NATURAL LANGUAGE ADDITION VIA DEGREES, EVENTS, AND FOCUS

By

Cara Feldscher

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Linguistics – Doctor of Philosophy

2019

ABSTRACT

NATURAL LANGUAGE ADDITION VIA DEGREES, EVENTS, AND FOCUS

By

Cara Feldscher

This dissertation began asking where do we see addition in natural language? This began by
reframing comparatives, it extended to other types of addition, looking at list environments and
opening up questions about the nature of the language that enables “adding to lists”, which in
turn effected a cross-categorical research project, building on work on degree semantics, event
semantics, focus, and discourse structure.

Work on comparatives is foundational in degree semantics and comparatives continue to be the
source of ongoing research in the field (Cresswell, 1976; von Stechow, 1984; Kennedy & Levin,
2008; Schwarzschild, 2008). Here I work on an understudied ambiguity that can be analyzed as
more creating an event summing reading instead of the typically studied reading.
I contribute
novel data showing a class of expressions participates in this ambiguity, supporting a compositional
analysis. Event semantics typically analyzes adjectival constructions as stative constructions, in
lieu of incorporating degrees (Davidson, 1967; Parsons, 1990). This research works in the interface
between these two subfields, and provides an argument for studying their interactions, as well as a
compositional account of one way we see degree constructions build to event constructions.

From there, I follow morphological link to discover a class of data that impressionistically adds
propositions to lists, including data with the focus sensitive particle also. Following Rooth (1992),
I provide an analysis of this list effect via the semantics of focus and focus sensitivity. This requires
assuming that propositions as a whole can be focused, which in turn requires precise assumptions
about how the discourse context is framed formally. I follow both the Table theory from Farkas &
Bruce (2010) and the conversational scoreboard model of Roberts (2004), showing that pieces of
both models can function as contextual restrictions on the focus semantic value for focus sensitive
expressions. Further investigation showed that other focus sensitive expressions can have similar

restrictions, so major contributions of this include not only this revised notion of how to view
“context”, but also the ability to use focus sensitivity to investigate the nature of the discourse and
what objects it contains.

The final section of this dissertation focuses on data linking these two previous sections.
The appearance of aspectual particles like still in comparatives has been noted in the literature
(Ippolito, 2007). This pretheoretically looks like an event related expression contributing to a degree
construction, which is the opposite direction from the data analyzed earlier in this dissertation.
However, following Ippolito’s lead in analyzing still here as a focus sensitive particle, I implement
the analysis of focus and contextual restrictions I laid out in the previous chapter. The result is that
no evidence is found for treating this case as an event construction building to a degree construction,
but also further evidence is given for my theory in which objects in the discourse are the contextual
limitations on focus semantic values.

The major contributions of this dissertation thus fall into two main categories or topics. On the
subject of degrees and events, novel data solidified a previously observed link. Then the analysis I
proposed supports a compositional and directional analysis where degree constructions can be built
into event constructions. This highlights the importance of research on the interface between topics
and theories within the same subfield, like degree and event semantics. On the subject of focus
and the discourse, again I contribute novel data showing a class of expressions, which supports
an analysis involving focusing whole propositions. This analysis gives evidence that objects in
the discourse are the “context” that restricts the focus alternatives. These restrictions are lexical,
showing that research in this area, looking at other focus sensitive expressions, gives us a new tool
to investigate the structure of the discourse with.

This dissertation is dedicated to Eleanor Parrish Molner Feldscher Riley.

iv

ACKNOWLEDGMENTS

First and foremost, significant thanks are due to Marcin Morzycki for first showing me that semantics
is fun and convincing me to do my dissertation in it, and second supporting me while I then
proceeded to write said dissertation. You are a wonderful adviser and I am grateful to have worked
with you. I also appreciate Alan Munn stepping in to be my official chair when I needed it. You
have always made me feel supported, even while you are reminding me that a semantics dissertation
does need some syntactic consideration. I do appreciate your linguistic insight as well, but your
support and mentoring in both teaching and research was incredibly valuable to me in my time at
MSU. On the subject of mentoring, Karthik Durvasula stands out in his drive to share knowledge.
You helped me more in my phonology projects, but I appreciate your dedication to help even when
I left your subfield to work in semantics. Somewhere around that time Cristina Schmitt joined my
committee, which I am hugely grateful for. Your support and insight has been so helpful.

In addition to my committee members, I want to thank a few other faculty members specifically.
I appreciate the years in which Yen-Hwei Lin was on my committee, as I always appreciate your
advice and comments. Suzanne Wagner took up the job of graduate program director in the past
few years as well, and single-handedly demonstrated how supportive and wonderful someone in
that role can be. I would like to be half as supportive and successful as you one day.

Someone incredibly important is purring on my lap as I type. Ellie is the best cat and possibly
one of the single best things for my mental health during graduate school. While she cannot read,
she still deserves a shout out in my acknowledgments of significant figures without whom this
dissertation would not have been possible. I am incredibly grateful to one of the other best things
for my mental health during graduate school, and that is my therapist. Thank you Parker for all of
the hours that you listened to me talk about my dissertation, for all of the times that you told me I
was doing a good job, and for all the work you put in helping me learn to tell myself that I’m doing
well. These skills in dealing with anxiety really helped with writing a whole dissertation, but they
also noticeably improve my quality of life. To anyone in graduate school considering therapy, I

v

highly recommend it.

On the subject of research support, I want to thank Josh, Ai, Adam, and Curt for years and years
of helpful feedback in Awkward Time, even when I called it things like “semantics lab”. You all are
wonderful friends, but in the context of dissertation acknowledgments, I want to acknowledge that
you’re also all wonderful semanticists, and I appreciate your help. The board game nights didn’t
hurt, either! On the topic of board games, Becca, please keep playing DnD with me, I adore you.
And Alicia, I think you were the best roommate I ever had and I adore you too. And on top of that,
you’re an amazing linguist and I appreciate the times we worked together. To the other members of
my cohort and office friends, Monica, Kaylin, Alex, Morgan, thank you for all the lovely times we
had together. Even the work hangs, not just the times we hung out just in a friend way!

I think this brings me to friends and family outside of MSU and the Linguistics Department. My
family has been very supportive during my time in graduate school, even if occasionally perplexed
that I still “had homework to do over break”! Thank you in advance for the coming years of
continuing to support me by laughing at linguistics jokes. Jane, you have also signed up for years
of laughing at the same jokes, and that’s what you get for being incredibly supportive and helping
me finish my dissertation! Seriously though, you have been incredibly supportive and wonderful,
and I do not have the words to express how appreciative I am. Luckily someone got me prescription
pads for when I became a doctor, so I could just write you a prescription for feeling as appreciated
as you are! I have a huge shout out to Rowan, Emily, and Nicole for not only being wonderful
supportive friends, but also for coming and sitting through my three hour dissertation defense to
finish it out with me. Robin, Bruno, and everyone else who couldn’t make it, I am relieved on your
behalf that you didn’t lose those three hours of your life to my defense, because I promise that you
have given me more than that in support over the last year, and it’s been so appreciated.

One final type of group that I would like to thank explicitly is the queer spaces that supported
me during this time. In addition to being a stellar therapist, one more thing I have to thank Parker
for is that they directed me to Salus Center in downtown Lansing. Thank you to all the people
at the support groups I have attended for your kind words and unwavering support on topics both

vi

LGBTQ-related and dissertation-related. And finally, around this time last year I joined the Asexual
and Aromantic Spectrum Discord to figure some things out, and wow but did they help me figure
things out, while making me hella new friends. Once I sent a picture of a few stuffed animals
who were keeping me company writing and called it my “dissertation support squad”, and a friend
photoshopped their profile picture in and sent it back. This started off a waterfall of support, where
one after another put themselves in my support squad, creating this lovely picture. That’s where I
would like to conclude the acknowledgments, with a (metaphorical) picture of what happens when
you tell your lovely supportive group of friends that you’re struggling through writing a dissertation.
Starting clockwise from the top right corner of the squad picture, I want to thank Neri, Fox, Jimmy,
Fiji, Viola, Centi, Thor, DarkNinja, Nido, Aez (with Zorro), and finally we end on SV who started
the photoshopping support waterfall.

vii

TABLE OF CONTENTS

LIST OF TABLES . .

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.

.

.

KEY TO ABBREVIATIONS .

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.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1

INTRODUCTION .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Overall framing . .
1.2 Relating degree semantics and event semantics
. . . . . . . . . . . . . . . . . . .
1.3 Focus, the structure of the discourse, and adding to lists . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
1.4 Links between these two major topics

.

.

.

x

xi

1
1
1
4
6

CHAPTER 2 BUILDING EVENTS OUT OF DEGREES . . . . . . . . . . . . . . . . . .
Introducing an ambiguity with the comparative . . . . . . . . . . . . . . . . . . .

9
2.1
9
2.2 Frameworks and analytical tools . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Wellwood’s theory of Degree Phrases . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Existing analyses of the ambiguity for more . . . . . . . . . . . . . . . . . 16
Summing up background . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.3
2.3 Case study 1: ambiguity with more . . . . . . . . . . . . . . . . . . . . . . . . . . 23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1
2.3.2 Case study 1.5: additive again . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 An analysis of more
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.3.1 Viewing comparative more as degree addition . . . . . . . . . . 34
2.3.3.2
Constructing event summing . . . . . . . . . . . . . . . . . . . 36
Side notes on addition and summing . . . . . . . . . . . . . . . 40
2.3.3.3
2.4 Case study 2: additive adjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4.1 Event summing analysis
2.4.2 Degree addition analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
. 51

2.5 Consequences of this analysis, and open questions . . . . . . . . . . . . . . . . .

Further data .

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.

.

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.

. .

3.1 Addition on a larger scale .
3.2 Further data . .
3.3 Framework and required tools

CHAPTER 3 DISCOURSE ADDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.1 Rooth’s model of focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.2 Discourse frameworks and context . . . . . . . . . . . . . . . . . . . . . . 69
3.4 An analysis - proposition level focus . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.1 Also and proposition level focus . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.2 Extending this to other instances of discourse addition . . . . . . . . . . . 90
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.5.1
3.5.2 Analyzing concessive only with proposition level focus and a discourse

.
Further data . .

3.5 Concessive only . .

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 100

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restriction .

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3.5.2.1
3.5.2.2

Establishing domain goals for the discourse restriction . . . . . . 100
. . . . . . . . . . . . . . . . . . . . . 112
Introducing impediments
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

. .

3.6

Interim conclusions .

.

.

.

. .

4.1 Chapter goals .
4.2
4.3 Aspectual particles in comparatives

CHAPTER 4 ASPECTUAL PARTICLES IN COMPARATIVES . . . . . . . . . . . . . . 124
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Iteration in comparatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
. . . . . . . . . . . . . . . . . . . . . . . . . 128
4.3.1 A summary of still from Ippolito (2007) . . . . . . . . . . . . . . . . . . . 129
. . . . . . . . . . . . . . . . . . 129
. 131
4.3.2 Extending concessive still to comparatives . . . . . . . . . . . . . . . . . . 136
Problems, and an analysis of at-phrases . . . . . . . . . . . . . . 138
Reanalyzing concessive still as proposition level focus . . . . . . 145
Extending that analysis to yet
. . . . . . . . . . . . . . . . . . . 156
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
. . . . . . . . . . . . . . . . . . . . . . 164

4.3.3 Returning to even .
Interim conclusions and related questions

4.3.1.1 An overview of the uses of still
4.3.1.2

Ippolito’s analysis . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2.1
4.3.2.2
4.3.2.3

4.4

CHAPTER 5 CONCLUSION . .

5.1 Overall contributions .
5.2 Between degrees and events
5.3 Between focus, discourse, and context
5.4 Unanswered questions .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
. . . . . . . . . . . . . . . . . . . . . . . . 168
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

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BIBLIOGRAPHY . .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

ix

LIST OF TABLES

Table 2.1: The cross-linguistic patterns of homophony from Thomas (2017)

. . . . . . .

. 22

x

KEY TO ABBREVIATIONS

CG Common Ground
PS Projected Set
FSP Focus Sensitive Particle
NPI Negative Polarity Item

xi

CHAPTER 1

INTRODUCTION

1.1 Overall framing

This dissertation is framed by analyses of data showing some of the ways we see addition in
natural languages, and as a result it walks through a wide variety of semantic frameworks. I will
analyze multiple phenomena that can be pre-theoretically described as involving some kind of
addition, and end up grouping them into two major topics. In discussing these topics, I touch on
degree semantics, event semantics, focus sensitivity, the structure of discourse, and what we want
“context” to mean in formal semantic and pragmatic theory. Each of the three content chapters
focuses primarily on one phenomenon, steps through an analysis, and then tries to investigate what
predictions it makes as thoroughly as possible before discussing what the resulting implications are
for formal semantics.

The first type of addition analyzed relates degree semantics and event semantics. I open this
topic in Chapter 2 with data showing a link between the two, where the data shows ambiguity
between adding degrees or events. In Chapter 4 I return to this topic with data that also looks to
show a link between degree semantics and event semantics. The other major topic models addition
on a discourse level in Chapter 3. This kind of addition moves away from what looks like numerical
addition toward what looks like listing, or adding propositions to a list. This discourse aspect makes
a major contribution by formalizing the role of context, specifically in a focus analysis. This topic
is also continued in Chapter 4, where the data that looks degree-related is better analyzed via focus
sensitivity.

1.2 Relating degree semantics and event semantics

To begin Chapter 2, I look at an addition related ambiguity that makes it clear there must be
a compositional link between degree semantics and event semantics. Both degrees and events are

1

primitive types in the model, but semantic work often focuses on one or the other, rather than
their interactions. Degree constructions (adjectival constructions) have been analyzed as states, as
opposed to events, where states and events are both types of eventualities (Parsons, 1990). This
would place degree constructions (roughly equivalent to adjectival constructions here) and event
constructions (most verbal constructions) in complementary distribution, with no immediately
obvious reason to try to link these two subsubfields. However, in this section I first contribute data
showing that there is a regular, compositional relationship between the two kinds of constructions.
My initial two observations on this research track were that more can be used to say something other
than A (cid:21) B, having a reading where it sums two events, and that several adjectives and phrases
follow the same pattern that more does in having these two readings.

(1)

John graded two papers. I graded three more papers than John. (I graded 2 + 3 papers.)

(2) Andrew and I have to grade all ten of these papers. He graded six papers, and I graded
(9 total, 6 for him, 3 for me)

three more (papers), so we’re not quite done.

The typical degree use of more in (1) contrasts explicitly with the event use in (2). The typical
degree use is most clearly “addition” in that it adds the degree before more with the degree in the
than-phrase. In the case of (1), it adds 2 + 3 papers. The use of more demonstrated in (2) is less
studied, and looks like a typical comparative but crucially it looks to be doing a different type of
“addition”. If (2) worked like a typical comparative, it would mean that I graded 3 + 6 papers, but
instead it means that we graded 3 + 6 papers between us. That is, the “addition” is pretheoretically
adding his paper grading event to my paper grading event to make a bigger event comprised of the
sum of the two. This is the first observation, which I will go into more descriptive detail for in
Chapter 2. This has been noticed in the past by a handful of other scholars, who have described
it mostly as homophony between the typical comparative and this event reading.
I will review
their analyses in that chapter in greater detail, but the second observation I make here encourages
me to make a different, compositional analysis rather than treat this as homophony. This second
observation is that several words and phrases exhibit the same apparent homophony, which leads

2

me to treat it as a compositional ambiguity rather than a true homophony. This is exemplified by
the following data with additional.

(3)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
an additional two (compared to him).
(5 in one go)
b. My weekly running goal is five miles. I ran three miles yesterday, and then I ran an
(2 today, 5 total)

additional two today, so I hit my goal.

The data in (3) has the adjective additional instead of a comparative, but it has the same effect
that more had. The first reading works like a comparative, having a degree meaning, and the second
instead has the effect of event summing, where it talks about the total between the two running
events, not just the one event today. In Chapter 2 I also lay out more novel data in order to show
that this is a full class of expressions with this ambiguity, in support of analyzing this phenomenon
compositionally instead of as homophony. After proposing an analysis for the dual meanings of
more, I will extend it to this adjectival data as well, achieving a unified analysis.

Research on the comparative usage of more constitutes the foundation of studies of degree
semantics in theoretical linguistics, but this is a use of more that is significantly less studied in
the literature. The first contribution this work makes is simply in expanding the body of work
on this use of more, and in contributing an array of novel data that illustrates this phenomenon.
Additionally, the fact that we see an event summing meaning result from a prototypical degree
construction is a sign that research on this topic allows us to investigate the interaction between the
two semantic subfields of degree semantics and event semantics. In this chapter of my dissertation,
I aim to use this data on addition in language to flesh out this apparent connection between addition
and degree and event semantics, and discover what that in turn tells us about how we conceptualize
comparison, addition, events, and time in natural language. The resulting compositional analysis
indicates that there is a directional relationship, where degree constructions can be built into event
constructions. I will return to the topic in Chapter 4 in order to look at data that appears related and
ask if there is a directional relationship in the opposite direction possible as well. In addition, my
analysis makes proposals about the nature of the comparative, and suggestions about what other

3

silent machinery might be involved in its workings. Extending the analysis to the type of adjective
that participates in this phenomenon allows me to also make conclusions about how these adjectives
must fit in to the theory.

1.3 Focus, the structure of the discourse, and adding to lists

In the next chapter of my dissertation, I add data showing something that I would pretheoretically
classify as “addition” in a way of “adding to a list”. While degree addition looked a lot like adding
two numbers, this pretheoretically looks more like the phenomenon I called event summing in the
previous chapter, where two events were combined in a way. This data follows a morphological
link from the previous chapter, but for the actual analysis I end up stepping away from the degree
semantics focus. The action of adding a proposition to a list is a move which operates more on
the discourse level. That is, I will analyze these cases as “adding to a list” by virtue of analyzing
how they relate to other propositions in the discourse structure, rather than by adding numbers or
events. A sample of the relevant data is as follows, where we are looking at in addition.

(4)

(5)

I did a lot of things last weekend!
In addition, I baked cookies!

I did a lot of things last weekend!
Also, I baked cookies!

I hung out with friends...

I went for a walk...

I hung out with friends...

I went for a walk...

Looking at the two examples given, the puzzle for this section appears in list environments, and
impressionistically it signals the continuation of the list along the lines of ‘p, q, and in addition,
r’. The appearance of in addition in (4) is an example of the morphological link to the data
in the previous chapter, where addition also appeared in the form of additional. Furthermore,
in Chapter 3 I will show further data again showing this to be a class of expressions, including
morphological links to more as well. However, the other example in (5) includes also, a particle
that appears in research on focus sensitivity instead of research on degree semantics. Its usual use is
to flag that p is true in addition to presupposing that q from the set of alternatives generated around
the focused material is also true. This data initially looks like also has a use without its usual

4

presupposition, where instead, it seems to flag something about how p fits into the discourse. I use
this as the starting point to frame a new analysis proposing the existence of proposition level focus,
and discussing how that explains the apparently lack of a presupposition in this and other cases. I
will propose that proposition level focus is available for focus sensitive expressions, but it makes it
clear we must carefully define what it means for “context” to restrict the set of alternatives. I will
propose that “contextual restriction” should be reframed as objects in the discourse acting as limits
on the set of alternatives. As a result, the analysis I propose for discourse addition does not end up
with a compositional link between it and the previous chapter’s analysis, despite the morphological
clues toward a link. Instead, my analysis is focus-based, and relies on a model of the discourse to
restrict the focus set of alternatives. I will use the Table model of discourse proposed by Farkas
& Bruce (2010), but some of the data in the second half of the chapter will merit incorporating
some discussion of a conversational scoreboard model from Roberts (2018) and previous work.
In either case, I will review the relevant models of discourse in the chapter itself.
In terms of
the analysis, it is unclear whether a compositional analysis can be created which builds discourse
addition from the other types of addition I discuss in the previous chapter, and my analysis will not
end up making this compositional link. Even without a compositional link to degrees and events,
the analysis of discourse addition has consequences for how we model discourse, the relationship
between propositions in the discourse, and the role of “context” in the semantics broadly and
in focus specifically. In order to further explore the predictions of this definition for contextual
restrictions, I then present data for a different case of a focus sensitive particle, only, which can also
interact with proposition level focus.

(6)

I wanted to bake, only I didn’t have any flour.

(7) Only Danny passed the exam.

The example of only in (6) is different from the typical use of only, shown in (7). The bold in
(7) indicates prosodic focus, where the interpretation of only is affected by what word is stressed,
in this case meaning that Danny passed the exam and no other contextually relevant individual

5

passed the exam. The use of only in (6) does not clearly interact with any individual focused
constituent, nor do the truth conditions of only act like it is interacting with any constituent smaller
than the proposition as a whole. I will extend my analysis of proposition level focus and contextual
restriction to this case of only, and importantly I will show that only must have a different contextual
restriction than also. This is an argument in favor of lexically encoding these contextual restrictions
for focus sensitive particles at least, rather than assuming contextual restriction applies as a uniform
discourse phenomenon in these cases. This is a novel way of analyzing how the context interacts
in the semantics, formalizing the pragmatic effect into the lexical semantics.
It also opens up
new questions and research avenues into how “context” works in other areas of semantics besides
focus. Should we see restrictions based on the discourse structure lexically encoded in other things?
Should we see some kinds of restrictions operating wholly independently and across the board?
One final major take away from this avenue of research is the ability to use focus as a tool for
investigating discourse structure. I will discuss this in greater detail in Chapter 3, but given that
the different focus sensitive expressions that I analyze in this chapter utilize different objects in the
discourse to restrict the results of proposition level focus, this means that one way to argue for the
existence of different objects in the discourse that speakers track would be to see if phenomena like
this can be analyzed as referencing those objects.

1.4 Links between these two major topics

In my analyses, these distinct addition-related phenomena from Chapters 2 and 3 will not share
as much of an analytical link as the morphological evidence suggests they might. However, their
analyses will have explored a variety of tools, linking degree semantics with event semantics in the
first chapter, and linking focus and context with the discourse structure in the second chapter. In
Chapter 4, I examine the case of a phenomenon that looks to fall in the space between these two
chapters, potentially linking the preceding two chapters. This case is the appearance of particles
like still or yet, which have been called aspectual particles, in comparatives, which can be seen in
the following examples.

6

(8) Andrew graded six papers. I graded still more.

(9) Andrew graded six papers. I graded yet more.

The typical uses of words like still and yet are to give temporal information about the sentential
In data like (8) and (9) however,
event, making them ostensibly involved in event semantics.
they are embedded in comparatives, making them ostensibly involved in degree semantics. Plus
the overall meaning of the sentences is much like the sentence without still or yet in that it still
contributes a degree interpretation instead of having added temporal information. The analysis
in Chapter 2 delineates a relationship where degree constructions can be compositionally built up
into event constructions. This kind of data on the surface looks to show the opposite direction,
with words that typically contribute event information adding to a degree construction. However,
following work on still by Ippolito, I find that this phenomenon is best analyzed as a focus sensitive
expression that happens to be located within a degree expression, rather than as an event time
expression contributing to a degree expression. While this analysis leaves behind the topic of
“addition”, it provides further support for the analyses in both previous chapters. For Chapter 4,
it contributes another example of a focus sensitive expression interacting with proposition level
focus, and adds further discussion to how the structure of the discourse can frame what it means
to to “contextually restrict” something. For Chapter 2, its support is in not proving something.
Rather, it shows that the data in (8) and (9), which could illustrate a relationship counter to the
direction of the one described in Chapter 2, does not have to be analyzed as such. Proving the lack
of something is difficult, and out of the scope of this dissertation, but this analysis counters some
data that functions as an immediate counter to the relationship in Chapter 2.

Some research does exist on some of the phenomena I investigate here, but the cross-categorical
nature of this research means that degrees, events, focus, discourse structure, and the pragmatics
and semantics of context are all relevant. Rather than squish all of those topics together staccato in
an introductory chapter, each chapter will contain its own relevant background. As far as I know,
several of the phenomena I investigate here are not discussed in the research, but where an analysis
exists, I flag them on a case-by-case basis. In all cases I aim to give enough background in the

7

overall subfield that the analysis makes sense, but exhaustively investigating the history, competing
theories, and problems with each of the subfields I work in is beyond the scope of this work. As a
result, the reader should not take any chapter’s background to be a comprehensive resource on any
of these overarching subfields. In terms of the unifying theme, the question of where do we see
addition in language is not one that has a body of research behind it, outside of possible links to
plurals. There is a huge literature on plurals specifically (Link, 2002), and this is a cross-categorical
and cross-linguistic phenomenon as well. In addition to plural individuals, pluractionality, or plural
events, shows that there might be some kind of summing strategy for the ontology. The topics I
pursue here are not dissimilar, but it is different. Rather than focusing on how to make atomic
types in the ontology plural, I focus here on how we see these and other things added in non-plural
constructions, ones that do not necessarily involve adding semantic primitives. Similarly, there
exists some work on numerals (Hurford, 1975), but this is also not quite my focus. Rather, I will
simply be assuming numbers exist, and not questioning any internal structure or anything for them,
as they are not the focus so much as a helpful thing for making addition clear.

In summary, the structure of this dissertation following the introduction is as follows.

In
Chapter 2, I present data showing an ambiguity between two different types of addition in language,
which in turn illustrates a relationship between degree constructions and event constructions, and
then I provide a directional, compositional analysis.
In Chapter 3, I introduce a third type of
addition, discourse addition. In order to analyze it, I model proposition level focus and propose
a formal way to model contextual restrictions on it, and then I discuss its implications for both
addition in language and how we model discourse topics as a whole. Next, in Chapter 4, I revisit
both these topics via an analysis of aspectual particles in comparatives. Finally, Chapter 5 concludes
and discusses the contributions of this dissertation.

8

CHAPTER 2

BUILDING EVENTS OUT OF DEGREES

2.1 Introducing an ambiguity with the comparative

The mainstream theories of adjectival constructions present them as degree constructions.
While “degree semantics” covers a wide variety of topics and phenomena, a considerable portion
of this subfield is built on and deals with more and comparatives (Cresswell, 1976; Kennedy,
1999; Schwarzschild, 2008; von Stechow, 1984). As I am incapable of summarizing the whole of
this subfield here, and as the puzzles I look at here specifically build on existing analyses of the
comparative, this will be the focus of my review here. In addition to being one of the best studied
degree constructions, the comparative “more” has a second use with the appearance of building
event meaning from a degree construction. Consider the following data.

(1)

John graded two papers. I graded three more papers than John. (I graded 2 + 3 papers.)

(2) Andrew and I have to grade all ten of these papers. He graded six papers, and I graded
(9 total, 6 for him, 3 for me)

three more (papers), so we’re not quite done.

The use of more in (1) is the prototypical A > B comparative use, rephrased by Feldscher
(2017a) as degree addition. The use of more in (2), however, describes what Feldscher (2017a)
calls event summing, where it indicates that the two events can be added together, instead of more
indicating an A > B scenario. They provide a compositional analysis for these homophonous
two readings of more by building the more complicated event summing from degree addition.
Additionally, as the following data shows, the adjective additional and some other phrases show
the same ambiguity between the two readings. Feldscher (2017a) argues that the existence of
multiple words and phrases with the same ambiguity supports a compositional analysis rather than
analyzing this as a homophonous two mores.
I will refer to adjectives with this ambiguity as
additive adjectives.

9

(3)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
an additional two (compared to him).
(5 in one go)

b. My weekly running goal is five miles. I ran three miles yesterday, and then ran an
(2 today, 5 total)

additional two today, so I hit my goal.

(4)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
an extra two (compared to him).
(5 in one go)

b. My weekly running goal is five miles. I hit my goal yesterday, and then I ran just one
(1 today, 6 total)

extra mile today, so I surpassed my goal.

The data in (3) and (4) shows the same degree addition / event summing ambiguity that more
did above, but with additive adjectives, highlighted in the bolded section. The (a) version of each
has context supporting a degree addition (like the typical comparative) reading, and the (b) version
has context supporting an event summing reading. As per the italics, the degree addition reading
in (a) adds together the two numbers like a differential comparative, but the event summing reading
in (b) does something more. The two events are added together to create a superevent, and the two
degrees are added for that summed event. The local1 event itself has no degree addition, which the
meaning given in italics makes clear. In further support of a compositional analysis, consider the
following data as well, where the same ambiguity appears with phrases larger than an adjective.

(5)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
two miles in addition to that.
(5 in one go)

b. My weekly running goal is five miles. I ran three miles yesterday, and then ran just two
(2 today, 5 total)

miles today in addition to that, so I hit my goal.

a.

(6)

I read more things than Andrew did. He only read two books, but I read three papers
on top of that.
(I read 5 things total)
1I will refer to the “local” event or degree to mean the one in the sentence, near to the additive
expression. “Non-local” then refers to the other, contextually relevant event mentioned, which is
non-local in that it is further from the additive expression and possibly in another sentence. The
“summed event” is these two events added.

10

b. Andrew and I need to grade all 10 of these papers. We are halfway done because
(2 for me, 5

Andrew graded three papers and I graded two papers on top of that.
together)

The data in (5) and (6) shows the same ambiguity as more and the additive adjectives, but via
more syntactically complex phrases. While in (5) repeats the same addition root, the phrase in (6)
seems completely distinct. If we were looking at just more, a homophony analysis is reasonable.
However, the reappearance of what looks like the same kind of ambiguity with the same two
meanings with different syntactic categories and in more complex phrases is a strong argument
in favor of a compositional analysis instead of a homophony analysis. Specifically, it supports
unifying the analysis for more, additive adjectives, and more syntactically complex phrases, and a
compositional account that works with all three is the most straightforward way to do this. In this
family of data, I will begin with an analysis for more, as comparatives are well studied, and there
is a wealth of research to start from. From there, I will extend the analysis to additive adjectives in
support of a compositional analysis.

If a compositional analysis is to link these two readings, then either degree addition can be the
base reading which is then built to event summing in some way, or event summing can be the base
reading which is then built to degree addition in some way. I will propose that degree addition
is the base, on account of some dialectal English data involving again. Again is a quintessential
event word dealing with iteration, although a number of related uses have been described (Ippolito,
2007; Von Stechow, 1996). The following data is only acceptable in some dialects of English, but
in those dialects, what I am referring to as additive again can appear with a degree interpretation
instead of an aspectual interpretation. On the surface, this could be interpreted as an event kind
of morpheme contributing to degree meaning instead of a degree morpheme contributing to event
meaning, but following Feldscher (2017b) I will analyze it differently.

(7)

‘Standard’ again (event repetition)

a.

I shut the door again.

11

b. She ran a marathon again.

(8) Additive again (degree addition)

a. These apples are half again as expensive as those oranges.

(apples 1.5x oranges)

b. She ran half again as many marathons as I did.

(she ran 1.5x what I ran)

Feldscher (2017b) proposes a noncompositional analysis, which I will walk through in greater
detail in this chapter, but a compositional analysis building one denotation for again from the other
seems unlikely. In addition to the complicated denotation that will be needed for an analysis of
degree again, consider its dialectal status. Again is prototypically seen in event constructions,
giving information about the (re)occurrence of a state or event. While some speakers have a degree
again available, not all do. In comparison, as far as I know, speakers can get both the degree and
the event readings out of more and the other additive expressions. As not all event expressions can
interpreted as degree constructions, but the degree expressions here all have event interpretations,
the analytical direction I will take is building event summing compositionally from a base of degree
addition.

In this chapter, I will first give a brief background on degree and event semantics to the extent
that I will use those frameworks and analytical tools, at which time I will also give a brief overview
of the work that has been done on this ambiguity for more specifically. Moving on from any
necessary background, I will provide some further data on more. Next, in order to begin to
analyze more, I will first walk though an analysis for additive again as a first step toward building a
compositional analysis for more, as previewed in the previous paragraph. With that starting point,
I will propose an analysis for more that builds event summing from degree addition. Finally, after
stepping through that analysis, I will then test it by extending it to additive adjectives.

2.2 Frameworks and analytical tools

This analysis necessarily works with both degree semantics and event semantics, so some
quick review of both is needed. In either case, a full background gets away from the topic of this
dissertation, but I will minimally review the analytical tools I will be using, and the frameworks I

12

will be working within. The framework that I will be working in assumes the existence of events
and states, which are grouped together as eventualities of type v (Davidson, 1967; Parsons, 1990).
While adjectival constructions are often studied in degree semantics frameworks, assuming them
to involve stative arguments is uncontroversial. However, I have analytical choices to make in terms
of the degree semantics framework I will use, so this section will first step through that. Next I
will provide a brief overview of what analyses have been proposed for this non-comparative use of
more, before summing up and moving on to my own analysis.

2.2.1 Wellwood’s theory of Degree Phrases

Two major theories of the comparative exist. There is a huge amount of work in the literature
on degree addition in the form of the comparative, and there is not a consensus on what theory
is precisely right. One main theory has the Degree Phrase as the extended projection of which
the Adjective Phrase is an argument (Abney, 1987; Kennedy, 1999), and the other has the DegP
within the AP and scoping out (Bresnan, 1973; Bhatt & Pancheva, 2004). Either has advantages
in dealing with certain issues. If the DegP is the extended projection of the AP, then this structure
parallels the functional head structure of X′ theory, building to a overarching generalization that
lexical categories are all nestled inside functional projections. This is a theoretical elegance that I
appreciate, but make no predictions about in my work. However, if the DegP moved out of the AP,
this predicts scopal ambiguities that are observed in some cases (Heim, 2000). While movement
does work well for dealing with scope, there does not appear to be any scopal issues in the data I
am working with. In order to work in a framework that actively enables my analysis, I consider the
data I need to account for.

In this dissertation, I will follow the Degree Phrase structure proposed by Wellwood (2015) in
order to take advantage of the cross-categorial nature of her analysis. The degree addition / event
summing ambiguity occurs with eventualities of multiple types, not limited to degrees occurring
with adjective phrases. Consider the following examples, where (9) has an adjective long which
should evoke a state of length (of time), and (10) involves book-reading events instead of adjectival

13

states.

(9)

I am trying to run for longer stretches of time. Earlier I ran for 10 minutes, and just now I
ran for 15 minutes longer.

(10)

I read a lot of books this week. Monday I read 2 books, and Tuesday I read 3 more books.

The more/-er in (9) interacts with the adjective long. As the previous subsection discusses, this
could be treated as a state of length. The more in (10) deals with an eventive verb, dealing with
a scale of quantity that maps on to the reading event, and again the ambiguity is present. In the
degree addition reading, I read 5 books on Tuesday, 3 more than on Monday. In the event summing
reading, I read 5 book total, 2 on Monday plus 3 on Tuesday. Wellwood’s cross categorical DegP is
well suited to this data, as it reflects the appearance of more, and this homophony, with eventualities
of multiple types.

Wellwood (2015) builds on Bresnan’s 1973 approach, not assuming the DegP to be a functional
projection of the AP, but also not involving QR. She breaks down comparative more into much-er,
where much provides a contextually supplied measure function (cid:22) via an assignment function A. She
argues that a measure function must be accessible that measures individuals and eventualities both,
using a scale that is monotonic on the eventuality or individual, following Schwarzschild’s 2006
work on measure phrases. Schwarzschild (2006) shows that measure phrases must be monotonic
on the mereology of the event or individual being measured in the case of partitives, meaning that
measure phrases need to use units that measure out parts of the individual, or that measure along
a dimension that coincides with the part structure of an individual. This generalization is on the
strength of data like (11).

(11)

* Bill poured 50 degrees of coffee.

The sentence in (11) is ungrammatical, due to the fact that a temperature scale does not
measure out parts of the coffee. Wellwood gives evidence, however, that there are still multiple
scales possible after non-monotonic scales like temperature or speed are ruled out. In (12) and

14

(13), more must be able to access multiple scales in the same construction, as multiple scales can
be explicitly set for comparatives that otherwise look the same. Consider the following examples.

8>>>>>>>>><>>>>>>>>>:

volume
weight
number of cups filled
*temperature

9>>>>>>>>>=>>>>>>>>>;

9>>>>>>>>>=>>>>>>>>>;

(12)

John poured more coffee than Bill did, in terms of

(13)

John ran more than Bill did, in terms of

8>>>>>>>>><>>>>>>>>>:

distance
time
number of marathons ran
*speed

In (12), the scales of volume, weight, or number of cups are all possible for the comparative
more coffee. All of these scales can be monotonic on the running event, whereas temperature, for
example, can not be, and is therefore ungrammatical there. In (13), ran more can be measured
in terms of distance, time, or number of marathons. A non-monotonic measure like speed cannot
be set as the scale. On this basis, Wellwood proposes that -er references a contextually relevant
measure function (cid:22). If the scale is explicitly set like in the above data, that would be the scale
for (cid:22). If there is no explicit scale, then something appropriate for the context and the thing being
measured is used, as (cid:22) is a free variable and the speaker is free to determine what fits best. Here
in (14) are the denotations Wellwood proposes, where applying much to -er produces the familiar
more, and where -er is flexible in the type of measure function that it takes in. Recall that A is the
assignment function, and the subscript (cid:22) references the contextually relevant measure function.

(14)

J-erK = (cid:21)g⟨(cid:11);d⟩(cid:21)d(cid:21)(cid:11):g„(cid:11)” > d
Jmuch(cid:22)KA = A„(cid:22)”
Jmore(cid:22)KA =J-erK„JmuchK”
Jmore(cid:22)KA = (cid:21)d(cid:21)(cid:11):A„(cid:22)”„(cid:11)” > d

15

I build my analysis using the denotation of more (much-er) from this paper for two reasons.
First, it is a reasonably straightforward denotation, and it is simpler to work with a theory without
movement to start with. Second, as has already been demonstrated in the data provided so far,
this ambiguity occurs in constructions measuring a variety of things, showing the scale-flexibility
Wellwood works with. It makes sense to work with a theory designed to capture that fact. However,
in this chapter’s analysis, I will start by assuming this simplified version in (15), where it is identical
to the final like in (14) except the assignment function is omitted.

Jmore(cid:22)K= (cid:21)d(cid:21)(cid:11):(cid:22)„(cid:11)” > d

(15)

2.2.2 Existing analyses of the ambiguity for more

Besides the small few references I mention here, the literature on degree semantics and event
semantics is huge and the phenomena I am working with here is not going to bear on it as a whole.
Instead, it is worth reviewing what there is in the literature on more specifically in the context of
event summing, which is a much smaller task. The main requirements for a denotation of event
summing more are (1) the local degree must measure the local event (for the asserted content of
the proposition), (2) there must be a non-local event that can be measured and can be summed with
the local event, and (3) the measure of the summed event is the measure of the local and non-local
events added together. There are two accounts in the literature of what they call either “incremental
more” or “additive more”, by Thomas (2010) and Greenberg (2010, 2012) respectively. Both of
these are the event summing version of more, but I will refer to both here as denotations for an
incremental more, to avoid any confusion with “additivity” possibly referring to adding degrees
or summing events. Both of these analyses assume the event summing incremental more to be a
separate morpheme from comparative more. Based on the robust ambiguity of additive expressions
in English, I propose that it is not, but for now I review their theories here.

Greenberg (2010, 2012) analyzes incremental more as a homophonous morpheme to compara-
tive more on the strength of the fact that they have different translations in Hebrew and in multiple
other languages. Incremental more is homophonous with the morpheme meaning still in Hebrew,

16

which invites a different comparison with eventualities, but comparative more is translated using a
different word. In their data below, yoter is the word that appears in comparatives, as opposed to
od, which is used for event-summing more and also for a meaning which is translated as still.

(16) Rina
Rina
‘Rina is still asleep.’

yeSena
asleep

od
still

(17)

axalti
I-ate

(etmol
(yesterday
‘(Yesterday I ate 3 oranges.) Today I ate some more (oranges).’

(tapuzim)
(oranges)

tapuzim)
oranges)

ha-yom
the-day

axalti
I-ate

od
od

3
3

(18) hayom
today
‘Today Danny interviewed three students. Yesterday he interviewed more (than three).’

ri’ayen
interviewed

ri’ayen
interviewed

studentim.
students.

yoter/#od
yoter/od

etmol
yesterday

dani
Danny

SloSa
three

hu
he

After they establish this argument for separating both uses of more into separate morphemes,
they describe what incremental more must do. The main thrust of their argument is that the
presupposition of additive more is that there is a previous event and it can be summed with this
eventuality to create a super-event. In order for events to be summable, they must both be stages of
the same super-event. That is, the super-event must be a more developed version of the two events
being summed (Landman, 1992). Based on the theory that states do not have time arguments,
Greenberg argues that they can also then not have stages, explaining the infelicity of additive more
with stative predicates. This is based off data like (19).

(19)

* Rina was dirty some more.

As dirty is a state, and some more should only result in an event summing reading, the
ungrammaticality of (19) is argued to be due to the fact that states are incompatible with event
summing. If this is the case, that states cannot have time arguments or have stages, then they are
predicted to not be summable in Greenberg’s theory. As was already mentioned, I will work with
eventualities as a whole in my analysis, rather than specifically work with events and not states.
While more difficult to sum, states can be added if the right context is created to make it felicitous,

17

as I demonstrate below in (20). Another example of building an appropriate context would be the
additive another context provided by Thomas (2011), which is also repeated here in (21).

(20)

I am measuring how tall a stack my books would make if I stacked them all. Previously it
was up to 4′10′′, but I just bought The Fireman, which is 1.5 inches more.

(1.5′′ Fireman, 4′11.5′′ stack)

(21) A: How wide are those two pieces of furniture together?

B: The cabinet is 4 ft wide. The shelves are another 3 ft wide.

(3ft shelves, 7ft total)

Using more, (20) is successfully interpreted as event summing with a state of height. On the
strength of this evidence that states can sum like events can, if supported with the proper context,
I will not deal separately with states and events with my own analysis, but rather classify them all
together as eventualities. Additionally, (21) supports that this is the case for additive adjectives,
which falls in line with the assumption that additive expressions and more work in the same way.
In (23) I provide the denotation for the nominal usage of incremental more that Greenberg
(2010) comes up with. This is in a sentence like (22), where the things being added are ostensibly
nominal things. The underlined portion of the denotation is a presupposition.

(23)

(22) Four children sang, and three more danced.

J(Nominal) moreaddK = (cid:21)d1:(cid:21)Q⟨e;t⟩:(cid:21)P1⟨e;⟨v;t⟩⟩:(cid:21)e1:»9x»Q„x” ^ P1„x”„e1” ^ (cid:22)„h„e1”” =
d1 ^ 9e2; P2; d2; y»P2„y”„e2” ^ Q„y” ^ (cid:22)„h„e2”” = d2 ^ (cid:28)„e2” (cid:20) (cid:28)„e1”^
9e3; P3; z;(cid:3)P3„z”„e3” ^ e3 = e1 + e2 ^ Q„z” ^ z = x + y ^ (cid:22)„h„e3”” = d1 + d2^
e3 >developed e2………

Here h is a homomorphism from eventualities to individuals, reflecting that the development
of this event is measured in the number of individuals that participated. The denotation for
incremental more says that more takes in a degree, a nominal predicate, and then a verbal predicate.
The assertion is that the local degree measure the local event. For the underlined presupposition,
from the first existential quantifier (9e2) until the second (9e3), this part of the presupposition says

18

that there is a different event e2, which is temporally prior to the local event e1, and that this event
can be measured by individuals numbering d2. The rest of the presupposition introduces a third
event e3, which is equal to the sum of e1 and e2, and the measure of it is equal to the sum of the
measures of e1 and e2. The final conjunct introduces the concept of stages, saying that the summed
event can be considered a more developed version of the first event e2. This does account for the
data, but it does not account for the ambiguity of readings I described, nor for how the entire class
of additive expressions patterns in the same way.

Greenberg (2010) additionally provides a slightly different analysis for the predicative useage
(Mary ran for a little while and then she walked two minutes more), in order to work with different
semantic types for different syntactic types. However, I will only discuss the one here as an example,
as the nominal analysis is along the same lines and discussing both will not add anything helpful to
my points. My arguments for a different analysis hold in the same way for the predicative iteration
of Greenberg’s analysis as it does for the nominal half.

The other proposal in the literature for event-summing more is by Thomas (2010). Thomas
returns to the topic from a slightly different in later research as well, which I will go into after. One
of the effects that Thomas aims to capture in his 2010 paper is that different types of events can be
summed, as shown in (24).

(24) A: How much did you exercise last week?

B: I ran for two hours and I biked for three hours more.

The response in (24) sums a running event and a biking event together for a greater exercising
event. In order to sum different types of events, he calls an a function alt in their denotation for
incremental more. The alt function generates a set of contextually relevant alternatives of the same
type of the thing to which it’s applied, much like focus is proposed to do. So in this case in (24),
biking is a relevant alternative to running, given the context of exercising.

Below, (25) shows the denotation for incremental more proposed by Thomas (2010). Again,
the underlined portion ia a presupposition, which in this case is just that there is alternative event.

19

Thomas argues that the summed event measuring the added measures of the local and non-local
event is asserted rather than presuppositional, as Greenberg analyzes it.

JmoreincKg;c = (cid:21)d:(cid:21)e′:(cid:21)D⟨d;⟨v;t⟩⟩:(cid:21)e:9d′9D′ 2 alt„D”»D′„d′”„e′”… ^ D„d”„e” ^ 9D′′ 2
alt„D”»D′′„d + (cid:14)”„e (cid:8) e′”…
where (cid:14) = (cid:19)d′»9D′ 2 alt„D”»D′„d′”„e′”……

(25)

While stylistically somewhat different, this denotation accomplishes much the same thing that
Greenberg’s does. There is a presupposition that there is an event in the alternative set of the
local event, and it asserts that this event is summed with the local event in order to measure an
amount that is the local degree and the measure of the presupposed degree added together. The
main difference between the two analyses I have reviewed here is that for Greenberg, the summed
event and its measure are a part of the presupposition, whereas for Thomas they are a part of the
asserted content. The presupposition is limited to the event that is summed with the local event.
Using his example (26) to illustrate, Thomas argues that the summed event (“incremental clause”)
here is the proposition that we have had four beers, two on the the table and two in the fridge, which
is contradictory to set up context in (26). As (26) lacks any contradictory feel, Thomas argues that
no presupposed summed event can be projecting out of the conditional.

(26) We only have two beers. They were on the kitchen table and Chuck drank them both. If

there were two more beers in the fridge, Chuck would drink them both.

Like Greenberg (2010), Thomas also argues in his 2010 paper that incremental more is incom-
patible with stative predicates like long, but in his later 2011 analysis of another, he deals with
eventualities as a whole in order to include states in addition to events. Consider his example
repeated in (27).

(27) A: How wide are those two pieces of furniture together?

B: The cabinet is 4 ft wide. The shelves are another 3 ft wide.

(3ft shelves, 7ft total)

In (27), another does event summing with a state of width, with the help of the supporting
context. This reading is event summing because there is no degree addition for the local eventuality,

20

which would make the shelves 7 ft wide, but rather the statement from Speaker B flags that these
two states of width can be summed. On the topic of the supporting context, for his denotation of
additive another in Thomas (2011), Thomas introduces the Question Under Discussion (QUD) as
a use condition, modeling a presuppositional requirement to using another in this way. Compare
(27) with another of his examples in (28).

(28) A: How wide are the shelves?

B: The shelves are (*another) 3 ft wide.

The question in (27) explicitly raises the summed state and its measure in the QUD. The question
in (28) does not, but only asks about the measure of the local state. Based on this, he reformulates
the presupposition to be that there exists a question in the QUD, in order to then assert something
about that question. For clarity, I have underlined the presupposition.

JanotherK = (cid:21)d′:(cid:21)d:(cid:21)P⟨s⟨d;t⟩⟩:(cid:21)w : 9Q 2 QUD„c”»R„Q” = ℜ ^ B„Q”„w”„d′+

(29)

(cid:19)d′′»P„w”„d′′”…”…:P„d”

To step through this denotation briefly, the first conjunct in the presupposition says that the
question in the QUD is restricted to the set of real numbers, and therefore is a degree question. The
second conjunct says that this question can be answered by adding the degree argument of another
to the degree that holds of the local property P. The asserted part of the denotation simply relates
the local degree to the local property.

To sum up this section so far, both Greenberg and Thomas have analyses that account for the
event summing reading of more, and Thomas similarly accounts for event-summing another. All
of these analyses successfully replicate the truth conditions of event summing more (and another),
but what these analyses do not account for, however, is the behavior of the class of additive
expressions in English as a whole, where multiple expressions with degree addition readings also
have event-summing readings.

Thomas (2017) more recently takes on a very related but slightly different homophony. He
does not look at the class of additive expressions, but rather at patterns of homophony between

21

comparison / degree addition, event summing (what Thomas calls additivity), and continuation
(as expressed by English still). He observes that cross-linguistically, there are languages where
comparison is homophonous with event summing (like English), languages where event summing
is homophonous with continuation (like Hebrew), and languages where all three are homophonous
(Romanian for example), but no languages in their study where comparison is homophonous with
continuation and not event summing. This pattern is shown in (2.1), where shared letters indicate
that shared / homophonous words are used to express those things in that languages.

Table 2.1: The cross-linguistic patterns of homophony from Thomas (2017)

Comparison Additivity Continuation

Languages
Romanian
English, French, etc.
German, Hebrew, etc.
Vietnamese
unattested?

A
A
A
A
A

A
A
B
B
B

A
B
B
C
A

The pattern observed is that all three can be homophonous, comparison and additivity can be
homophonous, or additivity and continuation can be homophonous, but comparison and continu-
ation cannot be homophonous with the exclusion of additivity. Thomas explains this pattern via
an analysis in Distributive Morphology. In Thomas’s analysis, what all three of these meanings
have in common in their theory is a rising scale segment (Schwarzschild, 2012). In Schwarzschild,
comparatives are analyzed as being composed of pieces that say that on a scale like height for
example, Andy is taller than Danni if there is a rising scale segment starting at Danni and ending at
Andy. Thomas extends this analytical tool to analyze not just comparison (degree addition), but also
additivity (event summing) and continuation. All three of these readings are not compositionally
linked, but rather all three involve a rising scale segment, and varying spell-out rules create the
pattern of homophony shown in (2.1). So in languages like Romainian, homophony is achieved by
assuming a Lexical Insertion rule that applies everywhere there is the Deg head RISE. This is a
rising scale segment, and in a comparative, it describes the difference between the two things being
compared. Similar to the theory I will propose here, a functional head ADD applies higher up and
sets it such that the rising scale segment describes the increase in the measure of the summed event,

22

making it event summing. Thomas goes on to create continuation (it is still raining) by adding
another functional head CON to this projection. The patterns of homophony in different languages
is then achieved by assuming different Lexical Insertion rules in different languages, where the
three meanings are spelled out with one, two, or three different lexical items. This accounts for the
pattern of attested and unattested homophony.

While the English more data that I am analyzing fits this cross-linguistic pattern, in this chapter
I am focusing on a related, but slightly different issue. Specifically, here I will address the issue
of a whole class of additive expressions featuring this degree addition / event summing ambiguity,
with the goal of explaining the persistent ambiguity within English. To that end, I will pursue a
slightly different analysis also building event summing from degree addition, but with the goal of
this analysis providing a compositional piece of machinery that works with additive expressions
other than more.

2.2.3 Summing up background

At this point, we have a flexible framework for the DegP that works with the relationship between
states and events that I am assuming. This is what I will be working with, although I will propose
a small change during my analysis itself. While previous analyses of the additive ambiguity with
more have been presented also, I have presented evidence that they will not suffice. In the next
section, I will analyze more as the first case study in this overarching ambiguity, with the goal
of presenting an analysis that extends cleanly to analyzing additive adjectives. That extension to
additive adjectives will be the second case study after that.

2.3 Case study 1: ambiguity with more

In this section I will propose an analysis for the ambiguity allowing more to add different things.
First I will walk through some further data (focusing on more but including some additive adjective
data), with the goal of fleshing out what allows or blocks this ambiguity, and secondarily with the
goal of fleshing out what differences may exist between more and other additive phrases. Then

23

I will walk through existing analyses of more as an independent morpheme that happens to be
homophonous to the comparative, before talking through my own compositional analysis.

2.3.1 Further data

Given the correct contexts, many sentences with more are fully ambiguous and can be used
felicitously to mean degree addition or event summing. There are, however, two ways (besides
heavily biased contexts) to disambiguate between the event summing and degree addition reading
by syntactically forcing one or the other. The first, which was observed by Greenberg (2010), is
that including an unstressed some with more ensures an event summing reading, as seen in (30).2

(30) Yesterday I ran 2 miles, and today I ran some more.

(cid:31) (Degree addition - I ran > 2)

✓ (Event summing - I continued running)

As is marked in the italics, the reading of today I ran more than 2 miles is unavailable, and this
has to mean instead that the speaker continued the running event for some amount. It is clear that
some is doing something here if we compare it with something like a little bit, which does not lose
the degree addition reading.3

(31) Yesterday I ran 2 miles, and today I ran a little bit more.

✓ (Degree addition - I ran > 2)

✓ (Event summing - I continued running)

To extend this to additive adjectives and larger additive phrases, the same effect results. All of
the sentences in (32) also have only the event summing reading, not the degree addition reading.
There are minor syntactic differences between different additive expressions, in terms of what
elements must be overt or covert, but I will return to that in more detail later.

2In all of these examples I am considering only the indefinite plural some, not the hedging some

that we might see in a sentence like They ran some five miles before they stopped.

3Thanks to Karthik Durvasula for suggesting this comparison.

24

(32)

a. Yesterday I ran 2 miles, and today I ran some

b. Yesterday I ran 2 miles, and today I ran some

extra

8>><>>: additional
9>>=>>; miles.
8>><>>: in addition (to that)

on top of that

9>>=>>;.

(cid:31) (Degree addition - I ran > 2)

✓ (Event summing - I continued running)

(cid:31) (Degree addition - I ran > 2)

✓ (Event summing - I continued running)

The second way to force one of the two readings works with more specifically, and not with the
other additive expressions. This method is that the inclusion of a standard degree in a than phrase
necessitates a degree addition reading, as shown in (33), an observation which was also made by
Thomas (2017).

(33) Yesterday I ran 2 miles, and today I ran more than I ran yesterday.

✓ (Degree addition - I ran > 2)

(cid:31) (Event summing - I continued running)

It is impossible to extend this method of disambiguation to the additive adjectives due to
syntactic differences, which brings me to the next group of data worth stepping through. The
different additive expressions listed here also have some syntactic differences from each other that
are worth discussing. The data given so far has shown that more can optionally have a than phrase
or not, although its presence ensures a degree addition reading. While they are optional with more,
than phrases are totally incompatible with additive adjectives.

(34) Today I ran two miles more (than I ran yesterday).

8>><>>: additional

extra

9>>=>>; two miles

8>><>>: *than I ran yesterday

*from what I ran yesterday

9>>=>>;.

(35) Today I ran an

In the case of one of the more syntactically complicated additive expressions, things get a little
murky and a little less regular. Shown in (36), on top of requires the standard degree, although it

25

is also then introduced with something other than than, appearing here as what I ran yesterday. In
the case of (37), the standard degree is optional again for in addition to, but it is introduced with
yet a different preposition, appearing with to instead of of.

(36) Today I ran two miles on top *(of what I ran yesterday).

(37) Today I ran two miles in addition (to what I ran yesterday).

Finally, one other difference between more and additive adjectives is that additive adjectives
often take a determiner, which is itself restricted in selection, as shown in (38). Additionally, an
overt non-demonstrative determiner is disallowed once the overt number is gone, as in (39).

8>>>>>>>>>>>><>>>>>>>>>>>>:
8>>>>>>>>><>>>>>>>>>:

(38)

I ran

(39)

I ran

9>>>>>>>>>>>>=>>>>>>>>>>>>;
9>>=>>; 3 miles.
8>><>>: additional
8>><>>: additional
9>>=>>; miles.

extra

*∅
an
the (only w/context)
that/those (only w/context)
*some
∅
*an (not meaning 1)
*the
those

9>>>>>>>>>=>>>>>>>>>;

extra

In some cases, a determiner is felicitous, but only in supporting contexts, such as where there
is already an established 3 miles under discussion. The determiners that are felicitous only in
supporting contexts are flagged as such, and are otherwise infelicitous without accommodating a
context like this. In the case of an in (39), this is grammatical if we interpret it as meaning one,
but if we interpret it as a generic indefinite, it is not acceptable. These distribution of determiners
changes again slightly if we consider the more syntactically complex additive expressions.

26

8>>>>>>>>><>>>>>>>>>:

∅
*a
the (only w/context)
those (only w/context)

9>>>>>>>>>=>>>>>>>>>; 3 miles on top of that.

(40)

I ran

In comparison, more does not take a determiner if there is an overt number, but there does
seem to be a position available if there is no overt number, to compare (41) and (42). While
the determiner here may be a part of the measure phrase and not belong to more in any way, the
distribution still shows a clear distinction from that of the additive adjectives, and there is evidence
that the two should be analyzed as syntactically distinct.

8>>>>>>>>><>>>>>>>>>:
8>>>>>>>>>>>><>>>>>>>>>>>>:

(41)

I ran

(42)

I ran

9>>>>>>>>>=>>>>>>>>>; 3 more miles.
9>>>>>>>>>>>>=>>>>>>>>>>>>;

*a
*the
*that/those
*some
*∅
a
*the
that (only w/context)
*some

mile more.

To sum up this section, I have walked through some ways to disambiguate the degree addition /
event summing ambiguity, and then through some ways in which more, the additive adjectives, and
the more syntactically complex additive phrases differ. They patterned similarly (where applicable)
in terms of disambiguations, which is another argument in support of a compositional analysis that
works similarly for more, additive adjectives, and additive phrases. The differences pose a potential
counterargument to that strategy, but I will propose that they simply result from different syntactic
categories, which is not counter to a compositional analysis working similarly across categories.

27

2.3.2 Case study 1.5: additive again

The first step I want to take in stepping through my own analysis of more is actually to provide
an analysis of something else, as a compositional explanation of homophony can involve building
directionally either from A to B or from B to A. The cross-linguistic data with the pattern of
homophony that Thomas (2017) describes supports an analysis where degree addition is composi-
tionally built into event summing, not vice versa, and this is indeed the direction of compositionality
that I will pursue. However, another argument in support of this directionality comes from English
data involving again. One other phenomena in the literature where “additivity” has been discussed
is with additive again, a use of again that I previewed at the beginning of this chapter, which deals
with degrees instead of the usual repetition or restoration of eventualities (Feldscher, 2017b). The
availability of this use of again varies by dialect, and it additionally has a very restricted syntactic
distribution, so it seems unlikely that a compositional analysis of additive again will be a strategy
we want to assume is freely available in language, unlike that of additive more. To illustrate the
difference the ‘usual’ use of again, showing repeating an event or restoring a state, is in (7), and
“additive”, or degree-adding again, is in (8).

(43)

‘Standard’ again (event repetition or state restoration)

a.

I shut the door again.

b. She ran a mile again.

(44) Additive again (degree addition)

a. These apples are half again as expensive as those oranges.

(apples 1.5x oranges)

b. She ran half again as many miles as expected.

(she ran 1.5x what was expected)

For the readers who do not have this use of again in their dialect, the truth conditions of the
sentences with additive again are glossed briefly in the parentheses. So (44a) means that the price
of the apples is equal to one and a half times the price of the oranges. This degree use in (44) is in
contrast to the standard non-degree use in (43), which should not be contentious among speakers
of English. Between speakers of dialects with this use of again, there is some variation on what the

28

structure of a sentence with additive again can look like. The British word order is the (b) version
in (45), as opposed to the American English word order in (45a). And additionally, while additive
again seems to appear most often with half, it is capable appearing without half. Some examples
with other factor phrases or versions without factor phrases are shown in (46).

(45)

a. Neville is half again as tall as Pansy.

b. Neville is half as tall again as Pansy.

(46)

a. Neville is a third again as tall as Pansy.

b. Neville is three quarters again as tall as Pansy.

c. Pansy is four feet tall. Neville is that again.

(1.5x Pansy’s height)

(1.5x Pansy’s height)

(1.33x Pansy’s height)

(1.75x Pansy’s height)

(2x Pansy’s height)

d.

I shall probably have paid at least as much again in call charges.

(Example from the OED, meaning 2x)

The Oxford English Dictionary glosses as much again as “an additional amount equal to that
mentioned, twice as much”, and half as much again as “an additional amount equal to half that
mentioned, one-and-a-half times as much”, and it includes examples from 1523 through 2005.

The “default” use of again, or the one that has been the focus of a lot of research, is the
one that repeats or restores eventualities. Traditionally the analysis has been that again has the
presupposition that this event has occurred before or this state has held before. However the degree-
addition use of again has no presupposition of a prior eventuality. To look at an eventive example
for clarity, (44b) is perfectly felicitous if the speaker has never ran any miles before, requiring only
that there be another degree to compare it with (the expected number of miles she would run) and
not requiring a previous mile-running event.
In Feldscher (2017b), I provided a denotation for
additive again that works with the structure in (47). While the denotation does not in any way rely
on the presence of the factor phrase half, additive again appears with significantly greater frequency
with a factor phrase than in any other environment. In an effort to ensure that additive again worked
cohesively with factor phrases, it was built to work with the framework that Gobeski (2011) works
in for his analysis of factor phrases, along with his ensuring assumptions about the structure of the

29

comparative. This structure is also compatible with a dialect that accepts A is as tall again as B
as grammatical. If working with a different theory of the structure of the comparative, an analysis
of additive again should be adaptable for any theory with an analysis of optional factor phrases.
As I take the stance that all of my data revolves around addition, rather than multiplication, I do
not further investigate multiplication in this dissertation, so for further discussion of half and other
multiplicative factor phrases, or multiplication in semantics, see Gobeski (2011). The analysis
from Feldscher (2017b) merged Gobeski’s syntax for half as tall with a type system including
eventualities for again, resulting in the structure in (47).

(47) half as tall again as Pansy

⟨v; t⟩

⟨d; ⟨v; t⟩⟩

d

⟨d; ⟨v; t⟩⟩

⟨⟨d; ⟨v; t⟩⟩; ⟨d; ⟨v; t⟩⟩⟩

as Pansy

half as tall

again

I assigned again a modifier type like Gobeski’s type for half, although it is a type for a system
with eventualities, rather than the modifier type in Gobeski’s original system. What additive
again then needs to accomplish in this particular case is to assert that the eventuality this sentence
describes, one of height, will have the measure that adds up to Pansy’s height plus half of Pansy’s
height. So it will explicitly reference degree addition with the + operator, and the measure of
eventualities, where the measure function is written as (cid:22)„v”. Feldscher (2017b) assumes that the
degree for half of Pansy’s height can be accessed by getting the measure of a state of being half her
height, since there is no degree already present in the structure for it, as there is for Pansy’s actual
height. In order to accomplish this, their denotation for additive again uses the symbol (cid:25) to write
the relation indicating that the two eventualities it links are ones of the same type. In this example,
this would be states of height. The actual denotation given for additive again is in (48), followed
by a sample computation for the phrase and tree in (47).
′ ^ f„d”„v

JagainaddK = (cid:21) f⟨d;⟨v;t⟩⟩(cid:21)d(cid:21)v:9v

′»v (cid:25) v

(48)

′” ^ (cid:22)„v” = (cid:22)„v

′” + d…

30

The denotation takes in something of the functional type of either half as tall or as tall, and then
calls for a degree and then an eventuality, and says that there exists another degree and eventuality
d′ and v
′. The first conjunct uses a similarity relation to state that these two eventualities are of the
same type. So in (47), they are both eventualities (states) of tallness. The second conjunct says that
′. The third
the local function holds of the local degree and the existentially quantified eventuality v
conjunct is where two degrees are added to get the measure of the local eventuality. To make this
clearer, consider (49), where I have stepped through the computation for the whole of half again as
tall as Pansy according to the tree in (47).

(49)

a. JagainaddK = (cid:21) f⟨d;⟨v;t⟩⟩(cid:21)d(cid:21)v:9v
′»v (cid:25) v
b. Jhalf as tallK = (cid:21)d′:(cid:21)v
′′»tall„v
′′” ^ (cid:22)„v
c. JagainK„Jhalf as tallK” = (cid:21)d:(cid:21)v:9v
d. Jhalf as tall againK = (cid:21)d:(cid:21)v:9v
e. Jhalf as tall againK„Jas PansyK” = (cid:21)v:9v
2 dPansy + dPansy…

(cid:22)„v” = (cid:22)„v

′” + d…

1

′»v (cid:25) v

′” ^ (cid:22)„v” = (cid:22)„v

′” + d…

′ ^ f„d”„v
2 d′…
′′” = 1
′ ^ (cid:21)d′:(cid:21)v

′′»tall„v

′′” ^ (cid:22)„v

′′” = 1

2 d′…„d”„v

′” ^

′»tall„v” ^ tall„v

′” ^ (cid:22)„v
′»tall„v” ^ tall„v

′” = 1
′” ^ (cid:22)„v

2 d ^ (cid:22)„v” = 1

2 d + d…

′” = 1

2 dPansy ^ (cid:22)„v” =

f. = a property of eventualities, holding of states of tallness measuring one and a half

times Pansy’s height

In the further computation in (49), (a) repeats the denotation for additive again, and (b) is what
it merges with, a state of being half as tall as d. In step (c), again takes half as tall as an argument.
The first conjunct of additive again, before the underline, ensures that the eventuality described by
the given sentence is also a state of tallness. In line (d), this is expressed by replacing this conjunct
with one directly stating that the local eventuality v is a state of tallness. Looking back to line (c),
the underlined section is the contribution of half as tall where additive again repeats it wholesale.
′ is a state of tallness,
This is simplified in the underlined portion of line (d), where it asserts that v
′
with a measure of half of d, which line (e) introduces as Pansy’s height. It is worth noting that v
is existentially quantified, and it will gain no other qualifications within the sentence at this point.

31

′ are vacuously true as long as the state of being half as tall as
Therefore these assertions about v
Pansy exists. There is no requirement that anyone be the bearer of this state, for example. The
final conjunct in (c) introduces the degree addition in the measure of the local eventuality directly.
′ as half of d, which line (e) introduces as being the degree of
Line (d) introduces the measure of v
Pansy’s height. As a result, the whole thing describes a property of eventualities which holds of
states of tallness measuring one and a half times Pansy’s height. This successfully replicates the
meaning of this phrase.

This effectively does the opposite of my expected analysis for more here, in that it takes a
morpheme that repeats events (comparable to adding events) and makes it into a construction that
adds degrees. My hypothesis is that the event summing reading of the additive expressions as a
whole can be compositionally built from the degree addition reading. This is because the existence
of additive again is dialectal; while every speaker of English has an eventive again, many do not
have a degree again. In contrast, the additive expressions unilaterally have both readings. I take this
mismatch as evidence that the additive expressions should be analyzed as being compositionally
built from a degree addition reading to an event summing reading. The reverse direction is not
guaranteed, otherwise we would expect additive again to be present in all dialects of English instead
of a few. This non-compositional analysis that I have presented here is not contradictory in that it
makes no unfulfilled predictions that all event related words should have degree interpretations as
well.

To preview some related data, again is not the only word that typically appears with event
constructions relating to event time that seems to have links to degree constructions. What have
been called aspectual particles also appear in degree constructions, looking to give other evidence
of a link between degree semantics and event semantics. In addition to additive again, consider the
use of aspectual particles in comparatives in (50)-(52).

(50) Andrew graded six papers. I graded still more.

(51) Andrew graded six papers. I graded yet more.

32

(52) Berta ist noch größer als Adam.
‘Berta is even taller than Adam.’

(from Umbach (2012))

Feldscher (2017b) provides an analysis for the dialectal degree addition use of again described
in this section, but data like (50) and (51), and (52) shows that this pattern of aspectual particles
appearing in comparatives is cross-linguistic, indicating there may a greater link between degree
constructions and event constructions to be explored. This data and related puzzles will be returned
to later in Chapter 4.

2.3.3 An analysis of more

To finally get to an analysis of more itself, I propose an analysis that accounts for the ambiguity
of more by building an event summing reading from a degree addition base. This directionality is
both on the strength of the pattern of ambiguity observed by Thomas (2017), and on the analysis
of additive again that I just gave. In addition to more’s robust cross-categorical ambiguity, both
readings have a shared thread of meaning, which can be characterized as addition. In terms of the
typical comparative use, A > B can be reframed as A (cid:21) B + C, where C is a positive nonzero
amount, and this small reframing allows us to construe the comparative as degree addition. The
event summing reading also has an element of degree addition in a slightly different way. As a
reminder, consider the following data.

(53)

I graded three more papers than John.

(I graded dJ:paper + 3 papers.)

(54) Andrew and I have to grade all ten of these papers. He graded six papers, so when I grade
(10 total, 6 for him, 4 for me)

four more (papers) we will be done.

Again, (53) shows typical degree addition, where three more papers than John is the number
John graded plus 3. However, in (54), four more papers does not mean that I graded 6+4, but rather
it only means that I graded 4. Instead, this sums Andrew’s paper grading event with my paper
grading event, to make a superevent of both of us grading papers. The event summing reading
involves adding two degrees, but degree addition involved is that the superevent measures 6+4

33

paper gradings. What an analysis here needs to do is to link how more adds two degrees to get the
measure of one event for the comparative / degree addition reading, but sums two events (along the
way adding the two degrees to get the measure of the superevent) for the event summing reading.
Following the analytical direction proposed for additive again in Feldscher (2017a) and reviewed
previously, I propose to compositionally build event summing from degree addition.

2.3.3.1 Viewing comparative more as degree addition

(55)

(56)

As previously mentioned, the comparative can already be thought of as involving addition, if we
think about what math we need to do to interpret it. Below I repeat the denotation adapted from
Wellwood’s denotation for the basic comparative repeated in (55), and then in (56) I rephrase it
slightly so as to overtly incorporate addition. The comparative is usually thought of as saying A>B.
The change I propose is mathematically equivalent: A>B iff A=(B plus some positive, nonzero
number).4

Jmore(cid:22)K = (cid:21)d(cid:21)(cid:11):(cid:22)„(cid:11)” > d
Jmore(cid:22)K = (cid:21)d(cid:21)(cid:11)9d′:(cid:22)„(cid:11)” (cid:21) d + d′
Here I use (cid:21) rather than =, in order to account for the fact that we can say Alex is 2 inches
taller than Danni if Alex is exactly 2 inches taller, but also if they are 3 inches taller. This should
be uncontroversial, but the important change was that (56) now explicitly includes addition of two
degrees. Another argument in favor of reconsidering the typical comparative morpheme to involve
4Note that this must be a positive, nonzero degree, so this is an ontological assumption about
what is assumed for degrees. This restriction could go in the denotation of more instead, but doing
so indicates that we expect natural language to deal with either zeros or negative numbers in other
places. While sentences with such are perfectly understandable, they do not sound appropriate in
a non-joking context.

i. # Alex is negative three inches taller than Cameron.
ii. # A unicorn is zero inches tall, because it doesn’t exist.
Based on the absence of sentences involving zeros or negatives that sound serious instead of like
math jokes, I assume here that I don’t need to specify that degrees be positive and nonzero in a
presupposition or anything, but rather we can assume this to be a characteristic of degrees.

34

addition comes from differential comparatives, which explicit reference a differential degree (von
Stechow, 1984).

(57) Neville is three inches taller than Pansy.

dN (cid:21) „dP + 3”

The presence of two local degrees in (57), three inches and than Pansy, means that differen-
tial versions of the comparative requires addition. This minimally changes the denotation for a
differential more to the denotation in (58), which calls for two degrees locally and adds them.

Jmore(cid:22)K = (cid:21)d(cid:21)d′(cid:21)(cid:11):(cid:22)„(cid:11)” (cid:21) d + d′

(58)

Schwarzchild & Wilkinson (2002) make an argument to unify the comparative morpheme used
in differentials (requiring two degrees) with the one used in cases with only one local degree. They
follow the same mathematical reasoning that A > B iff A = (B + something). Working in an
interval-based semantics to express this intuition, they propose a covert some which expresses the
“some positive amount / degree” part of this intuition. In non-differential comparatives, instead of
the overt differential degree some appears instead. This allows the differential and non-differential
comparatives to both call for two degree / interval arguments, making the two instances of the
comparative more unifiable to one morpheme. This gives the two comparatives a parallel visible
in (59) and (60).

(59) Neville is three inches taller than Pansy.

(60) Neville is some taller than Pansy.

dN (cid:21) dP + 3
dN (cid:21) dP + d (where d is a positive, nonzero degree)

Because it matches the intuition that the comparative involves degree addition, and rather than
ensure my analysis works with two different comparative more morphemes of different types, I
follow Schwarzchild & Wilkinson in my analysis in unifying both versions of the comparative to
one morpheme, and assuming something like their covert some applies with non-differential cases.
Thus from this point, the denotation for more that I will be working with is the differential one from
(58). As their some is formulated for a theory working with intervals instead of degrees, I do not
directly borrow their denotation. I assume there exists a similar formulation possible for degrees,

35

which would reflect their intuitions relating the quantifier some to this use in a nondifferential
comparative, but I do not attempt to formulate it here. Instead, I will simplify by treating it for
now as simply denoting some degree d, and assigning it the type d. While almost certainly a
simplification, further exploring this question steps slightly away from this section’s goal. At this
point, the intuition that the comparative denotes (degree) addition is realized analytically.

2.3.3.2 Constructing event summing

In this section I build the event summing reading from the degree addition reading, in order to
explain why English has a natural class of additive expressions, where if they have a degree addition
reading they also have the event summing reading. In order to fully explain this robust ambiguity,
I posit that a separate morpheme, what I’m calling e-sum, creates an event summing reading when
merged with a degree addition expression, rather than proposing that each additive expression has
a homophonous degree addition morpheme and event summing morpheme.

In most cases, unless there are heavy contextual hints, more is ambiguous between either reading.
For example, while this example below attempts to use context to push the event summing reading
as the intended meaning by stating a five mile goal, the following sentence is still ambiguous, and
a degree addition reading is still possible.

(61) Bill and I are doing a relay race together. He ran two miles, and I ran three more, so we
✓ (5 miles total, 3 for me)

hit the goal of five miles.

✓ (more than the goal, 7 miles total, 5 for me)

However, one way to unambiguously create the degree addition reading is crucial to my analysis.
As previously mentioned, the addition of a standard degree in an overt than phrase blocks the event
summing reading. This data is repeated in (62b), which only has a degree addition interpretation.

(62) Bill ran two miles...

a. and I ran three mile more.
b. and I ran three miles more than Bill ran.

(I ran 5 OR 3)

(I ran 5 NOT 3)

36

Given that e-sum must take an argument of type ⟨d; ⟨d⟨v; t⟩⟩⟩, the appearance of a than phrase
type-wise blocks the e-sum morpheme. That is, if a than-phrase has appeared within the DegP
and saturated one of its degree arguments, there will be no node of type ⟨d; ⟨d⟨v; t⟩⟩⟩ for e-sum to
take as an argument. This leads me to propose that e-sum applies to a DegP of type ⟨d; ⟨d⟨v; t⟩⟩⟩.
it must apply before any than-phrase can, as after more combines with a than-phrase the result is
type ⟨d; ⟨v; t⟩⟩. In (63) I show Wellwood’s tree for comparative more / standard degree addition,
adapted to the sentence from (62). In (64), the same structure appears, but instead of a than-phrase,
we see the event-summing morpheme e-sum, which I have labeled as the Add head of the Additive
Phrase, taking the DegP more as an argument.

(63) Degree addition (Wellwood, 2015)

V
⟨v; t⟩
run

VP
⟨v; t⟩

MP

d

3-miles

DegP
⟨v; t⟩

Deg′
⟨d; ⟨v; t⟩⟩

Deg

d

⟨d; ⟨d; ⟨v; t⟩⟩⟩

thanP

more

37

(64) Event summing
VP
⟨v; t⟩

V
⟨v; t⟩
run

MP

d

3-miles

AddP
⟨v; t⟩

Add′
⟨d; ⟨v; t⟩⟩

Add

⟨⟨d; ⟨d; ⟨v; t⟩⟩⟩;
⟨d; ⟨v; t⟩⟩⟩
e-sum

DegP

⟨d; ⟨d; ⟨v; t⟩⟩⟩

more

What Greenberg and Thomas accomplished with their incremental more denotations must be
accomplished by applying the e-sum morpheme to more. As a reminder, the event summing reading
requires (1) the local degree must measure the local event (truth-conditionally), (2) there must be a
non-local event that can be measured and can be summed with the local event, and (3) the measure
of the super event is the sum of the measure of the local and non-local events. The part that is
definitely asserted is the measure of the matrix eventuality. Its falseness can be objected to with a
direct “no”, as in (65).

(65) A: Bill ran two miles, and I ran three more.

B: That’s not true, you only ran one more!

In contrast, the ability to sum the local eventuality with a non-local eventuality is less clear in
what it is. Greenberg calls it as a presupposition, but Thomas argues that it is asserted, as reviewed
previously. The non-local event is modeled as asserted by Greenberg (2010); Thomas (2010), but
as a presupposed QUD in the analysis of another by Thomas (2011). Based on these pieces, here
is the denotation I propose for the event summing e-sum in (66).

38

(66)

Je-sumvK= (cid:21) f⟨d;⟨d;⟨v;t⟩⟩⟩(cid:21)d(cid:21)v
Je-sumvK„Jmore(cid:22)K” = (cid:21)d(cid:21)v

′»(cid:22)„v
′»(cid:22)„v

′” = d ^ f„(cid:22)„v””„d”„v (cid:8) v
′” = d ^ (cid:22)„v (cid:8) v

′”…
′” = d + (cid:22)„v”…

The event-summing morpheme e-sum references a contextually relevant eventuality v. This
is a shorter version of Greenberg and Thomas’s presuppositions and QUD conditions. Like a
pronoun refers back to an individual in the discourse, this similarly references an eventuality in the
discourse. In this denotation, e-sum first takes in a thing of type more, which produces the second
line in (66). The event summing morpheme e-sum builds in the event summing with the (cid:8) operator,
but the degree addition of more contributes the part of the truth conditions that the addition of
the measures of the subeventualities make the measure of the supereventuality. The two asserted
′ measures d, and that the measure of
conjuncts of this morpheme are that the local eventuality v
summed eventualities is the measure of the local eventuality (d) plus the measure of the non-local
eventuality v.

To continue the sample computation, it may be clearer to assume an example eventuality for v
in the computation. In (67), information for the contextually relevant non-local event v is included,
but underlined to set it off from the rest of the computation as being not actually present. In this
example, if we’re talking about how Bill ran the first 2 miles of the 5 mile relay, and I ran three
more, we can assume the underlined parts in the following version.

(67)

Je-sumv more(cid:22)K= (cid:21)d(cid:21)v
′»(cid:22)„v
′” = d ^ (cid:22)„vB(cid:0)run (cid:8) v
J3-miles e-sumv more(cid:22)K= (cid:21)v
′»(cid:22)„v
Jrun 3-miles e-sumv more(cid:22)K= (cid:21)v

′” = 3-mi ^ (cid:22)„vB(cid:0)run (cid:8) v
′»run„v

′”^ (cid:22)„v

′” = d + 2-mi…

′” = 3-mi + 2-mi…

′” = 3-mi^ (cid:22)„vB(cid:0)run(cid:8) v

′” = 3-mi +2-mi…

In (67), the underlined portions are the information that v should convey if we assume v to be
the event where Bill ran the first 2 miles of the 5 mile relay. Now that we have two degrees visible,
it is clear how the addition happens. At the end of this computation, the truth conditions are that
the local event is one of running, it measures three miles long, and that this event summed with
the contextually relevant non-local event measures 5 miles long. Thus it reaches the correct truth

39

conditions, and the event summing reading is directly enabled by the presence of degree addition
in the morpheme that e-sum applies to.

2.3.3.3 Side notes on addition and summing

The unacceptability of certain sentences has the potential to shed light on the conceptualization
of how we add either degrees or events. For example, if events are to be summed, they must be
In (68), things is acceptable because it creates a superset eventuality type that
the same type.
includes the original eventuality type. Book-readings count as thing-readings, but magazines is
not acceptable because book-readings and magazine-readings are different. Both can count as
thing-readings, as shown in (69, 70), but in (68) they are not explicitly grouped as thing-readings,
and therefore cannot be added.

(68)

I read one book last weekend and next weekend I think I’ll read two more

8>><>>: things

*magazines

9>>=>>;.

(69) This weekend I read one book and two magazines, and next weekend I think I’ll read two

more things.

(70) Alex: I read a book today.

Brady: Oh, you should read more things than that.

Alex: Well tomorrow I’ll read a book and two more magazines then!

Similarly, in (71), a running event and a swimming event can be added, but only when grouped
as exercising events. This mirrors the evidence Thomas (2011) provides for his “additive another”.
The explicit QUD establishes a way to group the eventualities so that they can be summed.

(71) Alex: How much did you exercise today?

Brady: I ran two miles this morning, and swam half a mile more this afternoon.

Schwarzschild (2006) shows that measure phrases must be monotonic on the mereology of the
event or individual being measured in the case of partitives, as I previously discussed in my review

40

of Wellwood’s DegP. It logically follows that if a measure is not monotonic on the mereology of
the eventuality or individual and cannot measure an amount of it, it will not be possible to use that
measure to then add amounts of that individual or eventuality. This is why (72) is ungrammatical;
the temperature of the water cannot be mapped onto the part-whole structure of the water, and if the
measure phrase cannot be used to add amounts of a thing if it cannot be used to measure amounts
of a thing to start with.

(72)

* After Bill poured coffee, I poured 10 degrees more water.

All in all, this analysis works with the English data so far, but there is cross-linguistic data
not yet accounted for. As was previewed in Greenberg’s Hebrew data, in other languages, this
event summing is done using the same word as that the language uses for event continuation (still
in English), indicating that there is an a link between those two meanings, just as there is a link
between degree addition and event summing. The following German data is from Umbach (2012)
and provides another example of this.

(73) Es regnet noch.
‘It’s still raining.’

(74) Otto hat noch einen Schnaps getrunken.

‘Otto had a schnaps in addition.’ / ‘Otto had another schnaps.’

Glossing over some details Umbach (2012) discusses about stress, (73) and (74) show this
homophony in German between the noch use for event continuation (still) and the event summing
use discussed previously. Other data from Thomas (2017) supports this link, with either this pattern
of homophony or with languages like Romanian where all three of these meanings are achieved
with the same word. As indicated by this pattern of homophony, in order to extend this analysis
compositionally, continuation must be built up from event summing as event summing was built
up from degree addition. This data supports a relationship where event structures contain degree
structure, but it does not weigh in on whether event structure necessarily or optionally contain

41

degree structure. Specifically, this data presents degrees as potentially building up the event time
information part of the event structure, or the aspect.

One other aspect of this data worth dwelling on is that still is an aspectual/iterative particle in its
prototypical use. The above data does have this iterative meaning, but in Chapter 4, I will discuss
several instances of aspectual particles appearing in degree constructions with degree meanings
instead of aspectual meanings. The relationship between event time and degrees is clearly present,
but at this time its exact nature is still opaque.

2.4 Case study 2: additive adjectives

The less well studied case of degree words being used for event summing is the case of other
additive expressions. Here I will focus on additive adjectives, for syntactic simplicity, and provide
an analysis of them in order to show that the analysis for more can be extended. Feldscher (2017a)
names adjectives like additional or extra “additive adjectives” because, like more, they can be
interpreted as degree addition or as event summing, given the right context. To repeat the data
from before as a reminder, here are example sentences with additive adjectives showing the same
ambiguity as more.

(75)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
an additional two (compared to him).
(5 in one go)

b. My weekly running goal is five miles. I ran three miles yesterday, and then ran an
(2 today, 5 total)

additional two today, so I hit my goal.

(76)

a.

I can run much further than Bill can. He can run three miles in one go, but I can run
an extra two (compared to him).
(5 in one go)

b. My weekly running goal is five miles. I hit my goal yesterday, and then ran just one
(1 today, 6 total)

extra mile today, so I surpassed my goal.

In (75) and (76), both of the (a) examples are constructed with context intended to push the
degree addition reading, paralleling the comparative more. Both of the (b) examples are constructed

42

with context intended to favor the event summing reading, showing that the same ambiguity as
more has appears for these adjectives too. While I am keeping the label “additive adjectives” here,
they might not function differently from the more syntactically complex additive constructions, so
this label shouldn’t be interpreted as asserting that they’re different. However, the easiest examples
for the next step of this analysis are syntactically simple adjectives before more complex phrases. In
addition to prepositional phrases being clearly more complex, data like a whole nother kettle of fish
suggests that another may be a complex determiner broken down as an+other, as well, so I am not
going to analyze that one at this time either.Here I will extend my analysis of more to only the purely
adjectival example additional, rather than complicate matters with determiners, prepositions, or
other phrases. Additionally, one other reason to step through an analysis of more and additional
specifically is that these two morphemes are ones that we will see return in Chapter 3, the chapter
on discourse addition. Although none of the types of addition I examine works only with these two
morphemes, these two appear with every type I examine. After extending this analysis from more
to additional, I hypothesize that the analysis of more complicated additive constructions should be
parallel to this one, albeit with a few more moving pieces.

Additive adjectives like additional are not syntactically interchangeable with more, but rather
they should be analyzed as adjectives that have denotations that parallel the Deg head more. As
(76) and (75) earlier showed, they appear in the Adj position between a determiner and a noun.
Additionally, they can follow the copula be although they are clumsy after seem, as shown here in
(77), likely because seem is sensitive to gradable adjectives and these are not gradable.

(77)

a.

I discarded the fifty third card because it

b.

I discarded the fifty third card because it

?seemed

8>><>>: was
8>><>>: was

?seemed

9>>=>>; additional.
9>>=>>; extra.

Finally, the -ly suffix that attaches to adjectives to create adverbs (rude-ly, wise-ly, frank-ly, etc.)
attaches to additional to create additionally. We can safely assume additional and other members
of its class are adjectives with a semantics like that of more, rather than stray Deg heads requiring

43

a syntactic explanation of where the comparative is appearing.

Assuming only minor differences between more and additional means the same analysis can
be extended fairly smoothly. Most of the differences we walked through earlier in Section 2.3.1
could be attributed to more appearing in DegPs and additional appearing in Adj positions, although
relevant differences will be reviewed as necessary in the following sections. Minimally, both must
have degree addition capability, but we can hypothesize that e-sum is compatible with multiple
syntactic types as long as they have the right semantic requirements.

2.4.1 Event summing analysis

I will begin this analysis with the event summing reading instead of with degree addition. To review
data from before, more can appear with an optional than phrase, as shown by (78), but additive
adjectives additional and extra cannot appear with a than phrase, as shown in (79). However, as
(80) shows, event summing for more is blocked by a than phrase.

(78) Today I ran two miles more (than I ran yesterday).

8>><>>: additional

extra

9>>=>>; two miles

8>><>>: *then I ran yesterday

9>>=>>;.

(79) Today I ran an

*from what I ran yesterday

(80) Yesterday I ran 2 miles, and today I ran more than I ran yesterday.

✓ (Degree addition - I ran > 2)

(cid:31) (Event summing - I continued running)

Given that additive adjectives can’t appear with a than-phrase, it instead makes sense to work
from the starting point of the event summing analysis proposed for more so that we can assume
that e-sum appears in the structure in lieu of a than-phrase. Recall also that additive adjectives are
heavily restricted in what determiners they can appear with, some evidence of which is repeated in
(81).

44

8>>>>>>>>>>>><>>>>>>>>>>>>:

*∅
an
the (only w/context)
that/those (only w/context)
*some

9>>>>>>>>>>>>=>>>>>>>>>>>>;

(81)

I ran

8>><>>: additional

extra

9>>=>>; 3 miles.

Definite determiners are only allowed when anaphoric to some specific amount in the context,
but the simplest case seems to be the indefinite an, which I can assume for simplicity is uninterpreted.
To the end of explaining a parallel between more and additive adjectives, the tree proposed for event
summing with more is repeated below, followed by a minimally changed version which is adapted
to event summing with additional.

(82) Event summing with more

V
⟨v; t⟩
run

VP
⟨v; t⟩

MP

d

3-miles

AddP
⟨v; t⟩

Add′
⟨d; ⟨v; t⟩⟩

Add

⟨⟨d; ⟨d; ⟨v; t⟩⟩⟩;
⟨d; ⟨v; t⟩⟩⟩
e-sum

DegP

⟨d; ⟨d; ⟨v; t⟩⟩⟩

more

45

(83) Event summing with additional

V
⟨v; t⟩
run

D
an

VP
⟨v; t⟩

DP
⟨v; t⟩

AddP
⟨v; t⟩

Add′
⟨d; ⟨v; t⟩⟩

Add

⟨⟨d; ⟨d; ⟨v; t⟩⟩⟩;
⟨d; ⟨v; t⟩⟩⟩
e-sum

AdjP

⟨d; ⟨d; ⟨v; t⟩⟩⟩
additional

MP

d

3-miles

Here I have given the adjective phrase additional the same semantic type as more, and assumed
that the determiner an is uninterpreted. As a result, the exact same types work for the adjectival
structure as for the comparative, with the event summing morpheme e-sum again merging with
the phrase in question, before merging with the measure phrase. In (84), the denotation used for
more is repeated, so it can be seen that the same denotation is given for additional here. As the
denotations are the same as in the analysis of more, it follows that the computation would be the
same as well, so the computation in (85) is only shown through the Add′ layer, rather than repeat
the whole computation from Section 2.3.3.2.

′” = d ^ f„(cid:22)„v””„d”„v (cid:8) v
′»(cid:22)„v

′” = d ^ (cid:22)„v (cid:8) v

′”…

′” = d + (cid:22)„v”…

(84)

(85)

Jmore(cid:22)K = (cid:21)d(cid:21)d′(cid:21)(cid:11):(cid:22)„(cid:11)” (cid:21) d + d′
Jadditional(cid:22)K = (cid:21)d(cid:21)d′(cid:21)(cid:11):(cid:22)„(cid:11)” (cid:21) d + d′
Je-sumvK= (cid:21) f⟨d;⟨d;⟨v;t⟩⟩⟩(cid:21)d(cid:21)v
′»(cid:22)„v
Je-sumvK„Jadditional(cid:22)K” = (cid:21)d(cid:21)v

46

The above denotation, when given a degree and the local eventuality in the sentence, will assert
that the measure of the local eventuality is equal to that degree, and that the measure of the local
and the non-local contextually relevant eventualities summed together is equal to that degree plus
the measure of the non-local eventuality. This is the same result as we saw in the more analysis,
and it accurately reflects the truth conditions of additive adjectives.

In support of assigning additive adjectives the same denotation as more, we cannot build
something like e-sum into their denotation directly because they have a degree addition reading
too, not just eventuality summing. So we have to build the event summing reading compositionally
in the same way we did for more. To add a parsimony argument in favor of giving additional
the same denotation as more, if we give the same denotation for either morpheme, then we
definitely do not need to posit different event summing morphemes to work with different syntactic
categories of additive expressions. This allows the same e-sum morpheme, rather than multiple
silent morphemes. It is worth pointing out that additional and extra do not convey precisely the
same meaning, and we probably do not want to assign every morpheme that participates in this
ambiguity precisely the same denotation. However, it’s equally worth pointing out that unraveling
the intricacies of the precise differences between each of these adjectives of phrases is outside
the scope of this study at this time. Instead, the goal is to lay out a framework in which additive
adjectives (and possibly more syntactically complex phrases) display the same ambiguity as more
does, with a minimal but explanatory analysis, and that this section’s analysis successfully makes
progress toward that goal.

2.4.2 Degree addition analysis

Now that we have a working event summing analysis for additive adjectives, we can work backward
to get degree addition from this event summing structure by removing e-sum from the structure,
In lieu of e-sum taking additional as an argument, additional can, like more, take
as in (86).
two degree arguments to add them. As additive adjectives cannot take a standard phrase or a
than-phrase, this does therefore mean that there can only be one overt degree argument. I favor

47

a parsimonious analysis that does not assume that morphemes that do degree addition have two
homophonous versions: ⟨d; ⟨d; ⟨v; t⟩⟩⟩ and ⟨d; ⟨v; t⟩⟩. Instead, I propose the tree in (86), which
maintains the same type for additional as in the event summing analysis.

(86)

I ran an additional 3 miles.

VP
⟨v; t⟩

V
⟨v; t⟩
run

D
an

DP
⟨v; t⟩

AdjP
⟨v; t⟩

Adj′
⟨d; ⟨v; t⟩⟩

Adj

⟨d; ⟨d; ⟨v; t⟩⟩⟩
additional

d

some

MP

d

3-miles

In the tree in (86), there is still only one overt degree argument, so following the precedent from
Schwarzchild & Wilkinson (2002), I substituted e-sum with a silent morpheme some in order to
maintain the required types. As a reminder, I am not directly following their theory, as they work
with intervals, but rather I am assuming it to act like a degree in this theory for convenience. This
preserves the overtly homophonous sentence but also results in the truth conditions that I ran three
miles plus some amount more running. In fact, if we parsimoniously do not change the type of
additional to only call for one degree argument, something like some must be used here in lieu of
e-sum, as there cannot be two overt degree arguments here. With the comparative, both the measure
phrase and the than phrase are optionally overt or covert, as shown in (87). But with additional,
the measure phrase is optionally overt and an overt than phrase is prohibited, as shown in (88).

48

(87)

(88)

a.

b.

c.

d.

a.

b.

c.

d.

Today I ran 3 miles more than I ran yesterday.

Today I ran 3 miles more.

Today I ran more than I ran yesterday.

Today I ran more.

* Today I ran an additional 3 miles than I ran yesterday.5

Today I ran an additional 3 miles.

* Today I ran additional miles than I ran yesterday.

Today I ran additional miles.

For more, we condensed all of the cases to an analysis assuming two degree arguments, and
relying on some to account for covert arguments. As just shown, this is doable for additive adjectives
as well. Even though additive adjectives never show up with two overt degree arguments, keeping
their analysis the same as that of more is still more parsimonious, allowing for the same event
summing morpheme to be used in both analyses. Given that the additive ambiguity is present both
with and without an overt measure phrase, positing multiple degree addition morphemes depending
on the number of overt arguments would mean that we would also have to posit multiple event
summing morphemes to build that reading from the multiple degree addition morphemes. So if
additive adjectives call for the same number of degree arguments that more calls for, the same event
summing morpheme should suffice for both. Additionally, as previously discussed, an overt than
phrase blocks the event summing reading for more, which I argued resulted from a type clash. If
there were a more that was used with one overt degree argument and a more that was used with
two overt degree arguments, a new explanation would be needed for why a degree argument in the
form of a measure phrase doesn’t block event summing but a degree argument in the form of a than
phrase does.

5It does seem acceptable to say Today I ran an additional three miles on top of what I ran
yesterday, but that includes two additive expressions, not just the one. While data including more
than one additive expression should be considered, here I am not yet considering it.

49

Following this argument for one more and one additional morpheme, both with the same type
calling for two degree arguments, there is no semantic reason for a than phrase to be blocked
for additive adjectives. Given that it is blocked regardless, this means that something like some,
a covert morpheme supplying some positive, nonzero degree, must be available for the degree
addition reading of additional. In fact, it is essentially mandatory, as all additive expressions in
this theory call for two degree arguments, type-wise, and if the than-phrase is disallowed from
supplying one of them, then some other strategy, such as some must be employed instead. Looking
back at (87), something like some must be fairly freely available for covert degree arguments
in comparatives in general, given that more can appear with any combination of overt or covert
arguments. The question only arises as to why the degree argument typically given by the standard
phrase is necessarily covert with additive adjectives, as was shown in (88). To look at what the
degree addition reading of something like I ran additional miles, two covert degree arguments
would be needed. This is the resulting tree below in (89).

(89)

I ran additional miles.

VP
⟨v; t⟩

DP
⟨v; t⟩

V
⟨v; t⟩
run

D
∅

AdjP
⟨v; t⟩

MP

d

some miles

Adj′
⟨d; ⟨v; t⟩⟩

Adj

⟨d; ⟨d; ⟨v; t⟩⟩⟩
additional

d

some

50

One final thing I should mention about the trees in this section is that I have not discussed
arguments about whether the MP or some should apply first, especially as both are optionally
covert, but in the analysis I gave I assume they apply in the same order that they do for more. To get
the event summing reading from more, the measure phrase must apply after the e-sum morpheme
merges in order for e-sum to be able to reference the degree e-sum provides. And following that,
the than phrase must also apply before the measure phrase because either the than phrase or e-sum
may come after more, but not both. I extend the same order to the analysis of additive adjectives,
but I have no constituency tests in addition to this reasoning to support this order of attachment.

2.5 Consequences of this analysis, and open questions

In this chapter, I improved upon existing analyses of event-summing more by compositionally
accounting for its homophony with degree addition. This provided an argument for generalizing all
cases of the comparative morpheme to a differential one involving explicit addition. The amount of
expressions that participate in this homophony also provide evidence that there is a compositional
relationship possible between morphemes with degree addition and event summing. In support of
this point, I also extended the analysis of this ambiguity to additive adjectives.

One thing worth noting is that if we directly extend the analysis for more to additive adjectives,
this makes a very odd type for adjectives, which are otherwise ⟨v; t⟩ in Wellwood’s framework
as used here. As per the previous arguments, though, we do want to assume that some of them
are syntactically adjectives regardless, even if some of the additive expressions are clearly more
syntactically complex. Therefore we must assume that they are simply adjectives with unusual
semantic types. Given that they also have unusual effects (for adjectives) and a distribution restricted
contexts with degree addition or event summing, having an unusual type does not necessarily seem
problematic. Additionally, if precisely the same semantics is extended from more to additional,
then the fact that the two words aren’t fully interchangable needs to come from something besides
the semantic type. As the semantics of the two are identical, it must be the job of the syntax to
block them being fully interchangeable, presumably as the result of more being a Deg head and

51

additional being an Adj.

Another issue this brings up is what the adapted some from Schwarzchild & Wilkinson (2002)
will need to consist of. Their choice of calling it some is not at random, but rather their denotation
is partially modeled after the quantifier some. But do we want some to just refer to some positive
nonzero degree, or do we want it to anaphorically reference something in particular? This some
would need to reference a contextually relevant degree in some cases, although not all. To make
this distinction clear, consider (90) and (91).

(90) Kaylin ran three miles. But I ran more than she did.

(91) Kaylin ran three miles. But I ran two more (than she did).

(9 d. d+3 miles ran)
(2+3 miles ran)

In the case of (90), there is no particular amount more than Kaylin that I ran, so we want the
covert argument to contribute the quantificational ‘by some amount’ reading. In contrast, in (91),
it’s understood that the second sentence means that I ran two miles plus the number that Kaylin
ran. So in that case, the covert degree argument in some must be able to anaphorically reference
the contextually relevant degree brought up in the previous sentence.

Perhaps one way to think about this optionally contextually relevant degree is underspecification.
In the event that there is an available degree in the context given, it is used. In the event there is
not, then the idea of “some positive nonzero” degree is the result. This might not be strictly enough
defined, as this loose definition leaves no space to explain what happens in sentences like (92),
which would have two somes.

(92) Yesterday I ran two miles. Today I ran additional miles.

(ran 2+d, where d is not necessarily 2)

In the case of these two somes, one should anaphorically reference the contextually relevant “two
miles” degree from the previous sentence, and the other shouldn’t, as this sentence is acceptable
in the event that I ran four miles, but it doesn’t necessarily mean that in its degree addition
interpretation. So if we go with the underspecification route, we now need to specify that some
refers to the available degree in the given context only if it hasn’t already been picked up by another

52

some. This seems a little involved for a specification within the denotation for one morpheme,
and there are not other rules that prevent something in the context from being referenced more
than once. Rather, things in the context are frequently referenced multiple times as conversation
continues on the same topic, if not even in the same sentence.

One other possibility is that there are two distinct silent degree arguments: a referential some
and a quantificational some. But how do you then make sure you get the right one in any case?
This question parallels asking if there’s only one some type morpheme, then how do we determine
if it’s going to be referential in any particular context, and how do we ensure that only one instance
is referential in instances like (92) for example? This opens up an interesting question about basic
comparatives as they appear without overt degree arguments.

In the scope of this dissertation what is the importance of this data and this analysis? As we
want to analyze these as adjectives, this informs us that the additive ambiguity is not a characteristic
of Degree heads, and therefore it must result from some aspect of these morphemes’ denotations
instead. This indicates that an analysis for the more complex phrases should be able to be constructed
following the same lines. This concludes the chapter on degree addition and event summing
however, as stepping through an analysis of any of the more complicated additive expressions
promises to add syntactic complexity without also promising to add further semantic discoveries.
The compositional analysis I have presented makes the prediction that if this relationship between
degrees and events is regular, we can assume that any construction that allows degree addition
(unless syntactically blocked) can be built into an event construction too. The reverse direction
is not predicted to be necessarily true; an event construction may be able to also denote a degree
construction, but it is not the case that all event constructions will be able to denote a degree
construction. Finally, this cross-categorical analysis indicates that the degree-event relationship is
firmly semantic rather than syntactic, as data showing an ambiguity only at Deg heads would have
allowed for a syntactic explanation.

One final open question from this section involves some of the messier data. I am confident
that the analysis for more and additive adjectives could be extended to the syntactically complex

53

phrases. However, some of those phrases are happy to double up with other additive expressions,
which is not predicted by my analysis.

(93)

(94)

I ran two miles more in addition to what I did yesterday.

? I ran two extra additional miles.

The example in (93) seems fairly natural, but it has both more and a syntactically complex
additive expression. Given that they do the same thing, we should expect a type clash, or minimally
redundancy. Instead it seem acceptable, and with the same meaning that either one of the included
additive expressions should deliver. Two additive expressions do not always mix well, as (94)
shows, where two additive adjectives together do create redundancy, even if it is not outright
ungrammatical. My analysis at this point cannot account for this data.

In the next chapter, more and addition reappear in a different sort of addition, one that appears
to be discourse-sized. In addition, further data will call for a detour to discuss focus, and focus
sensitivity, in a change of pace from this chapter.

54

CHAPTER 3

DISCOURSE ADDITION

3.1 Addition on a larger scale

This chapter’s data is potentially related to the previous types of addition that we’ve walked
through, given the reappearance of multiple morphemes from the previous chapter.
It appears
initially similar to event summing in that it could be pretheoretically characterized as adding events
to a list of events, but I argue it is distinct from the phenomenon analyzed in the previous chapter.
Discourse addition also appears with several different words and phrases, several of which hint
toward a morphological link to degree addition and event summing, but one of the easiest places
to begin looking at it is with the focus sensitive particle also. I will first walk through the data
with also to make it clear that something is going on, and then add data showing that it is a reading
available with several words and phrases, including the ones that suggest a morphological link with
other types of addition explored earlier in this dissertation. To make this discourse use of also clear,
I will first review the “typical”, non-discourse addition focus-sensitive use of also so the differences
of the discourse addition use will be clearly distinct. The following data in (1) provides the baseline
of the “typical”, non-discourse addition use of also, where prosodic focus is indicated by bolding.

(1) Context: A shipment of office supplies has come in, and someone is checking the package

against the shipping order. They say:

a. We also ordered pens.

b.

# We also ordered pens.

In the two options in (1), changing which word is prosodically stressed also changes whether
or not this response is felicitous in the given context. This is what makes also a focus sensitive
particle (FSP). In the case of (1a), this has the presupposition that they ordered something else in
addition to pens, which is fulfilled by the given context. In the case of (1b), this has a different

55

presupposition, one that the given context doesn’t fulfill. The sentence in (1b) presupposes that
they did something else with pens, maybe stocked them or sold them for example, in addition to
ordering them. This is the “typical” FSP use of also which is well covered in the literature and
often presented as a quintessential FSP. The usual analysis is that also asserts p and presupposes
the truth of another proposition q (the specifics of which are determined by the focus mechanism,
which we’ll return to in more detail later). Now that we have a clear sketch of this use of also, we
can contrast it with the discourse addition use of also that I am investigating. That use appears as
in (2).

(2)

I did a lot of things last weekend!
Also, I baked cookies!

I hung out with friends...

I went for a walk...

In the underlined sentence in (2), there is no presupposition that I baked anything else, nor does
there seem to be any presupposition about cookies or baking in general. Looking at the underlined
sentence, there is no clear presupposition about any related event at all. In a second major distinction
from the first use of also reviewed, it is not clear that changing the prosodic stress in that sentence
would change any contribution of the underlined assertion. Without a clear presupposition, it is
unclear what we would expect to change even. Instead, this also seems to contribute something else
to the effect of the proposition in the discourse, impressionistically signaling the continuation of a
list, and not otherwise affecting the asserted content of the sentence. In addition to also, several
other words and phrases have this effect, which is where the morphological relation to degree
addition and event summing appears. The following data shows some of the range of expressions
with discourse addition capability.

(3)

I did a lot of things last weekend! I hung out with friends... I went for a walk...

56

8>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>:

a.

Also
Additionally
In addition
Furthermore
Moreover
What’s more
To top it off

b.

I baked cookies

9>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>;
8>>>>>>>>>>>><>>>>>>>>>>>>:

, I baked cookies!

9>>>>>>>>>>>>=>>>>>>>>>>>>;

!

also
as well
in addition
too
to top it off

All of the above expressions share the same contribution where they pretheoretically seem to
signal that a list is being continued. In (3a) and (3b), we see the reappearance of addition(ally) and
more, which we talked about extensively in Chapter 2. Both appear in a few different syntactically
varied ways, as well. They are not appearing with measure phrases or with any immediately
apparent degrees, but rather they are appearing as sentential modifiers, so some differences are
predicted. It’s not immediately clear whether we expect this to be a compositional relationship
between these uses of addition(ally) and more and the previously discussed ones. The reappearance
of more in something like moreover is syntactically simple enough that a compositional relationship
may be possible, but the variety of structures appearing and the appearance of a more complicated
structure involving a WH-phrase in what’s more signals that a compositional relationship could be
much more complicated. We also see the syntactically complex phrase to top it off, which parallels
the additive phrase on top of. There are clear syntactic differences between the two, if not semantic
differences as well, but again this parallel signals a morphological link between degree addition,
event summing, and discourse addition. However, due to the variety of structures available, the
complexity of some of them, and the established foundation of research on FSPs like also, I intend

57

to begin this analysis from the starting point of also instead of with the more and addition data that
links with the previous chapter.

It’s also worth noting that some of the options in (3a) and (3b) are dialectal, or not accepted in
all dialects of English. At a minimum, too is perfect here in my dialect but not in others’, and some
speakers have reported a greater preference for a pause before some of these expressions whereas
others are fine without a pause. I will not account for variation or gradient judgments here, but
rather I will take the presence of several words and phrases patterning the same again as evidence
that some strategy is going on to allow for discourse addition.

It would be easy to simply propose a new denotation for discourse also to account for this,
different from the regular proposed FSP denotations, and suggest that it is just a lucky homophony
and focus is unrelated. However, in addition to also, too is also a prototypical FSP which also has
a discourse addition reading in some dialect, and it seems likely that as well or in addition could
show focus sensitivity in a similar way. Consider the following data testing for focus sensitivity
with as well.

(4) Context: A shipment of office supplies has come in, and A is checking the package against

the shipping order.

a.

b.

A: We ordered pens as well.

# A: We ordered pens as well.

The data in (4) is identical to the previous example showing the focus sensitivity of also, except
with also replaced with as well. As (4) shows, changing which constituent is focused in a sentence
with as well has the same effect as with a sentence with also, in changing whether the sentence is
felicitous. It is not just also and too that have a focus sensitive use, but rather some other phrases
that do discourse addition seem to be focus sensitive as well. This is a point that I will return to
later in this chapter in greater detail, but for the moment, it seems reasonable to establish an idea
of how focus works before working on an analysis for the discourse reading. Whether or not focus
is actually relevant to an analysis of discourse addition, I argue that the existence of multiple FSPs

58

that enable discourse addition is an argument that this is the right direction for the analysis, and
that this is not just a lucky homophony.

In addition to that argument for focus being relevant to discourse addition as a whole, I will argue
that proposing a denotation for also that is simply different from the ones that rely on focus is the
wrong move for another reason. Specifically, I will provide evidence indicating that default/typical
cases of also as an FSP are actually subject to the same restrictions that discourse also is subject
to. This point will be clearer once I have fleshed out what the restrictions for discourse also are,
but once the restrictions that discourse also is subject to are fleshed out, I will be able to argue for
a slightly different denotation for also, incorporating these restrictions and using discourse also as
a tool to discover this nuance of also as a whole.

In this chapter I first will walk through some further data to guide an analysis of discourse also,
then in Section 3.3 I will review the relevant background that I will be assuming and tools that I
will be using from models of focus and models of discourse structure. Once we have those tools on
the table, in Section 3.4 I lay out the framework for my analysis of how also creates its discourse
addition reading, before walking through the details of it in Section 3.4.1, and extending it back
to analyses of the usual FSP use of also. The next step, in Section 3.4.2, is to extend this analysis
to other expressions with discourse addition capability. At this point, my analysis for discourse
addition will be established, and I can begin talking about whether the predictions it makes are
held up. This takes the shape of an analysis of the phenomenon of concessive only, in Section 3.5.
Finally, Section 3.6 wraps up the chapter with what interim conclusions I can make at this time.

3.2 Further data

The previous chapter built an analysis around data starting with more, and while more itself
cannot appear in this position, some variations on more do appear. As a result, I want to give some
data showing that discourse addition is distinct from the event summing phenomenon exhibited by
more in the previous chapter. Although they appear similarly, the two cannot be freely substituted
for each other in the same contexts.

59

(5)

I had a lot of fun this weekend.
also I baked cookies!

I hung out with friends, I went for a walk, and

(6)

a.

* I had a lot of fun this weekend.

I hung out with friends, I went for a walk, and

more I baked cookies!

b.

* I had a lot of fun this weekend.

I hung out with friends, I went for a walk, and

I baked cookies more!

In (5) I give an example of discourse addition with also, and in (6) I show that directly
substituting more for also is ungrammatical. It would be reasonable to hypothesize that more is
only grammatical in this position if it is morphologically tweaked to something like furthermore
simply because it’s in a different syntactic position, in which case you could hypothesize that this
is further event-summing, not a distinct type of addition. This argument seems reasonable because
both event summing and discourse addition combine or link events across sentences in some way.
However, I argue that discourse addition is distinct from the event summing that more does. In this
particular case above, there is no clearly summable super-event. Recall from Chapter 2 that event
summing was only possible when the subevents mapped to the part-whole structure of the super
event, meaning that they were monotonic as defined by Schwarzschild (2002). For example, I ran
two miles, and you ran three more can be summed to a five-mile running event because the overall
event can be broken down by mile-running events. Baking cookies cannot be summed with hanging
out with friends and going for a walk. They are different kinds of events. Perhaps we could argue
that there is an overarching fun-having event in (5), but in that case, the sub-event of baking cookies
would not be monotonic on the fun-having event. The fun-having event could not be broken down
into smaller events of baking cookies, but rather it would have to be broken down into smaller
events of fun-having. This example situation is therefore incompatible with event-summing, which
prompts me to label it discourse addition instead. The reader might recall that we can use more
to sum events that seem to be distinct kinds of events, but only with the context that we use a
superevent to group them as the same kind of event. This is in cases like the following example.

60

(7)

I read a lot of things this week. I read three books on Monday, and I read two more papers
on Tuesday.

In (7), book-reading events and paper-reading events appear to be initially distinct, but the
context explicitly groups them both as types of thing-reading events via the first sentence saying
I read a lot of things, so event-summing more is acceptable. Therefore more can be used to sum
events that initially appear to be different kinds, but only if context can be managed to group them
as the same kind of event so they can still be interpreted as monotonic on the superevent. In this
case, three book-readings and two paper-readings add up to five thing-readings. While the new type
of addition is shown in (5) still could be characterized as adding some kind of sub-events together
for an overarching fun-having event, the lack of a monotonicity requirement on those sub-events is
how it patterns differently from event summing. I treat discourse addition as distinct from event
summing on the basis of this lack of a monotonicity requirement. As per the label I have given
“discourse addition”, the direction I am going to pursue with this analysis is discourse-oriented
instead of continuing to focus on sub-events.

I have characterized the impact of these discourse addition expressions as signaling the con-
tinuation of a list. Correspondingly, to look at where discourse addition is disallowed, also and
the other phrases that do this are infelicitious out of the blue, without supporting context or when
changing the topic.1

(8)

a.

# ...and that’s why I think Gritty is the hero we deserve. To totally change the topic,

also I broke my deadlifting record!

b.

# ...and that’s why I think Gritty is the hero we deserve. To totally change the topic, I

broke my deadlifting record in addition!

1There was much discussion at my defense about the felicity of an out of the blue also, you’re
an idiot or also, fuck you. For starters, I suggest that a totally out of the blue occurrence where
someone enters a room and says either of those things to someone already there is not actually
totally felicitous. They do seem to be acceptable in changing topics, but in those cases some list
of ‘things that are insulting the listener’ or something similar may be being compiled across the
discourse. At this time, I am not going to speculate further about insults or swearing, but rather I
will stick to simpler examples.

61

In (8a), also is definitely infelicitous with a topic change, or out of the blue, and in (8b)
replacing also with in addition is equally unacceptable. There is a kind of way where also can be
used seemingly out of the blue, but I will analyze that case as not actually out of the blue. In these
places it is contributing to an overarching discourse topic, and it still must follow the supporting
context, even if not immediately follow it. Consider the following example with considerably more
supporting context.

(9) Context: Alex and Brady are chatting with the explicit goal of catching up after some time
apart. Alex has told Brady about their studies, about recent books they’ve read, and about
their recent Pokemon Go addiction. While Brady is still responding to the Pokemon Go
topic, Alex can interrupt:

Alex: Oh, also I broke my deadlifting record!

This example in (9) clearly interrupts one topic with an overt topic change, but here also
is definitely felicitous. However, the supporting context involves a conversational goal of Alex
reporting to Brady all of the things they’ve done recently. As a result, a much shortened version
of this conversation could look like the I had fun this weekend example if it were lacking the
intervening responses from Brady and discussion. This point of the supporting context is so that
this conversation can be analyzed as working toward Alex and Brady informing each other about
their recent life events, or as answering the overarching question of something like “how have Alex
and Brady’s lives been recently?”. As a result the use in (9) is not out of the blue, but rather,
simply refers back to an overarching topic instead of the immediate one. It still appears in a list
environment, but the list of answers to this question is more widely spaced over the discourse in
this kind of example. The presupposition contributed by discourse also must be relevant to its
use in the discourse, resulting in this list effect by flagging how to consider p with respect to the
conversational topic, question, or related theoretical discourse structure. I am leaving this open
until we have stepped through some analysis of discourse structure and of the phenomenon itself,
but I will discuss this further later.

62

Finally, discourse also is not limited to appearing only in assertions, but rather it can appear

with other illocutionary forces, as shown below.

(10)

I know you had a lot of fun last weekend, hanging with friends and going on walks.
Also, did you bake cookies?

(11) Have fun at the party tomorrow! Also, don’t forget to bring the brownies you made.

In (10), discourse also appears in a question, and in in (11), it appears in an imperative. As like
its appearances in assertions, the question version of discourse also does not require that anyone
have danced with anything other than cats. The imperative version also does not require that the
listener refrain from forgetting anything else. What this means for the analysis is that discourse
also requires a denotation compatible with multiple types of illocutionary force.

In the next section, I will step away from the discourse addition data momentarily, in order
to review the tools that I expect to need in my analysis. In this case, I will be reviewing Rooth’s
model of focus and pieces of the Farkas & Bruce (2010) and the Roberts (2004, 2018) models of
the discourse structure, in order to focus on discourse also to start.

3.3 Framework and required tools

There are two main chunks of theoretical background or tools that I need for this chapter’s
analysis. In order to work with a theory of focus sensitivity, I will first introduce Rooth’s model
of focus. Then, given that I have already previewed how discourse also signals the continuation of
a list through the discourse, I will discuss some existing models of discourse. Specifically, in this
chapter I will be working in the Table model from Farkas & Bruce (2010), but I will also reference
pieces of or notions from the Conversational Scoreboard model discussed by Roberts (2004, 2018).

3.3.1 Rooth’s model of focus

The background of focus semantics is much larger than this quick section suggests, even if we stick
only to alternative semantics as Rooth worked on in his 1985 dissertation and further work. Focus

63

appears in analyses of many things, not just when analyzing adverbs that interact with focus. Rooth
(1992, 1996) steps through an analysis of contrastive focus, and the role that focus plays in whether
an answer (with focus) is a licit response to a question, at least, so focus has effects on the truth
conditions and felicity of a sentence even without an overt FSP. Consider the following examples
from Rooth (1996).

(12) Officers must escort ballerinas.

(13) Officers must escort ballerinas.

Imagine a context where a bank clerk escorts a ballerina. This violates the rule in (12), but not
in (13), even though the two sentences differ only in where the prosodic stress is placed. In contrast,
a situation in which an officer escorts a journalist violates (13) but not (12). Thus changing where
the prosodic focus is in a sentence does have an effect all by itself.

I will review how focus works specifically with regards to when it interacts with an FSP, rather
than reviewing the whole history of focus research and how it patterns in various situations. A
proposition with a FSP is not quite the minimal working example, but I feel that including something
like only can make the role of focus clearer, and more importantly this is the focus interaction that
we care about here. Prosodic focus interacting with a FSP works as briefly modeled earlier with
also, where the prosodically focused item in the sentence affects the meaning when it interacts with
a focus sensitive particle. It does this through the generation of a set of alternatives, the shape of
which depends on which element in the sentence is stressed. For example, consider the following
minimal pair. We know that also presupposes another proposition is true every time it appears,
but depending on where the focus is in the following sentences, a different set of propositions is
generated from which that presupposition can be satisfied.

64

(14) Erica also baked cookies.

(15) Erica also baked cookies.

(16) Erica also baked cookies.

8>>>>>>>>>>>><>>>>>>>>>>>>:
8>>>>>>>>>>>><>>>>>>>>>>>>:
8>>>>>>>>>>>><>>>>>>>>>>>>:

9>>>>>>>>>>>>=>>>>>>>>>>>>;

Erica baked cookies
Kaylin baked cookies
I baked cookies
Kevin baked cookies
...

Erica baked cookies
Erica ate cookies
Erica purchased cookies
Erica sold cookies
...

Erica baked cookies
Erica baked muffins
Erica baked brownies
Erica baked scones
...

9>>>>>>>>>>>>=>>>>>>>>>>>>;

9>>>>>>>>>>>>=>>>>>>>>>>>>;

In the case of (14), Erica is stressed, and correspondingly the presupposition is that some
proposition of the form x baked cookies is true, such as appear in the example set given. In (15),
the propositions (and the presupposition) are instead of the form Erica V’ed cookies, as the verb
baked is stressed. Finally, if we stress cookies, we get yet a third option, where the presupposition
is that some proposition such as the ones in the example set given is true, something of the form
Erica bakes x. In all of these cases, the asserted content is the same, but the presupposition ends
up different because a different set of alternatives is generated. So the important question is how is
this set generated formally.

Multiple theories for how this set is generated compositionally exist, and for simplicity, here I
will review what has been proposed by Rooth, whose model I am working in. Rooth works with a
two-dimensional theory of alternative semantics. Any constituent is represented in one dimension

as simply the ordinary value of the that expression, which we can write asJ(cid:11)Ko for the ordinary

65

semantic value. The same constituent is simultaneously represented in a second dimension with its

focus semantic value, which we can write asJ(cid:11)Kf. The focus semantic value contains minimally

the same thing as the ordinary semantic value, but if alternatives are generated, they are represented
in the focus semantic value and not the ordinary semantic value. As for how those alternatives
are generated by prosodic focus, here is what Rooth (1996) proposes on pg. 10 for a rule of focus
interpretation and generating alternatives recursively:

(17)

a. The focus semantic value of a focused phrase of semantic type (cid:28) is the set of possible

denotations of type (cid:28).

b. The focus semantic value of a non-focused lexical item is the unit set of its ordinary

semantic value.

c. Let (cid:11) be a non-focused complex phrase with component phrases (cid:11)1; :::; (cid:11)k, and let ϕ
be the semantic rule for (cid:11), e.g. function application. The focus semantic value of (cid:11) is

the set of things obtainable as ϕ„x1; :::; xk”, where x1 2J(cid:11)1Kf ^ ::: ^ xk 2J(cid:11)kKf.

What this means, is that everything has an ordinary semantic valueJ(cid:11)Ko and a focus semantic
valueJ(cid:11)Kf, but if there is no focus causing a set of alternatives to be generated, thenJ(cid:11)Kf is the
singleton set containing justJ(cid:11)Ko. However, the focus semantic value of constituents higher up the

tree is recursively generated, so once focus generates a non-unary set of alternatives somewhere in
a tree, all greater constituents will also have a non-unary set focus semantic value. This recursive
generation of further focus semantic values is done via pointwise function application (or whatever
other rule is applying at that node if a rule other than function application is applying). This allows
a set of alternatives generated at a small constituent to end up creating a set of alternatives for the
sentence as a whole, in the form of being the same as the original proposition except for the focused
constituent. To make this clearer, I am including Rooth’s step by step example, giving what the
focus sets of John introduced Bill to Sue looks like. (Note that the formalization here is as Rooth
wrote it, rather than matching the rest of the dissertation, and that focus is correspondingly marked
with a subscript instead of bolding.)

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(18)

JBillFKf = E, the set of individuals
JJohnKf = f jg, the unit setJJohnKo
JSueKf = fsg, the unit set ofJSueKo
JintroducedKf = fintroduceg, the unit set ofJintroducesKo
J[VPintroduced BillF to Sue]Kf = f(cid:21)xintroduce„x; y; s”jy 2 Eg, the set of properties of the
J[SJohn introduced BillF to Sue]Kf = fintroduce„j; y; s”jy 2 Eg, the set of propositions of

form ‘introducing y to Sue’

the form ‘John introducing y to Sue’

In this way, focusing a small constituent produces not just alternatives at that level, but also a
whole set of alternative propositions. At that point, FSPs can then interact with both the ordinary

semantic value and the focus semantic value both. So for example, also would assert thatJpKo is
true, and it would presuppose that one of the propositions generated inJpKf as above is also true.

However, the focus semantic value is drastically unrestricted. In the example above, the number
of propositions it contains should equal the number of members in the set of individuals. In order
to restrict this to something manageable, Rooth proposed that the constituent that is prosodically
stressed interacts with a covert focus-interpretation operator, written as (cid:24), which interacts with a
covert free variable C, which is a subset of the focus semantic valueJ(cid:11)Kf. This restricted set C

is then what the FSP interacts with in Rooth’s theory. Rooth (1996) defines C as a free variable,
where focus gives information about C, but also its form can be further restricted pragmatically.
Effectively, it is a contextually restricted subset of the set of alternatives generated by (cid:24) . Here in
(19) is how Rooth (1992) defines C.
(19) Where ϕ is a syntactic phrase and C is a syntactically covert semantic variable, ϕ (cid:24) C
introduces the presupposition that C is a subset ofJϕKf containingJϕKo and at least one

other element.

The focus interpretation operator (cid:24) effectively interfaces between the focus semantic value and
whatever requires access to alternatives, such as the FSP. Once a set of alternatives in a focus

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semantic value is generated, a subset C can be obtained via (cid:24), and then FSPs are free to interact
with it. In order to make this slightly more explicit, let’s continue to walk through some of Rooth’s
example from the 1996 paper. Below I give their denotation for only and the syntax (which I have
translated from brackets to a tree) they assume for John only introduced Bill to Sue.

(20)

S

only(C)

S

S

(cid:24) C

John introduced BillF to Sue

JonlyK = (cid:21)C(cid:21)p8q»q 2 C ^ ˇp $ q = p…

(21)

What this denotation does is assume that the FSP only interacts first with the covert free variable

C, which represents a subset ofJϕKf. A non-singleton set of alternates is generated at Bill, and

then every constituent higher up the tree also has a non-zero set of alternatives as generated in (18).
Only then applies at the level of the proposition p, and it asserts that for all propositions q in C, if

q is p (which is possible becauseJϕKo 2JϕKf), then p is true.

Before I move on, I want to address the questions that this C raises. One question I take away
from this analysis is where is C located syntactically? It seems to be the case that it is located
wherever is convenient for the FSP to apply, rather than being located somewhere syntactically
specific. Given that every constituent should have a focus semantic value available, it might make
better sense to say that only simply interacts with that, and the context is used in some way to
restrict the focus semantic value. Some people do work on focus without a C variable, and instead
just reference the focus semantic value or alternative set of a constituent. For example, work on
focus by Erlewine (2014) uses the following denotation.

Jonly (cid:11)K = 1 iff 8q 2J(cid:11)Kf»q ,J(cid:11)Ko ! q = 0…

(22)

In (22), we see the focus semantic value referenced instead of C. Context will necessarily
still play some role in restricting the focus semantic value, but this leaves it open as to how that

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restriction is done. This is less restrictive than a theory requiring a C, but it does not need us to
predict when or where C occurs, or assume it appears simply wherever a FSP requires one. A
second important question is brought up the moment we talk about “context” restricting something:
what is “context”, or formally speaking how is something “contextually restricted”? As Rooth’s C
is contextually restricted, this matters in Rooth’s theory as much as it does in a version where the
focus semantic value is contextually restricted when it is used. I will go into this further when I
flesh out an analysis, but for the moment it is worth flagging this issue of the theory not making
precise predictions. Is the context the discourse? If so, what structure are we assuming? Do we
want more elements than a Common Ground (CG), and if so, what do we need to include, and
are they all included in “context” or just some of them? For the moment I will just leave these
questions raised, but my goal is to formalize how to use the the discourse to contextually restrict C
or the focus semantic value.

For completeness, it is worth mentioning that in terms of other theories of focus, another main
track people follow is the movement theory of focus, where focus effects result from structure
where focused phrases scope higher (Chomsky, 1976; Von Stechow, 1982; von Stechow, 1985).
This theory is particularly useful for dealing with some issues like weak crossover effects with
focus, but, none of the issues that a movement theory of focus is specifically designed to deal with
are relevant to the data I discuss in this dissertation, so as a result, since it has no bearing on my
data here, I find it convenient to stick to the analysis with fewer moving parts.

3.3.2 Discourse frameworks and context

In order to capture this idea of “a list across the discourse”, where discourse also needs to follow
some related propositions, we need a model of the discourse. Where can the items of this list
be drawn from? An articulated model of the discourse that separates out distinct categories for
propositions, ones that interlocutors track, allows for precise predictions about what we’re referring
to when we refer to “propositions in the discourse”. An important question that I will be asking in
this chapter is what does “context” mean, given that in the model of focus that I just overviewed, C

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is contextually restricted. I ask this question specifically with regards to the phenomenon of focus
sensitivity, but I do not doubt that my conclusions here will provide a new angle for discussing
context in analyses of other semantic phenomena.

The idea of a Common Ground (CG) is uncontroversial, containing the propositions that speaker
assumes are shared knowledge (Stalnaker, 1978, 1996). Some world knowledge is assumed, but
minimally, things that the discourse participants have all agreed to would be entered into the CG.
However, we cannot view the discourse as consisting of just the CG, but rather we minimally need
something like individual discourse commitment sets for items that we do not agree on adding to
the CG. At this point, our discourse consists of multiple discrete objects that we can refer to, so
we must then consider the possibility of each one being able to be a part of what is restricting
something when we say “context” is restricting the options, and we need to be precise about our
assumptions about the structure of the discourse. Once we have expanded our discourse model to
include more than one object, it’s worth exploring what else might be available.

Here I will be following Farkas & Bruce (2010) in their Table model of discourse. In addition
to assuming the existence of the CG as a set of propositions, they add a few more categories to
their model. If two interlocutors disagree about a proposition, it cannot be added to the CG, but if
they agree to disagree, then p is added to the Discourse Commitments (DC) of the interlocutor that
committed to it, and not to the DC of the interlocutor that did not commit to it. Any interlocutor’s
DC is also a set of propositions. Anything that is proposed to enter the CG but not yet confirmed
or denied is on the Table. This is similar to the idea of a Question Under Discussion, and in fact
a question would go there, not just a proposition. The Table is a set of propositions, as a question
is a set of its answers (Hamblin, 1973; Karttunen, 1977), and it functions as a stack. This captures
how an overarching QUD can stay on the Table, as sub-questions get added to the top of the stack,
dealt with, and then removed, all without needing to remove or change the overarching QUD. I will
return to the idea of a QUD in a minute when I discuss Roberts’ work. And finally, the Projected Set
(PS) is the set of expected CGs after whatever is on the top of the Table stack is resolved. Note that
the other categories so far have been sets of propositions, but the PS is a set of sets of propositions

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instead. This is what I am assuming for the discrete objects in the discourse that interlocutors enter
propositions into. However, I also want to briefly discuss another model of discourse structure.

Roberts (2018) and previous work discuss a fleshed out scoreboard for a language game in
their strategy of determining whether conversational moves are relevant. Most of the pieces of her
framework will not be relevant here, so I will only walk through the elements that I will be using.
The piece of this scoreboard that I would like to bring up specifically is the part where interlocutors
must track a set of goals and priorities held by the participants in any given conversation. Roberts
separates “domain goals” from “discourse goals”. Domain goals are the things that the interlocutors
are publicly committed to doing in the real world (and the strategies they use in order to achieve
these goals), so they are effectively the real world goals that interlocutors have. This is both the
intuition and the object in the discourse that I will be referencing. Discourse goals, as she defines
them, are the subset of domain goals that are to be achieved within the discourse itself, such as
answer questions. This distinction is not one that I will be using here, and furthermore, Roberts
equates these to effectively QUDs, which I will be referencing as questions specifically. As a result,
I will not be using this notion of discourse goals, just domain goals, so for convenience I will usually
refer to “goals”. QUDs may arise indirectly from overt goals, but I will treat explicit questions here
as going on the Table (Farkas & Bruce, 2010), and I will model them as the set of their answers
(Hamblin, 1973; Karttunen, 1977), rather than as a goal. They may also appear in the category of
goals that interlocutors track in some way, but I will not be dealing with that. The intuition from
goals that I will be using in this analysis is that they guide the discourse and indirectly constrain
what moves are licit in the given conversation. Roberts uses a notion of Relevance here, which I
will review as well. Consider the following example, originally contributed by Asher & Lascarides
(1998), and discussed with regards to goals by Roberts (2004).
I have added the names to the
original example for clarity.

(23) Alex: I need to catch the 1:20 to Philadelphia. Where’s it leaving from?

Brady: Platform 7.
Alex: Where do I get a ticket?

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Brady: From the booth at the far right end of the hall.

Roberts (2004) identifies the first sentence in (23) as establishing a goal for Alex and, since
Brady does not object, adding it to the set of domain goals for the interlocutors. The goal guides
the following conversation in that all the following questions must be Relevant to this goal. Roberts
specifies that “to be Relevant to the established domain goal, subsequent discourse must attempt to
further it, directly or indirectly;”, adding that in the case of (23), “this is reflected in the addition
to the set of questions under discussion QUD of the question of how to catch the train.” So while
there is no explicit QUD overarchingly about how Alex can catch the train to Philadelphia as a
whole, the following questions make it clear that cooperative discourse is now currently dedicated
to enabling that goal, and following QUDs are about how to realize it. An unrelated question would
not be a relevant discourse move, and therefore this goal serves to guide the discourse. The notion
of “relevance” is unfortunately widely useful and needed, so here I copy the definition for the term
itself that she settles on in her 2018 paper. I first give an explicit definition of “address” that she
gives on pg. 8, and then the shorter definition for “relevance” that uses it from pg. 10. This is the
definition that I will reference later in this chapter.

(24) An utterance m addresses a question q iff m either contextually entails a partial answer to
q (m is an assertion) or is a part of a strategy to answer q (m is a question) or suggests an
action to the addressee which, if carried out, might help to resolve q (m is a suggestion).

(25) Given QUD q, a move m is Relevant iff m addresses q.

The notion of addressing a question is defined in (24), where a move can be an assertion, another
question, or an imperative. This is used for a shorter definition of relevance in (25), which I will be
working from later for convenience. However, Roberts has already made it clear that a similar use
of “relevance” with regards to goals is needed, as assertions can address questions, but questions
can address goals similarly. What I will do later in this chapter with this is formalize this distinction
by defining Relevanceg, or Relevance to a goal g, as opposed to relevance to a QUD q. This will
not by itself be quite enough to deal with the data in that section, so I will propose further notions

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from there, but this sums up the theoretical material that I will be building upon from Roberts’
work.

To summarize, in this chapter I will be working with focus sensitivity, with the goal of formal-
izing what “ discourse context” means. Toward that end, I have articulated what the stucture of the
discourse that I am assuming is. Interlocutors must be tracking more information in the discourse
than simply what propositions have been said, and past propositions must be able to be placed
into more categories than simply the Common Ground. Specifically, I am working with the Table
model of discourse structure from Farkas & Bruce (2010), and incorporating the notions of goals
and relevance from Roberts (2004, 2018) as well.

3.4 An analysis - proposition level focus

Given Rooth’s of model of focus, I expect that discourse also can be accounted for fairly
easily, and in a way that allows its analysis to be brought back to the “typical” FSP uses of also.
Specifically, I propose that discourse also is identical to the ‘normal’ FSP use of also. It appears
initially distinct from the uses of also that are typically analyzed because it doesn’t seem to have
an existing presupposition, and because nothing in the sentence stands out with prosodic focus.
However, the fact that it must occur in a list environment can be analyzed as meaning that there
is some presupposed existing proposition ensuring the existence of the previous item(s) in the list.
The immediate issue that makes this kind of presupposition look different is that those items don’t
need to match the structure of the existing proposition in the same way that the ‘normal’ FSP
also alternatives must. This, I argue, is because the focused constituent in the proposition is the
proposition itself, as a whole, rather than a smaller constituent. Once I have an analysis on the table
for discourse also involving focusing the proposition as a whole, I will use it to investigate how to
define “contextual restriction” in the context of how the discourse comes into play when restricting
the focus semantic value of a proposition to C. Next, I will take those conclusions and reapply
them to uses of also with smaller constituents focused.

To return to the first step, this analysis involving proposition level focus opens up the question,

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or questions, of what would it mean to focus an entire proposition. In terms of prosodic stress,
what would this look like? In terms of the semantics, what would this look like? I suggest that in
both cases, the result is likely to be uninformative. Prosodic stress is signaled in a few ways, such
as pitch, intensity, volume, or duration. However, due to speaker variation and variation of real
world conditions like obscuring noise and such, this must be interpreted relative to the rest of the
utterance. There is no obvious way for a speaker to pronounce a proposition and make it clear that
it’s more heavily stressed, when the usual way of making it clear that something is stressed is via
proposition-internal cues. So proposition level focus necessarily can’t be signaled in the same way
that focusing a word or small phrase within a proposition is signaled. So prosodically speaking,
focus could be signaled in some other way when it’s sentence-level, or if it’s signaled the same way,
it is likely hard to pick up on. Heim (1992) provides an argument for focusing silent arguments that
I repeat here. Consider the following sentence.

(26)

John wants to come too.

In (26), this can mean that John wants to come in addition to someone else coming. However,
if John is the focused element, then too attaches to the matrix clause, and the result should then
be that John wants to come in addition to someone else wanting to come, rather than the intended
meaning of John wanting himself and someone else to come with him. Therefore, Heim proposed
that the following representation in (27), where a silent pronoun bears the focus marking, is needed
in order to get the correct semantics.

(27)

John wants [PROF to come too].

If we accept this representation in (27) and its corresponding argument in favor of our ability
to focus silent elements, then stressing a full proposition must be possible even though it is likely
phonetically unmarked. As for what it means in terms of its semantics, we must consider how
focus generates a set of alternatives. In Rooth’s formula, the focus semantic value of a constituent
with prosodic focus is the set of possible things of that type, so in this case we should get the set
of possible propositions. In other words, there are no restrictions on what the propositions in the

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alternative set can be, making this a truly vast set of propositions. When smaller constituents are
focused, the focus semantic value of the proposition at the end bears a lot of similarity to the original
semantic value, because all but one element will remain the same. But if the whole proposition is
focused, then the whole proposition can vary. At a glance, proposition level focus seems wholly
uninformative in terms of its semantics, due to this wholly unrestricted set. As a result, the idea of
how it is “contextually restricted” would be crucial for determining how this becomes something
informative.

Putting this question of mechanics back aside for a moment, it would seem unlikely that multiple
FSPs coincidentally all participate in discourse addition even though the focus semantic value is
uninformative. This indicates that maybe whatever focus is contributing is not as uninformative
as it appears. Two elements are relevant to my analytical direction here. First, also and too are
analyzed as presupposing that another proposition from the set of focus alternatives is true. But
if the focus set is wholly unconstrained, then this would be satisfied for discourse also because
every possible proposition is in the set of alternatives, and that will necessarily contain some true
proposition. So this presupposition would be vacuously satisfied in every case rather than it being
an informative presupposition by being potentially satisfied but potentially not. The theory is that
“context” restricts the focus semantic value from everything of that type to whatever is contextually
relevant, which is what Rooth called C, but I would like to propose to make that more precise, in
a way that will also make the presupposition for discourse also informative. And second, recall
that discourse also must appear in a list environment to be felicitous, so one way to phrase this
formally would be that it must appear after some other relevant proposition has been entered into
the Common Ground, or some other relevant category in the discourse. One way of putting these
two pieces together is to propose that the set of alternatives that discourse also is presupposing
the existence/truth some relevant q from is the set of propositions in the CG / relevant discourse
category. Toward that end, I propose that discourse also is just the regular FSP also, where the
whole proposition is focused. Thus this analysis will assign the same denotation for both.

However, given that the whole proposition being focused is apparently uninformative before

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being contextually restricted, I will analyze the specific use conditions for discourse also as resulting
from how the focus semantic value is contextually restricted. Specifically, in order to get the effect
that the felicity of discourse also is affected by the shape of the discourse as a whole, I propose
that the contextual restriction is being restricted by some object in the discourse structure. This
is where the articulated assumptions for what the discourse structure consists of comes into play.
As a reminder, I am specifically working to define “context” using discourse structure for dealing
with focus sensitivity.
I do expect the consequences of my research will aid analyses of other
phenomena, but here I am focusing on just the one. In Rooth’s formalization, this is the restriction

that cutsJ(cid:11)Kf down to C. In a theory without an official C, and with just the understanding that

context restricts what we consider, this would be a restriction applied directly to the focus semantic
value of the proposition. This kind of restriction could be placed in the hands of an overarching
principle on focus interpretation, or in the lexical semantics of the morpheme itself, or potentially
somewhere else. The conclusion I will arrive at is that this should be lexically specified, but until I
present evidence for that, I will simply talk about C as already having this restriction in order to be
temporarily agnostic as to what applies it to get C.

In the next section of this chapter I will assume this kind of restriction on C in order to step
through an analysis of discourse also, before showing that this restriction actually applies to all
uses of also, indicating that this should be analyzed as a lexical restriction instead of as a sweeping
discourse principle. The existence of this kind of lexical restriction would make the prediction that
discourse also would not be the only FSP that is capable of interacting with focus when it applies at
the level of the proposition. Other FSPs could have a similar restriction allowing proposition level
focus to be interpretable, although lexical variation means that they would not necessarily all have,
or need, a restriction that allows proposition level focus to be interpretable. Therefore next I will
pursue this prediction and step through data for concessive only as an argument in favor of other
FSPs interacting with proposition level focus with the discourse restricting C.

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3.4.1 Also and proposition level focus

To step through this analysis, my proposal for discourse also is that it functions like ‘regular’ also,
but the proposition is the focused constituent. So it asserts p, and it presupposes the truth of some
q from the focus set of alternatives. Given that discourse also only appears in a list environment,
I propose that this is because in this case, C is restricted to propositions in the common ground
(CG) that relate to some QUD. This has the result that also is infelicitous if it is not at least second
in a list, because it presupposes that some other q is true, and that q has to be from the common
ground, so some related propositions have to already be entered into the CG. This is the first half
of the restriction, that all of the elements in C must be in the CG.

Like what would happen with a totally unrestricted C, if all the propositions from the CG were
in C, then discourse also’s presupposition of q from C also being true would be vacuously fulfilled
and still uninformative. So which propositions from the CG should be in C? The restriction must
be slightly more informative. This goes back to the idea that discourse also flags something about
how to consider p with respect to the QUD; there must be some proposition(s) in the CG already
in response to this QUD. Discourse also is infelicitous in a total topic change or utterly out of the
blue. Consider the following example.

(28) Alex: I heard you had fun at the party! What did you do?

Brady: I chatted with friends, I ate cake and also I danced with cats!

QUD: What did Brady do at the party?. C:

8>>>>>><>>>>>>:

I danced with cats
I ate cake
I chatted with friends

9>>>>>>=>>>>>>;

The example in (28) shows a use of discourse also, the relevant QUD, and the resulting set of
propositions that are both answers to the QUD and in the CG. That set is effectively the C that the
focus semantic value of the proposition is restricted to. The also presupposition is that some q from
C is also true, which is met here because all two of the non-p propositions in C have been asserted.
Discourse also is then predicted to have presupposition failure if there isn’t something relevant in
the CG already, which explains why it’s infelicitous to use discourse also out of the blue or when

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totally changing topics. However, this successfully predicts that discourse also is felicitous in the
context where it ‘reaches back’ to a previous topic, as in the example repeated here.

(29) Context: Alex and Brady are catching up. Alex has told Brady about their studies, about
recent books they’ve read, and about their recent Pokemon Go addiction. While Brady is
responding to the Pokemon Go topic, Alex can interrupt:

Alex: Oh, also I danced with cats this weekend!

In (29), the immediate context is unrelated to Alex’s interruption. However, discourse also
flags that it’s not actually unrelated, but rather that it’s a part of an answer to an established QUD,
and a continuation of an overarching topic. In fact, without the also, the interruption comes off
as totally out of the blue and much more unrelated than without it, so it appears that also is in
fact establishing that this proposition is not unrelated by virtue of it presupposing that there are
propositions related to the same topic in the CG already.

The use of also in (29) indicated that the propositions in C can at least include the propositions
in the CG. The next logical question is whether it can include propositions from other objects of the
discourse instead of just from the CG, which means we must flesh out what model of the discourse
we are working with. As a reminder, I am working here with the Table model from Farkas & Bruce
(2010) as a starting point, which means there are a few distinct objects that speakers are tracking in
their model of the discourse besides simply the CG. The other categories that a proposition can enter
include: the Table, where propositions that are proposed to enter the CG go; for any interlocutor
X we have the Discourse Commitments of X, which includes the propositions that X has publicly
committed to but have been blocked from entering the CG; and the Projected Set, which is a set
of expected CGs. The CG, Table, and each interlocutor’s DC are all sets of propositions. The PS
is a set of sets of propositions. Working with this discourse model allows us to independently test
which categories also can access, which both clarifies how discourse also is working and provides
evidence for these discrete objects in the discourse being ones that interlocutors access.

So far we have evidence that also can presuppose the truth of propositions in the CG. Next,
I show that also is not able to presuppose the truth of propositions in either a listener’s or the

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speaker’s DC. In order to tell if also can follow propositions in either the listener’s or speaker’s DC,
we need an example discourse where the participants disagree. This is the goal of the following
two discourses, where I first set up also to follow propositions in the listener’s DC, and then the
speaker’s. I have also underlined the also proposition for clarity, due to the length of the discourse
needed. In (30) below, this discourse aims to have also interact with a proposition in the listener’s
DC.

(30) Alex: I heard Jordan had a great time last weekend! They went to a party... They baked

cookies...
Brady: They said they were going to do both those things, but they did neither of them.
The party was canceled, and they were out of flour to bake.
Alex: No, they did those things!
Brady: Well, on the topic of the great time they had last weekend, also they broke their
deadlifting record!

In (30), the propositions that Jordan went to a party and that Jordan baked cookies cannot go
in the CG because the discourse participants are not in agreement on them. The interlocutors do
not sort this out, but rather they have to agree to disagree. This means that Alex has in their set of
discourse commitments both of those propositions, and Brady has negated versions of both instead
in theirs. If also can presuppose the truth of propositions from the listener’s DC, then Brady should
be able to felicitously use also in this final sentence in (30). However, the most natural reading here
seems to be that Brady is being sarcastic or uncooperative or something. Assuming a non-sarcastic
and totally cooperative intention, also does not seem felicitous here, which would mean that also
cannot presuppose propositions from the listener’s DC. This result is not surprising, because it
would be odd for a speaker to presuppose something they just explicitly negated. I tested it on one
hand for completeness, and on the other hand with the goal of making my theoretical assumptions
explicit. Here I have walked through a test for whether a FSP can interact with propositions in
the listener’s DC, which can be used in further cases of exploring what role the discourse and the
discrete objects within it play in contextual restriction. Between the listener’s and speaker’s DCs, it

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seems more likely that also would be able to presuppose propositions from the speaker’s DC than
from the listeners, which is what I test next.

(31) Alex: Jordan had a great time last weekend. They went to a party and they baked cookies!
Brady: They said they were going to do those things, but they did neither of them. The
party was canceled, and they were out of flour to bake.
Alex: I think we have to agree to disagree about what Jordan did last weekend.
Brady: We do.
Alex: Anyway, to return to the great time Jordan had last weekend, also they broke their
deadlifting record!

In (31), again the propositions that Jordan went to a party and that Jordan baked cookies cannot
go in the CG because the discourse participants are not in agreement on them. When they agree
to disagree, this again means that Alex has in their set of discourse commitments both of those
If also can presuppose
propositions, and Brady has negated versions of both instead in theirs.
propositions from the speaker’s DC, then Alex should be able to felicitously use it in this context.
However, given that this use in (31) does not seem felicitous, it seems that also can not presuppose
propositions from the speakers DC either.

So far also can presuppose the truth of propositions that are in the CG, but it cannot presuppose
the truth of propositions that are in either the speaker or listener’s DC. Two more discrete objects in
the discourse structure to also consider are the Table, the set of propositions under consideration to
enter the CG, and the Projected Set (PS), the set of projected upcoming CGs. Both of these objects
contain in some way the proposition(s) on the Table, but given that the PS is a set of sets, it is of a
different type than the CG, a set of propositions. The Table is also a set of propositions, and thus
talking about the Table will be an easier way to formally access propositions that are not yet in the
CG or someone’s DC than talking about the PS would be. The propositions in the sets in the PS
are not strictly2 a union of the Table and CG, but in simple cases like regular declarative sentences
2For example, a move could challenge something in the CG to propose changing it. In that case,
a union of the CG and the proposition on the Table would result in the empty set, so in this case

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and simple questions, that characterization suffices. As a result, and for compositional ease, I will
discuss the Table for propositions that have not yet been added to the CG or a speaker’s DC, and
not the PS. Stalnaker (1978) proposes that if there are no objections from discourse participants,
assertions are moved from the Table to the CG, but I do not know how quickly this should happen.
If propositions are added too quickly to the CG (even if no one is monologuing), then a slow or
belated objection requires downdating the CG to remove a prematurely added proposition, and
possibly readding something to the Table. But at the same time, how long is too long to wait
to add something? Conversation can move on very quickly, and it can be difficult to judge as an
interlocutor when everyone is done with an assertion or with a topic as a whole. Individual variation
is likely to make this even harder. Consider the following data showing that also can presuppose
the truth of propositions that I would argue are not yet entered into the CG. Here, some of the
examples I have so far been using might be relevant here if embedded in a larger discourse.

(32) Alex: Jordan had a lot of fun last weekend! They went to a party, they baked cookies, and

also they broke their deadlifting record!
Brady: No, they baked and went to a party the weekend before last. This last weekend they
stayed in. But I’m excited to hear about their deadlifting record!

The example in (32) gives an example where also is presupposing two propositions that have
not yet been entered into the CG, which is shown by the listener then overtly rejecting them. But
as the examples we just stepped though showed, also cannot presuppose the truth of propositions
from the speaker’s DC. Therefore, given that also is felicitous here, it must be able to presuppose
the truth of propositions from whatever other object in the discourse also contains those previous
propositions, which should be the Table. I must acknowledge that analyzing these sentences as
not yet having entered the CG is not necessarily a given. It is entirely possible that in the correct
analysis of (32), the party and baking propositions are already added to the CG when also is used,
and then Brady’s response necessitates downdating the CG. This seems possible, but unlikely, as
the PS should probably not contain supersets of the CG. These cases are undoubtedly interesting
ones, but they are equally undoubtedly not minimal ones, so I will be ignoring them here.

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the conjunction in the above example should likely be interpreted as the speaker attempting to
add multiple propositions to the CG simultaneously, rather than as the speaker leaving space for
interlocutors to agree or disagree between each proposition. So to follow the assumption that the
three conjoined propositions do not go one by one into the CG before the next one is lined up, the
example in (32) gives evidence that the propositions presupposed by also may include propositions
that have not yet entered the CG or an interlocutor’s DC. This leads me to conclude that the also
presupposes the truth of some proposition, which is in the set „CG [ T”, where T indicates the
Table, and in that way includes any propositions that are not yet entered into the CG or a DC.

To restate what a denotation of discourse also needs to included, when combined with a
proposition p, discourse also needs to assert only p. It then needs to presuppose the existence of
some other proposition q, which is drawn from the „CG [ T”. This cannot be just any proposition,
as that presupposition would be vacuously satisfied in any discourse where also appeared later on
than the very first sentence. Rather, they must be propositions that contribute to the same topic, in
as untheoretically-laden terms as I can manage. In terms of the Table format from Farkas & Bruce
(2010), the QUD goes in the section of the discourse called the Table itself. However, for the data
that they are modeling, they are looking at overt questions such as Is Sam home?, and not so much
on topic setting assertions like I had a lot of fun last weekend. As far as I know, later work on the
topic also focuses on the control case of simple questions, rather than looking at more complicated
ways of setting discourse topics. In the cases where the topic is set as something like I had a lot of
fun last weekend and then the following list of questions are adding detail to how that happened,
this can be considered as answering subquestions of the question how did I have fun last weekend?.
Thus this kind of topic setting could be considered as raising an implicit QUD asking for more
details. However, this question of how are QUDs set without explicit questions is out of the scope
of this work at this time, particularly as the Table format I am working in places questions in the
Table section of the discourse. So to slightly simplify the example we are working with, consider
the adjusted discourse below.

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(33) Alex: What did you do this weekend?

Brady: I went to a party, I baked cookies, and also I broke my deadlifting record!

In (33), an explicit question is raised as the QUD by Alex. As a question is modeled as the set
of its answers (Hamblin, 1973; Karttunen, 1977), this places this set of propositions on the Table.
The thing in common between all three of the propositions that Brady responds with is that all three
are partial answers to this QUD. Therefore, a way to model that discourse also must follow at least
one other proposition that is in response to the same question is to, in addition to requiring it follow
some q in „CG [ T” is to require that p and q are both members of an existing QUD currently on
the Table. This is effectively a restriction on C, considering that q is drawn from C, and that p is a
felicitous assertion if it addresses a QUD on the Table. Consider the following general denotation
for typical uses of also, where a C is included, but it is not yet formalized how it is “contextually
defined”.

JalsoK = (cid:21)p9q : q 2 C ^ q , p ^ ˇq:p

(34)

The denotation in (34) is simply a basic denotation for any use of also; it applies to a proposition
p, asserts p, and presupposes the truth of some proposition q (which is distinct from p) from C,
the set of alternatives that is a contextually restricted subset of the focus semantic value of the
proposition. For propositions with focus lower than proposition level, this should work just as
Rooth described. The prosodically focused element generates a set of alternatives for the focus
semantic value, and from that point up the tree, a non-singleton focus semantic value is available.
At the top, we should have the ordinary semantic value of whatever the proposition itself is, and the
focus semantic value of a set of propositions identical to the given proposition with the exception
of the focused constituent. So for example, we expect a proposition like in (35) to generate a set of
alternatives like below.

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JErica also baked cookies.Kf =

(35)

8>>>>>>>>>>>><>>>>>>>>>>>>:

Erica baked cookies
Kaylin baked cookies
I baked cookies
Kevin baked cookies
...

9>>>>>>>>>>>>=>>>>>>>>>>>>;

In Rooth’s theory, the focus semantic value is then restricted to what’s contextually relevant.
In this case, the set of propositions is already very restricted, so a loose definition of “contextually
relevant” of simply excluding any individuals that cannot be relevant to the discourse would
be enough to make sure that also is not vacuously satisfied. Applying also to this proposition
asserts p and presupposes that some other proposition from this set is true, which is perfectly
informative, so at a glance, no further restriction is strictly needed to make the usual denotation
for also work. However, we expect a proposition with proposition level focus to, before contextual
restrictions, generate an unrestricted set of alternatives, full of all possible propositions. Limiting
it to propositions that are in some way related to the context is not restricted enough, in case that
could restrict the alternative set, but to include propositions like in the example following.

JAlso, Erica baked cookies.Kf =

(36)

8>>>>>>>>>>>><>>>>>>>>>>>>:

Erica baked cookies
The oven is working
Cookies are things that can be baked
Erica is someone I know
...

9>>>>>>>>>>>>=>>>>>>>>>>>>;

The propositions in (36) are all ones that are immediately relevant to the context of the proposi-
tion Erica baked cookies, but they are also ones that will make the presupposition of also vacuously
true. So simply restricting to propositions that are “contextually relevant” will be too broad still,
and the discourse restriction I have fleshed out is needed. In order to make this set of alternatives
informative, C is restricted to propositions that are answers to a QUD on the Table, and in CG [ T.
To write out the restriction formally, this gives us (37).
(37) Discourse restriction for also: C (cid:26) „QUD \ „CG [ T””

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This restriction expresses the idea that the discourse itself is determining what counts as strictly
“relevant”, and it does so in a way that combines a formal representation of objects in the discourse
with a pretheoretical idea of “on topic”. Formally speaking, the propositions in C are limited to
the intersection of the propositions in the QUD and in either in the CG or on the Table. Given
that a question’s denotation is the set of its answers, this requires that all of the propositions in
C be answers to a question on the table. Additionally, all of the propositions are required to be
either in the CG or proposed to enter the CG. The Table and the QUD(s) on it can be thought of as
setting the topic for the discourse. The point of the conversation that this represents is is to answer
these questions, because then they can be removed from the Table, as their answers go into the CG.
By also requiring that C contain an answer to the QUD that is already in the CG or proposed to
enter the CG, also provides an informative presupposition that flags that p is a continued answer
to a current QUD, that this QUD should not have been removed from the Table yet, and that this
topic is still under discussion. If the previous QUDs were fully resolved with no further answers to
give, and if p were a topic change or in response to a new and unanswered QUD, then it would be
infelicitous to use. To illustrate this, look at the example set in the following example.

Brady: I went to a party, I baked cookies, and also I broke my deadlifting record!

(38) Alex: What did you do this weekend?

C forJI broke my deadlifting record.Kf =

8>>>>>><>>>>>>:

I broke my deadlifting record
I went to a party
I baked cookies

9>>>>>>=>>>>>>;

All three of the propositions Brady said are on the Table, and all of them are answers to the
QUD Alex posed. So their use of also presupposes the truth of one of the non-p propositions, which
accurately matches the felicity requirements for discourse also. In addition, this presupposition is
now an informative one, and using it makes it clear that p is in continued response to a QUD. The
effect is also one that accurately matches our overall goals for an analysis of discourse also: the
correct truth conditions and presuppositions are realized, the effect of flagging the continuation of
a topic or list is realized, and the analysis is compatible with a basic analysis of also as a FSP. One

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slight looseness with this analysis is that intuitively, in order to get this ‘list of answers’ effect, p
needs to be an answer to the same QUD as q is an answer to, and it is not immediately clear that
this is required by the current restriction if it refers to any QUD. I will for readability continue
to use this same notation, but realistically the QUD part of this restriction needs to be interpreted
as specifying a QUD. According to Rooth (1992), C needs to be a set that includes the ordinary
semantic value and at least one other proposition, meaning that if we look at this QUD variable in
(37) as referring to (the set of answers for) one question only, it must necessarily be the question
that p is an answer to.

This analysis is so far agnostic as to where this restriction is located, or when it applies to
take the focus semantic value and return C. Looking at uses of also with smaller constituents
focused the alternatives produced for the focus semantic value already seem restricted enough that
the presupposition of also is informative. However, I will show that also is only ever felicitous
when following this discourse restriction, even when smaller constituents are focused. Consider a
typical use of also with a smaller constituent focused in (39).

(39) Alex: We’re low on office supplies. Did you buy some?

Brady: Yes, I bought pens! I also bought paper, since it turns out I was out of that too.

In (39), paper is focused, which will make the focus semantic value of this proposition a set
of propositions of the exact same shape, but varying in what is where paper is in the original
proposition. This is much more restricted than what proposition level focus would generate without
further restriction, and so again there is no immediately apparent need for any discourse restriction
further than ignoring outlandish or totally unrelated propositions. However, examining uses of also
like in (39) shows that the same restriction is in fact still in play: also p must follow at least one
proposition that addresses the QUD and is in „CG [ T”. In this case, the explicit QUD is whether
Brady bought office supplies, and Brady’s first sentence answers that and is on the Table before
they use also in the next sentence. It is hard to prove the absence of something, and simply giving
more and more examples of uses of also that follow this restriction is not going to do it. But we can
talk through the idea at least. Uses of also are licensed when p follows some other q from its C.

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Effectively, all uses of also appear in a list environment. Discourse also with its proposition level
focus is the one that stands out in that its list environment is not immediately apparent because its
C is not immediately clear, and this is reasonably obvious for uses of also with lower focus. The
part of my proposed restriction that ensures that also appears toward the end of a list is the part
that restricts C to propositions in „CG [ T”. If also with lower focus did not follow this restriction,
we could expect it to appear toward the beginning of a list instead of at the end of one, because q
would not have to have been already stated.3

(40)

# I also bought pens. I bought paper. I bought a lot of things!

The example in (40) shows that also with lower focus cannot appear at the beginning of a list
environment, as it is infelicitous there. Instead, it must appear at the end of the list, like discourse
also. So it appears to also be following the restriction of limiting C to propositions in „CG [ T”.
The other part of the restriction limits propositions in C to only ones that are answers to the same
QUD. To think about this one specifically, if an assertion does not address a QUD in some way, it
is not a cooperative discourse move (Roberts, 2012). As a reminder, this part of the restriction was
introduced for discourse also as a way to handle the fact that it is not licensed when changing topic,
unless still answering an overarching QUD. So for discourse also, this restriction is needed to say
that p and q address the same QUD. With lower uses of also, does it have to be the same QUD for
p as for q? Consider the following discourse.

(41) Alex: What kind of pet do you have?

Brady: I have a black cat.
Alex: Cool, my sister also has a black cat!

In (41), Alex’s proposition using also and focusing my sister does not address the explicit
QUD for the conversation, but it does not sound infelicitous, and this sounds like plenty of real
3I am ignoring difficult cases where things may be entered into the CG in ways other than
I am sure there is a relevant case where someone can meaningfully
interlocutors saying them.
gesture to a pile of pens, and then the other person say I also bought pens, but I am equally sure I
would rather deal with clearer cases when trying to make my point, and it is reasonable to ignore
those cases.

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conversations I have heard. I worry, however, that this might be due to the flexibility of natural
conversation, outside of toy examples, and the ease of expanding the topic to something more
like pets that people have from the original topic of pets that Brady has.
In this example, the
interlocutors are likely willing to simply accommodate such a small expansion in the QUD. To
address the issue of flexibility in topic, I have composed an example that is admittedly slightly
unrealistic in regular conversation, in an effort to very strictly limit a model conversation to one
that will not change topic so easily.

(42) Alex: I have a new garden, and it gets full sun. Therefore, I wish to get your advice on
what flowering plants are suitable for planting in full sun, because I want to plant flowers
specifically. What flowers like full sun?
Brady: Sunflowers do well in full sun.
Cameron: Cedar trees also do well in full sun.

The example in (42) tries to very strictly limit the conversation to staying on the explicitly
declared QUD of flowering plants that like full sun by emphasizing both the full sun and the flowers
requirements. As a result, Cameron’s use of also p comes off at best as changing the topic, and at
worst uncooperative, if not infelicitous. This likely means the example in (41) would have been
strictly infelicitous with conversation participants who inflexibly stick to one QUD at a time, but it
comes off as acceptable because realistically speaking, interlocutors switch easily between QUDs
and topics. With stricter interlocutors, like in (42), switching QUDs between q and p is more
clearly disallowed. To take the strict stance, I am comfortable asserting that uses of also with
smaller constituents focused are also subject to the restriction that p and q must address the same
QUD. I am less comfortable dealing with how interlocutors are willing to accommodate expanding
or changing QUDs or topics without explicitly declaring them, but luckily I think that the intricacies
of different ways to do that without explicitly asking a new question are outside of the scope of this
work, so I am not going to deal with this way that it muddies the water.

Given that all uses of also follow this restriction, I argue that this is lexically encoded, rather than
this restriction being a discourse principle that only comes into play with proposition level focus.

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Rather, proposition level focus creates the conditions in which this restriction becomes apparent.
When smaller constituents are focused, the alternatives in C are already much more restricted,
and some elements of this restriction are hard to distinguish from simply being a cooperative
interlocutor. As a result, I propose a denotation for also as in (43) below.

(43)

JalsoK = (cid:21)p9q : q 2 C ^ q , p ^ ˇq:p
where C (cid:26) „QUD \ „CG [ T””

The denotation above in (43) is the same as the above denotation. However here, C is shorthand
for a precise subset of the focus semantic value of the proposition, rather than a contextually
restricted subset of it. Above I have specified that by defining C as a subset of the objects in the
discourse that I have argued make up its restriction, the QUD and „CG [ T”, and specifically it is a
subset of the focus semantic value of the proposition, so it could also be written as the intersection
of the focus semantic value and the restriction. This does mean that the variable C is not strictly
needed anymore, if it is shorthand for the intersection of these things that the interlocutors have
access to. We do not yet have a broad enough analysis from which I could propose eliminating
the variable C from all analyses of focus, so I do not wish to take that stance at this moment, but
if that were a reasonable expansion then this would allow us to no longer worry about the issues
it raised such as where is it structurally located, and how is it formed. This is a goal I would like,
but to make more modest statements for the moment about the outcome of an analysis like this,
eliminating C does at least mean that for an analysis of also we no longer need to worry about how
the contextual restriction is formed. We could rewrite the denotation to this following version, and
not rely on any “contextual restriction” at all.

JalsoK = (cid:21)p9q : q 2 „JpKf \ QUD \ „CG [ T”” ^ q , p ^ ˇq:p

(44)

The version in (44) removes C altogether from the denotation. In addition to the advantage
just discussed, this means that for this analysis at least, we do not have to worry about where C is
syntactically located, even if this analysis does not mean that we can dismiss this issue from all
analyses of focus as a whole. However, this version without C in (44) does have a possible related

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downside. All analyses of focus can be unified by including a shared element, C. Taking that
element out of the denotation could make the link between this analysis of also and other things
involving focus less clear. This is more of a potential downside in terms of having a beautiful
theory where the relation between related elements stands out clearly, and not an issue in terms
of predictions and dealing with the data. Furthermore, it may not be an issue at all. While I
have not done analyses of all other focus phenomena, it is entirely possible that all of them can

be reframed in their analyses to includeJ(cid:11)Kf instead of C, and then the former could be the new

unifying element across all focus phenomena, which is an endpoint that I would appreciate. That
said, while I appreciate this goal of eliminating C, I am for the moment going to continue to work
with the formalism in (43) instead of the one in (44), because I plan to investigate other phenomena
that involve focus and have current analyses with a C in them, and while the result may be that it
can be dismissed in all cases, it will be easier to work toward that conclusion instead of assume it
from the start.

This wraps up the immediate analysis for discourse also. The next step is to consider the other
phrases that do discourse addition, and see if this analysis can be extended, or if some enlightening
issue pops up. If this restriction is lexically encoded, then if other phrases behave in the same way,
chances are they should encode the same restriction. Recalling that also and too tend to be analyzed
identically, this extension looks easy. But recalling also that a variety of expressions actually share
this pattern, not just too, I will explicitly step through this in the following section.

3.4.2 Extending this to other instances of discourse addition

The analysis in Section 3.4.1 revolves around the fact that also is a Focus Sensitive Particle, as it is
a very prototypical FSP and well studied. However, as a reminder, several other words or phrases
acted in a similar way in terms of discourse addition. The previous data showing the variety of
expressions that do discourse addition is repeated below.

(45)

I did a lot of things last weekend! I hung out with friends... I went for a walk...

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8>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>:

a.

Also
Additionally
In addition
Furthermore
Moreover
What’s more
To top it off

b.

I baked cookies

9>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>;
8>>>>>>>>>>>><>>>>>>>>>>>>:

, I baked cookies!

9>>>>>>>>>>>>=>>>>>>>>>>>>;

!

also
as well
in addition
too
to top it off

Despite the fact that I began this analysis with also, it is significant to remember the morpholog-
ical link between discourse addition and the degree addition / event summing ambiguity in some of
this data, where we see variations on more and addition and on top of / to top it off reappearing (in
slightly syntactically different ways). Even though no clear compositional link has appeared in the
analyses between this chapter’s analysis and the previous chapter’s, I would like to maintain some
continuity by looking at an addition phrase and a more phrase in this section specifically However,
these words and phrases are not ones that have appeared in research on focus, nor are they ones that
are particularly well known as expressions that exhibit focus sensitivity. If all of these expressions
are focus sensitive, and act like other FSPs, then the analysis could be directly extended. However,
if some or all are not focus sensitive, then they would necessarily require a different analysis from
the one that I proposed for also. To start with an easy argument in favor of extending the same
analysis to more of these expressions, too is a prototypical FSP that appears in focus literature
almost interchangeably with also, so it follows that an analysis for one would work for the other. I
also showed some data in Section 3.2 indicating that as well shows focus sensitivity. Now, in order
to determine whether in addition is focus sensitive like also, consider the following data.

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(46) Alex: I baked cookies {in addition / also}.

Brady: Wait...

a. What else did you do with cookies?

b.

# What else did you bake?

(47) Alex: I baked cookies {in addition / also}.

Brady: Wait...

a.

# What else did you do with cookies?

b. What else did you bake?

(48) Alex: I baked cookies.

Brady: Wait...

a.

b.

# What else did you do with cookies?

# What else did you bake?

The above data shows two sets of minimal pairs, and marks whether the two given responses
are felicitous. The examples in (46) and (47) both include in addition (and also to compare),
and they differ based on where the prosodic focus is, as a FSP changes interpretation based on
what constituent is prosodically focused. The examples in (46) and (48) have the same constituent
focused, but they differ on whether or not in addition and also are included, so we can see if in
addition is making a contribution to the sentence like also does, or if the prosodic focus alone could
be doing the work or creating these felicity conditions. Looking at the (a) and (b) response options,
in all of these cases they are intended to probe whether in addition has the same FSP presupposition
as also, where also asserts p but presupposes the truth of some other proposition q from the set
of alternatives C. If baked is stressed, then C should be filled with propositions of the form Alex
(verbed) cookies, but if cookies is stressed, then it should be filled with propositions of the form
Alex baked (something). The (a) response flags a failure of presupposition of the first shape, and
the (b) response flags a failure of presupposition of the second shape. The (a) response is felicitous

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and the (b) response infelicitous for both also and in addition in (46), but for (47), the reverse is true
and the (a) response is infelicitous and the (b) response felicitous for both expressions. What this
shows is that also and in addition are patterning identically with respect to their presuppositions.
To compare (46) to (48), neither the (a) nor (b) responses are felicitous in (48) without also or in
addition in the preceding section. Therefore, it is not a presupposition that focus can bring up by
itself. Instead, in addition must be having the same focus sensitive presuppositional contribution
as also does.

Given that in addition is acting in a focus sensitive way identical to also, we can extend the
same analysis to it that I proposed in the previous section for also. That is, it could functionally use
the same FSP denotation that I used for also. The final denotation for also is repeated again for in
addition in (49), with the presupposition underlined again.

(49)

Jin additionK = (cid:21)p9q : q 2 C ^ q , p ^ ˇq:p
where C (cid:26) „QUD \ „CG [ T””

It is not worth repeating the analysis wholesale here, as the identical denotation in (49) should
act identically to the one in the previous section. That is, the same discourse restriction would
effectively restrict in addition to appear only in the same contexts in the same way. And again, I
argue that this restriction is clearly apparent with proposition level focus, but it is also present with
smaller constituents focused as well. To repeat the example from the previous section but with in
addition, here is a discourse with a smaller constituent focused.

(50) Alex: I have a new garden, and it gets full sun. Therefore, I wish to get your advice on
what flowering plants are suitable for planting in full sun, because I want to plant flowers
specifically. What flowers like full sun?
Brady: Sunflowers do well in full sun.
Cameron: Cedar trees do well in full sun in addition.

Like with also, given a discourse like (50) which strictly defines the QUD, in addition must
follow at least one proposition that addresses the same QUD. That is, C is restricted to propositions

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that are in the QUD (as answers) and are in the CG or on the Table. As a result, Cameron’s sentence
with in addition in (50) comes off as a topic change or an uncooperative answer because in addition
is infelicitous.

To take one more step, the same tests can be extended to one of the expressions with more in it,

although the judgments are less clear.4

(51) Alex: Furthermore, I baked cookies.

Brady: Wait...

a. What else did you do with cookies?

b.

# What else did you bake?

(52) Alex: Furthermore, I baked cookies.

Brady: Wait...

a.

# What else did you do with cookies?

b. What else did you bake?

In these cases, the judgments seem to be on the same page as for in addition and also, but
these ones are less clear. Minimally, the ones that are marked as infelicitous are definitely not
good responses. The ones that are not marked as infelicitous are acceptable responses to the given
statements, but they are perhaps not the most likely ones. The stress in either (51) or (52) is oddly
easy to interpret as contrastive focus to correct a previous statement, given that there seems to
be no reason why any particular stress out of the blue should be likely to get this interpretation.
That is, a response like Wait, I never claimed you did otherwise is perfectly good as well, and
if anything, seems very natural. To come back to that, given that the unmarked responses are
appropriate, this shows that furthermore can be acting the same as also or in addition in terms of
its presupposition. If furthermore can act the same in terms of a focus sensitive presupposition,
then again the same analysis can be extended here. However, why might this “correction” reading
4At least I simply do not have moreover in my dialect, and I find what’s more to be interpretable

but distracting due to its register or something similar.

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be more likely here than in other places? One possibility is that furthermore has some other use
besides the FSP / discourse addition use that I am focusing on here, and the possibility of that use
is being considered as well. Alternatively, at least in my dialect, the variations with more in them
are uniformly less frequent than the options with addition in them, if not totally missing. They
could seem odd to me as a function of being low frequency in American English, although that
is a less theoretically interesting hypothesis. Rather than exhaustively stepping through each and
every expression that conveys discourse addition, and examining the gradience in how natural each
one is for any particular dialect, I think this is a good stopping point. My analysis does not have
any predictions with regards to gradience, and gradience in semantics is out of the scope of my
research. Here I have shown that multiple expressions that can be used for discourse addition also
have a reading with the same focus sensitive presupposition as also, meaning that the analysis from
the previous section can be used successfully for more discourse addition expressions.

To step back and think about what this means as a whole, first this analysis has given evidence first
for the existence of proposition level focus. The analysis involving focusing the entire proposition
relies on using objects in the discourse to restrict C, which then makes it clear what it means in
a formal sense to “contextually restrict C”. Although the restriction is much clearer when the
proposition is focused than when a smaller constituent is focused, I then showed that in each case,
that restriction applies to uses of the FSP with smaller constituents focused as well. This supports
reanalyzing the denotation of FSPs like also in all cases to add this contextual restriction, rather than
proposing a special theory to deal with proposition level focus. Finally, I showed this restriction to
extend to all uses of focus sensitive discourse addition expressions. So this analysis makes some
contributions and some predictions. If these FSPs have this kind of restriction based on objects in
the discourse, then other FSPs could also have restrictions based on objects in the discourse. This
restriction applying to all uses of also is also an argument for it being lexically specified, rather
than it being some kind of principle that is relevant when the proposition is focused. The fact that
multiple expressions all have the same restriction might be an argument in favor of a broad principle
instead of a lexical specification, however. To tease apart these two options, it is worth looking at

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other FSPs, and asking whether they have the same restriction or not. Minimally, the prediction is
that they can have restrictions that reference objects in the discourse. However, whether or not they
have the same restriction is the next interesting question. Toward this end, the next section of this
chapter investigates another FSP use with proposition level focus.

One more issue to discuss for this analysis is that it sheds no light on the morphological link
between this data and the additivity data from Chapter 2. The sheer amount of morphological links
makes it look like this analysis is missing something in this way; assuming all of those are simply
coincidence would be quite a lot of coincidence. However, my analysis at this time leaves open
exactly what the link is.

3.5 Concessive only

The analysis in the previous section makes predictions that this section intends to test. Specifi-
cally, if also can have proposition level focus, then so could other FSPs. Additionally, if proposition
level reveals how objects in the discourse restrict C for also, then it might reveal similar kinds
of restrictions for other FSPs, but minimally these kinds of restrictions must be possible. These
predictions bear out with concessive only. The “usual”, well studied use of only asserts that while
p is true, no other q from the alternative set C is true. To see this, consider the data in (53), which
gives a minimal pair of sentences differing only in where the prosodic focus is.

(53)

a.

b.

I only ordered pens.

I only ordered pens.

In (53a), this is false if I ordered anything in addition to pens, but in (53b) I could have ordered
a whole host of other office supplies. In contrast, (53b) is false if I did anything else with pens, such
as unpack or refill them after ordering them. This is the “typical” use of only which displays clear
focus sensitivity. The other discourse / concessive use that I am interested is the one that appears
in the following two examples.

(54)

I wanted to bake, only I didn’t have any flour.

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(55)

I would go to your party, only I’m busy then.

In the used of only in (54) and (55), as with discourse also, note that there’s no need for
prosodic stress anywhere in the proposition with only.
Instead, it seems to impressionistically
mean something along the lines of “the only thing stopping the previously asserted thing from
happening is p”, with a concessive feel.

In Section 3.5.1, I will first step through a little more data to flesh out where we see concessive
only, and in the Section 3.5.2 I will walk through the actual analysis. In the analysis section, I
will first go through a first hypothesis showing that an analysis does not need to propose any new
theoretical notions, but then I will propose another hypothesis showing that the analysis is a better
fit if I do propose one new notion, that of impediments to a goal.

3.5.1 Further data

The primary important quality of concessive only is that only is typically focus sensitive, and that
this use does not appear to be. To step through a few other observations worth mentioning, it seems
to preferentially appear with modals, but the appearance of a modal is not totally necessary, as (56)
shows.

(56)

a.

b.

I went to the party, only I had to leave early.

I went to the party, only I left early.

In (56a), a modal does appear, but in the conjunct following only instead of the one before it.
In (56b), the modal is removed, and this sentence is still acceptable without any, although perhaps
not quite as good as the (a) version. The impressionistic paraphrase of “the only thing stopping the
previously asserted thing is p” does not seem to quite hold here anymore, either. Instead, they seem
to acquire a metalinguistic flavor of something like “the only thing that stopped me from wholly
counting as having gone to the party is p” or “I went to the party in all ways that count, except p”.
This use seems less natural to me, but still acceptable.

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Along the same lines, concessive only very often appears with negation, helping give it this
concessive flavor. Either there is overt negation, as in (54), or like in (55), it often appears with
words like busy, which can be rephrased as not free. This pattern of negation will be returned to
in the analysis later. To continue to step through slightly more data for now, only appears in one
other syntactic position with this concessive reading. It can appear before the proposition, as we
have seen, or it can appear in a cleft-like position after it’s.

(57)

a.

b.

c.

d.

I wanted to bake, only I didn’t have any flour.

* I wanted to bake, I only didn’t have any flour.

I wanted to bake. It’s only that I didn’t have any flour.

* I wanted to bake. Only it’s that I didn’t any flour.

As (57) shows, concessive only can appear high, but not lower in the sentence (with this intended
reading), or it can also appear in a position like a cleft after it as well, and with the same meaning.
This position is not exactly a cleft because it is not clear what it is a cleft of, or what it is clefting
out of, but it is clear that this is another high position at least. So in either case, it seems to be
appearing high and interacting with a clausal argument. In (57a), only appears to be conjoining
two propositions, but the two propositions do not need to appear in the same utterance.

(58) Alex: I want to bake.

Brady: Only the oven is broken. (So you can’t.)

The two sentences in (58) are spoken by different interlocutors. So only is not conjoining two
sentences, and cases like (57a) are likely due to a writing convention rather than an indication
of a type of conjunction. Related to the question of conjunctions, some of these sentences are
paraphrased well with but, except, or just, but these options have some syntactic differences from
only.

(59)

a.

b.

I wanted to bake, only I didn’t have any flour.

I wanted to bake, but I didn’t have any flour.

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(60)

c.

d.

a.

b.

c.

d.

I wanted to bake, except I didn’t have any flour.

* I wanted to bake, just I didn’t have any flour.

I wanted to bake. It’s only that I didn’t have any flour.

* I wanted to bake. It’s but (that) I didn’t have any flour.

* I wanted to bake. It’s except (that) I didn’t have any flour.

I wanted to bake. It’s just that I didn’t have any flour.

As can be seen above, just can’t appear where but and except can appear, and vice versa.
Specifically, (59) shows that just does not work in between two propositions, and (60) shows that
but and except do not work in this cleft-like position. So none of these other options can appear in
both the syntactic positions that only can appear in.

What ideas should we take away from these comparisons to bring to the analysis? Grice
(1981) suggested that but is essentially and with the added conventional implicature that the second
conjunct is surprising in light of the first, or it is unexpected, or something like that, which is a point
that I will return to later. As for except, it makes sense to say that it’s highlighting an exception,
which is impressionistically in line with what only typically does in terms of it says p is patterning
unlike the rest of its group. This kind of exception is exactly what the typical idea of only is if the
group being considered is C. To restate that, the propositions in C are false, with the exception
of p. To bring this back to the intuition about what concessive only is doing, it means something
like the thing just asserted prior is the goal, and p is the only thing preventing that goal. This
intuition of “the only thing stopping [this goal] is p” reflects the typical only pattern of ‘p is true
and no other q in C is true’ if C is the set of things stopping this goal from being realized. At this
point, an analysis can be worked out where concessive only is a form of regular only, as it can be
interpreted as having the same T/F pattern as only’s assertion is typically analyzed as having. This
is the direction I will be taking in the following section.

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3.5.2 Analyzing concessive only with proposition level focus and a discourse restriction

What I propose that concessive only is doing is that it is acting exactly like regular only, but again
with proposition level focus. As with discourse also, this data shows C is limited in some way by
elements in the discourse, which provides evidence for interlocutors tracking goals, and for a notion
of impediments to goals. I will step through two main options for how to frame this restriction.
First I show that if we incorporate structure from the conversational scoreboard model proposed by
Roberts (2004) to the Table format we have been working with, this fits the data reasonably well. I
next propose the notion of impediments to goals, and show that this slight loss of parsimoniousness
allows for a slightly better fit to the data. I will also discuss whether this is a restriction that applies
to all uses of only after.

3.5.2.1 Establishing domain goals for the discourse restriction

To start with, regular only asserts that p is true, and no other q from the alternative set C is true. If
concessive only has proposition level focus, then if C were wholly unconstrained by the discourse
then any proposition could be in it, making the sentence with only exceedingly unlikely to be true.
As a reminder, solely limiting C to propositions that are “contextually relevant” without strictly
defining that concept would be too unconstrained for a use of only with proposition level focus,
leading to a possible alternative set like the following.

(61) Alex: I wanted to bake

Brady: Only the oven is broken.

8>>>>>>>>><>>>>>>>>>:

JThe oven is brokenKf =

The oven is broken
There is an oven in this apartment
Alex wants to bake
...

9>>>>>>>>>=>>>>>>>>>;

The alternatives in (61) are a handful of propositions that are directly relevant to the context of
the oven being broken, and/or Alex wanting to bake, but this example set is still too unrestricted.
The assertion from only, that no other q in C is true, will necessarily be false. The first thing to

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check is whether we can extend the same restriction that also works with to an analysis of only.
That is, is only’s C limited to propositions that are both answers to a QUD and in the CG or on the
Table? I argue that it cannot be, as I have been unable to construct a context in which concessive
only is able to follow an overt question.

(62) Do you want to bake?

a.

b.

The oven is broken.

# Only the oven is broken.5

In (62), responding to the given question in an indirect way by objecting that the oven is broken
is fine. However, as the given minimal pair shows, this response cannot be prefaced by concessive
only.
In addition, only cannot respond to indirect or embedded questions either, as the same
acceptability pattern results in (63) below.

(63)

I’m asking whether we can bake.

a.

b.

The oven is broken.

# Only the oven is broken.

Unless concessive only were to somehow be sensitive to the clause types of whatever preceding
proposition that sets the goal, even if that goal is set in embedded clauses too, this is evidence
that it is not just the case that concessive only cannot follow a syntactic question. The issue must
be the semantics of a question, which is analyzed adding a question/QUD to the Table (Farkas &
Bruce, 2010; Taniguchi, 2017). While it is at the moment unclear why concessive only is wholly
unable to respond to new QUDs, this does mean that extending the same analysis as also to only
won’t work without making changes. Questions were key to the analysis of also, as also listed
further answer(s) to a QUD (even if the question does not have to be explicitly stated), but only
cannot be an answer to a question. Instead, it is worth considering other ways of thinking about
5People I show this data to often point out that this becomes perfectly good if prefaced with
yes or yeah. However, if we analyze “Yes” as including an elided version of the proposition it
agrees with, then this is actually Yes, I want to bake, only the oven is broken, which we expect to be
acceptable (Kramer & Rawlins, 2009; Biezma & Rawlins, 2012).

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topics, in which case it makes sense to think about something like I want to bake as setting a goal
within a discourse. Recall that referencing goals in a discourse requires stepping aside from the
Farkas & Bruce (2010) Table model of discourse to work with objects from the Roberts (2018)
conversational scoreboard model. To consider for the moment the union of these two models, we
have evidence for the semantics interacting with objects in the Table model, but a discourse does
only make sense when interpreted with respect to items on the scoreboard such as the interlocutors
and order of moves. There is some overlap between these two models in that both include space for
a QUD, but this is overlap rather than contradiction, and there is no reason not to take this idea of
goals and incorporate them into the Table model, and assume that the set of goals, G, is an object
in the discourse that speakers can access.

To return to concessive only and to repeat the example from (61), we can think of Alex’s
statement as setting a domain goal of baking. Relevant responses to questions are ones that narrow
the set of possible answers in some way, whether by giving options for what the answer is, or by
ruling out what the answer is not, so it helps to use Roberts’ work as a starting point for defining
relevant responses to goal-setting moves. A relevant follow up move to a goal setting assertion
could be to ask questions that would enable the goal, but assertions can be relevant responses to
goal-setting assertions as well. With the example goal of wanting to bake, questions investigating
how to go about this should be relevant responses. But to think about assertion responses, perhaps
some appropriate responses would be as follows.

9>>>>>>>>>=>>>>>>>>>;

I have a mixer
I have flour
The oven is working
...

(64) Alex: I wanted to bake.

Relevant assertion responses:

8>>>>>>>>><>>>>>>>>>:

The example responses in (64) are all about things that enable the goal that Alex set, and they are
all appropriate responses for an interlocutor to make. While it may be odd to assure an interlocutor
that your oven is working unless there is a worry that it might not be, if it is unknown whether or

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not there is a functional oven available, this is a perfectly natural response assuring Alex that their
goal should be achievable. Another way of thinking about what assertions are relevant is if you
consider that Alex might follow up their statement of baking intentions by asking what they need
in order to realize their goal, all of the assertions in the given set are both relevant and felicitous
in response to a general question about how to realize this goal. To work with this set of relevant
responses for the moment, this set is not a discrete object in the discourse with the current theory,
not in the same way that the Table or PS or goals now are. However, it is intuitively relevant to our
understanding of only, so I will return to Roberts’ formalization here in an effort to define this set
in a way that a speaker should be able to access. If we assume that speakers keep track of domain
goals, as Roberts does, then we can acquire this set by formally defining relevance to a goal, and
then taking the set of propositions that are relevantg. To start with the tools already available, I
repeat how Roberts (2018) defines relevance with regards to questions as in (65).

(65) Given QUD q, a move m is Relevant iff m addresses q.

This definition of relevance requires a QUD, not a domain goal, and as discussed, only strictly
cannot follow a question.
If I wanted to stick to this definition, we could follow Roberts in
assuming that bringing up a new goal implicitly brings up a new QUD of how to achieve this goal,
or something like that, which does seem reasonable. However, this would then bring up the issue
of why only can only deal with implicit questions, not explicit, which seems like it is going in the
wrong direction. Instead, I want a definition of relevance that does not rely on a QUD, but rather
on that follows a goal instead. To make a slight modification to Roberts’ definition, the following
is a definition for the notion of relevance with respect to a domain goal in the given discourse.

(66) Given domain goal g, a move m is Relevantg to g iff m addresses how to realize g.

To work with this definition in (66), we can describe the example set we’ve been working with as
the set of propositions which when asserted are relevantg moves in response to the just established
goal. If a speaker has the notion of relevanceg, then it stands to reason that they can access this
notion via a function. With discourse also, the “contextually relevant” propositions were the ones

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already listed, but with concessive only, we want a set of propositions that are relevantg to the same
goal, as defined by a relevanceg function. As the definition in (66) defines it, relevantg to a goal g
means it addresses how to realize g, and there is some wiggle room in what it means to “address
how to realize g”. As I will discuss in more detail later, I do not think individual interpretations
of what addresses how to realize a goal g will be a problem, but it does bring up an issue in terms
of how we should interpret “address” in the theory. In a nutshell, the question is whether both p
and :p should be relevantg to the same goal g. Thinking about negation, consider the two sets of
propositions given for the following example sentence.

(67)

I wanted to bake, only I didn’t have any flour.

9>>>>>>=>>>>>>;

9>>>>>>=>>>>>>;

a.

b.

I have no flour
I have no mixer
I have no oven

I have flour
I have a mixer
I have a oven

8>>>>>><>>>>>>:
8>>>>>><>>>>>>:

8>>>>>><>>>>>>:

The propositions in the (a) option have the negation pattern of the only p proposition, and the
ones in the second option have the negation removed for the set. Between the two options, the (b)
set, the one lacking the negation, is the one that seem more likely to be responses that are relevantg
to the goal with our given definition of relevanceg. Based on that, one way to think about the (a)
set, the ones matching the negation pattern, is that these are propositions that would block that goal.
However, remember that concessive only does not always appear with overt negation, although it
often does. As (68) reminds us, concessive only often appears with a word like busy instead of
overt negation.

(68)

I would go to your party, only I’m busy then.

9>>>>>>=>>>>>>;

a.

I am busy
I am disinterested
I dislike you

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8>>>>>><>>>>>>:

b.

9>>>>>>=>>>>>>;

I am free
I am interested
I like you

Instead of thinking of the (b) sets as the ones lacking the negation, in light of (68) it definitely
makes better sense to think of them as propositions that block the goal rather than specifying a
negation pattern. Intuitively, the set propositions that enable the goal are absolutely relevantg in
that they relate to realizing it, but are the ones that block the goal also relevantg? Going back to
Roberts’ definition for relevance for questions, a move is relevant if it addresses a question, and
that phrasing shares this same issue. It makes sense that you can respond to a question with a clear
answer, but another felicitous response to a question is ruling out options.

(69) Who is going to the party?

a. Erica and Will are going, at least.

b. Erica and Will aren’t going, at least.

Felicitous responses to the question in (69) include answers that are not exhaustive, but narrow
the set of possible answers. This can be done with a partial answer like (69a), which rules out
answers that do not include Erica and Will, but an answer like (69b) which rules out answer that do
include Erica or Will is also felicitous. If we take this pattern and apply it to relevanceg, it makes
sense that a helpful response to a goal could also be flagging what blocks it from realization. This
means that both the positive and the negative sets should count as assertions that are relevantg to
the given goal. However, this makes impossible predictions of concessive only. Consider a set of
propositions like the following one, which include both the propositions that enable the goal and
the propositions that block the goal.

9>>>>>>=>>>>>>;

105

8>>>>>><>>>>>>:

(70)

I wanted to bake, only I didn’t have any flour.

I have no flour, I have flour
I have no mixer, I have a mixer
I have no oven, I have an oven

Recall that only is analyzed as asserting that p is true, and no other q from the set of alternatives
is true, and that the hypothesis here is to extend the usual use of only to concessive only and say
that the discourse limits C to the set of relevant propositions.
If C is limited to the relevantg
propositions, with a set of relevantg responses like in (70) only would assert that contradictory
propositions, such as I have no mixer and I have a mixer for example, are both false. This is an
assertion that cannot be true with this hypothesis and this assumption about relevance. I intend to
test another hypothesis, but I would like to first fully explore the possibility of making this analysis
work with the tools like relevanceg that we can assume when we import goals, so we will work
with this slightly longer anyway. To avoid impossibilities, I am for the moment going to instead
make the assumption that only the positive set is returned by a relevanceg function, and negations
are “relevant” in terms of excluding members of the positive set, rather than by being members
themselves. However, the focus set is supposed to include the focused item itself, and if the focused
item is a negative proposition, then it would not be included. We also do not want C to be restricted
to the set of propositions that are not relevant, because this would allow too many vacuously true
propositions in and make only impossible to make true again. Effectively, we want C to be a set of
the propositions that are relevant to the goal, negated. This is a restriction we can formalize based
on the objects in the discourse, but it is worth mentioning that it seems to be an oddly specific.
While I intend to try out other options, the first version of the discourse restriction for only is as
follows.
(71) Discourse restriction for only v1: C (cid:26) fpjrelevantg„assert„:p””g

The restriction hypothesized in (71) limits C to only propositions that if negated are relevant
to the goal when asserted. With this restriction, a denotation for regular only should work totally
unimpeded; it affects only how the C is interpreted. This follows the same pattern as the analysis of
discourse addition in Section 3.4 laid out: a basic FSP denotation is provided, and then instead of
relying on a vague notion of context to limit the focus semantic value to a realistic C, a restriction
based on what objects are in the discourse is proposed. Toward that goal of continuing this pattern
and supporting that analysis, the general denotation for only that I intend to use is provided in (72).

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JonlyK = (cid:21)p8q : q 2 C ^ q , p»p ^ :q…

(72)

The denotation in (72) works for general cases of only, also applying at the proposition level,
for convenience. Here, it takes in a proposition, and asserts for all propositions p which are in C
but are not equivalent to p, p is true and q is false. That is, p is the only proposition in C that is
true. Like before, in the case of a sentence with a constituent smaller than the proposition focused,
we expect it to generate a set of alternatives in the typical fashion, as in (73).

JOnly Erica baked cookies.Kf =

(73)

8>>>>>>>>>>>><>>>>>>>>>>>>:

Erica baked cookies
Kaylin baked cookies
I baked cookies
Kevin baked cookies
...

9>>>>>>>>>>>>=>>>>>>>>>>>>;

In (73), only asserts that the first proposition in the given set (which is equivalent to p) is true,
and none of the others are true. This is the typical use of only. Again, in the event of proposition
level focus, if C were restricted to propositions that are “contextually relevant” without further
defining what it means to be contextually relevant, we could expect a loose set of propositions like
the example set contains in (74).

(74) Alex: I wanted to bake

Brady: Only the oven is broken.

JThe oven is brokenKf =

8>>>>>>>>><>>>>>>>>>:

The oven is broken
There is an oven in this apartment
Alex wants to bake
...

9>>>>>>>>>=>>>>>>>>>;

This example set of propositions in (74) are all relevant in some undefined way to the given
context, but a set of propositions like this would make only essentially necessarily false. There set
must be further restricted, and applying the hypothesized restriction in (71) to the basic denotation
of only in (72) creates the right predictions. This gives us the kind of set I have determined we need,

107

repeated in (75), where each proposition listed, when negated, asserts something that addresses
how to realize the goal of baking.

(75)

I wanted to bake, only I didn’t have any flour.

T- I have no flour
F- I have no mixer
F- I have no oven

Once we have this set in (75), only asserts the truth values marked next to each proposition. The
proposition equivalent to p is true, and the rest are false. This matches intuitions for concessive
only by asserting that the only thing stopping the established goal of baking is the lack of flour, not
the other potential issues listed. At this point the analysis works well, and supports the overarching
analysis for discourse addition and focus in this chapter.

However, to add a complexity, let’s look critically at the given truth values for the propositions
in the set in (75). Strictly speaking, only is not wholly asserting that the non-p propositions are
false. Rather, their being false is implicature, and cancelable, as (76) shows below.

(76)

I wanted to bake, only I didn’t have any flour. In fact, I don’t even have a working oven!

T- I have no flour
F- I have no mixer
T- I have no oven

8>>>>>><>>>>>>:

8>>>>>><>>>>>>:

9>>>>>>=>>>>>>;

9>>>>>>=>>>>>>;

In (76), one of the propositions that was previously marked false is now true, and this is perfectly
acceptable. The felicity of (76) tells us that only cannot be asserting that these other propositions
in the example set are necessarily false. Rather, there is an implicature that p is actually the only
thing blocking this goal from being realized. The usual use of only does not imply the falsity of the
other propositions but rather it asserts them. In (77), I give an example with only interacting with
a smaller focused constituent, and an unsuccessful attempt to cancel the implicature.

(77) Only Erica baked cookies. #In fact, Kaylin baked cookies too!

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8>>>>>>>>><>>>>>>>>>:

T- Erica baked cookies
T- Kaylin baked cookies
F- I baked cookies
F- Kevin baked cookies

9>>>>>>>>>=>>>>>>>>>;

The second sentence could not successfully cancel only’s assertion that p is the only true
proposition in C and give the truth values in the set above. Therefore in uses of only with smaller
constituents focused such as (77), only must be assserting that the non-p propositions are false, and
not implying them. This implicature as opposed to assertion could be seen as a difference between
concessive only and “standard” only, which is contrary to the unification approach I am taking in
this analysis. Furthermore it is an odd sort of implicature. It is not scalar, so the implicature could
not be arising from the existence of a stronger item on the scale. It is not due to competition with
some other lexical item that makes a stronger claim (as far as I can tell). Instead, I argue that this
implicature held by only only when it has proposition level focus can be explained as resulting
from the nature of the notion of relevance in the discourse restriction. As a reminder, in the current
hypothesis the discourse restriction is the set of propositions that are relevant to the goal, negated, as
was formally defined in (71). This is not a set of propositions that is explicitly clear in the discourse
in the same way that something like a speaker’s DC is. Things are entered into a speaker’s DC
when a speaker utters them, so it is totally clear what propositions would be there. In comparison,
it is up to the interlocutors to themselves determine individually what would block/enable the given
goal. For example, the speaker might not consider I have an mixer to be an issue worth considering
when they consider baking because they like mixing by hand, so they don’t need to bother negating
it. Therefore these other propositions are negated if they are in the alternative set C, but we can’t
know for certain what propositions are in C, so we don’t know for certain what propositions are
negated. The result is a type of implicature in that we can make inferences based on what is likely
to be in C, but we can explicitly exclude something from C to cancel that, as in (76). This predicts
that we can test this by (slightly unrealistically) explicitly listing what propositions need to be in C,
which is the scenario I attempted to build below.

109

(78) Alex: If you want to bake, I think you need a working oven, a mixer, and flour.

Brady: I agree.

Alex: And I want to bake. Only I don’t have flour! ?In fact, I don’t even have a working
oven!

8>>>>>><>>>>>>:

T- I have no oven
F- I have no mixer
T- I have no flour

9>>>>>>=>>>>>>;

In (78), both interlocutors have explicitly agreed upon what propositions enable the baking
goal, which is how we’ve defined the set of relevantg propositions. If the hypothesis is correct
that these propositions negated are the ones that then fill out C, then only should now assert that
they are false, rather than imply that they are false by our assumptions of whether they’re in C or
not. Which means that the scenario above would result in a contradiction. But it is not clear that
the scenario is more than odd; nothing seems totally contradictory. However, to make the oddness
clearer, contrast (78) with the version below, where only is replaced by but.

(79) Alex: If you want to bake, I think you need a working oven, a mixer, and flour.

Brady: I agree.

Alex: And I want to bake. But I don’t have flour! In fact, I don’t even have a working oven!

With but replacing only in (79), the scenario is no longer odd at all, showing a clear contrast
between only and but here. Perhaps “propositions that address how to realize the goal, negated” isn’t
the best characterization of how the discourse molds C, as the result wasn’t a clear contradiction
or ungrammaticality in this scenario, but this characterization does seem to be at least on the right
page, given that some oddness resulted for only and not but. At this point it makes sense to return
to the discourse restriction I have hypothesized. One issue that I previously mentioned (and tabled
for a few pages) was that this restriction seems somewhat stipulative. The analysis works and lines
up reasonably well with the intuitions for what concessive only is doing. Is this an indication that
the theory is wrong? Just because something can be stipulated does not mean it should be. To

110

consider all of the options, here I instead think about what it would mean to just take the set of
relevant propositions instead of them negated, and then ask what the predictions are. This version
of the hypothesis is the restriction in (80).
(80) Discourse restriction for only v2: C (cid:26) fpjrelevantg„assert„p””g

This takes out the negation in the restriction, and gives us only the propositions that are
relevantg to the given goal. While a reasonable step, this immediately hits a technical stumbling
block. Consider the following example set of relevant propositions.

(81)

I wanted to bake, only I didn’t have any flour.

8>>>>>><>>>>>>:

I have flour
I have a mixer
I have an oven

9>>>>>>=>>>>>>;

The set in (81) cannot be the relevant C, unless we remove some of the constraints Rooth
(1992) proposed. Specifically, C must contain the ordinary semantic value of the focused phrase,
in addition to at least one other distinct element. In this case above, the focused element is the
proposition I didn’t have any flour, which is not an element of the given set, and not a proposition
that is relevantg to the given goal of baking. This second hypothesized restriction will not work.

The strength of the first hypothesis is that it allows for the same denotation for all uses of only.
This supports the overarching hypothesis that propositions are constituents that can be focused,
FSPs can interact with proposition level focus, and that when they do we have seen issues with
the typical FSP analysis that makes it clear that an additional restriction based on elements in the
discourse must be in play. When we looked at discourse addition, reframing “contextual restriction”
to be clearly defined via objects in the discourse was clearly needed because otherwise focus was
uninformative. But when this analysis was extended to concessive only, the problem that would
have arisen with an unrestricted C would have been the impossibility of only’s truth conditions,
which is slightly different from uninformativity. The weakness of this analysis, however, is that
the discourse restriction for concessive only is somewhat stipulative, although still doable with a

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Table model of discourse in which we have imported goals and the notion of relevance from a
conversational scoreboard model of discourse. The concessive flavor of concessive only comes
from this discourse restriction, as this is where the negation is buried. A modified hypothesis that
takes the negation out of the hypothesis fails to produce a viable C. In an effort to better explain
the concessive flavor, I will introduce a new notion in the following section, but it is worth pointing
out that a plus of this section’s analysis is that it only requires adding goals to the model of the
discourse that we are using, and goals have been independently argued for in different discourse
models. Before moving on to the next hypothesis, I want to point out one more argument for trying
a new hypothesis, in the shape of data that does not pose a problem for this section’s analysis so
much as it does not fit comfortably within it. This is the data where only appears with sentences
without overt negation, as in (82).

(82)

I want to go the party, only I’m busy then.

The lack of negation is not necessarily a huge issue for the standing first hypothesis. I could
propose that busy is roughly equivalent to not free, meaning that if I am free then is relevantg to
the party-going goal, then I am busy then could be construed as the negation of that sentence. It
could be the case that busy could be decomposed into not free in its lexical semantics. However,
it still makes me uneasy with these analyses referencing :p with propositions that do not involve
overt negation. In order to both better deal with propositions lacking overt negation and take the
issue of “where is the negation stipulated” out of the solution, I will propose a third hypothesis for
this analysis, which better fits the data via introducing the notion of impediments.

3.5.2.2 Introducing impediments

The third hypothesis continues to work with domain goals, but it involves proposing a new notion
and corresponding function instead of relying only on things that have been proposed in the previous
work. Rather than stipulating negation in either the restriction or in the assertion of only, I would
like to take seriously the intuition that concessive only flags the only thing that blocks the goal, or

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that it flags the sole impediment to the goal. Instead of C being the set of propositions that, when
negated, are relevantg to the goal, I propose the following notion of something being an impediment
to the goal instead.

(83)

Impediments: The things that block a goal g from being realized.

This is not intended to be an object in the discourse along the same lines as goals are, but rather
this is a notion that interlocutors can apply to their conversational scoreboard in order to guide their
conversations, much like the notion of relevance. In terms of real world things that speakers must
track, this makes as much sense as speakers keeping track of what enables their goal realization,
and once you have a notion like this, you can define a corresponding function. In terms of linguistic
data supporting the hypothesis that this is a function that speakers can access, I will step through
the only analysis, and then discuss some follow up data with but indicating that it is not just an
analysis of only that would benefit from introducing this notion. In this analysis of concessive only,
however, the proposal is that C is restricted to the set of propositions that constitute impediments
to the goal. This is the following restriction.
(84) Discourse restriction for only v3: C (cid:26) fpjimpedimentg„p”g

The restriction in (84) is built to work with a standard denotation for only again, returning
to assuming the denotation given earlier in (72). So this version of the analysis regains that
element of parsimony of using only one denotation of only, and it is totally compatible with the
overarching hypothesis of a FSP interacting with proposition level focus which in turn illuminates
extra discourse restrictions attached to the FSPs. However, here no extra negations are needed, and
C has a simple restriction where only one function, which relies on only one object in the discourse,
is applied to determine what propositions qualify. This also makes it easy to deal with uses of only
without an overt negation, such as the example repeated in (85). With this restriction, we expect
possible members in C like the ones in the set in the following example, where the relevant goal is
underlined.

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(85)

I want to go to the partyg, only I’m busy then.

9>>>>>>=>>>>>>;

8>>>>>><>>>>>>:

I am busy then
I have a feud with the host
I have no transportation there

The potential impediments in (85) mostly lack overt negation, but they are all valid impediments
to the given goal of going to the party. Multiple interlocutors may not necessarily be in agreement
on what is an impedimentg, much like how interlocutors may not agree on what is relevantg. I
previously discussed how this lack of certain agreement creates the effect that the falseness of the
non-p propositions in the set is only implied by only instead of asserted, because interlocutors
cannot assume that any particular proposition is in C for everyone. This same explanation extends
to impediments, and works identically with this hypothesis. Interlocutors may have a different idea
of what constitutes an impediment to a given goal, and unless they have explicitly discussed and
agreed upon what constitutes the impediments to a specific goal g, they can only assume what
the other speaker has in mind. Consider the following discourse, where I have attempted to make
this set of impedimentsg explicit in order to test whether this implicature persists or whether the
falseness of the other propositions is now more clearly asserted.

(86) Alex: If you want to bake, I think the things that would stop you would be if you had no

working oven, no mixer, or no flour.
Brady: I agree. I cannot see any other impediments to baking.
Alex: I agree. And I want to bake! #Only I can’t find a bowl!
Brady: We literally just agreed that this would not stop you from baking.

In (86), the two interlocutors agree upon an explicit set of impediments, and they agree that it is
limited to these things. As long as the interlocutors stick to this set (shown above by Brady agreeing
to include nothing else in the set of impediments), concessive only is odd with a proposition that
is not in the explicitly listed set of impediments. In fact, as the final line of the example shows, an
interlocutor can explicitly object to what about the use of only was infelicitous here. This scenario

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supports an analysis of only as flagging the only member of the set of impediments to this goal that
is true.

To further support proposing a notion of impediments, I would also like to step away from FSPs
and talk about some data involving but. Proposing a new notion of impediments deals well with
this phenomenon of concessive only, but I expect it can shed light on other phenomena as well.
Grice (1981) suggested that but could be analyzed as conjunction, but with the implicature that the
second proposition is somehow contradictory to the first. It is not the case that but only conjoins
things that are full on contradictions, but it can be difficult to characterize exactly what is the link.
I propose that one way to think of it involves impediments. In (87), I substituted but in for only
from the previous example.

(87) Alex: If you want to bake, I think the things that would stop you would be if you had no

working oven, no mixer, or no flour.
Brady: I agree. I cannot see any other impediments to baking.
Alex: I agree. And I want to bake! #But I can’t find a bowl!
Brady: We literally just agreed that this would not stop you from baking.

In (87), but is as unacceptable as only was in (86), and the same objection about its infelicity
can be made. One way to explain this data would be to assume that but’s assertion is effectively
conjunction, but it also has the presupposition that the second proposition is in the set of impediments
to the given goal. The goal does not necessarily have to be in the first proposition it conjoins, but
rather but, like only, seems to be sensitive to a goal nearby. Consider the following example, where
the goal is underlined again.

(88)

I said I would hang out with you when I finish packingg. I have finished packing, but I am
too tired (to hang out with you) now.

The example in (88) shows that the proposition immediately before but, the first one conjoined,
does not have to set the goal, as the goal here is not finishing packing. Being too tired is an

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impediment to the speaker hanging out with their friend. So it looks like an analysis of but requires
simply that the second proposition be an impediment to the local goal.

When talking about discourse also, the restriction limiting C to propositions in the QUD and the
PS made sense in the context of adding to a list of answers to a question in the discourse. Looking at
the restriction for concessive only, the third option for an analysis makes the best sense: C for only
is restricted to the set of impediments to the goal in the discourse and then the assertion highlights
the exception. While the other analytical options listed also technically worked fairly well, this
option is clear about where the concessive flavor comes from without having to stipulate where
any negation(s) are. Proposing a notion of impediments to discourse goals is less parsimonious,
but it also promises to come in handy with other analyses, such as for but. In addition to a simple
discourse restriction, the same denotation works for all uses of only, which is in support of the
overarching hypothesis about proposition level focus. In the case of discourse also and other cases
of discourse addition, proposition level focus meant that the presupposition of also was totally
uninformative if we were not clear about what it means for C to be “contextually restricted”. In
the case of concessive only, an unrestricted C for proposition level focus results in an assertion that
effectively cannot be true. The next question is whether we see this same restriction active in uses
of only where smaller constituents are focused, because that would tell us if this restriction could
be lexically encoded, as I proposed for discourse also.

One immediate difference occurs when looking at data with smaller constituents focused, and
that has to do with responding to questions. Concessive only cannot follow a question, but only
with a smaller constituent focused can.

(89) Alex: Did you buy everything you needed?

Brady: I only bought paper. (The store was out of pens.)

In (89), only interacts with the focused phrase paper, and is perfectly felicitous in response to
a question. This is not totally predicted by extending the analysis of concessive only to “typical”
uses of only like this. However, we can still investigate whether the same restriction is in play,
overarchingly matching the pattern from discourse also. In examples like (89), it is very difficult to

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tell what the goal is. So consider an example like the following, where the goal is explicitly stated
as it was in the examples with concessive only.

(90) Alex: I want to throw a really fun party this weekendg.

Brady: Only Erica would be able to make it. Maybe you should wait until the following
weekend, when more people can make it.

In (90), there is a clear goal stated and underlined for clarity, followed by a use of only interacting
with a focused individual Erica. The previously discussed restriction for C for only is that it is
limited to propositions that are impediments to the goal. Here, because Erica is focused, the focus
semantic value is also limited to propositions of the form of x would be able to make it, where x is a
variable for individuals, so this restriction would apply to a set of propositions that is already much
more limited than proposition level focus creates. To step through this clearly, below I present a
hypothetical focus semantic value (before any discourse restriction applies) and then talk through
a hypothetical context for it.

9>>>>>>=>>>>>>;

8>>>>>><>>>>>>:

(91) Only Erica would be able to make it.

Erica would be able to make it, Kaylin would be able to make it.
Rowan would be able to make it, Emily would be able to make it.
Brad would be able to make it, Colton would be able to make it.

These propositions in (91) are all of the correct shape as to be included in the focus semantic
value for this sentence. In this hypothetical scenario, Erica, Kaylin, Rowan, and Emily are some of
the party planner’s favorite people. Not having them there would make having a really good party
more difficult, at least for the speaker. In contrast, while both Brad and Colton frequently appear
at parties in this crowd, they are jerks, and you honestly would not want them at your party. Them
coming would be more of an impediment to a good party than them not being able to make it. For
the sake of a minimal example, these are the only party-going individuals we will consider for this
example. With this information in mind, we can compare the truth values of saying only Erica
would be able to make it in two different scenarios: one where Erica is literally the only person in

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this set of six who would be able to make the party, and one where Erica can make the party but so
can Brad and Colton. If C is restricted to propositions that constitute impediments to the goal of
throwing a really fun party, then it should not matter whether or not Brad and Colton can make it,
just whether the other people can. So in that case, we predict that in both scenarios only p should
be true. If C is not restricted to propositions that constitute impediments to this goal, then only
p should only be true when Erica is the sole person in this list of six who can make it, and false
when Brad and Colton can also make it. The former prediction is borne out, not the latter, which
is illustrated with the truth values in (92) below.

8>>>>>><>>>>>>:

9>>>>>>=>>>>>>;

(92) Only Erica would be able to make it.

T- Erica would be able to make it, F- Kaylin would be able to make it.
F- Rowan would be able to make it, F- Emily would be able to make it.
T- Brad would be able to make it, T- Colton would be able to make it.

The truth values of the critical condition are shown in (92), where the bad party-goers can make
the party in addition to Erica. In this scenario, in response to a clear goal of having a really fun
party, it is perfectly acceptable to say only Erica would be able to make it, meaning that C has to be
restricted to not include the two propositions that do not constitute impediments to this goal. This
example is in support of an analysis where the discourse restriction of concessive only applying to
uses of only with smaller constituents focused as well. This analysis in turn adds strength to the
pattern I propose for also and other expressions of discourse addition, where the discourse addition
use results from proposition level focus and reveals a restriction on C that can then be seen to be
present in uses with smaller constituents focused as well. This allows me to propose that, like for
discourse addition, the restriction for only is lexically encoded, applying to all uses of only, not just
the ones with proposition level focus.

(93)

JonlyK = (cid:21)p8q : q 2 C ^ q , p»p ^ :q…
Where C (cid:26) frjimpedimentg„r”g

The denotation for only in (93) lexically encodes how C is contextually restricted, using the
discourse and knowledge of the goals in it. For this denotation the same question emerges of

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whether to replace the C in the first line with effectively the second line. Given that I discussed the
pros and cons of either of these equivalent notations in the analysis of discourse addition already, I
will not rehash it here, but just mention that this analysis could also be represented in either way.
It is worth pointing out that the case for lexically encoding this restriction so that it limits all
uses of only is murkier than the case for lexically encoding the restriction for discourse addition,
however. None of this analysis predicts that only would be able to follow a question except when the
focus alternatives are generated at the level of the proposition. This could be a sign that concessive
only is somehow different from “typical” only, which would weaken the argument for unifying all
uses of only with this denotation and restriction. In addition, some of those examples with only that
follow questions make it hard to determine a goal, which in turn makes it hard to classify whether
the only propositions are following a restriction that depends on knowing the goal. For a question
like in (89), it is easy to hypothesize a goal that fits, but consider a question like the following one.

(94) Alex: Who all showed up for the party?

Brady: Only Tommy didn’t show up.

In (94), Brady felicitously uses only, but there is no clearly defined goal, just a clearly defined
QUD from Alex’s question. We can accommodate some kind of goal for this conversation, or we
can discuss the divide in types of goals that Roberts (2004) discusses. As a reminder, the type
of goals that I have been talking about are what she calls “domain goals”, which are things that
interlocutors are committed to doing in the real world. She distinguishes discourse goals as a
subset of domain goals, the ones that deal with goals dealing with the conversation, like answering
a question. She equates discourse goals with QUDs. However, if a question denotes a discourse
goal, which it would represent a subtype of domain goals, then there is no immediately apparent
reason why something like concessive only, which is sensitive to a (domain) goal, would be unable
to follow a question, as a subtype of domain goals. If we only theorize questions as adding a QUD
to the Table, and not adding a goal to the conversational scoreboard, it is perfectly reasonable that
something sensitive to a goal might not follow a question well. However, as Roberts points out, it is
true that after a question, cooperative discourse addresses the question and attempts to answer it or

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make clear that it unanswerable, which does seem like evidence that there may be something like
a discourse goal as a high priority goal, but could just result from how a model of discourse like
the Table model works. Minimally, questions do not seem to be patterning with clear goal-setting
assertions. Outside of toy discourses built for clear examples in research, people deal well with
answering implied questions, accommodating presupposition failure, and interpreting discourse
that might not clearly follow Grice’s Maxims, so it makes sense to assume that in situations like
(94) interlocutors can accommodate some sort of goal.

I do not want to dismiss the problematic data by calling it too complicated and limiting my
view only to the simpler data, but it is easier to build a model with the cleaner data to start and
then expand it to the murky cases. More importantly, given that concessive only is relevant in that
it supports the overarching analysis for discourse addition and not because it is the focus of this
chapter, I do not want to linger here excessively in the details, though. So to conclude this analysis
for the moment, the FSP only can be analyzed along the same lines as also was analyzed earlier in
the chapter. The concessive case occurs when only interacts with proposition level focus, and the
restriction that emerges limits C to propositions that are impediments to the goal. Looking at cases
of only with lower focus, this restriction seems to be in play with some of them, but other cases
may pose a problem for this analysis.

3.6 Interim conclusions

At this point we have two examples of classic focus sensitive particles with a reading that can
be analyzed as proposition level focus. In each case, the use of this FSP with proposition level
focus illuminates some discourse restriction limiting C that can be expressed using objects in the
discourse. And in each case, that restriction is shown to extend to uses of that FSP with smaller
constituents focused. This presents evidence in favor of being able to focus propositions as a whole,
and builds a case in favor of the more precise idea of “contextually restricting C” using objects in
the discourse itself. In the case of discourse addition, I first proposed an analysis for also, making
a case for analyzing this as an effect of focus sensitivity. Then I extended it to the rest of the class

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of expressions that participate in discourse addition, in another argument for a cohesive analysis.
For expressions with discourse addition as a whole, I proposed that the thing that this whole class
of expressions has in common is focus sensitivity, and the same discourse restriction, which I am
repeating here in (95).
(95) C (cid:26) „QUD \ „CG [ T””

In terms of continuing the topic of “addition” in semantic computation from the previous
chapter, discourse also represents discourse addition by means of adding another answer for an
established QUD that already has an answer proposed. It does not strictly use addition in the same
way that the comparative and event summing data did, in that are no numbers or plus signs involved.
And analytically the link between the two is somewhat weak, due to the lack of a compositional
route between the data in either chapter. Discourse also involves no degrees, and if we define
“addition” for the moment as strictly one number plus another, this reading does not have it.
However, looking beyond also, there still seem to be multiple morphological indications that these
phenomena are related. This is not currently explained or predicted by the given analysis, but rather
explaining this link remains as an avenue for future research. Ignoring this issue, the restriction in
(95) intuitively explains why also and the other discourse addition expressions must “add to a list”.
Without precisely restricting C to items that are in the CG or on the Table and are also answers to
the QUD, also is uninformative and it is not predicted that it must appear in list environments. With
this restriction though, also’s presupposition requires that it follows a proposition that is an answer
to the same QUD and is already in the CG or on the Table proposed to enter the CG. Thus this
restriction naturally creates a list environment, also signals continuation of a list, and the effect of
“adding to a list” is realized. This analysis made the immediate prediction that other focus sensitive
expressions should be able to (a) interact with proposition level focus, and (b) have restrictions on
C framed in terms of objects in the discourse. This prediction bears out, which I show with an
analysis of concessive only.

In the case of concessive only, without precisely restricting C, only has truth conditions that
are impossibly strict and will never result true. This supports the prediction that other FSPs can be

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analyzed as involving a restriction on C that limits it using objects in the discourse. The fact that
only uses a different restriction from the one that creates discourse addition also tells us that this
restriction is lexically specified, and should be able to vary. The reoccurrence of the same restriction
with lower focus also supports these restrictions being lexically stored, rather than attached to a
principle of focus interpretation or anything like that. In addition to this support for the discourse
addition analysis, the discussion of concessive only made a few contributions that are distinct.
First I linked a Table model of discourse with a conversational scoreboard model of discourse in
order to incorporate the idea of domain goals into this model with clearly defined categories for an
interlocutor to access. While interlocutors tracking goals in the discourse allowed for a good fit for
the data, I then proposed the notion of impediments in order to better fit the concessive only data.
This does not require assuming more discrete objects for speaker to track in the discourse, but rather
it proposes a notion and a corresponding function defining whether something is an impediment to
a goal. This is an expansion of existing theories, but it promises to shed light on other phenomena.
For starters, I discussed the beginnings of an analysis of English but that derives its implicature
from the notion of impediments, but I expect this might be a useful tool in other analyses as well.
As it turns out, these two FSPs are certainly not the only examples of FSPs that interact with
proposition level focus, and we will see more in the next chapter. But given that this is an interim
conclusions section and a good place to speculate, a reasonable question to ask is should we be
able to see proposition level focus without an FSP in the sentence? There’s no reason why an FSP
should be required in order to focus any particular constituent, and there is plenty of research on
the role of focus in other situations, such as with question-answer congruence (Rooth, 1992, 1996).
However, one of the barriers to proposing proposition level focus is that there are no clear phonetic
cues for it. When a FSP is available, this could be thought of as a phonetic signal that there must
be focus in this sentence, and if no smaller constituent is clearly prosodically marked, then the
listener would consider whether the sentence as a whole is the focused constituent. If no overt word
requires focus for interpretation in addition to no overt prosodic cues for focus, then the listener
loses this cue that they should be looking for a focused constituent, and possibly considering focus

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at the level of the proposition.

In the next section, I will look at other avenues connecting this chapter and the one before
it. Specifically, I will return to some topics from Chapter 2 by looking at data involving degree
constructions, but I will end up proposing a focus-sensitive analysis instead of a degree semantic
analysis.

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CHAPTER 4

ASPECTUAL PARTICLES IN COMPARATIVES

4.1 Chapter goals

In this chapter I incorporate elements from the previous two chapters, examining the use of
aspectual particles in comparatives. Chapter 2 builds event structures out of degree structures, and
establishes this directional relationship. This opens up the question of if this is a unidirectional
relationship, or whether there are event type structures that build into degree structures as well.
On the surface, both aspectual particles appearing in comparatives, as in (1), and iteration in
comparatives, as in (2), appear to demonstrate this kind of relationship.

(1) Andrew graded six papers. I graded still more.

(2)

I graded more and more.

Both examples above appear to be comparatives, a prototypical degree structure. However, still
and iteration typically give event time information, and appear in event semantics instead of degree
semantics. So these two are immediate candidates for data that shows a directional relationship
building a degree construction using event structures. In this chapter, I will provide an analysis for
aspectual particles in comparatives, like in (1), but not for iteration in comparatives, like in (2).
Instead, I will step through some of the data and analysis from Beck (2012) indicating that iteration
in comparatives is patterning like pluractionality and should therefore be analyzed as an event
construction instead of a degree construction. This is not counter to the directionality in Chapter 2.
Then, taking the lead from that, I will show how aspectual particles in degree constructions should
also be analyzed independently, not as an event construction contributing to a degree construction.
I will propose that the aspectual particles are acting independently of the comparative, and they act
similarly in non-degree constructions as well, and in doing so I will directly involve my analysis from
Chapter 3. As a reminder, Chapter 3 proposed an analysis of discourse addition with focus sensitive

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particles which proposes proposition level focus and formalizes what “contextual restriction” is. In
my analysis of aspectual particles in comparatives, I rely on these tools of proposition level focus
and using objects in the discourse to “contextually restrict” the focus semantic value, linking the
two previous chapters.

The appearance of aspectual particles in comparatives has been observed in the past, and besides
my own in Chapter 2, there is other research linking degrees and events or event time. Specifically,
there is some research relating degrees to aspect. Kennedy & Levin (2008) relate degrees to aspect
explicitly for degree achievement verbs, building on the link between adjectives like wide and verbs
like widen. Additionally, Piñón (2008) creates a theory that builds aspect with degrees as a whole,
which would support a unilateral relationship where all event structures have degree arguments,
as opposed to event structures variably requiring, permitting, or disallowing degree arguments.
Whether or not all event structures have degree arguments, this research also falls in line with the
directionality I observed, where degree structures can build to or be contained in event structures.
In this chapter, I focus on data that appears to present a counter-argument, data where aspect things
seem to contribute to degree things instead of the opposite. I first step through some of the data
and analysis from Beck (2012) indicating that iterations in comparatives should be analyzed as
event structures instead of degree structures. Then, I tackle the appearance of aspectual particles
in comparatives, utilizing tools from Chapter 3 to show that this data can also be analyzed in a way
that does not support a counter argument to the directionality so far observed.

4.2 Iteration in comparatives

Iteration in English is often aspectual event repetition. However, a similar looking phenomenon
appears in comparatives, making it data that immediately pops up if you propose that there is
a directional relationship between degree constructions and event constructions. Consider the
following data.

(3)

(4)

I ate and ate.

I ate more and more.

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(5) They are taller and taller every time I see them.

In (3) we see a prototypical example of aspectual iteration, indicating that the eating event continued
for some time. A minimal pair appears in (4), where more is repeated instead of the verb itself. As
has been indicated about the direction of this analysis, this sentence indicates that the eating event
continued for some time, and there does not seem to be a typical comparative reading allowed.
Finally, the third example in (5) iterates the adjective, necessarily including the comparative -er
affix. A comparative reading of sorts is allowed in these cases. Looking at (4), this could be
paraphrased as someone eating more on one eating occasion than they did on the last, and in
(5), this could be paraphrased as someone is taller in each occasion than they were at the last.
However, these paraphrases in turn convey iteration and possibly an implied growing event, which
is emphasized by a modifier involving “every time”.

Beck (2012) calls this iteration in comparatives construction pluractional comparatives, and
provides an analysis that successfully parallels their analysis for verbal pluractionality. I do not
intend to show their whole analysis here, as I will not be building from it in the following section,
but I will show their tests showing that this is not acting like a degree construction, but rather an
event construction. Consider the following examples, where I added the (a) line for clarity here,
but the rest is from Beck (2012).

(6)

(7)

a.

b.

c.

a.

b.

c.

Otto ran faster than John.

Otto ran faster and faster.

* Otto ran faster and faster than John.

Otto ran three seconds faster.

* Otto ran three seconds faster and faster.

* Otto ran much faster and faster.

In (6), the first line shows a typical comparative which includes a standard degree in a than-
phrase, and the second shows iteration in a comparative. In (6c) we see that what looked like a
comparative can no longer take a than-phrase argument, which the typical comparative without

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the iteration is able to do. In (7), the first line again shows a typical comparative, this time with
a differential degree, as is typically allowed in comparatives. In the following two lines, we also
see that for the iterative version, a differential is blocked as well, both with a measure phrase and
with much. Again, this is allowed in a typical comparative, so above we see two arguments that
the iterative version is not patterning like a comparative. In addition to this data, Beck shows data
that orients pluractional comparatives toward an event analysis, showing that they work better with
event modifiers. Consider the following data.

(8) Between 2:30 and 6 pm, the talks got better and better.

(9) My crab apple tree grew taller and taller every year.

The prepositional phrase in (8) gives a beginning and end time, which fits with bounding an
event, not with a degree construction. If we interpret adjectives as having state arguments, this
still is not consistent with an adjectival interpretation, as states are often argued to not have time
arguments in the same way that events do (Parsons, 1990). Then in (9), we see an explicit quantifier
for a growing event, fitting in very well with a pluractionality analysis where an event of sorts is
repeated, which is the analysis Beck (2012) pursues.

Here I have presented starting data that on the surface appears to look like aspectual things
building degree constructions.
I have also presented the arguments that Beck (2012) proposes
for why this is not the case. Pluractional comparatives can be analyzed as eventive pluractional
constructions and do not behave like comparatives. I am not repeating all of Beck’s analysis here,
as I will go in a different direction in my analysis of aspectual particles in comparatives, using my
analysis from the previous chapter instead of pluractionality. However, the important contribution
to note here is this strategy of tests showing that the construction is behaving differently from how
it initially presents. In the following section I will present tests, building on work done by Ippolito
(2007), showing that aspectual particles in comparatives are behaving like focus sensitive particles
instead of aspectual particles.

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4.3 Aspectual particles in comparatives

The direction so far observed is that some words and constructions that are typically associ-
ated with degrees. For example, the comparative and the whole class or additive expressions can
reliably acquire an event interpretation, and the data showed by Thomas (2017) indicates that this
is a directional pattern that occurs cross linguistically. While this so far supports a directional
hypothesis, but so far the reverse direction has not been investigated and a handful of data on the
surface appears to support the opposite direction, event constructions composing degree construc-
tions. However, returning to the data previewed at the end of Chapter 2 and repeated below, we can
see a trend of aspectual particles surfacing in comparatives, where the overall construction retains a
degree-comparative meaning. This raises the question of whether this is an instance of the reverse
direction, event constructions compositionally being built into degree constructions, or does this
data present something else.

(10) Andrew graded six papers. I graded still more.

(11) Andrew graded six papers. I graded yet more.

(12) Andrew is pretty tall, at 6’1”. At 6’3”, I am still taller.

Adam.
(13) Berta
Berta
Adam
‘Berta is even taller than Adam.’

größer
taller

als
than

ist
is

noch
still

(Umbach, 2012)

As was previewed before, the data in (10-12) show particles like still and yet, which are typically
well known for aspectual uses, appearing in a comparative. As we can see in Umbach’s German
data in (13), this appears to be a cross-linguistic phenomenon as well. This data initially appears
to support an analysis where event denotations can compositionally construct degree meanings in
that the whole of the construction is a degree expression, but in this particular data, the aspectual
particle appears to contribute something extra on top of the comparative reading. If it were removed,
then the sentence would be a typical comparative, so it can’t be that the aspectual particle itself is
the thing constructing the comparative. Instead, as per the translation from Umbach (2012), the

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aspectual particle appears to contribute a sort of even reading, making a clear link to the focus
sensitivity topic of the previous chapter.

4.3.1 A summary of still from Ippolito (2007)

Here I review Ippolito’s (2007) analysis of various uses of still. They also include data for aspectual
particles that don’t appear in comparatives, which I review briefly for the sake of their argument,
but not extensively. They describe multiple uses of still, not all of which are crucial to the analysis
of aspectual particles in comparatives, but all of which I review here for completeness.

4.3.1.1 An overview of the uses of still

To focus on still, Ippolito (2007) breaks its uses into multiple types: aspectual, marginality,
concessive, and exclusive. The first use, aspectual, is what most people probably think of as the
typical use of still, the one that appears when discussing event time. Already has a similar use.

(14)

John is still cooking.

(15) Got an A! I was jumping for joy (internally, keep in mind it’s still 8am).

(16)

(17)

John is already cooking.

It’s already 5 o’clock.

The above examples show that the aspectual use of still is event continuation. In (14), it says
that the event is continuing. In (15), this use still appears to deal with event time, but note the
implication that this is earlier than expected. Ippolito indicates that not all English speakers accept
this use, and for the speakers that do, this use appears temporal, but should probably be reclassified
as the exclusive still. The aspectual use of already, as in (16), also flags that an event is ongoing,
but with the implication that it is an early time for the event. Ippolito highlights the subtle difference
that in (17), we see that the implication is similar to that of (15), but opposed in that still in (15)
implies that we are at this time of day later than expected and already in (17) implies that we are at

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this time of day earlier than expected. However, subtleties aside, both of these have the aspectual
use of dealing with event time.

The second use of still and already here are no longer in the domain of event time, but rather
they appear with gradable predicates. These, Ippolito calls marginality still and already. The
following examples assume a context where we are talking about how safe various types of cars
are, and possibly ranking them on a scale of car-safety.

(18) Compact cars are still safe; subcompacts start to get dangerous.

(19)

(Compact cars are still safe.) Subcompacts are already dangerous.

In (18) and (19), there is no event time information given, even though words like start or begin
appear in addition to these aspectual particles. Instead, these uses of still and already indicate where
something is on the scale of a gradable adjective. Some analogy can be made to the aspectual use
if we imagine for a moment that the scale is a physical path that we are treading. The context of
discussing the scale and ordering the cars is metaphorically the event of traveling from one end
In this metaphor, still and already make sense as they refer to either
of the scale to the other.
the continuation of being in the “safe” part of the scale or edging into the “dangerous” part of
the scale. Leaving the metaphor behind, the marginality uses of these aspectual particles are not
strictly temporal, and so Ippolito analyzes them as different. Another way of thinking about what
still and already are doing here is that they are flagging that this adjective holds of this thing, but
barely. So for (18), compact cars have a greater degree of safety than the amount to count as safe,
but not by a large amount, just by a marginal amount.

The use of still that I will argue is the most relevant is the one Ippolito calls concessive still.

This is exemplified in the following examples.

(20)

(21)

(Even) if the doctor tells him not to, Harry will still run the marathon.

John studied all night. He still failed the test, though.

In (20) and (21), these uses of still do not contribute meaning about the aspect of an event, nor
do they make a point about a gradable predicate. Instead, there still contributes meaning similar

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to even or even so, and impressionistically it highlights the (un)likelihood of something happening
given the circumstances. This is very similar to how still works in comparatives, and I will end up
arguing that these are in fact the same kind of use of still.

Ippolito notes in a footnote that still can also appear in a comparative, but despite appearing
with a clear gradable adjective, this is not a marginality use. This is what I am overarchingly
interested in here, but in their paper they give the following data to illustrate this kind of use.

(22) A still greater offer came from the Dean.

In (22), there is a clear scale, but marginality still flagged that the subject is within the bounds
of things that count as this adjective, or achieves a degree slightly greater than pos for that scale,
and this is not communicated in (22). This offer might be well above pos, or it even might be below
it, as long as it is greater than whatever offer was mentioned earlier in the (assumed) conversation.
In this chapter, I propose that a better comparison for this use of still is the concessive still. In
the following sections, I preview the analysis of various stills from Ippolito (2007) and attempt to
determine whether the concessive use is the right analysis for cases like (22) where still appears in
a comparative. Then, I will extend that analysis.

4.3.1.2 Ippolito’s analysis

Ippolito (2007) analyzes each of these uses as different, but hypothesizes that still and already
have the unifying factor of associating with focus. While each of the uses are focus sensitive,
they interact with the focus semantic value differently. Focus-sensitive particles are broken up into
additive particles like also, scalar particles like even, and exclusive articles like only. We’ve talked
about focus reasonably extensively in the previous chapter, but given that I am reviewing Ippolito’s
analysis, we’ll touch on how they model FSPs. Ippolito glosses each of these classes of FSPs as
follows, where the underlined part is presuppositional.

(23)

a.

[add1 [...F1...]]: [...F...]
9F′ , F»:::F′:::…

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b.

c.

[scal1 [...F1...]]: [...F...]
:9F′ , F»»:::F:::… <likely »:::F′:::……
[excl1 [...F1...]]: :9F′ ,F[...F′...]
[...F...]

In words, an additive focus sensitive particle associating with the focused element F asserts only
the truth conditions of F, truth conditionally, but it has the presupposition that there is some other F′
that holds as well. As a reminder, this is like also, which Chapter 3 discusses more thoroughly, but
which can be summarized as asserting p while presupposing q from p’s focus set. A scalar focus
particle also contributes only the truth conditions of F truth conditionally, but the presupposition is
that F is the least likely of the relevant alternatives. This is like even, which does essentially assert
p while presupposing that p is less likely than the other propositions in its focus set. An exclusive
focus particle presupposes F, but truth conditionally asserts that no other options F′ hold. This is
exactly what the FSP only does, assert that p is true and no other p from its focus set is true. The
analysis provided by Ippolito (2007) is that aspectual and marginality still are additive particles,
concessive still is a scalar particle, and for the dialects that have an exclusive still it is an exclusive
particle.

Ippolito (2007) gives aspectual/temporal still the following denotation:

(24)

(25)

John is still cooking.

JstillK = (cid:21)t 2 Di:(cid:21)e 2 Dl :(cid:21)P 2 D⟨l;⟨it⟩⟩ : 9t»P„e”„t′” = 1…:P„e”„t” = 1

The denotation mirrors that of an additive particle from (23), in that what is actually contributed
is the temporal ordering saying that this event has occurred before. The temporal ordering (this
event has held previously) is reversed for a version of aspectual already. This use of still seems
clearly distinct from the use in a comparative, so I will not discuss it further here.

Marginality still is also an additive particle, in this case one built to interact with a gradable
predicate, as Ippolito assigns it a wholly distinct denotation. As a result, Ippolito’s denotation

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parallels the previous one in terms of the distribution of presupposition and truth condition, but
differs in terms of working with the gradable predicate instead of event time.

(26) Compact cars are still safe.

JstillK = (cid:21)x:(cid:21)P⟨d;⟨et⟩⟩ : 9y , x»9d»C„d” ^ P„y” (cid:21) d……:9d»D„d” ^ P„x” (cid:21) d…

(27)

Here, still is designed to work with with something like safe, of the type Ippolito assigns to
gradable adjectives instead of propositions. However, the design is immediately reminiscent of
aspectual still in terms of presupposition and truth conditions. A parallel use of already is also
provided in their paper, again with minor ordering tweaks.

While marginality still works with a gradability and a scale, Ippolito voices the intuition that
this is not the still that appears in comparatives. The still in comparatives gives an emphatic even
so reading, suggesting a scalar particle rather than an additive particle. Given that I share this
intuition, I will move on from this use of still to Ippolito’s analysis of the relevant scalar use.

Finally, concessive still is defined as a scalar particle, reflecting its similarity to even instead of
an additive particle like too. Ippolito gives the following definition in (29), where I have added a
gloss of the denotation in prose in the (b) line for readability. For this denotation, Ippolito makes
the following syntactic assumptions in (30).

(28)

(29)

John studied all night, but he still failed the test.

JstillK = (cid:21)p⟨st⟩:(cid:21)q⟨st⟩ : max(cid:20);wcfw : w 2 p^ w 2 qg <likely max(cid:20);wcfw
qg:q„w” = 1
a. For any proposition p, any similarity relation (cid:20), and any world w : max(cid:20);wc„p” = fw

′ 2 :p^ w

′ : w

′ 2

′ :

p„w

′” = 1&8w

′′ : p„w

′′” = 1 ! w

′ (cid:20)w w

′′g

b. Given proposition p and proposition q, the set of worlds (that are maximally similar to
the actual world) in which both are true are less likely than the the (maximally similar
to the actual world) set of worlds in which p is false and q is true.

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(30)

S′

D

S

[John studied all night]2

⟨⟨st⟩; t⟩

⟨st⟩

still

⟨⟨st⟩; ⟨⟨st⟩; t⟩⟩

proF;2
⟨st⟩

he failed the test

This denotation makes still a scalar particle like even, using the same likeliness scale that
even uses. There is no temporality or scale from a gradable adjective needed, but rather there is
an intensional ordering involved, where sets of worlds maximally similar to the actual world are
ordered by likeliness for the relevant scale. Here, still obtains a high scope where it manages to
interact with two propositions by joining with a pro coindexed with the previous sentence (John
studied all night), and then with the next sentence (he failed the test). The given syntax shows
parallels with the structures Ippolito assigns for their analysis of the other uses of still, in terms of
still interacting with a covert variable, bound by something higher, and focused. While focusing
something silent still seems odd, and at least in terms of prosodic implementation, impossible,
Ippolito cites the argument from Heim (1992) which I reviewed in Section 3.4 in favor of being able
to focus a silent element. It’s worth noting that their analysis does not reference alternatives in the
same way that Rooth does. Rooth assumes the prosodic focus itself generates sets of alternatives

and then the FSP can refer toJ(cid:11)Ko andJ(cid:11)Kf both in its denotation, but instead Ippolito works in an
does not then referenceJ(cid:11)Kf or C. This is a methodological note though, not an incompatibility of

intensional semantics where still simply refers to sets of worlds in a built in sort of way. Ippolito

analyses note.

To plug the example of concessive still from (28) in to this denotation and structure, we get
that John studied all night is proposition p and he failed the test is proposition q. Although the
presupposition should vanish from the computation once it is checked, I have for clarity included
it underlined in the first line in (31) to show what requirement it is that has already been checked,

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(31)

′ 2 :JJ-studyK ^ w

′ : w

rather than including a step by step computation of the whole. Then the whole thing is paraphrased
in prose after.

JstillK„JJ-studyK”„JJ-failK” = max(cid:20);wcfw : w 2JJ-studyK ^ w 2JJ-failKg <likely
max(cid:20);wcfw
The set of worlds (maximally similar to the actual world) in which John both studied all
night and failed the exam is less likely than the set of worlds (maximally similar to the
actual world) in which John failed the test but did not study all night.

′ 2JJ-failKg:JJ-failK„w” = 1

This correctly gets the truth conditions that John failed the test, with the presupposition that
this is very unlikely given the context of him studying all night. Note also that this is essentially
equivalent to the use of the scalar particle even here, which I will return to later.

Finally, Ippolito notes that there are dialects that accept an exclusive still. This use has a scalar

meaning like only, for which they give the following denotation.

(32)

(33)

It is still 5 o’clock.

JstillK = (cid:21)D⟨st;t⟩:(cid:21)p⟨st⟩:8q 2 C»q„w” ! „p (cid:18) q”…

In this case, still interacts with this variable C ranging over a salient set of propositions. Focus

is expected to generate the correct salient set of propositions, in this example, with focus on five.

One thing worth highlighting about this analysis is that each denotation is linked by being a
FSP, and there are similar syntactic assumptions made, but other than that, these denotations don’t
share commonalities. Each use of still has its distinct analysis. They deal with different semantic
types, and they assert or presuppose different things. This is reasonable based on how different
uses of still do appear with different types of things, but it opens up the question of why there is a
morphological link or homophony between these uses. Nor is there a compositional link apparent
between different uses of still. So is there some sort of spell-out rule that takes similar FSPs and
pronounces them the same on the basis of the shared focus-sensitivity? Or what? These questions
aside, this analysis successfully deals with the data that Ippolito sets out to deal with. I will take
their analysis of concessive still and extend it to the relevant use of still in a comparative, before

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proposing my own variation on their FSP theory. It is worth flagging, however, that this overall
analysis already looks to be heading in a focus direction, instead of a degree direction, indicating
that this may look more like a link between degree constructions and event constructions than it
actually is.

4.3.2 Extending concessive still to comparatives

An analysis of concessive still can be extended directly to uses of still in a comparative. To hedge
before I start, it’s worth noting that the following sentences don’t all seem to be completely identical.

(34)

a. Andrew is tall. I am still taller.

b. Andrew is tall. I am taller still.

c. Andrew is tall. Still, I am taller.

The versions in (34a) and (34b) seem to be slightly different from (34c), but not in a way that is
truth conditionally distinct. In addition, some native speakers express a preference between the (a)
and (b) options. However, if we shelf this ineffable distinction for the moment to discuss the overall
phenomenon, the analysis of concessive still can be directly extended to still in comparatives, if
we assume a structure like Ippolito’s as well. In Ippolito’s footnote discussing uses of still in a
comparative, they observe that, like concessive still, this use of still in a comparative paraphrases
well with even and suggests a similar to concessive still. While the argument in the previous
chapter took disparate looking uses of FSPs and analyzed them as actually resulting from the same
denotation, the reverse trend is occurring here, and Ippolito analyzes all of these different uses of
still as different morphemes. Besides the homophony, the unifying factor is that they are FSPs, but
Ippolito gives them their own denotation and assumes they appear in different structural positions
to match. In addition to the different meanings and uses that Ippolito has separated out, there may
be further syntactic evidence to treat at least some uses of aspectual particles as different from
other homophonous uses. In this argument I will first consider data involving yet instead of still,
because aspectual yet is known to be a negative polarity item (NPI), but recalling from the previous

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data, both still and yet are aspectual particles that appear in comparatives. Consider the following
contrast.

(35) She has *(not) left yet.

(36) He has mud on his boots. Yet it would be rude to refuse to let him in.

In (35), we can see that the aspectual use of yet is indeed an NPI, as it is ungrammatical outside
of a downward entailing environment like negation. However, in (36) a use of yet like Ippolito’s
concessive still appears perfectly grammatically outside of an NPI environment. As yet can, like
still, appear in a comparative in some dialects of English, we can see the same lack of NPI restriction
again when we look at it there as well.

(37)

a. Andrew is pretty tall, at 6’1”. At 6’3”, I am taller yet.

b. Andrew is pretty tall, at 6’1”. At 6’3”, I am yet taller (than he is).

This is not a known downward entailing environment, as yet does not appear to be in the
standard phrase of the comparative. Given that the aspectual use of yet is an NPI and must appear
in a downward entailing environment, the concessive and comparative uses of yet must be different
from the aspectual use. While still is not an NPI and we therefore cannot run the same test on it, it
seems reasonable to assume that this use of still could be a different one as well, given that they are
seem to be otherwise doing the same thing semantically.

With this argument in addition to the previous ones, I will for the moment follow Ippolito in
assigning a different denotation to different uses of still, and directly extend their denotation for
concessive still to uses of still in a comparative, assuming other uses of still to be distinct. Below
I have given a use of still in a comparative, the structure Ippolito would assume for it, and then
a direct extension of their analysis for it. Again, the presupposition is included underlined even
though what I have shown represents the end point of the computation, after the presupposition
has been checked, so that we can see what has been checked. Then the whole result is paraphrased
immediately after.

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(38) Andrew is pretty tall. (At 6’3”), I am still taller.

(39)

(40)

S′

[Andrew is tall]2

D

still

S

⟨⟨st⟩; t⟩

⟨st⟩

⟨⟨st⟩; ⟨⟨st⟩; t⟩⟩

I am taller

proF;2
⟨st⟩

′ 2 :JA-tallK ^ w

JstillK„JA-tallK”„JI-am-tallerK” = max(cid:20);wcfw : w 2JA-tallK ^ w 2JI-am-tallerKg
′ 2JI-am-tallerKg:JI-am-tallerK„w” = 1
<likely max(cid:20);wcfw
The set of worlds (maximally similar to the actual world) in which Andrew is tall but I am
taller is less likely than the set of worlds (maximally similar to the actual world) in which
Andrew is not tall but I am taller.

′ : w

In the above tree, I directly replaced the relevant sentences, and kept Ippolito’s structure and
denotations. The asserted meaning of the result is that I am taller than Andrew, which matches
speaker intuitions of what the given proposition asserts. The presupposition is that it is less likely
to be the case that Andrew is tall but I am taller than it is to be the case that Andrew is not tall
and I am taller. Or, to put it less technically and more succinctly, it was relatively unlikely that I
am taller than Andrew, given that he is pretty tall to start with. This is generally how the emphatic
effects of even is analyzed, in terms of a presupposition that this proposition was less likely than
competing propositions, so this seems to have worked out appropriately as well. At this point,
extending Ippolito’s analysis of concessive still to uses of still in comparatives works perfectly well
and returns the correct results.

4.3.2.1 Problems, and an analysis of at-phrases

Here I will walk through two problems with this analysis, as motivation for reanalyzing concessive
still (in or out of a comparative) as still with proposition level focus. First, I will provide some data

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showing that still can’t be interacting with just the two adjacent propositions, which is an argument
against the coindexed pro setup. Second, I will show that when still appears in a comparative with
at-phrases, it ends up contributing solely a tautological presupposition. Both of these things will
be an issue with directly extending Ippolito’s analysis, but the changes I will end up proposing will
address them.

To start with, still needs to be able to interact with more than just the one preceding proposition.
Ippolito’s structure represents sentences within a discourse and assumes they have a syntactic
connection, so this analysis is capable of dealing with examples like (41), assuming that this is a
syntax that can link the speech of two interlocutors. However, the pro in their theory is coindexed
with a single sentence, so examples like (42) present an issue.

(41) Alex: John had mud on his boots.

Brady: Still, I let him in my house. Even though I hate mud in the house.

(42) Alex: John had mud on his boots.

Brady: He also insulted the host on Facebook the night before.
Cameron: To top it off, he showed up visibly drunk.
Danni: Still, I let him in my house. (Even though I hate mud in the house and rude guests.
Although honestly I don’t mind when John is drunk and I thought that was funny.)

This use of still in (42) seems to reflect on the context of Alex’s, Brady’s, and Cameron’s
utterances, not just the context of the previous sentence. If we include the parenthetical sentences,
this shows that Still, I let him in my house cannot be taking into account the previous sentence only,
and in fact does not need to take the previous sentence into consideration at all. Instead, the sentence
immediately before is explicitly dismissed, meaning that still must be taking into account the two
sentences before that in this case. This could be the result of still interacting with (some element
of) the discourse context as a whole, or just interacting something other than the previous sentence.
Following the previous chapter, if elements in the discourse are restricting what propositions could
be interacting here, this is a thing we can test for, which I will return to when fleshing out my

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analysis. For this section fleshing out issues with the current analysis, one more test for whether or
not still interacts with the previous sentence is to include an embedded clause giving the relevant
context.

(43) Alex: I heard that John had mud on his boots.

Brady: Still, I let him in my house.

8>><>>: Even though I hate mud in the house.

?Even though you heard that.

9>>=>>;

In (43), this does not mean that Brady let John in their house even though Alex heard something,
as it seems very odd to follow the sentence up by mentioning that. Rather, this means that Brady
let John in their house despite the thing that Alex heard. It is totally natural to follow up by talking
about the mud, not the hearing. This means that still cannot be necessarily interacting with the
proposition before it in the discourse. Rather, the fact that it can be interacting with an embedded
clause shows that it has to be interacting with something contextually present in the discourse. One
concern about this embedding test is that I heard that might be acting as an evidential here, but I
argue that it isn’t a true evidential here, as it can be challenged (Murray, 2009).

(44) Alex: I heard that John had mud on his boots.

Brady: You didn’t hear that! You saw it yourself!

In (44), the truth conditions of the embedding clause can be challenged, indicating that it isn’t a
true evidential. In that case, (43) shows that the alternative set can be generated from a syntactically
embedded proposition if it is generated from a proposition. Additionally we see this reoccur in
different environments, such as more syntactically complex embeddings which are unlikely to be
evidentials, like in (45) and under questions like in (46).

(45) Alex: Danni told me that John had mud on his boots.

Brady: Still, I let him in my house.

(46) Alex: Didn’t John have mud on his boots?

Brady: Still, I let him in my house.

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The embedding in (45) could be interpreted as obliquely indicating how Alex heard the em-
bedded proposition, but it isn’t necessarily the case, as they could just be informing Brady that the
news of John’s muddy boots is out. We do not want to analyze this as an evidential. As for (46),
given that questions are usually analyzed as sets of propositions or sets of answers (Hamblin, 1973;
Karttunen, 1977), it’s not entirely clear what still would be interacting with in (46). The operator
would have to be modified to interact with a set of propositions, or it could be interacting with the
proposition below the question operator that theoretically generates the set, which would again be
still interacting with something embedded. At this point, I conclude that Ippolito’s analysis needs
to be tweaked to at least make it clear how still can interact with something contextually relevant
other than the previous proposition. The question is how to restrict the sentences that still can
interact with more strictly than just saying the ones that are “contextually relevant”. In order to
have a good hypothesis that makes clear predictions, I want ask a question like what element(s) in
the discourse does this interact with?

Another problem with this analysis of concessive still involves looking specifically at when
still appears in a comparative, whereupon if an at-phrase is included, this makes it clear that
still is potentially including only a tautological presupposition. To illustrate what the problematic
tautological presupposition is, consider the following data where comparatives are shown that
include adjunct at-phrases.

(47)

a. Andrew is pretty tall, at 6’1”.

b. At 6’1”, Andrew is pretty tall.

c.

d.

I am taller than Andrew, at 6’3”.

I am, at 6’3”, taller than Andrew.

e. At 6’3”, I am taller than Andrew.

These at-phrases are optional, and as (47) shows, they can appear in a variety of positions in the
sentence. I will sketch out a brief analysis for the sake of the point here, but a short approximation
of what (47a-b) should mean for example, is something like Andrew is pretty tall ^ Andrew is 6’1”.

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In the comparative in (47c-e), it again has this conjunctive meaning like I am taller than Andrew ^
I am 6’3”.

This data indicates that these at-phrases are syntactically adjuncts. In addition to its optionality
and it syntactic position being flexible, it is often set off by pauses, as when fronted. In terms of
their semantics, though should they be analyzed as a regular part of the proposition or something
different? It could be an asserted part of the sentence, or if not, perhaps it could be like an appositive
or another parenthetical. Consider the structures in the following data from Potts (2003).

(48)

a. Ames, a successful spy, is now behind bars.

b. Ames, who was a successful spy, is now behind bars.

The at-phrases in (47) do look like the appositive and relative clause in (48). Potts (2003)
argues that appositives, some relative clauses, and some similar structures are conventional im-
plicature (CI). Unlike conversational implicature, conventional implicature is not cancelable, and
their contribution to the semantics has to be computed within a sentence rather than inferred from
the discourse. The idea in Potts’ analysis is that conventional implicature is calculated within a
sentence, but on a separate level from the other asserted parts of the proposition. For this tentative
analysis of at-phrases, I am not going to take a stance on whether they are CIs or not, as they
will pose a problem for Ippolito’s analysis regardless and they will be dealt with in my analysis
regardless. I will simply assume that they are present somewhere in the truth-conditions of the
proposition as a whole.

At-phrases certainly aren’t a part of the basic comparative structure, but like many adjuncts,
they can be paraphrased conjunctively. As I am not fleshing out a full analysis of at-phrases here
and it does not need to slot in to my analysis of comparatives from Chapter 2, I would like to
borrow an intuition from Schwarzschild (2012), where his analysis of comparatives is constructed
conjunctively, in order to present this analysis clearly.

When we plug a comparative with at-phrases into our extension of Ippolito’s analysis of con-
cessive still to still in comparatives, the problem that emerges is a subtle one of uninformativeness.
The following example is not stepped through, but rather for clarity and brevity the propositions

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are left un-unfolded. As a reminder, the presupposition is included in the underlined portion, even
though it should have already been checked at this stage of the derivation. Here, it is the important
part to look at for finding the uninformativeness.

(49) Andrew is pretty tall, at 6’1”. At 6’3”, I am still taller.

S′

[Andrew is tall at 6’1”]2

D

still

S

⟨⟨st⟩; t⟩

⟨st⟩

⟨⟨st⟩; ⟨⟨st⟩; t⟩⟩

proF;2
⟨st⟩

At 6’3” I am taller

(50)

(51)

JstillK„JA-6’1”-tallK”„JI-am-taller-and-6’3”K” = max(cid:20);wcfw : w 2JA-6’1”-tallK ^ w 2
JI-am-taller-and-6’3”Kg <likely max(cid:20);wcfw
′ 2JI-am-taller-and-6’3”Kg:JI-am-taller-and-6’3”K„w” = 1

′ 2 :JA-6’1”-tallK^

′ : w

w

The set of worlds (maximally similar to the actual world) in which Andrew is 6’1” tall but
I am 6’3” and taller than him is less likely than the set of worlds (maximally similar to the
actual world) in which Andrew is not 6’1” tall but I am 6’3” and taller than him.

The more likely set of worlds here are the ones in which Andrew is not 6’1”, I am 6’3”, and I
am taller than him. If Andrew is not 6’1”, then he is necessarily shorter than that, as technically an
individual who reaches 6 feet of height also reaches 5 feet, 4 feet, and so on. Therefore, if Andrew
is shorter than 6’1” and I am 6’3”, it is necessarily true that I am taller than he is. Therefore the
more likely set of worlds are ones in which this tautology is true. The less likely set of worlds are
the the otherwise equivalent worlds in which Andrew is 6’1”, and I am 6’3” and taller than he is. I
may or may not be taller than he is if I am 6’3”, as if Andrew is 6’3” he could technically be taller,
as long as he is no shorter. So this proposition is not a tautology. Therefore, the only difference
between these two sets of worlds is that the more likely set has a proposition that is tautological,
and the less likely set has instead a proposition that isn’t. This presupposition is necessarily met

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with this sentence, meaning it is semantically uninformative. The contribution of still is generally
analyzed as being in the weight of the presupposition, as the asserted content is just p, so still is not
going to be semantically informative in the asserted content either.

Although this analysis of still predicts that it is semantically uninformative, this sentence
is perfectly normal, no oddness from superfluous phrasing, nor does it even sound redundant.
Instead, it only comes off as a more emphatic sentence than it would be without still. Additionally,
while this example is with Ippolito’s denotation for concessive still, remember that this analysis for
concessive still is essentially identical to an analysis of even. Even can, just like concessive still go
in similar high positions, and in exactly the same position within a comparative, and also it also
sounds perfectly natural and neither odd nor redundant in those positions.

(52) Alex: John had mud on his boots.

Brady: Even so, I let him in my house.

(53) Andrew is pretty tall, at 6’1”. At 6’3”, I am even taller.

(54)

a. This game was bad. That one was even worse.

b. This game was bad. That one was still worse.

Given that this analysis presents this issue for still and that Ippolito’s analysis for still is
constructed identically to how even works, this is also a problem for even in sentences like (52) and
(53). This uninformativity isn’t a problem that seems like it should result in ungrammaticality, so
much as it predicts a result similar to the effects of repetition. A sentence like A dog entered and
then the one dog sat down is a good correlate, where it is uninformative by repeating that there’s
one dog when we already know this from it’s introduction. This sentence is not ungrammatical,
just it sounds odd in that it is repetitious.

While I will suggest a different analysis that explains how this presupposition may not be
uninformative, I want to first mention that there is a way to analyze the uninformativity of the
presupposition as contributing something anyway. The uninformativity could be in a Gricean way
the root of the contribution of still. Impressionistically the contribution could be described as some

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kind of emphasis. The principle of Maximize Presupposition suggests that if a presupposition
can be used, it must be used (Heim, 1991; Sauerland, 2008). Cooperative interlocutors make the
strongest claims possible when speaking, in order to maximize informativity (Grice et al., 1975).
In this case of a tautological presupposition, the uninformativity of the presupposition does not
make for a stronger claim. This seems to negate the pragmatic benefit of using the strongest
presupposition possible, but it could be analyzed as being the reason that an emphatic flavor results
instead. One could argue that the emphasis results from using a form with a theoretically stronger
presupposition than a form without one because including still or even makes for a more marked
form than not including them. Even though still or even contribute only tautological information,
the use of a more marked form itself contributes something pragmatically. According to Acton
(2014), part of the work that a listener does in a conversation is compare the phrasing they hear
with what seems like viable alternatives, working on a sort of “what does it mean that they said it
in this way not that way” question. Therefore, using a marked form when a less marked form exists
pragmatically indicates that must be a reason why the speaker used the more marked form instead.
Returning to the question of the tautology, if the alternative has effectively the same meaning, then
the reason for using the marked form can’t be due to a slight change in meaning. The contribution
of still or even here could be a pragmatic emphasis in lieu of an informative presupposition or
assertion. While I do not find this argument unconvincing, it doesn not present a clear argument
in favor of any semantic analysis, Ippolito’s or otherwise. Instead, the analysis I will propose for
concessive still provides an explanation for why it conveys emphatic flavor while providing an
analysis in which the presupposition is not tautological.

4.3.2.2 Reanalyzing concessive still as proposition level focus

Ignoring for the moment the issue brought up with at-phrases, the first problem for Ippolito’s
analysis is that it has still use the preceding sentence, whereas I have presented evidence that the
preceding proposition is not necessarily the context it should interact with. Instead, it needs to
interact in some way with the larger discourse context. I propose that reanalyzing concessive still

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and even as regular FSPs involving proposition level focus would solve this problem.

As a reminder, I proposed that proposition level focus is possible, and focus sensitive expressions
can interact with it, but the examples we have seen so far showed that some further restriction must
be in play as well. According to Rooth (1996), focus should generate the set of possible things
of the same type as the focused constituent. So in the case of focusing a proposition, this should
generate a set of possible propositions. This is not restricted in any way that would make sure
these propositions are semantically or syntactically similar to the focused element, just restricted
to things that are possible propositions. This was too unrestricted to be informative for discourse
also, and for concessive only it was too unrestricted to result in a true assertion. Instead, in both of
these cases I proposed that the discourse serves in some way to further restrict the alternative set

in order to make it informative. Instead of C being a “contextually restricted subset ofJ(cid:11)Kf”, it is a
subset ofJ(cid:11)Kf that is defined using objects in the discourse, thus formally defining what it means

to be “contextually restricted”. Given Ippolito’s analysis of still as a FSP, and the parallel with the
prototypical FSP even, I have the same expectations here that an analysis of these with proposition
level focus could reveal a discourse-based contextual restriction that yields these results.

The asserted content of even p is usually assumed to just be p, in Ippolito’s analysis and others.
In this case, the presuppositional effect even or still should have is to say that p is true, and it is less
likely than the other options q in the focus set of alternatives. Ippolito added a conjunctive element
in their analysis of concessive still specifically, which could be paraphrased as it is less likely that p
and q are true than it is that p is true and q is false. In order to think about that, let’s look at some
data involving proposition level even, as it seems to parallel proposition level still.

(55)

John failed the exam even though he studied all night.

(56)

John studied all night. Even so, he failed the exam.

(57)

# Even, [John failed the exam]F.

Both (55) and (56) have 2 propositions, linked by even as though it were a conjunction linking
propositions. In the latter, so can be analyzed as referring to the previous proposition, so it might

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not necessarily have to be syntactically a full proposition here, so much as have the semantics of
one. This data indicates that even with proposition level focus, or concessive even, must necessarily
appear with (at least) two propositions. In (57), if we assume proposition level focus and do not
prosodically stress any smaller constituent, this is ungrammatical without any anaphoric so included
after even. In comparison, consider a use of even with a smaller constituent focused.

(58) Even John failed the exam.

In (58), even only interacts with one proposition and it is perfectly grammatical. We do need to
accommodate that the likelihood of John failing was slim, or something, but it is perfectly fine for
this use of even to appear with only one proposition. Unless this is because the second proposition
is that John was likely to fail, and this proposition is extremely easy to accommodate, this appears
to be a difference between the two uses. Even so, it is possible that it is not a difference, and we are
accommodating some presupposition, but consider the difference between (58) and (59).

(59)

# Even so, [John failed the exam]F.

Neither is perfect out of the blue, as some accommodation is needed for (58), but the sentence in
(59) is definitely worse, being totally unacceptable out of the blue. Perhaps this is because we cannot
accommodate that something happened that would have made it less likely for John to fail. However,
there is no immediately apparent reason why one presupposition can be accommodated that much
easier than the other if they are both simply presupposing the veracity of another proposition. The
presupposition of (58) can also be directly addressed with a hey-wait-a-minute style test, but trying
to run one with (59) is noticeably harder, and it is not immediately clear what objection should be
made.

(60) Alex: Even John failed the exam.

Brady: Hey wait a minute, I thought John was someone we thought likely to fail! That’s
not surprising!

(61) Alex: Even (so), John failed the exam.

Brady: Hey wait a minute...

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a.

b.

# I didn’t know he studied!

# I didn’t know he bribed the instructor!

c. Was there some reason we thought he wouldn’t?

d.

You didn’t say anything about him being unlikely to fail.

In the case of (60), the presupposition is easily targeted, and it can be flagged when there is
failure of presupposition. In (61) this is not as easy. An objection can be made, but it is very odd
to try to accommodate a specific reason that it was unlikely or surprising that John failed the exam,
as (a) and (b) show. The most successful follow up seems to be the metalinguistic sort of objection
that doesn’t accommodate a specific reason but rather just flags a failure of presupposition, as
we see in (c) and (d).
It is not entirely clear why this presupposition failure is unrecoverable,
unless it is the case that this is not presupposition failure, but rather even requires two propositions
locally when interpreted with proposition level focus.This looks like an argument that for even,
its requirements are slightly different between its use with proposition level focus and its use with
smaller constituents focused. This is not totally in line with the argument in the previous chapter,
which predicts that if an expression is focus sensitive with smaller constituents focused, it should
have the potential to interact with a focused proposition. However, this potential is all that is
predicted, not a necessary interaction, as something else could potentially block any particular
focus sensitive expression from interacting with a focused proposition. Regardless, this is evidence
that even must have two propositions locally when interacting with proposition level focus, but not
when interacting with smaller focused constituents. To return to still, we do see a similar effect if
there are not at least two proposition in the discourse for it to reference, although there are syntactic
differences in how the propositions are linked, which I will return to imminently. The following
two uses of still attempt to mirror the distinction with even, but given that still does not typically
have a focus sensitive use with focused constituents smaller than a proposition, I have shown its
typical temporal use in comparison. The temporal use of still presupposes that the state or event
was previously ongoing, as it asserts that it is currently ongoing. The concessive use of still is like
even with proposition level focus in its presupposition that this is unlikely, given something else.

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(62)

John is still cooking.

(63)

# Still, John failed the exam.

Again we can easily accommodate the temporal presupposition and he was cooking before from
(62), but the concessive use in (63) is very difficult to accommodate, and for me at least it is fully
infelicitous out of the blue. It makes sense to continue to analyze even and still along the same lines
here, but even has already shown itself to be a little less straightforward than also was. To return to
the syntactic differences with even and still, it is the case that concessive even must either overtly
connect two propositions, or appear as even so when attached to only one full proposition. So has
been analyzed as being anaphoric to a handful of things, including events, in which case it makes
sense to analyze so as being anaphoric to another proposition in this case (Landman & Morzycki,
2003). Even with proposition level focus cannot appear with only one proposition locally. However,
still does not pattern the same. It does not replaces a conjunction when linking two propositions
nor does it appear with an anaphor like so. Instead, still needs the help of an overt conjunction if it
is going to link two propositions. Exact minimal pairs are not possible because the order of the two
propositions switch for even and still, but consider the following attempt at near-minimal pairs.

(64)

a. John failed the test, even though he studied all night.

b. John studied all night. Even *(so), he failed the test.

(65)

a. John studied all night, *(but/and) still he failed the test.

b. John studied all night. Still (*so), he failed the test.

In (64), even necessarily interacts with two propositions locally, as has been discussed. However,
in (65), still necessarily has only one overt proposition locally, although it still needs at least one
other proposition available recently in the discourse, and can’t appear out of the blue. When it
appears between two propositions in the (a) version, a conjunction is needed, and still is simply
incompatible with the propositional pronoun so in (b). One possibility is that still could involve
two propositions like concessive even if it were to have a covert pronoun like so, corresponding
with the other proposition. However, I think this is not quite the right analysis. Concessive even

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must explicitly take in two propositional arguments. But still may be taking in one propositional
argument, and accessing the other in the traditional FSP way of referencing the focus semantic
value of the same proposition, different from how even appears to be acting when it has proposition
level focus. Instead, this is more on par with an analysis of even with a smaller constituent focused,

in that it only involves one proposition locally, and anything else comes fromJpKf. This also makes

sense with the earlier data showing that still can be accessing a proposition or propositions that
are not immediately adjacent, and are in fact across discourse participants. So still can only have
one proposition syntactically local, like even with low focus, but it needs at least one proposition
available in the discourse already, like even with proposition level focus. Given how concessive
even appears to differ syntactically from still, it makes sense to analyze the two as slightly different
in how they access the two propositions in their denotation, but overall I think it makes sense
to follow Ippolito’s conjunctive approach in the denotation for still and even. This does involve
deviating slightly from what even without proposition level focus is said to do, but to reconsider
two previous examples, still does not pattern like that even.

(66) Even John failed the exam.

(67)

# Still, John failed the exam.

Unlike even in (66), still in (67) is not recoverable without further background. Out of the blue
it is totally unacceptable, whereas even can be accommodated in (66). A denotation for still should
take into account that something else is needed, if not syntactically locally, then close by in the
discourse. Regular analyses of even generally intend to assert p, with the presupposition of p is
less likely than other propositions q (which is from the focus set of alternatives). To incorporate
this conjunctive approach from Ippolito’s analysis of concessive still, concessive even or still would
still asset p, but the presupposition would be something like p and q both being true is less likely
than p and :q being true.
valueJ(cid:11)Kf, in addition to referencing p. Rooth (1996) references a contextually restricted version

To start with still, as a typical FSP, it should access some proposition q via the focus semantic

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of the focus semantic value, C, but I would like to, following my proposals in the previous chapter,
more precisely define how the alternatives in the focus set are restricted. So far I have assumed
a Table sort of format, of the kind developed by Farkas & Bruce (2010) and further refined by
Taniguchi (2017), and provided arguments for adding goals to this discourse structure. This kind
of articulated discourse structure allows us to make more precise predictions about what we mean
when something is affected by “the context”. What I propose to do here is to do the same thing
as in the analysis in the previous chapter: work with a general FSP style denotation for still which
assumes a C that is restricted in some way, then define exactly how C is restricted from the focus
semantic value. So to start, here is a denotation for FSP still that follows Ippolito’s conjunctive
approach as discussed, but is adapted to only syntactically interact with one proposition p and
access a C for its q.1

JstillK = (cid:21)p : 9q»q 2 C ^ „„p \ q” <likely „p \ :q””…:p

(68)

In terms of the denotation for still in (68), I am assuming again for convenience that still applies
high, taking in a proposition with a non-unary focus semantic value. I have simplified the formalism
from Ippolito’s version, but here I also have the asserted content as just pm and the presupposition
is that is is less likely that both p and q are true than it is that p is true and q is not. Unlike in the
previous chapter, this is not a general denotation intended to work for all uses of this FSP, but again
following Ippolito’s arguments for different versions of still, this will only work for concessive still,
and it must interact with focus. This moves somewhat away from the cohesion of the previous
chapter, but I think enough evidence has been presented to show that still is an odd case and merits
being treated as such. The next step is to figure out what objects in the discourse seem to be what
is restricting the focus semantic value of that proposition to C. This analysis assumes proposition
level focus, which if unrestricted, generates a focus semantic value containing the set of possible
propositions. Given the denotation in (68) above, this will end up, like with also and discourse
1Note that I have drastically simplified the intensional aspect of Ippolito’s formula here. While
the intensionality is important, it is not the focus here. Given that a proposition denotes a set of
worlds, we are interpreting p\q to be the set of worlds consistent with both. I write :q as shorthand
to indicate the set of worlds in which q is not true.

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(69) Still, [John failed the exam]F

JJohn failed the examKf =

John took the exam.
John tried to pass the exam.
...

8>>>>>><>>>>>>:

9>>>>>>=>>>>>>;

addition in the previous chapter, being uninformative by the presupposition being vacuously met.
If every possible presupposition is in C, then it must be the case that there exists some proposition
q in there that makes it more likely for p to be true if it is true than if it is not. For example, consider
the following set of propositions, which is a subset of what could be generated with an unrestricted

JpKf.

In (69), these are two of the possible propositions that would be generated in an unrestricted

JpKf, and both of them I think fulfill the presupposition in (68) in that they effectively need to be true

in order for p to be true. The C needs to be further restricted in order to make this presupposition
meaningful. In addition, the right restriction would explain when still is felicitous and when it is
not, based on what is in the discourse. So far, we have seen evidence that still can take a q from the
CG, but I propose that, like also, still can also take a proposition q from the Table. Consider the
following example showing that the q for still can come from something not yet entered into the
CG.

(70) Alex: John studied all night, and still he failed the exam.

Brady: I know for a fact that he studied until 11pm and then he came to my party, actually.
But he definitely did fail that exam!

In (70), the relevant q that makes p more likely is that John studied all night. Here, I argue
that it is still on the Table, not on the CG, because Alex gave two propositions at once, rather than
waiting for their interlocutor to agree to add q to the CG, and because Brady then explicitly rejected
that proposition, blocking it from entering the CG. Based on this, the restriction I am proposing
looks as follows.
(71) Discourse restriction for still: C (cid:26) „CG [ T”

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The restriction in (71) predicts that still should now only be able to access things that have
already been said when looking for a q that makes p more likely to be true, and achieves the
effect that still does not need to be immediately after the relevant q. This vastly restricts the set
and will rule out vacuous options like in (69), predicting that still will only be felicitous when it
follows an overt proposition that makes p more likely. This is also a very simple restriction, easy
to frame using objects in the discourse and not needing anything new. Like the analysis in the
previous chapter, it makes sense to treat this discourse restriction as something lexically encoded,
and therefore existing within the denotation for still, although in (71) I only included the restriction,
not the whole denotation. This hypothesis works for cases like the one repeated here in (72), where
we want still to interact with multiple propositions, or not necessarily the preceding one.

(72) Alex: John had mud on his boots.

Brady: He also insulted the host on Facebook the night before.
Cameron: To top it off, he showed up visibly drunk.
Danni: Still, I let him in my house. (Even though I hate mud in the house and rude guests.
Although honestly I don’t mind when John is drunk and I thought that was funny.)

In (72), still is considering the propositions said by Alex and Brady, but ignoring the one from

Cameron. IfJpKf contains propositions in The CG or on the Table, then it should look as follows.

The set in (73) includes all of the propositions that are in „CG [ T” in this toy example.
However, considering the part in the parentheses in (72), one of these propositions should not affect
the likelihood of them letting John in their house. This proposition does not meet the requirements
of still’s presupposition, which I have marked about by striking it out. Either of the other two
should check that presuppostion, though, so still is felicitous. In the event that still is interpreted

153

8>>>>>><>>>>>>:

(73) Still, [I let him in my house.]F

C =

John had mud on his boots
He insulted the host on Facebook the night before.
He showed up visibly drunk.

9>>>>>>=>>>>>>;

as meaning p is true even though both of these propositions is true, I think this still works. If two
propositions p and q are both in the „CG[T”, then we want to conclude that this set contains p^ q.
If we consider that some proposition r is equivalent to p ^ q, then this set also contains r. In this
example, r is equivalent to John had mud on his boots and he insulted the host on Facebook the
night before, and this is the proposition considered in the presupposition for still.

This analysis of still as a FSP with proposition level focus and a discourse restriction on C is
working for far for concessive uses. At this point, we should be able to apply this concessive use to
uses of still in a comparative, and then if the analysis is successful, it is an argument that aspectual
particles in comparatives do not support a theory where event structures can be built into degree
structures. To look at a use in a comparative, we expect the following to be the focused element.

(74) Andrew is pretty tall. I am still taller.

Still [I am taller]F

The focus in (74) is on the proposition as a whole, which means that the focus semantic value
is the set of possible propositions. The discourse restriction cuts that down to only propositions in
„CG [ T” to get C, at which point C contains Andrew is pretty tall. This gives us the following
result with our given denotation for still, where for clarity the presupposition is included past where
it should have been checked, but underlined. This computation is broken down into steps in order
to make it clear how the presupposition is checked with the given discourse, and what the result is.

(75)

a. JstillK = (cid:21)p : 9q»q 2 C ^ „„p \ q” <likely „p \ :q””…:p
b. JstillK„JI-am-tallerK” = (cid:21)p : 9q»q 2 C ^ „„p \ q” <likely „p \ :q””…:»p…„JI-am-tallerK”
= 9q»q 2 C ^ „„JI-am-tallerK \ q” <likely „JI-am-tallerK \ :q””…:»JI-am-tallerK…

Where C (cid:26) „CG [ T”

c. C contains whatever propositions are in „CG [ T”, but Andrew is pretty tall is the one

that should check the presupposition, so it would work for q.

=JAndrew-tallK 2 C ^ „„JI-am-tallerK \JAndrew-tallK” <likely „JI-am-tallerK\

:JAndrew-tallK””»JI-am-tallerK…

d.

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The above computation in (75) is broken into steps. In (a) I have repeated the new denotation
for still, and in (b) I have applied it to the proposition I am taller, which then substitutes for p.
The presupposition is included, but underlined in (b), as I have separated out the presupposition
checking step into (c) for clarity. In theory C would contain more propositions than just the prior
one in a full discourse. However, the prior one is the one we care about here, as it checks the
proposition, and then we see it replace q in (d), where the presupposition is underlined to show
clearly what requirement has been met. However, the final assertion is just that I am taller than
Andrew. Thus the requirement for still that it follow something making p unlikely is met via the
presupposition, and correctly it then does not affect the asserted content of the proposition.

This analysis successfully extend concessive uses of still to include uses in comparatives.
However, as the previous section showed, comparatives with at-phrases posed an extra issue for
Ippolito’s analysis of concessive still.
I argue that this analysis of FSP still with a discourse
restriction successfully deals with this data.

(76) Andrew is pretty tall, at 6’1”. At 6’3”, I am still taller.

As a reminder, data like (76) posed an issue to Ippolito’s model because it presupposed some-
thing like it is less likely that Andrew is 6’1” and I am 6’3” and I am taller than he is than it is than
he is less than 6’1”, I am 6’3”, and I m taller than him. This is necessarily true, which makes still
contribute nothing, and raises the question of why this is acceptable if it is totally redundant. If we
look at this with my analysis, we expect a C like the following one.

This set in (77) includes the propositions that we can expect „CG [ T” to include from (76).
Whether we take the at-phrase to be conventional implicature or asserted content, both Andrew
is pretty tall and Andrew is 6’1” should end up in the CG or on the Table. No matter how the

8>>>>>><>>>>>>:

(77) Still, [at 6’3”, I am taller]F

C =

Andrew is pretty tall, at 6’1”.
Andrew is pretty tall.
Andrew is 6’1”.

9>>>>>>=>>>>>>;

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at-phrase is interpreted, the content of the first sentence in (76) should beJAndrew is pretty tallK ^
JAndrew is 6’1”K, even if the second conjunct is added to the CG via a different mechanism than
the first conjunct. If the CG contains „p^ q”, then we can conclude that the CG also contains p, and
it also contains q, which means that the second and third lines in the above set are in „CG [ T”, and
therefore members of C with the current discourse restriction for still. Given that the denotation
I am working with follows Ippolito’s, two of them will create the same issue of redundancy and
uninformativity. Like in the previous example, those two are struck out above. However, this
leaves one proposition that does not make the contribution of still’s presupposition redundant. That
proposition checks the presupposition without it being totally redundant or uninformative.

Switching from Ippolito’s analysis to this slightly modified one thus solves both of the issues I
have pointed out. The conjunctive approach has been maintained, but the reliance on proposition
level focus allows the multiple local propositions to be involved, not just the two adjacent ones. The
issue of at-phrases is solved in the same way. Interpreting at-phrases conjunctively, and drawing C
from „CG [ T” allows still to reference just one of those conjuncts. This modification to Ippolito’s
analysis works well to extend a FSP analysis of concessive still to uses of still in a comparative. At
this point, this working analysis means that seeing a typically aspectual particle in a comparative is
not automatically data that supports a link where event constructions compositionally building to
degree constructions.

4.3.2.3 Extending that analysis to yet

The data I began this chapter with included still and yet both in comparatives. Therefore I must now
ask whether this analysis works for yet as well, or does that data present a possible link between
event constructions and degree constructions still? I previously presented NPI data showing that the
yet that appears in comparatives and with the same concessive use is not an NPI, as opposed to the
canonical temporal yet. In addition, we see the same pattern of at least two different uses of yet, a
temporal one and this concessive one. I suggest this is evidence that, like my and Ippolito’s treatment
of still, we should be treating this as simply a different yet than the temporal one. Minimally, I just

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take this as evidence that I can assign concessive yet its own denotation independent of its temporal
use. However, if yet follows the full FSP paradigm that Ippolito sketches out for still, that would be
evidence in favor of a parallel analysis for yet. Below I have repeated the data that Ippolito gives
for different types of still in the (a) versions, and created parallels with yet in the (b) versions.

(78) Aspectual still/yet

a. John is still cooking.

b. John is not yet cooking.

(79) Marginality still/yet

a. Compact cars are still safe; subcompacts start to get dangerous.

b. Compact cars are not yet dangerous; subcompacts start to get dangerous.

(80) Concessive still/yet

a. John studied all night. He still failed the test, though.

b. John studied all night. Yet he failed the test.

(81) Exclusive still/yet

a. Got an A! I was jumping for joy (internally, keep in mind it’s still 8am).

b. Exclusive yet: Got an A! I was jumping for joy (internally, keep in mind it’s 8am yet).2

(82) Use in a comparative

a. A still greater offer came from the Dean.

b. A yet greater offer came from the Dean.

Although I analyzed the use of still in a comparative as a type of concessive still in the previous
section, above I include it separately. For each of Ippolito’s examples with still, I created a parallel
2Recall that Ippolito said this use is dialectal, and it was particularly hard for me to construct
a parallel with yet. For me, yet had to be an NPI when I tried, and adding negation made it hard
to see if it was acting as an exclusive particle. Instead, I consulted a speaker of American English
who has non-NPI yet in their dialect, and they confirmed this is acceptable to them, although they
preferred it’s early yet over specifying 8am.

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version with yet. These are not necessarily minimal pairs, as some uses of yet are NPIs, so I needed
to add negation in those cases to license them. This is the case for the aspectual and marginality
uses in (78) and (79). In (80), the concessive use of yet is not an NPI, but as can be seen above, yet
must be in a different position than still. I do not want to say much about the exclusive case in (81),
due to dialectal difficulties, but I am assured that this exclusive use is acceptable, and again we see
only minor syntactic differences. Then in the comparative cases in (82), still and yet are totally
interchangeable. While this only shows some of the FSP uses that Ippolito discusses, the additive
and scalar, this presents evidence that we can treat yet as having different focus sensitive uses here
the same as still does. I am not going to copy in the analysis of all of the different uses of still to
apply them to yet, as this strays away from my goal here, but I will instead extend the analysis of
concessive still in and out of comparatives to yet. Directly extending an analysis and denotation
from still gives a structure as follows.

(83) Andrew is pretty tall. I am taller yet.

Still [I am taller]F

In (83), as before, the focus semantic value is the set of possible propositions. Then the
discourse restriction cuts that down to only propositions in the the CG or on the Table, at which
point C contains Andrew is pretty tall. This gives us the following result, where for clarity the
presupposition is included past where it should have been checked, but underlined. I have again
broken the process down into steps which include explicitly checking the presupposition.

(84)

a. JyetK = (cid:21)p : 9q»q 2 C ^ „„p \ q” <likely „p \ :q””…:p
b. JyetK„JI-am-tallerK” = (cid:21)p : 9q»q 2 C ^ „„p \ q” <likely „p \ :q””…:»p…„JI-am-tallerK”
= 9q»q 2 C ^ „„JI-am-tallerK \ q” <likely „JI-am-tallerK \ :q””…:»JI-am-tallerK…

Where C (cid:26) „CG [ T”

c. C contains whatever propositions are in „CG [ T”, but Andrew is pretty tall is the one

that should check the presupposition, so it would work for q.

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=JAndrew-tallK 2 C ^ „„JI-am-tallerK \JAndrew-tallK” <likely „JI-am-tallerK\

:JAndrew-tallK””»JI-am-tallerK…

d.

The steps in (84) are identical to those in the analysis with still, which matches the native
speaker intuitions that still and yet are effectively interchangeable in these concessive locations and
in comparatives. Speakers do tend to have preferences between still and yet in comparatives, in
addition to preferences about whether they come before or after the adjective, and this analysis
says nothing about why that is. However, extending the analysis of still to yet makes one important
overarching point. Again, I have presented data that appears to create a degree interpretation
using expressions that are typically analyzed as having event related meaning. And again, I have
presented an analysis for it that shows that this can be explained in a different way. An analysis like
Ippolito’s, but one where it relies on proposition level focus and discourse restrictions on C, fits the
data well, meaning that this is also not evidence of event constructions compositionally building
into degree constructions.

4.3.3 Returning to even

While all of the data I have promised to address has been addressed, the relation of still and yet
with even in this analysis brings up the question of how to bring this analysis back to even: what
differences do we want a denotation of concessive even to have from regular denotations for even,
and what differences do we want it to have from still? To start with, even has to syntactically
interact with two propositions, not one, and not in the same order as still does.

(85)

John studied all night. Still, he failed the test.

(86)

John failed the test, even though he studied all night.

In both of these, we can paraphrase this as John failed the test (which was unlikely considering
he studied all night), which I will for the moment relabel as p (which was unlikely considering q).
In (85), we see that still merges with p, but in (86), we see that even merges first with q and second

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with p. So the order of the arguments needs to change when adapting the denotation for still to
concessive even. The following denotation incorporates these two changes.

JevenconcessiveKv1 = (cid:21)p(cid:21)q : „q \ p” <likely „q \ :p”:p

(87)

In (87), the order of the propositions in the presupposition are changed, and q is now required
via lambda instead of existentially quantified. Otherwise, the denotation is the same. It is worth
checking whether the assertion should be the same, or if the different syntactic configuration is also
correlated with a different assertion configuration as well. That is, is q now asserted in addition to
p?

(88) Alex: John failed the test, even though he studied all night.

a. Brady: That’s not true! He didn’t fail the test! (He did study all night though.)

b. Brady: That’s not true! He didn’t study all night! (He did fail the test though.)

In (88), speakers report that the sentences in the parentheses feel redundant, like there’s no need
to mention that it’s true when that is the default assumption, but they otherwise find both objections
acceptable. This shows that the truth of both p and q is asserted, as both can be straightforwardly
rejected as false. Incorporating that gives us the following denotation.

JevenconcessiveKv2 = (cid:21)p(cid:21)q : „q \ p” <likely „q \ :p”:p ^ q

(89)

In the second version in (89), the additional change is that both p and q are now asserted. This
deviates from standard analyses of even, but I will return to that topic later, once we’re done with
concessive even. At this point, this second version denotation has a working argument structure,
presupposition, and assertion in line with how concessive even functions. This analysis should
work. However, another thing to note is that, as with Ippolito’s original denotation for concessive
still, this is now a denotation for a FSP that does not incorporate the focus semantic value or C to
utilize its focus sensitivity. So while this denotation works, and is not even very oddly specified, it
is a very odd denotation for an FSP. This lack of interaction with focus is easily remedied, but the
remedy comes at the cost of a differently odd specification. Both propositions must be arguments

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in order to match the syntactic facts, but q can be drawn from C by effectively limiting the focus
semantic value to propositions that are equal to q. This is incorporated in the following third version
of a denotation for even.

JevenconcessiveKv3 = (cid:21)p(cid:21)q : 9r ^ r 2 C ^ „„r \ p” <likely „r \ :p””:p ^ q

(90)

Where C (cid:18) fqg

The denotation and restriction in (90) does bring C back onto the field, but in a way that does
add needless pieces. Given that two propositions are required syntactically, and both of them
are referenced in the presupposition and the assertion, as I showed in (88), including a reference
to C does not mean that we can include reference to fewer propositions.
Instead, in order to
reference a proposition from C, we need to effectively define C as being equivalent to one of those
propositions. This is not necessarily in line with any of the previous discourse restrictions on
C that I have proposed for any FSPs I have analyzed. Perhaps this is an argument that ‘the set
containing the proposition said next’ should be an accessible object in the discourse in the same
way that something like a speaker’s discourse commitments are, but I am not familiar with any other
evidence for such a set. That is, I do not know of any linguistic phenomena that require referencing
the following sentence or proposition. Furthermore, it seems unlikely that the restriction for C
should be able to access q if it is written as is. Recalling the discussion in the previous chapter
about whether it is worth eliminating C by writing the restriction into the denotation directly, this
would eliminate some of the redundancy in (90) but not all. Regardless, this denotation will be
slightly redundant if it includes reference to even’s focus sensitivity.

Unlike the examples of FSPs in the previous chapter, with even we do not want to extend this
updated analysis back to all cases of even with constituents smaller than the proposition focused.
For starters, there is the syntactic difference mentioned before, where concessive even requires two
propositions locally, but “regular” even does not. And I have already established the other difference
where even is typically acceptable out of the blue, with minimal presupposition accommodation,
but concessive even is totally unacceptable. I take both of these pieces to show that concessive even
is about the interaction of two specific propositions, and even with smaller constituents focused is

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not. As a result, their presuppositions work in different ways and are currently incompatible. The
concessive even presupposition as written above is that q ^ p is less likely than q ^:p. The typical
presupposition for even is that p is less likely than other members of C. Recall that C is a subset of
the focus semantic value of p, so we should expect an example set like the following one for even
with a smaller constituent focused.

8>>>>>>>>><>>>>>>>>>:

Erica failed the test.
Rowan failed the test.
Emily failed the test.
...

(91) Even [John]F failed the test.

JJohn failed the testKf =

9>>>>>>>>>=>>>>>>>>>;

Looking at the example members of C in (91), you could argue that if other people are failing
the test, it is more likely that John failed the test just in terms of it being a failable test. However,
consider this hypothetical situation. Erica and John are both likely to fail any test, Erica more so
than John. So if Erica fails, John probably did too. Rowan and Emily are very unlikely to fail. In
the event that Erica and John both fail the test and Rowan and Emily both pass, it is not felicitous
to say Even John failed the test, even though there exists some proposition q in the focus set (Erica
failed the test) such that q ^ p is less likely than q ^ :p. So directly extending the presupposition
from concessive even back to other uses of even makes incorrect predictions, but at the same time,
this kind of conjunctive presupposition is needed to incorporate how concessive even incorporates
its two propositions. Furthermore, the discourse restriction I proposed for concessive even (or
concessive still) should not be extended back to all uses of even. The fact that typical uses of even
work out of the blue means that their C cannot be restricted to only include propositions that are in
the CG or on the Table, that are syntactically local, or that are already overtly in the discourse at all.
In (91), I would expect none of these propositions to be overt in the discourse anywhere. Instead,
the knowledge the interlocutors need is something along the lines of ‘out of the propositions in C,
p is less likely to be true than the others are’. And finally, to move on to the assertion, as I have
showed that the assertion for concessive even asserts both p and q, this relies on two propositions.

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With lower focus, even only has access to the one specific proposition.

It is not immediately clear why the typical use of even does not seem to be appearing with
proposition level focus. Given that they take a different number of arguments, I do not expect a
problematic ambiguity would result if both could interact with proposition level focus, so there is
no immediately obvious reason why the typical use of even could not also appear with proposition
level focus. Consider the following data.

(92) This cooking attempt was a disaster. The meat is burned... The sauce is overly salted...

a. And the microwave meal even exploded when we gave up and tried that instead.

b. And even the microwave meal exploded when we gave up and tried that instead.

In (92), I have attempted to create a case where even appears with proposition level focus, but
different from concessive even or concessive still in that it is not a conjunctive case. The goal
was to create the reading that out of all of the propositions listed, p occurred and was least likely,
which I do seem to get from this data. However, it is not clear that this data could not be explained
as focusing smaller constituents. In (a), perhaps the microwave meal was more likely to just over
or undercook, rather than totally explode, and in (b), perhaps other things seemed more likely to
explode than the microwave meal. Or, it could be that p is unlikely because of these factors. This
is difficult to tease apart. Given that I do not have any tests to distinguish what is happening in
this data, I will leave it for future research and claim decisively that there may or may not be cases
of the typical use of even interacting with proposition level focus, but this is not the focus of this
chapter so I will not worry about it further.

Given that it shows differences from typical even and requires a totally distinct denotation,
concessive even is already slightly problematic for the overarching theory from the previous chapter,
and it might make sense to just consider this one as something lexicalized. So what does this say
about the FSP even in general? The prediction from Chapter 3 is that FSPs should simply be able
to interact with any size constituent focused, including propositions and smaller constituents both,
and that they should then act the same in all cases. Discourse restrictions may be easier to spot

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when the proposition is focused, as that creates a very unrestricted focus semantic value, but they
should apply just the same in cases with smaller constituents focused. It is not predicted that FSPs
should have an alternate version for when different constituents are focused. Far from even’s usual
status as a prototypical FSP, in this case even stands out as being slightly irregular, but I lean it is
not so irregular as to constitute a counter example to this overarching theory.

4.4 Interim conclusions and related questions

In this chapter, I stepped through an analysis of aspectual particles in comparatives. Initially
they look like a degree construction where a typically event-related expression contributes, counter
to the direction of the analysis in Chapter 2. However, my analysis links these uses of yet and
still to what has been observed by Ippolito (2007) and called concessive still. Following the lead
of that paper, I use the tools developed in Chapter 3 to propose a modified analysis that takes the
appearance of still in comparatives to simply be another instance of concessive yet, and analyses
all of these uses as FSPs interacting with proposition level focus. I extend the same analysis to yet,
and then explore what this means for even, which wraps up slightly less neatly than the “aspectual”
particles do.

At this time, none of the data that I have analyzed presents a situation where the analysis must
be one where an event construction is built up into a degree construction. As is, these analyses
support the conclusion that there is a directional relationship between degrees and events. Degree
constructions can be built into or be arguments of event constructions, but there is currently no
evidence of the reverse relationship.

One small factor that this analysis has not addressed is the fact that still and yet can co-occur in

the same sentence without sounding repetitive.

(93)

I tried to straighten the painting several times, yet still it hangs crooked.

This analysis does not predict that they should not be able to co-occur, but it would make sense
that it would at least sound repetitive since they contribute the same thing. To also bring up some
data that looks related but has not been covered, still and yet can appear with some adjectives

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outside of a comparative. However, they do not work with all adjectives outside of a comparative.
Compare the following sentences.

(94)

(95)

(96)

Danny painted their kitchen two colors, and their living room {yet / still} different colors.

* Danny painted their kitchen bright colors, and their living room {yet / still} bright colors.

? Danny painted their kitchen two colors, and their living room even different colors.

The gradable adjective bright is not acceptable here in (95), but different is in (94). Given that
different is an odd adjective, it seems likely that something else is going on here involving that.
This data indicates that there is more to be done with still and yet, but it may not totally parallel even
in this case, as (96) shows even to be unacceptable in the same place. It is clear there is more work
to be done on this topic, even as it wanders away from the overarching topic of this dissertation.

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CHAPTER 5

CONCLUSION

5.1 Overall contributions

In this dissertation, I have investigated a wide variety of topics, and wandered through more
subfields than any one of these phenomena would have suggested were related. These overarching
subfields within semantics included degree semantics, event semantics, focus sensitivity, and
discourse. In addition to linking some of these compositionally, I also worked on formalizing the
theory of how they might be linked in terms of “context”. As a result, this work does not dive
too deeply into any one of these topics, but rather it examines what conclusions we can draw from
studying their interactions. The fewer the variables in the experiment, the better controlled it is, and
that is an argument for not typically spreading research across subfields. However, studies like this
one are invaluable for removing artificial divides that we have created for research convenience.
Our goal is to model what a speaker of a language knows and computes, and in theory the speaker
can involve all of these subfields at once, and in much more complex conversation.

To break down the conclusions of this dissertation, it can be split into two main theoretical
interactions. First I will discuss my conclusions for the interaction of degrees and events. Second I
will discuss my conclusions for the interaction of focus, discourse, and context. And finally, I will
wrap up by discussing what this dissertation did not answer.

5.2 Between degrees and events

The first major interaction this dissertation addressed was the relationship between degree con-
structions and event constructions, providing analyses of some English data to draw conclusions.
Chapter 2 dealt with data that evidenced a link between degree constructions and event construc-
I laid out data showing an ambiguity with more, but also with several other adjectives
tions.
and expressions, where each expression allowed a degree addition reading or an event summing

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reading. This ambiguity was robust, appearing in the same way with multiple expressions, and
with only mild syntactic variation. On the basis of this data, and some other evidence, I proposed
a compositional analysis that assumed the degree addition reading to be the base, and constructed
the event structure by building from that. To start with, I argued that all uses of more should
be analyzed as a differential more, rather than assuming two different more denotations. This
introduces questions about what silent degree arguments do we have and how do they work, but
it also directly introduced degree addition into the denotation for the comparative morpheme, and
from there, I proposed a morpheme that interacts with degree addition to create event summing.
At this point I could bring this analysis back to some of the other additive expressions, focusing
on the adjectives for syntactic simplicity. Extending my analysis from the comparative to additive
adjectives supported my proposal of a morpheme that applies to syntactically diverse constructions
as long as they fit the semantic requirement of incorporating degree addition. This does require an
interesting and nonstandard semantic type for some of these adjectives, but these would hardly be
the only adjectives that act in unique ways.

What were the main takeaways of this chapter’s analysis in terms of the theory itself? This
provided evidence that there is a link between degree constructions and event constructions, and
specifically a directional one where degree constructions build to event constructions. This opens
up questions as to whether this is the only direction possible in this relationship, or whether the link
between degree and event constructions is more varied.

I continued to investigate this topic and these new questions in Chapter 4, with other data that
looks to bridge these two subfields. Other analyses do exist that link degree and event semantics,
but here I focused on related data, staying with the comparative. Specifically, I brought up data
involving the comparative where it initially looks like an expression typically associated with event
semantics is contributing to a degree interpretation. This is iteration in comparatives, and aspectual
particles still and yet in comparatives. This is by no means to say that this is the sum of the
related data and I can draw all the meaningful conclusions from what I have here, but rather this
data naturally follows the focus on comparatives from Chapter 2, and ostensibly looks to show the

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opposite direction of analysis. For the iteration, I briefly reviewed Beck’s analysis indicating that it
is better analyzed as an event construction, even if it looks like a degree construction. I then took
that lead, and determined that while aspectual particles in comparatives are degree expressions
overall, still and yet are contributing something different and unrelated. That is, they just happen to
appear in comparatives. This is not evidence in favor of a relationship where event constructions
compositionally build to degree constructions. Absence of evidence is not evidence of absence,
but surveying all of the possible counter examples is out of the scope of one dissertation, and the
goal of countering immediately obvious data was achieved.

So what do we want to take away from this focus? There is clearly space for further research
at the intersection of degree semantics and event semantics. One directional relationship has been
established, but are there other routes between these two constructions? If speakers have one
way to build a degree construction into an event construction, they could have more than one.
Comparatives certainly are not the only type of degree construction, so it seems entirely possible
for a different morpheme to compositionally build a different degree expression into an event
expression. In addition, I have not proved the absence of any directional relationship in the other
direction. The slim body of related research does not suggest that a structure that takes an event
construction and builds it compositionally into a degree expression is likely, but its possibility is
not disproven.

5.3 Between focus, discourse, and context

The second major interaction this dissertation addressed was how focus semantics relies on
the model of the discourse and what we mean by “context”, again analyzing English data to draw
conclusions about what this relationship must look like. Chapter 3 introduced data that looks
morphologically related to the data from Chapter 2, but impressionistically dealt with adding
things to lists in the discourse rather the numerical or mathematical addition. After making this
analytical link, however, it became clear that the best analysis of this data grew from the data that
involved also instead of the morphologically linked more or addition, and an analysis relying on

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focus sensitivity makes sense. I proposed an analysis where discourse also was actually simply an
aspect of typical also that was previously not discussed. I provided arguments in favor of it being
the typical use of also interacting with a focused proposition, provided that we formally define what
it means for the focus semantic value of something to be “contextually restricted”. In terms of this
formal definitions, I proposed that the objects in the discourse themselves can be the contextual
restrictions on the focus semantic value. I worked mainly with the Table model of discourse, as
it makes clear predictions for what objects exist that interlocutors can access, but this theory also
then provides arguments for considering categories for interlocutors to track on the basis of what
contextual restrictions we see, which I will return to momentarily. So in the case of also and the
other data I began this chapter with, the discourse addition effect comes from how also presupposes
the truth of another proposition from the focus set of alternatives, which is here restricted to
include only propositions that were already said in the discourse. Thus functionally describing list
environments. To take this one step further, I showed that the same discourse restriction applied to
all uses of also, indicating that current analyses of FSPs may be missing discourse restrictions that
become more clear when looking at uses with otherwise unrestricted proposition level focus.

This made the prediction that other FSPs could appear with proposition level focus, and may
have discourse restrictions that previous analyses have missed, given that they examined cases
where the focus semantic value was already quite restricted based on where alternatives were first
generated. I immediately supported this analysis with data involving only, which confirmed that
this prediction bears out. This analysis also brings back the point that this analysis provides an
argument for including a category in the discourse if the focus alternatives being considered are
limited to that category. In the case of only, a few options exist. The most parsimonious ones only
involve including goals like the domain goals proposed by Roberts (2004, 2018), but the analysis
that is least complicated in terms of the formalism required gains this clarity by proposing we add
the notion of impediments. Given that there are multiple options that worked with this data, this
was not a clear-cut case for arguing that impediments must be a notion that interlocutors can access
with regards to tracked goals, but I also supplied some data suggesting that the notion would be

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useful at least in analyzing the implicature of but. Analyzing only made it clear also that only and
also are restricted by the discourse in different ways, meaning that this kind of restriction must be
lexically specified.

To take a moment and highlight the important parts here, Chapter 3 made several contributions.
First, I provided an analysis showing that the proposition as a whole can be focused in an informative
fashion. My analysis showed that proposition level focus would cause issues with some of the
typical FSP denotations unless we formally define how the context and the discourse restrict the
focus semantic value, and I proposed a formal method for doing so based on the discourse structure.
While I wrote this using Rooth’s C notation, this method is compatible with removing C from the

formalism and simply specifying the limitation onJ(cid:11)Kf within the denotation lexically. While I have

no evidence to suggest that every FSP would need to be rewritten to include a contextual restriction
via objects in the discourse, this shows that at least some of them would be more accurately analyzed
in this way. And finally, I showcased how this analysis allows us to in turn investigate the structure
of the discourse as well, as the case of only provided an argument for adding at least goals, if not
also impediments, to the list of what interlocutors must be tracking in a discourse.

This analysis came into play in Chapter 4 as well. I extended Ippolito’s analysis of concessive
still as a FSP to uses of still in comparatives, and then reanalyzed it in the framework I proposed in
Chapter 3 in order to deal with some otherwise problematic data. From there, I extended Ippolito’s
reasoning to defend the interpretation of still in its different uses as all involving focus sensitivity
to uses of yet as well, and correspondingly extended the same analysis. This successful extension
added support for the framework I proposed in Chapter 3. However, this use of still and yet is very
similar to even, and discussing how even interacts in these cases of proposition level focus brought
up weaker points in this analysis. Specifically, this comparable use of even has different syntactic
properties and a working denotation for it necessarily does not work for the typical use of even with
lower focus. This is counter to the prediction made in Chapter 3, which predicted that a FSP should
(unless blocked for some other reason) be able to interact with proposition level and sub-proposition
level focus just the same. That is, there is no reason why a different denotation should be needed for

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a different sized focused constituent. That said, even does not pose a problematic counter-example
to this theory, in that lexicalized or idiomatically different versions of things exist all the time,
and the specificity of even looks like that. Overall, more data is in support of this hypothesis than
against it.

Again, to sum up the takeaways, the main contribution of this section was the overarching
reanalysis of the interaction between focus and context. I have proposed a formal way to define
contextual restrictions, at least for focus interpretation, which allows us to make testable hypotheses,
precisify our understandings of FSPs, and explore what objects and notions make up the discourse.

5.4 Unanswered questions

First, I began this work with the intention of connecting various places in language where we
see things that can be characterized as “addition”, and as I worked I discovered I was migrating
away from that overarching topic. While the analyses here do satisfy me in terms of dealing with the
data and the theory, the morphological link between the data in Chapter 2 and the data in Chapter 3
does not fall out from what I have here. As of now, I have no explanation for this link, so that is
left for future research.

Second, while I have formalized contextual restrictions for FSPs, that is not the only place
“contextual restriction” appears. For starters, focus sensitive expressions are not the only place
where focus is relevant, as I briefly glossed when introducing Rooth’s theory in Chapter 3. Surely
context matters for other uses of focus, but given that my analysis embedded this restriction lexically,
this might present an issue for how focus relates to things that are not rooted in a single morpheme.
In addition, much like the lure of a “pragmatic wastebin” for dealing with difficult points of an
analysis, “context” is easy to call on to hand wave away some small problems. Is this a method that
we can use to resist this habit via formalizing exactly how “context” works in the semantics?

In conclusion, in this dissertation I have asked many questions, some of which I have even
answered. These questions investigated the relationship between degree constructions and event
constructions, and the relationship between focus and the discourse structure. I have shed some

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light on these things, but I consider the paths I have opened for further research to be an important
contribution as well.

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