of the mereological
system I will use, drawing much from the work of Landman and others for the core as-
sumptions about plurality. I depart from Landman in some of the details mentioned in
the previous section; particularly by pursuing a total separation approach to argument-
hood. However, implementing these ideas into a mereological program will be relatively
straightforward.
2.2.2 Ontological commitments
It has become common in event semantics to assume a sorted domain of discourse,
one subdomain for individuals, D, and one for events E. Each subdomain contains their
respective atomic entities (first-order individuals and events), plus all the mereological
sums that can be formed from these atoms. I will define the sum operator ⊕ as a function
from sets of entities to entities such that for each non-empty set X , if X ⊂ D, then
⊕X ∈ D; or if E ⊂ E, then ⊕E ∈ E. Thus, each sub-domain is closed under sum
formation. I use the common short hand of representing ⊕{a, b} as a ⊕ b. It is also
37
necessary to define a part-of relation ≤: X ≤ Y iff X ⊕ Y = Y 14.
The sum operation can put together atomic individuals to create a new plural in-
dividual (a sum) consisting of just those atoms, or it can put together two sums and
create a new sum. An atom is an entity that has only itself as a part: ATOM(X) iff
¬∃Y : Y ≤ X & Y ̸= X . In algebraic terms, the sum operation creates domains of
discourse that have the structure of an i-join semilattice.
(2.47)
a⊕ b⊕ c
a⊕ b a⊕ c b⊕ c
a b c
Lattice structures have many other interesting formal properties, but I put these aside as
they do not have direct relevance to this dissertation.
A central feature of mereology theories is that just as the domain of individuals is
closed under sum formation, so are the denotations of number-neutral predicates. That is
if P (X) and P (Y ), where P is either a simple or complex predicate of entities, then it
follows that P (X ⊕ Y ). Note that P may have X ⊕ Y in its denotation without having
either X or Y ; this would be the case with essentially plural predicates discussed above.
Relational predicates are also closed under sum formation: if R(X, Y ) and R(X ′, Y ′),
then R(X ⊕X ′, Y ⊕ Y ′).
14The part-of relation ≤ is a partial-ordering on each domain: it is a relation that is transitive, reflexive,
and antisymmetric.
38
Some remarks are in order about variable names. I will adopt the convention of
treating uppercase variable letters as number neutral: they can be assigned values that
are either atomic entities or non-trivial sums. For ease of exposition, I will use lowercase
variable letters solely for atomic values; that is, instead of writing ∃X [ATOM(X)...] I will
just write ∃x[...] . When the distinction matters, I will use letters at the end of the alphabet
for variables ranging over the domain of individuals (x, y, z and X, Y, Z), and the letter
E with or without primes for event variables (e, e′, e′′ and E,E ′, E ′′).
When intensionality phenomena are discussed in Chapter 6, I will introduce new
ontological categories such as possible worlds and contexts. These require additional
subdomains for each category, but they will have the same mereological properties out-
lined here.
2.2.3 Interpreting the open-class lexical categories
With the mereologial ontology in place, I now turn to the interpretation of the open-
class lexical categories. I start with a discussion of the nominal categories of nouns and
adjectives. For these categories, I offer a “pluralization” of standard textbook treatments
as can be found for example in Heim and Kratzer (1998). I then discuss the interpretation
of clausal categories: verbs and adverbs. For this section I will build on the results form
the last section; the total separation approach to verb meaning. In sum, I follow the strong
neo-Davidsonian thesis that each of these four categories can be interpreted as monadic
predicates; in the nominal cases as predicates of individuals, and in the clausal cases as
predicates of events.
39
2.2.3.1 Nominal categories: N and Adj
It is standard to treat nouns and adjectives as denoting properties of individuals. In
the type-system assumed here, this corresponds to the claim that nouns and adjectives are
interpreted as type ⟨e, t⟩ functions.
(2.48) !alienN" = λx.ALIEN(x)
(2.49) !blueA" = λx.BLUE(x)
There are several cases that are problematic to this simple view. For one, there are rela-
tional nouns such as kinship terms (e.g., brother, mother, friend, etc.). While I will not
focus on such examples here, it is worth noting that such nouns can be viewed as monadic
following reasoning along the lines of thematic separation of verbs discussed in the pre-
vious section. That is, while it might be conceptually necessary that a brother is always a
brother of someone, it does not follow that that someone needs to be grammatically rep-
resented as an argument, syntactically or semantically. As for adjectives, Higginbotham
(1985) among others notes that some adjectives require an additional parameter for inter-
pretation. For example, the property SMALL(x) seems to require some qualification, as an
elephant can be small for an elephant, but it seems odd to say that it is small simpliciter.
The smallest elephant is still big when compared with a mouse. Again, I put these cases
aside as they are not directly relevant, and I will treat all adjectives as denoting monadic
properties.
The question now is what to do about nouns and adjectives when plurality is in-
volved. To start, let us address the issue of plural morphology. Nouns can be used to
40
speak of more than one individual that bears a certain property. In languages like English,
this is often accompanied by plural number morphology. In Link’s (1983) classic paper,
nouns are treated as singular by default, and the plural morpheme closes the denotation
of the singular noun under sum formation.
In the works of Schein, nouns are number-neutral by default. In the current frame-
work, this corresponds to the claim that nouns denote a number-neutral property that can
hold of either singular or sum individuals. The definition in (2.48) is modified to include
a number-neutral variable.
(2.50) !alien" = λX.ALIEN(X)
For Schein (2005), drawing on Borer (2005), plural morphology does not pluralize, but
contributes a property like COUNTABLE(X) as virtually all nouns with plural morphol-
ogy in languages like English resist mass interpretations15. The idea that nouns start as
number-neutral gains support from languages that do not have nominal number morphol-
ogy, such as Chinese, Japanese, Hindi, among others. In these languages, the same noun
form is used to speak of both singular and plural individuals.
In this dissertation, I focus only on count nouns, though there is a large body of
related literature connecting patterns of number morphology with mass and generic in-
terpretations; see for example Carlson and Pelletier (1995) and Chierchia (1998). I leave
these issues unaddressed, and I will assume number-neutral meanings like (2.50). For
the next several chapters, the semantic contribution of the plural morpheme will not be
relevant, though I will return to this issue when discussing plurality in De Se report in
15Gillon (1987) points out a small class of counterexamples of mass-denoting nouns with plural mor-
phology, such as brains and guts.
41
Chapter 6.
Adjectives will be treated on par with nouns in that I give them number-neutral
meanings.
(2.51) !blue" = λX.BLUE(X)
Noun-adjective combinations can be interpreted by Predicate Conjunction with the result
being a complex number-neutral predicate, as in the following example.
(2.52) !blue alien" = λX.BLUE(X) & ALIEN(X)
Before moving on, there is one further issue that will be relevant later in regards
to plurality and nominal lexical categories. If a property holds of plurality, one wants
to know if it also holds of the mereological parts of that plurality. This is an empirical
question, and as far as noun meanings go, the answer seems to be positive. This property
can be illustrated by the following valid inference.
(2.53)
Theyi are dogs
.
Each one of themi is a dog ∴
The conclusion speaks just of atomic individuals, but a similar valid inference can be
constructed, with some mereological vocabulary, if the conclusion spoke of each sub-
plurality of themi. Note that for this inference to go through, number morphology on the
noun has to change from premise to conclusion. It does not follow from the premise in
(2.53) that each of them is dogs. But this is a relatively innocent assumption especially
42
given our assumptions about the number-neutral nature of noun meaning. As such, we
can generalize to the following inference schema, with N as a variable for most if not all
noun.
(2.54)
Theyi are N.
Each one of themi is a N ∴
We may thus say that the following principle, whatever its source, is part of the gram-
mar16.
(2.55) Property homogeneity of nouns
For every property P denoted by a noun, if a plurality X is such that P (X) then
for every X ′ such that X ′ ≤ X , P (X ′).
Nouns may be unique among open-class lexical categories in this regard17 In the
next section I will show that similar inferences do not hold in with clausal categories. It
can be shown that adjectives in general do not always give valid inferences of the form
[They are A] → [Each of them is A]. For example, if theyi are numerous, it does not
follow that each of themi is numerous, and not even that each sub-plurality of themi is
numerous.
16If the noun is a gerund, it may not be the case that property homogeneity holds. This might have to
do with gerunds being more like verbs than nouns; see discussion in the next section about the principle of
Variety.
17A possible exception to property homogeneity are collective/group nouns such as band, committee, or
group. However, it has been argued by some that the parts of that make up a the denotation of a singular
collective noun are not relevant linguistically, these items function as singular noun. As a singular noun, it
picks out a linguistic atom that cannot be further divided by the linguistic part-of operator ≤. See Barker
(1992), Schwarzschild (1996), and Pearson (2011) for discussion.
43
I will treat proper names meanings as monadic predicates of individuals. This is a
departure from the classic analysis of proper names as type e; I follow others that while
NPs containing proper names may be of type e, the proper names themselves are pred-
icative. Burge (1973) pointed out that proper names can appear in the same syntactic
environment as common nouns in quantification NPs, such as in the following examples.
(2.56) Every Norbert that I know is a linguist
(2.57) There are three Johns in this year’s freshman class
Proper nouns can also serve as common nouns in definite descriptions. In languages like
Greek, proper names must appear with a definite article; providing further support for a
type e over ⟨e, t⟩; see for example Holton et al. (2004).
(2.58) *(i)
*(the)
Maria
Mary
‘the Mary’
Again following Burge and others, I adopt the following definition for proper names.
(2.59) !John" = λX.X is properly called John
The above definition undoubtedly requires some modifications; for example, to be prop-
erly called by a name it is not enough to have someone just call you that name on one
occasion, perhaps by mistake. Some regularity of going by that name seems to be called
for. I will not pursue these issues here; the relevant point is that proper names can be
given a monadic meaning, fitting with other common nouns.
I will soon introduce an ι operator as an implementation of definiteness, which will
compose with proper names and other nouns to yield type e NPs. However, for expository
44
reasons, instead of writing ιX [X is properly called John], I will stick with the convention
of using individual terms like j in the metalanguage. It would do no harm to the main
points of thesis if one were to assume that proper names are of type e; though I believe
that the type ⟨e, t⟩ analysis is preferable not just for the reasons that Burge pointed out,
but also because it provides unified monadic analysis; see Pietroski (2005) for discussion.
2.2.3.2 Clausal categories: V and Adv
The clausal categories will be treated on par with the nominal ones, with the crucial
difference being that while the latter are associated with monadic predicates of individu-
als, the former are monadic predicates of events. Treating adverbs as such has become the
norm in event semantics since Davidson’s seminal work. As for verbs, treating them as
monadic event predicates is a consequence of adopting the total separation approach to ar-
gument structure. As with the nominal categories, the “pluralization” of these predicates
involves a number-neutral plural variable. I assume that such predicates are pluralized
by default, thus not requiring a Link-style *-operator to differentiate singular and plural
predicates.
(2.60) !sleepV " = λE.SLEEP(E)
(2.61) !furiouslyAdv" = λE.FURIOUSLY(E)
As discussed in the beginning of this section, such predicates are closed under sum forma-
tion, so that if two atomic events of sleeping (whatever theymight be) are in the denotation
of SLEEP(E), then so is the sum of those two events.
45
What about the other direction; if a sum E is in the denotation of an event predicate
like in (2.60) and (2.61), does that mean that parts of E also are? As intimated in the
previous section, this is not the case. Consider the verb plant in the following sentence
from Kratzer (2000), Chapter 3.
(2.62) Alan, Brian, Campbell, and Dunn planted the rose bush
The actions of the agents might be divided into digging a hole, dropping the plant in,
and covering the hole with soil. None of these actions alone counts a planting, though
the sum of each of these smaller events will. Contrary to nouns, the behavior of verbs in
this regard can be characterized as the following principle, which I take from Williams
(2009). We can let V here stand for a monadic event predicate denoted by a verb.
(2.63) Variety
An event E that satisfies a description V may have an event E ′ that does not
satisfy V as a proper part.
Similar examples can be constructed for adverbs. To anticipate an important exam-
ple in §2.2.6, an event of eating a bag of potato chips may satisfy SLOWLY(E), while the
eating of each chip may be done in a rapid fashion, thus not satisfying SLOWLY(E).
2.2.4 (In)definiteness
The combination of a noun with its modifiers is a type ⟨e, t⟩ predicate. We thus need
some mechanism for turning such predicates into individual denoting expressions when
dealing with referential noun phrases. I will follow Link (1983), who in turn follows
46
Sharvy (1980) in defining an ι operator that is suitable for plural referential NPs. The iota
operator corresponds to the notion of a supremum in mereology theory. For any set X
partially ordered by the ≤ relation, the supremum of X is the smallest value in X such
that for any Y ∈ X , Y ≤ X . I will represent this in the metalanguage as ⊕P , the sum of
all the elements that fall under the property P .
(2.64) !ι" = λP⟨e,t⟩.⊕ P
(2.64) can serve as the definition of the definite article when one appears overtly, other-
wise I assume bare referential NPs (such as proper names in English) have a silent ι as
a determiner-like element in the NP. Alternatively, one may treat (2.64) as type-shifting
operation instead of a silent definite article. A benefit of using (2.64) as a formal im-
plementation of definiteness is that the supremum is necessarily a unique element, and
definite descriptions are well-known to be used felicitously only when there is such a
unique element. In the case of a singular description, this will be the unique atomic indi-
vidual in the domain that satisfies P ; for a plural description, it will be the unique largest
plurality that satisfies P 18.
In the course of this dissertation, we will also encounter indefinite noun phrases,
especially bare numeric ones such as (2.65).
(2.65) three musketeers
18There is a slight empirical problem with treating the denotation of a definite NP as the supremum of
a poset. If plural NP picks out the largest element that satisfies the descriptions associated with the NP,
then there should be no outliers; i.e., individuals that were not referred to but fall under such a description.
However, when large enough pluralities are concerned, such outliers are possible. One can truthfully utter
The students threw water balloons at the principal if 198 out the 200 students gathered in the auditorium
threw water balloons, and two students abstained. Note that there is a sharp contrast with a sentence that
differs minimally by including all: All the students threw water balloons at the principal would be false
in this situation. In other words, the ι operator seems to better model all the rather than simply the. See
Brisson (1998) for discussion.
47
First there is the issue of what to do with the numeral by itself. I assume that such
expressions are adjectives, and thus of type ⟨e, t⟩.
(2.66) !three" = λX.THREE(X)
This has the benefit of giving a unified denotation whether or not numerals appear in bare
constructions like (2.65), or in definite noun phrases like the three musketeers.
I assume that indefiniteness19 is given by a sometimes silent determiner or type-
shifting operation on par with (2.64). I notate this operator as ∃X , not to be confused with
the Davidsonian event operator ∃e defined in (2.21).
(2.67) !∃X" = λP⟨e,t⟩.λΘ⟨e,⟨v,t⟩⟩.λEv.∃X [P (X) & Θ(E,X)]
This operator takes a ⟨e, t⟩ restrictor argument and an adposition and returns a predicate
of events that is conjoinable with further ⟨v, t⟩ predicates by Predicate Conjunction.
As an illustration of ι and ∃X , I provide below a simplified derivation for the sen-
tence (2.68).
(2.68) The boys ate three cookies
(2.69) a. !ΘTH ∃X three
cookies" = λE.∃X [THREE(X) & COOKIE(X) & THEME(E,X)]
b. !ate three cookies" =
λE.EAT(E) & ∃X [THREE(X) & COOKIE(X) & THEME(E,X)]
c. !ΘAG the boys" = λE.AGENT(E,⊕BOY)
19I focus here only on existential uses of indefinites, not specific ones.
48
d. !∃E the boys ate three cookies" =
∃E[AGENT(E,⊕BOY) & EAT(E) & ∃X [THREE(X) & COOKIE(X) & THEME(E,X)]]
For ease of exposition, I will simplify the logical representation of numeric indefinites:
instead of λE.∃X [THREE(X) & COOKIE(X) & Θ(E,X)]], I will write λE.Θ(E, 3C).
2.2.5 Cumulativity of thematic relations
Like monadic predicates, I will treat thematic relations as pluralized by default and
thus have denotations that are closed under sum formation, see for example Krifka (1986).
That is, if the pairs ⟨E,X⟩ and ⟨E ′, Y ⟩ are in the denotation of some thematic relationΘ,
then so is ⟨E ⊕ E ′, X ⊕ Y ⟩.
As discussed in §2.1.3.3, thematic relations are determined by adpositions, either
overt or covert. I repeat a schema for the definition of adpositions below with the mod-
ification of including number-neutral instead of singular variables. This is so for both
clausal (2.70) and nominal (2.71) adpositions.
(2.70) !PΘ" = λXe.λEv.Θ(E,X)
(2.71) !PΘ" = λXe.λYe.Θ(Y,X)
With pluralized thematic relations in place, we can now turn to the neo-Davidsonian
treatment of cumulativity phenomena. As first noticed by Scha (1984), sentences with
multiple plural NPs give rise to what is often called cumulative readings.
(2.72) John and Bill danced with Mary and Sue
49
The sentence can be truthfully uttered as a report of several different types of situations.
A cumulative interpretation of (2.72) is one where say John only danced with Sue, and
Bill only danced with Mary. That is each part of the agent plurality danced with merely a
proper part of the theme plurality; and conversely each part of the theme plurality danced
with just a proper part of the agent plurality. Fortunately, a truth-theoretic explanation of
this phenomena is already implicit in the way plural thematic relations are defined.
Given that thematic relations are closed under sum formation, we know that if
Θ(E,X) holds, then for each atomic e ≤ E, there is at least one x ≤ X such thatΘ(e, x),
and likewise for each atomic x ≤ X , there is at least one e ≤ E such that Θ(e, x). Let us
call this theΘ Cumulativity Principle; see Krifka (1992), Schein (1993), Landman (2000)
for discussion. This of course holds for both nominal and clausal thematic relations.
(2.73) The Θ Cumulativity Principle
Θ(E,X) ⇔ ∀x ≤ X∃e ≤ E[Θ(e, x)] & ∀e ≤ E∃x ≤ X [Θ(e, x)]
The truth conditions of (2.72) are as follows.
(2.74) ∃E[AGENT(E, j ⊕ b) & DANCE(E) & THEME(E,m⊕ s)]
These truth conditions are compatible with a number of different verifying situations; all
they express is that there are some events of dancing with John and Bill as agents and
Mary and Sue as themes. The event description can be satisfied if each agent danced with
just one theme (with either of the two pairings available), or stronger situations such as
each agent dancing with both themes. Pluralized thematic relations allow for any of these
available interpretations, without the use of operators to derive certain readings. That is
50
not to say that such operators (e.g., distributivity or group operators) are incompatible
with this approach, especially if there are further reasons for positing their existence.
Note that this is not the only approach to cumulativity. There are non-event theories
which I will not review immediately, though I will bring them up in discussion with De
Se reports in Chapter 6. As we will see, these are not without their flaws. One particular
argument for the eventive approach to cumulativity with distributivity will be discussed
in the next section.
2.2.6 Distributive and collective interpretations
One of the most well-known observations about sentences with plural expressions is
their potential for distributive and collective interpretations. While some sentences seem
to favor either a distributive (2.75) or collective (2.76) construal based on idiosyncrasies
of the predicate involved, others present a case of ambiguity (2.77).
(2.75) They are left-handed
(2.76) They formed a circle
(2.77) They carried a piano up the stairs
In order to account for this range of interpretations, semanticists often treat one of these
readings as basic, and the other derived by means of some silent operator. Both options
have been pursued; for those that take collectivity as the basic interpretation, distributivity
is derived by a distributivity operator; see Link (1984), Roberts (1987), and Lasersohn
(1995), among others. A non-eventive distributivity operator based on the work of these
authors is given below.
51
(2.78) !D" = λP⟨e,t⟩.λXe.∀x ≤ X [P (x)]
In examples (2.75) and (2.77), this operator attaches to the VP and yields truth conditions
stating that each atom in the subject plurality bears the property denoted by the VP.
Landman takes the other route20. For him distributivity is the default form of plu-
ral predication, and collective readings are derived by a group forming operator ↑ which
applies to noun phrases. Landman assumes a sum-based theory of plurality where pred-
ication of a simple sum is distributive predication, and predication of a group individual
corresponds to collective predication.
(2.79) a. Al, Bob, and Chaz carried the piano
b. Distributive: CARRY-PIANO(a⊕ b⊕ c)
c. Collective: CARRY-PIANO(↑ (a⊕ b⊕ c))
There are many issues relevant for the debate concerning which reading is the basic and
which is derived, and I will not attempt to review them here. Although, there is at least
one straightforward argument supporting VPs being the source of ambiguity, and not NPs.
Lasersohn (1995) provides an argument from conjoined VPs where one VP is interpreted
distributively, and the other collectively.
(2.80) They are left handed and arranged in a circle
Sentences like this provide evidence for the VP being responsible for the ambiguity, per-
haps implemented as the first VP bearing a D operator and the other not. If NPs were re-
sponsible for the ambiguity, it becomes difficult to explain (2.80) as the same NP would,
20See Landman (1989a), Landman (1989b), and Landman (2000).
52
assuming Landman’s approach, have to both lack a ↑ operator when interpreting its com-
position with the first VP, and posses this operator for its composition with the second.
2.2.6.1 Distributivity in event semantics
The topic of distributivity in event semantics can be traced back to the work of
Taylor (1985)). Taylor addressed the logical form of sentences containing the distributive
determiner each, and in particular how such items interacted with adverbial modifiers.
He observed that in certain sentences containing each, adverbs construed as monadic
predicates of events seem to have more than one option as for which events they modify.
This is perhaps easiest to see in sentences that have two such adverbs, as in the following
example taken from Taylor.
(2.81) Gracefully, Sally ate each crisp quickly
This sentence can be used to describe a situation such as the following: in one sitting,
Sally ate an entire bag of chips gracefully; and as far as each individual crisp was con-
cerned, it was eaten quickly. As the paraphrase suggests, there seems to be two sorts of
events that are relevant in the meaning of (2.81): the totality of eventsE which correspond
to those events that culminate in the eating of the entire bag, and also sub-events of E,
each of which is such that a single crisp is eaten quickly. Taylor’s suggestion was that the
logical form of (2.81) include two event quantifiers, the Davidsonian clause-level event
quantifier, and another which has narrow scope with respect to each. Taylor’s quantifier
quantifies over sub-events of the larger events associated with the clause-level quantifier.
Given the assumptions presented above, this can be regimented as follows.
53
(2.82) ∃E[GRACEFULLY(E)AGENT(E, s) & EAT(E) & ∀x : CRISP(x)[∃E ′ ≤
E[THEME(E ′, x) & QUICKLY(E ′)]]
The crucial component is that the sub-event quantifierE ′ ≤ E scopes immediately below
the universal quantifier associated with each; essentially apportioning sub-events of the
appropriate type to each atomic individual that is universally quantified over, in this case
the crisps. This has the effect of generating truth conditions stating that each crisp is a
theme in some sub-events of E and those sub-events are quick.
Schein (1993) builds on Taylor’s suggestion about the logical form of sentences
with distributive morphemes when giving his seminal argument for thematic separation
(i.e., total separation). According to Schein, such a view of distributivity together with
the total separation approach to argumenthood is necessary for capturing certain interpre-
tations of sentences that mix distributivity with cumulativity such as (2.83).
(2.83) Josh and Ben made each customer three sandwiches
The relevant reading of this sentence is one where Josh and Ben did all the work, and
as a result each customer received three sandwiches. This does not say how much work
Josh and Ben did for each customer; for example, some customer might have had his three
sandwiches all made by Josh, another customer having two made by Josh and one by Ben,
another customer having 1.25 sandwiches made by Josh and 1.75 made by Ben; etc. For
this reading to be available, Josh and Ben and three sandwiches must be scopeless with
respect to each other. Schein shows that this is not possible with theories that have verbs
interpreted as polyadic predicates21. He claims that the only way to give adequate truth
21This includes alternatives with branching quantifiers, Sher (1990).
54
conditions that capture this reading is with total separation and the view of distributivity
given by Taylor, as expressed in the logical form in (2.84).
(2.84) ∃E[AGENT(E, j ⊕ b) & MAKE(E) & ∀x : CUSTOMER(x)[∃E ′ ≤ E
[GOAL(E ′, x) & ∃Y [THREE(Y ) & SANDWICH(Y ) & THEME(E ′, Y )]]]]
Eventive theories without thematic separation, nor even partial separation, are unable
to account for such readings since they specify in the lexical entries for verbs that the
conjunct associated with the verb as well as the thematic conjunct associated with the
verb’s arguments have the same event parameter.
I now turn to a specific implementation of Taylor’s and Schein’s approach to dis-
tributivity in the compositional system given here. I accomplish this by positing a lexical
axiom for the distributive element each, which relies on several other aspects of compo-
sition discussed above; in particular the Conjunctivist approach to argument composition
couched in a total separation version of neo-Davidsonianism. I will treat each as one
instantiation of the D operator, thus the following definition will serve not just for the
cases discussed by Taylor and Schein, but for other examples where one might posit a D
operator. I turn to these other cases shortly.
(2.85) !D" = λXe.λΘ⟨e,⟨v,t⟩⟩.λP.⟨e,t⟩.λEv.∀x ≤ X [∃E ′ ≤ E[Θ(E ′, x) & P (E ′)]]
Like the quantificational approach to indefiniteness in §2.2.4, D will compose with a
canonical restrictor argument as well as the adpositional thematic element. Note that
I depart from the traditional approach of Generalized Quantifier Theory by assuming a
type e plural restrictor argument instead of the usual predicative type ⟨e, t⟩. This is a
relatively innocent modification, as both types have the effect of picking out a plurality
55
of individuals for which to quantify over. The motivation for the type e approach will
become clear in later chapters when discussing anaphoric constructions; since the first ar-
gument is of type e, it can be bound and receive values via the assignment function. The
third argument of D is its canonical scope argument, which will correspond to the sub-
event portion of logical form. The final argument of D is an event argument. Though D
will never compose with an event value, the last argument position has the effect of turn-
ing D when composed with its first three arguments into a monadic predicate of events,
thus allowing it to compose with other such predicates by Predicate Conjunction. The
composition of D with its arguments is diagrammed in the following tree.
(2.86) ⟨v, t⟩
Θ
each Xrestrictor
Pscope
I will end this section by discussing how the version of the D operator presented
here can be used in place of the non-eventive D-operator in order to account for dis-
tributive/collective contrast. This will also be the first argument motivating the particular
implementation details of the restrictor argument in (2.85); in particular why I chose a
type e instead of type ⟨e, t⟩ restrictor. The crucial claim here is that when the D oper-
ator does not appear in canonical argument positions as an each-DP, then the restrictor
argument is a plural variable whose value is shared by another plural DP; I put off de-
tails about how this value is determined until the next section. This claim will be very
important for analyzing the cases of plural anaphora in the next chapters, in which cases
the other DP is the one traditionally assumed to be the anaphor’s antecedent. Put differ-
56
ently, for cases where the D element is not in an argument position, the restrictor value
will be represented twice in logical form; once in its argument position, and again as the
restrictor. For a simple intransitive sentence with a distributive construal, I assume there
is a silent D with restrictor adjoined to the VP (2.87a), and the restrictor shares its value
with the plural subject. The truth conditions given present assumptions are presented in
(2.87b)
(2.87) a. The girlsX [V P [D + X ][V P smiled]]
b. ∃E[AGENT(E,⊕GIRL) &
∀x ≤ ⊕GIRL[∃E ′ ≤ E[AGENT(E ′, x) & SMILE(E ′)]]]
Champollion (2010) criticizes an event-based version of distributivity that is very similar
to my own, which he attributes to Lasersohn (1998). In (2.88) I provide Lasersohn’s
version of the meaning of (2.87a) as reported in Champollion (p. 168, example (17a)), up
to the introduction of existential closure. I use the notational conventions presented here.
(2.88) λE.∀y ≤ ⊕GIRL[∃E ′ ≤ E[SMILE(E ′) & AGENT(E ′, y)]]
Champollion gives a convincing argument showing that Lasersohn’s rendition suffers
from the problem of leakage; it can apply to events in which more goes on than sim-
ply girls smiling. I agree that this is an unsatisfactory state of affairs. The present account
avoids this problem as follows. My logical form specifies what the agents of the larger
events E are, and not merely the agents of the sub-events E ′ as with Lasersohn’s version.
This fact, together with the independently required principle of Thematic Uniqueness
from §2.1.2 tell us that the only types of events which can serve as values of E are those
57
that have the girls and only the girls as agents. Lasersohn’s conditions are weaker, stating
that only each of the relevant sub-eventsE ′ have girls as agents. Thus, we avoid the prob-
lem of leakage. Note that this is not to say that Champollion’s account of distributivity
(not reviewed here) is wrong22; it just shows that the present account at the moment does
not suffer from leakage problem discussed above. I will return to the issue of leakage in
the following chapter.
2.3 Chapter summary
In this chapter I have outlined the formal system that will be put to use throughout
the dissertation. There will be reasons for modifications and additions, but the core system
of a neo-Davidsonian semantics for plurality will remain unchanged. I first introduced a
view of argumenthood that pushes Davidson’s original suggestion about events to the
extreme: not only are event values semantic arguments of action verbs, they are the only
arguments of action verbs. Noun phrases are bearers of thematic roles, either by Θ-
features or through composition with adpositions, and they are interpreted as thematic
predicates. Following some ideas of Pietroski, Predicate Conjunction is taken to be central
for the composition of both arguments and adjuncts. The event approach has also proven
useful for addressing plurality phenomena in natural language. The most important aspect
of this program that I will put to use in the following three chapters is the approach to
distributivity first developed by Taylor and Schein. I plan on showing that the event-
22Champollion develops of theory of distributivity that is also meant to account for certain properties of
aspect and measurement which are irrelevant for our purposes here. I believe though that the discussion of
anaphora here can be implemented in Champollion’s system with all its extra theoretical machinery for a
more comprehensive theory that links anaphora and these other semantic subdomains.
58
version of the distributivity operator in (2.85) can be used to give a unified analysis of
various local plural dependencies discussed in the literature.
59
Chapter 3: Distance Distributivity
Over the course of the next three chapters, I will extend the Taylor-Schein anal-
ysis of distributivity to cases where the distributive element appears separated from its
restrictor argument. I will argue that the same lexical entry given for determiner uses of
each can also be used for these cases of distance distributivity; relying on some of the
general features of Conjunctivist composition together with some proposals about how
the thematic roles and restrictor values are determined for “each” in such cases. In this
chapter, I focus on constructions that have previously been called distance distributivity,
in particular floating and binominal each. This will serve as an introduction for how the
analysis can be further extended to reciprocals and plural reflexives in the following two
chapters.
3.1 An overview of distance distributivity
In this section I will provide a brief empirical overview of the two sorts of construc-
tions that have been labelled as cases of distance distributivity: floating and binominal
each. I focus on English distance distributivity items and their core distributional and
semantic properties, though I draw on other languages for comparison. My hope is that
the proposals offered in this chapter can be extended beyond English, though I leave this
60
for future work. I will not attempt a detailed theoretical review of past syntactic or se-
mantic analyses of these constructions, nor will I give a survey of the similarities and
differences of these constructions across languages; for these issues I refer the reader to
the comprehensive study of Zimmermann (2002) and Bobaljik (2002). What I provide be-
low are the ingredients that are important for giving a Taylor-Schein treatment of distance
distributivity.
3.1.1 Floating each
The study of floating each began with Kayne (1969), a seminal work on floating
quantifiers in general. Focusing on French, Kayne observed that certain determiner-like
elements can appear in positions other than the canonical prenominal determiner position.
(3.1) Tous
all
les
the
enfants
children
ont
have
vu
seen
ce
this
film
movie
‘All the children have seen this movie’
(3.2) Les
the
enfants
children
ont
have
tous
all
vu
seen
ce
this
film
movie
‘All the children have seen this movie’
The same sort of constructions can be observed with the distributive item each in English,
which can appear either in a typical determiner position or floated in the middle field.
(3.3) Each of the children have seen this movie
(3.4) The children have each seen this movie
61
Floating each has a limited range of the kinds of antecedents that it can take. Focus-
ing on bare or article-marked nominals1, the antecedents to floating each must be plural;
they cannot be singular or mass denoting.
(3.5) (The/some) children can each go down the slide
(3.6) *A child can each go down the slide
(3.7) The *(bottles of) wine has/have each satisfied the judges
There are several positions in the clause where a floating quantifier may appear. For
English and related languages, floating instances of each can appear in a range of positions
from immediately following the subject to immediately preceding the verb phrase. In
(3.8), the possible occurrences of floating each with a subject antecedent/associate are
given.
(3.8) The students (each) could (each) have (each) been (each) doing that
One of the central debates in the syntactic literature on floating quantifiers is that
status of the positions in which these element can appear. Sportiche (1988) argued that
the positions where floating quantifiers appear are A-positions; the floating element and
its antecedent begin their derivational life together in a VP-internal subject position, and
while this constituent moves cyclically through various A-positions to its final case po-
sition, the quantifier element becomes stranded while its complement, the antecedent,
continues to the case position2.
1I consider only antecedents that are not headed by proportional determiners, which involve additional
problems that are beyond the scope of this dissertation.
2Benmamoun (1999) follows Sportiche for most of the positions of floating quantifiers, though he argues
that floating quantifiers that immediately follow the subject are still a constituent with the subject.
62
Alternatively, some authors have argued that floating quantifiers appear in adverbial
positions. Previous proponents of this approach take it that the quantifier never forms a
constituent with its antecedent; see for example Dowty and Brodie (1984). Support for
this idea comes from canonical adverbs which can appear in the same positions as floated
quantifiers in (3.8).
(3.9) The students (often) could (often) have (often) been (often) doing that
Further support for an adverbial analysis comes from examples in Slavic languages where
the quantifier may appear in certain adverb positions that could not possibly be A-positions,
barring ad hoc remnant movement of other elements in the clause. For example, in Serbo-
Croatian, a quantifier may appear to the right of a right-adjoined VP-adverb.
(3.10) Studentii
students.NOM
su
AUX
poloz˘ili
passed
ispit
exam
uspes˘no
successfully
svii.
all.NOM
‘All the students passed the exam successfully.’
An additional challenge for stranding analyses is what Kayne (1969) called L-tous
in French, which is apparent leftward movement of the floating quantifier. In (3.11), the
quantifier appears to the left of its direct object antecedent, in a position which is typically
not taken to be part of an A-chain associated with direct objects.
(3.11) Elle
she
a
has
tousi
all
voulu
wanted
lesi
them
lire
to-read
‘She wanted to read them all’
Some authors (Kayne (1969), Sportiche (1988), Déprez (1989)) have argued that the cases
of floating considered above and L-tous involve distinct operations. Part of the motivation
63
for this comes from the fact the L-tous is only possible with a pronominal/clitic direct
object.
(3.12) *Elle
she
a
has
tousi
all
voulu
wanted
lire
to-read
ces
these
livresi
books
Intended meaning: ‘She wanted to read them all these books’
This restriction is not observed in other languages though. For example, Serbo-Croatian
allows leftward dislocation of the distributive svaki/svi from a non-pronominal direct ob-
ject.
(3.13) Student
student
je
AUX
svakui/svej
each/all.ACC
brzo
quickly
proc˘itao
read
knjigui/knjigej .
book/books.ACC
‘The student read each book / all the books quickly.’
While the above data points pose problems for stranding analyses, languages with
morphologically rich determiners support a connection between the antecedent and the
floating quantifier, contrary to the views of most adverbial analyses which maintain that
there is no such connection. For example, French floating quantifiers must agree in gender
with their antecedents, and as seen in the above Serbo-Croatian sentences (3.10) and
(3.13), the antecedent and floating quantifier show case agreement.
(3.14) Elles
they.FEM
sont
all.FEM/*all.MASC
toutes/*tous
gone.FEM.PL
allées
to
à
the
la
beach
plage
‘They all went to the beach’
Above I reviewed some key points of both stranding and adverbial theories of quan-
tifiers float since the analysis I will develop in the remaining sections of this chapter will
be hybrid of the two. I agree with the aspect of stranding analyses like Sportiche’s that
64
the distance distributivity element and its antecedent value form a constituent in the form
of a head-sister construction, the syntactic relation standardly assumed to hold between
a quantification determiner and its restrictor argument. I leave open two possibilities for
the syntax of the silent element that acts as the restrictor sister for the floated quantifier
in surface syntax: either this element is a trace stranded by movement of the antecedent
nominal, as in Sportiche’s analysis, or the silent element is a covert pronoun that is refer-
entially dependent on the antecedent nominal (i.e., there is no movement chain connecting
the two positions); see §3.2.2 for further discussion. While I borrow this crucial aspect
of local composition (at some point in the syntactic derivation) common in stranding type
analyses, I reject that the stranding happens only in A-positions. I believe that it is benefi-
cial to characterize the possible positions of distance items as adverbial. On the one hand,
this accounts for the similarities with adverbs like often and also the possibility for L-tous
and right-VP-adjoined floating elements in other languages. On the other hand, it allows
for a uniform analysis of floating and binominal each, where the latter instances of each
are clearly not A-positions in the movement chain of each’s antecedent.
One may argue that the data observed in other languages tells us nothing about
English, where we do not see agreeing determiners nor the range of possible positions
and antecedents seen in other languages. However, given their similarities in meaning, it
might be suggested that the same core syntactic and semantic mechanisms are at work,
and that a uniform analysis should be pursued. I believe that at least the semantics of
floating quantifiers is the same across languages, though there may be additional factors
in a given language that restrict or widen the range of possible positions and antecedents
for the quantifier.
65
I will discuss one last empirical point about floating quantifiers that are relevant for
us here, their relative scope properties. Dowty and Brodie (1984) observed that sentences
with floating quantifiers exhibit so-called surface scope; see also Déprez (1994). I use
the phrase “surface scope” to refer to the relative scope interpretation where the wide
scope quantifier c-commands (and often linearly precedes) the narrow scope quantifier in
surface syntax; i.e., before the covert transformations that derive an LF representation. For
comparison, determiner uses of each in sentences with negation give rise to an ambiguity;
they have both surface scope and inverse scope interpretations. Sentences like (3.15)
are typically taken to be true if some but not all of the men kissed Mary, supporting the
conclusion that the negative operator can take inverse scope with respect to the distributive
operator.
(3.15) Each man didn’t kiss Mary
Consider now the floating examples (3.16) and (3.17). Given Dowty and Brodie’s hypoth-
esis about surface scope, (3.16) should only allow the ∀ > ¬ interpretation and (3.17)
should only allow the ¬ > ∀ interpretation.
(3.16) The men each didn’t kiss Mary
(3.17) The men didn’t each kiss Mary
(3.16) is unambiguous; it can only be true of situations where each man is such
that he didn’t kiss Mary. In other words, (3.16) only has the surface scope interpreta-
tion where each scopes over negation. The (un)ambiguity of (3.17) is harder to diagnose.
This is because, unlike (3.16), the inverse interpretation entails the surface interpretation:
66
∀x¬P (x) entails that ¬∀xP (x). Thus, it may be that the there is only the surface interpre-
tation, but we cannot tell for sure since the situations that verify the inverse interpretation
will also verify the surface one. For the purposes of parsimony and giving a unified anal-
ysis of floating and binominal each, I maintain that surface interpretations are the only
ones available for distance each. This will be shown in the following section where we
see a wider range of scopal elements for distance each to interact with.
3.1.2 Binominal each
Safir and Stowell (1988) brought an apparently different sort of distance distributiv-
ity construction to the attention of theoreticians. They labeled this variety “binominal3”
each, as the meaning seems to be derived from the quantifier forming a relation between
two nominal expressions, its distance antecedent and the host noun phrase that it appears
immediately adjacent to4.
(3.18) The men saw two women each
Safir and Stowell noticed that there are some restrictions to the type of noun phrases
binominal each can appear adjacent to. They claim that this must be a numeric noun
phrase, or a noun phrase modified with certain adjectives that express vague quantities
such as several5. Following Safir and Stowell, I use “%” below to indicate that there are
3The type of distance distributivity is sometimes referred to as adnominal instead of binominal.
4Safir and Stowell (1988) use the terms Range-NP and Distributing-NP for what I call the antecedent
and host NPs, respectively. In Zimmermann (2002), my “antecedent” corresponds to his “Dist-Key”, and
my “host” to his “Dist-Share”. Later in the chapter, the host-NP will be cast as a specific example of the
distributor’s scope.
5My own judgements are such that noun phrases containing many and few are mildly deviant hosts for
a binominal each.
i . ?The men saw many/few women each
67
some speakers of English who find acceptable non-cardinal indefinites with the indefinite
article, and some who do not. Although Safir and Stowell do not mention this point,
there also seems to be some speaker variation in the acceptability of some jewels each,
especially when some is deaccented; thanks to Paul Pietroski (p.c.) for bringing this to
my attention. Examples below are from Safir and Stowell (1988)), p. 428.
(3.19) The men saw five jewels each
(3.20) The men saw several jewels each
(3.21) The men saw one jewel each
(3.22) %The men saw a jewel each
(3.23) *The men saw the/those jewels each
(3.24) *The men saw some/certain jewels each
(3.25) *The men saw both/most/all jewels each
Binominal each shares some properties with its floating counterpart. For example,
both require an antecedent that is a non-singular count noun phrase: singular count (3.26)
and mass (3.27) noun phrases cannot serve as antecedents.
(3.26) *A man saw two women each
(3.27) *Water covered two women each
Like floating each, binominal each appears to be restricted to surface scope relative
to other operators such as negation and existential indefinites. For example, (3.28) can be
68
true if one man saw two women, but the other men saw only one6; and (3.29) requires a
single man doing all the introducing (it would not be true if a different man introduced
each professor).
(3.28) The men didn’t see (exactly) two women each
(3.29) A/Some man introduced the professors to two students each
A notable difference between floating and binominal each is that the former, at
least in English, is restricted to having just subjects as antecedents. As evidenced from
(3.29), the antecedent to binominal each can be a direct object. It appears that the proper
generalization for what can act as an antecedent to binominal each is decided by height,
and not by particular argument positions. For example, in a double object construction,
it is often assumed that the indirect object asymmetrically c-commands the direct object,
and so in this construction the indirect object can antecede the binominal each that appears
following the direct object.
(3.30) I gave three professors two papers each
I will return to the details behind the syntax and interpretation of binominal each in di-
transitive constructions in §3.3.
While both floating and binominal each allow for a variety of antecedents, in par-
ticular ones containing quantificational elements, I will limit my discussion to cases of
(non-kind denoting) definite and indefinite noun phrases.
6Note that this does not technically rule out a lack of ambiguity, since the surface scope interpretation is
entailed by the inverse scope interpretation. At the least though, we can rule out the inverse interpretation
as being the only interpretation. The existential example (3.29) provides stronger support against the pos-
sibility for a wide-scoping binominal each, since unlike the negation example, the surface interpretation is
not entailed by the hypothetical inverse interpretation.
69
3.2 Extending the Taylor-Schein approach
Distance distributivity provides a challenge to compositional semantics. These ele-
ments behave like determiner each in that they quantify over a restricted domain of indi-
viduals determined by their restrictor. However, for distance distributivity, the restrictor is
separated in the syntax from the quantifier. The first challenge in giving a compositional
account for distance distributivity items is to reconcile the composition of the quantifier
with a suitable restrictor value. The next challenge is to account for the two types of dis-
tance distributivity: floating each, at least in English, appears in the middle field between
the subject and the VP; while binominal each appears immediately adjacent to a host
noun phrase. Given the similarities in meaning between the varieties of distributivity, we
should ask if these elements have the same lexical and compositional properties. Granted,
some languages use different morphemes for determiner each and distance distributivity
items, and some languages show a difference between a distributor in a canonical floated
position versus a binominal distributor; see Zimmermann (2002) for discussion. For En-
glish though, the same morpheme appears to be involved in each of these constructions,
so one should consider if there is a unified analysis for these items: a single lexical entry
suitable for the various occurrences of each. 7 I will argue that there is a single lexical
7One case of DD that is particularly interesting to the present study is the prefix po- that appears in some
Slavic languages. In Czech, po- can appear prenominally, in which case it is interpreted is a binominal
distributor; see Zimmermann (2002), p.41 example (54i), data attributed to Hana Filip.
i. Chlapci koupili po dvou párcích/párkách
boys bought each two sausages.LOC
‘The boys bought two sausages each’
Filip and Carlson (2001) observe that po- can also be used as a verbal prefix, and when this happens, there is
an obligatory distributive interpretation. When po- is absent, either a distributive or collective interpretation
is possible. Data from Filip and Carlson (2001), p.8 examples (6a) and (6b) respectively.
iia. Deˇti se schovaly
70
entry for each that is compatible with its various positions discussed above. This is the
Taylor-Schein distributivity operator introduced in the previous chapter.
3.2.1 The distance composition of the Taylor-Schein distributor
In Chapter 2, I introduced the proposals of Taylor and Schein concerning a par-
ticular neo-Davidsonian approach to the truth conditions of sentences involving deter-
miner each. I then implemented their ideas in a Conjunctivist approach to composition,
where virtually all binary branching nodes are interpreted as a type ⟨v, t⟩ number-neutral
monadic predicate of events. I showed how this definition of the distributivity operator
can be used to model the behavior of the determiner each and also as a variant of the VP-
level distributivity operator proposed by authors such as Link (1987) and Schwarzschild
(1996). Below I will show how the same distributivity operator can be used for a compo-
sitional analysis of distance distributivity.
For convenience, I repeat the proposed definition of the distributivity operator below
as (3.31) and the schematic tree representing the composition of D with its arguments
(3.32). Of particular importance for present concerns is the non-standard claim that the
external/scope argument of each is a monadic predicate of events, even when each is not
raised.
children REFL hide.PAST.3PL
‘The children hid’ (collective or distributive)
iib. Deˇti se po-schovaly
children REFL po- hide.PAST.3PL
‘The children hid’ (only distributive)
In the present system, po- can be treated as a Taylor-Schein distributivity operator like other DD elements;
it just happens that in Czech the range of projections which D can attach to include the verb in addition to
numeric nominals.
71
(3.31) !D" = λXe.λΘ⟨e,⟨v,t⟩⟩λP⟨v,t⟩.λEv.∀x ≤ X [∃E ′ ≤ E[Θ(E ′, x) & P (E ′)]]
(3.32) ⟨v, t⟩
Θ
D Xrestrictor
⟨v, t⟩
Pscope
Extending this approach to distance distributivity items requires the following: (i) pro-
posals about how the restrictor value is determined by the antecedent, (ii) proposals about
composition with scope argument in distance distributivity constructions, and (iii) show-
ing that the resulting truth conditions are appropriate.
As for the restrictor argument, I propose that D composes with a Θ-marked silent
plural pronoun whose semantic value and thematic role are determined by the antecedent
to the distance distributor. Recall from Chapter 2 that the Taylor-Schein approach in effect
attributes sub-events of a particular type to each atomic individual contained within the
restrictor value, and states that that individual has a particular thematic role in those sub-
events. The proposal about distance distributivity is that this thematic role is determined
by the canonical role assigned to the argument position where the antecedent nominal
resides, and the type e value of the antecedent also serves as restrictor argument to D. I
take up the technical details behind how theΘ and type e values are determined in §3.2.2,
though this informal proposal will serve for the time being.
The scope argument to D will be of type ⟨v, t⟩. In a Conjunctivist semantics, nodes
with this type are ubiquitous. In Chapter 2, I showed how D composed with its restrictor
and Θ value further composes as a subject nominal: since the sister of the subject is a
⟨v, t⟩ node, it serves as a suitable scope argument. The main syntactic proposal here is
72
that D with its first two arguments can attach in adjoined positions as well. In the case of
floating each, the adjunction site is the VP, so the VP will be the scope ofD; for binominal
each, the scope is smaller, it is just the nominal host which is the scope of D. In each
case, the scope corresponds to the sub-event domain in logical form. Given the surface
scope properties of distance distributivity items discussed in 3.1, we do not have to worry
about ambiguity: the scope argument to floating and binominal each will always be the
sister node it appears in construction with in surface syntax.
Consider first cases of binominal each like the following:
(3.33) The men saw two jewels each
The Θ-marked host nominal is interpreted as a ⟨v, t⟩ predicate: λE.THEME(E, 2J). This
is exactly the sort of meaning that can serve as the scope argument for D. I represent the
composition of binominal each in (3.34) below.
73
(3.34) t
∃e ⟨v, t⟩
⟨v, t⟩
ΘAG The meni
⟨v, t⟩
⟨v, t⟩
saw
⟨v, t⟩
⟨v, t⟩
ΘTH two jewels
⟨⟨v, t⟩,⟨v, t⟩⟩
ΘAG D Xi
With the above assumptions about distance D composing with its antecedent’s referential
value Xi and thematic role ΘAG, the truth conditions generated by our rules applied to
(3.34) are as follows.
(3.35) ∃E[AGENT(E,⊕MEN) & SEE(E) &
∀x ≤ ⊕MEN[∃E ′ ≤ E[AGENT(E ′, x) & THEME(E ′, 2J)]]]
The second line of the truth conditions represent the contribution of each composed with
its silent antecedent value and its scope; each of the men is attributed the property of being
an agent in sub-events of E, and the themes of each man’s sub-events are two jewels.
Because two jewels falls within the scope of D, we have the covariant interpretation each
man saw two jewels that are possibly distinct from the jewels seen by the other men.
Turning now to the floating case (3.36), each is in an adjoined VP position, as
74
represented in the tree (3.37). This again will be a type ⟨v, t⟩ predicate of events.
(3.36) The men each saw two jewels
(3.37) t
∃e ⟨v, t⟩
⟨v, t⟩
ΘAG The meni
⟨v, t⟩
⟨⟨v, t⟩,⟨v, t⟩⟩
ΘAG D Xi
⟨v, t⟩
⟨v, t⟩
saw
⟨v, t⟩
ΘTH two jewels
(3.36) differs from its binominal counterpart in that D has a slightly wider scope; it con-
tains the entire VP. The sub-event portion of logical form will thus include more than in
the binominal case.
(3.38) ∃E[AGENT(E,⊕MEN) &
∀x ≤ ⊕MEN[∃E ′ ≤ E[AGENT(E ′, x) & SEE(E ′) & THEME(E ′, 2J)]]]
While the resulting truth conditions (3.38) appear to be synonymous with those of
(3.35) there are some slight meaning differences depending on the attachment sight of
the distributor. In §3.3, I address ditransitive sentences where there is a clear difference
in meaning relating to whether the whole VP is within the scope of each, as it is in
75
the floating cases, or whether just a host nominal acts as the scope, which we see with
binominal each. I will first discuss some issue of how the semantics of the antecedent
factors into the composition of distance D8.
3.2.2 The distance restrictor
Above I proposed that the first two arguments of distance D, the restrictor and Θ
arguments, are determined by the antecedent of D; in particular, the restrictor shares a
referential value with the antecedent, and the thematic role of the antecedent is the same
role that acts as the Θ argument to D. Below I propose some specific details about the
compositional system to implement these ideas.
3.2.2.1 The semantic value of the restrictor
In the floating quantifier literature, it has been noticed that the restrictor of a de-
terminer each is morphologically singular, though the antecedent to floated each is mor-
phologically plural. This raises several questions; for one, if the determiner and distance
examples differ only in that for the former the antecedent does not strand the quantifier,
but in the latter it does, then why do we see different number morphology? Furthermore,
there is the semantic type of the restrictor to consider. When it appears with a non-floated
8The analysis of distance distributivity developed relies on the assumption that the subject and theme
nominals in the same clause are interpreted as thematic predicates of the same event. On the one hand,
this can be viewed as an attractive feature of the present account; if all argument in a clause are tied
together by the same event variable (as in Davidson (1967b) and Castañeda (1967), for example), and if
distance distributivity requires arguments that are tied to the same variable, then it follows that distance
distributivity should be a local phenomenon, which it is standardly claimed to be. On the other hand, there
have been some analyses, especially of causativity(Parsons (1990), among others), that argue for multiple
event variables per clause. The values of these variables are not related to one another by the part-of relation
as they are in the proposed treatment of distributivity. As such, the present account is incompatible with
multiple-event-variable analyses of clauses. See especially Williams (in press) for discussion of the two
analysis of causatives, and arguments in favor of single-variable analyses for these constructions.
76
determiner, the restrictor is standardly taken to be type ⟨e, t⟩. However, the antecedent of
a distance D, which is in an argument position, should be a type e plural nominal.
To account for these issues, I propose that the non-floated counterpart of distance
distributivity constructions is not each Nsg, but rather each of the Npl. I treat the preposi-
tion of as vacuous; following Vergnaud (1974), Chomsky (1986), and Sportiche (1988),
the preposition of is treated as the morphological spell out of genitive case in the non-
floated construction. When this plural partitive restrictor is separated from the quantifier,
case is assigned by a clausal argument position such as nominative case when it appears
as a subject. Assuming this underlying partitive form, we thus have an explanation for
the plural morphology of the antecedent in distance distributivity constructions. Note that
this does not speak against the thesis for a univocal each; there is still one each that,
when it appears as a determiner, can have either a singular bare restrictor or a plural par-
titive restrictor. The proposal here is that distance distributivity corresponds to the latter
determiner use9.
There is a semantic argument for going with the plural partitive over the bare sin-
gular as the restrictor for a distance distributivity element. Schein (2005) noticed that
for the two determiner uses, there is a slight meaning difference between the two: for
a determiner each with a plural partitive restrictor such as (3.39), there is an ambiguity:
there can either be table-sized custards, each of which alone can cover a table; or smaller
custards which together do the work of covering a single table. For the singular restrictor
9The similarity between each Nsg and each of the Npl is further supported by the idea that in both
cases the restrictors range over a plurality of individuals. The standard claim about the denotation of an
⟨e, t⟩ is that it is a set of individuals. In a way, so is the denotation of a plural type e expression. The
difference between each Nsg and each of the Npl seems not to be in the semantics of each, but in the
number morphology on the restrictor. See Schein (2005) for further discussion.
77
case (3.40), there is no ambiguity; it speaks only of table-sized custards.
(3.39) Each of the custards that covered a table contains two tablespoons of vanilla
(3.40) Each custard that covered a table contains two tablespoons of vanilla
Consider now floated and binominal variants of these sentences. As one might expect
since distance distributivity requires a plural antecedent, these sentences allow the same
range of meanings as the plural partitive determiner sentence (3.39); they can be true
of small custards that collectively cover a table. This paradigm supports the claim that,
at least in English, the restrictor value in distance distributivity constructions is like the
plural partitive in the non-distance counterpart, instead of the bare singular restrictor.
(3.41) The custards that covered a table each contain two tablespoons of vanilla
(3.42) The custards that covered a table contain two tablespoons of vanilla each
Furthermore, since the partitive restrictor is presumably type e in the non-distance case
as suggested by its occurrence with a definite determiner, this provides an explanation for
why the separated antecedent is also type e10. The type e constituent can then serve as an
argument to a Θ/adposition head or as the appropriate type of input for the Theta Rule.
This analysis can then maintain that bare-singular restrictors are still ⟨e, t⟩, in accordance
with standard practice.
10It is well-known that partitive elements allow only a small range of determiners: each of the/?three
boys/*most/*few/*many/*all boys; see Gagnon (2013) for an overview and discussion. However, the an-
tecedents of distance distributivity elements appear to be licit with a larger range of determiners. Since I do
not consider such quantificational antecedents in this dissertation, I leave this issue as a problem for future
research.
78
I now turn to discussion of how the proposed silent restrictor of distance distributive
elements is valued by the antecedent nominal. I believe that there are several mechanisms
from the literature that can account for this covaluation, and I will briefly outline each
of them below. One option is syntactic binding; the antecedent and silent restrictor bear
an index, and there is a local binding principle akin to Principle A (Chomsky (1981)
and others) that forces (i) the antecedent to c-command the silent restrictor pronoun and
(ii) the index of the antecedent and the restrictor pronoun to be the same. Alternatively
one can pursue a movement analysis. Following one idea from Sportiche, the antecedent
and quantifier at one point in the derivation form a constituent, and then the antecedent
nominal separates and moves to its case position. The quantifier then composes with
the silent trace/copy of the antecedent with which it is covalued. There is the issue of
how such movement proceeds if the distance distributor is in an adverbial position as I
have suggested here11; this differs from the part of Sportiche’s analysis which states that
the distributor appears only in A-positions. However, I believe that it is preferable to
maintain the adverbial status of each to give a unified analysis of floating and, especially,
binominal occurrences. I believe that this issue can be resolved by certain aspects of
movement in modern Minimalist syntax; in particular the idea of sideward movement;
see Nunes (2004), among others. Under this view, constituents can be constructed in
11If movement of a referential noun phrases leaves a trace in an adjunct that corefers with the nominal
in an argument position, then one might wonder why it is impossible to say things like (i) to mean “John
found a spider under himself”.
(i) Johni found a spider under ti
Some theorists argue that this structure is in fact possible when coreference is intended, and that there
are rules of pronunciation (PF rules) which result in the trace being pronounced as himself. This is the
movement theory of reflexives, advocated by Hornstein (2000) among others. The theory of reflexives
developed in Chapter 5 is compatible with the general idea that himself appears in (or very near) the position
where the antecedent moves from.
79
separate derivational work spaces, and there is the possibility for constrained copy-merge
operations to hold between such work spaces. For distance distributivity, the proposal
is that each composes with its restrictor, the restrictor is then copied, and moved to a
different work space. The resulting [each <restrictor>] constituent can then be adjoined
to an appropriate position, such as to the VP or a host DP, and later in the derivation the
copied restrictor merges to its argument position.12,13
Since the antecedent like other nominals is interpreted as a predicate of events, this
rules out the option of semantic binding in this framework, where the sister of the an-
tecedent nominal is interpreted as a λ-expression evaluated with a modified assignment
function; see Heim and Kratzer (1998). This approach would treat the sister of the an-
tecedent as a type ⟨e, t⟩, but in this framework the antecedent is not type e, but rather
⟨v, t⟩. It may be possible to modify the rules associated with lambda abstraction to apply
12Antecedence to distance each has to be determined by something more than mere c-command in this
system. For one, there is leftward displacement of quantificational elements in some languages. Further-
more, the semantics proposed here is compatible with LFs where the restrictor and scope of each are the
same, and unsatisfactory state of affairs.
(i) John kissed [[three women]i each Xi]
There is nothing in the system that rules out (i) as an acceptable sentence. However, there might be syntactic
reasons for ruling out such structures. For example, if movement is involved such structures could be ruled
out as an anti-locality violation: the movement is to short; see Grohmann (2011) discussion and references.
Furthermore, even without movement, there could be some economy-based reasons for ruling out each
having the same plurality be both its restrictor and scope. Perhaps even a semantic-based notion of economy
is at work; in which case (i) can be rule out as its truth conditions derived by the Taylor-Schein approach,
shown in (ii), do not contribute any real difference from the sentence if each is absent. The other cases of
distance distributivity we looked at would mean something different (or maybe less precise) if each were
removed.
(ii) ∃E[AGENT(E, j) & KISS(E) & ∀x ≤ 3W [∃E′ ≤ E[THEME(E′, x)]]]
13As mentioned previously, in some languages the distance distributor agrees in φ or case features with
its antecedent. For the movement approach outlined in the main text, I follow Chomsky (1995), Chapter
3, in that nominal elements enter the derivation with case, and check these features from an argument
position with the appropriate case heads. This accounts for distance distributors sharing the same case as
its antecedent even though it never was located in a case position.
80
to ⟨v, t⟩ nominals, though I do not explore this option here14.
3.2.2.2 Locating the thematic role of each
In addition to each having a restrictor argument that shares a referential value with
its antecedent, I claim that for suitable truth conditions each must also share a thematic
role with its antecedent. Below I discuss how the two approaches to thematic role inter-
pretation from Chapter 2, the adpositional approach and the Θ-feature approach, can be
used to implement this dependency.
For the adpositional approach, all nominal expressions compose with a possibly
silent adposition specified with a thematic role. The proposals about D so far have been
that its second argument is such an adposition, whetherD appears in an argument position
or one of the adjoined positions associated with floating and binominal each. For these
latter cases I proposed that the silent adposition is valued by whatever thematic role the
antecedent of D has. However, notice that in proposed decomposition of distance D,
the Θ adposition is discontinuous with the silent pronominal restrictor, even though the
values of Xant and Θant are both determined by the same antecedent nominal.
(3.43)
Θant D Xant
Pscope
Given this decomposition, it is unclear how and why the values of Xant and Θant are
determined by the same expression.
14I refer the reader to Champollion (2010) and his subsequent working for a type-shifting approach
raises the semantic type of thematic constituents to the appropriate quantificational type. For him, this
type-shifting applies to nominals composed with thematic heads similar to the adpositional approach to
neo-Davidsonianism discussed in Chapter 2.
81
The Θ-feature approach fares better in this regard, since the thematic role is not
located on an adposition, but on the nominal expression itself. Under this view, the silent
restrictor contains both the relevant thematic and referential properties which it shares
with the antecedent. As mentioned above with regards to Minimalist approaches to fea-
ture transfer, case and φ features of a nominal can get passed to the determiner that it
composes with. We have seen morphologically rich languages in §3.1 which have float-
ing quantifiers that agree in case and φ features with their antecedents; similar observa-
tions will be made about reciprocals in Chapter 4. I propose that Θ-features pass to the
determiner in the same way as case and φ features; the Θ-marked restrictor passes the
Θ-feature to each, and so each itself becomes Θ-marked with the appropriate role.
(3.44)
each restrictorφ,Θ,Case
An alternative definition of D following thisΘ-feature approach is given below, where D
bears a Θ-feature instead of receive a thematic role value by composing with an adposi-
tion.
(3.45) !DΘ" = λXe.λP⟨v,t⟩.λEv.∀x ≤ X [∃E ′ ≤ E[Θ(E ′, x) & P (E ′)]]
Using Θ-features requires a type-shifting rule like the Theta Rule from Chapter
2.15 While this adds an additional rule to the set of phrasal axioms, it has the benefit of
allowing an analysis of distributivity where the proposed thematic and referential prop-
erties are determined solely by the restrictor of each. This line of reasoning follows a
15I assume that the Theta Rule applies as a last resort like most other type-shifting rules. If a nominal is
type e and its complement type ⟨v, t⟩, then the rule applies because of a type mismatch. However, the Theta
Rule is not necessary for the interpretation of DΘ composed with its restrictor, since this is already of the
appropriate type to compose with a ⟨v, t⟩ sister.
82
well-established principle in modern syntactic theory that determiner-like elements, such
as each, match the feature values of their complements.
3.3 Binominal each in a variety of argument positions
In the beginning of this chapter I showed that binominal each in ditransitive con-
structions has a number of potential host nominals it can attach to. Below I give a ditran-
sitive paradigm showing the attachment possibilities for both the prepositional dative and
double-object constructions.
(3.46) Josh and Ben gave five dishes to [[three judges] each]
(3.47) Josh and Ben gave [[five dishes] each] to three judges
(3.48) Josh and Ben gave [[three judges] each] five dishes
(3.49) Josh and Ben gave three judges [[five dishes] each]
In this section I will demonstrate how the analysis of binominal each accounts for the
compositional interpretation of these sentences. In particular, I will show how proposals
about the thematic role given to each by its antecedent and its scope argument consist-
ing solely of the host nominal yield suitable truth conditions. I will then turn to the
scopal differences between binominal and floated each and show that the subtly differ-
ent truth conditions capture the subtly different meanings we see with certain ditransitive
sentences.
83
3.3.1 Antecedence in ditransitives
As shown in §3.1, the generalization concerning possible antecedents of English
binominal each is that a plural noun phrase that c-commands the host NP can be an an-
tecedent16. Following standard syntactic analyses of ditransitives such as Larson (1988),
we predict the following patterns of antecedent.
(3.50) • Prepositional dative ditransitives
– A direct object host can have only a subject as an antecedent
– An indirect object host can have a subject or direct object as an
antecedent.
• Double-object ditransitives
– A direct object host can have either a subject or indirect object as an
antecedent
– An indirect object host can have only a subject as an antecedent
To test these predictions, I use constructions with singular noun phrases so there is no
ambiguity as to what the antecedent is, since it was already shown that singular noun
phrases cannot antecede binominal each.
16Outside of English some varieties of floating quantification do not require the antecedent to c-command
the floating quantifier. This is arguably the case with the French L-tous movement and other cases of
leftward quantifier float discussed in §3.1.
84
(3.51) Prepositional dative paradigm:
• Direct object host
a. The men showed two jewels each to Mary
b. ??John showed two jewels each to them/the appraisers
• Indirect object host
c. The men showed a jewel to three women each
d. John showed ten jewels to three women each
(3.52) Double-object paradigm:
• Direct object host
a. The men showed the woman ten jewels each
b. John showed three women ten jewels each
• Indirect object host
c. The men showed three women each the jewel
d. ??John showed them/the appraisers each ten jewels
The predictions seem to be borne out, though there is some speaker variation with regards
to two types of sentences, as indicated by the ?? in (3.51b) and (3.52d). For these cases,
the antecedent noun phrase does not c-command binominal each. While this may limit
the range of syntactic accounts of ways of determining antecedence, it does not affect
the semantic proposals. For each of these cases, even the marginally acceptable ones, the
antecedent will contribute a plural referential value to act as the restrictor of each and
85
the thematic role associated with the antecedents argument position. I will show now
that the resulting truth conditions derived by the proposals here appropriately capture the
meanings of this range of sentences.
What sets the ditransitive examples apart from the previous ones is that the sub-
ject need not be the antecedent to each, and so there can be a plural value from another
argument position that determines the restrictor of each, and also each can be marked
with a thematic role different from those typically associated with subjects. For example,
consider a prepositional dative sentence where an indirect object acts as the host nominal
to each and its antecedent is the direct object: (3.51d). This sentence describes events
where there are ten jewels and each jewel is such that it was shown to three women. Since
the direct object is the antecedent to each, the ten jewels plurality acts as the restrictor
argument to each and each is associated with the theme thematic role. The resulting truth
conditions are as follows, where the sub-event conjunct is represented in the second line.
(3.53) ∃E[AGENT(E, j) & SHOW(E) & THEME(E, 10J) &
∀x ≤ 10J [∃E ′ ≤ E[THEME(E ′, x) & GOAL(E ′, 3W )]]]
For double-object constructions like (3.52b), the indirect object will be the an-
tecedent of each, so its restrictor will be the “three women” plurality and it receives the
goal thematic role. This sentence reports that each woman is such that she was shown 10
jewels, which is captured by the following truth conditions.
(3.54) ∃E[AGENT(E, j) & SHOW(E) & GOAL(E, 3W ) &
∀x ≤ 3W [∃E ′ ≤ E[GOAL(E ′, x) & THEME(E ′, 10J)]]]
86
Notice that there is no conjunct in the truth conditions that says that John is the
agent of the relevant sub-events, but this is given by the Θ Cumulativity Principle from
Chapter 2. With this principle, AGENT(E, j) entails that each atomic event e ≤ E has
John as an agent and the totality of events E has John as its sole agent (given Thematic
Uniqueness), and so any event E ′ ≤ E has John as its agent.
As a further consequence of Thematic Uniqueness, the truth of (3.51d) requires
that there are no more than ten jewels involved in the verifying events; and it clearly
lacks a reading where the ten jewels covary with each woman. Similar remarks hold
of (3.52b). This intuition is further sharpened if the modifier exactly is added to the
antecedent. The proposed semantics accounts for this fact since the antecedent nominal
is not within the scope of each, and so its corresponding event variable is bound by the
clause-level existential quantifier, and not the sub-event quantifier. I will elaborate on
this detail in the next section, but bring it up here to aid discussion with the observed
ambiguity in antecedence with ditransitives, which I turn to immediately.
From the paradigm in (3.51) and (3.52), we predict that when there are two potential
antecedents that are both plural, then ambiguity should arise. We can see this in the
following example.
(3.55) [John and Bill]i showed [exactly 10 jewels]k to exactly three women eachi,k
The ambiguity can be seen by considering what sort of events verify not just (3.55), but
the unambiguous examples where the non-antecedent argument is singular. Consider first
the case where the subject is singular, which means that the direct object will antecede
each as in (3.51d) above. Since women can covary with the jewels, a verifying situation
87
for this sentence can involve at most thirty women; the presence of exactly rules out any
higher number of women. Now consider a sentence where the subject is plural, but the
direct object singular.
(3.56) John and Bill showed the Hope Diamond to exactly three women each
Here, the women can covary with John and Bill, and since there are only two agents, the
maximum number of women in the verifying events is six; again exactly rules out any
higher numbers. As for (3.55), its ambiguity lies in the fact that it can have either the
six-women or the thirty-women reading; for the former, this is because the subject is the
antecedent to each (like (3.56)), and for the latter, the direct object antecedes each (like
(3.51d)).
3.3.2 Scope differences between floating and binominal each
If the proposals about distance distributivity are correct, floating each in English has
a wider scope domain than its binominal counterpart; for the former, the scope domain is
the entire VP (and possibly negation and auxiliary verbs), while for the latter the scope
domain is just the host nominal. For simple transitive sentences, this difference does not
appear relevant, though it does no harm in assuming such a scope difference. Essentially,
it captures the synonymy of pairs like (3.57).
(3.57) a. The men each stole two diamonds
b. The men stole two diamonds each
As mentioned briefly in the last section, ditransitive sentences present a situation where
the scope differences are more clearly observed. In this section, I focus on a particular
88
property of interpretation that results from being in the scope of a distributivity opera-
tor; the covariance of indefinite noun phrases. Below I present a well-known observation
about covariance, which will soon be cashed out in the neo-Davidsonian framework as-
sumed here.
(3.58) Principle of covarying indefinites
A covariance interpretation of singular indefinite and bare numeral noun phrases is
possible only when the noun phrase is within the scope of a distributivity operator.
We can see this principle at work with determiner each below, where the girls associated
with singular and numeric indefinite objects in (3.59) and (3.60), respectively, can covary
with each boy.
(3.59) Each boy loves a/some girl
(3.60) Each boy loves three girls
Covariance is also observed when the direct object is distributive and the subject is indef-
inite, as in the following sentences. This is due to the ability of distributive objects to take
inverse scope, accounted for by Quantifier Raising or some sort of type adjustment.
(3.61) A/Some girl loves each boy
(3.62) Three girls love each boy
It is well-known that the scope potential of a distributivity operator is clause-bounded,
and so a distributivity operator in a finite embedded clause cannot take inverse scope over
an indefinite noun phrase in the main clause. As such, the following examples do not
exhibit the covariance interpretations we see above.
89
(3.63) A/Some boy thinks that each girl loves flowers
(3.64) Three boys think that each girl loves flowers
Returning to distance distributivity, we now have some predictions about ditransi-
tives given the assumptions about the scope properties of floating versus binominal each.
First, the scope of floated each scopes over the whole VP, so a covariance interpretation is
expected of indefinites within the VP. Second, the scope of binominal each is only its host
nominal, so if there is an indefinite in the VP distinct from the host nominal, its value(s)
should not covary with the antecedent of binominal each. Keep in mind that inverse scope
interpretations are not possible for distance each, as discussed above in §3.1.1. The pair
of sentences in (3.65) show that these predictions are borne out.
(3.65) a. Josh and Ben each gave two desserts to (exactly) three judges
b. Josh and Ben gave two desserts each to (exactly) three judges
It is possible to interpret (3.65a) as describing a situation with six judges total: Josh gave
two desserts to judges 1,2, and 3; and Ben gave two desserts to judges 4,5, and 6. Note
that it is possible that (3.65a) can be used to describe a situation where they gave desserts
to the same three judges, but the important observation here is that a six-judge reading is
possible. For (3.65b), the six-judge reading is absent; this sentence is true only if there
are three judges total. Below I give the LFs and truth conditions of these two sentences
given the above proposals about the composition of floating and binominal each.
90
(3.66) a. [Josh and Ben]i [each Xi [gave two desserts to three judges]]
b. ∃E[AGENT(E, j ⊕ b) & ∀x ≤ j ⊕ b[∃E ′ ≤ E
[AGENT(E ′, x) & GIVE(E ′) & THEME(E ′, 2D) & GOAL(E ′, 3J)]]]
c.
ΘAG J&Bi
ΘAG each Xi
Scope
gave
ΘTH 2D Vt ΘGL 3J
(3.67) a. [Josh and Ben]i gave [[two desserts] each Xi] to three judges
b. ∃E[AGENT(E, j ⊕ b) & GIVE(E) & ∀x ≤ 4W [∃E ′ ≤ E
[AGENT(E ′, x) & THEME(E ′, 2D)]] & GOAL(E, 3J)]
c.
ΘAG J&Bi
gave
Scope
ΘTH 2D
ΘAG each Xi
Vt ΘGL 3J
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The crucial difference between the above truth conditions is the event variable in the
GOAL conjunct. For the floating example, it is the sub-event variable bound by the quan-
tifier introduced by D since the indirect object is within the scope of floating each. For
the binominal example, the event variable in the GOAL conjunct is bound by the clause-
level event quantifier and not the sub-event quantifier, because it is not within the scope
of binominal each. For the latter case, the proposals about scope together with Thematic
Uniqueness guarantee that this sentence is true only when there are exactly three judges
in the relevant events, as desired. For the floating case, since the goal nominal is associ-
ated with sub-events of each agent, covariance is possible and so a six-judge reading is
licensed.
The same pattern is observed with singular indefinites. A singular indefinite within
that VP can covary in a sentence with floated each (3.68), though a covariance inter-
pretation is missing when it is within the VP and the other object argument is a host to
binominal each (3.69).
(3.68) a. Josh and Ben each gave two desserts to a/some judge
b. ∃E[AGENT(E, j ⊕ b) & ∀x ≤ j ⊕ b[∃E ′ ≤ E
[AGENT(E ′, x) & GIVE(E ′) & THEME(E ′, 2D) & GOAL(E ′,a/some judge)]]]
(3.69) a. Josh and Ben gave two desserts each to a/some judge
b. ∃E[AGENT(E, j ⊕ b) & GIVE(E) & ∀x ≤ j ⊕ b[∃E ′ ≤ E
[AGENT(E ′, x) & THEME(E ′, 2D)]] & GOAL(E,a/some judge)]
In the double object versions of (3.68) and (3.69), the same pattern of covariance obtains;
(3.70) allows for covariance, but (3.71) only allows the interpretation where there is only
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a single judge involved.
(3.70) a. Josh and Ben each gave a/some judge two desserts
b. ∃E[AGENT(E, j ⊕ b) & ∀x ≤ j ⊕ b[∃E ′ ≤ E
[AGENT(E ′, x) & GIVE(E ′) & GOAL(E ′,a/some judge) & THEME(E ′, 2D)]]]
(3.71) a. Josh and Ben gave a/some judge two desserts each
b. ∃E[AGENT(E, j ⊕ b) & GIVE(E) & GOAL(E,a/some judge)
& ∀x ≤ 4W [∃E ′ ≤ E[AGENT(E ′, x) & THEME(E ′, 2D)]]]
For the sake of completeness, I show two sentences where the antecedent to binom-
inal each is a non-subject, and the subject is an indefinite. I use a singular indefinite to
rule out ambiguity, and I only show this with the distransitives constructions where the
antecedent c-commands the host, since non-commanding antecedents are prone to gra-
dient acceptability among speakers, as discussed above17. The predictions appear to be
borne out; for both the prepositional dative and double object construction, the subject
indefinite cannot covary with the antecedent to each.
(3.72) a. A/some philosopher introduced Chomsky and Davidson to five students
each
b. A/some bastard gave Josh and Ben five slaves each
In this section I have shown that two predictions made by the proposals about
scope in distance distributivity are borne out. For floating each, covariance with an-
17Floating examples are not added to this paradigm since in English only subjects can be antecedents to
floating each, and here the interest is in non-subject antecedents.
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tecedent/restrictor values is possible for indefinites within the VP. On the other hand, bi-
nominal each only allows covariance with the nominal host since other indefinites within
the VP are outside of its scope domain. For distance distributivity constructions, the scope
of each is determined by its surface syntactic configuration, so only indefinites within the
c-command domain of floated and binominal each in surface syntax can covary. Co-
variance was implemented by again appealing to the sub-event treatment of distributivity
proposed by Taylor and Schein, where the indefinites within the scope of each are inter-
preted as thematic predicates bound by the sub-event quantifier.
3.3.2.1 Comparison with Champollion 2012
In a recent paper, Champollion (2012) develops a theory of distance distributivity
that is similar to the one proposed here. He uses a neo-Davidsonian semantics to at-
tempt a uniform analysis of distributivity items, including the element jeweils in German;
though here, I will limit the discussion to his claim about English distance distributivity18.
Champollion achieves morpheme univocality for each up to type-shifting to account for
the composition of determiner versus floated versus binominal each. However, he focuses
just on transitive constructions, and the particular details of his system do not account for
the scopal differences discussed in the previous section.
I will first present the technical details of Champollion’s account. Champollion
posits a basic eventive distributivity operator which he calls a “reformulation of Link’s D
18Extending the analysis I presented here to jeweils, at least its property of distribution to non-atoms, can
be done in the same manner suggested by Champollion. He uses Schwarzschild’s cover-based approach to
distributivity from Schwarzschild (1996), and assigns a meaning to jeweils such that it distributes over con-
textually determined covers of a plurality, where atomic distributivity represents just one way of covering
the plurality.
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operator”; I will label this operatorC (3.73). He then shows howC can be used as a silent
VP-level operator to account for basic distributive interpretations of subjects in sentences
like (3.74), which has truth conditions (3.75). He assumes that C is theta-marked with an
antecedent, similar to the account of DΘ in (3.45), and he uses a functional notation for
thematic predicates.
(3.73) !CΘ" = λV⟨v,t⟩λE.[E ∈ ∗λE ′[V (E ′) & ATOM(Θ(E ′))]]
(3.74) The children CAG saw two monkeys
(3.75) ∃E[AGENT(E) = ⊕CHILD & E ∈ ∗λE ′[SEE(E ′) & THEME(E ′) =
2M & ATOM(AGENT(E ′))]]
Champollion offers the following prose paraphrase of (3.75): “This formula is true
just in case there is an event E whose agent is the children, and which consists of seeing-
two-monkeys events whose agents are atomic” (Champollion (2012), p.7). With this
operator defined, he gives the following axioms to floating and binominal each.
(3.76) !eachfloat" = !CΘ"
(3.77) !eachbinom" = λP⟨e,t⟩.λΘ⟨v,e⟩.λV⟨v,t⟩.λEv.[!CΘ"(λE ′.[V (E ′) & P (Θ(E ′))])(E)]
The present account has the advantage of not assigning different meanings to floated and
binominal each. Although Champollion uses the C operator in both definitions, they do
have different types and the functions do have different bodies. Since the present account
relies on Conjunctivism, it is not required to assign different semantics types to floating
and binominal each since the scope argument of both varieties of distance distributivity
will always be ⟨v, t⟩.
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Champollion’s account also suffers from an empirical problem. Though it is able to
account for transitive cases where floating and binominal each pairs seem to be synony-
mous, it is unable to account for ditransitive sentences where there are meaning differ-
ences between a sentence with floating each and its binominal counterpart, as discussed
above. This particular problem lies in the V argument in Champollion’s definition of bi-
nominal each in (3.77): this argument represents the predicate that is taken to hold of the
relevant sub-events. For the cases Champollion examined, this is the monadic predicate of
events contributed by a transitive verb. However, for ditransitive cases like the following,
the wrong predicate of events is chosen.
(3.78) Josh and Ben gave four meals each to exactly three judges
Given a standard approach to ditransitives, the sister node of the direct object will contain
the indirect object. For Champollion, this means that the indirect object’s interpretation
is part of the V argument, and thus is part of the predicate of events that is taken to
hold of the sub-events associated with each agent. As such, his account predicts that
this sentence can have “three judges” covarying with the agents. However, as mentioned
above, this sentence lacks the “six-judge” reading. For the account proposed here, this
lack of covariance is accounted for by having the scope of binominal each include just its
host nominal.
3.4 Leakage revisited
In §2.2.6.1 of Chapter 2, I introduced leakage as a problem that some accounts of
distributivity might suffer from. I showed there that the Taylor-Schein approach does not
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suffer from leakage as far as the antecedent of D is concerned. However, given the way
Taylor-Schein distributivity is currently defined, it is susceptible to leakage when it comes
to non-antecedent nominals in the scope of the distributivity operator. I will first outline
the problem, and then suggest a way to modify some current assumptions in order to fix
the problem.
Consider a modified version of Kratzer’s rose bush sentence, which we encountered
in §2.2.3.2 when discussing Variety; see Schein (1993), Schwarzschild (1996) and others
for discussion of similar facts.
(3.79) Alan, Brian, Campbell, and Dunn planted two rose bushes each
Recall that Kratzer’s original example, repeated below, was meant to illustrate that a
sentence can still be true if the actions of each individual agent do not fall under the
property denoted by the verb; e.g., each agent need not be involved in a planting even
though what the agents collectively do counts as a planting.
(3.80) Alan, Brian, Campbell, and Dunn planted a rose bush
(3.79) differs from the original examples in that each agent must be an agent of a planting;
more specifically, he must be the agent of an event of planting two rose bushes (which may
be different from the rose bushes that the others plant). Let us see if the truth conditions
of (3.79) given by the Taylor-Schein approach to binominal each sufficiently captures this
aspect of meaning.
(3.81) ∃E[AGENT(E,⊕{a, b, c, d}) & PLANT(E) &
∀x ≤ ⊕{a, b, c, d}[∃E ′ ≤ E[AGENT(E ′, x) & THEME(E ′, 2RB)]]]
97
The truth conditions correctly capture that each agent has sub-events where two rose
bushes are themes, and these rose bushes may differ from agent to agent. However, there
is nothing in the truth conditions that say what types of sub-events these are other than
who their agents and themes are. Put differently, there is nothing preventing these sub-
events from being non-plantings; each agent’s sub-events may be a trimming, a dropping-
into-a-hole, a covering-with-dirt, and so on. This is unsatisfactory for the binominal
example (3.79), which clearly expresses that each agent was an agent of a planting.
The goal now is to modify the Taylor-Schein approach so that the events appor-
tioned to each individual quantified over are specified to be of certain type: they are
events that satisfy the monadic predicate contributed by the verb. One option is to aban-
don the principle of Variety so that if some events satisfy some predicate V (E), then so
do all E ′ ≤ E, but this move would run into immediate problems with sentences like
the original rose bush example. However, I want to pursue the possibility that Variety is
abandoned when it comes to the sub-events associated with the distributivity operator in
particular.
For the sake of comparison, consider what counts as a “sub-individual” with respect
to distributivity. In a sense, distributivity has to know where to stop, it has to know what
counts as an atom. As far as distributivity goes, what matters are linguistically relevant
atoms, which typically are not atomic by any physical or metaphysical definition. Thus,
when one utters (3.82), we know that if a single dog has more than two fleas, the sentence
is false; even though each dog might be further divided into parts such that each part has
two fleas.
98
(3.82) Each of the dogs has (exactly) two fleas
What makes the distributivity operator know where to stop? It seems obvious that this is
in someway related to the fact that the restrictor contains the item dogs. Since the noun is
dog, each distributes over atomic dogs, regardless of one’s knowledge that dogs are made
up of parts.
This is by no means a new observation, but it is an important one: distributivity
knows where to stop. For the Taylor-Schein approach, both sub-individuals and sub-
events are quantified over in the logical form of the distributivity operator. My suggestion
is that distributivity knows where to stop for sub-events just as it does for sub-individuals.
That is, just as it knows to consider only sub-individuals that are dogs, it also knows to
consider just sub-events that are plantings in the case of (3.79), and thus we avoid the
leakage problem.
There is a tension that needs to be addressed: on the one hand, Kratzer’s original
rose bush example demands that the sub-events associated with each agent are not plant-
ings, while the binomimal each rose bush example demands that these sub-events are
plantings. But the crucial difference is that the binominal examples has a distributivity
operator, and my suggestion is that part of what it means to be a distributivity operator is
to know where to stop for both sub-individuals and sub-events. When sub-events are ref-
erenced elsewhere, such as in the formulation of the Cumulativity Principle from Chapter
2, they are governed by Variety. I claim that at least distributivity is special in that it
quantifies over just homogenous parts of both individuals and events19.
19Distributivity has been claimed to be “special” in other regards as well; see the volume Szabolcsi
(1997) for papers about the unique syntax and scope taking properties of distributive quantifiers.
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Formally, my claim is about the portion of each’s logical form that introduced the
sub-events: ... ∃E ′ ≤ E[...]. The claim is that an event E ′ can be a sub-event of E
which satisfies V (E) iff V (E ′). This is not meant as a general rule whenever the logical
constituent E ′ ≤ E is used in the metalanguage, but a specific rule about how sub-
event referenced by the distributivity operator are restricted. As mentioned previously,
this claim dovetails with the standard assumption that the distribution over individuals
associated with each is also homogeneous. There are some further issues that need to
be addressed which I leave for future work, such as if it is only the verbal predicate that
restricts sub-events, or if modifier predicates do also.20
3.5 Chapter summary
In this chapter I have extended the Taylor-Schein approach to distributivity to give
a a uniform interpretation for each, whether it appears as a determiner or a distance dis-
tributivity item. Unlike determiner uses of each, distance distributivity constructions have
their restrictor argument separated from them in the syntax. I have proposed, following
some classic ideas from the floating quantifier literature, that distance each composes with
a silent restrictor that is covalued with a plural antecedent nominal. I have argued that the
antecedent determines not just the plurality of individuals that is distributively quantified
over, but also that the argument position in which the antecedent resides determines the
thematic role assigned to each.
I have shown how this analysis can be applied to both varieties of distance distribu-
20I think it is obvious that thematic predicates that hold of the main event need not hold of the sub-events,
as evidenced by Schein’s (1993) sentences used to argue for thematic separation (see discussion in Chapter
2 above) as well as the ditransitive sentences discussed in this chapter.
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tivity. This was made possible by Conjunctivist ideas about composition, as the scope
argument to each is a type ⟨v, t⟩ monadic predicate of events. Under the total separa-
tionist approach to argumenthood, both VPs and NPs are type ⟨v, t⟩ predicates, making
both types of nodes suitable scope arguments for distance each. This still leaves room for
syntactic differences among these different varieties of distance distributivity; i.e., why
in some languages floated each can appear in a wider range of positions, and binominal
each can attach locally to more than just numeric noun phrases. The proposals here are
about semantic uniformity, and given the apparent similarities in meaning (and often mor-
phological form, as in English) between these distributive elements, I believe that a single
lexical axiom that applies to all cases is a welcome result.
This analysis was shown to work for a variety of constructions, especially for oc-
currences of binominal each in distransitive sentences; an issue that has received little
attention in previous studies. The main observation there was that the apparent synonymy
of minimal pairs with floating and binominal each can be teased apart when more nom-
inals are involved aside from the antecedent and host. In particular, I built on the well-
known property of indefinites to receive covariance interpretations within the scope of a
distributive operator to show that floating each has a wider scope domain than binominal
each, a difference that is captured within the current framework. I also argued that the
present account is superior to a close neo-Davidsonian alternative given by Champollion
in that it uses the same type for the composition of both floating and binominal each, and
it accounts for the scope differences observed in ditransitive sentences.
The ditransitive cases involving binominal each provide a further argument for total
separation. Like Schein’s (1993) original ditransitive cases, these are scopeless sentences
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that mix distributivity and cumulativity. I have argued that a proper analysis of binominal
each requires that some thematic conjuncts (even THEME conjuncts) have a different event
variable than others, as in the decomposition that Schein argues for.
This was the first step in extending the Taylor-Schein analysis beyond just deter-
miner uses of each. In the next two chapters, I will address reciprocity and plural reflex-
ivity phenomena. As I will show, distributivity is involved in these constructions as well,
and I will argue that they are merely different varieties of distance distributivity to which
the Taylor-Schein analysis can be applied.
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Chapter 4: Reciprocity
4.1 Introduction
In this chapter I present a semantic analysis of reciprocal anaphors such as each
other in English. I build on the results from the previous chapter and suggest that these
anaphors are another sort of distance distributivity construction. For the large majority of
its occurrences, I propose that each other has the same fundamental syntax and semantics
as binominal each in the sense that the distributivity operatorD attaches to a host nominal;
in canonical instances of binominal each the host is a numeric noun phrase, but in the case
of reciprocals, the host contains a morpheme expressing distinctness: other.
It is important to stress from the start that the proposals offered here are for each
other type reciprocals, or perhaps slightly more generally for what I call bipartite argu-
ment reciprocals (henceforth, BARs), so named because they appear to consist of two
morphemes, and they occur in typical argument positions. The analysis is not meant to
apply to other types of reciprocal constructions, such as clitic/affixal reciprocals or recip-
rocals that appear in adverbial positions.
Given the roles that I will attribute to each part of a BAR construction, I will label
the first element the Distributor and the second the Differentiator. Part of the conceptual
motivation for the analysis offered here is that BARs can be decomposed into essentially
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the same meanings that the Distributor and Differentiator have outside of reciprocal con-
structions. In particular, the analysis I give to the Distributor is exactly the same Taylor-
Schein analysis that was offered for distance distributivity constructions in the previous
chapter. One of the conceptual arguments for this analysis is that it supports the univocal
analysis of the distributivity operator D that is argued for throughout this dissertation.
I will show that apart from supporting the parsimonious theory of a univocal each,
the analysis has benefits in explaining two other important properties of reciprocal anaphora.
The first is a major topic in the reciprocal literature: how reciprocal sentences have the
ability to describe situations with varying amounts of reciprocated action; often called
the strength of reciprocity. The second topic has received relatively little attention in the
literature, and that is accounting for the composition of reciprocals in a wide range of
argument positions. While previous accounts have focused primarily on BARs in direct
object position, I will show that the Taylor-Schein approach to distributivity allows for a
unified account of BARs in a much more diverse range of argument positions.
4.2 Issues in the semantics of bipartite argument reciprocals
In this section I will briefly review three closely related issues that I believe are
paramount to our understanding of reciprocal semantics. Any adequate account of the
semantics of BARs should address these issues to some extent. First, I will discuss the
range of meanings available to reciprocal sentences. I then turn to the compositional
status of reciprocal expressions: how they are internally composed (if they are at all)
and how they interact compositionally with the rest of the sentence. The third issue is the
104
syntactic distribution of reciprocal expressions, that is, all the syntactic positions in which
they are licit. The first two have received much attention in the literature1, while the third
has remained relatively unexplored.
4.2.1 The polysemy problem
Perhaps the most discussed aspect of reciprocity in natural language is the fact that
reciprocal sentences can be used to describe situations with varying amounts of recipro-
cated actions. The problem can be demonstrated by considering all the situations that can
make the (4.1) true.
(4.1) The dots are pointing at one another
The issue is often characterized in terms of strength, where stronger types of reciprocity
involve more reciprocated action. The diagram in (4.2) demonstrates the strongest type
of reciprocity, where each dot is both pointing and being pointed at by every other dot.
(4.2)
a
b c
d
However, as remarked upon by practically every paper on the semantics of reciprocity,
weaker situations can make (4.1) true. The table in (4.3) is a recent collection of all the
1I will not review all of the literature that has contributed insight on these issues, but I refer the reader
to Dotlacˇil (2010) for an excellent overview and source of references.
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hypothesized truth conditions available for reciprocal sentences, taken from Beck (2001).
In order to remain theory-neutral in what follows, I will not refer to such formulas as
“truth-conditions”, as this implies that there is a compositional semantics responsible for
deriving each one of these formulas. Nor will I refer to them as “readings” of a sentence,
since this invites comparison with ambiguous sentences that clearly have multiple read-
ings. Instead, I will use the theory-neutral term formal descriptions of verifying situations,
FDVSs for short.
(4.3)
FDVSS FOR RECIPROCAL SENTENCES
1. Strong Reciprocity (SR) ∀x ∈ A[∀y ∈ A[x ̸= y → xRy]]
2. Partitioned Strong Reciprocity (PSR)
There is a partition PART of A such that
∀X ∈ PART[∀x ∈ X [∀y ∈ X [x ̸= y → xRy]]]
3. Intermediate Reciprocity (IR)
∀x ∈ A[∀y ∈ A[∃zi...zn ∈ A[x = zi
& y = zj & ziRzn & ...zn−1Rzn]]]
4. Weak Reciprocity (WR)
∀x ∈ A[∃y ∈ A[x ̸= y → xRy]
& ∀y ∈ A[∃x ∈ A[x ̸= y → xRy]
5. One-way Weak Reciprocity (OWR) ∀x ∈ A[∃y ∈ A[x ̸= y & xRy]]
6. Inclusive Alternative Ordering (IAO) ∀x ∈ A[∃y ∈ A[x ̸= y & (xRy ∨ yRx)]]
Notice that the two weakest FDVSs (5 and 6) in (4.3) are compatible with situations
where no “reciprocating” is involved. Consider the diagram in (4.4), which is arguably
among the weakest type of reciprocal situations that can make (4.1) true; for each dot
pointing, the pointee does not point back at the pointer. Also notice the rightmost dot, the
one that does no pointing at all. Capturing this type of outlier is the hallmark of IAO, the
weakest type of reciprocity, an issue we’ll return to in §4.5.
(4.4)
IAO
a b c d
An interesting property of the FDVSs available to reciprocal sentences is that the
logical forms often used to describe them exhibit a certain entailment relation. This was
106
first noticed by Langendoen (1978), though he was only working with a subset of the
FDVSs shown in (4.3). Below is a diagram showing the entailment relations for the more
recent list of FDVSs in (4.3).
(4.5)
SR
IR
WR
PSR
OWR IAO
Langendoen put forth a semantic theory for reciprocal sentences that was built
around these entailment facts. He suggested that we could uniformly associate recip-
rocal sentences with a certain weak type of reciprocity, since any situation that validates
the conditions imposed by a stronger type of reciprocity can also validate the conditions
imposed by any type that is weaker than it2 (abstracting away from things like the exis-
tence of partitions and sequences used in (4.3)). For example, we can see that the diagram
in (4.2), even though it exemplifies SR, validates the weaker conditions ofWR, OWR, and
IAO.
Underspecification approaches like Langendoen’s were called into question in the
influential work of Dalrymple et al. (1998). They point out that such approaches predict
a sentence like (4.6) to be true in situations where there is less than full mutual acquain-
tance; as in a possible situation where Groucho and Harpo know each other, and Chico
and Zeppo know each other, but that’s all the knowing involved, as if each pair were al-
ways separated from the other. However, (4.6) sounds infelicitous when used to describe
2The account developed in Sternefeld (1998) employs a similar methodology.
107
such a situation. As pointed out by Fiengo and Lasnik (1973), reciprocal sentences with
stative verbs seem to allow only a strong interpretation, but underspecification approaches
to reciprocity leave us without an explanation for why this might be so.
(4.6) The Marx Brothers know each other
It was concerns like this that lead Dalrymple et al. to propose their Strongest Meaning
Hypothesis, an influential method for deriving meanings for reciprocal sentences3.
However, I believe that such objections to underspecification analyses of reciprocity
are misguided since the strength imposed by stative verbs can be shown to exist outside
of reciprocal constructions. This is shown in (4.7), a sentence that seemingly lacks a
cumulative reading (one where John and Mark know each other, and Mary and Sue know
each other, and no other knowing relations exist).
(4.7) John and Mary know Mark and Sue
Like the reciprocal sentence (4.6), this sentence requires a situation of full mutual ac-
quaintance in order be true4.
Notice also that both types of constructions equally allow for outlier effects when
large pluralities are involved, showing that the stative strength restriction is just a prefer-
ence, and not a hard-and-fast semantic rule. Both sentences ((4.8) and (4.9)) can be used
to talk about how members from the Jets know members from the Sharks and vice versa,
3The Strongest Meaning Hypothesis is a mechanism for deriving meaning that factors in non-linguistic
information supplied by the context, as well as encyclopedic knowledge of the denoted verbal relation,
and then provides for the sentence the logically strongest reciprocal interpretation that respects these non-
linguistic facts and particular lexical idiosyncrasies involved. The mere fact that the Strongest Meaning
Hypothesis is dependent on non-linguistic information shows that it computes "extra-semantic" meaning.
If we are interested in just the compositional semantics of reciprocal sentences, that is, the interpretation of
phrase markers by general semantic principles, the Strongest Meaning Hypothesis gives us too much. See
§4.5 for more on the difference between “reciprocal meaning” and “reciprocal semantics”.
4I thank AlexanderWilliams (p.c.) for bringing to my attention the fact that replacing know in (4.7) with
resemble, which is another stative verb, seems to facilitate weaker interpretations.
(i) John and Mary resemble Mark and Sue (respectively)
This is not a problem for my account, but again shows that the strength previously observed with stative
verbs is not a firm rule.
108
and both sound felicitous even if there are a few Jets that don’t know every single Shark
and vice versa.
(4.8) The Jets know the Sharks
(4.9) The members of the two gangs know each other
Facts like this show that the strength imposed by stative verbs does not hold of re-
ciprocal sentences in particular, but of sentences involving plural arguments in general.
Furthermore, the strength requirement is not absolute: sentences reporting on large plural-
ities allow for some outlier individuals. Thus, a semantic theory of reciprocal expressions
should not need to make special concessions to account for these strength phenomena.
And if this is so, then perhaps Langendoen’s methodology of a general weak interpreta-
tion strategy for reciprocal expressions can be revived.
The analysis developed in this paper will utilize such an underspecification ap-
proach, and we will see in 4.4 that the proposed interpretation is analogous to the fifth
FDVS in (4.3), One-way Weak Reciprocity. I say analogous because the logical forms
offered later in the paper are given in a language that differs from what we see in (4.3),
in that they make use of higher-order quantification over both individuals and events, and
verbs are treated as monadic predicates of events rather than relations, related to their “ar-
guments” indirectly through thematic predicates. The choice of a meaning comparable
to OWR is not arbitrary, but as I will show it follows from applying the Taylor-Schein
analysis of distributivity to a reasonable syntactic decomposition of BARs. I will also ad-
dress in §4.5 why a Langendoen-type underspecification analysis should not go too weak
to have IAO as the underlying meaning of reciprocals.
4.2.2 The composition problem
I now turn to previous treatments about the composition of BARs. I will limit the
discussion here to the following competing hypotheses. This first hypothesis is that BARs
109
are non-decomposable primitives, and the second is that BARs are complex structures
whose parts compose in a way that yields a reciprocal meaning. I will address these
hypothesis in turn, and for each I will discuss some of the issues that are at stake and also
give a brief overview of what has been said in the literature about them.
4.2.2.1 Primitive polyadic quantification
I will start with what is probably the less intuitive of the two approaches, the one that
says that BARs are primitive elements. I say less intuitive because on superficial inspec-
tion of these expressions, it appears that there are two morphemes involved. But what
these approaches lack with regard to accounting for the apparent morphemes involved,
they usually make up for in their power to handle the polysemy problem. This power
comes from treating the BAR as a polyadic quantifier, as done in Dalrymple et al. (1998),
Peters and Westerståhl (2005), Sabato and Winter (2005), and Dotlacˇil (2010) among oth-
ers.
A polyadic quantifier is a type of relation quantifier. To illustrate, let us first con-
sider some familiar relation quantifiers, quantificational determiners. It is standard to
treat determiners as higher-order relations that relate the sets denoted by the restrictor and
nuclear scope, as shown in (4.10).
(4.10)
SCOPE
⟨e, t⟩
QUANTIFICATIONAL
DETERMINER
⟨⟨e, t⟩, ⟨⟨e, t⟩, t⟩⟩
RESTRICTOR
⟨e, t⟩
We may classify such relations, as is done in modern Generalized Quantifier Theory (see
Peters and Westerståhl (2005)), as “monadic quantifiers”, since the arguments for the
higher-order relation are one-place predicates. A polyadic quantifier then is a higher-
order relation that has at least one argument that is a polyadic predicate. In the case of
110
reciprocals, we can analyze them as polyadic quantifiers whose polyadic argument is the
relation denoted by the verb5. These accounts take the other argument of the polyadic
quantifier to be the plurality denoted by the reciprocal’s antecedent; since nothing in the
present discussion hinges on how the antecedent is treated, I will simply assume here that
a reciprocal’s antecedent denotes a plural individual, which I notate as ePL.
(4.11)
ANTECEDENT
ePL VERB
⟨e, ⟨e, t⟩⟩
RECIPROCAL
⟨⟨e, ⟨e, t⟩⟩, ePL⟩
Viewing reciprocals as functions that take relations and plural entities as arguments allows
us to make reference to these arguments in the body of the function. Thus, tracking the
range of polysemy becomes a relatively straightforward task: we can simply copy the
conditions stated in (4.3) into the body of function associated with the reciprocal. One
way of doing this is to do essentially what Dalrymple et al. (1998) do: treat reciprocals as
ambiguous between certain functions, each of which has as its body something similar to
one of the conditions in (4.3). Another option explored by authors like Dotlacˇil (2010) is
to posit a single interpretation of BARs, though still making reference to these arguments
in the body of the function associated with the BAR.
While polyadic quantifier analyses allow us to easily track polysemy, this comes
at a price. Below, I will discuss two conceptual problems that these types of approaches
face, and one empirical problem. The first of the conceptual problems was already men-
tioned: treating BARs as primitive leaves us without an explanation for why BARs ap-
pear to consist of two morphemes. This is even more troubling when we consider the
morphemes involved. As we will see soon, BARs cross-linguistically are generally made
up of the same morphemes, and the apparent morphemes involved look suspiciously like
5Szabolcsi (1989), working in a CCG framework, was the first to use a version of polyadic quantification
to explain the semantics of anaphors, in particular the semantics of reflexives. Under this view, we can think
of reflexives under her view as binary functions that map a relation and an individual to a truth value as
follows: !REFLEXIVE" = λRλx.Rxx.
111
morphemes that might play a role in deriving a reciprocal meaning. It is striking that we
never find BARs like two another, few other, or coffee cup, but under a polyadic quantifier
approach, it is unclear why these could not be possible reciprocal expressions.
The second conceptual problem concerns the semantic type of BARs under a polyadic
quantifier approach. Although the standard recursively defined typology allows for end-
lessly many possible types (see (2.16) in Chapter 2), it is undeniable that natural language
only uses a small handful of these. We should be wary about including expressions that
have types that are not well established, especially when these types are posited to account
for just a very small number of phenomena (i.e., just reflexives and reciprocals). If the se-
mantic type of polyadic quantifiers that was mentioned previously is a possible semantic
type in natural language, we should wonder why the only flavors of polyadic quantifica-
tion are reflexivity and reciprocity. I believe that making the decision to include these in
our typology should only be done if there are no satisfactory parsimonious explanations
of the phenomena.
The big empirical problem for polyadic approaches to BARs is easy to see, yet
not so easy for these approaches to recover from. The approach only works if there is a
polyadic predicate around for the BAR to compose with. However, BARs can appear in
places where it is far from obvious how they could possibly be in the correct configuration
with the verb in order to meet the compositional demands of (4.11).
(4.12) The newlyweds met each other’s parents
(4.13) The professors read papers about each other
To the best of my knowledge, there are no attempts in the literature to make a polyadic
quantifier analysis work with DP-internal BARs. This is not to say that polyadic quan-
tifiers cannot be defined for these occurrences of BARs, but it does so at the cost of
positing massive ambiguity and/or type-shifting principles; and these principles have to
be constrained in such a way as not to overgenerate (i.e., predicting reciprocal-antecedent
112
relations in illicit configurations). In sum, not only is the polyadic quantifier type ques-
tionable to begin with, it cannot even handle the full range of facts. See Büring (2005)
for discussion of this problem; and for a more comprehensive taxonomy of the argument
positions in which BARs can appear, see §4.2.3.
These issues should make semanticists skeptical of such analyses. We will see in
§4.3 more reasons that the primitive approach is empirically unjustified. Even though
this analysis can handle the range of the FDVSs (though only when reciprocals appear in
certain positions), I believe it is ultimately a flawed approach and cannot be the correct
analysis of BARs. In the next section we will address some issues in the literature that
have been brought up by those wanting to uphold the idea that BARs are complex and
that these expressions, somehow, consist of the morphemes that are apparently involved.
Although, we will see that these accounts have their shortcomings too.
4.2.2.2 Compositional complexity
The advocates of complexity6 developed theories that make use of the apparent
morphemes involved in BARs. Instead of reviewing all of the different takes on com-
plexity offered throughout the years, I will discuss two classic accounts that are related to
each other, and the present approach, in interesting ways.
Perhaps the earliest investigation into the composition of BARs is the work of
Dougherty (1970). Dougherty believed that the reciprocal each other was related to float-
ing quantifier constructions that keep everything else (virtually) the same but differ with
respect to the position of each. For him, the reciprocal sentence with each other (4.18)
fills in the paradigm consisting of some seemingly closely related sentences.
(4.14) Each of the men will speak to the others
(4.15) The men each will speak to the others
6Among them are: Dougherty (1970), Heim et al. (1991b), Roberts (1991), and Sauerland (1998).
113
(4.16) The men will each speak to the others
(4.17) The men will speak, each to the others
(4.18) The men will speak to each other
For Dougherty, (4.14) represents the deep structure from which all the sentences in (4.15)
through (4.18) are derived7. This account, as far as I can tell, is the closest analog to the
syntactic proposals that will be developed in this chapter. Though his approach and mine
differ in several respects, we both share the idea that the Distributor is best treated as a
type of distance distributivity item.
Fiengo and Lasnik (1973) raised some objections to Dougherty’s analysis. Al-
though they offer several arguments (p. 465-467) against the floating quantifier analysis,
the most convincing in my opinion is that the canonical floating quantifier sentences dis-
allow the floating quantifier’s associate to be a quantificational noun phrase, as shown in
(4.19) and (4.20). On the other hand, the sentences involving BARs ((4.21) and (4.22))
allow for quantificational antecedents8.
(4.19) *Most boys each will speak to the others
(4.20) *Most boys will each speak to the others
(4.21) ?Most boys will speak each to the others
(4.22) Most boys will speak to each other
An approach like Dougherty’s that treats the floated quantifier as a determiner that has
somehow been dislocated from its associate noun phrase faces serious problems if another
7Dougherty actually derives the sentences in (4.15) through (4.18) with two transformations: first, Quan-
tifier Postposition derives (4.15) from (4.14), and then all the others are derived from the result of this by
the transformationQuantifier Movement. See Dougherty (1970), Fiengo and Lasnik (1973), and Dougherty
(1974) for the details of these transformations.
8Several native speakers of English have informed me that sentences such as Most of the men each
bought a book are acceptable. If this is so, then perhaps the problem is not as severe as previously assumed,
thus deepening the syntactic similarities of reciprocal and floating quantifier constructions.
114
determiner is present, assuming that such determiners occupy the same position (e.g.,
D0). See Chapter 3 for alternative views on the syntax of floating quantifiers that could
reconcile these facts.
Heim et al. (1991b) develop an account that is a sort of inverse of Dougherty’s.
Dougherty takes the Distributor to be a floated quantifier, starting its derivational life in
close syntactic proximity to its antecedent, whence it undergoes a lowering transforma-
tion. Heim et al. claim that the Distributor starts in the same noun phrase as the Differen-
tiator, and then covertly raises. For them, the LFs for reciprocal sentences are as in (4.23)
(taken from Heim et al. (1991b), p.66 example (7)).
(4.23) The men saw each other⇒ [S [NP [NP the men]1 each2][V P saw [NP e2 other]3]]
The view that each starts in a different noun phrase as the reciprocal’s antecedent can
account for the fact that BARs allow for quantificational antecedents, thus avoiding the
problem that Dougherty faced.
Both Dougherty and Heim et al.’s accounts attempt to derive reciprocal meanings
from the composition of the apparent morphemes involved in BARs; however, they suffer
from various difficulties that have been noted in the literature9. One germane problem that
both of the complexity analyses face is that they do poorly in accounting for the polysemy
problem. For instance, the semantics given in Heim et al., which involves a high-scoping
each, works only for situations of Strong Reciprocity; see discussion of this issue in Beck
(2001), p. 70-72. I present further problematic issues with Heim et al.’s scopal account in
Chapter 6.
It seems that each of the two approaches discussed in this section succeeds in one
respect, but fails in the other. The primitive polyadic approaches can account for the
range of polysemy discussed above with the power of polyadic quantification, but they
do so without incorporating the morphemes that apparently constitute BARs. On the
9As mentioned before, problems for Dougherty can be found in Fiengo and Lasnik (1973). Williams
(1991) gives a reply to Heim et al. (1991b), and in Heim et al. (1991a), they acknowledge that the issues
raised by Williams present major problems for their original analysis.
115
other hand, the complexity approaches try to uphold morpheme univocality (i.e., each
and other always mean the same thing, even when composed as a reciprocal anaphor),
though doing so has often limited their potential to account for the polysemy problem. I
believe that these limitations are a result of assuming a semantics that lacks the tools of
the neo-Davidsonian. In the sections to come, we will see that with these tools in place, a
complexity analysis is possible; one that treats the elements involved in a straightforward
way, which is in several respects empirically superior to previous analyses from both
camps that were discussed in this section.
4.2.3 The syntactic distribution of BARs
The last issue that I think a proper account of reciprocal semantics should address is
the range of syntactic distribution of BARs. Many previous studies have focused only on
sentences where the reciprocal is the direct object in transitive constructions, what Lan-
gendoen (1978) called elementary reciprocal sentences. A notable exception is Dotlacˇil
(2010), where an analysis is presented that can handle ditransitive reciprocal construc-
tions, but only double-object constructions where the reciprocal is the indirect object;
that is, where it is string adjacent to the verb. The account developed in this thesis will
work with a larger range of constructions, which I present below.
BARs can appear in virtually any argument position, so long as they are close
enough to an antecedent to satisfy the locality and c-command demands of a binding
condition like Condition A (Chomsky (1981)). For example, they can appear as indirect
objects, in both double object and prepositional dative constructions. Notice the ambigu-
ity in (4.24); this will be addressed and accounted for later in the chapter.
(4.24) The gnomes put hats on one another
(4.25) The gnomes gave each other hats
As mentioned earlier, BARs can also appear inside of noun phrases. They can
116
appear in possessor position (4.26), where the antecedent is outside of the noun phrase.
(4.26) They reviewed each other’s papers
They can also appear as complements to nouns. In some cases, their antecedent is noun
phrase internal (4.27); where in other cases, their antecedent is outside of the noun phrase
(4.28).
(4.27) I read the employees’s reports about each other
(4.28) The artists painted pictures of one another
We have seen that polyadic quantifier approaches are limited in only being able to
account for a small range of the syntactic distribution of BARs. I believe that Dotlacˇil’s
(2010) analysis is the most descriptively adequate so far, though it can only work when
the reciprocal is string adjacent to the verb (i.e., reciprocals as direct objects or as indirect
objects in double-object constructions). The reason for this is that Dotlacˇil relies on a
polyadic analysis of each other, albeit an event alternative to the more familiar polyadic
analyses, thus requiring the anaphor to be close enough to its verbal argument to compose
with it via Function Application.
The analysis developed here will capture a broader range of the syntactic distribu-
tion, as well as account for several nuances in meaning that appear in more constructions
that are more complicated than elementary reciprocal sentences. For instance, the am-
biguity mentioned above with prepositional dative constructions where the reciprocal is
the indirect object. Another issue that will be addressed with regards to ditransitive con-
structions is an interesting contrast mentioned by Williams (1991). He noticed that the
reciprocal sentence (4.29a) is compatible with real-world situations, but the minimally
dissimilar non-reciprocal sentence (4.29b) is not (the # indicates that the sentence can
only be used to describe a bizarre real-world situation, abstracting away from cases where
patients have had multiple nose jobs.)
117
(4.29) a. The doctors gave each other new noses
b. #The doctors gave each patient new noses
I will show that this paradigm represents essentially the same contrast observed between
floating and binominal each in the previous chapter.
We will see that the approach developed here fares quite well at handling the poly-
semy problem, and does so without positing any ambiguity, while also being compatible
with BARs occurring in any of their licit syntactic positions. This will be accomplished
by treating the BAR as compositionally complex, and consisting of essentially the same
each and other that we see outside of reciprocal constructions, and the each here is given
the same interpretation as in distance distributivity constructions. Before pursuing this
line of thought, we will first consider some data from various languages that pose seri-
ous problems to any approach that claims that the reciprocal is a primitive element, thus
providing further support for internal compositional complexity in BARs.
4.3 Decomposing bipartite reciprocals
In this section I will give an overview of some explananda that call for a complex
treatment of BARs. We will first look at three phenomena that bear on this issue: article
distribution, preposition placement, and case distribution. While each phenomenon by
itself might not be enough to convince one of complexity, I think that taken together they
are more than suggestive. After arguing for complexity, we will examine some of the
consequences of treating BARs as being composed of morphemes that can exist outside of
reciprocal constructions. To this end, we will look at the behavior of each, one and other
as cross-sentential anaphors. The issues raised throughout this section point to a certain
type of syntactic treatment of the elements involved. In the following section, we will
evaluate this suggested treatment with the proposals about Taylor-Schein distributivity
given in previous chapters.
118
4.3.1 Article distribution
Certain languages allow article morphemes to surface within the BAR. These in-
clude Spanish (4.30), French (4.31), Romanian (4.32), and Bulgarian (4.33)10.
(4.30) Los
the
estudiantes
students
se
CL
seguian
follow
los
the
unos
ones
tras
behind
los
the
otros
others
‘The students are following one another’
(4.31) Les
the
étudiants
students
se
CL
sont
AUX
frappé
hit
les
the
uns
ones
les
the
autres
others
‘The students hit one another’
(4.32) Baˇie?ii
Boys.DEF
s
CL
au
have
urmaˇrit
followed
unul
one.DEF
pe
ACC
celaˇlalt
other.DEF
‘The boys followed one another’
(4.33) Gostite
guests.DEF
tancuvaha
danced
edin-ija
one.DEF
s
with
drug-ija
other.DEF
‘The guests danced with one another’
Notice that when articles do surface, it is possible to have two articles within the BAR.
While some languages allow two article morphemes per DP, such as the Scandinavian
double definiteness languages like Norwegian (4.34), Swedish (4.35), and Faroese (4.36)
(data from Julien (2005)), the languages mentioned above do not allow this. Thus, we
can take the occurrence of two articles in BARs as evidence that the BAR consists of two
separate nominal expressions.
(4.34) dei
DEF.PL
to
two
gul-e
yellow-W
skjort-e-ne
skirt-PL-DEF
‘the two yellow shirts’
10It should be noted that several Romance and Slavic language have an anaphoric clitic, se, which allows
for a reciprocal reading even without a BAR present. However, this clitic is not limited to reciprocal
readings; it can also be used to express reflexivity and in impersonal/middle constructions, though when the
BAR is present, only the reciprocal interpretation is available.
119
(4.35) det
DEF.N.SG
gul-a
yellow-W
hus-et
house-DEF.N.SG
‘the yellow house’
(4.36) tann
DEF.M.SG.NOM
svart-i
black-W.M.SG.NOM
kettlingur-in
kitten-DEF.M.SG.NOM
‘the black kitten’
The crux of this argument is that two articles can appear within BARs. However, it
remains unclear what meaning difference, if any, is associated with definite or indefinite
marked reciprocals. I leave this as an issue for future research.
4.3.2 Preposition placement
Next we will consider the placement of prepositions that interact with BARs. Al-
though Germanic BARs are usually the ones addressed in the literature, we can see that
the placement of prepositions in these languages seems to be an exception to the general
pattern we find across Indo-European languages. In Germanic languages, prepositions
generally precede the BAR complex, with both one another- and each other-type recip-
rocals, as shown below in English (4.37) and German (4.38).
(4.37) The students danced with one another
(4.38) Sie
they
erzählten
talk
voneinander
about-one-another
‘They talk about one another’
However, in most11 of the non-Germanic Indo-European languages where BARs are pro-
ductive, the preposition always intervenes between the Distributor and Differentiator. I
show this below for French (4.39), Spanish (4.40), Romanian (4.41), Bulgarian (4.42),
Serbo-Croatian (4.43), and Ukrainian (4.44).
11Hindi has postpositions that follow the entire BAR complex.
120
(4.39) Les
the
étudiants
students
se
CL
sont
AUX
donné
gave
des
some
livres
books
les
the
uns
ones
aux
to-the
autres
others
‘The students gave books to one another’
(4.40) Los
the
estudiantes
students
presentaron
introduced
los
the
profesores
professors
el
the
uno
one
al
to-the
otro
other
‘The students introduced the professors to one another’
(4.41) Oaspe?ii
guests.the
au
have
dansat
danced
unul
one.the.NOM
cu
with
cel?lalt
other.the.ACC
‘The guests danced with one another’
(4.42) Te
they
stojat
stand
edin
one
do
beside
drug
other
‘They are standing beside one another’
(4.43) Gosti
guests
su
AUX
plesali
danced
jedni
one
s
with
drugima
other
‘The guests danced with one another’
(4.44) Divcˇata
girls
hovoryly
talk
odna
one.NOM
pro
about
odnu
one.ACC
‘The girls are talking about one another’
If the BAR were a primitive expression, as polyadic quantifier analyses suggest, it
should come as a surprise that it is possible to break it up with prepositions, though we
find this to be pervasive in the Indo-European languages that have BARs. Although the
data mentioned in this regard above have only shown the position of prepositions in one-
another-type reciprocals, we have seen in Dougherty’s paradigm (4.2.2.2) that English
allows the each of each-other-type reciprocals to precede a preposition. Admittedly, this
type of construction varies in its acceptability among speakers, but given that it is possible
in just some cases is enough to make the point.12
12Paul Pietroski (p.c.) has brought to my attention that (4.45) has a stronger interpretation than its coun-
terpart with each other:
i. The men will talk to each other
121
(4.45) ?The men will talk each to the others
I will treat all these cases, whether the preposition is within or outside the BAR
complex, as having the same semantics. This again will lead back to the discussion of the
two approaches to thematic role interpretation from Chapter 2: the preposition approach
and the Theta Rule approach. I take up this issue in the next section. What is important
now is that analyses that take BARs to be primitive elements have no way of accounting
for the appearance of prepositions within the BAR.
4.3.3 Case distribution
The last empirical problem for primitive accounts of BARs that I will discuss con-
cerns case morphology within BARs. Languages with BARs vary with regard to the
amount of case morphology expressed on each element of the BAR. Some languages,
like English, show no case morphology at all. Some languages, like Russian (4.46) and
Hindi (4.47), have only the Differentiator inflecting for case, while the Distributor remains
in a fixed form.
(4.46) Oni
they
udarali
hit
drug
other
druga
other.ACC
‘They hit one another’
(4.47) Unho-NE
they.ERG
ek
one
dusre-ko
second.OBL-P
dekhaa
saw
‘They saw one another’
There are also languages that have both the Distributor and Differentiator inflecting for
case. Languages of this last type present a source of deep insight into the inner workings
of BARs.
I suspect that this difference in strength has to do with the combination of the definite article and the plural
morphology on others in (4.45) that is absent from (i). In the former, it is required that each talk to the
totality of the plurality denoted by the others; while for the latter it seems to suffice that each man talked to
at least one other of the men. Furthermore, (4.45) does not have to be necessarily interpreted as a reciprocal
sentence; the others could refer to some previously mentioned plurality in the discourse that need not be
men. This contrasts with (i), which can only have the reciprocal interpretation.
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We see the double-case property in some Slavic languages, like Ukrainian and
Serbo-Croatian. Interestingly, in these languages, the case of the Distributor and that
of the Differentiator are generally different13. This can be seen in Serbo-Croatian (4.48)
and Ukrainian (4.49) below.
(4.48) Studenti
students.NOM
su
AUX
udarali
hit
jedan
one.NOM
drugog
other.ACC
‘The students hit one another’
(4.49) Studenty
students.NOM
vdaryly
hit
odyn
one.NOM
odnoho
one.ACC
‘The students hit one another’
Considering just these elementary reciprocal sentences, it seems that the case of
the Distributor must be nominative and the case of the Differentiator must be accusative.
However, when we look beyond these simple cases, we see that a deeper generalization
emerges. Below are ditransitive constructions in Serbo-Croatian ((4.50a), (4.51a)) and
Ukrainian ((4.50b), (4.51b)) where the BAR is an indirect object. In (4.50), the inter-
pretation is one where the students introduced the professors to others students (among
the students), where in (4.51) the interpretation is one where the students introduced the
professors to other professors (among the professors).
(4.50) a. Serbo-Croatian
Studenti
students.NOM
su
AUX
predstavili
introduced
profesore
professors.ACC
jedni
one.NOM
drugima
other.DAT
‘The students introduced the professors to one another’
b. Ukrainian
Studenty
students.NOM
predstavyly
introduced
profesoriv
professors.ACC
odni
one.NOM
odnym
one.DAT
‘The students introduced the professors to one another’
13I am aware of one exception where the case on each element is the same, and this is when the reciprocal
antecedent is nominative, thus making the Distributor nominative (which will be explained shortly), and a
certain preposition is used that also happens to assign nominative. So the case of the Distributor and
Differentiator are generally the same, except where there is a preposition involved that happens to assign
the same case to its complement as the case of the reciprocal antecedent.
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(4.51) a. Serbo-Croatian
Studenti
students.NOM
su
AUX
predstavili
introduced
profesore
professor.ACC
jedne
one.ACC
drugima
other.DAT
‘The students introduced the professors to one another’
b. Ukrainian
Studenty
students.NOM
predstavyly
introduced
profesoriv
professors.ACC
odnyx
one.ACC
odnym
one.DAT
‘The students introduced the professors to one another’
The English sentences that comprise the translations for (4.50) and (4.51) are ambiguous.
Serbo-Croatian and Ukrainian have no such ambiguity because of the case morphology
within the BAR. Based on the meaning differences between the two pairs of sentences,
in (4.50), it is the subject that appears to act as the antecedent for the BAR, while in
(4.51) it appears that the direct object is the antecedent. This semantic fact is reflected
by the case morphology of the BAR. In (4.50), where the subject acts as the reciprocal’s
antecedent, the case of the Distributor is nominative, the case typical of subjects. In
(4.51), where the direct object is the antecedent, the case of the Distributor is accusative,
the case typically associated with direct objects. In both (4.50) and (4.51), the case of
the Differentiator does not vary. Thus, the proper descriptive generalization of these case
facts in these languages seems to be that (i) the case of the Distributor will always match
the case of the BAR’s antecedent, and (ii) the case of the Differentiator will always be
the case the we would expect based on the position of the BAR. In (4.48) and (4.49),
since the BAR is in direct object position, so the case of the Differentiator is accusative.
In both (4.50) and (4.51), the BAR appears in indirect object position, thus the case of
the Differentiator is dative, the case typical of indirect objects. These facts again show
that BARs consist of what looks like two DPs. A primitive analysis cannot account for
productive case morphology on the parts of the BARs since for these approaches, BARs
do not have parts. We will return to these cases of multiple potential antecedents and the
different meanings involved, as well as the importance of the Slavic case facts, in later
sections.
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The facts that we have seen so far in this section show, at the very minimum, that
there are some languages that have BARs that simply cannot be analyzed as primitive
expressions. Of course, one could argue that the BARs in languages like English can
still be analyzed as polyadic quantifiers since they lack (for the most part) intervening
prepositions, BAR-internal articles, and case inflection within BARs. But to do so would
require saying that one another in English and its equivalent in Serbo-Croatian are totally
different syntactic/semantic entities, that just happen to look alike and have the same
meaning. If a suitable theory for complex BARs can be developed that can account for the
polysemy problem just as well as the primitive approaches, then I’m inclined to generalize
the results of this section to all BARs in the Indo-European languages and say that they
are all complex expressions with the same interpretation, rather than adopt the mixed
approach.
4.3.4 Cross-sentential anaphora
In the introduction, I said that we should not only view BARs as being complex, but
also that we should view them as being composed from essentially the same each, one,
other, etc. that we find outside of BAR constructions. In this section I will discuss the
relevant properties of these elements as they appear in cases of cross-sentential anaphora.
I will not address here when elements like one take on a distributive character, as I am
claiming that they always do in BAR constructions (an issue we will return to in §4.4).
Instead, we will focus here on the relevant anaphoric properties of the morphemes that
comprise BARs when they appear outside of BAR constructions.
Consider first the use of other as a cross-sentential anaphor. We can see from sen-
tences like (4.52) that it is impossible for (an)other to refer to the individuals denoted by
its antecedent. Rather, it must refer to something other than what its antecedent refers to,
and other than the parts that comprise what its antecedent refers to.
(4.52) Three boys wore hats. Another wore a sweater.
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Unlike other, elements like one and each(one) do have the ability to refer to an individual
that is part of the plurality picked out by the antecedent. As we can see below, the sen-
tences in (4.53) can have the same meaning as their counterparts in (4.54) that have an
explicit partitive pronoun that is coreferential with the antecedent.
(4.53) a. Three boys wore hats. One (also) wore a sweater.
b. Three boys wore hats. Each (also) wore a sweater.
(4.54) a. [Three boys]i wore hats. One of themi (also) wore a sweater.
b. [Three boys]i wore hats. Each of themi (also) wore a sweater.
Unlike each, the partitive construal of one as a cross-sentential anaphor seems to be
optional, as we see that the one in (4.55) is able to refer to some boy that is different from
the three mentioned in the previous sentence.
(4.55) Three boys walked in. One walked out.
What is important for us is that these elements can, on some occasions, be used as a sort
of partitive anaphor, referring to a part of what its antecedent refers to, in sharp contrast
with cross-sentential other.
When one is used partitively, it can act as an antecedent for other so that otherness
can be determined with regards to something within a plurality, a referential option that is
not available in (4.52). We can see this at work in (4.56), where other is linked indirectly
to three boys by having one as its antecedent, and then one acts as a partitive anaphor
directly anteceded by three boys.
(4.56) Three boys wore hats. One wore a sweater. Another wore a scarf.
I believe that the anaphoric chain that we see in (4.56) is also at work in BARs; the
Differentiator in BARs inherits the Distributor’s partitivity, and as a result otherness is
determined by what the Distributor picks out. (4.57) shows a schematic representation of
the structure of BARs under this approach.
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(4.57) [S ...Antecedenti ... [DP ...each one of themi ... ]k ... [DP ...other than thatk ...
]... ]
This representation encodes that other is dependent on the partitive anaphor for determin-
ing its reference. If other were directly anteceded by the canonical reciprocal antecedent,
represented as Antecedenti in (4.57), then distinctness should be determined in a man-
ner parallel to what we see in (4.52). This is clearly not the case with BARs. As such,
if we chose to view BARs as complex entities that are composed from the same each,
one, other, etc. that are found outside of reciprocal constructions, and the Distributor and
the Differentiator are separate expressions, then the linking in (4.57) is the only possible
linking available given what sentences with BARs mean. This specific view of referential
dependency will be an important part of the analysis, and we will return to it again at
several points in the remaining sections.
In this section we examined several phenomena that suggest a complex decom-
position of BARs. We have also begun to see what a proper syntactic treatment of the
Distributor and Differentiator should look like. For one, the case facts seem to suggest
that two nominal expressions are involved, since each of these elements generally have
different cases. The distribution of articles provides further evidence that two nominals
are present. This idea is also reenforced by the anaphora data: since we know that BAR
constructions involve distinctness that is determined with regard to parts of what its an-
tecedent refers to, then the Differentiator should be linked somehow to some proper part
of the antecedent and not directly to the whole plurality denoted by the canonical recipro-
cal antecedent. The Distributor can serve this purpose. In the next section, I will elucidate
the syntactic and semantic details of this type of approach to the complexity problem.
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4.4 Reciprocals as distance distributivity phenomena
In this section I will extend the Taylor-Schein approach to BARs. The basic idea,
apart from some minor qualifications, is that the each of each other is just like binominal
each with the exception that it does not attach to a numeric host, but a Differentiator host:
an other-NP. This means that the restrictor argument of each is the canonical reciprocal
antecedent, and the scope argument of each is the Differentiator.
(4.58)
Θ
each XANT
DP
other
Below I will discuss what is needed for this account to be applied to elementary
reciprocal sentences. I first discuss the semantics of the Differentiator host; in particular,
how the distinctness inherent to other is determined by the Distributor, and how the Dif-
ferentiator requires a partitive argument to restrict its values to members of the antecedent
plurality. I then turn to how the analysis can be extended to BARs apart from the each
other variety, with discussion about how the cross-linguistic range of preposition place-
ment from §4.3.2 fits with the different ways of implementing thematic separation, and
also how the proposed analysis gains support from the case facts from §4.3.3.
4.4.1 The semantics of the Differentiator host
As discussed in §4.3.4, the semantics of other requires an antecedent nominal that
distinctness can be determined with regards to. Based on considerations from cross-
sentential anaphora, this nominal cannot be the canonical antecedent to the reciprocal,
since then the value of other must be distinct from all the parts which comprise the an-
tecedent’s semantic value. This cannot be the case with reciprocal sentences, since they
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report that individuals within the antecedent plurality performed actions on other mem-
bers of the same plurality. It was suggested from considering the anaphoric properties of
(4.56) that the antecedent to other covaries with the Distributor.
The Taylor-Schein analysis offers a straightforward way to implement this idea.
As outlined in (4.57), the antecedent of the Differentiator is the Distributor. Following
the proposal that the Distributor is interpreted in the Taylor-Schein fashion, the logical
form a reciprocal sentence will involve apportionment of sub-events to each individual
thematic participant x of the antecedent plurality. Distinctness is then determined for each
x within its appropriate sub-events. This is achieved by the following proposals since the
Differentiator is within the scope of each. I give a first-pass of the truth conditions for
(4.59) below as (4.60).
(4.59) The students saw each other
(4.60) ∃E[AGENT(E,⊕STUDENT) & SEE(E) & ∀x ≤ ⊕STUDENT[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y [OTHER(Y, x) & THEME(E ′, Y )]]]]
I treat the Differentiator as an indefinite noun phrase with existential force, comparable
to an other/some others; though see §4.5 for possible reasons for treating it as definite
instead. I remain uncommitted as to whether other is an adjective or a noun in BARs; but
I treat it as a special open class lexical category by associating it with the dyadic predicate
OTHER(X, Y ). This is to make explicit which value(s) the value of the Differentiator is
distinct from. I give the following definition for the predicate OTHER(X, Y ).
(4.61) OTHER(X, Y ) =df ¬∃Y ′[Y ′ ≤ Y & Y ′ ≤ X ]
This definition says that for OTHER(X, Y ) to be true then neither Y nor any part of Y can
be an improper part (i.e., part of or equal to) of X .
In the case of reciprocals, the proposal is that the semantic value of the Differentia-
tor covaries with the Distributor; for the case of (4.59), each student x is associated with
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its own sub-events E ′, such that when x is the agent of E ′, the theme is some Y distinct
from x.
The truth conditions given in (4.60) require a further modification. Notice that the
values of Y associated with the Differentiator can be anything so long as they are distinct
from the agent x; for example, Y can be assigned values that are teachers and not students.
This would predict that (4.59) can be true in situations where students did not see other
students, but teachers instead. This is an unwelcome result; the truth of (4.59) requires
students to see other students; and not just any students, but students which are also
part of the value determined by the reciprocal’s antecedent. In order to account for this
restriction, I propose that the semantic values of the Differentiator are restricted by a silent
partitive phrase of them, where them is coreferential with the reciprocal’s antecedent. This
will ensure that values Y above are not just distinct from x, but also come from the same
plurality of which x is a part.
This is not the first time that partitivity has been argued to be crucial to the in-
terpretation of reciprocals. Beck (2001) suggests a similar decomposition; for her the
interpretation of the BAR can be paraphrased as “the others among them”, where them
corefers with the reciprocal’s antecedent. This approach is different from the present
approach since I am arguing for the partitivity to be represented twice; once on the Dis-
tributor (as all distance D operators have a partitive restriction), and then once again on
the Differentiator. Having partitivity represented twice will have payoffs that we will see
below.
This analysis of the Differentiator has similarities with so-called double-index ap-
proaches to reciprocity.14 These approaches argue that two values (i.e., indices) are re-
quired for the interpretation of reciprocal expressions: the first is a contrast value for
which distinctness is determined with regards to, the other a range value which represents
the plurality of individuals that reciprocated action holds among. The present approach
14For double-index approaches, see Fiengo and Lasnik (1973), Heim et al. (1991b), Heim et al. (1991a),
Schwarzschild (1996), Sauerland (1998), Sternefeld (1998), and Beck (2001).
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maintains that contrast and range values are required, but in specific way. The range value
corresponds to the partitive argument on both the Distributor and Differentiator, and this
is always covalued with the reciprocal’s antecedent. The contrast value will covary with
the values of x given by the Taylor-Schein distributivity operator, as discussed above.
The range value on the Distributor has already been discussed with regards to distance
distributivity in the following chapter, and since I am viewing the Distributor essentially
as binominal each, the same remarks apply to its composition in BARs. As for the Dif-
ferentiator, I will represent it as having two indices; the first is the contrast, the second is
the range. I thus give the following ⟨e, t⟩ definition of the Differentiator.
(4.62) !Differentiatori,k"g = !otheri of themk"g = λX.X ≤ g(k) & OTHER(X, g(i))
The value i will also be part of the antecedent plurality k; this is given by the Distributor.
For the time being, I will assume that this type ⟨e, t⟩ meaning in (4.62) feeds existential
closure (see Chapter 2); and so the Differentiator is interpreted as indefinite. It is also
possible for iota closure to apply, the result being a type e definite Differentiator. I will
make some comments about this in the next section, following some suggestions from
Schein (2003). Furthermore, allowing both definiteness and indefiniteness within the
BAR might be useful for explaining languages which mark BARs thusly; see §4.3.1.
Whether definite or indefinite, the resulting expression will be marked with the thematic
role typically associated with the argument position of the BAR; in the case of (4.59), this
will be the THEME role.
With these proposals about the Differentiator in place, I now give the following
truth conditions for (4.59) in (4.63). The crucial difference is the partitive restriction on
the Differentiator; as shorthand, I represent this immediately following the existential
quantifier ∃Y instead of as a separate conjunct.
(4.63) ∃E[AGENT(E,⊕STUDENT) & SEE(E) & ∀x ≤ ⊕STUDENT[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y ≤ ⊕STUDENT[OTHER(Y, x) & THEME(E ′, Y )]]]]
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Notice that the truth condition above is rather weak; it requires that each student sees at
least one other different student, and nothing more. I return to discussion of this with
respect to the polysemy problem in §4.5.
Officially, my position is about the semantics of each other BARs, since these
clearly have a distributive element (each) and a differentiating morpheme (other). How-
ever, the analysis can be extended to other types of BARs if one is willing to assume covert
distributivity. This has not necessarily been an issue in past accounts of distributivity: as
mentioned in Chapter 2, Link and Schwarzschild have proposed silent distributivity op-
erators to account for distributive interpretations of VPs, and Beck (2001) has proposed
silent distributivity operators to account for Strong Reciprocity.
Concerning one another type reciprocals found in English and other Indo-European
languages, these can be accommodated into the present account by assuming that they are
decomposed as [[each one] [another]]. In other words, the one is taken to be part of the
Distributor; see LaTerza (2010). This analysis of one another reciprocals is motivated
by the case facts observed in §4.3.3. Recall that for languages like Serbo-Croatian and
Ukrainian, the case of one matches the case of the reciprocal’s antecedent, while the case
of other is that which is typically associated with the argument position which that BAR
occurs in. This is similar to the distance distributivity facts from Chapter 3, where in
languages with rich case systems, the case of the distributivity morpheme matches that of
its antecedent. Furthermore, these case facts parallel the proposed thematic role assign-
ment: just as the case of the Distributor matches the case of its antecedent, the thematic
role required for the proper implementation of Taylor-Schein distributivity requires that
this too is shared with the antecedent. The Distributor in these languages is assigned the
case associated with the reciprocal’s argument position, and likewise I proposed that the
Distributor be assigned a thematic role determined by the reciprocal’s argument position.
This links the Distributor with the appropriate thematic relation in logical form, within
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the sub-event domain, on par with the nominal host in binominal each constructions15.
4.4.2 Prepositions and Thematic Roles within BARs
In this section I will discuss the cross-linguistic range of preposition placement
within BARs and how this might help determine the choice between the adpositional
approach and the Theta Rule approach to neo-Davidsonian composition. In §4.3.2 , it
was observed that BARs across languages, and to a limited extent within English, can
have prepositions that are placed either outside of the entire BAR complex or intervening
between the Distributor and the Differentiator.
(4.64)
P
Distributor Differentiator
(4.65)
Distributor
P Differentiator
Regardless of where the preposition is placed, the common feature is that it is associated
with a thematic role that I have argued to be assigned to the Differentiator. This pattern of
thematic role assignment is strengthened by the case facts from §4.3.4: the Differentiator
is case marked by the case typically associated with that preposition.
Recall from Chapter 2 the two proposed theories of thematic interpretation in the
total separation approach to argumenthood. For the preposition approach, the thematic
15BARs in other languages can be assigned the same semantic values as the Distributor and Differentiator
here, although the motivation for doing so becomes weaker when considering the morphemes involved. For
example, the Russian BAR is drug drugi (lit., “other other”) and the Hindi (lit., “one second”). While
it not clear how these morphemes can take on the meanings as each and other in the appropriate way, it
is also not clear how the morphemes involved can work together to compose a reciprocal meaning. For
example, Russian seems to involve two sorts of distinctness, and not distributivity, while Hindi suggests
that ordering is somehow involved. I thus believe that the analysis presented in the main text applies to just
each other and one another type BARs, though I leave open the possibility that BARs in other languages
can receive the same treatment if one were to assign the meanings I gave the Differentiator and Distributor
to morphemes that appear to have different meanings.
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content is located in the preposition itself, which composes with a nominal meaning to
yield a monadic predicate of events with the appropriate thematic relation.
(4.66) !PΘ" = λXe.λEv.Θ(E,X)
For the Theta Rule approach, the preposition is essentially semantically vacuous: the
nominal bears the thematic role which is type-shifted by the Theta Rule.
(4.67) Theta Rule
!NPΘ" = λE.Θ(E, !NP")
Under the latter view, the role of the preposition is not to assign a thematic role, though it
could possibly participate in a syntactic feature checking relation with an NP/DP which
bears the appropriate role.
For cases where the preposition intervenes between the Distributor and the Dif-
ferentiator, the choice between the two theories does not matter. However, when the
preposition appears outside of the BAR complex, as it often does in English and other
Germanic languages, it appears the Theta Rule is preferred. Following the assumption
that the Distributor is syntactic adjunct to the Differentiator nominal, and the c-command
domain of the Distributor corresponds to the sub-event domain in logical form, then the
preposition cannot compose with the Differentiator in the appropriate way.
(4.68) PP
P DP
Distributor DP
Differentiator
Within the present framework, not only will Differentiator not be assigned a thematic
role, but it will not be of the appropriate type (⟨v, t⟩) to compose with the Distributor.
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The problem is avoided under the Theta Rule approach, since the DP by itself bears a the-
matic role, so the Differentiator will be type-raised to the appropriate thematic predicate
without needing to compose with the preposition. As such, this is another theory-internal
reason for preferring the Theta Rule over the adpositional approach for a neo-Davidsonian
interpretation of nominals16.
4.5 Accounting for polysemy
Using Taylor-Schein Distributivity produces logical forms for BARs that are roughly
equivalent to the ones associated with One-way Weak Reciprocity (OWR) as it is shown
in the table (4.3) from §4.2, repeated below.
(4.69) One-way Weak Reciprocity
∀x ∈ A[∃y ∈ A[x ̸= y & xRy]]
The main differences are the use of events, total thematic separation, and higher-order
variables, all of which have benefits when accounting for the range of syntactic distribu-
tion of BARs, as will be discussed in the next section. Furthermore, the choice of this
weak semantic meaning was not arbitrary; it came about from the proposed lexical entry
of D composed with a partitive other morpheme.
Considering just elementary reciprocal sentences, the present approach shares im-
portant similarities with OWR in that they both involve a sort of distributive apportion-
ment by having a universal quantifier scope above an existential, and they both do not
express “genuine” reciprocity in the sense that if x did something to y, then y necessarily
did something to x. Given this similarity and the entailment facts from §4.2, this means
that the neo-Davidsonian logical forms used here can be judged true by any situation
that meets the conditions for OWR or any stronger type of reciprocity. This leaves out
16The preposition account can potentially be saved by treating the surface position of the preposition as
derived from by movement: in other words, the base structure of (4.68) is like (4.65), where the preposition
can locally compose with the Differentiator. The problem with this alternative is the unmotivated head-
movement around an adjoined Distributor to yield (4.68).
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the sixth alleged reading, an issue we will return to shortly. But first let us examine the
logical form of the sentence that we first used to illustrate the polysemy problem.
(4.70) The dots are pointing at one another
(4.71) ∃E[AGENT(E,⊕DOT) & POINT(E) &
∀x ≤ ⊕DOT[∃E ′ ≤ E[AGENT(E ′, x) & ∃Y ≤
⊕DOT[OTHER(Y, x) & AT(E ′, Y )]]]]
We can paraphrase (4.71) as follows: there are some events of pointing with the dots as
their agents, and each of those dots have their own sub-events in which that dot pointed
at one or more other dots. This underspecified approach is compatible with very weak
situations, say where the dots are arranged in a circle, and each dot only points at the
dot immediately to its left; but it is also compatible with the strongest types of reciprocal
situations (see (4.2)), since there it is still true that each dot points at at least one other
dot.
Admittedly, there are some situations where a reciprocal sentence used to describe
it would be predicted to be true under the current approach, but speakers’ judgments say
otherwise. However, I believe that these apparent counterexamples reflect extra-semantic
contributions to meaning, such as the role of context and typicality17. In Sternefeld’s
(1998) words, “...it appears that the problem of salient readings, which cannot be dealt
with in a purely semantic theory, is independent of the particular issue connected with
reciprocity” (p. 318, fn 9). I take it that what is meant by a “purely semantic theory”
is one that focuses just on the compositional aspects of meaning. This is not to say that
these compositional aspects are all there are; of course things like context and lexical
idiosyncrasies factor into restricting the possible meanings of utterances, and thus affect
speakers judgements about truth or falsity. But the concern of Sternefeld’s, which I share,
is that if we are purporting to give a semantics for reciprocals, we should focus on those
17See Kerem et al. (2009) for discussion of the role of typicality in reciprocal expressions.
136
aspects of meaning that are context independent, indefeasible, and follow from general
principles regarding compositional interpretation.
The proposal offered here addresses the compositional semantics of BARs, and to
do so requires disentangling some aspects of meaning that I think have been mistakenly
grouped into this category. Below, I will discuss two cases that I think illustrate this
“problem of salient readings”, with the understanding that the general line of reasoning,
particularly of how these facts should not be accounted for in a purely semantic theory for
BARs, can be extended to similar circumstances. I then turn to purported weakest type of
reciprocity, Inclusive Alternative Ordering.
4.5.1 Typicality preferences are extra-semantic
The first case of typicality I will discuss involves the well-known examples of things
like telephone poles being equally spaced from one another (see Dalrymple (1998)).
(4.72) The telephone poles are spaced 500 meters from one another.
(4.72) would normally be used to describe situations in which there is a line of telephone
poles, and each telephone pole is connected to two others, and is separated from each of
them by 500 meters. Were one of the poles to be separated by only 200 meters, (4.72)
would be a very awkward way of describing that situation; some might even say that
(4.72) is false in that situation. The present approach offers no reason why this might be
so, but I do not think that it has to. I believe that there is nothing about the way that the
lexical items are composed in (4.72) that is accountable for this awkwardness, but rather
this can be attributed to how we typically think of situations involving telephone poles,
and situations that expressions like is spaced x meters from are typically used to report
on. All that one needs to show that this is the case is a situation where the telephone
poles are not related by the transitive closure of the is spaced 500 meters from relation
(see Schein (2003)), but yet speakers will judge (4.72) true in that situation. Here is one
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such situation.
Imagine that Dr. Frankenstein requires pairs of telephone poles for his new exper-
iment. Each pole in the pair is connected by wires to the other pole, and also must be
spaced 500 meters from the other. Crucially, it does not matter how far each pair is from
any other pair. Some pair might only be 10 meters from another pair, which entails that
one of the poles in that pair is 10 meters from one of the poles in the other pair; but these
do not matter to Dr. Frankenstein, since only the poles that are connected pairwise by
wires have to be spaced 500 meters. Suppose then that the doctor’s assistant Igor sets up
the poles according to the doctor’s wishes, following the rule that each member of the
pair be spaced 500 meters from the other member, but to save space, he packs the pairs
tightly together such that if a pole is next to another pole that it does not form a connected
pair with, then they are only spaced by 10 meters. In such a situation, Igor can speak
truthfully if he uttered (4.72), even though all of the poles are not related by the transitive
closure of the is spaced 500 meters from relation. And since (4.72) can be true in situa-
tions other than the ones typically assumed for such sentences, then it cannot be a rule of
compositional semantics that (4.72) has to be interpreted in such a way that makes only
the typical situation true and not weaker ones.
Another example, also brought up by Dalrymple et al. (1998), can be demonstrated
with a situation of a six on one fight. If the situation were such that a gang of six were
attacking a single victim, and each member of the gang punched that victim, but the victim
only got to hit one of the gang members, then the sentence in (4.73) sounds strange when
uttered by an observer of the fight.
(4.73) They are punching one another
I believe that this too is something that the compositional semantics should not have to
account for. This oddity might be pragmatic in nature, as (4.73) is not the most infor-
mative way to characterize the situation. But notice that it cannot be this configuration
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of combatants that makes (4.73) strange, since if we took the same ratio of gang mem-
bers and victims but multiplied it, so that there were three 6-vs-1 fights of the sort just
described, then the acceptability of (4.73) improves drastically. We see again the defeasi-
bility of these apparent restrictions on the meaning of sentences with reciprocals, which
implies that these restrictions should be kept separate from the general interpretive rules
of compositional semantics.
4.5.2 Inclusive Alternative Ordering
I will turn now to a problem that cannot be attributed to extra-semantic factors:
the problematic situations that caused researchers to posit Inclusive Alternative Ordering
(IAO), the weakest FDVS for reciprocal sentences. We saw an example of this in §4.2,
where there was a line of dots doing some pointing, but the rightmost dot was not pointing
at anything. Similar situations can be described by sentences like (4.74).
(4.74) The plates are stacked on each other
The issue here is how to account for the plate at the bottom of the stack. My proposed
treatment, as well as OWR, require that for every plate, there is another plate on which it
is stacked; put differently, with these logical forms, this sentence could be true iff we are
talking about infinitely many plates. However, speakers judge (4.74) to be true in real-
world situations where there are a finite number of plates stacked, and the bottommost
plate is not on top of any other plate. The way that IAO fixes this problem is to have a
disjunctive participation statement.
(4.75) Inclusive Alternative Ordering
∀x ∈ A[∃y ∈ A[x ̸= y & (xRy ∨ yRx)]]
This would make (4.74) true iff for each plate x, either x is stacked on top of another
plate, or another plate is stacked on top of x.
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Before I address how the present approach can be modified to handle this problem,
let us reflect on the methodology that I have been urging. I have tried to revive Langen-
doen’s underspecification approach for the reasons discussed above. Why is it then that I
proposed something analogous to the penultimately weakest reading, and not the weakest
one? Something like IAO is able to capture these problematic cases, so why not go that
weak?
The first reason is a compositional one. The logical forms proposed here were ar-
gued to arise from the syntactic configuration of the Distributor and the Differentiator.
I showed that with this syntax, and certain rules for interpretation in a neo-Davidsonian
framework, we arrive at a logical syntax that works well for reciprocals, but these are the
same rules of interpretation that can be used independently of reciprocal constructions. I
have argued in previous chapters that the same lexical axiom I use for the Distributor in
BARs can also be used for the semantics of distributive determiners and distance distribu-
tivity items. It just so happens that when we take these interpretive rules and apply them
to reciprocals, then the result is something analogous to OWR. However, to incorporate a
disjunctive participation statement into logical form is ad hoc, and does not follow from
any independently motivated rules of interpretation.
There are also two empirical reasons which argue against theories with IAO. First,
let us consider reciprocal sentences with negation. If, following Langendoen, reciprocals
have a weak interpretation in the sense discussed above, then we would predict that the
negation of a reciprocal sentence should yield relatively strong truth conditions18. This
prediction appears to be borne out, as the sentence (4.76) can only be true if little to no
hitting happened.
(4.76) The boys didn’t hit each other
18I will not be giving an explicit compositional treatment of negation in the neo-Davidsonian system used
in here. For present purposes it will serve to assume that negative sentences involve the same logical forms
as their positive counterparts, plus the addition of a logical negation operator scoping above the clause level
existential event quantifier.
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Interestingly, sentences like (4.76) can be true if just a little bit of hitting happened. For
example, one can truthfully say Ali and Liston didn’t hit each other if Ali had a first-round
knockout and Liston didn’t get a chance to do any hitting. In general, it appears that a
negative reciprocal sentence can be uttered truthfully when some of the relevant action
takes place, but would become false if that action were reciprocated. Theories with IAO
make incorrect predictions here. Consider the negation of the IAO schema:
(4.77) ¬[∀x ∈ A[∃y ∈ A[x ̸= y & (xRy ∨ yRx)]]]
To paraphrase, this says that not every atom in the antecedent plurality was involved in the
relation. For (4.76), this would give truth conditions that are paraphrased as “not every
boy was involved in a hitting (either as a hitter or hittee)”; this conditions are clearly not
satisfied by the first-round-knockout situation just described. Importantly, (4.76) can be
true of this situation. Truth conditions based on (4.77) would come out false in the Ali-
Liston situation, contrary to speakers’ intuitions. We do not run into this problem with
the slightly stronger OWR, nor the present approach which it is based on; these can be
paraphrased as “not every boy was an agent in a hitting”, which is true of the Ali-Liston
situation as desired.
While a theory that includes IAO can account for the problematic edge cases men-
tioned above, it makes wrong predictions with many sentences involving comparison19.
19As is well-known, these constructions are felicitous when they embedded under certain operators.
Heim et al. (1991), among others, observe that sentence like (i) have perfectly reasonable interpretations;
the crucial factor seems to be that the comparative reciprocal clause is embedded under an attitude verb.
i. They think they are taller than one another
I will return to such constructions in De Se chapter. I will leave unaddressed how other comparative sen-
tences, such as (ii) can receive non-contradictory interpretations.
ii. They sang better than each other
This sentence can be used to describe instances where say A sings better than B on day 1, but B sings better
than A on day 2. While I believe an explanation for sentences like (ii) is already implicit in the framework
involved here, which relies on plural existential quantification over events, I will not explore this matter
further. What is important for the argument in the main text is that there are some comparative sentences
that are clearly infelicitous/contradictory, and accounts with IAO do not provide an explanation for why
this is so.
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(4.78) #The students are taller than one another
(4.79) #The students exceed one another (in height)
A theory with IAO would predict these sentences to be true just as long as one individual
is taller than the rest . The approach developed here predicts a contradiction, a prediction
that is borne out. Below is the logical form of (4.79) in the system presented here20.
(4.80) ∃E[AGENT(E,⊕STUDENT) & EXCEED(E) & ∀x ≤ ⊕STUDENT[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y ≤ ⊕STUDENT[THEME(E ′, Y ) & OTHER(Y, x)]]]]
Paraphrasing, each student is associated with another student such that the former is taller
than the latter. This is something that cannot be true of each student, hence the infelicity.
It appears that we are left with a choice between two flawed theories; the current
one, where we have to make exceptions for edge effects, or a theory with IAO, which
runs into problems with negation and comparatives. It is worth stressing here that this
is not a problem specific to my particular proposal, but a challenge for any theory of
reciprocal semantics. I will now briefly outline two possibilities for fixing the problem in
the present approach. The first is to keep the semantic framework given above the same,
but add a pragmatic condition like Sauerland’s (1998) Benevolence, which allows for a
certain amount of exceptions when judging such sentences to be true.
(4.81) Benevolence (from Sauerland (1998), p. 200)
Assume that an assertion is true in at least one situation compatible with common
world knowledge.
Sauerland argues that certain verbal predicates like follow X into the room are associated
with typically non-reflexive following relations in the real world, and given our knowl-
edge about such situations, we know (according to Sauerland) that there is “...no possible
20I choose to give the logical form of (4.79) and not (4.78), since giving the logical form of the latter
would require a neo-Davidsonian treatment of comparative constructions, which cannot be done here. I
refer the reader to Fults (2006) and Wellwood (2014) for discussion.
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situation compatible with our world knowledge about following someone into the room
where it is true for a group of children that each child followed every other child”. For
Sauerland, this provides a case for which Benevolence can be used. For the present ac-
count, we can modify the alleged world knowledge along the lines that there is no possible
situation where every child follows at least one other into the classroom since there will
always be the child at the head of the line who does not follow anyone.
The other option for accounting for these outlier cases is to modify the logical forms
in the way that Schein (2003) did to account for such examples. He argues that the logical
forms of reciprocal sentences should include information about temporal orientation, and
his amendment to logical form can be paraphrased as such: each plate is stacked on the
other plates that have been stacked. For him, the definite description associated with
Differentiator does not have necessary existential import, so we could interpret it as “the
others that were already stacked, if there are any”. With this modification, (4.74) would
come out as true since the plate on the bottom is in fact stacked on the zero or more other
plates that have already been stacked. I hope that future research will help decide which
of these two options are better, but I think that both are plausible. As for theories that
use IAO, I see no way that they could recover from the inconsistency involving negation
and comparatives, nor do I see how to implement the disjunctive participation statement
associated with IAO in a non-stipulative way that makes due with just the morphemes
involved in BARs.
In this section we saw how the independently motivated rules from the last sec-
tion derive neo-Davidsonian logical forms that have been shown to be able to handle five
out of the six FDVSs listed in the table in (4.3). I have argued that the concerns about
adopting an underspecification approach are unwarranted when our task is to give a com-
positional semantics for reciprocals. In this section, we focused on several extra-semantic
factors that should be kept as extra-semantic in analyses like the one offered here. Correl-
atively, as we saw in §4.2, there are certain properties of meaning concerning sentences
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that involve plurals in general, specifically the strength imposed by stative verbs and the
possibility of outlier participants, which should be accounted for by a larger theory of
plurality of which reciprocity is a part. In other words, we should not attribute special
properties to reciprocal expressions to handle these problems, but a theory of plural ex-
pressions should be developed so that it accounts for these issues in both reciprocal and
non-reciprocal sentences. As for the sixth FDVS, Inclusive Alternative Ordering, we saw
that allowing this as a possible reading for reciprocal sentences causes problems when
considering reciprocals in negative and comparative sentences. If we eliminate Inclusive
Alternative Ordering as a possible reading, then the only problems to be overcome are
the edge cases. So, if we find a way to account for edge cases, and I provided two possi-
ble ways above, the account offered here is underspecified enough to account for the full
range of polysemy, barring extra-semantic restrictions on speaker meaning.
4.6 Beyond elementary reciprocal sentences
I now turn to how the interpretation strategy for BARs presented here can be ap-
plied to a wide range of their syntactic distribution. The literature on reciprocals has
offered little discussion of cases that are not elementary reciprocal sentences, and almost
no discussion of reciprocals that appear within noun phrases. I will show that the present
approach can be modified in a simple way that can account for nominal reciprocals with
the same mechanism that accounts for clausal reciprocals. If this approach is right, the
modification will offer new insights into the nature of Taylor-Schein Distributivity.
We have already seen how BARs are interpreted when they are in elementary recip-
rocal sentences, where the presence or absence of a preposition makes little difference. In
what follows, we will first examine more complex cases of clausal reciprocals, in partic-
ular ditransitive constructions, and then turn to cases of reciprocals that appear inside of
noun phrases21.
21It is worth pointing out that while this approach shares some similarities with Schein’s (2003) take on
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4.6.1 BARs as indirect objects
Consider the sentence in (4.82), which is ambiguous between a reading where the
gnomes put hats on each other’s heads, and a reading where the gnomes stacked hats on
top of other hats. These are the cases that languages like Serbo-Croatian and Ukrainian,
with rich case morphology on BARs, disambiguate by varying the case of the Distributor.
(4.82) The gnomes put the hats on one another
The ambiguity is relatively straightforward to capture under the present approach. We can
attribute each reading to the reciprocal having a different antecedent, as evidenced by the
Case facts from §4.3. For us, this means two things: having different potential binders
for the pronoun in the partitive restrictor that the Distributor and Differentiator share, and
also having different potential sources for the Distributor to get a thematic role from. In
the case where the subject is the antecedent, the Distributor will have the AGENT role, and
the BAR will provide information about how parts of what the gnomes picks out interact
with one another. This reading is shown by the logical form below.
(4.83) ∃E[AGENT(E ′,⊕GNOME) & PUT(E) & THEME(E,⊕HAT) & ∀x ≤
⊕GNOME[∃E ′ ≤ E[AGENT(E ′, x) & ∃Y ≤
⊕GNOME[OTHER(Y, x) &ON(E ′, Y )]]]]
When the direct object is the antecedent, the Distributor will have the THEME role, and
the partitive restrictors will be valued by the hats. The logical form for this reading is
shown in (4.84).
reciprocals, it differs in important ways. The logical forms used here and in his work on reciprocals have
some differences, but I think the crucial difference lies in how we treat the syntax of BARs. For him, the
BAR represents a sort of reduced adverbial clause. For example, the sentence they hit each other for him
would involve the matrix clause they hit, onto which is adjoined the reduced adverbial clause each...other.
While he is not explicit about the exact syntax of such adverbial clauses, I believe that what he has in mind
is a sort of gapping construction. This works well for elementary reciprocal sentences, but it is not clear
how to extend this analysis beyond these simple cases. Cases like they met each other’s parents and they
read books about each other present clear problems for such an approach.
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(4.84) ∃E[AGENT(E ′,⊕GNOME) & PUT(E) & THEME(E,⊕HAT) &
∀x ≤ ⊕HAT[∃E ′ ≤ E[THEME(E ′, x) & ∃Y ≤ ⊕HAT[OTHER(Y, x) &ON(E ′, Y )]]]]
For these cases, it is just a matter of determining the reciprocal’s antecedent. Once that is
done, the rest falls out as in the simpler cases we saw earlier22. Notice that the analysis of
this ambiguity is parallel to the analysis of ambiguous binominal each ditransitives, such
as (3.55) from Chapter 3.
4.6.1.1 The Williams paradigm
The present approach also allows us to explain the following contrast noticed by
Williams (1991), mentioned in §4.2.3.
(4.85) a. The doctors gave each other new noses
b. #The doctors gave each patient new noses
To explain this contrast requires us to assume the standard approach to the structure
of double-object constructions discussed in Chapter 2, where the indirect object DP c-
commands the direct object DP. We have formulated Taylor-Schein Distributivity in a
way that the c-command domain of the distributivity operator corresponds to the sub-
event portion of logical form. Non-reciprocal double object sentences like (4.85b) have
the distributive DP as the indirect object, and so given the standard syntax just mentioned,
this means that this DP will c-command the direct object, and the interpretation of such
direct objects will include sub-event variables in their thematic conjuncts23. Below is the
logical form for the non-reciprocal sentence (4.85b), derived with our rules from the last
section.
22As far as I can tell, this is the first time this ambiguity has been addressed.
23The sentences used in Schein’s argument for thematic separation (see Chapter 2) have a numeral DP as
the direct object, and the argument requires the narrow-scope reading where such DPs are interpreted within
the scope of the distributive indirect object. In (4.85b), the direct object is a bare plural, which have been
known since Carlson (1977) to only have narrow-scope readings, so unlike the corresponding sentences
with numeral direct object DPs, we do not have to control for wide-scope readings.
146
(4.86) ∃E[AGENT(E,⊕DOCTOR) & GIVE(E) & ∀x ≤ ⊕PATIENT[∃E ′ ≤
E[GOAL(E ′, x) & THEME(E ′,new noses)]]]
The sub-event portion of this logical form says that for each patient, that patient had sub-
events E ′ where he/she is the goal, and where he/she received new noses. Although we
have left out discussion about the semantic contribution of the plural morpheme, in this
case it appears to cause the values of the new noses above to be two or more in number24.
As such, the themes of the sub-events above will be more than two in number, and the
infelicity arises because we do not normally think of each rhinoplasty patient as receiving
any more than one new nose.
On the other hand, the Distributor in the BAR sentence (4.85a) will only c-command
the Differentiator DP, given the syntactic decomposition proposed for BARs. As such, the
sub-event section of logical form will include the interpretation of the Differentiator, but
not the direct object DP. So the logical form of (4.85a) will be as follows, where the the-
matic conjunct associated with new noses will include the main-event variable E, and not
the sub-event variable E ′, in contrast to the logical form of (4.85b).
(4.87) ∃E[AGENT(E,⊕DOCTOR) & GIVE(E) & ∀x ≤ ⊕DOCTOR[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y ≤
⊕DOCTOR[OTHER(Y, x) & GOAL(E ′, Y )]]] & THEME(E,new noses)]
This logical form is weaker than the previous one in the sense that we know that new noses
are involved, but nothing is said about how they are related to each individual patient (in
the case of (4.85a), the doctors are also patients). This is similar to dependent plural
constructions such as unicycles have wheels, where we know that unicycles and wheels
are involved, but nothing tells us how to apportion wheels to unicycles, and the sentence
24The multiplicity aspect of bare plural meaning has been argued by Zweig (2008) to be an implicature,
and as such, it should be cancelable. I agree with this treatment for most cases, as sentences with bare
plurals in downward-entailing contexts seem to have the “one-or-more” interpretation: one can answer yes
to Do you have children if one only has a single child. However, making a question out of (4.85b) still
seems to require each patient receiving two or more new noses: Did each patient get new noses.
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still sounds felicitous even though we know that each unicycle only has one wheel; see
Zweig (2008) for a neo-Davidsonian treatment of dependent plurals.
This paradigm is similar to the contrast observed between floating and binominal
each ditransitives in §3.3.2 in the previous chapter. Like the floating examples, (4.85b)
has a wider scope domain for each that contains more arguments than their counterparts,
thus more thematic conjuncts in logical form. The reciprocal example is on par with the
binominal each sentences: the scope domain of each is just the host nominal to which
it is attached, so other nominals will not be interpreted as being bound by the sub-event
quantifier, but rather the clause level event quantifier.
Williams’ contrast is accounted for by this theory by positing a syntactic difference
between the pair of sentences, already motivated from distance distributivity phenomena
in Chapter 3. Both sentences involve distributive elements, but only in the non-reciprocal
sentence is the direct object in the scope of the distributivity operator, thus, only in this
sentence is a plurality of noses apportioned to each patient given our approach to distribu-
tive sub-event apportionment. In the reciprocal sentence, we are only told that new noses
are themes in events of giving, events that have doctors being both agents and goals, but
we are not told how many noses each doctor received, just as we are not told how many
wheels each unicycle has in the dependent plural sentence above.
Examples similar to Williams’s paradigm can also be accounted for by this ap-
proach. Consider cases where instead of a bare plural direct object, there is a singular
indefinite.
(4.88) a. The doctors gave each other a new car
b. The doctors gave each patient a new car
Recall the Principle of Covarying Indefinites from Chapter 3; the observation that a co-
variance interpretation of singular indefinites is only permitted when they are within the
scope of a distributivity operator. It follows then, given our assumptions about the syntax
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and semantics of ditransitives, that (4.88a) allows only the interpretation where there is
a single new car that is being passed back and forth among the doctors, while (4.88b)
allows a covariance interpretation.
4.6.1.2 Nominal BARs with nominal antecedents
We will now turn to nominal reciprocals, such as (4.89).
(4.89) John read the professors’ reviews about each other
In (4.89), the professors acts as the reciprocal antecedent, and as such we would expect
this DP to bind the partitive restrictor, and pass its thematic role to the Distributor. I will
assume that the relevant thematic role is the possessor role POSS, which corresponds to the
POSS(X, Y ) relation in logical form; see Chapter 2. The account requires some revisions
though, as we run into a problem when we use Taylor-Schein Distributivity to interpret
the Distributor in cases like (4.89). So far, this rule adds sub-events to logical form, and
the individuals picked out by Distributor were taken to be participants in these sub-events.
But in those cases, the Distributor was associated with eventive thematic roles of the form
Θ(E,X). In (4.89), the Distributor is associated with a non-eventive thematic role, which
means that while we are able to talk about sub-events with Taylor-Schein Distributivity,
we do not have a way of saying how the professors participated in those events.
To fix this problem, I propose a modification of Taylor-Schein Distributivitywhereby
it introduces a sub-entity existential quantifier, which I intend to be a generalization of
sub-event quantification. Depending on the syntactic configuration that the distributive
DP finds itself, it will either introduce an existential quantifier that ranges over the do-
main of events E, or an existential quantifier that ranges over the domain of entities D.
In the cases of clausal reciprocals, which include elementary reciprocal sentences and the
ditransitive sentences we were considering, then the quantifier will range over E, which
is just the version of Taylor-Schein Distributivity we have been assuming so far. How-
ever, in cases of nominal reciprocals, where reciprocals appear inside of noun phrases, the
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sub-entity quantifier will range over the domain of individuals,D, and not the domain of
events E.
This generalization can be implemented as follows. Recall that the final argument
of the Taylor-Schein proposed definition of D, repeated below, is an event argument.
(4.90) !D" = λXe.λΘ⟨e,⟨v,t⟩⟩.λP⟨v,t⟩.λEv.∀x ≤ X [∃E ′ ≤ E[Θ(E ′, x) & P (E ′)]]
This has the effect of turning D with all its other arguments (whether or not Θ is an
adpositional argument or given as a Θ-feature on D) into a monadic predicate of events
that can be conjoined with other ⟨v, t⟩ nodes. Crucially, an event value is never given
to these ⟨v, t⟩ constituents, but instead the corresponding event variable is closed by an
existential quantifier. A parallel state of affairs holds in the nominal domain, where ⟨e, t⟩
predicates are conjoined, and eventually closed by either ∃X or ι; see §2.2.4.
My proposal is that the final argument to D is underspecified, or polymorphic, in
the sense that it can compose with either predicates of events or predicates of individuals.
In other words, D is able to be conjoined with a ⟨v, t⟩ when it appears clausally or ⟨e, t⟩
when it appears internal to nominals. When the former is chosen, the logical form corre-
sponding to D will mention sub-events, and when the latter is chosen the local form will
mention sub-entities – subparts of a plurality of individuals.
There is of course the issue of deciding which type of monadic predicate D com-
poses with in particular cases. When the closure operator is introduced either at the root
of the clause or the nominal, this polymorphic variable can be resolved to appropriately
range over events or entities. Alternatively, this value can be decided by whether the
scope argument of D is of ⟨v, t⟩ or ⟨e, t⟩; whatever type the scope is will be the type of
the composition of D with its scope. I thus give the final version of the D operator, where
its final argument is marked as type α, which is the polymorphic variable ranging over
events or entities. I also use α and α′ as the polymorphic variables in the sub-event/entity
domain of logical form:
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(4.91) Taylor-Schein Distributivity, polymorphic version
!D" = λXe.λΘ⟨e,⟨α,t⟩⟩.λP⟨α,t⟩.λα.∀x ≤ X [∃α′ ≤ α[Θ(α′, x) & P (α′)]]
Let us apply this new to the problem at hand, and we will see how it derives a
satisfactory representation for (4.89).
(4.92) ∃E[AGENT(E, j) & READ(E) & ∃Y [POSS(Y,⊕PROF) & REVIEW(Y ) & ∀x ≤
⊕PROF[∃Y ′ ≤ Y [POSS(Y ′, x) & ∃Z ≤ ⊕PROF[OTHER(Z, x) & ABOUT(Y ′, Z)]]]]]
The BAR’s contribution to logical form can be paraphrased as such: for each professor, x,
there are some “sub”-reviews Y ′ that x is Poss-related to, such that those reviews Y ′ are
about some professor(s) Z other than x. Notice that instead of sub-events E ′, there are
sub-entities Y ′ which are one or more reviews associated with each professor. These truth
conditions capture the fact that (4.89) can be used regardless of whether each professor
possessed one or several reviews (number-neutrality of Y ′) and whether those reviews are
about one or several other professors (number-neutrality of Z).
The polymorphic rendition of Taylor-Schein D allows for the semantics to remain
the same internal to D, but the types of its arguments are determined by whether the
reciprocal appears clausally or nominally. This type adjustment is not like other type-
shifting rules, which add or shuffle the arguments values of some expression. Instead,
the proposal is a sort of bleaching of types; a single rule that can be used for eventive
arguments or entity arguments.
As an alternative theory, instead of an underspecified/polymorphicD one may posit
two items for this issue DE and DX depending again on whether it appears clausally or
nominally. (4.90) represents DE , the D operator used outside of nominals which has
been discussed since Chapter 2. (4.93) below defines DX , the D operator used within
nominals. The sole difference is that wherever a v is used in DE, e is used in DX .
(4.93) !DX" = λXe.λΘ⟨e,⟨e,t⟩⟩.λP⟨e,t⟩.λYe.∀x ≤ X [∃Y ′ ≤ Y [Θ(Y ′, x) & P (Y ′)]]
151
In sum, the proposal is that there are two varieties of distributivity, clausal dis-
tributivity and nominal distributivity. Clausal distributivity involves apportionment of
sub-events to the individuals quantified over, while nominal distributivity involves appor-
tionment of sub-individuals to the individuals quantified over. In each case, the D oper-
ator still performs the same core operations with its arguments as it had since Chapter 2,
but now it allows some flexibility with regards to the basic types, events and individuals.
In the case of events, we have clausal distributivity, and thus the thematic role associ-
ated with D relates individuals to events, the scope of D is a predicate of events, and D
with all its arguments (save the last one which is always existentially closed) is itself a
monadic predicate of events. In the case of individuals, we have nominal distributivity,
and so the thematic role associated with D relates individuals to individuals, the scope of
D here is a predicate of individuals, and D with all its arguments is a monadic predicate
of individuals.
4.6.1.3 Possessor BARs
I now turn to BARs that appear in possessor position. It might come as a surprise
that I will not be treating these as as a case of nominal reciprocals, but we will see why
soon enough. To interpret these in a way that captures their meaning correctly, we have
to assume that the syntax of a possessor DP like the one in (4.94) is as in (4.95)25.
(4.94) The newlyweds met each other’s parents
25Note that we already saw reasons to believe that the Distributor and Differentiator need not form a
constituent to the exclusion of all other items; recall the presence of articles and prepositions from §4.3.
152
(4.95) DPi
DPj
...each...
DPi
DPk
...other...
D’i
Di
’s
CompD
This syntax might strike some as strange, as one might expect both the Distributor and
Differentiator to be in SpecDP. The syntax that places both in SpecDP is compatible
with the present approach, and it would look like the other cases of BARs that we have
been considering thus far, where the Distributor is adjoined to the Differentiator DP. This
possible tree is shown in (4.96).
(4.96) DPi
DPk
DPj
...each...
DPk
...other...
D’i
Di
’s
CompD
The reason why (4.96) is not the structure that I will assume is that it will derive a logical
form that does not suffice to represent the meaning of possessor reciprocal sentences.
The problem is similar to the one that lead us to the revised version of Taylor-Schein
Distributivity: it creates a logical form where the sub-entity quantifier is quantifying over
the wrong types of things. In both cases, since the BAR is anteceded by the clausal
subject, the Distributor will have the AGENT role. In (4.96), for the Distributor within
the nominal we should be using the nominal variety of D, not the event version. Thus
when we use the revised Taylor-Schein Distributivity rule, the sub-α quantifier will range
over entities, not events, which is the wrong type for a Distributor with the AGENT role.
However, in (4.95), the Distributor is adjoined outside of the nominal, meaning that the
event version of D will be used. This is because the Distributor attaches to the entire
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DP/PP containing other, and this DP/PP is a type ⟨v, t⟩ expression.26 So, assuming this
structure, the logical form of (4.94) would be (4.97), which correctly captures the meaning
of the sentence.
(4.97) ∃E[AGENT(E,⊕NEWLYWED) & MEET(E) & ∀x ≤ ⊕NEWLYWED [∃E ′ ≤
E[AGENT(E ′, x) & ∃Y [PARENT(Y ) & THEME(E ′, Y )& ∃Z ≤
⊕NEWLYWED [OTHER(Z, x) & POSS(Y, Z)]]]]]
Note that the syntax that I am claiming is necessary for possessor reciprocals is com-
patible with the distance distributivity analysis of reciprocals. While in many cases the
Distributor attaches directly to Differentiator DP, it is entirely possible for it to be adjoined
to something that properly contains the Differentiator DP, as I have already suggested is
the case for BARs with intervening prepositions in some languages.
4.6.1.4 BARs in picture-NPs
The last type of construction we will be looking at involves nominal reciprocals that
have clausal antecedents; i.e., antecedents that appear outside of the nominal as in (4.98).
(4.98) The artists drew pictures of each other
These cases pose a minor problem for the present approach, though there are two plau-
sible ways to fix this. But first, let us consider what the problem is. As one might have
expected, it lies in the value-types of the relevant constituents, in this case, the Distribu-
tor. The Distributor in (4.98) appears within a nominal, so our generalized Taylor-Schein
Distributivity rule would produce sub-entity quantification over individuals, not events, in
logical form. However, the reciprocal antecedent has the clausal AGENT role, and given
our assumptions that the Distributor gets its thematic role from the reciprocal antecedent,
26The choice among DP or PP depends on which approach to total separation discussed in Chapter 2 is
being used: the Theta Feature approach would have the Distributor adjoining to a DP, while the adpositional
approach would have the Distributor adjoining to a PP.
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then the Distributor also has the AGENT role. This means that we are placing conflicting
demands on the logical form conjunct associated with the Distributor’s thematic role; on
the one hand, this conjunct should have an event variable in it because the Distributor has
an eventive thematic role, on the other hand, the revised Taylor-Schein Distributivity tells
us that this conjunct should have an individual variable, and not an event variable, since
the Distributor appears inside a noun phrase.
There are two ways around this impasse. The first is to take the Chomsky (1986)
analysis of picture-NPs, which says that there is a covert pronoun in the SpecDP posi-
tion. For the present approach, this pronoun would have to be bound by the reciprocal
antecedent. The benefit of this approach is that it treats (4.98) on par with how we treated
sentences like (4.89), where the reciprocal antecedent is a possessor DP. Under this view,
the antecedent for the BAR in (4.98) would be the covert pronoun in SpecDP, which would
have the nominal role POSS instead of the clausal role AGENT. Thus, the value-type of
the Distributor will match the value-type of the sub-entity quantifier. The syntax of the
relevant DP in (4.98) under this approach is given in (4.99), and the corresponding logical
form for this sentence is given in (4.100).
(4.99) DP
DP
pro
D’
D
(’s)
NP
N
pictures
PP
P
of
DPi
DPk
...each...
DPi
...other...
(4.100)
∃E[AGENT(E,⊕ARTIST) & READ(E) & ∃Y [POSS(Y,⊕ARTIST) & PICTURE(Y ) & ∀x ≤
⊕ARTIST[∃Y ′ ≤ Y [POSS(Y ′, x) & ∃Z ≤ ⊕ARTIST[OTHER(Z, x) & OF(Y ′, Z)]]]]]
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Another way around the issue, brought to my attention by Paul Pietroski (p.c.), is
to posit a short quantifier movement of the Distributor so that it adjoins to the picture-DP,
as shown in (4.101).
(4.101) DPi
DPk
...each...
DPi
Di NP
N
pictures
PP
P
of
DP
tk DP
...other...
Under this approach, we can view the Distributor as taking the overt subject DP as its
antecedent, which would give it the AGENT role, which is fine now since it appears outside
of the nominal. This means that the sub-α quantification will be over events, which
matches the role of the Distributor. While the other option made both Distributor role and
sub-alpha quantification associated with individuals, this option makes both associated
with events. The logical form for (4.98) under this quantifier movement approach is given
in (4.102).
(4.102) ∃E[AGENT(E,⊕ARTIST) & DRAW(E) & ∀x ≤ ⊕ARTIST[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y [PICTURE(Y ) & THEME(E ′, Y )& ∃Z ≤
⊕ARTIST[OTHER(Z, x) & OF(Y, Z)]]]]]
To recapitulate, in this subsection we have proposed a generalized version of the
Taylor-Schein approach to distributive quantifiers. The result is a single rule of interpre-
tation that can be used for the Distributor of BARs, regardless if its appears clausally or
nominally. This allows us to give an elegant semantics for all occurrences of BARs, and
as far as I know, this is the first analysis that tries to accomplish such a task.
156
Notice that the approach offered here is only possible once we assume total thematic
separation. We need to be able to manipulate variables in thematic conjuncts without
affecting the variable in monadic verbal conjuncts. Moreover, approaches that advocate
polyadic quantifiers require a verb as one of the reciprocal’s arguments. While this might
work for some cases of clausal reciprocals, it fails when considering noun phrase internal
reciprocals. These considerations provide further support to the neo-Davidsonian who
wishes to eliminate the idea of verbs being interpreted as relational predicates.
4.7 Chapter summary
In this chapter I presented another application of the Taylor-Schein approach to
distributivity. I have argued that BARs are a sort of distance distributivity construction,
where the Distributor component of the reciprocal is treated in exactly the same way as
the distance D operator in the previous chapter. Like binominal each, the Distributor of
BARs has a very limited scope domain, in most cases just scoping over the Differentiator.
Also like binominal each and distance each in general, the antecedent nominal provides
the appropriate plural value and thematic role needed to compute suitable truth conditions.
I have argued that BARs should be decomposed into two components, preferably
the same each and other used outside of reciprocal constructions. This should be the null-
hypothesis for the semantics of BARs. Previous approaches have advocated a primitive
analysis in terms of polyadic quantification, but I have argued that such accounts are both
conceptually and empirically untenable.
The truth conditions derived for reciprocal sentences in this approach are relatively
weak. This approach is in essence a revival of Langendoen’s proposal that reciprocal sen-
tences uniformly have weak semantic meanings. Making this claim required some discus-
sion and ancillary claims about how extra-semantic aspects of meaning factor into judg-
ment of truth for reciprocal sentences, but I believe these are empirically well grounded.
Finally, the approach developed here can account for a much larger range of the
157
syntactic distribution of BARs than what has been addressed in previous analyses. This
was made possible by the total seperationist neo-Davidsonian assumptions I have adopted
together with the Taylor-Schein D operator.
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Chapter 5: Plural Reflexives
5.1 Introduction
In this chapter I extend the general neo-Davidsonian framework offered previously
to give a semantics for plural reflexive anaphors. The discussion will focus on what
I will call essentially distributive plural reflexives; a common type of reflexive found
among the worlds languages that exhibits a certain type of distributive interpretation. I
will introduce the core properties of such reflexives in the next section; §5.2. I will show
that some languages have two types of reflexives: one that is essentially distributive, and
one that is not; this latter type I will refer to as cumulative reflexives. We will see that
essentially distributive reflexives are typically morphologically complex when compared
to the cumulative ones, and each type is associated with certain semantic properties.
For the essentially distributive reflexives, I offer an analysis that fits within the
neo-Davidsonian framework pursued here. I will treat reflexives as another sort of dis-
tance distributivity construction, on par with the phenomena discussed in the previous
two chapters. Although these anaphors do not wear their distributivity on their sleeves
like reciprocals do, I believe positing a covert distributivity operator in the right position
explains the core facts of essentially distributive plural reflexives. What sets this analysis
apart from others, such as Cable (2014), is the proposal that the distributivity operator
composes directly with a nominal host, like binominal each and the Distributor in BARs.
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5.2 Essentially distributive plural reflexives
Previous work on English reflexives has shown that the range of interpretations
available to them are restricted in a certain way. I call this property the essential dis-
tributivity of plural reflexives, and it can be demonstrated by the following entailment
relation.
(5.1) The essential distributivity of plural reflexives
Theyi V themselves⇒ Each of themi V itself
Consider for example the sentence (5.2) with a plural reflexive. This sentence seems to
report that Brutus and Caesar engaged in self-kicking.
(5.2) Brutus and Caesar kicked themselves
It may also be true that Brutus and Caesar engaged in reciprocal kicking in addition to
self-kicking, but it for (5.2) to be true, self-kicking would have to take place, regardless if
any other kicking happens.
In a recent typological study, Heine and Miyashita (2008)) report that 61% of the
languages they surveyed have plural reflexives that are essentially distributive. Other
varieties of plural reflexives exist that do not exhibit this property; these are what I will
call cumulative reflexives, which I will describe in detail shortly.
The existence of two types of plural reflexives with different meaning properties
raises the question of whether these items should be grouped into a natural class. Al-
though I will not explore all the relevant issues here, it seems that the expression “reflex-
ive” may be a misnomer; in part because some reflexives do not need to express reflexivity
at all in a particular sentence for that sentence to be true (such as the se clitic in Romance
and Slavic). Furthermore, what a linguist might label as a reflexive anaphor in one lan-
guage may differ in its licensing domain (see Büring (2005) on this) and other subtle
160
differences in meaning (i.e., the logophoric behavior of so-called long-distance reflex-
ives in languages like Icelandic (Thráinson (2007)) and Chinese (Anand (2006)), among
others).
Regardless of how a comprehensive taxonomy of reflexives works out, we can still
focus on language specific forms that share certain properties. For example, English
essentially distributive reflexives must be locally bound and appear in the position of
other nominal expressions (though see below for qualifications). There are several other
Indo-European languages that have reflexives that behave this way.
I am putting aside cases of sentences that have what looks like reflexives but are
used in a non-reflexive way. For example, English has certain adverbial uses of forms like
himself that are used to indicate a sort of exclusivity.
(5.3) My kid went to the bathroom himself
(5.4) I built this boat myself
One may felicitously utter (5.3) if his child were potty-training and finally acquired the
necessary skills where he can use the toilet alone. Likewise, (5.4) can be used if I wanted
to express that I built the boat with no help from others. Other adverbial uses of apparent
anaphors can be used as intensifiers, often appearing string adjacent to the noun phrase
that they are intensifying.
(5.5) Chomsky himself doesn’t believe in Deep Structure anymore
These uses share the property that they appear in what seems to be adverbial positions.
While these may share some common properties with canonical reflexives, I do not ex-
plore this here. I will keep the focus in this chapter on reflexives that appear in argument
positions.
I also put aside long-distance uses of reflexives. Although this phenomenon does
not exist in English, some languages have a use of reflexives that can be used as a sort
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of logophoric expression. These forms often correspond to the cumulative variety of
reflexives in language.
Below I will provide two diagnostics tests for recognizing essentially distributive
reflexives. They are essentially Truth Value Judgment tests, where one judges a reflexive
sentence assuming some information which is provided previously. These background
situations are such that the conclusion in (5.1) does not hold for these situations. As
will be shown, test sentences with English reflexives and other essentially distributive
reflexives from other languages are judged false in these situations. On the other hand,
when cumulative reflexives are used instead, speakers often judge the sentence true in
these situations. Before moving on to these tests, I will give a very brief overview on the
morphology of essentially distributive and cumulative reflexives in some Indo-European
languages.
5.2.1 The long and short of plural reflexives
Several European languages have two types of morphemes to express reflexivity;
in this section, I will examine Dutch, French, German, and Serbo-Croatian. I will label
these “short form” and “long form” reflexives. Very often, the long form reflexives seem
to be composed of the short form plus some additional morpheme.
162
(5.6) Long and short form reflexives
SHORT FORM LONG FORM
FRENCH se se...eux-mêmes
GERMAN sich sich selbst
SERBO-CROATIAN se sebe
With the exception of French, the forms in these languages do not inflect for φ-features
(importantly, not number morphology). French long form reflexives always have the clitic
se together with an inflecting anaphor that appears in argument positions; I thus refer to
this long-form construction as se...eux-mêmes.
These languages fall into two classes regarding the syntactic distribution of their
reflexives. For Dutch and German, both the short and long form reflexives appear in
argument positions. For French and Serbo-Croatian, only the long form reflexives appear
in argument positions, while the short forms appear in the appropriate clitic position in
that language.
I now turn to the meaning differences between these two forms. It is well-known
that short-form reflexives are in some ways less restrictive than long forms, see Cable
(2014) and references within. When anteceded by a plural nominal, short-form reflexives
fall under what I have been calling cumulative reflexives, while long forms typically bear
the marks of essentially distributivity. In what follows, even though many languages do
not show number morphology on the reflexive anaphor, I will use the expression “plural
reflexive” to refer to reflexives that have a plural antecedent.
5.2.2 Purely reciprocal situations
A purely reciprocal situation would be one where each atomic individual did not
perform the relevant action on him/herself, but only on another. For example, suppose
Brutus kicked Caesar, and Caesar kicked Brutus, and neither kicked himself. The follow-
ing English sentence is reported to be false in such a situation.
163
(5.7) Brutus and Caesar kicked themselves
Furthermore, long-form reflexives in other languages are also judged false in this
purely reciprocal situation.
(5.8) French:
Brutus et César se sont donnés des coups de pied a eux-mêmes
(5.9) German:
Brutus
Brutus
und
and
Caesar
Caesar
haben
have
sich
SICH
selbst
self
getreten.
kick
‘Brutus and Caesar have kicked themselves’
(5.10) Serbo-Croatian:
Brut
Brutus
i
and
Cezar
Caesar
su
AUX
s˘utali
kicked
sebe.
self
‘Brutus and Caesar kicked themselves.’
One the other hand, the short-forms in these three language can be used to describe
the purely reciprocal situation.
(5.11) French:
Brutus et César se sont donnés des coups de pied
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(5.12) German:
Brutus
Brutus
und
and
Caesar
Caesar
haben
have
sich
SICH
getreten
kick
‘Brutus and Caesar have kicked themselves/each other’
(5.13) Serbo-Croatian:
Brut
Brutus
i
and
Cezar
Caesar
su
AUX
se
SE
s˘utali.
kicked
‘Brutus and Caesar kicked themselves/each other’
The insistence on “purely” reciprocal situations is enforced since there can be a situation
where each of Brutus and Caesar kicked the other and himself. As expected, long-form
reflexives can be used truthfully to describe this situation since the inference in (5.1)
holds, it is just that each is not exclusively kicking himself.
On a similar point, Murray (2008) and Cable (2014) bring up example situations
with mixed amount of reflexive and reciprocal action. For example, imagine half the
senators performed only self-kicking, and the other half performed only other-kicking.
For such situations, the short-form reflexive sentence (5.14a) can be used truthfully, yet
still the long-form sentence (5.14b) is false. I provide an example from Serbo-Croatian to
illustrate this point.
(5.14) a. Senatori
senators
su
AUX
se
SE
s˘utali.
kicked
‘The senators kicked themselves.’
b. Senatori
senators
su
AUX
s˘utali
kicked
sebe.
self
‘The senators kicked themselves.’
This shows the motivation behind the universal force in (5.1): it does not suffice for just
some individuals in the plurality to be self-kickers, each individual must be a self-kicker.
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5.2.3 Purely collective situations
A purely collective situation here is one where, for some antecedent value A and
verbal relation R, each atom in A stands in the R relation to A as a plurality, even though
that that atom may not stand in the R relation to itself. Consider the case of a rock band.
Each rockstar in the band hates himself. But out of this depression and self-loathing, good
music is born. The band as whole makes great music, and each rockstar loves the band
that he plays in. Assuming the Heim and Kratzer (1998) analysis of indexed expressions
with some plural modifications (possibly even with Landman-style groups, see Chapter
2), one might expect a sentence like (5.15) to be true in this situation; see the next section,
§5.3, for details on Heim and Kratzer’s analysis of reflexives.
(5.15) The rockstars love themselves
(5.15) is clearly false in the situation described. Compare with a sentence that differs
minimally from (5.15) in that the plural reflexive is replaced with the singular description
the band. As expected, the latter sentence is able to express that the rockstars collectively
love the band, even though each rockstar may hate himself.
(5.16) The rockstars love the band
Interestingly, the judgements about short and long form reflexives cross-linguistically
are a bit murky with these examples. While no speaker finds a long-form example to be
true in this situation, some also find the short-forms to be unacceptable. This is clearly
a case where more data collection is called for, but the conclusion drawn here is still a
useful one, especially for long form reflexives. Nonetheless, the example here can be
used to show that essential distributivity is required for long-form reflexives. This fact
becomes useful for cases where it seems that a group interpretation is intended, such as
in the following.
(5.17) The collaborators praised themselves
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One could imagine (5.17) being used to describe a situation where the praising was about
the collaboration, and not at any point about any singular collaborator. In other words,
each collaborator praised the collection of collaborators. One may then go on to use ex-
amples like (5.17) to argue that this is a use of reflexives that goes against the general
inference pattern in (5.1). A counterargument could then take the form that even cases
like (5.17) are an instance of essential distributivity: by praising a collection that contains
yourself, you are still considered to be praising yourself. The counterargument becomes
more convincing with the rockstar example: there, there is no question about whether
the rockstar stands in the love relation to himself, it is given as a premise that each rock-
star hates himself. In this way, the situation accompanying (5.15) counts as a “purely”
collective situation in a way the situation accompanying (5.17) does not. One claiming
that plural reflexives have a collective interpretation based on (5.17) must then provide an
explanation for why that interpretation is missing in (5.15). I offer the alternative account
that English-type plural reflexives are essentially distributive, even (5.17) counts as a case
of this, and the rockstar example is then predicted to be false.
5.3 Heim and Kratzer (1998) on reflexives
Before giving my analysis of plural reflexive semantics, I present a well-known
textbook treatment. I will show that this analysis, together with standard mereological as-
sumptions, provides a good account of cumulative reflexives, but falls short in explaining
the behavior of essentially distributive reflexives.
Heim and Kratzer (1998) treat reflexives like other indexed expressions in their
system; e.g., pronouns and traces. The indexed expression receives its semantic value
from an assignment function g. As a way of extending this system for plurality, assume
that both atomic and sum values in the domain are indexed; for example, index g(3) could
have the value b⊕ c, the plurality consisting of Brutus and Caesar. If this is the case, the
semantic value of Brutus and Caesar loved themselves could be given as (5.18) in Heim
167
and Kratzer’s system. Recall that Heim and Kratzer use a non-Davidsonian approach to
argumenthood, hence the lack of event variable and thematic roles below.
(5.18) ![Brutus and Caesar]3 love themselves3"g = LOVE(b⊕ c, b⊕ c)
Applying another standard assumption, let us take it that the relation LOVE in (5.18) is
cumulative. As such, there are several types of models that could satisfy the truth condi-
tions in (5.18): (i) a model M1 where LOVE(b, b) and LOVE(c, c), (ii) a model M2 where
LOVE(b, c) and LOVE(c, b), and (iii) a model M3 where LOVE(c, b⊕b) and LOVE(c, b⊕c).
Of course there can be models where the more than one of these states of affairs can hold
at once, but the important point here is that the denotation of LOVE in the basic three
models mentioned above will make (5.18) true under the assumption that LOVE is closed
under sum formation.
In prose, M1 corresponds to the situation where Brutus loves Brutus, Caesar loves
Caesar, and no other loving is taking place; call this a reflexive situation. M2 corresponds
to the situation where Brutus loves Caesar, Caesar loves Brutus, and no other loving
is taking place; call this a reciprocal situation. Finally, M3 corresponds to the situation
where Brutus loves the plurality containing him and Caesar, and Caesar loves the plurality
containing him and Brutus; call this a collective situation1.
Coupling a standard approach to the semantics of reflexives together with a standard
assumption about nominal denotation in mereological approaches to plurality, we predict
that the English sentence in (5.18) should be true in any of the three situations mentioned
above. As I have shown in the previous two sub-sections, these predictions are not borne
out for English type reflexives, and arguably the long-form reflexives in languages that
make the long/short distinction. Sentences with these forms can only be true relative to
reflexive models like M1, and not (purely) reciprocal or collective models. On the other
1Depending on the details in whatever system of plurality one is using, further qualifications on the
model might be needed for characterizing the collective situation. For example, in Landman’s system
with Groups (Landman (1989a)), Landman (1989b), Landman (2000)) the relevant collective interpretation
would be given with the ↑ operator: LOVE(b, ↑ (b ⊕ c)) and LOVE(c, ↑ (b ⊕ c))
168
hand, short-form variants of the sentence in (5.18) have been argued to allow truth in
all three situations. Indeed, one way of analyzing this is that short form reflexives are
the sort of indexed elements that Heim and Kratzer are addressing. Their ability to be
used to describe the range of situations mentioned above is attributed to the closure of
the verbal predicate under sum-formation. In other words, the sentence in (5.18) should
have the same range of meanings as other transitive sentences with two plural argument
nominals; see Chapter 2. It is for this reason that I call such reflexives “cumulative”: they
are consistent with the same range of models that would make non-reflexive cumulative
sentences true.
The question now is, why are long-form reflexives different? There has to be some-
thing beyond the standard structures assumed by Heim and Kratzer that accounts for their
essentially distributive nature. I will now turn to an analysis of long-form reflexives that
accounts for their essential distributivity, applying the Taylor-Schein approach yet again.
5.4 A Taylor-Schein analysis of long-form reflexives
One way of accounting for the semantic properties of plural reflexives is to treat
them as another sort of distance distributivity construction. My proposal for this is to
posit a silent distributivity operator that attaches to the argument nominal in the position
where the plural reflexive resides. While reciprocals were proposed to involve an element
like binominal each attaching to a Differentiator host, the proposal here is parallel, where
instead of the host each composing with an other morpheme, it composes with a self
morpheme.
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(5.19) Proposed syntactic decomposition of plural reflexives
PP
ΘANT
each XANT
PP
PΘ SELF
In Chapter 4, an almost identical decomposition is given for reciprocals in (4.58). Again,
the only difference between the two LFs is the host nominal of distributivity operator:
for reciprocals, the host is [...other...], and for reflexives the host is [...self...]. There is
also the difference that for reflexives, at least in English type languages, the distributivity
operator is always covert, while this is not the case with reciprocals. I will return to this
issue shortly.
The LF of the sentence (5.7) given the proposed decomposition of reflexives is
represented as follows.
(5.20) a. Brutus and Caesar kicked themselves
b. [Brutus and Caesar]i kicked [each Xi [SELF]]
I will treat the semantic contribution of the abstract SELF morpheme as a vari-
able bound by each. As such, the truth conditions for (5.7) given the proposed syntactic
decomposition of reflexives together with the proposals from previous chapters are as
follows2.
(5.21) ∃E[AGENT(E, b⊕ c) & KICK(E) & ∀x ≤ b⊕ c[∃E ′ ≤
E[AGENT(E ′, x) & THEME(E ′, x)]]]
2Note that this treatment is sufficient for singular reflexive constructions as well. The distributivity
operator quantifies over all x that are part-of the antecedent value. Because the part-of relation is reflexive
(for all a, a ≤ a), the antecedent value can be singular and the truth conditions will be appropriate for
singular cases.
170
In prose, this says that there are events of kicking E with Brutus and Caesar as agents,
and for each of Brutus and Caesar, there are sub-events of E where he is both the agent
and the theme of those sub-events.
Cable (2014) offers a similar proposal for essentially distributive reflexives, where
he argues for a VP adjoined D operator. For him, this operator is only licensed under
certain conditions involving focus. I will not address the focus issues here; indeed, it
may be the case that the D operator I propose here, though it differs in syntactic position
from Cable’s D operator in reflexive construction, might be licensed by the same sort
of focus considerations. This would account for the alleged ability of English-type re-
flexives to sometime not have their typical distributive character. My point of contention
with Cable is not whether the D operator is always involved with English-type reflexives
and whether focus is responsible for its appearance; rather, I wish to argue against his
proposed location of the D operator.
There are some attractive features of Cable’s account that can be carried over to
the present one. Perhaps most interesting are Cable’s claims about the optionality of the
D operator in reflexive constructions. He observed that in some limited circumstances
(which I will not explore here), English plural reflexives can be interpreted as cumula-
tive reflexives. This means that the observed essential distributivity is not a hard-and-fast
property of reflexive interpretation, even though it may represent a preferred interpre-
tation. Again, my point of disagreement with Cable is in the position of the silent D
operator in reflexive constructions; I leave open the possibility that Cable’s focus-based
semantics can be used to determine which contexts allow the D operator to appear or not
in reflexive sentences.3
Cable essentially treats the D operator in reflexive constructions as the silent ele-
ment that authors like Link (1987) and Schwarzschild (1996) used when accounting for
3A point of similarity between the two accounts is that neither Cable nor I provide an explanation
for why the plural reflexive, at least in English, has plural morphology. I take this to be some type of
morphosyntactic agreement process that does not have an effect on the semantics. See the previous footnote
for how singular reflexives are handled in the present account.
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the distributive construals of some sentences (see Chapter 2). This claim is on par with
what I have observed about floating quantifiers: because D is attached to the VP, it takes
scope over the entire VP. Regardless of any particular implementation of the D operator,
this has the result of attributing a property associated with the entire VP’s meaning to each
individual in the subjects denotation. I offer two counterarguments to this general idea.
First, there are cases where the VP contains elements that do not describe the action of
each member in the antecedent plurality, but those members as a collection. Second, there
are cases where the antecedent to the reflexive is contained within the VP, in which case
a VP adjoined D operator is in a sense “too high” to provide appropriate truth conditions
for the sentence.
5.4.1 A scope argument for a local D operator
Consider first ditransitive sentences that contain a singular indefinite together with
a plural reflexive within the VP.
(5.22) The students introduced themselves to a professor
According the Principle of Covarying Indefinites from Chapter 3, an indefinite within the
scope of a distributivity operator should be able to covary with the individuals distribu-
tively quantified over. However, there is no such reading of (5.22); this sentence can only
be true if there was a single professor that they introduced themselves to. The point is
made more precise when the indefinite is modified by different.
(5.23) The students introduced themselves to a different professor
This sentence cannot mean that the professor that one student introduced himself to is dif-
ferent from that of another student. Indeed, difference in (5.23) can only be with regards
to another professor mentioned within the discourse; for example: The parents intro-
duced themselves to one professor, and the students introduced themselves to a different
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professor. Compare this to a case where different is clearly within the scope of a distribu-
tivity operator (e.g., a distributive subject), and as such difference can be determined with
regards to the individuals distributively quantified over.
(5.24) Each of the students introduced himself to a different professor
The lack of covariance is unexplained under Cable’s proposal of a VP-adjoined D oper-
ator; which could scope over the indefinite contained within the VP. Under the account
proposed here, the lack of covariance is explained by having the D operator have a very
limited scope: it scopes only over the self morpheme in the direct object position, and the
indefinite is then not within the scope of the D operator.
5.4.2 An antecedence argument for a local D operator
Another argument against a VP adjoined D operator for plural reflexive sentences
comes from cases where the subject is not the antecedent of the reflexive. Cable (2014)
only considers transitive sentences, where the only possible antecedent is the subject, and
so there is no harm in positing the VP-adjoinedD operator. However, that analysis cannot
explain cases like (5.25).
(5.25) God showed us to ourselves
The VP adjoined operator here does nothing to explain the distributive interpretation of
reflexives occurring within the VP.
The problem cannot be escaped by assuming QR of the antecedent plurality, and
then attaching the D operator to its derived sister. Consider first a variant of (5.25) with a
bare plural subject.
(5.26) a. Gods showed us to ourselves
b. QR LF: [Usi [D [gods showed ti to ourselves]]]
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Like other dependent plural sentences, (5.26a) can be true if for each x of us, a single god
showed x to itself. However, the LF (5.26b) suggests that a plurality of gods were shown
to each individual, since bare plurals take obligatory low scope with respect to operators
such as D; see Carlson (1977), for example.
Similarly, if Gods in (5.26a) were replaced with A god as in (5.27a), then there
should be a covariance interpretation since the subject would be in the scope of the D
operator according to an LF like (5.26b) , but no such interpretation exists.
(5.27) a. A god showed us to ourselves
b. QR LF: [Usi [D [a god showed ti to ourselves]]]
We have a further argument for a local D operator, one that can scope over only
certain parts of the VP and not others. In this case, the present account would have the D
operator attaching to the indirect object as its host, and its antecedent would be the direct
object. This gives us appropriate truth conditions without appealing to QR.
(5.28) ∃E[AGENT(E, g) & SHOW(E) & THEME(E,us) &
∀x ≤ us[∃E ′ ≤ E[THEME(E ′, x) & GOAL(E ′, x)]]]
5.4.3 Advantages over polyadic quantification approaches to reflexives
As with reciprocals, there have been accounts of reflexives that treat them as higher-
order functions, or polyadic quantifiers; see discussion in previous chapter. One of the ear-
liest polyadic analysis of reflexives is Szabolcsi (1989); working within the CCG frame-
work, she models the semantics of the reflexive anaphor off of the W-combinator from
combinatory logic. The claim is that the reflexive takes a relational argument and then in
effect duplicates the value of the reflexive’s antecedent.
(5.29) !REFL" = λR.λX.R(X,X)
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One of the benefits of this analysis is that it incorporates the content of Principle A into
the semantics of the reflexive: the second argument to the reflexive will be its antecedent,
and it follows from this that this argument will always be a higher coargument in the same
clause as the reflexive.
The problem with this approach is the same as with treating reciprocals as polyadic
functions: the definition in (5.29) only works for reflexives that are in direct object posi-
tion, though reflexives can appear in more argument positions than this. Büring (2005)
p. 43-45, offers many cases that are problematic for this approach to reflexives. Below
I provide “pluralized” versions of Büring’s examples. For one, there are cases where the
antecedent to the reflexive is not the next highest coargument of the relation.
(5.30) They introduced God to themselves
Furthermore, there are cases where the reflexive and its antecedent are not coarguments
at all. Compare with nominal-internal reciprocals from the previous chapter.
(5.31) The CEOs despised those recent articles about themselves
A very difficult case that Büring points out concerns reflexives coordinated with another
nominal, such as the following example from his p. 44, fn 10.
(5.32) Polsen painted pictures of himself and Mary
As he observes, the problem is even more severe on the non-distributive reading of (5.32),
where a single picture contains images of both Polsen and Mary.
An advocate of the polyadic approach may respond by saying that it is possible
to assign polyadic types to reflexives in these argument positions, and that reflexives are
ambiguous in as many ways as there are argument positions in which they can licitly ap-
pear. However, as Büring states and as was pointed out in the last chapter, advocates of
such a view must provide a way to constrain such an ambiguity. A further challenge is to
explain the conjunction data (5.32). Virtually all views on the semantics of conjunction
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(and especially the CCG theory that Szabolcsi assumed) have it that both conjuncts have
the same type. This means that whatever complicated higher-order type is given to the
reflexive in (5.32), the simple proper name Mary must also be given the same type; and it
follows further that simple proper names must then be as many ways ambiguous as reflex-
ives when they appear conjoined with them. Given the massive amounts of ambiguity or
type-shifting involved in this approach, which to the best of my knowledge has not been
shown to be constrained in any way, an alternative should be sought. The Taylor-Schein
approach which I provide does not require different semantic types for reflexives; just
referential and thematic role values that are determined by its antecedent.
On a different note, polyadic treatments of reflexives also need to take into account
essentially distributive reflexives. While (5.29) will work for cumulative reflexives4, it
requires non-trivial modifications to account for essentially distributive reflexives. While
it might seem that simply applying a D operator after the reflexive composes with its
relation argument, see the previous two sections for reasons why this strategy cannot
extend to more complicated sentences beyond simple transitives.
5.4.4 A unified analysis of local plural anaphora
This has been a relatively short chapter, but not without reason. I have argued that
the case of essentially distributive plural reflexives is but another instance where Taylor-
Schein distributivity provides a simple explanation. Again, we see that that Taylor-Schein
approach works just as easily when we move beyond simple transitive constructions, and
again provides a superior account to competing analyses when the empirical explananda
is extended thusly.
As such, the chapter summary here will take on a different form from previous
chapters. Now that we have seen sum of local plural anaphoric phenomena I will discuss
4Büring notes that there are some languages where a polyadic analysis of reflexives might work. In
these languages, the reflexive marker appears as a verbal affix, not as an anaphor that may occupy various
argument positions. A similar story might also be applicable to clitic reflexives in Romance and Slavic, and
further might be used to explain their cumulative behavior in plural sentences.
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in this dissertation, we can now reflect on what the similarities and differences among
these constructions mean for theories of grammar and meaning.
The main proposal from these last three chapters is about the distributivity operator
D, often realized overtly as each and its equivalents in other languages. I have pursed
the route of morpheme univocality, arguing that the semantic value of D is the same
regardless of where it appears. It always has the same type, and always performs the
same operation with its arguments. This includes in-situ determiner uses of each and also
cases of distance distributivity.
What I have done in the last two chapters is argue that local anaphors, reciprocals
and reflexives, are but another type of distance distributivity construction. I have argued
that both anaphors share an important property with binominal each, namely that they
are all constructions where the Taylor-Schein D operator attaches directly to a nominal
expression. This is made possible by the separationist assumption that nominals are in-
terpreted as thematic predicates. A question that I have left unexplored is why there are
only certain types of nominals that D can attach directly to. Under the present account,
this includes the numeric nominals that binominal each attaches to, the Differentiator in
bipartite argument reciprocals, and the abstract self morpheme in essentially distributive
reflexives. While this treatment raises the question of which nominals can act as appro-
priate hosts for D, one of the benefits is that provides a way of stating the duality of
reflexives and reciprocals. Under the present approach, both have the same underlying
structure, and differ only by whether the host nominal is, abstractly, OTHER and SELF.
(5.33) Reciprocal LF: PP
ΘANT
each XANT
PP
PΘ OTHER
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(5.34) Reflexive LF: PP
ΘANT
each XANT
PP
PΘ SELF
As a final remark, all of the constructions I have looked at so far are local anaphoric
phenomena in the sense that their semantic values are dependent on an antecedent ex-
pression contained in the same local domain. Now, consider my proposal that all of these
phenomena involve the same element, a distance D operator. This opens the way for the
novel syntactic hypothesis that the locality of canonical distance distributivity construc-
tions and canonical cases of local anaphora can be reduced to one another. In a sense, all
of these constructions are distance distributivity. The hypothesis then, which I leave to
future syntactic research, is that whatever syntactic operation is responsible for “floating”
of the D operator explains the locality of these constructions: Principle A can then be
explained away by whatever principles govern such quantifier movement.
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Chapter 6: Plurality and De Se reports
6.1 Introduction
The previous chapters focused on anaphors that exhibit an obligatory referential
dependency with a local plural antecedent. In this chapter, I will turn attention to a type of
plural anaphor that does not have to be locally licensed, but still is obligatorily dependent
on a grammatical antecedent. This is the case of the plural De Se pronoun. I will focus
on the semantics of sentences like (6.1) where PRO, a De Se pronoun, is anteceded by a
plural attitude holder nominal.
(6.1) Obama and Romney want PRO to win
Intentionality phenomena such as propositional attitude reports have provided a
wealth of problems for a proper treatment of meaning in natural language. Within this
domain, the issue of De Se attitudes ascription, or essential indexicality, deepens the
challenge. Linguists and philosophers have developed several approaches to the seman-
tics of De Se attitude reports, and indexicality in general; however, there is very little
discussion of cases of plural attitude ascription. Below I present a case study on obliga-
tory De Se ascription to a plurality of individuals. I start with an overview of the relevant
data, reviewing previous insights on plurality in attitude reports and also introducing De
Se phenomena in different languages. I will draw attention to the distinction between
obligatory and optional De Se reports, and why my focus here is primarily about the for-
mer. I then turn to arguments about the essential plurality of De Se pronouns, where I will
address problematic issues from majority of previous approaches that treat bound plural
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pronouns in attitude reports as semantically singular. Lastly, I will develop a semantics of
plural De Se pronouns by modifying existing accounts of the semantics of attitude reports
and indexicality. I will show that the general notion of distributivity is in a sense funda-
mental to the semantics of plural De Se reports, but not in the way that previous accounts
have suggested.
6.2 Empirical overview
Higginbotham (1981) observed that sentences like (6.2a) can be used to ascribe two
different types of attitudes to the plurality of attitude holders, Obama and Romney. Since
then many have taken this to indicate that such sentences are ambiguous between a group
reading (6.2b) and a dependent reading (6.2c).
(6.2) a. Obama and Romney think that they will win the election
b. Group: Each of Obama and Romney think: “Obama and Romney will win”
c. Dependent: Each of Obama and Romney think: “I am going to win”
While authors have argued about the source of such an ambiguity, one idea seems to be
prevalent: for at least the dependent reading, the semantic value of the embedded pronoun
is treated as semantically singular. This provides an explanation for why the dependent
readings report attitudes about a singular individual1.
Heim et al. (1991b) observed that the availability of dependent readings is deter-
mined by the presence of a pronoun in the embedded clause that is referentially dependent
on the attitude holder nominal2. Beck and Sauerland (2000) give the following example
1See Stechow (2003), Maier (2006), Schlenker (2012), among others. A notable exception is Rullmann
(2004), Rullmann (2008) who argues for uniform semantically plural pronouns for finite reports that op-
tionally report a De Se attitude.
2That dependent readings require a referentially dependent pronoun in the embedded context is evi-
denced by replacing Bill in (6.3) with the pronoun he, resulting in a report that still lacks a dependent
reading:
(i.) Max and Peter said that heb will marry Ann and Amy (*respectively)
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that shows that without a pronoun it is impossible to bring about the dependent reading
even with the help of respectively.
(6.3) Max and Peter said that Bill married Ann and Amy (*respectively)
The relevant unavailable interpretation of (6.3) is one where Max said that Bill will marry
Ann, and Peter said that Bill will marry Amy. (6.3) only has the interpretation where each
of Max and Peter said the same thing: that Bill will marry two women, Ann and Amy.
The paraphrase in (6.2c) indicates another important property of dependent read-
ings, namely that each attitude holder holds an attitude about himself. As others have
noticed, there does not seem to be a “crossed” reading of (6.2a), where Obama thinks
only Romney will win, and Romney thinks only Obama will win3. These facts suggest
that the dependent reading of plural reports cannot be characterized simply as cumulation
between attitude holders and the contents of embedded clauses (see Dimitriadis (2000)
on this point). Rather, the proper generalization for dependent readings seems to be that
they report about a plurality of self-directed attitudes.
De Se reports are another, perhaps related, phenomena concerning self-directed
attitudes. One has a De Se attitude about oneself in a way that it is impossible to be
mistaken as to who the self is; see for example Lewis (1979) and Perry (1979) . In the
terminology of the philosophy literature, I will label this crucial feature of De Se attitudes
as the property of immunity to error through misidentification4.
Furthermore, this may be tied to the further condition that the pronoun be read De Se. Since I focus on
obligatory De Se reports, and these issues are specifically about optional De Se reports, I leave them to
future research.
3The observation that crossed readings do not exist has been made by Higginbotham (1981) and
Heim et al. (1991b). Dotlacˇil (2010) suggests that such readings might be available for sentences that
express reciprocity in the embedded clause, though the previously mentioned authors say that such read-
ings are impossible even then. Based on my own intuitions about the meanings of such sentences, I am
inclined to agree with Higginbotham and Heim et al. that crossed readings are always disallowed.
4Recanati (2012) distinguishes between different types of De Se attitudes, what he calls implicit and
explicit De Se. According to him, it is implicit De Se attitudes that are immune to error through misiden-
tification. I assume that obligatory De Se reports report on implicit De Se attitudes based on the truth of
sentences in contexts like (6.4) in the main text.
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Some types of attitude reports in natural language obligatorily report De Se at-
titudes, such as subject control constructions in English and Italian (Morgan (1970),
Chierchia (1989)). The truth of a De Se report depends not only on whether an individual
has a self-directed attitude, but also whether that attitude has the property of immunity
to error through misidentification. In a situation where just the former condition is met
(6.4a), the obligatory De Se report (6.4b) is false. For comparison, I provide an attitude
report with a finite embedded clause (6.4c), which has been known to optionally report
De Se attitudes. Accordingly, in situation (6.4a), (6.4c) can be true even though (6.4b)
cannot.
(6.4) From Schlenker (2012), p. 1573:
a. John is so drunk that he has forgotten that he is a candidate in the election.
He watches someone on TV and finds that person is a terrific candidate, who
should definitely be elected. Unbeknownst to John, the candidate he is
watching on TV is John himself.
b. False: John hopes PRO to be elected
c. True: John hopes that he will be elected
Another type of obligatory De Se report are those that involve shifted indexicals
(Schlenker (1999), Anand (2006)). In languages like Amharic, a first-person indexical
pronoun in certain attitude reports can have its reference determined by the attitude holder
noun phrase instead of the speaker of the report, as in (6.5) from Schlenker (2003). When
this happens, the indexical must be read De Se.5
(6.5) jˇon
John
jˇ@gna
hero
n@-ññ
be.PF-1SO
y1l-all
3M.say-AUX.3M
“John says that he himself is a hero”
5The English translation in (6.5) includes the phrase he himself to indicate that this is an obligatory
De Se report. See Higginbotham (2003) and references within for the De Se properties of he himself in
English.
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Some authors have suggested that what sets obligatory De Se reports apart from
other attitude reports is the presence of a special pronominal element in the embed-
ded clause; see Schlenker (2012) for discussion and references. We have already seen
that PRO and shifted indexicals are associated with obligatory De Se reports; others
have suggested that logophors also fit into this category (for example, Clements (1975),
Hyman and Comrie (1981), Schlenker (2012)). Below is a speech report in Ewe (data
from Clements (1975)) with the logophoric pronoun yè. As Clements and Schlenker
note, yè must refer to the attitude holder and it must be read De Se.
(6.6) kofi
Kofi
be
say
yè-dzo
LOG-leave
“Kofi said that he (= Kofi) left’
The existence of special pronominal forms such as PRO, shifted indexicals, and logophors
opens up the possibility for a strong hypothesis that all of these “De Se pronouns” have
the same or very similar lexical semantics6. I will adopt this hypothesis throughout this
chapter, because as we will see, at least English PRO and Amharic shifted indexicals
behave the same with respect to plurality.
I now turn to the main empirical focus of this chapter, one that has received little
attention in the literature: the behavior of obligatory De Se reports with plural attitude
holder noun phrases such as (6.1). These reports too have dependent readings. In fact
some authors such as Higginbotham (1981) and Heim et al. (1991b) take it that for control
constructions like (6.7), the dependent reading is the only one available. Their evidence
for this comes from sentences that involve a reciprocal in the embedded clause.
(6.7) They want to visit each other
It may be that (6.7) may strongly favor a dependent construal where each attitude holder
simply wants to visit others, with no desires about people visiting him. However, I do not
6Though see especially Anand (2006) who argues for different ways of deriving De Se interpretations
for these different constructions.
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think that it should be false if a group reading was intended; e.g., a reading where each
attitude holder wants to visit and be visited by other attitude holders. It may be the case
that a report is true under the dependent construal if there are self-directed attitudes, but
not if and only if there are self-directed attitudes. This suggests another way to look at
the group/dependent contrast: there is no ambiguity, but truth conditions that are general
enough to allow for both group and dependent readings. I will return to the hypothesis
in §5. Although, regardless of how group readings factor into the theory, the existence of
dependence readings by itself poses interesting questions for semantic theorizing, a fact
that will drive much of the discussion in this chapter.
It can be shown, with suitable conversational situations, that the dependent constru-
als of plural De Se reports require that each singular attitude holder holds a De Se attitude
about himself. This means that at the very least, each attitude holder has a thought about
himself that is immune to error through misidentification. To see this, consider (6.1)
spoken in a situation where there is an identification error (6.8a). Here the report (6.1),
repeated below as (6.8b), is judged false.
(6.8) a. Situation: Each candidate is regretting his decision to enter the election.
Each feels that another individual would do better in his place, and so each
desires that he himself will lose and that another will win instead. While
wallowing in despair at the prospect of winning something they don’t want,
each candidate is in his respective hotel room drinking heavily. At the same
time, they are watching past debates looking for another candidate to replace
them, and each candidate finds such a person and exclaims “I want him to
win”. Little do they know, each candidate is talking about himself.
b. False: Obama and Romney want to win
In Amharic, plural reports with plural shifted indexicals can have a dependent read-
ing, on par with the English (6.1). The sentence (6.9) can be true if each candidate said “I
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will win” even though the embedded clause has the form “We will win”; see LaTerza et
al. (2013).
(6.9) atS’u-wotStS-u
candidate-PL-DEF
1nn1-Sänf-all-än
1PL-win.IPFV-AUX-1PL
al-u
say.PFV-3PL
‘The candidates said we will win’
This parallel between the two languages is expected if shifted indexicals and PRO are part
of a natural class of De Se pronouns with the same or similar lexical semantics.
As discussed above in connection to group readings, each individual in a plurality
of attitude holders may hold attitudes about other individuals as well. However, for oblig-
atory De Se reports the attitude holder’s thoughts about other individuals are susceptible
to identity errors. For example, suppose each of Obama and Romney mistake the other
for their respective vice presidential running mates. In such a situation, (6.1), repeated
below as (6.10) can be true under the group construal where Obama wants himself and
Romney to win, and Romney wants himself and Obama to win; however, neither candi-
date knows that the other person he wants to win is actually his opponent. This might be
expected, since the immunity property of De Se attitudes concerns an individual attitude
holder’s thoughts about himself; thoughts that are about other individuals are not immune
to identity errors.
(6.10) Obama and Romney want to win
Concerning optional De Se reports like English (6.2a), repeated below as (6.11) it
could be the case that the dependent construal implies that each individual has a De Se
attitude about himself.
(6.11) Obama and Romney think that they will win the election
Many English speakers find that the report (6.11) cannot be true in the mistaken identity
situation described above in (6.8a). This invites the novel hypothesis that all dependent
185
readings are De Se. I will not however pursue this here, since optional De Se reports
present some complications that do not exist for obligatory reports7. Furthermore, it is
not clear that the De Se properties of optional and obligatory reports are derived in the
same way; see Anand (2006). Therefore, in this paper I will limit the focus to obligatory
De Se reports, though I hope the discussion here will be insightful for future work on
optional De Se reports.
The existence of dependent readings and the obligatory De Se nature of reports
like (6.1) provide good reasons for treating the embedded De Se pronoun as semanti-
cally singular. Nonetheless, I will argue in the next section for treating such pronouns as
semantically plural.
6.3 Arguments for plural De Se pronouns
To argue for the plurality of De Se pronouns like subject controlled PRO in sen-
tences like our parade case (6.1), repeated below as (6.12) I will present a “singularist”
strategy for interpreting plural De Se reports with which the plural alternative presented
in later sections can be compared. Under this singularist view, PRO is treated as a singu-
lar variable bound by a (possibly covert) universal operator that scopes above the attitude
7For example, we have seen that dependent readings surface at least in cases where there is an embedded
pronoun that is referentially dependent with the attitude holder nominal. Dimitriadis (2000) has suggested
that dependent readings can also arise when the pronoun’s reference is determined by a noun phrase other
than the attitude holder nominal as in (i).
i. The lawyers who represent John and Mary think they will sue each other
(Dimitriadis (2000), p. 58)
However, similar constructions to (i), such as (ii), seem to resist a dependent reading where the embedded
pronoun is referentially dependent on some noun phrase that is not the attitude holder nominal.
ii. The people that listen to Debussey and Saint-Saens think that they are brilliant (#although Debussey
fans think Saint-Saens is not brilliant, and vice versa for Saint-Saens fans)
This issue does not arise for obligatory De Se reports, where the value of the De Se pronoun is always
determined by the attitude holder nominal This observation has been made by syntacticians for subject
control constructions; see Chomsky (1981) and references within. Since the focus here is on obligatory De
Se reports, we will only be dealing with cases where the value of the embedded pronoun is determined by
the attitude holder nominal.
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verb (6.13). Although there has been no previous accounts (at least that I am aware of) that
explicitly address obligatory plural De Se reports in this manner, the approach has been
suggested by Maier (2006) and others to account for the dependent readings of optional
De Se reports like (6.2a).
(6.12) Obama and Romney want to win
(6.13) Singularist truth conditions for (6.12):
∀x : x ∈ {Obama,Romney}[x wants x to win]
I am putting aside the De Se and other intentionality properties of the report for the time
being, and so (6.13) is simplified to not express anything about De Se content. The reason
for this is that the arguments in this section focus on the singular nature of the variable
associated with PRO, not about its intentionality properties. In later sections I will return
to the De Se properties of these reports and show how they can be integrated into the
semantics given the results from this section.
Having said that, I think that it is important to at least recognize that the De Se prop-
erties of sentences like (6.12) provide some initial motivation for a singularist account.
De Se attitudes are about an attitude holder’s self, and I take this to be a fundamentally
singular notion. If we take PRO and other De Se pronouns to be the locus of De Se infor-
mation, then it is plausible that these pronouns should be treated as semantically singular.
Furthermore, these reports allow dependent readings, which are characterized as report-
ing the attitudes about a singular individual. This provides further support for singularist
truth conditions like (6.13).
Despite these reasons, I will argue that the semantic value of PRO is alway plural
when anteceded by a plural noun phrase8. The argument for a plural PRO comes from
8The semantic value of PRO may be plural in other cases as well. For example, in partial control
constructions like (i); see Landau (2001) for further data and discussion. It has been suggested that PRO in
such examples refers to its controller plus some contextually salient others.
i. John wants PRO to meet at 6
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plural De Se reports where the embedded clause expresses cumulativity or reciprocity.
These phenomena have been argued to require the presence of a local plural noun phrase.
In the cases that interest us, only PRO can fit this role; and therefore since these construc-
tions are well-formed, then PRO must be plural. For each of these phenomena I will also
consider salient alternative analyses that account for their respective phenomena without
a semantically plural PRO (and if not PRO, then an overt plural pronoun when English
optional De Se cases are considered). I will then present counterarguments for each of
these alternatives from the literature arguing that they are empirically inadequate, sup-
porting the conclusion that reciprocity and cumulativity are licensed in a clause when that
clause also contains another noun phrase that is plural and sufficiently local.
Before turning to the arguments proper, which are semantic in nature, I will discuss
some reasons for thinking that PRO is morphologically plural in plural De Se reports.
Since PRO is silent, its morphological plurality has to be diagnosed from other elements
in the sentence9. The clearest evidence of this type comes from languages with inflective
infinitives such as Brazilian Portuguese, where the verb with PRO as its subject shows
plural agreement (data from Carolina Petersen, p.c.).
(6.14) Obama
Obama
e
and
Romney
Romney
temem
fear
PRO
PRO
terem
have.PL
perdido
lose
a
the
eleic
"
ão
election
“Obama and Romney are afraid that they will lose the election”
However, these such reports have been known to resist reciprocity and cumulativity in the embedded clause;
(ii) is unacceptable, and (iii) lacks a reading where John wants to kiss onlyMary and for some relevant other
to kiss Sue; it can only have the distributive meaning where John wants to kiss both Mary and Sue.
ii. *John wants PRO to meet each other
iii. John wants PRO to kiss Mary and Sue
These data call into question whether the PRO in partial control constructions is semantically plural in the
same way as the PRO in the cases that interest us here where the attitude holder noun phrase (i.e., the
controller) is semantically plural. Since my focus here is only on the latter construction, I will leave issue
of the semantic plurality of partially controlled PRO for future research.
9The morphological plurality of other De Se pronouns like Amharic plural shifted indexicals is obvious;
the suffixed pronominal elements are plural, and the verb to which they affix shows plural agreement.
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While there may be reasons to treat PRO as morphologically plural, this does not
entail that it has to be semantically plural. Semanticists have posited rules like (6.15)
that essentially remove the morphological φ-features, including number, from a bound
pronoun; see Stechow (2003), Maier (2006), and Heim (2008)10.
(6.15) FEATURE DELETION
Delete the features of all variables that are bound
(Stechow (2003), via Anand (2006))
This rule has been used as a way to explain dependent readings despite the pres-
ence of a plural pronoun by treating the morphologically plural pronoun as semantically
singular. The arguments that I turn to now are of a different sort. I will use essentially
plural phenomena as diagnostics for semantic plurality. In particular, I draw on leading
ideas from the semantics of cumulativity and reciprocity that strongly suggest that PRO
must be semantically plural. One of the consequences of PRO being plural is that we can
abandon rules like (6.15), at least as far as number φ-features go, and treat morphologi-
cally plural pronouns as semantically plural. The thesis pursued here can be viewed as a
null-hypothesis, where morphological and semantic plurality go hand in hand.
6.3.1 Cumulativity
Cumulative interpretations of plural sentences were first observed in the semantics
literature by Scha (1984), and are characterized by having parts of one plurality related to
parts of another but not exhaustively. Consider the following sentence which has a clear
cumulative interpretation11.
10It is assumed in Feature Deletion accounts that the removal of φ-features corresponds to a singular
semantic value. It is not clear that this is a necessity of the system: several authors working on plurality
and mass semantics have suggested that the bare variable, without any number features, is number neutral.
See Schein (1993) and others. Thus, it may be that there are conceptual problems with the formulation of
Feature Deletion, aside from the empirical problems I raise in the main text.
11Beck and Sauerland (2000), p.350, use the phrase “cumulative interpretation” to refer to “...all cases
where a sentence containing two plurals has truth conditionsweaker than those of a doubly distributive para-
189
(6.16) Obama and Romney danced with Michelle and Ann
This sentence can be true if each candidate danced with his own wife and no one else;
Obama only danced with Michelle, and Romney only danced with Ann. This is the cu-
mulative interpretation of (6.16). Crucial for our purposes is that the meaning of (6.16)
does not require that each of Obama and Romney have the property of dancing with both
Michelle and Ann; see Chapter 2 for further discussion and references.
When (6.16) is embedded in a plural De Se report like (6.17), the result allows a de-
pendent reading where Obama wants to dance only with Michelle, and Romney only with
Ann. For the sake of making the dependent reading clear, assume that neither candidate
has any desires about the other candidate dancing.
(6.17) Obama and Romney want to dance with Michelle and Ann
Assuming the singularist truth condition strategy (6.13), (6.17) would be assigned
truth conditions like (6.18).
(6.18) ∀x : x ∈ {Obama,Romney}[x wants x to dance with Michelle and Ann]
This says that each of Obama and Romney want to dance with both Michelle and Ann,
which predicts that (6.17) should be false when each candidate only wants to dance with
a single woman. This prediction is not borne out, as (6.17) can be true in a cumulative
desire situation; e.g., a situation where each candidate only wants to dance with his own
wife.
Similar facts can be observed in Amharic in sentences with plural shifted indexicals.
Speakers judge (6.19) to be true in situations where each candidate said that he will only
dance with one woman; this data comes from LaTerza et al. 2013.
phrase”. This definition will suffice for most of the sentences discussed here, though see Schein (1993) and
Sternefeld (1998) for generalized notions of cumulative interpretation suitable for cases with an arbitrary
number of plural noun phrases.
190
(6.19) atS’u-wotStS-u
candidate-PL.DEF
kä-Michelle-na
with-Michelle-and
Ann
Ann
gar
with
1nn1-däns-all-än
1PL-dance.IPFV-AUX-1PL
al-u
say.PFV-3PL
‘The candidates said we will dance with Michelle and Ann’
The problem with (6.18) is the singular value associated with the De Se pronoun,
resulting in the condition that some singular candidate wants himself to dance with a
plurality of wives. If the De Se pronoun were plural in this case, these problems would
not arise since local plural values license cumulative interpretations. See Chapter 2 for the
details of how cumulative interpretations are represented in the neo-Davidsonian system.
6.3.1.1 Against non-lexical approach to cumulativity
We have seen that the basic singularist treatment of sentences like (6.17) is inade-
quate because it forces a distributive interpretation, though we have seen that cumulative
interpretations are possible. There has been one previous account of such cases that I am
aware of that is still singularist in the sense that it treats PRO as receiving a singular value,
but it is unlike (6.13) in that it does not force distributivity. This is the account given by
Beck and Sauerland (2000), which utilizes a double-star theory of cumulativity (Krifka
(1986)). Beck and Sauerland define the **-operator as follows.
(6.20) **R(X, Y ) = 1 iff ∀x ∈ X∃y ∈ Y [R(X, Y )] & ∀y ∈ Y ∃x ∈ X [R(X, Y )]
A crucial point for Beck and Sauerland’s account of cumulativity in plural De Se reports is
that the **-operator can apply not only to lexical relations (e.g., transitive verb meanings),
but also relations that are derived in the syntax. They assume that definite plural noun
phrases can Quantifier Raise and leave behind a variable that is λ-bound, and the resulting
λ-expression can host the **-operator. For (6.17), Beck and Sauerland would assign the
following LF (compare with their example (40), p. 363).
(6.21) (Obama and Romney)(Michelle and Ann) **λyλx[x wants x to dance with y]
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While the **-approach can account for the cumulative cases that interest us here
while assuming a singular PRO, it has been criticized as being empirically inadequate
for other reasons. For previous counterexamples, I refer the reader to Kratzer (2005)
objections against using *-operators to derive non-lexical cumulative relations based on
examples involving durative adverbs, and Schein (1993) for arguments against pluraliz-
ing relations in general, based on sentences that mix cumulativity and distributivity, as
discussed in Chapter 2. Below, I offer some new counterarguments based on plural De Se
reports. Consider the following example, and its LF given Beck and Sauerland’s theory
(6.22) a. Those twenty mechanics want to fix these 100 cars in one week
b. (Those twenty mechanics)(these 100 cars) **λy.λx.[x wants x to build y in
one week]
According to the **-approach, the truth of (6.22a) depends on each single mechanic want-
ing to fix at least one car this week and each car being fixed by at least one mechanic. But
one could imagine situations where this condition would not be met, yet (6.22a) would
still be judged true. For example, it might be the case that each mechanic is assigned a
specific task; e.g., rebuilding an engine, working on the electronic systems, attaching the
wheels to the axles, etc. In such a case, no single mechanic is fixing a single car, nor is
any car being fixed by a single mechanic. According to the definition of the **-operator
from (6.20), (6.22a) is incorrectly predicted to be false in this situation.
The adverbial modifier in one week presents additional problems for the **-approach.
(6.22a) can be true if what each individual mechanic wants is to do his job in less than
a week, but as a group, the twenty mechanics work to fix 100 cars in one week. Such a
situation would not verify (6.22a) since, according to the LF in (6.22b) and the definition
of the **-operator, each mechanic’s desire is to do his job in one week.
I conclude from the discussion above, as well as the counterarguments from pre-
vious literature, that the **-approach is inadequate for the so-called non-lexical cases of
192
cumulativity. However, there still seems to be a place for lexical cumulativity where the
**-operator can be of use, as suggested by Kratzer (2005). Under this view, cumulativity
arises only between plural coarguments (and possibly adpositional modifiers) of a verb
to which the **-operator has been applied. Thus, the cumulativity we see in the plural
De Se report (6.17) strongly suggests that PRO is plural since it is the only other plural
coargument of the embedded verb.
6.3.2 Reciprocity
It is standardly assumed that reciprocal anaphors must be bound by local seman-
tically12 plural antecedents (Chomsky (1981) among others). Based on ECM examples
like (6.23) and (6.24), we can see that the relevant local domain for English reciprocals
is the subject domain of the reciprocal, and not its tense domain (see Büring (2005) for
discussion).
(6.23) [The professors]i want [the students]j to praise [each other]∗i,j
(6.24) [The girls]i believed [the boys]j to have kissed [each other]∗i,j
Since each other in (6.23) and (6.24) can only take the ECM subject as its antecedent, its
binding domain must be its subject domain; if the binding domain were the reciprocal’s
tense domain, we would expect the matrix subject to also be a potential antecedent13.
12Fiengo and Lasnik (1973) offer arguments based on pluralia tantum nouns that it is not enough for the
reciprocal’s antecedent to be merely morphologically plural. This is evidenced by the unacceptability of (i)
when talking about a single pair of scissors.
i. *The scissors are connected to each other
13It should be noted that reciprocals do not require the most local potential antecedents to be their an-
tecedents. Recall from Chapter 4 that a sentence where there are multiple c-commanding NPs within the
reciprocal’s subject domain, either can be the antecedent, as shown by the ambiguity in (i):
i. [The gnomes]i put hatsj on [one another]i,j
If the subject acts as the antecedent, we have the reading where gnomes put hats on other gnomes. If the
object is the antecedent, we have the reading where the gnomes stacked up hats.
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In §2 we saw that reciprocals can be used in the embedded clause of English subject
control constructions, and that on the dependent construal of such sentences the content of
the reported attitude for each attitude holder does not have to involve reciprocated action.
For example, the sentence (6.25) does not have to mean that each candidate wants mutual
destruction, but it could express that Obama wants to destroy Romney, and Romney wants
to destroy Obama.
(6.25) Obama and Romney want PRO to destroy each other
Given that the reciprocal in (6.25) must be bound by a local plural antecedent in its subject
domain, and since (6.25) is grammatical, it follows that PRO is the local plural antecedent
of the reciprocal.
The singularist treatment from (6.13) would assign a singular value to PRO, and for
sentence (6.25) would yield the truth conditions shown in (6.26).
(6.26) ∀x : x ∈ {Obama,Romney}[x wants x to destroy each other]
Since reciprocals require semantically plural antecedents, the above truth conditions pre-
dict the same sort of infelicity for (6.25) as we see in (6.27). These predictions are not
borne out for the plural De Se report, which suggests that the singularist treatment is
inadequate for these constructions.
(6.27) *He destroyed each other
Amharic again provides support that such behavior is not limited to PRO, but sur-
faces for other De Se pronouns like shifted indexicals. In the following example, the
embedded clause with a plural shifted indexical expresses reciprocity by means of an
anaphoric infix. Similar to (6.25), (6.28) can be true if each animal said that he would kill
another and remain alive himself.
(6.28) 1nsäsa-wotStS-u
animal-PL-DEF
1nn1-ggädd1l-all-än
1PL-kill.RECIP.IPFV-AUX-1PL
al-u
say.PFV-3PL
The animals said that we will kill each other
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6.3.2.1 Against scopal theories of reciprocals
There have been accounts of embedded reciprocals that get by with only a singular
value for the embedded pronoun. The paradigm example of this approach is Heim et al.
(1991b). The central idea of their analysis is that the each of each other undergoes quan-
tifier raising and binds a singular variable associated with the embedded pronoun. Their
resulting truth conditions can be paraphrased as (6.29), which they use to account for the
dependent reading of the sentence.
(6.29) Obama and Romney each wants that he destroys the other
As the paraphrased truth conditions show, we do not need a semantically plural local an-
tecedent under this view to derive an appropriate meaning for this sentence. For Heim et al.
(1991b), the reciprocal is not a simplex anaphor requiring a semantically plural antecedent,
but a complex constituent containing a quantifier that can raise and bind a singular vari-
able associated with the canonical local antecedent.
Several objections have been raised against this analysis of reciprocals. First, there
is the direct reply to Heim et al. (1991b) given by Williams (1991). One of his counterar-
guments came from the fact that the dependent reading that Heim et al. (1991b) were try-
ing to capture with this account of reciprocals is found in constructions even when there
is no reciprocal present; we have seen several examples of this already, such as (6.1).
Correlatively, Dalrymple et al. (1994) show that there are some languages where recip-
rocal expressions are monomorphic verbal affixes, and as such, they have no distributive
component that can participate in quantifier raising as Heim et al. (1991b) suggest.
Even if one were to assume a covert distributivity operator that is available even
when an overt one is not supplied by the reciprocal, Williams shows that the resulting
truth conditions suffer from being too restrictive. Consider the following De Se report
based on Williams’s counterexample sentences which were discussed in Chapter 4.
(6.30) The plastic surgeons want to give each other new noses
195
After quantifier raising, the truth conditions for (6.30) in the system of Heim et al. (1991b)
can be paraphrased as follows.
(6.31) The plastic surgeons each wants that he gives another new noses
The crux of the argument is that (6.30) can be true if what each surgeon wants is to give
just one other surgeon exactly one new nose. According to the truth conditions in (6.31)
though, the sentence is true if and only if what each wants is to give a plurality of noses
to another doctor.14
Asudeh (1998) offers further arguments that the scopal theory of reciprocals is in-
correct. If each QRs, then we expect it to be susceptible to familiar quantifier scope
ambiguities. He shows with a variety of scope-sensitive operators that there is almost
always no wide-scope universal construals with sentences containing these operators and
reciprocals. Consider (6.32) for example.
(6.32) At the stroke of midnight, John and Mary showed a diamond ring to each other
Universal indirect objects usually can scope over indefinite direct objects (Larson (1988))
as in cases like (6.33).
(6.33) At the stroke of midnight, John and Mary showed a diamond ring to each jeweler
The sentence with the reciprocal indirect object does not have the same covariance ambi-
guity as (6.33); it can only mean that there is a single diamond ring that John and Mary
showed each other. If the reciprocal contained a universal quantifier, we expect a wide
scope universal reading where there could be several diamond rings, as in (6.33), but this
reading is missing from (6.32). Asudeh shows similar scope tests involving negation,
modals, wh-words, and ellipsis constructions that show that reciprocals do not have the
scope-taking potential one would expect if they contained universal quantifiers.
14This argument does not rely on particular assumptions about bare plurals. In fact, bare plurals are not
even necessary to make the argument; if the bare plural is replaced with a singular definite (e.g., a new car),
we still see the relevant contrast. These facts parallel those discussed in connection to scope and covariance
in Chapters 3, 4, and 5.
196
I conclude from this discussion that reciprocals do in fact require semantically plu-
ral local antecedents, as has been suggested by most of the reciprocity literature. This
provides further support that PRO must be semantically plural in plural De Se reports,
despite the apparent singularity associated with De Se attitudes and dependent readings.
6.3.3 Section summary
In this section I presented arguments for plural De Se pronouns using cumulativity
and reciprocity. For reasons independent of plural De Se reports, these phenomena have
been argued to require the presence of a local semantically plural noun phrase. In the
examples we looked at, the relevant local domain is the complement clause of the attitude
verb. In these clauses, the only suitable local noun phrase that could license these essen-
tially plural constructions is the De Se pronoun, and since the relevant interpretations are
licensed, we can conclude that these De Se pronouns are semantically plural.
I considered alternative analyses of these phenomena that treat the pronouns as
semantically singular, and presented several counterarguments to these analyses. The ar-
gument is strengthened by the fact that each alternative approach only deals with one type
of essentially plural phenomena; Beck and Sauerland (2000) say nothing about recipro-
cals, nor does Heim et al. (1991b) say anything about cumulativity or dependent plurality.
The facts when taken together suggest that the plurality of De Se pronouns in these con-
structions forms the basis of a unified analysis for these different plural phenomena, and
also supports the conclusion drawn by previous research about the relevance of locality
to these issues.
For the remainder of the chapter I develop two separate neo-Davidsonian approaches
to the semantics of De Se reports. The first approach builds on context-based approaches
to De Se interpretation; as in Schlenker (1999) and Anand (2006), for example. One of the
central properties of this approach is that attitude verbs do not have their arguments sev-
ered; they take both an embedded clause and subject argument. In the second approach,
197
I sketch a separationist approach to attitude verb meaning where subject and embedded
clause meanings are related to the verb’s meaning only indirectly through thematic rela-
tions, comparable to the analysis of single clause constructions seen in previous chapters.
I first outline some of the relevant theoretical background required for the context-based
analysis.
6.4 Theoretical background on neo-Kaplanian De Se semantics
In this section I will outline a context-based approach to the semantics of De Se
reports, drawing primarily from the work of Schlenker (1999, 2003, 2012). I will put this
to work in the next section while developing a context-based approach to plural De Se re-
ports. The issues that the semantics is meant to address are undoubtedly compatible with
a number of different approaches to the semantics of De Se reports; I chose to cast the
analysis in Schlenker’s neo-Kaplanian framework because of its familiarity and because
of certain formal details that facilitate the modifications needed to account for plural re-
ports. Below I sketch the aspects of this framework that are required for the analysis to
be presented in later sections; I refer the reader to Schlenker’s (2012) survey article and
cited references for further details.
Formally, contexts are tuples that model attitudinal situations of speech and thought.
At the minimum, a context specifies the author (the individual who is speaking or think-
ing; i.e., the attitude holder) of such a situation and the possible world in which the situ-
ation occurs. The members of a context are often called the coordinates of that context.
It is common to include other coordinates in contexts such as the addressee, time, and lo-
cation of an attitudinal situation. However, I omit these other coordinates for expository
reasons; for the purposes of this chapter it is necessary to focus only on the author and
world coordinates.
The exact details of how contexts figure into the compositional details of De Se
reports with different types of De Se pronouns is currently being debated. My concern
198
is not to distinguish among competing theories, but rather to address two core assump-
tions that virtually all of these theories share: (i) the lexical axioms for attitude verb
involve universal quantification over contexts, and (ii) embedded clauses are interpreted
as functions from contexts to truth values. These assumptions are a mild deviation from
traditional approaches to the semantics of attitude reports where clauses are treated as
functions from possible worlds to truth values, and attitude verbs quantify over possible
worlds; Hintikka (1969), von Fintel and Heim (2012). Using contexts instead of possible
worlds allows for more fine-grained distinctions in meaning that cannot be captured by
appeal to standard propositions; in particular certain indexical aspects of meaning such as
obligatory De Se interpretations. Schlenker constructs this argument for natural language
following essentially what philosophers such as Lewis (1979), Perry (1979), and Kaplan
(1989) have done for the proper representations of indexical thoughts; I refer the reader
to these papers for the relevant arguments.
A standard claim about the truth conditions of attitude reports is that they are uni-
versal generalizations stating that the predicate denoted by the embedded clause holds of
each context (or world) that is accessible to the attitude holder. Different attitude verbs
determine different accessibility relations that in turn determine which set of accessible
contexts is universally quantified over. For instance, the verb think is associated with a
doxastic accessibility relation; a relation that determines a set of contexts that are consis-
tent with the beliefs of a given attitude holder in a certain context of evaluation. Below
I give examples of accessibility relations; I use the function WORLD(c) to give to world
coordinate of context c.
(6.34) a. Rthink(x, c) = {c′ : c′ is compatible with x’s thoughts in WORLD(c)}
b. Rwant(x, c) = {c′ : c′ is compatible with x’s desires in WORLD(c)}
c. Rsay(x, c) = {c′ : c′ is compatible with what x said in WORLD(c)}
A crucial component of using contexts over worlds is that the set of accessible contexts
199
determined by the relation R(x, c) will always have x, the attitude holder, as the author
coordinate for each accessible context. Put differently, for a context to be accessible to an
individual, that individual must be the author of that context. This property of accessibility
will play a role in developing an account of plural reports in the next section.
With this notion of accessibility in place, the semantics for attitude verbs given by
Schlenker and others in the De Se literature can be given as follows. Below the lexi-
cal axioms I provide a schematic LF for all attitude reports (6.36), which will remain
unmodified in later sections.
(6.35) a. !think" = λc.λp.λx.∀c′ ∈ Rthink(x, c)[p(c′) = 1]
b. !want" = λc.λp.λx.∀c′ ∈ Rwant(x, c)[p(c′) = 1]
c. !say" = λc.λp.λx.∀c′ ∈ Rsay(x, c)[p(c′) = 1]
(6.36)
λc1
NP
V c1
λc2 embedded clause
The first argument to the attitude verb is a silent context argument bound by the nearest
λc operator; this value is used to determine the relevant set of accessible contexts for
the attitude holder x15. Again, these definitions are meant to showcase the two relevant
assumptions I mentioned previously; I omit for present purposes other aspects concerning
the fine details of attitude verb meanings.
Given assumption (ii) above, clauses are associated with predicates of contexts.
This corresponds to the claim that there are λc operators at the root of each clause; repre-
sented schematically in (6.37).
(6.37) λc1 John said λc2 Mary is smart
15In other approaches, this context value is not given as a silent argument, but is represented as a param-
eter on the interpretation function; see Anand (2006) for discussion.
200
I remain neutral as to whether the λc operator is present in the object language, possibly
in the form of a diagonalization operator (see Anand (2006), Schlenker (2012) for discus-
sion); or if it is introduced by a semantic rule like Intensional Function Application (see
Heim and Kratzer (1998)), von Fintel and Heim (2012)). The presence of λc operators,
whatever their source, are important for the present account in the following ways: they
create a type ⟨c, t⟩ function (a function from contexts to truth values) to serve as the sec-
ond argument to attitude verbs, and being lambda operators, they can bind c variables in
their scope. I will now turn to this latter property.
In Schlenker’s (2003) account, the meanings of De Se pronouns are determined by
the author coordinates of contexts. He follows Cooper (1983) in treating the φ-features
of pronouns as presuppositions: pronouns receive their semantic value by the assign-
ment function s16, and any φ-features on the pronoun determine presuppositions that the
semantic value of the pronoun must satisfy or else induce presupposition failure. For
first-personal pronouns, Schlenker posits AUTH(x, c) as the presupposition given by first-
person features: the value of the pronoun, x, satisfies this presupposition if it is the author
of the relevant context c.
Following insights from Kaplan, Schlenker attributes the immunity property of De
Se attitudes to the author presupposition. He suggests that all De Se pronouns be treated
as having such a presupposition whether they are indexical in form (shifting indexicals in
Amharic) or not (e.g., PRO and logophors), and the differences among these pronouns be
treated as a lexical specification on the pronoun restricting which contexts c the referential
values x can be authors of. In other words, different pronouns will have slightly different
presuppositions of the general form AUTH(x, c). For instance, in Amharic the c variable
of the author presupposition is a free variable, and thus can be bound by either the matrix
16I follow Schlenker (2003) in using s instead of g for assignment functions; the former is representative
of a modification of the classical Tarskian approach to assignment. Schlenker suggests, following others,
that “...the theory must specify that the assignment function in question correctly captures the referential
intentions of the speaker. This may be done by simply requiring that the original assignment function be
properly determined by the context. Thus if the speaker meant to refer to John by ’he2’, s(2) should be
John.” (Schlenker (2003), p. 51).
201
or embedded λc operator (6.38). Depending on which operator binds the free c variable,
either a non-shifted (6.39a) or shifted (6.39b) interpretation will arise. In the following
definitions, I will use the δ notation of Anand (2006) to notate presuppositions.
(6.38) !IAmharic"s = s(n) & δAUTH(s(n), c)
(6.39) a. John said In am a hero
b. Amharic non-shifted LF:
λc1 John said λc2 [s(n) is a hero & δAUTH(s(n), c1)]
c. Amharic shifted LF:
λc1 John said λc2 [s(n) is a hero & δAUTH(s(n), c2)]
On the other hand, English first person indexicals are associated with the presuppo-
sition that the value of the pronoun is always the author of the actual speech context c*,
and thus English indexicals will never shift under attitude verbs.
(6.40) !IEnglish"s = s(n) & δAUTH(s(n), c*)
Following Chierchia (1989) and Schlenker (2012); PRO is always bound by the
closest λc operator, and so the value of the pronoun must be the author of an embedded
context. The definition of PRO looks much like the Amharic indexical in having a free
context variable, but the values of this variable are restricted by the condition (6.41) and
so PRO will always be unambiguous17.
(6.41) Syntactic condition on PRO (adapted from Schlenker (2012))
When embedded under an attitude verb, PRO must be bound by the closest c-
commanding λc-operator.
17Presumably this definition will work for PRO in other languages such as Italian, since they both give
rise to obligatory De Se interpretations and the reference of PRO is determined by the closest attitude
holder NP. However, I leave it an open ended question as to the semantic value of PRO in so-called “back-
wards control” constructions, another type of obligatory De Se report found in languages like Tsez, see for
example Polinski and Potsdam (2002). PRO appears in the subject position of the attitude verb, and the
referential NP in the embedded position where PRO would appear in languages like English and Italian. In
such languages, it seems the referential noun phrase acts as De Se pronoun, suggesting that there might be
more than just the shape of the noun phrase that gives rise to the obligatory De Se interpretation.
202
(6.42) !PRO"s = s(n) ∧ AUTH(s(n), c)
There are many aspects of De Se semantics that will go unmentioned here. What I
provided above is a simple presentation of the pertinent ideas from previous work in this
area; specifically how to interpret attitude verbs, their complement clauses, and De Se
pronouns in Schlenker’s neo-Kaplanian system. These ideas will serve as a benchmark;
in the next section I will build off of them to develop an account for plural De Se reports.
6.5 A context-based semantics for plural De Se reports
For the remainder of the chapter, I will focus on developing a semantics for plural
De Se reports. In this section I will build a context-based theory, while in the next section
I will build a theory where attitude verbs have their arguments severed. Let us first take
stock of the properties of plural obligatory De Se reports that a proper semantics should
take into consideration. Below I provide a list of the core properties we saw in previous
sections.
(6.43) Properties of plural obligatory De Se reports
i. They report that each attitude holder has a De Se attitude about himself.
ii. They can have both dependent and group readings.
iii. They do not have a crossed reading.
iv. They contain De Se pronouns that are semantically plural.
v. They have embedded clauses that describe the attitudes of a plurality taken
together.
To begin with, consider the following consequence that property (iv) above has for
standard accounts of propositional attitude reports. If De Se pronouns can be semantically
plural (i.e., they can denote non-trivial sums), then the propositions (⟨c, t⟩ functions) de-
noted by embedded clauses in plural De Se reports have the form λc.[...they...], where
203
they represents the value of the De Se pronoun. This poses a problem for traditional Hin-
tikkan approaches to attitude reports where a proposition is taken to hold universally of
each accessible context; see (6.35) above. Consider again (6.1), repeated below.
(6.44) Obama and Romney want PRO to win
Simplifying the semantic representation somewhat, the embedded clause denotes the
proposition λc.[theyo⊕r win in c]. For the dependent reading, there is no context ac-
cessible to either Obama or Romney where a plurality associated with them wins, and
so the Hintikkan approach would incorrectly predict falsity. It seems that the truth of
the dependent reading does not require a plurality to win in each accessible context; we
observed earlier that (6.1) can be true if Obama desires Obama to win in Obama contexts
and Romney desires Romney to win in Romney contexts. The issue now is how to con-
struct a compositional account that captures this while still treating the De Se pronoun as
semantically plural, in accordance with the arguments from §3.
Here I pursue one possible answer: the proposition denoted by an embedded clause
can, sometimes, hold of a plurality of contexts taken together. Compared to familiar
approaches to the truth of attitude reports (6.45) involving universal quantification, I offer
an alternative involving plural predication that can be schematized as in (6.46).
(6.45) A believes/hopes/wants p = True
iff each c of A’s belief/hope/want alternatives C is such that p(c)
(6.46) A believes/hopes/wants p = True
iff the plurality C corresponding to A’s belief/hope/want alternatives C is such that
p(C)
Below I offer two proposals for how to implement these ideas. First there is a modification
of attitude verb semantics so that the proposition λC.[they win in C] does not need to
hold of each accessible context, but in some cases it can hold of the accessible contexts
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collectively. As for the semantic value of De Se pronouns, I will develop a hybrid of
Schlenker’s account with a thematic role approach to De Se suggested by Higginbotham
(2003).
This section is organized as follows. I first address the issue of the interpretation of
the clausal complements of attitude verbs, assimilating the Davidsonsian event quantifier
with a context-based theory of clause meanings. I then turn to the interpretation of attitude
verbs. I make claims about how to modify Schlenker’s claims about attitude verb meaning
to be suitable for plural reports, starting with modifications on how accessibility relations
are defined, and then moving on to one of the central claims of this chapter: the possibility
for attitude verbs to express collective predication of contexts. Following this, I present
the second central claim: a thematic role based interpretation of De Se pronouns.
With these ingredients in place, I turn to the truth-conditional derivation of plural
De Se reports. I will show how the proposals put forth here can account for the both
group and dependent readings uniformly, without appealing to ambiguity. I will also
show how the hypothetical crossed reading is ruled out, and how non-De Se reports lack
dependent readings. I then use reciprocity in De Se reports to provide an argument for the
thematic approach to De Se pronouns argued for here, as well as showing an extension
of this approach to embedded predicates of personal taste. The final issue brought up in
this section is an outline of a problem for future research, centered around the issue of
thematic separation in attitude reports.
6.5.1 Embedded clause interpretation
In Chapter 2 I presented a standard view of sentence meaning in (neo-)Davidsonian
semantics, namely that they are type t existential generalizations of events. As reviewed
in the previous section, standard accounts of attitude reports make the intension of the
embedded clause for its compositionwith the attitude verb, where the intension of a clause
meaning in the neo-Kaplanian framework is a type ⟨c, t⟩ function from contexts to truth
205
values.
There are several ways to get from the basic type t to its intensional type ⟨c, t⟩. As
mentioned previously, several options explored in the literature include positing a silent
operator in the object language, or by making use of the rule of Intensional Function
Application. I explore a different possibility: the silent existential event operator used in
previous chapters can be defined in a way that its composition with its ⟨v, t⟩ complement
yields the intension of a clause.
(6.47) First pass definition
!∃E" = λP⟨v,t⟩.λCc.∃E[P (E)]
So far this intensional version of the ∃E creates the correct type for composition with an
attitude verb after composing with its first argument. Notice that the context variable C is
number-neutral. This will become important in the following sections where I will argue
that there are certain cases where a non-trivial plurality of contexts is required.
There is still an issue that needs to be remedied. In the framework for intensionality
assumed here, the embedded clause described events that take place in possible worlds
(which are coordinates of the contexts) that are accessible to the attitude holder. So far,
nothing about (6.47) requires that the events that are existentially quantified over exist in
any particular world. This can be fixed by use of a metalanguage predicate IN(E,W ),
which is satisfied if the event(s) E take place in world(s) W . In the revised definition, I
use Cw to refer to the world coordinate of context C.
(6.48) Final definition
!∃E" = λP⟨v,t⟩.λCc.∃E : IN(E,Cw)[P (E)]
This will be the version of ∃E that I will put to use in what follows. We still have all the
benefits of Davidsonian event analyses for explaining clause-internal aspects of meaning,
but the type of the clause is now an intensional type of the appropriate sort to compose
with attitude verbs.
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6.5.2 Attitude verb interpretation
I now turn to a “pluralization” of attitude verb meaning. I first modify the general
form of accessibility relation definitions, and then use this to give attitude verb definitions
that incorporate the idea of collective predication of contexts introduced above.
6.5.2.1 Pluralized accessibility relations
The standard definitions of accessibility relations ((6.34) above) are defined only
for singular attitude holders; given an attitude holder x and context of evaluation c, an
accessibility relation determines a set of contexts accessible to x in c. When faced with
the issue of how to modify accessibility relations for cases involving a plurality of atti-
tude holders, there are two plausible options for how to determine the appropriate set of
accessible contexts: it is either the union or the intersection of the each singular attitude
holder’s respective sets of accessible contexts. Given that there are dependent readings, it
seems that union is the correct choice.
To see what goes wrong with the intersection approach, consider again the depen-
dent construal of (6.1). Assume that each candidate’s respective accessible contexts are
determined by the standard singular accessibility relations; (6.34) from §4. If the plural
attitude report used the intersection of Obama and Romney’s accessible contexts, then in
the relevant model associated with the dependent construal this would be the empty set.
This is so because Obama’s contexts are all and only those where Obama wins and Rom-
ney loses, and Romney’s contexts are those where Romney wins and Obama loses; there
are no contexts accessible to both Obama and Romney where each gets what he wants,
and so the intersection of their respective desire contexts is empty. The truth conditions of
the report would involve universal quantification over the empty set, which is an unsatis-
factory state of affairs. Initially it might not seem so bad if a universal generalization can
be true if the domain of quantification is empty, a standard assumption in modern logic.
207
This would correctly capture the truth of our report, but it does so at the cost of allowing
any proposition to hold when the set of accessible contexts is empty. In other words, in
cases where Obama and Romney do not want the same thing, a desire report about them
will always be true regardless of the embedded clause used.
Dependent readings thus suggest that the truth of the report is determined in part by
contexts that only some individuals of the plurality of attitude holders are accessible to.
It therefore seems appropriate to include these contexts in the relevant set that determines
the truth of a plural attitude report; and so this set should be given by the union/sum
of each singular attitude holder’s respective accessible contexts. The general form of an
accessibility relation R is given below. Keep in mind that lowercase variables are for
atomic values, and uppercase variables are number neutral.
(6.49) Plural accessibility relation - set version
R(X,C) = {c : ∃x ≤ X [c′ is R-accessible to x in WORLD(C) and AUTH(x, c′)]}
In prose, a context c is accessible to a plurality of attitude holders X if c is accessible to
at least one singular attitude holder x in X .18
To keep things consistent with a mereological approach, accessibility relations should
determine a sum of contexts, not a set. Appropriate sums of accessible contexts are given
by simply applying⊕ to the sets of accessible contexts given by (6.49).
(6.50) Plural accessibility relation - mereology version
R(X,C) = ⊕{c : ∃x ≤ X [c′ is R-accessible to x in WORLD(C) and
AUTH(x, c′)]}
This assumes that contexts and their coordinates are part of a sorted domain of discourse,
and each subdomain is closed under sum formation. There is precedent for sorted domains
18In order to avoid the problems with an empty set of accessible worlds/contexts, I assume that every
attitude holder has at least one accessible world/context for each attitude. Note that this is not an issue
particular to my account; the standard Hintikkan definitions of accessibility relations and attitude verbs
require the same stipulation or else truth is predicted whenever an attitude holder has an empty set of
accessible worlds/contexts (i.e., in cases where an attitude holder does not want/think/etc. something).
208
in the event literature on plurality, where there is a subdomain for individuals, and another
for events, and each have the usual algebraic structure; see Chapter 2. I propose that
other ontological categories such as worlds also have a mereologial subdomain closed
under sum-formation. Furthermore, contexts themselves can be summed by summing
their coordinates; given ⟨auth1, world1, ...⟩ and ⟨auth2, world2, ...⟩, their sum would be
⟨auth1 ⊕ auth2, world1 ⊕ world2, ...⟩. This latter assumption will be important for the
semantics of De Se pronouns and the attitude reports that contain them.
6.5.2.2 Generalizing the Hintikkan approach
The traditional Hintikkan approach can be likened to a certain type of plural pred-
ication: distributive predication of a plurality of contexts. I propose that there is a place
for the other variety of plural predication in attitude reports; specifically, that (at least)
De Se reports involve collective predication of the same sort of plurality. I will leave the
technical details behind the satisfaction conditions of such predicates for later sections.
For now it is enough to just work with an informal characterization of the proposal, as in
(6.46), for the purpose of giving the lexical semantics of attitude verbs.
Let us first consider how to cast the traditional Hintikkan approach as distributive
plural predication. The first step is to replace set notions with mereological ones in the
lexical axioms of attitude verbs. For an attitude verb AV and its corresponding accessi-
bility relation R, this can be done as follows.
(6.51) !AV" = λC.λP.λX.∀c′ ≤ R(X,C)[P (c′)]
Once given its arguments, the attitude verb yields truth conditions stating that every
atomic context in the sum of accessible contexts determined by R satisfies the predi-
cate P . There is another way to implement this in a mereological system; instead of
universal quantification, a distributivity operator can be used. The same plurality that was
quantified over now becomes an argument to the predicate DP .
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(6.52) !AV" = λC.λP.λX.DP (R(X,C))
So far, this is just a notational variant of a standard idea. But treating attitude reports as in-
volving plural predication, instead of universal quantification, leaves open the possibility
that other types of plural predication might be involved in some attitude reports.
I propose that De Se reports represent a case where the distributivity operator is not
present, and as such there is collective predication of a sum of accessible contexts. In
other words, the embedded clause for De Se reports describes the attitudes of a plurality
collectively, even if it does not describe the attitude of any singular attitude holder. In
the past, authors have posited a De Se/non-De Se ambiguity for attitude verbs; I too posit
such an ambiguity, but what sets De Se and non-De Se versions of attitude verbs apart is
whether or not a distributivity operator is present19. Below I give the general form of a
De Se attitude verb denotation.
(6.53) !AVDeSe" = λC.λP.λX.P (R(X,C))
This is the first step in capturing the idea of collective satisfaction behind (6.46). For
(6.1), the complement clause will have the form λC.[they win in C]. A De Se attitude
verb will take this proposition as an argument an apply it to the sum of Obama and Rom-
ney’s accessible desire contexts. After λ-conversion, this sum will be the value of the
variable C in the proposition associated with the embedded clause. Thus, the truth of the
report, according to the De Se attitude verb denotation, will be decided by whether this
sum of contexts collectively has the property that Obama and Romney win in those con-
texts. Because collective predication is at work, the truth conditions make no reference to
19I do not deny that there may be more to the De Se/non-De Se ambiguity than just the former being
collective and the latter distributive. For example, in Chierchia’s (1989) well-known analysis of De Se
reports, he develops a system where De Se attitude verbs take property-denoting clausal arguments while
non-De Se attitude verbs take proposition denoting ones; building on insights from Lewis (1979). However,
both types of attitude verbs for Chierchia involve universal quantification, and are thus susceptible to the
plurality problems discussed above. So even if one were to assume the property/proposition dichotomy, I
argue that this is not enough: De Se attitude verbs must also be collective in some sense in order to account
for cases where the embedded clause property (which might contain a reciprocal component or express
cumulativity) does not hold of each attitude holder.
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atomic contexts, and so we have an explanation for why (6.1) can be true even though the
proposition λC.[they win in C] does not hold of any single accessible context.
There is still the task of providing criteria for when a proposition holds collectively.
I suggest that this has to do largely with how plural De Se pronouns are defined, which I
turn to immediately.
6.5.3 Plural De Se pronouns
In this section I will modify the Schlenkerian approach to De Se pronouns to ac-
count for plural cases. The crucial parts of Schlenker’s analysis that I wish to make use
of are: (i) the meaning of De Se pronouns contain a free context variable, which eventu-
ally gets bound by a λC operator; and (ii) the meaning of a De Se pronouns is bipartite,
containing a referential component that is valued on par with other pronouns, and a pre-
suppositional component that is responsible for the obligatory De Se interpretation.
The core modification that I will explore here is a revised presuppositional compo-
nent. The presupposition will still make use of the notion of authorhood, but will do so
in a way that involves the thematic role associated with the De Se pronoun. I will show
in later sections that this particular presupposition provides a way to properly account for
the both group and dependent readings without appealing to ambiguity, while also ruling
out crossed readings. I will also show that this approach has the additional benefit of
explaining a subtle nuance in meaning regarding reciprocity in De Se reports.
6.5.3.1 Thematic roles strike again
Higginbotham (2003) suggests that the meaning of PRO makes crucial use of the
thematic role associated with the argument position where PRO resides. This addition
is compatible with several of Schlenker’s main claims about De Se reports; e.g., the use
notions such as context and author, and the idea that different De Se pronouns have slight
variations in meaning that differentiate PRO, shifted indexicals, and logophors. Appeal-
211
ing to thematic roles opens the way for a neo-Davidsonian account of De Se pronouns,
one that I will argue works particularly well in accounting for the properties of plural De
Se reports.
Higginbotham’s motivation for using thematic roles comes from what he calls the
internal property of PRO. This is a property of PRO that exists in addition to the property
of immunity to error through misidentification. Higginbotham focuses on the use of PRO
in certain gerundive complements of intensional transitive verbs such as remember.
(6.54) a. Only Churchill remembers his giving the speech
b. Only Churchill remembers PRO giving the speech
This rather famous pair, discussed in Fodor (1975), illustrates an important point. When
Churchill gave the “Blood, Sweat, and Tears” speech, there were other people there lis-
tening; and with this premise in mind, (6.54a) is clearly judged false. On the other hand,
assuming further that no one but Churchill gave this speech, (6.54b) is judged true.
We may characterize this dichotomy as follows. (6.54a) is used to report the re-
membering of a proposition, in particular the proposition that Churchill gave the speech.
People other than Churchill can remember this proposition too; such as people who were
in attendance during the speech. Since other people also remember this proposition, when
the exclusivity morpheme only is used in sentences like (6.54a), the sentence is thus
judged false. On the other hand, (6.54b) is judged true as a report of the same situa-
tion. This suggests that what Churchill is reported to remember here is not a proposition.
If it where a proposition, we would expect the same judgements as (6.54a), since the same
proposition would be involved. However, this is not the case, as (6.54b) seems to com-
municate that what Churchill remembers is something more private and perspectival than
what is reported to be remembered in (6.54a).
So what is Churchill reported to remember then in the case of (6.54b)? He remem-
bers participating in an action. He remembers standing at the podium, looking over the
212
audience, and speaking the words of the speech. In other words, he remembers being a
thematic participant of some sort in the events described by the complement of remem-
ber.20 Since no one else was a participant in such events, they cannot remember being
such a participant (assuming that memory modification or some other device of science
fiction is not at work here), thus (6.54b) is true.
This is what is meant by the internal nature of PRO. The complement of the at-
titude verb does not describe a proposition that concerns the attitude holder, but instead
describes an action that the attitude holder stands in some relation to. The attitude holder’s
role in the action is determined by the thematic role assigned to PRO; since PRO receives
an agent role in (6.54b), we know that what Churchill remembers is being an agent in the
action of given the speech. Furthermore, he remembers this in a way that is immune to
error through misidentification; that is, he remembers in a De Se way. This is a special
property of PRO, and arguably other De Se pronouns, which is lacking in the more basic
pronouns as exhibited by (6.54a).
For present purposes, Higginbotham’s proposal can be viewed as a way of extend-
ing Schlenker’s account, which already provides a way of addressing immunity to error
through misidentification by appealing to the author of an embedded context. Abstracting
away from certain details, Schlenker’s proposal of (6.55) can be represented as (6.56), and
Higginbotham’s can be given as (6.57) which crucially specifies which thematic relation
holds of the author.
(6.55) John wants PRO to ...
(6.56) John wants λc.AUTH(c) ...
(6.57) John wants λc.∃E[AGENT(E, AUTH(c)) ...]
20This should not be confused with the similar claim that what is remembered is an action: the claim is
that what is remembered is the performing of an action. Onlookers can remember an action of Churchilll,
but they cannot remember participating as Churchill in that action.
213
There are many details of Higginbotham’s account that are not presented here, as they
are not critical to the issue at hand. What is important for present purposes is the use of
thematic relations to account for De Se properties of certain pronominal elements. In the
following section, I will use Higginbotham’s insight as a key ingredient in the proposal
for a modified presuppositional component of De Se pronouns.
6.5.3.2 A new semantics for De Se pronouns
The goal now is to “pluralize” both the referential and presuppositional components
of De Se pronouns. The referential component is relatively straightforward: the semantic
value is determined by the antecedent, and when the antecedent is plural, so is the ref-
erential component of the De Se pronoun. In this way, the De Se pronoun is like other
referential nominals. As a nominal element, it will be a bearer of a thematic role, and
thus be interpreted as a monadic predicate of events. For this discussion, I will use the
Theta Feature approach discussed in previous chapters (see especially Chapter 2). Thus,
the beginnings of a general rule for De Se pronouns would look as follows.
(6.58) !DSPn,Θ"s = λE.[Θ(E, s(n)) & [De Se presupposition]]
The index n on the pronoun will act as an argument of the assignment function s. In
textbook treatments of the interpretation of indexed structures (Heim and Kratzer (1998)),
each pronoun bears an index, and the assignment function takes that index as an input and
assigns an atomic value as an output. This view can be modified by allowing non-trivial
sums to be assigned to a given index. I illustrate this below with a sample assignment
function s that assigns atomic values to some indices and plural values to others.
214
(6.59) s =
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
1 = a
2 = b
3 = a⊕ b
4 = c
5 = a⊕ b⊕ c
...
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Alternatively, one can follow the suggestions of Lasnik (1986) where plural pro-
nouns have not just a single index, but an index set. Under this view, each atom referred
to by the pronoun has an index, and the index set of the plural pronoun has as members the
various indices associated with these atomic values. This approach may have advantages
over the single index approach to plural pronouns; see Büring (2005)) for references and
discussion. For the following discussion I will stick to the single index approach, though I
consider the index set approach to be a viable alternative that does not require substantial
changes to the main ideas presented here.
I now turn to the presuppositional properties of plural De Se pronouns, which will
be an important ingredient in giving proper truth conditions of De Se reports in the next
section. I will draw on Higginbotham’s insight, and incorporate a thematic relation into
the presupposition. The particular thematic relation is again determined by the Theta
Feature on the De Se pronoun. The question now is how exactly to formulate this thematic
presupposition in a way that correctly captures the meaning of both singular and plural
De Se pronouns.
I propose that the De Se presupposition is a universal generalization over the con-
texts that are accessible to the attitude holder(s). This is where the context variable,
contained in Schlenker’s original presuppositions, is put to use. The difference here is
that the context variable is number-neutral, and receives the value of the plurality of con-
texts that are accessible to the attitude holders. The presupposition thus states properties
that hold universally of each atomic context within these accessible contexts. Drawing on
215
Higginbotham’s insight, I propose further that this property describes sub-events in which
atomic authors participate in on their respective atomic worlds.
(6.60) Proposed De Se presupposition:
∀c ≤ C[∃E ′ ≤ E[IN(E ′, cw) & Θ(E ′, ca)]]
In prose, the presupposition states that for every atomic context c in C, there are
sub-events E ′ of the events described by the complement clause E such that E ′ takes
place in cw and the Θ of E ′ is ca. I now present the final schema for De Se pronoun
interpretation, incorporating both referential and presuppositional components.
(6.61) !DSPn,Θ"s = λE.Θ(E, s(n)) & δ[∀c ≤ C[∃E ′ ≤ E[IN(E ′, cw) & Θ(E ′, ca)]]]
The variable C in the presupposition is bound by the λC operator introduced by the ∃E
defined in (6.48). The variable E is bound by the λE operator introduced by the Theta
Rule, the same operator that binds the event variable in the referential component of the
De Se pronoun, see (6.58).
The work of the De Se presupposition can be appreciated by comparing it to pre-
vious accounts of De Se ascription, in particular the property self-ascription view (Lewis
(1979), Chierchia (1989)). Chierchia treats the embedded clauses of obligatory De Se
reports as properties, where the position of PRO has been abstracted over. He follows
Lewis in treating De Se attitudes not as involving propositions, but as the self-ascription
of a property by the attitude holder. For Chierchia, the embedded clause of the recipro-
cal sentence, repeated below as (6.62), would be interpreted as in (6.63) (number-neutral
variables are my addition).
(6.62) Obama and Romney want to destroy each other
(6.63) !PRO to destroy each other" = λX.X destroy each other
If one assumes that attitude verbs universally distributive the property denoted by em-
bedded clauses (as in (6.63)) to each individual agent, then (6.62) should be false or
216
infelicitous since a reciprocal property cannot hold of a singular individual, as discussed
previously. Now let us try the suggestion that universal quantification is not at work as I
suggested above, and the truth conditions involve collective satisfaction of the predicate
in (6.63). This avoids the problem of giving the reciprocal a singular antecedent value.
However, it does so at the cost of removing precision about De Se content; it raises ques-
tions about why there are a lack of crossed readings, or why there should be dependent
readings, and why each attitude holder has a De Se thought himself. The De Se pre-
supposition I defined above is meant to avoid these issues. Under the present account,
property self-ascription is still at work in capturing De Se content, but it is a different sort
of property than the ones given by λ-abstraction on the position of the De Se pronoun. In
particular, the proposal here is that each individual attitude holder self-ascribes a thematic
property: the property of being the Θ of some events E ′. For (6.62), it is reported that
Obama self-ascribes the property of being the agent of some events E ′, and Romney self-
ascribes the property of being the agent in some events E ′′. The proposed truth conditions
of (6.62) do not say much about E ′ and E ′′, except that together E ′ ⊕E ′′ count as events
where Obama and Romney destroy each other. To summarize, property self-ascription is
still at work in De Se reports, but they are properties of being a thematic participant in
some type of sub-event.
6.5.4 The truth conditions of plural De Se reports
We are now in a position to put the proposals about the semantics of embedded
clauses, attitude verbs, and De Se pronouns to work. I will first present a derivation of
our parade case, repeated below as (6.64).
(6.64) Obama and Romney want PRO to win
I then turn to discussion of how the derived truth conditions can account for both group
and dependent readings. The approach developed here is such that these are not two sep-
217
arate “readings” in the sense that (6.64) is ambiguous; rather, the truth conditions are
underspecified in a way that they are compatible with both group and dependent constru-
als of (6.64). I will also discuss how the hypothetical crossed reading is ruled out in this
system, and how non-De Se reports lack a dependent interpretation. I then present an ar-
gument from reciprocity in De Se reports that supports the thematic approach developed
here.
Before deriving the truth conditions of (6.64), some preliminary remarks about the
LF of De Se reports are in order. Below I provide LF phrase marker of (6.64) that will act
as input to semantic interpretation.
(6.65)
[Obama and Romney]n
want c*
∃E
PROn,ag
to win
The attitude holder nominal and the De Se pronoun, PRO, are coindexed with n; this
results in the referential component of PRO’s meaning having the same semantic value
as the subject of the attitude holder: o ⊕ r. As mentioned previously, the De Se pronoun
is treated on par with other nominals in the neo-Davidsonian system pursued here in that
it is interpreted as a monadic predicate of events by being Theta-marked with the feature
ag; however, the subject of the attitude holder is interpreted simply as a type e value. In
§6.5.6, I suggest that this argument too should also be treated as a monadic predicate of
events.
The attitude verb composes with a context argument, in this case c*, that is used
to generate the appropriate plurality of alternative contexts: BOUL(o ⊕ r, c*). I will sim-
plify the embedded clause somewhat by treating the infinitival marker to as semantically
vacuous; in other words, I assume !to win" = !win". With all this in mind, I provide the
derivation of the truth conditions of (6.64) below in (6.66).
218
(6.66) i. !win"s = λE.WIN(E)
ii. !PROn,ag"s = λE.AGENT(E, s(n)) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & AGENT(E ′, ca)]]]
iii. !PROn,ag win"s = λE.AGENT(E, s(n)) & WIN(E) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & AGENT(E ′, ca)]]]
iv. !∃E PROn,ag
win"s = λC.∃E : IN(E,Cw).AGENT(E, s(n)) & WIN(E) & δ[∀c ≤
C[∃E ′ ≤ E[IN(E ′, cw) & AGENT(E ′, ca)]]]
v. !want"s = λC.λP.λX.P (BOUL(X,C))
vi. !want c*"s = λP.λX.P (BOUL(X, c∗))
vii. !want c* ∃E PROn,ag win"s
= λX.[λC.∃E : IN(E,Cw).AGENT(E, s(n)) & WIN(E) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & AGENT(E ′, ca)]]]](BOUL(X, c∗))
viii. !Obama and Romney want c* ∃E PROn,ag win"s
= ∃E : IN(E,Cw).AGENT(E, s(n)) & WIN(E) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & AGENT(E ′, ca)]]](BOUL(o⊕ r, c∗))
= ∃E : IN(E, BOUL(o⊕ r, c∗)w).AGENT(E, o⊕ r) & WIN(E) & δ[∀c ≤
BOUL(o⊕ r, c∗)[∃E ′ ≤ E[IN(E ′, cw) & AGENT(E ′, ca)]]]
The last step [viii] gives the truth conditions of (6.64). In prose, it states that there are
events E that take place in the collection of Obama and Romney’s desire worlds; these
are events of winning with Obama and Romney as their agents; lastly, there is the presup-
position that each atomic context c in Obama and Romney’s desire alternative contexts
are such that the author of c is the agent of some sub-event E ′ ≤ E, and E ′ takes place
on the world of c.
I will now turn to discussion of how these truth conditions are satisfied by models
associated with the group and dependent construal of (6.64), and how a model associated
219
with the crossed reading does not satisfy these truth conditions.
6.5.4.1 The range of interpretations of plural De Se reports
Let us consider what a model for the dependent reading of (6.64) looks like. Recall
that this represents a situation where Obama wants just Obama to win, and Romney wants
just Romney to win. This corresponds to a model where Obama’s desire contexts are such
that the author of each of those contexts wins and Romney loses; likewise, Romney’s
desire contexts are such that the author of each of those contexts wins and Obama loses.
The sum of Obama and Romney’s desire contexts in c*, BOUL(o⊕r, c*), is then such that
there are events E which contain sub-events where Obama wins and different sub-events
where Romney wins. Thus, the totality of E may be characterized as having both Obama
and Romney as agents of winnings. Of course, each of these winnings takes place in
different possible worlds; Obama wins in Obama worlds and Romney wins in Romney
worlds. Both those worlds (and the contexts they are coordinates of) taken together are
such where Obama and Romney win in them. It follows then that the portion of the
truth conditions before the De Se presupposition are satisfied: ∃E : IN(E, BOUL(o ⊕
r, c∗)w).AGENT(E, o⊕ r) & WIN(E).
Let us now consider what each atomic desire context looks like in this model. For
each of Obama’s contexts c, Obama as an author ca wins in each atomic world cw. In
other words, each of Obama contexts are such that the author of that context is an agent
of winning events. Vice versa for Romney; for his contexts, the author of each of those
contexts is an agent of a winning events in a Romney world. The presupposition is thus
satisfied in this model. Furthermore, by making a statement about the author of each
individual context, we have an explanation for the obligatory De Se content of the report,
in the same way that De Se content is accounted for in Schlenker’s system.
Consider now the group construal of (6.64), where Obama and Romney each wants
the plural consisting of the two of them to win. This is probably not the case with the
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election, but perhaps they bowl on the same team and they want to win the bowling
competition. In a model associated with this case, each of Obama’s contexts will be
such where both the author of the context and Romney21 are agents of winning in the
world of that context. Likewise, in each of Romney’s contexts, the author of that context
and Obama win in the world of that context. This situation ends up satisfying the truth
conditions of (6.64) since the De Se presupposition does not require of each context c that
ca is the only agent of the winning on cw. The truth conditions are thus underspecified
enough to be satisfied by models associated with dependent and group construals, without
appeal to ambiguity22. Of course, the task now is to make sure that the truth conditions
are not too underspecified. I will take up this issue shortly. But first, some remarks about
the principle of Variety are in order.
Recall from Chapter 2 predicates of sums of events are such that there is no guar-
antee that the predicate will hold of any of the parts of the sum. This was represented by
the principle of Variety. This is relevant for the present case, since the truth conditions
in (6.64) state that the sum of events E are such that WIN(E). In the presuppositional
portion of the truth conditions, we see a statement about each author being the agent of
some sub-events E ′ ≤ E. Does this mean that they are agents of winning? By the prin-
ciple of Variety alone, this is not guaranteed. However, consider the fact the main events
E are a sum of winning events that take place in different possible worlds. From Vari-
ety alone, we cannot conclude that the part of E are also winnings; but would the state
21Or perhaps some counterfactual version of Romney.
22If there is no ambiguity involved, we would expect truth of cases where the embedded clause contains
conjoined VPs, where one VP receives the dependent construal and the other VP receives the group con-
strual (thanks to Neil Myler, p.c., for bringing this predication to my attention). As is shown below, this is
indeed possible.
i. Obama and Biden want to win and (then) kill each other
Notice however that such examples alone do not rule out an ambiguity approach in general; they just show
that the ambiguity does not lie in the subject, PRO, or some operator above it. For example, one could
analyze the group/dependent dichotomy a property of VPs, in which case the VPs in (i) could be viewed as
ambiguous (perhaps one of the construals is given by some VP-level operator). This line of reasoning is on
par with the discussion of ambiguity regarding collective/distributive ambiguities discussed in Chapter 2.
221
of affairs hold if E counts as winnings but its sub-events do not? In theory, this could
be a case where Obama did something in his worlds, and Romney did something in his
worlds; their actions alone did not count as a winning, but the sum of their actions would.
Unless we assume a metaphysics built around modal realism and travel among worlds is
possible, where the actions in one world can influence and be influenced by actions in
another world, it is very hard to see how the events E can be winnings while its parts E ′
that may take place in an Obama world for example are not a winning. I believe then that
it is safe to assume that if E counts as winnings, and these describe events that take place
in multiple worlds, then it is fair to assume that sub-events E ′23 of E that take place in a
single world also count as a winning.
The hypothetical crossed reading of (6.64) is one where Obama wants himself to
lose and Romney to win, and Romney wants himself to lose and Obama to win. If it
were not for the De Se presupposition in the truth conditions of (6.64), there would be
nothing to rule this out. Without the presupposition, the truth conditions would sim-
ply be that Obama and Romney are agents of winning in events that take place in the
collection of Obama and Romney’s accessible desire context. Nothing is said about indi-
vidual contexts, specifically who is winning on the worlds of those contexts. While these
presupposition-less truth conditions can be satisfied by models associated with group and
dependent construals, they can also be satisfied by a model where Obama’s worlds are
such that Obama loses and Romney wins, and vice versa for Romney.
The presupposition rules out this case by its appeal to authorhood. In particular, the
statement that the author of each context is the agent of a winning in the world of that
context. For each of Obama or Romney’s contexts, the author loses; so while it may be
true that the totality of Obama and Romney’s desire alternatives can be characterized as
having Obama and Romney win, it does not hold that the author of each context wins in
23This is not to say that the events E′ ≤ E that take place in a single world also have all their parts
count as winning; for example, part of Obama’s winning might have been due to his campaigning, but his
campaigning alone does not count as winning. This suggests that variety might be viewed as a condition
that only holds of events that take place in a single world.
222
the world of that context. In essence, the crossed-reading is ruled out by the component
of meaning that is responsible for the obligatory De Se interpretation.
For the sake of completeness let us consider a non-De Se report like Beck and
Sauerland’s (6.3), repeated below as (6.67), which lacks a dependent construal.
(6.67) Max and Peter said that Bill married Ann and Amy
A dependent situation would be one where Max said that Bill married Ann, and Fred
said that Bill married Amy. In other words, each of Max’s alternative contexts are such
that Bill married Ann, and each of Peter’s alternative contexts are such that Bill married
Amy. In §6.5.2.2 we drew a distinction in the semantics of De Se versus non-De Se
reports to account for this. In particular, non-De Se attitude verbs are interpreted in the
classical Hintikkan fashion, implemented in here with a distributivity operator that forces
the predicate associated with the embedded clause to hold of each accessible context;
while on the other hand, De Se attitude verbs are interpreted without the distributivity
operator, and we thus have the effect of collective predication which I have argued gives
rise to dependent construals. Since (6.67) is not a De Se report, then the proposition
λc.[Bill married Ann and Amy] is taken to hold of each of Max’s contexts and each of
Peter’s. But none of these contexts satisfies the proposition that Bill married Ann and
Amy, since each attitude holder in this case only said that Bill will marry just one woman,
and therefore (6.67) should be judged false, as desired.
6.5.4.2 Reciprocity as an argument for the thematic approach
One may wonder whether using thematic relations in the De Se presupposition is
necessary. A possible alternative that still treats these De Se pronouns as plural would be
that the pronoun simply refers to the plurality of authors. Our parade case (6.64) would
then have truth conditions paraphrasable as “the authors of C win in the worlds of C”.
This would still derive both group and dependent readings with the same truth conditions,
223
and crossed-readings are ruled out because in that case there are no authors winning. Why
then go through all the trouble with a convoluted De Se presupposition?
One argument for the thematic approach comes from embedded reciprocal expres-
sions of the kind discussed earlier.
(6.68) Obama and Romney want PRO to destroy each other
If the antecedent to the reciprocal in such cases is the De Se pronoun PRO, then the
alternative account just outlined would have the antecedent value of the reciprocal be
“the authors”. This could be implemented by a slight modification to Schlenker’s non-
thematic De Se presupposition that replaces his singular variables with number-neutral
ones: δAUTH(X,C). The resulting truth conditions would then be as follows given the
account of reciprocity argued for in Chapter 424. For ease of exposition, I will use C as a
shorthand for BOUL(o⊕ r, c∗)
(6.69) ∃E : IN(E,Cw).AGENT(E, o⊕ r) & δAUTH(o⊕ r, C) & DESTROY(E) & ∀x ≤
o⊕ r[∃E ′ ≤ E[AGENT(E ′, x) & ∃Y ≤ o⊕ r[OTHER(Y, x) & THEME(E ′, Y )]]]]
The problem here is the presupposition that Obama and Romney are authors. While this
does account for the De Se properties of the report, it provides the wrong sort of in-
formation to the reciprocal. With “the authors” as the reciprocal’s antecedent, the truth
conditions state that the authors are both the agents and the themes of the destruction
events. However, (6.68) can be used to report Obama’s desire to destroy Romney and not
be destroyed himself; and vice versa for Romney. This would be a dependent construal of
(6.68). Reflecting a bit on a model associated with this situation, we want whatever coun-
terfactual version of Romney that exists in Obama’s worlds not to be a Romney-author
value, since that would imply that Romney wants himself to be destroyed. Likewise for
the counterfactual version of Obama on Romney’s worlds. In other words, we want the
24This argument does not require my particular approach to reciprocals. Any approach which relies on a
single local plural antecedent to compute the reciprocal’s meaning would run into the same problem.
224
values of the themes of destruction to not be authors in order to account for this dependent
reading. The non-thematic approach does not offer a solution here; it merely states that
Obama and Romney are authors, regardless of which thematic role they assume.
The thematic De Se presupposition offers exactly what we need to avoid this prob-
lem. This presupposition attributes authorhood not to individuals per se, but to partici-
pants under some thematic guise. Consider the truth conditions of (6.68) given the account
developed here.
(6.70) ∃E : IN(E,Cw).AGENT(E, o⊕ r) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & AGENT(E ′, ca)]]] & DESTROY(E) & ∀x ≤ o⊕ r[∃E ′ ≤
E[AGENT(E ′, x) & ∃Y ≤ o⊕ r[OTHER(Y, x) & THEME(E ′, Y )]]]]
The non-presuppositional contribution of the truth conditions are just as before: Obama
and Romney’s desire contexts are such that Obama and Romney destroyed each other.
Again the reciprocal takes as its antecedent the referential value of the De Se pronoun, in
this case o ⊕ r. The De Se presupposition adds the further conditions that the agent of
the destructions for each atomic context is the author of that context. Therefore, for each
atomic context c, the theme of the destruction in c will be the other candidate, but there is
nothing in the truth conditions that says that the other candidate is also an author in c, just
that the agent is an author in c.
In brief, the distinction between the accounts can be summarized thusly: the non-
thematic account says simply that Obama and Romney are authors, while the thematic
account says that the agent of the destruction in each atomic context is an author. The
former treats Obama and Romney as authors regardless of whether they are agents or
themes, while the latter states just that Obama and Romney as agents are authors, but
nothing is said about the themes. Of course, the themes could be authors too; this would
correspond to a group construal where each wants mutual destruction. But this is not a
necessary interpretation of the report; and the non-thematic approach does not provide an
explanation for a dependent interpretation.
225
6.5.5 Plural ascription of predicates of personal taste
In this section I will examine an alleged non-subject occurrence of PRO, and show
that the account developed here accounts for plural versions of these cases as well. Stephenson
(2010), following insights from Lasersohn (2005), argues that embedded predicates of
personal taste involve a silent PRO that acts as an experiencer argument that is referen-
tially dependent on the attitude holder nominal. The crucial aspect of meaning here is
that what tastes good is evaluated based on John’s tastes; not, for example, the speaker’s
tastes.
(6.71) John wants the cake to taste good PROj
I will not review here the exact details and arguments for Stephenson’s approach, I will
build on her account and show how her proposals about the role of PRO in embedded
predicates of personal taste can be easily extended to plural variants of this construction.
The first step is accounting for the experiencer PRO. This is relatively straightfor-
ward in the present approach: PRO is assigned an experiencer Theta Feature, and this
yields an experience relation in the De Se presupposition. Thus, we get truth conditions
of (6.71) that can be paraphrased as John desired states of the cake tasting good relative
to the tastes of the author (i.e., John) who experiences that taste. This is just a case where
PRO receives a thematic role different from agent: everything else remains the same.
Consider now plural versions of the constructions that interested Stephenson, such
as (6.72).
(6.72) Obama and Romney want the cake to taste good PROo⊕r
Interestingly, (6.72) can be used truthfully even if Obama and Romney have conflicting
ideas about what tastes good. This is, again, another sort of dependent reading which can
be accounted for by the present approach. Simplifying to avoid extraneous details, the
truth conditions of (6.72) are given below.
226
(6.73) ∃E : IN(E,Cw).EXP(E, o⊕ r) & CAKE-TASTES-GOOD(E) & δ[∀c ≤ C[∃E ′ ≤
E[IN(E ′, cw) & EXP(E ′, ca)]]]
In prose, Obama and Romney’s desire contexts are such that the cake tastes good in
those contexts, but as far as each individual context is concerned, what counts as good is
determined by the author of that context.
6.5.6 Severing the arguments of attitude verbs
In this section I will outline an issue about the standard semantic type of attitude
verbs. For much of this dissertation I have pursued a strong neo-Davidsonian thesis: the
total separation approach to argumenthood. In standard theorizing, canonical attitude
verbs are typically assigned definitions where they receive at least two arguments, the
meanings of the embedded clause and the attitude holder nominal25. A question then
arises if attitude verbs, like all other verbs, are monadic predicates of events/states. If
so, we are lead to the further question about how to to represent the argument of attitude
verbs as separated thematic conjuncts.
One hurdle in pursuing this line of thought is reconciling separation of the subject
argument with the generation of the relevant set of alternative contexts. In standard ap-
proach to attitude verb meaning, the composition with the subject provides a type e value
used to generate the set of alternative contexts that are accessible to that value (with re-
spect to an evaluation context). The particular accessibility relation to be used is generally
taken to be part of the attitude verb’s meaning, but this relation only determines the ap-
propriate set when it is given the type e value, provided by the subject nominal. Function
Application thus seems to be perfect for the composition of the attitude verb with its sub-
ject. If one were to pursue thematic separation, an explanation would be required for how
25Here, for simplicity, I have followed others in positing a third context-of-evaluation argument. This is
not necessary though, as other approaches represent this value as a parameter of the interpretation function,
not as an argument to the attitude verb. I focus in the main text only on those more traditional “arguments”
of attitude verbs.
227
to generate the alternative contexts for the attitude verb which does not directly compose
with a value that tells us who the contexts are accessible to.
Another issue is the composition of the attitude verb with the embedded clause. I
have followed previous approaches in treating the attitude verb as a sort of higher order
function, which takes a ⟨c, t⟩ function as an argument and applies it either to each con-
text (on the classical Hintikkan approach) or to the plurality of accessible contexts itself
(on the present approach). This type of composition is again easily accommodated by
Function Application.
The choice to separate the arguments of attitude verbs is a step towards a more par-
simonious theory with the same approach to argumenthood applied to all verb meanings.
Not only that, but there is a further unification of clause meanings that could be sought.
Most clause meanings in this dissertation are existential generalizations of events; not so
with attitude reports, as the attitude verb is responsible for producing a type t meaning
after composition with its arguments, without the need for existential closure.
Furthermore, there are empirical reasons for pursuing separation, at least internal
to the theory developed here. I have argued for an analysis of De Se pronouns that
makes crucial use of them being assigned thematic roles and being interpreted in a neo-
Davidsonian fashion. As mentioned previously, this is not so with the subject of attitude
verbs, which is treated here as a standard type e expression. A problem arises when we
consider cases of iterated attitude reports like (6.74).
(6.74) John wants PRO to want to win
There are conflicting demands on the semantic value of PRO in this system. On the one
hand, we want PRO to be treated as a type ⟨v, t⟩ expression (i) to fit with all other neo-
Davidsonian nominals, and more importantly (ii) this type is required to compute the
meaning of the De Se presupposition put forth above. On the other hand, we want PRO to
be a type e expression so that it can compose with the embedded attitude verb, and thereby
create the appropriate set of alternative contexts. The problem can be fixed if the external
228
arguments to attitude verbs were separated, and then PRO could always be interpreted
as ⟨v, t⟩. Alternatively, another unified approach is to not separate any arguments, but
this would require all arguments being of type e, and this goes against the plethora of
arguments for thematic separation.
In the next section, I sketch a theory where the arguments of attitude verbs are
severed, and introduce some issues in this line of reasoning for future research.
6.6 A separationist account of De Se reports
In this section, I will show how far the tools used in previous chapters can go in
explaining some of the puzzles of plural De Se reports. I will not add much to the general
neo-Davidsonian system here; the goal is to show that much of the problems we saw
previously can be addressed by the neo-Davidsonian theory of plurality presented here if
we put aside some issues about the interpretation of attitude verbs and De Se pronouns.
The focus will be on ideas that should be familiar by now, such as thematic separation
and how cumulativity is related to thematic roles. To close this section, I make some
suggestions about how to “intensionalize” this account.
6.6.1 The task
The general goal here is to give a neo-Davidsonian decomposition of attitude re-
ports. This means taking standard truth conditions of attitude reports, which are universal
generalizations of worlds/contexts (6.75), and representing them instead as an existential
generalization of eventualities (6.76).
(6.75) ∀W ∈ R(X,W ′)[p(W )]
(6.76) ∃E[Θ1(E,X) & V(E) & Θ2(E, p)]
As discussed in §6.5.6, this is not a trivial task. However, I believe that the primary diffi-
culty is reconciling intenstionality properties of attitude reports with the neo-Davidsonian
229
decomposition in (6.76). As such, I will put off discussion of intensionality until the end
of this chapter, and show how far a neo-Davidsonian approach to attitude verb meaning
can go in explaining the cumulative (or non-cumulative) properties of attitude reports we
have observed thus far.
Below I repeat the list of relevant semantics properties exhibited by plural De Se
reports that need to be addressed.
(6.77) Properties of plural obligatory De Se reports
i. They report that each attitude holder has a De Se attitude about himself.
ii. They can have both dependent and group readings.
iii. They do not have a crossed reading.
iv. They contain De Se pronouns that are semantically plural.
v. They have embedded clauses that describe the attitudes of a plurality taken
together.
6.6.2 The internal argument of attitude verbs
Let us start with the related observation that not all attitude reports in natural lan-
guage have property (v). This was evidenced from Beck and Sauerland’s example (6.3)
repeated below as (6.78). Compare with a sentence that differs minimally from (6.78) by
having a pronoun that is coreferential with the attitude holder (6.79).
(6.78) Max and Peter said that Bill will marry Ann and Amy (*respectively)
(6.79) Max and Peter said that they will marry Ann and Amy (respectively)
As remarked upon earlier, (6.78) reports that Max and Peter said the same thing: Bill
married the two women. On the other hand (6.79) can report that each said a different
thing; namely that he will marry just one of the women. This is where we can see property
230
(v): the embedded clause of (6.79) does not describe the attitude(s) of either Max or Peter,
but seems to describe their plurality of attitudes when taken together.26
We have seen this state of affairs previously, not in the domain of attitude reports,
but with simple action sentences. Starting in Chapter 2, we saw that the object of an action
verb can denote something that a plural subject is not related to exhaustively. Simple
cumulative sentences exemplify this.
(6.80) Max and Peter married Ann and Amy
Although (6.79) can report that each man married two women, it can also be used to report
that each man married one of the women. Likewise, (6.79) can be used to report that each
said that he will marry two women (the group reading), or it can be used to report that
each wants to marry one woman (the dependent reading).
The action monoclause (6.80) is accounted for by having both subject and object
associated with thematic relations with plural arguments. This idea has been extended
to the domain of attitude reports by Dotlacˇil (2010). Putting details aside, he argues
that the embedded clauses of attitude reports be associated with a plurality of events.
This account has much in common with accounts of perception reports like (6.81) which
have also been argued to involve a verb that takes an event-denoted complement; see
Higginbotham (1983).
(6.81) a. John saw Brutus stab Caesar
b. ∃E[AGENT(E, j) & SEE(E) &
∃E ′[THEME(E,E ′) & AGENT(E ′, b) & STAB(E ′) & THEME(E ′, c)]]
In both the classic analysis of perception reports and Dotlacˇil’s analysis of attitude reports,
the events denoted by the embedded clause must meet the event description associated
26Again, I am not claiming that this is a property specific to obligatory De Se reports, as the optional
report (6.79) has this property. As Beck and Sauerland observed, presence of a pronoun is a crucial factor.
It may further be the case that when the dependent reading is intended with an optional report like (6.79)
then it must also be De Se; but I put this issue aside as optional De Se reports are not my focus here.
231
with the embedded clause. For (6.81), the events that are themes of the seeing must be
events of stabbing where Brutus is the agent and Caesar is the theme. Likewise, for a De
Se report like (6.82), the things wanted are events where Obama wins.
(6.82) Obama wants PRO to win
If attitude verb’s have separated arguments like other verbs, then the attitude verb
is interpreted as a monadic predicate of events (or states), and its internal argument is
associated with a thematic relation. It does not matter for present purposes what we label
this thematic relation, so I will just call it INT, short for internal. Under this view, action
sentences and attitude reports do not look very different, save that the internal argument
for the former is individual denoting, while for the latter it is event denoting.27
(6.83) a. Obama wants cookies
b. ∃E[AGENT(E, o) & WANT(E) & ∃X [COOKIE(X) & THEME(E,X)]]
(6.84) a. Obama wants PRO to win
b.
∃E[AGENT(E, o) & WANT(E) & ∃E ′[AGENT(E ′, o) & WIN(E ′) & INT(E,E ′)]]
Dotlacˇil’s general idea also provides a way to explain group and dependent readings
in plural reports. The explanation proceeds along the same lines for how sentences like
(6.80) above can have both distributive and cumulative readings. For the distributive
reading, each agent did something to the entirety of the theme, while for the cumulative
reading, each agent did something to only a part of the theme. Consider now our parade
case (6.1), repeated below.
(6.85) Obama and Romney want PRO to win
27An interesting question arises whether the internal thematic role is really different in both cases. See
Pietroski (2005) for discussion.
232
Let us idealize and assume that PRO is simply a pronoun that is covalued with Obama
and Romney. As such, the embedded clause denotes events of Obama and Romney win-
ning. For the group reading, each individual wants both Obama and Romney to win. If E
is the plurality of denoted by the embedded clause (events where both Obama and Rom-
ney win), then both Obama and Romney want E: E is the theme of both Obama’s and
Romney’s wantings. Compare with the distributive reading of the action sentence (6.80),
where both agents married the entire plurality denoted by the theme.
Conversely, for the dependent reading of (6.85), neither Obama nor Romney by
himself wants all of E, since E has both candidates winnings and each candidate wants
just one candidate to win: himself. That is to say, each candidate wants just a proper part
of E, namely those parts where he is the winner. This is comparable to the cumulative
reading of the action sentence (6.80), where each agent does not marry the entirety of the
theme, but just a part of it. For (6.80), what is required is that Max and Romney together
married Ann and Amy, even if no single agent married Ann and Amy. Likewise, for
(6.85), what is required is that Obama and Romney together want Obama and Romney to
win, even though no single agent wants the Obama-Romney plurality to win.
In sum, the tools to derive group and dependent readings are already present mech-
anisms needed to handle distributivity and cumulativity. As it stands, this analysis of cu-
mulativity predicts crossed readings of plural De Se reports to be possible, but we know
that this is not the case. I will turn to this issue shortly.
6.6.3 Intenstionality, attitudes De Se, and separation
We have so far accounted for properties (ii), (iv), and (v); we still need to address
the obligatory De Se properties and the lack of crossed readings. I believe that these two
properties are very closely related; and I will discuss their interdependency in both this
section and in §6.5. As a way of leading into this topic, let us consider one problematic
aspect of Dotlacˇil’s account: he does not provide a way to account for the limited range of
233
readings with Beck and Sauerland type examples. Dotlacˇil gives his analysis for attitude
reports in general, but the crucial point of Beck and Sauerland’s examples is that only
attitude reports with embedded pronouns that refer to the attitude holders allow dependent
readings. Another way of putting this is that without the pronoun, attitude reports must
be understood distributively in the sense described above.
Let us assume that it is not just the presence of a pronoun that gives rise to depen-
dent readings, but a pronoun read De Se. This would mean that only De Se reports allow
the cumulative interpretation (the dependent reading), while non-De Se reports only al-
low the distributive interpretation (the group reading). Several authors have argued that
the grammar of De Se reports differs from that of non-De Se reports; see for example
Chierchia (1989), and Percus and Sauerland (2003), among others. I propose that there is
a difference in the interpretation of De Se versus non-De Se reports, and that difference
lies in the interpretation of their respective embedded clauses. In particular, I propose that
Dotlacˇil’s analysis is only correct for De Se reports: only De Se reports have embedded
clauses that denote a plurality of events, and so only De Se reports exhibit cumulativity
between the agents and these events.
The question now is what is the interpretation of non-De Se embedded clauses
if they are not a plurality of events. I propose that these embedded clause pick out a
proposition, as they do in classical accounts of attitude reports. What is important for
the present account is that each embedded clause picks out one proposition, a singular
thing, and this is what is crucial for explaining the absence of cumulative interpretation in
non-De Se reports. Again, let us make a comparison with a monoclausal action sentence,
this time with a singular theme.
(6.86) a. Obama and Romney saw Michelle
b. ∃E[AGENT(E, o⊕ r) & SEE(E) & THEME(E,m)]
Since the theme argument is singular, we know that Michelle is the theme of both Obama
and Romney’s seeing. In a case like (6.80) above where the theme is plural, cumulativity
234
is possible asE may be divided into proper parts where Ann is the theme and proper parts
where Amy is the theme. This is not the case with (6.86): here Mary is the sole theme, so
both agents must have seen Mary in order for (6.86) to be true.
If non-De Se reports have a singular internal argument (a proposition), then the lack
of a cumulative reading for Beck and Sauerland’s (6.78) is explainable in the same terms
as the lack of cumulativity in (6.86). With the proposed dichotomy between De Se and
non-De Se embedded clause interpretation, the logic of cumulativity allows us to account
for another puzzling property about these plural reports.
Appealing simply to cumulativity between agents and events incorrectly predicts
that crossed readings should be possible. There is nothing so far that restricts the parts
of E that are events of Obama’s winning as being strictly the objects of Obama’s desires,
and vice versa for Romney. Put differently, the truth conditions of (6.85), given in (6.87),
are satisfied if some wanting events E ′ that is a part of E is such that Obama is the agent
of E ′ but the internal of E ′ are events of Romney winning, and if there are other parts
of E, E ′′, where Romney is the agent of E ′′ and the internal of E ′′ are events of Obama
winning.
(6.87) ∃E[AGENT(E, o⊕ r) & WANT(E) & ∃E ′[AGENT(E ′, o⊕
r) & WIN(E ′) & INT(E,E ′)]]
The system must have a way to restrict the interpretation of (6.85) so that such interpre-
tations are not possible.
So far, we have not spent much time considering what types of events act as the
internal argument of attitude verbs in De Se reports. Canonical attitude reports about
belief, desire, etc. are about mental states, so presumably the types of events that are
objects of attitudes are internal/mental in a way that other events are not. Maybe the
events of an individual winning take place in the world of that individual’s imagination,
or in the parlance of possible world semantics, these events take place on a world that is
bouletically accessible to an individual in the case of a desire attitude. This “internalness”
235
is also a key feature of what makes a De Se attitude De Se. The immunity property
mentioned previously concerns an attitude holder’s way of thinking about himself, or
internally representing himself in such a way that he cannot be mistaken about the identity
of the individual represented.
When we are reporting a De Se attitude, we are reporting about the mental state of
one or more attitude holders. The proposal is that the events that are objects of attitude are
in some sense “mental events”, and as such, exist in the mind of only the individual who
is holding the attitude. If we are reporting about a plurality of attitude holders, then the
plurality of events that are the internals must be linked to their respective attitude holders.
Under this view, it makes no sense for an event that is conceived of in the mind of Obama
to be the internal of Romney’s desire. I propose that this is part of the reason why crossed
interpretations are ruled out: while cumulativity alone allows (6.87) to be satisfied by in
the crossed situation, idiosyncratic knowledge of what it means to be an event of wanting
disallows certain assignments of sub-events to the agents and the themes.
This idea can be implemented formally on par with centered worlds. Essentially, a
centered world ⟨w, x⟩ pairs a world and an individual such that w is experienced from the
perspective of x. The notion was introduced by Lewis (1979) when addressing De Se at-
titudes, and has been used in several analysis of De Se attitudes since; see Pearson (2012)
for a recent overview. If worlds can be centered, then why not events? If centered-events,
not just events, are the internal arguments of some attitude verbs then De Se interpreta-
tions can be accounted for on par with their treatment in centered-worlds accounts: De
Se pronouns pick out the centers, similar to how they pick out authors in a context-based
approach. We also can clarify the restriction on crossed readings: an individual attitude
holder x cannot be the agent of an attitudinal event if the events that are the INT do not
have x as the center. In other words, Obama cannot be the agent of an event whose INTs
have Romney as the center; the events that Obama wants must be Obama-centered events.
De Se interpretation is not the only intensionality phenomena observed in attitude
236
reports. As such, even centered-events do not explain why a proper name in the scope of
an attitude verb cannot substituted for salva veritate. I will now make some brief sugges-
tions for how this issue might be addressed in future work. First, worlds can be brought
back into the picture, so that we can talk about intensions of (possibly centered) events
and not just events. Under this view, event-denoted complements of attitude verbs are
interpreted as event concepts, functions from possible worlds to events. One could also
argue that the internal arguments are centered-worlds or contexts that contain events, sim-
ilar to the suggestions about the relationship between events and contexts discussed in the
previous section. Both of these suggestions draw on the possible worlds to explain inten-
sionality phenomena. An issue to be addressed is how exactly the relevant possible worlds
are determined when the attitude verb’s arguments are severed. In standard accounts, the
attitude verb relies on its composition with the subject argument to determine the relevant
set of accessible possible worlds. Under a separationist approach, it seems that a variable
over worlds is required somehow in the internal argument, and the value of this variable
is determined by either binding from the subject or supplied by context. Alternatively,
one may wish to abandon the possible world approach to intensionality altogether. One
theory that does this is the Interpreted Logical Form (ILF) approach to attitude reports;
see Larson and Ludlow (1993) and references within. Although I cannot review all the
details of this approach here, the main idea is that the internal argument of attitude verbs
is a phrase marker (specifically, an LF phrase marker) where each node is pair ⟨x, y⟩ such
that x is the syntactic expression typically associated with that node, and y is x’s semantic
value. Opacity is accounted for under this view since substituting one name for another
might preserve the semantic value, but it does not preserve the form of the syntactic ele-
ment in the pair. The main modification to the Larson and Ludlow approach would be to
allow the S (or TP or CP) nodes to sometimes have eventive semantic values, specifically
when it comes to perception reports and De Se reports. For De Se reports, the semantic
value may be a centered event, as previously suggested. As a final suggestion, regardless
237
of which approach to intensionality a total-separationist adopts, I believe that much of the
work standardly attributed to the attitude verb can be delegated to the INT thematic role.
One might even find reasons to further divide the types of thematic relations available to
clausal complements, such that some of them induce intensionality (i.e., attitude verbs)
and some do not (i.e., perception verbs). It might even be the case that obligatory De Se
interpretation is tied to a particular thematic role.
In this section I have sketched an account of attitude reports, and De Se attitude in
particular, where there is thematic separation of the argument of attitude verbs. While the
principles of plurality and event semantics used so far were somewhat successful with De
Se reports, the biggest issue is accounting for intensionality phenomena. The conclusion
is that simple events cannot be the internal arguments of attitude verbs; but this does not
mean that a slightly more refined or intensionalized notion of event cannot be used. To
this end, I suggested some options that include centering events in a Lewisian fashion,
using intensions of events or event concepts, or using ILFs where the semantic value of
sentences are events. It is my opinion that attitude verbs are the next frontier for total
separation, and if some of the issues on intensionality can be resolved, it is possible for a
uniform theory in which all verbs are interpreted as monadic predicates of eventualities.
6.7 Some remarks about optional De Se reports
As I mentioned at the outset, my focus in this chapter is on obligatory De Se reports.
In this final section of content, I will outline some problematic issues concerning optional
De Se reports that need to be addressed in future work.
The issues are mainly empirical, and rely on the results of some rather subtle judg-
ments about the meanings of these reports. Consider first an example that has been im-
portant in determining when dependent readings are available: Beck and Sauerland’s
sentence, repeated below as (6.88).
238
(6.88) Max and Peter said that Bill will marry Ann and Amy (*respectively)
The relevance of this data point in the above discussion was to show that without a bound
pronoun in the embedded clause, only the group reading is available. That is, the only
reading available is the one where Max and Peter said the same proposition. Now, suppose
that some speakers do not agree with this judgement and allow a reading where Max and
Peter said different things, one about Ann and one about Amy, and as such the use of
respectively is acceptable to these speakers. This wouldmean that there can be cumulation
across finite clauses. In the present system, this is not necessarily problematic: it just
means that the proposal about collective satisfaction for De Se verbs applies to all attitude
verbs, whether De Se or not. In other words, we could completely abandon the Hintikkan
approach and remove universal quantification from the truth conditions of attitude reports.
This is one area where more serious data collection is required, as at least some speakers
of English that I have asked do not find the cumulative reading completely unaccessible.
My own personal judgements are in line Beck and Sauerland’s claims, but this might be
an area for speaker variation, and the theory of attitude verbs meaning in general will
ultimately have to address speakers’s intuitions about these kinds of data.
Another area of questionable data concerning optional De Se reports is the presence
of a De Se interpretation with dependent readings. Consider the plural case of mistaken
used above to show the De Se properties of obligatory De Se reports; except this time the
test sentence is an optional De Se report.
(6.89) a. Situation: Each candidate is very depressed the night before the election.
Each feels that another individual would do better in his place, and so each
thinks that he himself will lose and that another will win instead. While
wallowing in despair at the prospect of losing, each candidate is in his
respective hotel room drinking heavily. At the same time, they are watching
past debates looking people who will win instead of them, and each
239
candidate finds such a person and exclaims “I think he will win”. Little do
they know, each candidate is talking about himself.
b. Obama and Romney think that they will win
The question now is whether (6.89b) is true or false in this situation. The situation is set up
in such a way that only a dependent interpretation could be true since each does not think
the group consisting of Obama and Romney will win. If the judgement of this sentence is
false, then we could attribute it to the mistaken identity, on par with the obligatory De Se
cases. If true, we have a puzzling state of affairs. It would mean that there is self-directed
relation that holds between the antecedent and the pronoun, but this is not the De Se same
self-directed relation.
My own intuitions and those of several other English speakers are that optional
De Se reports like (6.89b) are false of mistaken identity scenarios like (6.89b). This
suggests that dependent readings must be De Se, even when they are found in optional
De Se reports. As such, we could analyze the pronoun they as being ambiguous between
a regular pronoun and a De Se pronoun (see Schlenker (2012) for discussion of De Se
interpretations of “regular” pronouns in English). When it is interpreted De Se, a De Se
attitude verb could be used an thus collective satisfaction is possible. The consequence of
this view is that whenever there is a dependent reading, then the report is must be read De
Se. Note that his assumes that dependent/cumulative readings are not always available,
as argued for by Beck and Sauerland; see previous paragraphs for issues about these data.
However, suppose that some speakers find (6.89b) true of the mistaken identity
situation. This would mean that dependent readings are not tied to De Se interpretation.
This would not be such a issue if it where not for the lack of crossed readings in optional
reports, as shown by Higginbotham (1981) and others. If cross-readings were allowed,
then we could attribute the less-than-group readings to cross-clausal cumulativity. But this
cumulativity is restrained in a way where each attitude holder has to have an attitude about
himself. The De Se analysis provided an independent reason for why self-directedness
240
might be involved: it is because the report is De Se and De Se attitudes by definition
are about one’s self. Thus, if (6.89b) does not have to be read De Se on the dependent
construal, we need another mechanism for restricting the range of interpretations for these
optional De Se reports. Of course, the first step is again more serious data collection to
see how speakers judge cases like (6.89); but supposing that speakers consistently judge
(6.89b) true, then more work needs to be done on finding a way to restrict dependent
readings without appealing to De Se.
Above I discussed two data issues that are paramount in the analysis of plural op-
tional De Se reports. For both of them the judgements are subtle and at least for the
latter issue, a convoluted mistaken identity scenario has to be considered while making
the judgement. Furthermore, even if De Se is a crucial property in explaining both op-
tional and obligatory De Se reports, it is not clear that a De Se interpretation is derived
uniformly for both optional and obligatory reports; see Anand (2006). As such, I leave
this issues to future work with the hope that the discussion in this section, and in this
chapter as a whole, can be insightful and informative in developing new theories.
6.8 Chapter summary
The chapter was devoted to the semantics of an understudied pronominal element:
the plural De Se pronoun. These pronouns are responsible for obligatory De Se ascription
to a plurality of individuals. We observed that plural De Se pronouns give rise to group
and dependent interpretations, though they lack a crossed interpretation. The fact that
these pronouns are De Se and can have dependent interpretations suggest that they, at
least sometimes, are interpreted as semantically singular. I have argued using reciprocity
and cumulativity phenomena that plural De Se pronouns are always semantically plural,
even for dependent interpretations.
I pursued two ways of looking at the meaning of De Se reports. For the first ap-
proach, I abstracted away from most of the intensional properties of the report, seeing
241
how much can be explained by just appealing to the theory of plurality and event seman-
tics used so far. I showed that the mechanisms for capturing distributivity and especially
cumulativity in basic sentences can be extended to De Se reports once some modest as-
sumptions are in place. I then developed an alternative analysis drawing on familiar ideas
from semantic theories of attitude reports, especially from context-based approaches to
De Se reports. I have argued that if De Se pronouns are semantically plural, then the
classical Hintikkan approach to attitude verb meaning which crucially relies on universal
quantification is unsuitable for plural De Se reports. I then developed a theory building
on Schlenker’s context-based neo-Kaplanian semantics for De Se reports. The core re-
vision was defining attitude verbs as expressing plural predication. For cases where the
Hintikkan approach might still be of use, I have suggested that the attitude verb expresses
distributive predication of contexts. On the other hand, at least plural De Se reports,
where the Hintikkan approach falls short, are suggested to express collective predication
of contexts. Additionally, I proposed a thematic-based interpretation for De Se pronouns
drawing on ideas from Higginbotham. The resulting system with these new definitions
of attitude verbs and De Se pronouns were then shown to be able to derive both group
and dependent readings, and rule out crossed readings. I then argued that the account
draws further support from its treatment of reciprocity and predicates of personal taste in
the embedded clause of plural De Se reports. I ended the chapter with a plan for future
research, specifically whether or not thematic separation, a crucial component through-
out the earlier chapters of this dissertation, can and should be applied to attitude verb
meanings.
242
Chapter 7: Concluding Remarks
In this dissertation I have presented a neo-Davidsonian event semantics for several
plural anaphoric dependencies. Below I will summarize the main results of the disserta-
tion.
The first part of the dissertation was a pursuit of morpheme univocality. The mor-
pheme in question is a distributivity operator, represented overtly in English as each.
The particular semantics I assigned to the distributivity operator is based on proposals of
Barry Taylor and Barry Schein about determiner uses of the distributivity morpheme. I
have argued that given a Conjunctivist view of composition, where nominal arguments
are interpreted as conjoinable thematic predicates, it is possible to assign a single lexical
axiom to the distributivity operator that is suitable for both determiner uses and cases of
distance distributivity.
I first considered canonical distance distributivity phenomena: floating and binom-
inal each. I then argued that familiar local anaphors, such as reciprocals and reflexives in
English, can also be treated as a type of distance distributivity construction. In particular,
I linked reciprocals and reflexives to binominal each in the sense that in all three cases
the distributivity operator composes directly with a nominal host, which is made possi-
ble by neo-Davidsonian approach to noun phrase meaning pursued here. In all of these
cases, the Taylor-Schein view of distributivity was argued to be at work. I have provided
several arguments for this view throughout the dissertation, though in my mind one of the
strongest conceptual arguments is that such a large range of phenomena can be accounted
for with a univocal definition of each.
243
The analysis of distributivity also has a wider empirical coverage than previous
studies. A common theme through Chapters 3 through 5 is the relevance of ditransi-
tive sentences and other sentences with multiple arguments. Prior research has focused
on these anaphors as direct objects in simple transitive sentences, and in many cases
these analyses do no extend to sentences when the anaphors occur in other syntactic po-
sitions. Furthermore, sentences with multiple nominals often present multiple sources of
antecedence for these anaphors, often leading to ambiguity. The Taylor-Schein analysis
was argued to be superior to its competitors in its capacity to uniformly account for the
compositional interpretation of these anaphors in a variety of argument positions.
Beyond these local anaphors, I also examined plural versions what I call “De Se
pronouns” in Chapter 6. Examples of these types of pronouns are obligatory subject con-
trolled PRO, shifted indexicals, and logophors in certain languages. These pronouns all
share the property of requiring an obligatory De Se interpretation. I have shown that plu-
ral De Se reports present some puzzling characteristics that are not seen in their singular
counterparts, particularly a wider yet restricted range of possible interpretations. The cen-
tral empirical claim of this chapter is that whenever a De Se pronoun is anteceded by a
plural attitude holder noun phrase, then the De Se pronoun must be interpreted as seman-
tically plural. I addressed previous proposals that treat plural pronouns in attitude reports
as semantically singular, and I provide several arguments against these views.
I essentially offer two analyses of these plural De Se phenomena. The first analysis
abstracts away from the intensional properties of these reports while pushing the plural
event semantics used previously in the dissertation to account for the core properties of
plural reports. The second analysis incorporates a specific theory of intentionality in De
Se reports, specifically the neo-Kaplanian context-based approach presented in the work
of Philippe Schlenker.
I hope that both analyses of plural De Se can serve as benchmarks for future re-
search. The first analysis requires more fleshing out of the intentionality aspects of De Se
244
reports, though I believe that remaining theory-neutral in this respect makes the core ideas
of the first analysis extensible to several different approaches to intentionality. The sec-
ond theory incorporates some specific claims about intentionality and De Se in particular,
and thus I believe it to be more precise in capturing the semantic nuances in these reports.
However, it does so at the cost of being rather convoluted. My goal with presenting two
ways of viewing the semantics of plural De Se reports is to give options for subsequent
research. Some may not be interested in exactly how the psychological aspects of De Se
reports work out, perhaps because of skepticism about how much of this actually has to
do with the language of attitude reporting, and thus may find the first analysis to be more
insightful. Others may be more interested in a semantics that incorporates these psycho-
logical aspects, as is done with several previous accounts of De Se reports. Future work
in this camp may find the second analysis more useful.
A common theme of the various analyses presented here is that the sentences ex-
amined were argued to have relatively weak meanings, with various ways of making
them true. Consider the well-known observation about reciprocal sentences that they
can be true in a variety of situations. While others have posited ambiguity in account-
ing for this fact, I believe that it is better to assign weak truth conditions to reciprocal
sentences that are compatible with the variety of ways of making a reciprocal sentence
true. Similar remarks apply to plural De Se reports, which were observed to have both
group and dependent interpretations. This was another area where previous research has
posited ambiguity, though I showed that it is possible to give uniform truth conditions
that are compatible with either construal. Methodologically, I believe that the single-
weak-meaning thesis of any phenomena is always worth considering. On the one hand,
there is the attraction of parsimony: accounting for more with less. On the other hand,
a single-weak-meaning theory attempts to account for a wide range of data with sparse
theoretical machinery, making such theories more easily falsifiable and thus making it
easier for future researchers to evaluate and criticize.
245
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