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The grammar of individuation, number and measurement

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The grammar of individuation, number and measurement

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Content THE GRAMMAR OF INDIVIDUATION, NUMBER AND MEASUREMENT
by
Luis Miguel Toquero-Pérez
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(LINGUISTICS)
August 2024
Copyright 2024 Luis Miguel Toquero-Pérez

Dedication
To my father and my uncle who, despite boarding Charon’s boat too soon, have since been and will always
be in my heart.
sunt lacrimae rerum et mentem mortalia tangunt (Virgil, Aeneid, 1.461 ff.)
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Acknowledgements
I remember getting a call from an unknown caller on a Monday of March 2018. Upon picking up the phone,
the caller, whose name I couldn’t fully hear, asked me, were they to buy me a ticket, would I be willing to
fly to Los Angeles (California) the next morning to visit the Linguistics department at USC. At the time,
I’m thinking, about that whole situation: one part prank, with a dash of “an offer you can’t refuse”. It
was, however, not a prank and not an irrefutable offer, because I turned it down, or rather I bargained to
be flown at a different time. Six years, a few months and a broken clavicle later, I find myself writing this
rather long document, which, I have been told, puts an end to my time as a USC graduate student. Had that
unknown caller not called, I wouldn’t have met the people that I did and received the support that I got, both
indispensable conditions for this manuscript to exist. This section is an ode to them.
I have always wanted to start this section by repeating Snoop Dogg’s inspiring lyrics and speech: “I
wanna thank me; I wanna thank me for believing in me; I wanna thank me for doing all this hard work; I
wanna thank me for having no days off; I wanna thank me for, for never quitting; I wanna thank me for always
being a giver and tryna give more than I receive; I wanna thank me for tryna do more right than wrong; I
wanna thank me for just being me at all times”. But, the truth is I wasn’t the person who always believed in
me and encouraged me, not only not to quit but to keep making progress. That was Roumi Pancheva, co-chair
of this dissertation and my advisor since the end of my second year of grad school. I have been extremely
lucky to have her by my side, and anything I say is probably not going to do justice to how much I owe her
academically, professionally and personally.
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You get an idea of how enthusiastic Roumi is about syntax when, during the first day of second semester
syntax class, she explicitly states “syntax is the queen of cognitive science”. But that is just the tip of the
iceberg, and at the base is a strong willingness to make her students be as enthusiastic as she is. This is
something she achieves by showing an outstanding interest in an idea or puzzle, helping you shape up that
idea into a bigger project and constantly reminding you of how exciting the project is. Roumi will gently push
your boundaries as much as you let her, suggesting (though really asking you) that you submit an abstract to
some conference, submit the squib to a journal, write a grant proposal etc. Throughout the years I experienced
this, and it could be a lot to handle at times, but truth be told I am extremely grateful that she pushed me to
do all these things and took the time to discuss different aspects of each project. In fact, any class or series
of extended discussions I had with her turned into at least a conference proceedings. The point being here
that every conversation or interaction I had with Roumi was productive enough to plant the seed for a new
project, or push an existing one forward that had been in the doldrums for some time.
Every project, including this dissertation, evolved a great deal after having multiple back-and-forths with
her who would give productive and charitable pushback. In fact, most of what I know about the topic of this
dissertation is thanks to her. She first introduced me to the empirical domain of measure expressions and
comparatives in 2019, and then she slowly transitioned to number and numerals in 2021. When narrowing
down the topic of the dissertation, she adamantly said “stay away from the count-mass distinction”, which I
fully agreed with at the time calling it a “pit of snakes”. For some reason I have a tendency to fall into these
pits every once in a while (e.g. subextraction, clitics in Romance, pseudo-partitives) and despite her efforts
and my original intention, I did not abide by this and ended up writing a dissertation about the count-mass
distinction. However, at the defense she expressed that I had managed to say something original, coherent
and interesting about it; and she was glad I did not stay away from it. I take this to be a huge compliment.
And I want to thank her again for her unconditional support.
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On a personal level, I will always be indebted to her. She took care of my advising at the worst possible
time for everyone: April 2020. We would have weekly zoom meetings where she would help me deal with
some of my personal troubles. I remember a moment in June of that same year when there was a lot of
uncertainty with visas and I was really freaking out. Roumi would call me every day or every other day to
check on me, get the latest updates and offer to help in any way she could. The simple fact that she did this
was so reassuring and validating that I will never forget how much this meant to me. After the pandemic, this
support turned into advice about the job market, academia and life in general. And when it came to making
a decision about my future, she made sure I understood what was best for me.
Thank you Roumi for everything you have taught me, for all your patience, for all your advice! Thank
you for inviting me to Santa Cruz and showing me around! And thank you for coming to LA for both the
graduation ceremony and the dissertation defense!
The person co-chairing this dissertation was Alexis Wellwood. Alexis came into my academic life in the
fall of 2020 as a committee member of my second screening project and took an advisory role in January
2023. She has been indispensable since! Among the many things that I have learned from her is to be
critical. I would come to our meetings with, what I thought were, compelling arguments, and she would
challenge every single one of them and propose alternative ways of thinking about the data. I would leave
those meetings thinking about every one of those possible alternatives and come to the next meeting with
more arguments, which she would also challenge. I found that this charitable and healthy pushback helped
me make an incredible amount of progress, especially during the last year.
Alexis has taught me that minute attention to detail is crucial, from checking for typos and punctuation
marks to framing the questions and the conclusions in the most compelling way. Alexis is one of the fastest
and sharpest thinkers I know. Five minutes into our meetings, she’d already be making the most impressive
connections between the data, the formalism and the larger theoretical implications. She has helped me
identify where a project is strongest and where it needs the most work, always providing viable lines to
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improve it. I have to thank her for her patience in discussing semantics and bearing with me when I did not
understand even the most basic concepts or misused the relevant terminology. In fact, she would make sure
that I did not leave a meeting or discussion until I had completely understood what was at issue.
Alexis is incredibly busy running a lab, pretty much a department, doing research, mentoring students
and teaching and I wanted to be mindful of her time. When I asked her whether she would not mind to be my
advisor, her immediate response was “mind?! I’d love to be your advisor, and let’s make it possible that this
is in tandem with Roumi!”. I knew that asking her was the right call, but after hearing her say that I knew
there was no better choice because she would go to bat and do anything possible to support me at all times,
which she did! And despite her busy schedule, she would always find weekly slots for us to meet (usually
longer than originally assumed).
Like Roumi, Alexis was an outstanding source of non-academic support and she was always encouraging.
We would usually spend the first few minutes of our meetings simply catching up, and during times when I
needed it the most, she acted as a friend and would come up with advice that made me feel at ease. Thank
you Alexis for always being on board! Thank you for those very uplifting chats over coffee or Korean food!
Thanks for having me and my mom over on your rooftop with 360 degree views of LA! I do not think she
will ever forget that.
I am also very grateful to the rest of my dissertation committee. Travis Major has acted in many ways as
unofficial advisor, from giving feedback on projects and handouts to helping me shape the dissertation in a
way that would make sense and also “made my life easier” (as he kept on repeating for the last two years).
Thanks to him, I could get started doing fieldwork, a part of which turned into chapter 5 of the dissertation.
I will miss those unscheduled meetings around GFS during which we would start talking about topic X only
soon to realize we came up with a brand new generalization worth thinking more about. Travis gave me
a lot of advice about the job market, and sat through endless research presentations to help me polish my
materials. This led to, what I would like to think, a good friendship (though we should probably ask Travis).
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I am glad to be around for the time being so we can hang out more and I can see Jack grow up into a fine little
man. Deniz Rudin has always been available to sit with me, listen to my ideas and give me very thoughtful
comments. He was able to reframe my thinking into a streamlined and organized narrative while pointing out
important and exciting predictions but also flaws that I was not aware of. We both came to USC Linguistics
in 2018 and since then we joked about how we were part of the same cohort. Now, the 2018 cohort is just
you, nothing beside remains! Gabriel Uzquiano accepted to be part of this enterprise for my quals and I am
happy he decided to be part of the dissertation too. I thank Gabriel for his advice and willingness to help at
every point! Plus, he is a Barça fan; could anyone ask for more?
Besides my committee, I am very grateful to all the faculty in the linguistics department at USC. While
I will always be grateful to every single one, I would like to give special thanks to the following people.
Sandra Disner was the best and most generous person to TA for and thanks to her I was awarded the General
Education Graduate Assistant Award in 2022. Elsi Kaiser taught me to build an experiment, manage data and
analyze those data when chairing my second screening. Andrew Simpson was involved in my first screening
and my quals, and he was always happy to discuss ideas and data when asked. Khalil Iskarous was the person
who made that phone call back in 2018 and I am thankful that he did. He also gave me some very valuable
advice, which I truly appreciated, during the job interview process in 2024. Maria Luisa Zubizarreta always
checked up on me and my progress making sure that it was all good. That trip to Mexico with her, Roumi
and Alexis to attend SALT32 was unforgettable. Stephanie Shih taught (and very well so) one of the most
practical and useful classes at USC: getting ready for the job market. She provided very good feedback on
the job application dossier, making it easier to write. Mary Washburn acted as interim advisor for me (and
my cohort) during my first semester of grad school, and for the next six years she would help me navigate
the bureaucratic steps and manage important deadlines and paperwork. She was also the instructor for my
last class as a TA at USC, and I want thank her for making our TA jobs as smooth and straightforward as
possible.
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I also want to thank two people who, while not at USC any more, played a very important role in the early
stages of my academic development. Rachel Walker, currently at UCSC, gave me very insightful comments
on my screening projects. Most importantly, and in the time span of two semesters, she helped me master
the art of abstract writing. Rachel had the difficult job at the time to keep everyone in her class calm with
everything going on: the start of a global pandemic, the first important milestone in the program and the
anxiety of 5 students navigating it all. And she did excellent, reassuring everyone that the department had
our backs, while teaching us how to structure a defense and making a safe space for us to express our anxiety
at the beginning of every class.
The other person is Stefan Keine, currently at UCLA. Stefan was my first official advisor at USC and
he was the one who taught me how to think like a syntactitian and how to write a syntax paper. During the
first year of my grad school experience, I was a bit lost and I found in Stefan the best person to steer me
in the right direction both personally and research-wise. From Stefan I also learned that “the devil is in the
details” (as he used to say), and that special attention should be paid to even the shortest footnote. I was
always impressed by Stefan’s LaTex skills and I learned about the importance of having a beautiful handout.
He helped me get started with some basic templates, and by the end of my second year I was proud that my
files compiled with no errors. I am also thankful to him for helping me and giving me advice from the other
side of town.
A special shoutout goes to the 2018 cohort: Ian Rigby, Chloe Gfeller, Jesse Johnson, Sung Hwang and
Peifen Chen. I still remember the first semester when we met every other weekend for Phon-Friday to work on
our phonology assignments in the reading room. We spent so many hours trying to figure out those problem
sets. As difficult and frustrating as the problem sets were at the time, I cherish those days with all my heart.
And when the semester was over, we went to the arts district for food and beer on a random Tuesday in early
December. While there was strong bond between all of us, I am particularly thankful to Ian and Chloe for
their friendship: a night at flaming saddles in WeHo, the Blade Runner screening at Hollywood Forever, the
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trip to Santa Monica where we ended up at Wetzels Pretzels for Chloe to try it for the first time, beers in my
garden, dinner at Alcove in Los Feliz, bowling night at Shatto lanes etc. And while it was sad to say goodbye
to Chole because she got a job in Europe, we were happy for her because we both knew how much that meant
for her.
Funny thing is that the first time I met Ian, I did not have the best impression of him: he came in late,
refused to grab lunch with Chloe and I and then stormed off. Chloe and I both told each other “Who does
this guy think he is?”. Little did we know at the time that he had just arrived from Seattle and had to rush to
sign his lease before it expired, and that is why he could not stay longer. This fact he did not disclose until
we asked him about it months later over a beer once we were all friends, which made us all laugh. Ian has
always been there for me, helped me through the thick and thin. How much I wish I could have taken the top
off of that convertible camaro when I picked him up in the flower district while playing Aqua’s Barbie girl!
I value Ian’s friendship with all my heart ever since the beginning of our grad school days and now, we both
graduated, got jobs, bought cars and still live in the same city at least for the time being. The simple fact that
we can still see each other and make good memories together makes me happy. Thanks for everything!
Outside of my cohort, I am grateful to many: Sarah Lee, Daniel Plesniak, Miran Oh, Jesse Storbeck,
Betul Erbasi, Bhamati Dash, Madhu Datta, Anna Besserman, Reed Blaylock, Charlie O’Hara, Yifan Yang,
Elango Kumaran, Tommy Tsz-Ming Lee, Yijing Lu and Silvia Kim. In particular, I want to thank Tommy
who was always around and ready to talk syntax. We would spend countless hours in that little office with a
chalk board trying to make sense of wh-movement and head movement facts, phases, unlocking effects and
so much more. We would read each other’s drafts, gave each other suggestions and ask for data. I was happy
to see you graduate on time and move home with Ellie but frankly you were much missed! I am also thankful
to Yijing Lu and Silvia Kim who I ended up cohorting with in my last year. While originally on Tommy’s
cohort (i.e. 2017), we were the most senior students left and we all had the aim to graduate and find a job
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by the end of summer 24. One of the funniest moments of this our last year was us playing that bizarre card
game over that humongous burrito from La Barca. It was an honor to walk with you both on May 8th.
I also want to thank my collaborators through the years: Antonio Cleani, Colin Davis, Carol-Rose Little
and Brian Tsagaadai. When Antonio and I wrote that abstract about much and many, little did we know that
it would receive the highest rating at SALT32 (according to the organizers). I hope we can find some time
soon to finish that other project that has been in the back burner for too long now! Colin introduced me
to the fascinating world of parasitic gaps and we came up with this novel generalization about rural Iberian
Spanish, which is now a WCFFL40 proceedings. Carol-Rose and I met at the virtual LSA in 2021, and we
never met in person until June 2022 in Mexico City! She invited me to Chiapas for a ‘field experience’, and
it will say it was unforgettable. I know it was a lot and I am really thankful that she offered to do that. I
also want to thank Carol-Rose for sharing a lot of her teaching materials and job market advice, for keeping
me in mind when organizing great and fun workshops! It is good that we always have a whatsapp line open.
Brian is my Mongolian consultant who spent many days and hours sitting in front of me while I asked him
questions like if Batar bought big apple, did he buy one or several?. Without his willingness to share his
time and language with me, none of chapter 5 would have been possible.
Beyond the world of linguistics, I cannot forget the people from the Normandie house where I lived for
almost 6 years. I only thought of Brad Foley and Eliseo Melero as my landlords when I first moved in during
the summer of 2018. I had no idea how big of a role they would have in my life here in LA. I was so lucky
to find them! They became the family I was missing, and had it not been for them I would have dropped out
a semester into the program. That is how important they have been. They took me in, showed me around,
shared amazing food with me, increased my spice tolerance, made sure that I was okay, took care of me when
I was sick and broke my clavicle. We have made so many memories together and they have helped me grow
in such an imaginable way that anything I say about them is never going to be close to enough. So I will just
say THANK YOU for giving this “españolito” a chance!
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In addition to them, I want to thank many of the people who I lived with at the Normandie house during
this time. Sam Affif introduced me to bougie coffee making and showed me how to change a tire in the
middle of the i-10. He is the kind of person who can show you how to have a fun time, because he was
always energetic and full of good energy, and I envied him for that. He would often talk about “the darkness”
though and told me I would only understand when writing my dissertation. I guess I did, for some time at
least. Sam, Brad, Eliseo and me spent the worst of the pandemic in the house trying our best not to drive
each other crazy. Among the ways we coped was watching 80s movies up until 2am in Sam’s tv; and let me
tell you, most of those movies were bad! We also played Catan, until it got very heated and then we had to
stop. Those were dark times, but we made it work as best as we could.
Lacey Schauwecker was the first one from the house I ever met in person after she picked me up from
LAX. I have always admired how smart Lacey is and how valuable her advice has ever been. Sometimes
I felt that our experiences overlapped very much despite having grown in very different parts of the world.
We would sometimes go running (I remember that one time we went to Griffith in March of 2019 which was
gorgeous although I could not keep up with her pace) or walking together, and it was always a good time. It
was a blast to see her get married and attend her wedding at her parents’ yard in Phoenix. Thanks for being
understanding and validating of my feelings, and I hope I was, and did, too for you.
Raed Jaffal, alias “Topo”, and I became close in the summer of 2023. Every weekend we would go on
a date somewhere for food, coffee, a walk or all of the above. And we have been keeping up with that, as
much as we can, ever since. Some of those trips have been more fortunate than others, but overall we tend to
have fun while we commiserate about life, talk about soccer, play fifa and give each other probably not the
best advice you could think of (though it all comes from the bottom our hearts, which is what matters in the
end). I want to thank Topo for throwing me a lifeline when I needed it.
Chad Geib and Cynthia Lee did not live in the house, but they spent a lot of time there and I am glad
they did! They were around for most events and many Saturday nights, up until very late holding all sorts of
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conversations which usually involved Chad and Brad arguing healthily to finally agree to disagree. I want to
thank them for including me in their plans, parties and tours of LA in addition to being very considerate and
kind at all times. I also want to thanks Shuyi Zhou for always being around with a smile and for teaching me
things about Chinese food and culture I had no idea about; Marilyn Schotland for discussions of art, movies,
literature and recommendations about trendy LA coffee shops; Kyndra and John who were always fun to be
around and showed me some of the current gen Z slang, which I still do not understand.
I cannot forget Dr Christina Mohajerani. She helped me navigate the complicated and eventful (sometimes also eventless) tides that life would bring for four years. And while it took this little nut a bit of time
to finally crack open, she uncovered parts of me that I had no idea existed and worked hard towards figuring
out who I was and wanted to be. She taught me to be as kind and gentle with myself as I am with others and
to distinguish between facts and feelings, and how to process each of them. She is excellent at coming up
with metaphors on the spot and a terrific story-teller, and at times she would tell a story to make a point about
something that was at issue that day. I will always remember the community garden story and that what we
may think is a worry is just a woodchuck in the garden.
Last but not least, I want to thank ALL my family in La Pedraja de Portillo. I know it has not been
easy for them to cope with the idea of me being so far away for so long: plenty of missed birthdays, phonecalls, family events, Christmases, summers, more or less special occasions that meant a lot for them. Things
became harder during the pandemic, when I could not go see them for two years. And yet, they accepted and
supported my decisions all the way, making clear how proud they were of me. In fact, when push came to
shove, my mom and my brother flew to LA to take care of me after my surgery. I will forever be grateful!
My parents, each in their own way, taught me, as Tennyson perfectly puts it, “to strive, to seek, to find, and
not to yield”; and I believe it is this motto that led me to where I am and to accomplishing all that I have
until now. I was very happy my mom could make it to my graduation and I wish my dad had been here with
her because I know how much he would have loved it and how proud he would have been. As homage, this
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dissertation is addressed to you, dad. Dear family, you have always had my back, and I love you yesterday,
today and tomorrow.
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Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 General background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Structure of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 2: The Count-Mass Distinction in English and Spanish: The Morpho-Syntactic Facts . . . . 15
2.1 Setting the baseline: ‘canonical’ mass and count nouns. . . . . . . . . . . . . . . . . . . . . 17
2.2 Plural mass nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Object mass nouns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Taking stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 3: A Theory of Individuation and Number for the Count-Mass Distinction . . . . . . . . . . 58
3.1 The Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.1.1 Some necessary basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.1.2 The active players: Individuation and number . . . . . . . . . . . . . . . . . . . . . 62
3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.1 Count vs. canonical mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.2 Plural mass nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2.3 Object mass nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.4 Determiner selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2.4.1 Determiner Classes 1, 2, 3 & 5. . . . . . . . . . . . . . . . . . . . . . . . 93
3.2.4.2 Determiner Class 4: all and QAs. . . . . . . . . . . . . . . . . . . . . . . 96
3.3 Variation in the distribution of [COLL] feature . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3.1 Group nouns do not have [COLL]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3.2 [COLL] on n or Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter 4: Canonical Dimensions of Measurement: when more N means ‘cardinality’ . . . . . . . . 119
4.1 Meaning asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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4.1.1 The interpretation of QAs with plural count and canonical mass nouns . . . . . . . . 125
4.1.2 The interpretation of QAs with plural mass nouns . . . . . . . . . . . . . . . . . . . 131
4.1.3 The interpretation of QAs with object mass nouns . . . . . . . . . . . . . . . . . . . 133
4.2 Taking stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.3.1 The interpretation of terminal nodes . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.3.2 Some basic derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3.3 Adding QAs into the mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.3.4 Deriving the ‘Cardinality Generalization Redux’ . . . . . . . . . . . . . . . . . . . 156
4.4 Ramifications of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.4.1 Shifts between classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.4.2 QAs, plural-markedness and the dimension of measurement beyond English and
Spanish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Chapter 5: Accommodating Number Neutrality: Markedness and Semantic Interpretation . . . . . . 178
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.2 Alasha Mongolian: Some background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.3 Core data: unmarked NPs and PL-marked NPs . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.4 A novel diagnostic for number neutrality: much/many and unmarked NPs . . . . . . . . . . 197
5.4.1 Some background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.4.2 Applying the much/many-test to Alasha Mongolian . . . . . . . . . . . . . . . . . . 199
5.5 Taking stock and generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.6.1 Setting up the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
5.6.2 The basic syntactic structure of (count) nouns . . . . . . . . . . . . . . . . . . . . . 207
5.6.3 Deriving the exclusive/inclusive ambiguity with plural-marked nouns . . . . . . . . 211
5.6.4 Adding (non-classificatory) APs and numerals into the mix . . . . . . . . . . . . . . 221
5.6.5 A note on QA allomorphy and the dimension of measurement . . . . . . . . . . . . 228
5.7 Conclusion: Broader implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Chapter 6: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
6.1 Contributions of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
6.2 Moving forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
xv

List of Tables
2.1 Determiner correspondences English-Spanish based on the count-mass distinction . . . . . . 24
2.2 Morpho-syntactic properties of ‘canonical’ mass & count nouns (to be updated) . . . . . . . 29
2.3 Restrictions on determiner selection (to be updated) . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Morpho-syntactic properties of ‘canonical’ and plural mass & count nouns (to be updated) . 38
2.5 Restrictions on determiner selection (to be updated) . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Plural marking on noun-noun compounds with two count nouns . . . . . . . . . . . . . . . 38
2.7 Morpho-syntactic properties of all mass & count nouns (final version) . . . . . . . . . . . . 49
2.8 Restrictions on determiner selection (final version) . . . . . . . . . . . . . . . . . . . . . . 49
2.9 count and object mass doublets in English . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.10 count and object mass doublets in Spanish . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.11 Number marking and choice of QA by noun type in English and Spanish . . . . . . . . . . . 55
3.1 Typology of features for the mass-count distinction . . . . . . . . . . . . . . . . . . . . . . 66
3.2 Ellipsis options: licensors, [E]-bearers and exponence . . . . . . . . . . . . . . . . . . . . . 75
3.3 Verbs and adjectives based on plural mass noun roots . . . . . . . . . . . . . . . . . . . . . 84
3.4 Inherent features on Determiners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5 Variation in √MEAS-exponence (English) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1 Number marking, choice of QA, and semantic interpretation by noun type (not final) . . . . 136
4.2 Variation across-languages in the licensing of root-meanings . . . . . . . . . . . . . . . . . 168
xvi

4.3 Number marking, choice of QA, and semantic interpretation by noun type . . . . . . . . . . 176
5.1 The interpretation of number in languages with unmarked and plural-marked forms (to be
extended) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.2 Unmarked and PL-marked bare nouns in Alasha Mongolian . . . . . . . . . . . . . . . . . . 181
5.3 Number interpretation of unmarked nPs in Alasha Mongolian . . . . . . . . . . . . . . . . . 201
5.4 Number interpretation of plural-marked nPs in Alasha Mongolian . . . . . . . . . . . . . . 201
5.5 Syntactic distribution of olin and cardinal numerals with count nouns . . . . . . . . . . . . . 203
5.6 Flavors of n in Alasha Mongolian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
5.7 The interpretation of number in languages with unmarked and plural-marked forms (final
version) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
6.1 The roles of IND and Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
6.2 NP classes based on their underlying features . . . . . . . . . . . . . . . . . . . . . . . . . 241
6.3 Dimensions of measurement by NP and VP type . . . . . . . . . . . . . . . . . . . . . . . . 246
xvii

List of Figures
3.1 Inner vs. outer domains within nominals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1 Predicting countability asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.2 Individuated semi-lattice for thing generated from atoms a, b, c . . . . . . . . . . . . . . . 145
4.3 Individuated semi-lattice for thing generated from atoms ab, cd, ef . . . . . . . . . . . . . . 145
5.1 Individuated semi-lattice generated from atoms {a, b, c}: extension of [n[IND] √ROOT] . . . . 205
5.2 Predicting countability asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
xviii

Abstract
This dissertation presents a new view on what it means to be ‘count’ (book(s) vs. water) and ‘countable’
(i.e. can the noun in question be measured in terms of cardinality) and their role in the architecture of the
grammar. To accomplish this goal, the proposed research aims to develop the basis for a comprehensive
theory of individuation and number by probing the distribution of individuation and number features in the
nominal domain, as instantiated by the count-mass distinction. I argue that individuation and number are
two distinct properties both of which are part of Universal Grammar’s inventory of features and they affect
the words’ ability to occur in different morpho-syntactic environments within and across languages. Individuation is responsible for making discrete units available, i.e. sometimes referred to as atoms, and number
is responsible for determining whether the word in question refers to the minimal units (i.e singular) or nonminimal units (i.e. plural). In a nutshell, I make the case that what makes a noun ‘count’ is markedness for
both individuation and number, whereas countable nouns need only be marked for individuation. Variation
depends on which of the two features are available. The general picture that emerges is one where being
count entails being countable, but being mass does not entail being non-countable. I then go on to show
how the proposed theory (i) makes predictions about, and accounts for, different form-meaning mismatches;
and (ii) enables us to establish robust cross-linguistic generalizations that link syntactic structure to form and
meaning, illuminating our understanding of the interactions between the different modules of the grammar.
xix

Chapter 1
Introduction
1.1 General background
Languages may manifest morpho-syntactic differences in the distribution of Noun Phrases (NPs). For example, the NP car can appear in the contexts in (1a) while the NP blood in (1b) cannot.
(1) a. Barney saw every light-red car, and Marshall saw a dark red one.
b. * Barney saw every light-red blood and Marshall saw a dark red one.
First NPs such as car can occur with universal determiner every and be the antecedent of the pronominal
form one. Second, when someone utters (1a) we understand that they saw every single car. On the contrary,
NPs such as blood in (1b) cannot occur with every or be the antecedent of one. Besides, when they utter (1b)
we do not understand the utterance to mean that they saw every discrete unit of blood like ‘a drop’ or ‘a vial’.
NPs such as those in (1a) are classified as ‘count’ NPs, whereas those in (1b) are classified as ‘mass’ NPs.
From now on, I will be using the following conventions: ‘*’ to mean an expression is ungrammatical (i.e. it
is syntactically ill-formed or it has no interpretation); ‘#’ to mean the expression is semantically odd (i.e. it
may be grammatical but does not have the intended interpretation); ‘?’ to indicate my and my consultants’
understanding that the sentence is grammatical but slightly marked; ‘%’ to indicate that there is speaker
variation.
1

While the class of count NPs is largely uniform, i.e. every count NP has the same morpho-syntactic
properties, there are differences within the class of mass. For example, NPs like suds and dregs are overtly
plural-marked but they lack a singular counterpart and cannot be modified by numerals (Ojeda 2005): *a
sud, *two suds. While most mass NPs cannot be modified by size adjectives, some like jewelry or furniture
can: large jewelry, large jewels vs. #large blood and *large suds.
In addition, there are differences across the classes of count and mass across languages. For example, an
NP may be count in one language, but mass in another (Chierchia 2010, 2021). The NP furniture is mass in
English, but the Spanish counterpart is count as evidenced by the possibility of overt plural-marking, as in
(2).
(2) Spanish
mueble(-s)
furniture-PL
English
furniture
‘furniture (item)’
Languages can also differ in their ability to perform count-to-mass shifts and mass-to-count shifts (Kiss
et al. 2021). For example, in English water is canonically a mass noun but it can shift into a count noun with
a container interpretation (Bunt 1985). Other NPs like blood are much less unlikely to undergo this class
shift, as commented above. There are languages on both sides of the spectrum: a) languages like Nez Perce
are more permissive and allow any mass noun to appear in a count frame with a container interpertation as in
(3) adapted from Deal (2017); b) languages like Alasha Mongolian do not seem to allow any mass-to-count
shifts with the intended interpretation as shown in (4).
(3) Nez Perce
a. kike’t
blood
‘blood’ (substance)
b. lepit
two
kike’t
blood
‘two drops of blood’
2

c. kuus
water
‘water’ (substance)
d. lepit
two
kuus
water
‘two bottles of water’
(4) Alasha Mongolian
a. os
water
‘water’ (substance)
b. # xoirV-n
two-ATTR
os
water
Int(ended): ‘two units of water’
c. tsos
blood
‘blood’ (substance)
d. # xoirV-n
two-ATTR
tsos
blood
Int.: ‘two units of blood’
In terms of the semantic properties, what largely distinguishes between the two class is the asymmetry
in (5), as observed by Bale and Barner (2009). NPs like cars can be counted, while NPs like blood cannot.
(5) a. Barney saw more cars than Ted did. CARDINALITY, #VOLUME
b. Barney saw more blood than Ted did. #CARDINALITY, VOLUME
We can call the NPs that can be measured in terms of cardinality ‘countable’. In contrast, ‘non-countable’
are NPs that cannot be counted. While the countable/non-countable distinction overlaps to a large extent with
the classes of count and mass NPs respectively, there are also well-known exceptions. Those include NPs
like jewelry or furniture which pattern like mass and yet they are countable, as evidenced by (6).
(6) Barney saw more jewelry than Ted did. CARDINALITY, #VOLUME
The data about the count-mass distinction raise important questions about the encoding of ‘being count’
and ‘being countable’. In particular, we can list the following questions:
• What makes an NP count as opposed to mass?
• What do countable NPs, both count and mass, share in common? (i.e. do they form a natural class in
any way?)
3

• What determines variation?
Some have argued that the count-mass distinction is largely lexically encoded (Pelletier 1975; Krifka
1989; Chierchia 1998b). In this approach, nouns are already sorted in the lexicon as mass or count. Languages thus differ idiosyncratically with respect to what goes into the ‘count’ or ‘mass’ bin. In addition, it
is already determined in the lexical entries of these nouns whether they make reference to discrete units that
enable counting or not. The argument for what nominal expression has discrete units comes from the observation that nouns that denote objects or elements with clearly identifiable boundaries are generally countable
and those those that denote substances or have less clear boundaries are generally non-countable (Soja et al.
1991; Chierchia 1994; Rips and Hespos 2019). Generally under this family of approaches, plural or number
marking is contingent upon the nominal expression having discrete units in its extension. In other words,
plural-marking entails countability (i.e. ‘the property of being countable’).
While it might be the case that there are lexical factors that influence what is count or not and whether
a nominal expression is countable or not, a fully lexical approach misses important generalizations. For
instance, determiners are sensitive to the syntactic properties of the NPs they occur with (Abney 1987),
and ellipsis operations, including one replacement (Harley 2005; Merchant 2014), are also syntactically
conditioned. In addition, the lexical approach has to stipulate which nouns are subject to shifting classes and
which ones are not. There is also an issue with plural-marking: count nouns are just a subset of the NPs that
are plural and the other subset of plural-marked NPs is not countable (e.g. suds, dregs, Rothstein 2021).
An alternative family of approaches has located the count-mass distinction in the syntax of nominal expressions (Gillon 1999, 2012; Borer 2005a; Bale and Barner 2009; Cowper and Hall 2009, 2012, 2014). I
will briefly comment on two proposals. An influential proposal is found in Borer (2005a) who argues that (a)
nominal roots denote undivided matter and (b) in the absence of a dedicated functional head that performs
division of matter, her DIV(ision), the NP will have a mass syntax and semantics. This is schematized in (7).
4

For Borer, DIV is realized by plural-markers in languages like English or classifiers in languages like Chinese. Singular number, sometimes realized as the indefinite determiner a, as well as numerals and Quantity
Adjectives (QAs) are structurally above DIV, in what she labels # (for Quantity).
(7) a. [DP D [#P # [DIVP DIV [NP N ]]]] = count
b. [DP D [#P # [NP N ]]] = mass
Semantically, this operation of division imposes minimal parts that are themselves non-divisive (Cheng
1973) and constitute the basis for counting. That is, having DIV, is responsible for making NPs have a count
syntax but also for making NPs (semantically) countable. It is unclear, however, how furniture-type nouns
are to be derived in Borer’s system: on the one hand, they are mass and thus lack DIV; on the other, they
must have an extension which is similar to that of plural-count nouns given that they allow counting. It does
not solve the suds-problem either: if plural-marking is a divider, why do these NPs have a mass syntax and
are non-countable?
A slightly different version from Borer is found in a series of papers by Cowper and Hall (2009, 2012).
They propose a theory of Number-marking that can account for the count-mass distinction. Like Borer, the
crucial difference between count and mass NPs is the presence or absence of structure. In their case, the key
syntactic piece is a Number head. Mass NPs lack Number while count NPs project Number. They propose
a feature geometry according to which plural, i.e. [> 1], is contained by what they call an individuator, i.e.
[#]. Schematically, this looks like (8), where the ‘:’ on the feature bundle indicates ‘contained by’.
(8) a. [DP D [NumberP [#] [NP N ]]] = singular count
b. [DP D [NumberP [#: > 1] [NP N ]]] = plural count
c. [DP D [NP N ]] = mass
The individuating feature [#] in (8a) and (8b) acts as Borer’s (2005a) divider and it is additionally in
charge of singular-marking. Unlike Borer, plural itself does not perform division, but requires the NP to be
5

already individuated. The proposal suffers from similar issues as Borer’s: how are furniture-NPs different
from count NPs? And if plural-marking is dependent on the NP being count, how do we explain suds?
In Cowper and Hall (2014), they propose a revised version of the system. In their new system, singular
count NPs are the most featurally unmarked NPs (i.e. unspecified for any number feature), while mass and
plural count NPs form a natural class: they are both [Non-Atomic]. According to Cowper and Hall (2014,
p.69), if a nominal lacks the feature [Non-Atomic] “it will be interpreted as atomic (i.e. contrastively not
Non-Atomic) and thus as both count and singular”. To further distinguish between mass NPs and plural
count NPs they propose that the latter are also marked for a feature [Discrete]. The bundle [Non-Atomic:
Discrete] spells-out plural -s. A schematic representation of the feature distribution is in (9) from Cowper
and Hall (2014, p.69, ex: 10).
(9) a. Singular Count
Ø
b. Mass
[Non-Atomic]
c. Plural Count
[Non-Atomic: Discrete]
[Non-Atomic] is in charge of introducing the property of divisibility, something that both mass and plural
count NPs share (Cheng 1973; Krifka 1989), and [Discrete] makes sure that the NP has separable atoms that
can be counted. While the bundling of mass and plural count nouns as a natural class is empirically justified,
this new proposal does not solve either puzzle mentioned above. In the case of furniture, they speculate that
these NPs are lexically specified for [Non-Atomic]. However, given that these NPs are countable, they must
also be specified as [Discrete]. This brings us back to the same issues raised above. Second, suds spell-out -s
which in their system is the bundle [Non-Atomic: Discrete], and yet they denote non-discrete undivided stuff.
The approach also raises further questions about determiner selection: if singular count NPs are unspecified
for any features, how do we explain the fact that some determiners like every or each require the NP to be
both count and singular?
6

Taking a step back from the specific implementation and assumptions of each proposal, there are some
valuable insights that they all share. First, they all share the intuition that individuation, i.e. making discrete
units that can be counted available, is encoded syntactically: DIV for Borer, [#] or [Discrete] for Cowper and
Hall. Second, mass NPs are syntactically impoverished or unmarked compared to count NPs: by virtue of
lacking a Number feature or a dedicated syntactic projection encoding Number. For these proposals, however,
individuation and Number-marking are fused into one element which leads to certain empirical issues (e.g.
furniture-NPs, suds-NPs, determiner selection). But, what if these two functions, that is individuation and
Number-marking, are performed by distinct elements, both of which are syntactically represented? In other
words, what if there is an element X that marks the nominal for individuation, and another element Y that
marks the nominal for singular or plural? Having both X and Y would entail that the noun is count, whereas
having lacking Y (i.e. number) would result in a mass syntax regardless of individuation properties.
This dissertation is concerned with these issues: understanding the grammatical encoding of being count
and the grammatical encoding of countability. To accomplish this goal, the proposed research aims to develop
a comprehensive theory of individuation and number by probing the distribution of individuation and number
features in the nominal domain, as instantiated by the count-mass distinction.
There are a series of morphological, syntactic and semantic asymmetries that are observed in the nominal
system of the world’s languages. Among the morpho-syntactic properties, we can distinguish the list in (10).
In terms of the semantic properties, what largely distinguishes between countable and non-countable NPs is
the property in (11).
(10) a. Does the noun make a singular/plural distinction?
b. Can the noun be modified by cardinal numerals?
c. Can the noun be modified by size/shape adjectives?
d. Does the noun allow number mismatches under ellipsis?
e. Can the noun be a target for one-substitution?
7

f. Is the noun (dis)allowed to combine with certain determiners or quantifiers?
(11) Does the noun allow measurement in terms of ‘cardinality’ (in particular when modified by measure
words such as more, much, many etc. or numerals)?
By probing these distributional and interpretive properties of NPs, I will argue that the roles of individutaion and number-marking are to be separated into two distinct sets of features, both of which are part of
Universal Grammar’s inventory. The distribution of these features affects the words’ ability to occur in different morpho-syntactic environments within and across languages. Individuation is responsible for making
discrete units available, i.e. sometimes referred to as atoms (Link 1983; Gillon 1992). While similar in spirit
to Borer’s DIV and Cowper and Hall’s individuator, individuation is not to be conflated with number features.
The other set of features is subsumed under the umbrella of number: number is responsible for determining
whether the word in question refers to the minimal units (i.e singular) or non-minimal units (i.e. plural),
(Link 1983; Krifka 1995; Schwarzschild 1996; Sauerland 2003; Harbour 2007).
I will argue that these units, i.e. individuation and number, serve their own distinct morphological,
syntactic and semantic purpose. In a nutshell, I will make the case that what makes an NP count is markedness
for both individuation and number; being mass is the absence of a dedicated Number projection hosting
singular or plural features. That is, building on insights from previous proposals (Borer 2005a; Cowper and
Hall 2009, 2012), Number is at the core of the count-mass distinction. Mass nouns may however be marked
for individuation features: this I argue is the case of furniture-NPs. Plural-marking need not depend on
the NP being individuated: suds-NPs are an example of (lexical or low) plural-marked NPs in the sense of
Alexiadou (2004, 2011, 2015); Acquaviva (2008) and are not individuated. As a result, by virtue of separating
individuation from Number, we have a way of decomposing countability: countable NPs are those that are
marked for individuation, whereas non-countable NPs are those that are unmarked for individuation.
The general picture that emerges is one where count NPs are a subset of the NPs that are countable:
{count NPs} ⊂ {count NPs, furniture-NPs}. This accounts for the following twofold generalization: (a)
8

plural-marking on the noun does not universally entail the noun being countable (e.g. Rothstein 2021), and (b)
plural-marking on the noun does not entail having count syntax. I then go on to show how the proposed theory
(i) makes predictions about, and accounts for, different form-meaning mismatches; and (ii) enables us to
establish robust cross-linguistic generalizations that link syntactic structure to form and meaning illuminating
our understanding of the interactions between modules of the grammar. Cross-linguistic variation results
from the way that the syntax puts terminal nodes together in concert with the satisfaction of the different
requirements at the interfaces (both PF and LF). These requirements may vary on a language-by-language
basis. In what remains of this chapter, I provide a brief overview of the dissertation by chapter.
1.2 Structure of the dissertation
Chapter 2 focuses on establishing the morpho-syntactic generalizations that distinguish the class of count
nouns from the distinct classes of mass nouns. Drawing on data from English and Spanish, I concentrate on
4 major asymmetries: availability of singular/plural contrast, numeral and adjectival modification modification, selectional restrictions by determiners and ellipsis options. I conclude that the class of count nouns is
uniform (i.e the answer to the all the questions in (10) is ‘yes’), whereas ‘mass’ is better understood as the
absence of ‘count’ properties. What is more, I establish important differences within the class of mass nouns.
Some of these observations are novel including, but not limited to, the fact that plural-marking on mass nouns
is structurally different than in count nouns. In addition, I outline a series of empirical generalizations that
are concerned with number-marking and countability, and how these two properties play a crucial role in (i)
the surface form of QAs such as much/many and their Spanish counterparts, (ii) the choice of determiner,
and (iii) ellipsis-licensing. The relevant empirical generalizations include the following listed below, which
serve to motivate the theory developed in the following chapters.
(12) the Plural-Count generalization (i.e. plural-marking does not entail count syntax);
9

(13) the Plural-QA-markedness generalization (i.e. Quantity Adjectives such as much/many and their
counterparts in Spanish are sensitive to number marking);
(14) if a determiner is sensitive to the NP being count, it will also be sensitive to number-marking but not
the opposite; and there is no determiner that exclusively selects for mass nouns.
Chapter 3 develops the theory of individuation and number that accounts for the data described and generalizations formulated in Chapter 2. The theory is couched in the framework of generative minimalist syntax
(Chomsky 1995, 2000, 2001, et seq.) in tandem with the principles of Distributed Morphology (Halle and
Marantz 1993). I propose that count nouns are decomposed into an acategorial root, an n categorizer marked
for [INDIVIDUATED] and a Number head which may be [SINGULAR/PLURAL]. The [INDIVIDUATED] feature is
responsible for making available discrete individuals that can be counted later on (i.e. atoms). Number has
a complementation feature that requires its complement’s n-head to be specified for [INDIVIDUATED]. Thus,
in the absence of such a feature, Number cannot be merged.
Being ‘mass’ can come into different shapes and we must distinguish (at least) three classes: canonical
mass nouns (i.e. unmarked, water), plural mass nouns (e.g. dregs) and object mass nouns (e.g. baggage).
These classes all share the fact that they lack a Number projection. Most of the asymmetries follow from this
fact. Despite their not having a Number projection, I will further show that mass nouns differ in whether or not
they are marked for individuation. That is, while canonical and plural mass nouns lack the [INDIVIDUATED]
feature, and thus discrete individuals, object mass nouns will be specified as [INDIVIDUATED]. This feature is, I
propose, what they share in common with count NPs, accounting for the observation that count noun roots and
object mass roots overlap giving rise to doublets in many cases. Unlike the count noun counterparts, however,
they will not be singular or plural-marked because they do not project Number. Instead, they will be composed
of a feature that I call [COLLECTIVE]. Such a feature will be spelled out as -ery, -ment, -age, -ware and be
located on an outer n-head that competes with Number to satisfy its selectional requirements: the two heads
10

are in complementary distribution.1 The insight is that object mass nouns are morpho-syntactically complex
objects which are built on an individuated constituent. A schematic summary of the relevant structures is in
(15).
(15) a. [[⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟ √ROOT n[INDIVIDUATED]
jewel
]nP Number ⏟⏟⏟⏟⏟⏟⏟ [SG/PL]
Ø/-s
]NumberP ‘count’
b. [√⏟ROOT n
water
]nP
‘mass’
c. [√⏟ROOT
dreg ⏟n[PL]
-s
]nP
‘plural mass’
d. [[⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟ √ROOT n[INDIVIDUATED]
jewel
]nP n⏟[COLL]
-ery
]nP
‘object mass’
I further show that this restrictive theory can account for the generalizations about number-markedness
and determiner restrictions. In a nutshell, while features on determiners can enter a dependency with [INDIVIDUATED]
and/or [SG/PL], there is no mass specific feature which explains the lack of mass-only determiners. With
respect to measure words, I advocate for an analysis that maintains that they are allomorphs of the same underlying measure root (Bresnan 1973; Hackl 2000; Bobaljik 2012; Wellwood 2015; Dunbar and Wellwood
2016): the most marked surface form is conditioned by the presence of a plural feature on the Degree head.
See the contrasts in (16). This part of the analysis has important and welcome consequences for the semantic
computation in the next chapter.
(16) a. many/muchos
Deg
√MEAS Deg
[𝑢PL: PL]
[PL]
...
b. much/mucho
Deg
√MEAS Deg
n √ROOT
1The way I am using complementary distribution is different from the way it is used in phonology. In phonology, two elements
𝑋 and 𝑌 are in complementary distribution if they occur in different environments. Here I mean two elements X and Y are in
complementary distribution if 𝑋 and 𝑌 can both occur in context 𝐶 and the choice between the two can indicate a difference in
meaning. In phonology, this type of distribution is called overlapping or parallel (Bale and Reiss 2018).
11

Before concluding, I discuss the status of the [COLLECTIVE] feature. I argue that this feature is located
on a nominalizing n-head instead of Number in English and Spanish, as observed by different nominalization processes and the unacceptability of numeral modification. However, languages might vary as to the
location of this feature; if this feature is located on Number, we would expect numerals to be acceptable
with [COLLECTIVE]-marked NPs. Based on data from Czech (Grimm and Docekal 2021), I propose that this
prediction is in fact borne out. Thus, just like [PL] can be on n or Number, so can [COLLECTIVE] giving rise
to different morpho-syntactic properties.
Chapter 4 concentrates on a well-known semantic generalization: object mass nouns and plural count
nouns are measured in terms of cardinality when modified by measure words (Bale and Barner 2009). I
start by casting doubt on (semi-)lexical approaches to the generalization that correlate the surface form of a
measure word with a particular semantic interpretation, e.g Uniform Dimensionality (Solt 2009, 2015; Snyder
2021). I show that said approach or set of approaches fails to capture the generality of the observation, which
in fact makes it a good candidate for a language universal. Based on this fact, the decompositional approach
to measure words and the hypothesis that measure roots are underspecified for the dimension of measurement
(Wellwood 2015, 2018, 2019; Cleani and Toquero-Pérez 2022), I propose that the value of cardinality can be
predicted from the syntactic structure in concert with the smantic properties of the relevant constituent to be
measured. Namely, the universal is better stated as follows: when a Degree-head, i.e. [√MEAS Degree], has
an individuated plurality in its scope, the associated dimension of measurement is cardinality. I refer to the
generalization as the Cardinality Generalization Redux, whose structural description is in (17): ‘>’ indicates
scope.
(17) a. [Deg √MEAS Deg] > [PL] > n[INDIVIDUATED] ⇝ CARDINALITY
b. [Deg √MEAS Deg] > [COLL] > n[INDIVIDUATED] ⇝ CARDINALITY
12

an nP marked for [INDIVIDUATION] denotes an individuated semi-lattice generated from the set of atoms
and sums of atoms; [PL] on Number restricts the denotation of the noun to the sums of atoms (atomic nonminimal parts). [COLL] takes an individuated semi-lattice as argument and has a semantics similar to associative plurals (in the sense of Tomioka 2021): it maps the individuated semi-lattice to a property of pluralities
for every part of which there is an atomic minimal part that stands in some relation with the member of the
plurality. The underspecified relation is meant to capture the intuition that there is a ‘cohesion’ group relation (Corbett 2000) between the members that qualify as jewelry or footwear: sometimes it can be ‘made of’
as in jewelry, or ‘worn/located in’ as in footwear. Based on this semantics, these two types of nouns denote
individuated pluralities and can be measured along cardinality scales. The other types of mass nouns are not
specified for [INDIVIDUATION] and the conditions for the assignment of cardinality are not met: (18).
(18) a. [Deg √MEAS Deg] > n[PL] ⇝ #CARDINALITY
b. [Deg √MEAS Deg] > n ⇝ #CARDINALITY
I then discuss how the syntactic and semantic proposal can account for ‘shifts’ between classes, i.e.
nominal flexibility (Pelletier 1979; Bunt 1985; Bach 1986b; Borer 2005a): shifts between classes of NPs can
be accounted for by pairing a root with a different categorizer. At the interfaces, the root has to be licensed:
at PF it must be mapped to an exponent via a possible Vocabulary Insertion rule; and at LF, the categorizer
must select a meaning for the root from the set of root allosemes that matches the conditions imposed by the
categorizer. There is no need for shifts to be performed via covert operators; variation thus results from the
way that the syntax puts terminal nodes together in concert with the satisfaction of the different requirements
at the interfaces.
Last but not least, I provide additional cross-linguistic evidence from Greek and Telugu for the Cardinality
Generalization Redux and the hypothesis that the dimension of measurement is not contingent upon the
surface form of the measure word.
13

Chapter 5 focuses on the number system of the understudied language Alasha Mongolian. I present data
from Alasha Mongolian (Mongolic) arguing that unmarked inanimate nouns are number neutral whereas their
animate counterparts are strictly singular (cp. Bylinina and Podobryaev 2020, for Buriat). Unmarked inanimates, however, can denote a singleton if modified by non-classificatory APs (e.g. expensive). In addition,
like in English, plural-marked nouns can be exclusively or inclusively plural depending on upward/downward
entailingness. I propose that these properties, and number neutrality in particular, can be accomodated within
th system I developed in previous chapters. Unmarked number neutral nouns are [INDIVIDUATED] and as
such they are true of atomic minimal and non-minimal parts. They, however, lack NumberP, responsible
for restricting the denotation of the noun to single atoms (i.e [SG]) or non-singletons (i.e sums [PL]). Their
animate counterparts always project Number, and are thus number-marked. I argue that inanimates may
project NumberP if there is morpho-syntactic evidence to do so (non-classificatory APs, numerals and overt
plural-marking). Having Number enables adjectival modification and the adjunction of numerals higher in
the structure, a fact that corroborates our analysis of English and Spanish in Chapter 3. In addition, I propose
a new solution for the inclusive/exclusive ambiguity of the plural: it is the result of syntactically conditioned
allosemy at LF. Last but not least, the results of the analysis paired with cross-linguistic observations about
number give rise to a novel generalization that correlates morphological markedness and semantic interpretation.
Chapter 6 summarizes the main findings of the dissertation and concludes.
14

Chapter 2
The Count-Mass Distinction in English and Spanish: The Morpho-Syntactic
Facts
Nouns across languages are often classified into two major and broad descriptive categories such as ‘count’
and ‘mass’. For example, nouns like water or the Spanish equivalent agua are mass whereas nouns like book
or libro are considered count. But how can we determines whether a particular noun fits the ‘count’ or ‘mass’
description?
It has been generally observed that these two classes of nouns behave differently with respect to grammatical and distributional properties (Doetjes 1997; Borer 2005a; Wiltschko 2012). In other words, the encoding
of ‘count’ or ‘mass’ is syntactic. For example, there are important morpho-syntactic asymmetries between
the two classes. This chapter is concerned with these.
The first asymmetry is related to the availability of overt number marking. ‘Count’ nouns show singularplural distinctions, while ‘mass’ nouns generally resist overt number-marking, thus lacking plural counterparts. A second asymmetry is concerned with modification by some constituents. For instance, ‘count’
nouns can be modified by numerals and certain adjectives (e.g. big, large, round etc.) called Stubbornly
Distributive adjectives (Quine 1960; Schwarzschild 2011; Deal 2017), but ‘mass’ nouns cannot.
There are, however, two paradoxical cases that do not seem to fit these descriptive generalizations. One
paradoxical case is exemplified by nouns such as suds, dregs, hops etc. These nouns appear to be overtly
15

plural-marked, and yet they seem to have the same distribution as water, e.g. no numeral modification.
Due to the overt plural marking, they are sometimes referred to as ‘lexical plurals’ or ‘plural mass nouns’
(Alexiadou 2004, 2011, 2015; Acquaviva 2008). The other paradoxical case is exemplified by nouns such
as jewelry, footware or furniture. Like other mass nouns, they resist pluralization, but like count nouns they
allow modification by Stubbornly Distributive adjectives: big/large/round furniture. Any unified theory of
the count-mass distinction must address and explain these paradoxes.
The third asymmetry refers to the nouns’ sensitivity to determiners and QAs, e.g. much, many, few,
most. In particular, while some determiners are ‘count-only’ determiners (sometimes also showing sensitivity
to number-marking on the noun) such as every, each or several, mass-only determiners are rarely, if ever,
reported (Doetjes 1997, 2021; Chierchia 1998a; Bale 2016). What is more, even though distinctions in the
domains of QAs like the much/little-many/few distinction are sometimes argued to be lexical (much+‘mass’
but many+‘count’, Bresnan 1973; Hackl 2000; Bhatt and Pancheva 2004; Solt 2009, 2015), they have been
analyzed as allomorphs of the same underlying morpheme: many/few being the marked vocabulary item
whose exponence is triggered by the presence of plural feature (Wellwood 2015, 2018, 2019; Bale 2016;
Smith 2021; Cleani and Toquero-Pérez 2022).
The fourth and last asymmetry that I will focus on in this chapter is associated with ellipsis. Namely,
while ‘count’ nouns allow number mismatches under ellipsis stranding a numeral or a QA, ‘mass’ nouns do
not. In addition, the former but not the latter allow for a smaller type of ellipsis referred to as one-substitution
(Bloomfield 1933; Harley 2005; Bale and Gillon 2020): I bought many Spanish books, and you bought a
French one too vs. *I drank too much Spanish wine, and you drank too much French one too.
In this chapter, I concentrate on describing the empirical landscape relevant to these morpho-syntactic
asymmetries. By the end of the chapter, the picture that will have emerged is one where we seem to have a
good descriptive understanding of what it means to be ‘count’. Mass, in contrast, seems to be better understood as the absence of ‘count’ properties. In addition, I will outline a series of empirical generalizations that
16

are concerned with number-marking and countability, and how these two properties play a crucial role in (i)
the surface form of QAs such as much/many and their Spanish counterparts, (ii) the choice of determiner,
and (iii) ellipsis-licensing.
2.1 Setting the baseline: ‘canonical’ mass and count nouns.
Number-marking and modification. There are different hallmark properties that distinguish count nouns
from ‘canonical’ or unmarked mass nouns, e.g. Jespersen (1924); Bloomfield (1933); Quine (1960); Pelletier
(1975); Bach (1986b); Chierchia (1998a,b); Borer (2005a). These properties include availability of a singular
(unmarked) plural (marked) distinction, as in (1); direct modification by cardinal numerals, as in (2); and
modification by Stubbornly Distributive adjectives (Schwarzschild 2011), as in (3). In the case of adjectives,
I illustrate the situation with adjectives in both attributive (inside the DP) and predicative (predicate of the
copula) position. Again, the ‘#’ on the example indicates that the expression does not have the intended
interpretation, i.e. a substance interpretation in the case of mass nouns.
(1) singular/plural contrast
a. Barney dropped the {book/ books}.
b. Barney drank the {water/ #waters}.
(2) direct cardinal numeral modification
a. Barney dropped {one book/ three books}
b. # Barney drank {one water/ three waters}.
(3) modification by Stubbornly Distributive adjectives
a. The book on the shelf is small.
b. Barney picked the small book.
c. The books on the shelf are small.
17

d. Barney picked the small books.
e. # The water on the floor is small.
f. # Barney drank the small water.
The properties in (1) and (2) show that only count nouns have a singular/plural distinction and can be
directly modified by cardinal numerals. Other nouns like water are mass. While they may be plural marked,
their meaning is no longer referencing a substance but rather a unit or a kind (Bunt 1985; Bach 1986b):
‘two units of water’ or ‘two types of water’ (e.g. tap vs. sparkling). Subsequent cardinal modification is
only possible under the shifted interpretation.1 The shifted interpretation has been argued to have underlying
count noun syntax (Borer 2005a; Mathieu 2012). In order to avoid a container interpretation of substance
mass nouns like wine or water, I will be using verbs that require their complement to be liquids rather than
physical containers: drink and pour are such verbs, Cowper (see 1992).
The same facts illustrated for English also hold in Spanish. Only some nouns have a singular/plural
distinction, allow for direct cardinal numeral modification, and modification by stubbornly distributed predicates. This is the class of nouns referred to as count. Relevant examples are in (4)-(6).
(4) singular/plural contrast
a. Barney
Barney
cogió
took
{ el
the.M
libro/
book/
lo-s
the.M-PL
libro-s}.
book-PL
‘Barney took the book/books’
b. Barney
Barney
bebió
drank
{ el
the.M
vino/#
wine/
lo-s
the.M-PL
vino-s}
wine-PL
‘Barney drank the wine/ #wines’
(5) direct cardinal numeral modification
1This is similar to the interpretation obtained with an overt measure or container noun in pseudo-partitives (Lehrer 1986;
Schwarzschild 2006) such as (i).
(i) pseudo-partitive with mass nouns
Barney drank the two {bottles/ glasses} of water
18

a. Barney
Barney
cogió
took
{ un
one.M
libro/
book/
tres
three
libro-s}.
book-PL
‘Barney took one book/ three books’
b. # Barney
Barney
bebió
drank
{ un
one.M
vino/
wine/
tres
three
vino-s}
wine-PL
‘Barney drank one wine/ three wines’
(6) modification by Stubbornly Distributive adjectives
a. El
the.M
libro
book
en
in
la
the
estantería
shelf
es
is
pequeño.
small.M
‘The book on the shelf is small’.
b. Barney
Barney
cogió
took
el
the.M
libro
book
pequeño.
small.M
‘Barney took the small book’
c. Lo-s
the.M-PL
libro-s
book-PL
en
in
la
the
estantería
shelf
son
are
pequeño-s.
small.M-PL
‘The books on the shelf are small’.
d. Barney
Barney
cogió
took
lo-s
the.M-PL
libro-s
book-PL
pequeño-s.
small.M-PL
‘Barney took the small books’
e. # El
the.M
vino
wine
en
in
la
the
mesa
table
es
is
pequeño
small.M
‘The wine on the table is small’
f. # Barney
Barney
bebió
drank
el
the.M
vino
wine
pequeño.
small.M-PL
‘Barney drank the small wine’
As we saw for English, mass nouns like vino ‘wine’ can shift into a container/kind interpretation. In
such a case, vinos ‘wines’ in (4b) are acceptable with the plural marker. Again subsequent cardinal numeral
modification is possible only in those cases.
19

Determiner selection. In addition, the choice of determiner is not only sensitive to whether the noun is
count or mass, but also to whether the noun is singular or plural-marked (Chierchia 1998a, 2021; Borer
2005a; Gillon 2012; Cowper and Hall 2014; Bale 2016; Bale and Gillon 2020, a.o). Some determiners are
only compatible with singular count nouns as in (7), some are only compatible with plural-marked count
nouns as in (8) and others are compatible with both mass and (singular/plural) count as in (9).
(7) Singular-count-only determiners: {a, every, each}
a. Barney dropped {a/ every/ each} book.
b. * Barney dropped {a/ every/ each} books.
c. # Barney drank {a/ every/ each} water.
(8) Plural-count-only determiners: several
a. * Barney dropped several book.
b. Barney dropped several books.
c. * Barney drank several water.
(9) Determiners underspecified for number and the count-mass distinction: {the, some, any, no,
this/these}
a. Barney dropped {the/ some/ no/ this} book.
b. Barney dropped {the/ some/ no/ these} books.
c. Barney drank {the/ some/ no/ this} water.
To the classes of determiners in (7)-(9) we need to add the following two observations: first of all, there
is no determiner that is sensitive to only mass nouns; second of all, QAs like much, many, more, most and
universal all require that the noun they modify be mass or plural count, but not singular count. In the case of
QAs, many is found when the noun is count and plural but much is found elsewhere. This is shown in (10)
20

(10) Mass and plural count determiners/quantifiers
a. * Barney dropped {all/ much/ many/ more} book.
b. Barney dropped {all/ ∗much/ many/ more} books.
c. Barney drank {all/ much/ ∗many/ more} water.
Looking at Spanish, we first need to note that determiners and quantifiers always agree in gender and
number with the noun, a process that is generally referred to as ‘nominal concord’. Determiners in Spanish
are also sensitive to the noun being count and the number properties of the noun in question (Bosque 1999,
ch.1). We can identify the same four classes of determiners that we identified for English: singular-countonly determiners in (11), plural-count-only determiners in (12); mass and plural-count determiners in (13),
and determiners underspecified for the count-mass distinction in (14).
(11) Singular-count-only determiners: cada ‘each’ cualquier ‘any’.2
a. Barney
Barney
coge
takes
{ cada/
each/
cualquier}
any
libro
book
de
of
la
the
biblioteca.
library
‘Barney takes {each/ any} book of the library.’
b. * Barney
Barney
coge
takes
{ cada/
each/
cualquier}
any
libro-s
book-PL
de
of
la
the
biblioteca.
library
‘Barney takes {each/ any} books of the library.’
c. # Barney
Barney
bebe
drinks
{ cada/
each/
cualquier}
any
vino
wine
de
of
España.
Spain
‘Barney takes {each/ any} wine from Spain.’
(12) Plural-count-only determiners: vari-o/a-s ‘several-M/F-PL’
3
a. * Barney
Barney
coge
takes
varios
several.M.PL
libro
book
de
of
la
the
biblioteca.
library
‘Barney takes several book from the library’
2Cualquier ‘any’ is glossed as any here, but it should not be understood as Negative Polarity Item (NPI) any. It is more of a free
choice determiner.
3The determiner varios ‘several’ is number-invariant. That is, it is always plural-marked and it lacks an unmarked counterpart:
*vario/varia.
21

b. Barney
Barney
coge
takes
varios
several.M.PL
libro-s
book-PL
de
of
la
the
biblioteca.
library
‘Barney takes several books from the library’
c. * Barney
Barney
bebe
drinks
varios
several.M.PL
vino
wine
de
of
España.
Spain
‘Barney drinks several wine from Spain.’
(13) Mass and plural-count determiners: todo el (lit. ‘all the’) ‘all’, QAs (e.g. mucho ‘much’, tanto ‘as/so
much’, más ‘more’)
a. * Barney
Barney
saca
takes
{ todo
all.M
el/
the.M/
mucho/
much.M/
más}
more
libro
book
de
of
la
the
biblioteca
library
Lit.: ‘Barney takes {all/ much/ more} book from the library.’
b. Barney
Barney
saca
takes
{ todo-s
all.M-PL
lo-s/
the.M-PL/
mucho-s/
much.M-PL/
más}
more
libro-s
book-PL
de
of
la
the
biblioteca
library
‘Barney takes {all/ many/ more} books from the library.’
c. Barney
Barney
bebió
drank
{ todo
all.M
el/
the.M/
mucho/
much.M/
más}
more
vino
wine
de
of
la
the
botella.
bottle
‘Barney drank {all/ much/ more} wine from the bottle.’
(14) Underspecified for the count-mass distinction: demonstratives and definite article
a. Barney
Barney
sacó
took
{ el/
the.M/
este}
this.M
libro
book
de
of
la
the
biblioteca
library
‘Barney took {the/ this} book from the library.’
b. Barney
Barney
sacó
took
{ lo-s/
the.M-PL/
esto-s}
this.M-PL
libro-s
book-PL
de
of
la
the
biblioteca
library
‘Barney took {the/ these} books from the library.’
c. Barney
Barney
bebió
drank
{ el/
the.M/
este}
this.M
vino
wine
de
of
la
the
botella.
bottle
‘Barney drank {the/ this} wine from the bottle.’
To these four classes, we need to add one more: a class of determiners that only select for count nouns
regardless of the number on the noun. These are exemplified in (15). The determiners are unmarked for
number if the noun is also unmarked, but they will be overtly plural-marked if the noun is plural-marked.
22

From now on, and in order to reduce confusion, I will gloss bare todo(s) in Spanish as ‘every’ given that
it is a universal that only occurs with count nouns. I will gloss todo el/ todos los as ‘all the’ given their
compatibility with both count and mass nouns.
(15) Count-only determiners: algún/un ‘some/a’, ningún ‘no’ todo ‘every’ ‘every’4
a. Barney
Barney
sacó
took
{ algún/
some.M/
un/
a.M/
todo}
every.M
libro
book
de
of
la
the
biblioteca
library
‘Barney took {some/ a/ every} book from the library.’
b. Barney
Barney
sacó
took
{ alguno-s/
some.M-PL/
uno-s/
a.M-PL/
todo-s}
every.M-PL
libro-s
book-PL
de
of
la
the
biblioteca
library
Lit.: ‘Barney took {some/ a/ every} books from the library.’
Int.: ‘Barney took {some/ all} books from the library.’
c. # Barney
Barney
bebió
drank
{ algún/
some.M/
un/
a.M/
todo}
every.M
vino
wine
de
of
España.
Spain
Lit.: ‘Barney drank {some/ a/ every} wine from the library.’
Int.: ‘Barney drank {a/ every} wine from Spain’
For ease of reference, we can summarize the correspondences between English and Spanish determiners
in Table 2.1. The table pairs the determiners based on their distributional properties instead of their literal
translation. Thus, while some is an existential indefinite, generally translated as algún/un, they differ in their
distribution and thus occupy different rows on the table. To generalize across languages, I will label each
class as “Class #” followed by a descriptive name.
Ellipsis options. Mass and count nouns differ in their ellipsis options. First of all, it has been observed
that count nouns allow number mismatches under ellipsis (Lobeck 1995; Merchant 2014; Saab 2019). That
is, the antencedent of ellipsis may be singular, while the target may be plural or viceversa. This is shown in
(16).
4Unless used in the preverbal subject position, ningún ‘no’ is a negative concord item subject to matrix negation (Bosque 1980;
Vallduví 1994). Since none of the examples include negation, I have refrained from using ningún in them. We can assume that its
distribution is identical to algún with the additional requirement of negation.
23

Table 2.1: Determiner correspondences English-Spanish based on the count-mass distinction
Classes of Determiners English Spanish
Class 1: Count-only – Todo(s), algún(os), ningún(os), un(os)
Class 2: SG-count only each, a, every cada, cualquier
Class 3: PL-count only several varios
Class 4: Mass and PL-count all, QAs todo el/todos los, QAs
Class 5: Underspecifed the, this/these, some, no el/los, este/estos
(16) Number mismatches under ellipsis
a. Barney read {many/ three} books, and Ted read one book too. PL/SG
b. Ted read {one/some book} and Barney read {many/three} books. SG/PL
In (16a), the antecedent books is plural and the target is singular whereas in (16b) the opposite pattern is
found. In both cases, either a numeral (e.g. one in 16a or three in 16b) or a QA (e.g. many) act as ellipsis
remnants delimiting the ellipsis site.
This type of ellipsis is independently unavailable for mass nouns given their lack of a singular/plural
contrast (modulo the container or kind interpretation which patterns with count nouns). Mass noun ellipsis
is still possible though, as long as the the remnant of the ellipsis is a QA. An example is in (17).5
(17) NP-ellipsis with mass nouns
a. Barney poured that much water into his soup, but I didn’t pour ({so/ that/ as}) much water into
mine.
b. Barney drank too much Spanish wine at lunch and Robin drank {as/ too} much Spanish wine
too.
5
It is worth noting that bare much in English is an NPI and it cannot occur in positive polarity contexts (Klima 1964; Israel 1996;
Doetjes 1997; Solt 2009). Modified much, e.g. too/ that/ as/ so much, is not an NPI. That is why, as, too, that are optional in (17a)
but obligatory in (17b).
24

The data in (17) show that the unmarked QA much can demarcate the ellipsis site. What is more, when
there is an classificatory adjective like Spanish, said adjective cannot survive the ellipsis. If it does, ungrammaticality obtains even if the adjective is contrastive with the one on the antecedent. This is shown in the
continuation to the sentence in (17b) in (18).
(18) * …and Robin drank {as/ too} much
⎧
{
{
{
⎨
{
{
{
⎩
Spanish
Italian
⎫
}
}
}
⎬
}
}
}
⎭
wine too.
Apart from full NP ellipsis with cardinal numbers or QAs as remnants, English allows another type of
nominal ellipsis: one-substitution (Jackendoff 1977; Abney 1987; Harley 2005; Payne et al. 2013). Onesubstitution seems to target a smaller syntactic constituent, i.e. the nominal head itself (Harley 2005). Since
Bloomfield (1933), it has been observed that one-substitution is sensitive to the count-mass distinction. More
specifically, it is sensitive to the noun being count: only count nouns can serve as antecedents and targets for
one-substitution (Bale and Gillon 2020, p.17). This is shown in (19).
(19) one-substitution
a. Barney touched the apple on the table and Ted touched the one(s) on the shelf.
b. * Barney drank the water that Mary poured and Ted drank the one that Marshall poured.
If number mismatches under ellipsis and one-substitution are conditioned by the syntax, these facts are
tracking an underlying structural difference between mass and count nouns. In particular, for any mismatches
to occur under ellipsis, the relevant feature must outside of the ellipsis site. This entails that whatever head
encodes number must be present in the syntax of count nouns and survive the ellipsis, (Merchant 2014; Lipták
and Saab 2014). Similarly, smaller ellipsis options like one-substitution must be sensitive to the selectional
and featural properties of the noun (Harley 2005; Merchant 2014): in this case whatever is responsible for
grammatically marking the noun as ‘count’.
25

Similar facts obtain in Spanish. Like in English, number mismatches under ellipsis are acceptable (Picallo
2008; Eguren 2010; Lipták and Saab 2014; Toquero-Pérez 2023b): a singular antecedent can license ellipsis
of a plural NP constituent, and viceversa. The sentence in (20b) is adapted from Lipták and Saab (2014, p.9),
and the one in (20a) is modelled after it to illustrate the parallelism.
(20) Number mismatches under ellipsis
a. Juan
Juan
compró
bought
un
one
libro
book
de
of
Borges
Borges
y
and
María
María
compró
bought
{ dos/
two/
mucho-s}
much.M-PL
libro-s
book-PL
de
of
Cortázar.
Cortázar
‘Juan bought one book by Borges and María bought {two/ many} by Cortázar’ SG/PL
b. Juan
Juan
compró
bought
{ dos/
two/
mucho-s}
much.M.PL
libro-s
book-PL
de
of
Borges
Borges
y
and
María
María
compró
bought
un-o
one-M
libro
book
de
of
Cortázar.
Cortázar
‘Juan bought {two/ many} books by Borges and María bought one by Cortázar.’ PL/SG
When the noun modified by the numeral uno is overt as in (20a), the class marker of the numeral, i.e. the
masculine gender exponent -o, is deleted; but when such noun has undergone ellipsis as in (20b), the class
marker is retained (Arregi 2013).
Again, number mismatches under ellipsis are independently ruled out for mass nouns given their lack of
a singular/plural contrast. However, as we observed for English, mass noun ellipsis is possible with a QA
remnant. As in English, if there is a classificatory adjective like español ‘Spanish’, the adjective cannot be
outside of the ellipsis site. This is shown in (21).6
(21) Juan
Juan
bebió
drank
mucho
much.M
vino
wine
español...
Spanish
‘Juan drank too much Spanish wine ...’
6
In Spanish it is possible for the classificatory adjective to survive ellipsis if the adjective in the second conjunct or disjunct is
contrastive with the adjective in the antecedent. This is shown in (ii).
(ii) Juan
Juan
bebió
drank
mucho
much.M
vino
wine
español,
Spanish,
y
and
María
María
bebió
drank
mucho
much.M
{* español/
Spanish/
francés}
French
también.
too
‘Juan drank too much Spanish wine and Mary drank as much French wine too’.
One possible explanation is that the AP vacates the ellipsis site as a result of focus movement, e.g. Eguren (2010), prior to the
licensing of ellipsis.
26

a. y
and
María
María
bebió
drank
much-o
much-M
español
Spanish
vino
wine
también.
too
‘and María drank (too) much too’
b. * y
and
María
María
bebió
drank
much-o
much-M
español
Spanish
vino
wine
también.
too
‘and María drank (too) much Spanish too’
English one-substitution has sometimes been correlated with N-gapping in Spanish (Saab 2019), where
the noun head is completely absent from the surface string of the DP. However, this is not quite the same,
given that N-gapping is not sensitive to the count-mass distinction as the examples in (22) show.
(22) a. El
the.M
libro
book
de
of
Borges
Borges
y
and
el
the.M
libro
book
de
of
Cortázar.
Cortázar
‘The book by Borges and the one by Cortázar’
b. Lo-s
the.M-PL
libro-s
book-PL
de
of
Borges
Borges
y
and
lo-s
the.M-PL
libro-s
book-PL
de
of
Cortázar.
Cortázar
‘The books by Borges and the ones by Cortázar’
c. El
the.M
vino
wine
de
of
la
the
botella
bottle
y
and
el
the.M
vino
wine
de
of
la
the
jarra
jar
‘The wine from the bottle and the wine from the jar’
If gapping paralleled one-substitution, the sentence in (22c) with the mass noun vino, which has a substance reading, would be marked unacceptable. And yet, it is perfectly acceptable for native speakers. Instead
of the N-gapping strategy, however, Spanish can make use of the pronominal form otro ‘other’ preceded by
a definite article or a demonstrative. This strategy gives rise to the paradigm in (23).7
7From now on, I will be using the demonstrative to illustrate otro-substitution. But it is important to note that if the demonstrative
is replaced by the definite article, the same judgments are obtained. See (iii), which is parallel to the one in one-substitution.
(iii) otro-substitution with definite article
a. Juan
Juan
leyó
read
el
the.M
libro
book
de
of
Borges
Borges
y
and
María
María
leyó
read
el
el.M
otro
other.M
de
of
Cortázar.
Cortázar
Lit.: ‘Juan read the book by Borges and María read the other by Cortázar’
Int.: ‘Juan read this book by Borges and María read this one by Cortázar’.
b. Juan
Juan
leyó
read
lo-s
the.M-PL
libro-s
book-PL
de
of
Borges
Borges
y
and
María
María
leyó
read
lo-s
the.M-PL
otro-s
other.M-PL
de
of
Cortázar.
Cortázar
Lit.: ‘Juan read the books by Borges and María read the others by Cortázar’
27

(23) otro-substitution
a. Juan
Juan
leyó
read
este
this.M
libro
book
de
of
Borges
Borges
y
and
María
María
leyó
read
este
this.M
otro
other.M
de
of
Cortázar.
Cortázar
Lit.: ‘Juan read this book by Borges and María read this other by Cortázar’
Int.: ‘Juan read this book by Borges and María read this one by Cortázar’.
b. Juan
Juan
leyó
read
esto-s
this.M-PL
libro-s
book-PL
de
of
Borges
Borges
y
and
María
María
leyó
read
esto-s
this.M-PL
otro-s
other.M-PL
de
of
Cortázar.
Cortázar
Lit.: ‘Juan read these books by Borges and María read these others by Cortázar’
Int.: ‘Juan read these books by Borges and María read these ones by Cortázar’.
c. * Juan
Juan
virtió
poured
este
this.M
vino
wine
de
of
la
the
botella
bottle
y
and
este
this.M
otro
other.M
de
of
la
the
jarra.
jar
Lit.: ‘Juan poured this wine from the bottle and this other from the jar’
Int.: ‘Juan poured this wine from the bottle and this one from the jar’.
The example in (23a) shows that otro can replace a singular count noun libro ‘book’. Likewise, pluralmarked otro in (23b) stands for the the plural count noun root libro plus overt plural-marking. However, what
otro cannot replace is a mass noun like vino; attempting to do that is considered ungrammatical as shown in
(23c). This is the exact parallel of English one-substitution: count noun roots, regardless of whether they are
unmarked or plural-marked, can be the target of one/otro, but mass nouns cannot.8
We have now set the baseline for what it means to be a count noun and a canonical mass noun in both
English and Spanish at least.9 The diagnostics are summarized in Table 2.2 and Table 2.3, which will be
Int.: ‘Juan read the books by Borges and María read the ones by Cortázar’.
c. * Juan
Juan
virtió
poured
el
the.M
vino
wine
de
of
la
the
botella
bottle
y
and
el
the.M
otro
other.M
de
of
la
the
jarra.
jar
Lit.: ‘Juan poured the wine from the bottle and the other from the jar’
Int.: ‘Juan poured the wine from the bottle and the one from the jar’.
8
I am using the label ‘noun root’ purely descriptively to refer to the (unmarked) bare form of the noun, e.g. book, water, jewel. I
am not making any claims as to whether roots are categorized in the lexicon. In fact, under DM assumptions, which will be spelled
out in Chapter 3, the descriptive term ‘nominal/noun root’ corresponds to the analytic object n+√ROOT.
9Some of these diagnostics may not be applicable to other languages. See Doetjes (1997, 2021); Chierchia (1998b, 2021); Lima
(2014); Deal (2017); Rothstein (2017, 2021) among others.
28

updated section-by-section. We can use these findings to probe the properties of other nouns that seem to lie
in the middle or which may share some properties with either class.
Table 2.2: Morpho-syntactic properties of ‘canonical’ mass & count nouns (to be updated)
Canonical Mass Count
SG/PL distinction * ✓
Direct modification by numerals * ✓
Modification by Stubbornly Distributive adjectives * ✓
Number mismatches under ellipsis NA ✓
one/otro-substitution * ✓
Table 2.3: Restrictions on determiner selection (to be updated)
Class of Determiner Canonical Mass Count
SG PL
Class 1: Count-only * ✓ ✓
Class 2: SG-count only * ✓ *
Class 3: PL-count only * * ✓
Class 4: Mass & PL-count ✓ * ✓
Class 5: Underspecifed ✓ ✓ ✓
In addition to the two large classes of nouns that have been identified, there are two other types of nouns
that are typically discussed: plural mass nouns (e.g. suds, fumes etc.) and aggregate or object mass nouns
(e.g. furniture, weaponry, jewelry etc.).
2.2 Plural mass nouns
Number-marking and modification. A non-exhaustive list of plural mass nouns is in (24a) for English
(see Ojeda 2005, p.2: ex.1; and also Wellwood 2019, p.108), and in (24b) for Spanish, (Bosque 1999, ch1,
p.29).
(24) Plural mass nouns
a. clothes, oats, hops, guts, brains, fumes, suds, dregs, goods, valuables … (English)
29

b. agujetas
muscle sores
celos
jealousy.PL
víveres
provisions
babas
drooling.PL
represalias
reprisals
(Spanish)
From the list in (24), it is clear why they are referred to as ‘plural’: they are overtly plural-marked. In
this respect, they differ from canonical mass nouns and resemble plural count nouns. However, unlike plural
count nouns, they lack a singular or unmarked counterpart (when used nominally). Thus, the following
contrasts in (25) for English and (26) for Spanish obtain.
(25) Lack of a singular/plural contrast in English
a. Barney inhaled the fumes.
b. * Barney inhaled the fume.
(26) Lack of a singular/plural contrast in Spanish
a. El
the
ejército
army
mandó
sent
lo-s
the.M-PL
vívere-s
provision-PL
desde
from
Madrid.
Madrid
‘The army sent the provisions from Madrid’
b. * El
the
ejército
army
mandó
sent
el
the.M
vívere
provision
desde
from
Madrid.
Madrid
‘The army sent the provision from Madrid’
Overt plural-marking on these nouns triggers obligatory plural agreement DP-internally and externally.
In English, due to the general lack of nominal concord inside DPs, DP-internal plural agreement is only
observed with demonstratives, as shown in (27a). In Spanish, plural concord DP-internally is visible with
determiners and adjectival modifiers, e.g. (28a), and DP-externally with the verb and passive participles, e.g.
(28b).
(27) Obligatory plural agreement in English
a. Miners shouldn’t breathe {*this/ these} fumes.
30

b. The fumes {*was/ were} produced by the mixture of the spilled chemicals with rain and
snow.10
(28) Obligatory plural agreement in Spanish
a. El
the
ejército
army
mandó
sent
esto-s
this.M-PL
vívere-s
provision-PL
necesario-s
necessary.M-PL
desde
from
Madrid.
Madrid
‘The army sent these necessary provisions from Madrid’
b. * El
the
ejército
army
mandó
sent
este
this.M
vívere-s
provision-PL
necesario
necessary.M
desde
from
Madrid.
Madrid
‘The army sent these necessary provisions from Madrid’
c. Lo-s
the.M-PL
vívere-s
provision-PL
{* fue
was.3SG
enviado/
sent.M/
fueron
were.3PL
enviado-s}
sent.M-PL
desde
from
Madrid.
Madrid
‘The provisions were sent from Madrid’
Despite their overt plural-markedness and the fact that cardinal numerals higher than ‘1’ require that the
noun they modify be plural-marked, plural mass nouns cannot be directly modified by numerals (Bosque
1999; Ojeda 2005). Some examples are in (29)-(30). Likewise, these nouns also disallow modification by
Stubbornly Distributive adjectives (Ojeda 2005), as illustrated in (31)-(32).
(29) Impossibility of direct numeral modification in English
a. * There are five clothes on the table.
b. * Barney found three dregs at the bottom of the cup.
(30) Impossibility of direct numeral modification in Spanish
a. * Andrés
Andrés
tiene
has
cinco
five
agujeta-s
muscle sore-PL
en
in
los
the
cuádriceps.
quadriceps
‘Andrés has five muscle sores in his quadriceps’
b. * Tres
three
baba-s
drool-PL
le
CL.3SG
colgaban
hanged
de
of
los
the
labios.
lips
‘Three drools hanged from his lips’
10https://www.upi.com/Archives/1986/03/13/Six-treated-for-inhaling-toxic-fumes/4543511074000/
31

(31) Impossibility of modification by Stubbornly Distributive adjectives in English
a. * The dregs at the bottom of the cup are large.
b. * Barney found the large dregs at the bottom of the cup.
(32) Impossibility of modification by Stubbornly Distributive adjectives in Spanish
a. * La-s
the.F-PL
baba-s
droo-PL
que
that
le
CL.3SG
colgaban
hanged
de
of
los
the
labios
lips
eran
were
grande-s.
big-PL
Int.: ‘The drools that hanged from his lips were large’
b. * Yo
I
no
NEG
paraba
stopped
de
of
mirar
to.stare
la-s
the.F-PL
baba-s
drool-PL
grande-s
big-PL
en
in
los
the
labios
lips
de
of
Andrés.
Andrés
‘I couldn’t stop staring at the drools on Andrés’ lips’
With respect to these diagnostics, they behave as unequivocally mass nouns. Thus, their massiness in
combination with overt plural markedness has led to the term plural mass nouns.
Determiner selection. As mass nouns, they are also restricted to the type of determiners and quantifiers
that they can occur with (Bosque 1999). In particular, they are ungrammatical with count-only determiners in
Spanish (i.e. Class 1) such as algún, un, todo, e.g. (33); likewise they are also ungrammatical with singularcount-only determiners in both languages like a, every, each and cada, cualquier (i.e. Class 2). This is so
given that they lack a singular counterpart. These restrictions are shown in (34) and (35).
(33) Class 1: count-only determiners in Spanish
a. * El
the
ejército
army
mando
sent
{ alguno-s/
some.M-PL/
uno-s/
a.M-PL/
todo-s}
every.M-PL
vívere-s
provision-PL
desde
from
Madrid.
Madrid
Int.: ‘The army sent {a/ every} provisions from Madrid’
b. * Andrés
Andrés
sufre
suffers
{ alguna-s/
some.F-PL/
una-s/
a.F-PL/
toda-s}
every.F-PL
agujeta-s
muscle sore-PL
en
in
la
the
pierna
leg
derecha.
right
Lit.: ‘Andrés suffers from {a/ every} muscle sores in his right leg’
(34) Class 2: singular-count only determiners in English
32

a. * Barney found {a/ each/ every} dreg at the bottom of the cup.
b. * {A/ every/ each} fume was coming out of the nuclear station.
(35) Class 2: singular-count only determiners in Spanish
a. * El
the
ejérecito
army
necesita
needs
{ cada/
each/
cualquier}
any
vívere-s.
provision-PL
Lit.: ‘The army needs {each/ any} provisions’
b. * Mi
my
fisio
physiotherapist
te
CL.2SG.DAT
quita
removes
{ cada/
each/
cualquier}
any
agujeta-s.
muscle sore-PL
Lit.: ‘My physiotherapist will elminiate {each/ any} muscle sores from you.’
Importantly, despite their being plural-marked, plural mass nouns are also incompatible with determiners
like several or Spanish varios, (i.e. Class 3). Thus, the label ‘plural-count-only’ seems an appropriate one
for this class of determiners. This is shown in (36) for English and (37) for Spanish.
(36) Class 3: plural-count-only determiners in English
a. * Barney found several dregs at the bottom of the cup.
b. * Several fumes were coming out of the nuclear station.
(37) Class 3: plural-count-only determiners in Spanish
a. * El
the
ejército
army
mandó
sent
varios
several.M.PL
vívere-s
provision-PL
desde
from
Madrid.
Madrid
‘The army sent several provisions from Madrid’
b. * Tengo
have.1SG
varias
several.F.PL
agujeta-s
muscle sore-PL
por
for
ir
to.go
a
to
correr
run
ayer.
yesterday
‘I have several muscle sores for going running yesterday’
Like mass nouns, and plural count nouns, they are compatible with Class 4 determiners: all and Spanish
todos los ‘all the’ and QAs. This is shown in (38) and (39).
(38) Class 4: Mass & Plural-count determiners in English
33

a. Barney removed {all / much/ %many/ more} dregs at the bottom of the cup.
b. {All / Too much/ %Many/ More} fumes were coming out of the nuclear station.
(39) Class 4: Mass & Plural-count determiners in Spanish
a. El
the
ejército
army
mandó
sent
{ todo-s
all.M-PL
lo-s/
the.M-PL/
mucho-s/
much.M-PL/
tanto-s/
as.much.M-PL/
más}
more
vívere-s
provision-PL
desde
from
Madrid.
Madrid
Lit.: ‘The army sent {all the/ many/ as many/ more} provisions from Madrid.’
Int.: ‘The army sent {all/ much/ as much/ more} provisions from Madrid.’
b. Andrés
Andrés
tiene
has
{ toda-s
all.F-PL
la-s/
the.F-PL/
mucha-s/
much.F-PL/
tanta-s/
as.muchF-PL/
más}
more
agujeta-s
muscle sore-PL
en
in
la
the
pierna
leg
derecha.
right
Lit.: ‘Andrés has {all the/ many/ as many/ more} muscle sores in the right leg’
Int.: ‘Andrés has {all/ much/ as much/ more} muscle sores in his right leg’
Interestingly, the English data in (38) indicate that, despite the noun being overtly marked plural, speakers
seem to prefer the unmarked form of the QA, e.g. much (Solt 2009). Smith (2021, ch.8, p.234-235) notes that
intuitions about choosing much over many with plural mass nouns are unclear. Smith reports a corpus search
showing that (i) few tokens with a plural mass noun modified by a QA were found, and (ii) of those found,
there was a preference for many. My own elicitations with native English seem to confirm this variation.
Thus, the ‘%’ indicates that there is speaker variation.
This situation is completely different from what we observe in Spanish: the QAs mucho ‘much’ and tanto
‘as/so much’ require overt plural-marking. For now, it is simply worth noting that English and Spanish differ
in this respect: the former prefers the unmarked form much though it does not preclude the more marked one
many; the latter requires the QA to be marked for number if the noun is plural-marked.11
11Despite the claims made by Solt (2009, 2015); Snyder (2021) that the surface form many is semantically conditioned by the
dimension of ‘cardinality’, the Spanish facts seem to suggest otherwise: the plural-marked form of the QA surfaces, just like with
count nouns, and yet the noun is measured in terms of volume or weight. Similar facts are observed in Greek (Tsoulas 2006, 2009)
and Telugu (Smith 2021). In Chapter 3 and Chapter 4, I will show that the surface form of the QA is sensitive to there being a plural
34

Last but not least, plural mass nouns are compatible with the set of determiners that are underspecified
for the count-mass distinction, i.e. Class 5. The data is in (40) for English and in (41) for Spanish.
(40) Class 5: Determiners underspecified for the count-mass distinction in English
a. Barney removed {the/ some/ no/ these} dregs at the bottom of the cup.
b. {The/ Some/ No/ These} fumes were coming out of the nuclear station.
(41) Class 5: Determiners underspecified for the count-mass distinction in Spanish
a. { Lo-s/
the.M-PL/
esto-s}
this.M-PL
vívere-s
provision-PL
llegaron
arrived
desde
from
Madrid.
Madrid
{The/ These} provisions arrived from Madrid.’
b. Juan
Juan
se
SE
limpió
cleaned
{ la-s/
the.F-PL/
esta-s}
this.F-PL
baba-s
drool-PL
de
of
la
the
cara.
face
‘Juan cleaned {the/ these} drools off his face.’
It is worth noting that the data about determiner selection indicates the following: the determiners compatible with plural mass nouns track plural-marking, not the noun being count. For instance, they are acceptable with plural demonstratives but are unacceptable with several or varios which require the noun to
be count in addition to plural-marked. This indicates that we need to disentangle being plural-marked from
being count. As we will see shortly, the source of number-marking in plural mass nouns differs from differs
plural-marked count nouns.
Ellipsis options. Number mismatches under ellipsis with plural mass nouns are independently ruled out
given that they lack an unmarked singular counterpart. In this respect, they pattern like canonical mass nouns.
As such, they allow noun and classificatory adjective ellipsis with a QA remnant. This is shown in (42) and
(43).
(42) This beer company buys too {much/ %many} Spanish hops...
feature, as originally proposed by Wellwood (2015). The dimension of measurement in the semantics, as I argue in Chapter 4, is
independent of the surface form. This is in line with proposals such as Wellwood (2015, 2018); Cleani and Toquero-Pérez (2022).
35

a. and that beer company buys too {much/ %many} Spanish hops as well.
b. * and that beer company buys too {much/ %many}
⎧
{
{
{
⎨
{
{
{
⎩
Spanish
Chinese
⎫
}
}
}
⎬
}
}
}
⎭
hops as well.
(43) Este
this.M
país
country
recibió
received
mucho-s
much.M-PL
vívere-s
provision-PL
español-es...
Spanish-PL
Lit. ‘The country received many Spanish provisions’
Int. ‘The country received (too) {much/ %many} Spanish provisions’
a. y
and
aquel
that
recibió
received
mucho-s
much.M-PL
vívere-s
provision-PL
español-es
Spanish-PL
también
too
Lit.: ‘and that one received many too’
Int.: ‘and that one received (too) {much/ %many} as well’
b. * y
and
aquel
that
recibió
received
mucho-s
much.M-PL
vívere-s
provision-PL
español-es
Spanish-PL
también
too
Lit.: ‘and that one received many Spanish too’
Int.: ‘and that one received (too) {much/ %many} Spanish as well’
We can test, however, whether they pattern like canonical mass or count nouns in terms of one-substitution.
If they are really underlyingly mass despite plural-marking, one-substitution will not be acceptable. The relevant data are in (44) and (45).
(44) one- substitution
a. Ted saw the bubbles on the sponge and the one(s) on the sink.
b. * Ted saw the suds on the sponge and the ones on the sink.
(45) otro-substitution
36

a. Juan
Juan
vio
saw
esto-s
this.M-PL
lote-s
batch-PL
en
in
el
the
almacén
storehouse
y
and
María
María
vió
saw
{ esto-s
this.M-PL
otro-s/
other.M-PL
este
this.M
otro}
other.M
en
in
la
the
despensa.
pantry
Lit.: ‘Juan saw these batches in the storehouse and María saw {these others/ this other} in the
pantry.’
Int.: ‘Juan saw these batches in the storehouse and María saw {these ones/ this one} in the
pantry.’
b. * Juan
Juan
vio
saw
esto-s
this.M-PL
vívere-s
provision-PL
en
in
el
the
almacén
storehouse
y
and
María
María
vió
saw
{ esto-s
this.M-PL
otro-s/
other.M-PL
este
this.M
otro}
other.M
en
in
la
the
despensa.
pantry
Lit.: ‘Juan saw these provisions in the storehouse and María saw {these others/ this other} in
the pantry.’
Int.: ‘Juan saw these provisions in the storehouse and María saw {these ones/ this one} in the
pantry.’
The example in (44a) is the baseline with a plural count noun which is semantically similar, e.g. bubbles,
to the plural mass suds as an antecedent. The pronominal form one, regardless of whether it is plural-marked
or not, can replace the noun in the second conjunct. The sentence contrasts with the one in (44b), where
bubbles has been replaced with suds. One-substitution is unacceptable in this context, just like with saw with
water in (19b). Likewise, in Spanish, otro can replace the (count) noun lote ‘batch’ in (45a); but, when otro
targets the plural mass noun víveres ‘provisions’ for substitution, the result in (45b) is unacceptable.
Up to this point, the summary of the morpho-syntactic properties of plural mass nouns is given in the
updated version of Tables 2.2 and 2.3.
The data in Table 2.4 and Table 2.5 indicate that plural mass nouns are really mass and have little in
common with count nouns apart from overt plural-marking. This overlap in plural-markedness raises the
question of where plural marking is coming from. In other words, does the realization of plural have the
37

Table 2.4: Morpho-syntactic properties of ‘canonical’ and plural mass & count nouns (to be updated)
Canonical Mass PL Mass Count
SG/PL distinction * * ✓
Direct modification by numerals * * ✓
Modification by Stubbornly Distributive adjectives * * ✓
Number mismatches under ellipsis NA NA ✓
one/otro-substitution * * ✓
Table 2.5: Restrictions on determiner selection (to be updated)
Class of Determiner Mass Count
Canonical PL SG PL
Class 1: Count-only * * ✓ ✓
Class 2: SG-count only * * ✓ *
Class 3: PL-count only * * * ✓
Class 4: Mass & PL-count ✓ ✓ * ✓
Class 5: Underspecifed ✓ ✓ ✓ ✓
same source in dregs, fumes, suds as in toys, chairs, children? We can empirically test whether plural in
these two different types of noun classes comes from the same syntactic source by looking at Noun-Noun
compounds.
The source of plural marking Descriptively, noun-noun compounds in English are right-headed, which
means that the rightmost noun is the head of the compound while the leftmost noun is a modifier or complement of that head (Williams and di Sciullo 1987; Snyder 1995, 2012). Number inflection in compounds
always surfaces on the head noun, never on the non-head. What is more, the non-head noun can never be
plural-marked. This is all shown in Table 2.6.
Table 2.6: Plural marking on noun-noun compounds with two count nouns
unmarked compound plural head noun plural non-head noun plural on both nouns
a. street dogH street dogs *streets dog *streets dogs
b. bus driverH bus drivers *buses driver *buses drivers
38

The non-head nouns in the examples in Table 2.6 are count nouns which allow overt plural marking
outside of compounds: street-s and bus-es. The fact that they disallow plural marking in the non-head position
of compounds is generally taken to indicate that the non-head constituent is syntactically small: it consists of
the root and the categorizer, but no additional functional structure such as Number (Wiltschko 2008; Harley
2009).
If the source of plural-marking on plural mass nouns is the same as in count nouns, we expect these nouns
to be unmarked for number when occurring as the non-head of noun-noun compounds. If, on the contrary,
the source of plural marking is different and has a ‘more lexical’ source, we expect plural marking to remain
unaffected.12 The relevant data are in (46).13
(46) Number marking on noun-noun compounds with a plural mass non-head
a. Suds dispenser(s) *sud dispenser(s)
b. Dregs filter(s) *dreg filter(s)
c. Fumes extractor(s) *fume extractor(s)
d. Hops meter(s) *hop meter(s)
All the data in (46) are canonical noun-noun compounds: they are right headed as indicated by the possibility of plural-marking. What is crucially different from the examples in Table 2.6 is that plural-marking
on the non-head is obligatory. In fact, lack of plural-marking leads to unacceptability. This is a novel observation about plural mass nouns and it has important consequences for the syntactic structure of these nouns:
12I am using the expression ‘more lexical’ purely descriptively to refer to the pieces of morpho-syntax that impose unpredictable
idiosyncrasies on certain objects such as roots. Analytically, by ‘lexical’ in this context, what I have in mind is the role that a
certain local morpheme (or syntactic terminal) has in determining the interpretation or form of a root: the closer to the root a
syntactic terminal is, the more likely it will be to trigger semantic or phonological changes in that root (see Embick 2015, for an
overview). Typically in DM-style syntax, which is assumed throughout this dissertation, categorizers are more local to the root than
other functional heads (i.e. Number or D) and may have an impact on the form and/or interpretation of the root if certain locality
conditions are met (Marantz 1997, 2001, 2013; Harley 2014; Embick 2015; Moskal 2015; Moskal and Smith 2016; Wood 2016,
2023).
13The judgments have been verified by 10 different native speakers of North American English (9 from the US, and 1 from
Canada).
39

the source of plural-marking is structurally closer to the root than the source of regular plural-marking with
count nouns.14
We can employ the same diagnositcs for Spanish. In Spanish, noun-noun compounds are left-headed as
opposed to English (Piera 1995; Snyder 1995, 2012; Toquero-Pérez 2020): in an endocentric compound that
has two nouns, the head of the compound is the noun on the left. This noun carries number inflection and
triggers agreement with determiners (and modifiers). The non-head can never be inflected for number. This
is shown in (47).
(47) Plural marking on noun-noun compounds with two count nouns in Spanish
a. ‘bracelet watch’ (i.e. watch that has a strap)
i. El
the.M
relojH
watch.M
pulsera
bracelet.F
ii. Lo-s
the.M-PL
reloj-es
watch.M-PL
pulsera
bracelet.F
iii. * El
the.M
reloj
watch.M
pulsera-s
bracelet.F-PL
iv. * Lo-s
the.M-PL
reloj-es
watch.M-PL
pulsera-s
bracelet.F-PL
b. ‘bus pumpkin’ (i.e. pumpkin that is similar to or functions as a bus)
i. La
the.F
calabazaH
pumpkin.F
autobús
bus.M
ii. La-s
the.F-PL
calabaza-s
pumpkin.F-PL
autobús
bus.M
iii. * La
the.F
calabaza
pumpkin.F
autobus-es
bus.M-PL
iv. * La-s
the.F-PL
calabaza-s
pumpkin.F-PL
autobus-es
bus.M-PL
Given that the non-head noun in a compound never inflects for number, as illustrated in (47a-iii) and
(47b-iii), there are two potential outcomes for plural mass nouns in compounds: (i) plural mass nouns must
be unmarked for number in this syntactic context; (ii) plural mass nouns must retain plural marking in this
syntactic context. If (i) is borne out, this is evidence that plural-marking in both baba-s ‘drooling’ and
autobús-es ‘buses’ has the same syntactic source; if (ii) is borne out, then we can conclude that the sources
14A potential exception to this observation comes from oats, which may appear unmarked in the non-head position: oat milk, oat
latte vs. *oats milk, oats latte.
40

of plural-marking are different, just like we did for English. The data in (48) have been accepted by 10 native
Spanish speakers from Spain with the meanings indicated in parenthesis.15
(48) Number marking on noun-noun compounds with plural mass non-head in Spanish
a. ‘drooling boy’ (i.e. boy that has/does a lot of drooling)
i. El
the.M
niño
kid.M
baba-s
drool.F-PL
ii. Lo-s
the.M-PL
niño-s
kid.M-PL
baba-s
drool.F-PL
iii. * El
the.M
niño
kid.M
baba
drool.F
iv. * Lo-s
the.M-PL
niño-s
kid.M-PL
baba
drool.F
b. ‘muscle sores exercise’ (i.e. exercise that causes muscle sores’)
i. El
the.M
ejercicio
exercise.M
agujeta-s
muscle sore.F-PL
ii. Lo-s
the.M-PL
ejercicio-s
exercise.M-PL
agujeta-s
muscle sore.F-PL
iii. * El
the.M
ejercicio
exercise.M
agujeta
muscle sore.F
iv. * Lo-s
the.M-PL
ejercicio-s
exercise.M-PL
agujeta
muscle sore.F
The noun-noun compounds in (48a-i) and (48b-i) show that the plural mass nouns babas ‘drooling’ and
agujetas‘muscle sores’ can be plural-marked when they occur as non-heads in compounds. The acceptability
of these compounds is in stark contrast with (48a-iii) and (48b-iii): removing the plural marking from the
mass noun results in unacceptability. As (48a-ii) and (48b-ii) and their counterparts in (48a-iv) and (48b-iv)
show, plural marking on the non-head is not contingent on the head being plural-marked. The conclusion
that we can draw from this is that the source of plural-marking on plural mass nouns differs from the source
of plural marking in plural count nouns. This is the same observation that we extracted for English.
15It is worth noting that noun-noun compounding in Spanish is not as creative as it is in English, i.e. a process is creative “if
it is available for automatic, impromptu use whenever a new word is needed to fit the occasion” (Snyder 2016, p.91). This entails
that speakers are less readily open to accept novel noun-noun combinations. In fact, as Toquero-Pérez (2020) shows, few semantic
relations underlying noun-noun compounds seem to be readily available in Spanish.
41

2.3 Object mass nouns.
The last class of nouns that is relevant for the count-mass distinction encompasses those nouns that denote
collections or groups of objects that stand in some kind relation with each other. A non-exhaustive list of
nouns that have been generally identified as belonging to this class is given in (49). The English data have
been taken from Lieber (2016); Cohen (2020).16
(49) a. Jewelry, drapery, baggage, luggage, footwear, daywear, carpeting, lighting, furniture …
b. joyería,
jewelry
cubertería,
silverware
peonaje,
construction workers
follaje,
foliage
accionariado,
shareholders
profesorado,
faculty
armamento,
weaponry
bastimento,
supply
mobiliario
furniture
…
A first look at these nouns seems to indicate that they are morphologically complex. For example, certain
affixes can be identified in both languages such as -ery, -age, -wear in English and -ería, -aje or -ado in
Spanish. While one might be concerned with the possibility that the distributional properties of these nouns
differ based on the affix, I will show that this is not the case. Thus, from now on I will use nouns with different
affixes as an illustration. We will go back to morphological considerations towards the end of this section.
Number marking and modification. These nouns all trigger singular agreement both DP-internally and
externally, as in (50). In addition, they resist plural-marking (Bunt 1985; Gillon 1992, 1999; Doetjes 1997;
Chierchia 1998a, 2010, 2021; Borer 2005a; Bale and Barner 2009). This property is illustrated in (51).
(50) Singular agreement
a. {This furniture was/ *these furniture were} brought in this morning.
16Nouns ending in -ería in Spanish can have a count interpretation when referring to a location. For example, joyería in (iv) picks
out the store were jewelry is sold. In this section, and in the dissertation, I will not discuss these cases. We can assume that the
underlying structures of the location and object mass nouns must differ, despite the fact that the same vocabulary item is used (De
Belder 2011; Lieber 2016).
(iv) { La
the.F
joyería/
jewelry
la-s
the.F-PL
joyería-s}
jewelry-PL
de
of
la
the
calle
street
Serrano
Serrano
de
of
Madrid
Madrid
‘The jewelry store(s) in Calle Serrano in Madrid’
42

b. {This jewelry is/ *these jewelry are} not suitable for piercing.
c. { Este
this.M
mobiliario
furniture
llegó/
arrived.3SG
*Esto-s
this.M-PL
mobiliario
furniture
llegaron}
arrived.3PL
por
for
la
the
mañana.
morning
‘{This furniture/ these furniture} arrived in the morning.’
d. { Esta
this.F
joyería
jewelry
es/
is.3SG
*Esta-s
this.F-PL
joyería
jewelry
son}
are.3PL
solo
only
para
for
punkies
punks
‘{This jewelry is/ these jewelry are} only for punks.’
(51) Incompatibility with plural-marking
a. * the furniture-s, the jewelr-ies, the baggage-s, the footwear-s
b. * Lo-s
the.M-PL
mobiliario-s,
furniture-PL
la-s
the.F-PL
joyería-s,
jewelry-PL
lo-s
the.M-PL
follaje-s,
foliage-PL
lo-s
the.M-PL
profesorado-s
faculty-PL
The unavailability of plural-marking with these nouns also correlates with the unavailability of cardinal
numeral modification. Cardinal numerals cannot directly modify object mass nouns. Numeral modification
is only possible via a pseudo-partitive structure (Doetjes 1997; Chierchia 1998b, 2010, 2021; Borer 2005a;
Bale and Barner 2009). This is shown in (52) for English and in (53) for Spanish.
(52) Impossibility of direct numeral modification in English
a. * Barney bought three jewelry(-s). ⇝ Barney bought three pieces of jewelry.
b. * Mom can’t find one silverware. ⇝ Mom can’t find one piece of silverware.
(53) Impossibility of direct numeral modification in Spanish
a. * Barney
Barney
compró
bought
tres
three
joyería(-s).
jewelry-PL
⇝ Barney
Barney
compró
bought
tres
three
piezas
pieces
de
of
joyería
jewelry
‘Barney bought three jewelry(-s) ⇝ Barney bought three pieces of jewelry’
b. * Mamá
mom
no
NEG
encuentra
finds
una
one
cubertería.
silverware
⇝ Mamá
mom
no
NEG
encuentra
finds
una
one
pieza
piece
de
of
cubertería
silverware
‘Mom can’t find one silverware ⇝ Mom can’t find one piece of silverware’
These two properties, i.e. impossibility of overt-plural marking and direct numeral modification, make
this class of nouns pattern with the two classes of mass nouns described so far. Nevertheless, unlike these
43

classes of mass nouns, object mass nouns allow modification by stubbornly distributed adjectives (Schwarzschild
2011; Deal 2016a, 2017; Doetjes 2021). This is shown in (54) for English and in (55) for Spanish.
(54) Modification by Stubbornly Distributive adjectives in English
a. The furniture in this room is large.
b. The large furniture in the room was mounted overnight.
(55) Modification by Stubbornly Distributive adjectives in Spanish
a. El
the.M
mobiliario
furniture
en
in
esta
this
habitación
room
es
is
grande.
large
‘The furniture in this room is large’
b. El
the.M
mobiliario
furniture
grande
big
de
of
esta
this
habitación
room
se
SE
instaló
installed
por
for
la
the
noche.
night
‘The large furniture in this room was mounted overnight’
In both (54a) and (55a), the adjective large/grande can be used as a predicate of a copula whose subject
is the DP the furniture/el mobiliario. Likewise, the same adjective can be used DP-internally, to modify the
noun furniture/mobiliario as in (54b) and (55b). In this respect, they pattern with the class of count nouns.17
Determiner selection. Up to this point, the data indicate that nouns like jewelry, weaponry, furniture,
luggage etc. show mixed properties: on the one hand, they largely pattern with mass nouns; on the other,
they do not. Data from determiner selection will help us make a more accurate characterization of this class
of nouns. Starting with Class 1, the Spanish data in (56) show that determiners that require the noun to be
count cannot combine with the nouns in question.
(56) Class 1: count-only determiners in Spanish
17Bale and Barner (2009) observe that object mass nouns pattern with plural count nouns in their semantic interpretation when
modified by comparatives: more furniture and more chairs are both interpreted in terms of cardinality. In Chapter 4 I will concentrate
on this property.
44

a. * Enviaron
sent.3PL
{ algún/
some.M/
un/
a.M/
todo}
every.M
armamento
weaponry
desde
from
la
the
base.
base
Int.: ‘They sent {a/ every} weaponry from the base’
b. * { Algún/
some.M/
un/
a.M/
todo}
every.M
equipaje
luggage
se
SE
perdió
lost.3SG
en
in
LAX.
LAX
Int.: ‘{A/ Every} luggage was lost at LAX’
The unmarked form of Class 1 determiners is not acceptable to occur with armamento ‘weaponry’ and
equipaje ‘luggage’ in (56). Similarly, Class 2 determiners are also unacceptable with these nouns as the
English and Spanish examples in (57) and (58) show.
(57) Class 2: singular-count only determiners in English
a. * {A/ Every/ Each } jewelry was made of gold.
b. * Mom auctioned {a/ every/ each} silverware.
(58) Class 2: singular-count only determiners in Spanish
a. * { Cada/
each/
Cualquier}
any
joyería
jewelry
de
of
la
the
tienda
store
es
is
de
of
oro.
gold
‘{Each/ any} jewelry in the store is made of gold’
b. * Mamá
mom
perdió
lost
{ cada/
each/
cualquier}
any
equipaje
luggage
en
in
LAX.
LAX
‘Mom lost {each/ any} luggage at LAX’
Determiners that track plural-count nouns, that is Class 3, are also unacceptable with these nouns. As
shown in (59) and (60), several/varios cannot occur with jewelry-type nouns. It is worth noting here that
making the noun overtly plural in these context is independently ruled out as already discussed.
(59) Class 3 plural-count only determiners in English
a. * Barney bought several jewelry in Downtown LA.
b. * Several weaponry was found in the back of Barney’s truck?
45

(60) Class 3 plural-count only determiners in Spanish18
a. * Compré
bought.1SG
varias
several.F.PL
joyería
jewelry
a
DOM
mi
my
mujer
woman
en
in
el
el
Corte
Corte
Inglés
Inglés
‘I bought several jewelry for my wife in El Corte Inglés’
b. * La
the
policía
police
incautó
seized
varios
several.M.PL
armamento
weaponry
en
in
la
the
frontera
border
con
with
Francia
France
‘The police seized several weaponry at the French border’
The determiner data presented so far are important because they indicate that syntactically these nouns
are not count, but actually mass. The “mystery” is then the situation with adjectival modification.
Class 4 determiners are perfectly compatible with these mass nouns. This is shown in the examples in
(61) and (62).
(61) Class 4: Mass & Plural-count determiners in English
a. Barney bought {all/ so much/ *many/ more} furniture in Ikea.
b. {All/ So much/ *Many/ More} jewellery is yet to be pawned.
(62) Class 4: Mass & Plural-count determiners in Spanish
a. Barney
Barney
compró
bought
{ todo
all.M
el/
the.M/
mucho/
much.M/
tanto/
as.much.M/
más}
more
armamento
weaponry
en
in
el
the
mercado
black
negro.
market
‘Barney bought {all/ (so) much/ as much/ more} weaponry in the black market.’
b. Últimamente,
lately
nadie
nobody
lleva
carries
{ toda
all.F
la/
the.F/
mucha/
much.F/
tanta/
as.much.F/
más}
more
joyería
jewellery
puesta.
put.F
‘Lately, nobody wears {all/ (so) much/ as much/ more} jewellery’
If we look at the English data in (61), it is important to note that the marked form of the QA, i.e. many,
is unacceptable. Only the unmarked form, much, is grammatical. In the Spanish data in (62), we see that the
lack of overt plural marking on the noun results in a lack of plural marking on the QA and other determiners.
18El Corte Inglés is a department store in Spain. The equivalent in the US would be something like Macy’s or Nordstrom.
46

Last but not least, all the determiners from Class 5 are acceptable with this class of mass nouns. This is
expected if these determiners are underspecifed for the count-mass distinction. The relevant data are in (63)
and (64).
(63) Class 5: Determiners underspecified for the count-mass distinction in English
a. Barney stole {the/ some/ no/ this} jewelry from Tiffany’s.
b. {The/ Some/ No/ This} stolen luggage has been returned to us.
(64) Class 5: Determiners underspecified for the count-mass distinction in English
a. Robaron
stole.3PL
{ la/
the.F/
esta}
this.F
joyería
jewelry
cara
expensive
de
of
Tiffany’s.
Tiffany’s
‘They stole {the/ this} expensive jewelry from Tiffany’s’
b. { El/
the.M/
Este}
this.M
armamento
weaponry
llegó
arrived
finalmente
finally
a
to
su
his
destino.
destination
‘{The/ This} weaponry finally reached its destination.’
Ellipsis options. Turning to ellipsis, the lack of an overt plural counterpart makes number mismatches
under ellipsis with these nouns impossible. As illustrated in (17), however, it is possible for the whole mass
NP to be deleted under identity stranding a QA. Some examples are in (65).
(65) Mass NP ellipsis under QA
a. Barney bought too much wooden furniture, but Ted didn’t buy as much wooden furniture.
b. * Barney bought too much wooden furniture, but Ted didn’t buy as much wooden furniture.
c. Barney
Barney
compró
bought
mucho
much.M
mobiliario
furniture
europeo,
european
pero
but
Ted
Ted
no
NEG
compró
bought
tanto
as.muchM
mobiliario
furniture
europeo
european
‘Barney bought too much european furniture, but Ted didn’t buy as much’
47

d. * Barney
Barney
compró
bought
mucho
much.M
mobiliario
furniture
europeo,
european
pero
but
Ted
Ted
no
NEG
compró
bought
tanto
as.muchM
mobiliario
furniture
europeo
european
‘Barney bought too much european furniture, but Ted didn’t buy as much european’
The data in (65) show that a QA can serve to delimit the ellipsis site. Once again, when there is a
classificatory adjective like wooden or europeo ‘European’, the adjective must be contained in the ellipsis
site. Failure to do so results in unacceptability as the sentences in (65b) and (65d) show. This is evidence
that what is being elided is larger than just the nominal root itself.
Despite the inability to test for number mismatches under ellipsis, we can apply the one/otro-substitution
test. This test has proved successful in determining whether a noun is syntactically count or not. None of the
classes of mass nouns so far described allow for one/otro-substitution, whereas count nouns do. The relevant
data for object mass nouns are given in (66) and (67).
(66) one-substitution
a. Ted pawned the jewel from his grandmother and the one from his mom.
b. * Ted pawned the jewelry from his grandmother and the one from his mom.
(67) otro-substitution
a. Ted
Ted
empeñó
pawned
esta
this.F
joya
jewel
de
of
su
his
abuela
grandmother
y
and
esta
this.F
otra
other.F
de
of
su
his
madre.
mother
Lit.:‘Ted pawned this jewel from his grandmother and this other from his mother’
Int.: ‘Ted pawned this jewel from his grandmother and this one from his mother’
b. * Ted
Ted
empeñó
pawned
esta
this.F
joyería
jewelry
de
of
su
his
abuela
grandmother
y
and
esta
this.F
otra
other.F
de
of
su
his
madre.
mother
Lit.:‘Ted pawned this jewelry from his grandmother and this other from his mother’
Int.: ‘Ted pawned this jewelry from his grandmother and this one from his mother’
48

Once again, we observe that when a count noun root, in this case a singular one (66a) and (67a), is in
the first conjunct, its counterpart in the second conjunct can be a target for one/otro-substitution. However,
when the nominal root in the first conjunct is an object mass noun root, one/otro-substitution cannot target
such constituent in the second conjunct. This is observed in (66a) and (67a), where the object mass noun
jewelry/joyería shares the same morphological base as its count counterpart jewel/joya.
Up to this point, the summary of the morpho-syntactic properties of object mass nouns is given in the
final version of Table 2.2 and Table 2.3, here labeled Table 2.7 and Table 2.8.
Table 2.7: Morpho-syntactic properties of all mass & count nouns (final version)
Canonical Mass PL Mass Object Mass Count
SG/PL distinction * * * ✓
Direct modification by numerals * * * ✓
Modification by Stubbornly Distributive adjectives * * ✓ ✓
Number mismatches under ellipsis NA NA NA ✓
one/otro-substitution * * * ✓
Table 2.8: Restrictions on determiner selection (final version)
Class of Determiner Mass Count
Canonical PL Object SG PL
Class 1: Count-only * * * ✓ ✓
Class 2: SG-count only * * * ✓ *
Class 3: PL-count only * * * * ✓
Class 4: Mass & PL-count ✓ ✓ ✓ * ✓
Class 5: Underspecifed ✓ ✓ ✓ ✓ ✓
The nouns under discussion in this section have patterned like all mass nouns except for the fact that they
can be modified by stubbornly distributed predicates, which none of the other mass noun classes allowed.
In addition, it is worth noting that these nouns, unlike canonical mass nouns, resist pluralization at all costs:
while pluralization of canonical mass nouns is unacceptable with a substance interpretation but it is acceptable under a container or a kind interpretation, potentially suggesting count syntax (Borer 2005a; Ott 2011;
Mathieu 2012; Mathieu and Dali 2021), pluralization of object mass nouns is always ungrammatical.
49

Object mass nouns: morphological complexity It is not uncommon to assume that object mass nouns
are listed in the lexicon with the same underlying form that they surface with (Chierchia 1998a, 2010, 2021;
Bale and Barner 2009; Rothstein 2010, 2017). Under this view, object mass nouns do not have a complex
morphological structure: there is a root morpheme √JEWELRY and that morpheme is mapped to the surface
form jewelry. However, a closer examination of the data shows that a significant number of object mass nouns,
if not all of them, is morphologically complex and falls under the umbrella of productive nominalization
processes (De Belder 2011; Alexiadou 2015; Lieber 2004, 2016; Cohen 2020).
First of all, the root morphemes that participate in the class of object mass nouns also participate in the
class of count nouns. In other words, the set of count noun roots overlaps with the set of object mass roots.
As a result, languages with a productive class of object mass nouns tend to have doublets like the ones in
Table 2.9, organized by the morphemes identified in Cohen (2020).
Table 2.9: count and object mass doublets in English
-ware -wear -(e)ry -age -ing
Count Object Mass Count Object Mass Count Object Mass Count Object Mass Count Object Mass
kitchen kitchen-ware foot foot-wear jewel jewel-ry bag bagg-age light light-ing
table table-ware beach beach-wear drape drap-ery lug lugg-age carpet carpet-ing
silver silver-ware day day-wear gadget gadget-ry word word-age bed bedd-ing
gift gift-ware neck neck-wear image imag-ery sign sign-age pipe pip-ing
Looking at the data in Table 2.9, we observe that the same root morpheme that is found in a count noun
is also found in object mass nouns. This is a common pattern across all the 5 morphemes identified. Second
of all, the data indicate an additional pattern: the count noun seems to serve as the base for the object mass
noun, but not the opposite. This generalization seems too robust to be ignored.
Despite the fact that doublets are common and productive (Lieber 2016; Cohen 2020), it is not always
the case that object mass nouns have a count noun counterpart. This is the situation with furniture, cutlery or
equipment. There is no vocabulary item *furnish, *cutle or *equip that means ‘furniture piece’, ‘cutting tool’
or equipment piecerespectively. The lack of the count vocabulary item can thus be seen as a lexical gap in the
50

English lexicon. However, the fact that these prototypical object mass nouns lack a count noun counterpart
does not entail that these nouns are morphologically simplex. In fact, vocabulary items like furniture and
cutlery can be decomposed into smaller parts. In the case of the former, the surface form is related to
expressions such as furnish (verb) and furnishing (gerund, noun): all three forms share a root √FURNI(SH).
Similarly, in the case of cutlery, the noun is related to the expression cutlet (noun) which is also related to cut
(noun, verb): all three vocabulary items are related by virtue of sharing the same root √CUT. The situation
with equipment is the same: equip (verb) and equipment both share the same root √EQUIP. Therefore, it does
not seem unreasonable to hypothesize that these object mass nouns are also morphologically complex.19
It is also worth noting that some of the morphemes in Table 2.9 (namely -age, -ing and -ery) may give
rise to (at least) two different types of object mass interpretations: (i) a collective interpretation, i.e. ‘the
collection of X-related things’; and, (ii) an eventive interpretation, i.e. ‘the result of doing X or being an
X’. The difference between the two has been typically argued to be due to the base to which the object mass
morpheme attaches (Alexiadou 2015; Lieber 2016; Cohen 2020): the collective interpretation arises when
the base is a noun, whereas the eventive interpretation arises when the base is a verb. As a result some object
mass nouns may be ambiguous between the two: carpeting ‘a collection of carpet-looking items’ or ‘the
result of covering a surface with a carpet’.
The same sets of facts are found in Spanish as well. As seen in Table 2.10, there are several count-object
mass doublets. In this case too, the count counterpart is less morphologically complex and the object mass
noun seems to be built on top of it. Some morphemes, namely -aje, -ería are more productive.
As also observed in Table 2.10, the object mass affix may trigger suppletion on the root: mueble[count]
‘piece of furniture’ vs mobil-iario[object mass] ‘furniture’; cubierto[count] ‘piece of silverware’ vs cubert-ería[object mass]
‘silveware’. In addition, a subset of these object mass affixes can give rise to eventive interpretations. These
19We can think about the relation between these forms in parallel to the relation that exists between sing(s), singer, sang and song:
they are not lexical primitives, but are all related to the root √SING (Embick 2015, p.18).
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Table 2.10: count and object mass doublets in Spanish
-aje -ería
Count Object Mass Count Object Mass
peón
‘laborer’
peon-aje
‘collection of laborers’
joya
‘jewel’
joy-ería
‘jewelry’
mestizo
‘mestizo’
mestiz-aje
‘collection of mestizos’
chiquillo
‘little kid’
chiquill-ería
‘collection of little kids’
equipo
‘outfit/utensil’
equip-aje
‘baggage’
cubierto
‘silverware piece’
cubert-ería
‘silverware’
hoja
‘leave’
foll-aje
‘foliage’
piel
‘fur’
pele-tería
‘furriery’
-mento -ado -(i)ario
Count Object Mass Count Object Mass Count Object Mass
arma
‘weapon’
arma-mento
‘weaponry’
profesor
‘teacher’
profesor-ado
‘collection of teachers/faculty’
mueble
‘furniture piece’
mobil-iario
‘furniture’
carga
‘load’
carga-mento
‘collection of goods’
accionario
‘shareholder’
accionari-ado
‘collection of shareholders’
equipo
‘outfit/utensil’
equipa-miento
‘utensils’
primarily include -aje ‘-age’ and -mento ‘-ment’. Thus, an object mass noun like the one in (68) may be
ambiguous between the two interpretations described for English.
(68) arma-mento
weapon-MENT
Lit.: ‘weapon-ment’
Int.: ‘weapon-ry’
a. collection of weapons
b. the result or action of equipping with weapons
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Based on these observations about the morphological form and the potential interpretive ambiguities that
these object mass nouns may give rise to in English and Spanish, we can summarize the generalizations with
the pretheoretical structural descriptions in (69).20
(69) a. [[√⏟⏟⏟⏟⏟⏟⏟ ROOT COUNT
carpet
] OBJECT MASS ⏟⏟⏟⏟⏟⏟⏟
-ing
] ⇝ ‘collective’
b. [[√⏟⏟⏟⏟⏟⏟⏟ ROOT VERB
carpet
] OBJECT MASS ⏟⏟⏟⏟⏟⏟⏟
-ing
] ⇝ ‘eventive’
As the generalizations illustrate, there is more structural complexity to object mass nouns than it is sometimes assumed; and certainly, the nouns of this class are more complex morphologically than the other subclasses of mass nouns described. In particular, (i) the possibility to morphologically decompose nouns belonging to this class and (ii) establishing a connection between count noun (and verb) bases and object mass
nouns can shed some light on why these nouns show some degree of overlap between canonical mass nouns
and count nouns.
An interesting hypothesis that we may entertain at this point, and that I will ellaborate more on in Chapter 3 Section 3.2.3 is that object mass nouns, at least on the collective interpretation, are always formed on
top of count noun bases. That is, a morpheme like -aje/-ery etc. always requires a count nominal root as
input. This intuition seems to receive support from the semantic interpretation of nouns when modified by
QAs. As it has been observed (Bale and Barner 2009), and I will describe as well in Chapter 4, both plural
count nouns and object mass must be measured along the same scale: more jewelry and more jewels are
always interpreted in terms of cardinality. If object mass nouns are built on top of a count noun root, then we
might have a potential avenue for explaining this parallel: the object mass noun inherits the count structure
compositionally.
In addition, another potentially welcome consequence of this hypothesis is the relation between object
mass morphemes and number inflection, which is generally hard to explain. If object mass noun morphemes
20For more details and similar cross-linguistic patterns, see De Belder (2011, 2013, for Dutch), Alexiadou (2015, for Greek) and
Cohen (2020, for French, English and Hebrew).
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require a count noun as input, and so does the projection hosting number morphemes, then both types of
morphemes need the exact same requirement to be syntactically met. As a result, under this view one can
think of the distribution of number morphemes and the object mass morpheme as complementary:21 when
you find one, you do not find the other. Thus, the unacceptability of plural-marking on object mass nouns
can be modeled in terms of competition.
2.4 Taking stock
The data discussed so far has served to group nouns into two descriptively adequate categories based on a
series of grammatical properties such as number-marking, numeral and adjectival modification, sensitivity
to determiners and availability of one-substitution. Nouns that show all these are ‘count’ while those that do
not allow any or most of these are referred to as ‘mass’. Within ‘mass’, there are three classes: canonical or
unmarked mass, plural mass and object mass. Regarding the last of them, the class shows some overlap with
the class of count nouns; namely, stubbornly distributed adjective modification and the existence of count
noun root counterparts from which they seem to be derived.
An empirical observation that can be formulated is concerned with being plural-marked and being count.
It is summarized in (70).
(70) The Plural-Count Generalization
In some languages (e.g. English and Spanish) plural-marking on the noun does not entail count noun
syntax.
The generalization captures the fact that plural count nouns are just a subset of pluralizable nouns. This
generalization is consistent with Rothstein’s (2021) observation that plural-marking on a noun is not contingent upon said noun being count, contrary to what is often presupposed, e.g. Chierchia (1998a, 2010). A
21I want to remind the reader that what I mean by ‘complementary’ is what phonologists refer to as ‘overlapping’ or ‘parallel’.
See footnote 1 in Chapter 1 for details.
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conclusion from this is that the semantic effect that pluralization has (i.e. sum formation or grouping) needs
to be separated from whatever grammatical mechanism is responsible for individuation or the introduction
of discrete units that enable count syntax and semantics.
Related to this, we can also concentrate on the classes of nouns identified and their relation to numbermarking and the surface form of QAs. This is summarized in Table 2.11.
Table 2.11: Number marking and choice of QA by noun type in English and Spanish
Langs. Agreement QA form
Type of N SG PL Unmarked
(much/mucho)
PL-Marked
(many/muchos)
Canonical Mass English ✓ * ✓ *
Spanish ✓ * ✓ *
Object Mass English ✓ * ✓ *
Spanish ✓ * ✓ *
PL Mass English * ✓ ✓ %
Spanish * ✓ * ✓
PL Count English * ✓ * ✓
Spanish * ✓ * ✓
Looking at Table 2.11, there is an important observation that deserve attention. There seems to be a
very strong correlation between plural-marking as instantiated on the noun, plural agreement with the verb
or DP-internally, and the surface form of the QA. I summarize this descriptive generalization, at face value,
in (71).
(71) The Plural-QA-markedness Generalization
Overt plural marking on the noun
a. forces the QA to be plural-marked in Spanish, and
b. makes it possible for the QA to surface as many in English.
The generalization narrows down the contexts in which the more marked forms of QAs can be found:
namely, when modifying plural count nouns and plural mass nouns. It is worth emphasizing that there is
55

a slight difference between the two languages discussed regarding whether markedness in the form of the
QA is enforced or simply made possible, given the variation observed in English plural mass nouns (e.g.
much/% many suds). Nevertheless, such variation can be indicative of the following: while inserting the
marked vocabulary item is the default when the noun is plural-marked, failing to do so can be the result of
impoverishment. In other words, a morphological rule deletes the relevant plural features before vocabulary
insertion of the marked item (Bonet 1991, 2008; Arregi and Nevins 2007, 2012, 2013). Variation can thus
be reducible to the availability, or lack there-of, of such a rule prior to vocabulary insertion.
The last set of generalizations is concerned with the selectional requirements that some determiners
impose on the noun with which they occur. I summarize the descriptive generalizations in (72):
(72) Determiner Selection Generalizations
a. If a determiner is sensitive to the noun being count, it will be also sensitive to number features.
b. If a determiner is sensitive to plural-marking, it need not be sensitive to the noun being count.
c. There is no determiner that is exclusively sensitive to the noun being mass.
These generalizations capture the fact that determiners such as every, each, several in English or todo(s),
cada, varios in Spanish track both the noun being count and it being number-marked. The statements in (72)
also appropriately describe that this is not a bidirectional relation: there are determiners that show sensitivity
to the noun being plural-marked but not necessarily to the noun being count (e.g. demonstratives, QAs,
definite determiners in Spanish etc.). This is very much in line with the Plurality-Count Generalization in
(70).
Last but not least, the findings lead to the conclusion that there is no determiner that occurs only with mass
nouns. While some might argue that this is not entirely true of QAs given the much/many and little/few asymmetries (Borer 2005a; Solt 2009), by separating these QAs into a ‘mass-only class’ and the plural-count-only
class respectively, we would loose an important language internal and also cross-linguistic generalization:
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the strong correlation between many/few and plural-marking. Besides, if much requires a mass constituent,
regardless of its label, it is unclear why in cases of imperfective telic predicates, which have been argued to
roughly correlate with plural count nouns (Mourelatos 1978; Bach 1986a; Krifka 1989; Borer 2005a,b; van
Geenhoven 2005; Wellwood et al. 2012), only much is acceptable. This is shown in (73).
(73) Barney ran to the store as {much/ *many} as Bill did.
In the next chapter, I propose a theory of individuation and number that derives the 4 morpho-syntactic
asymmetries between the classes of count and mass nouns. The proposal also accounts for the descriptive
generalizations put forth here. In fact, I will show that these empirical observations are rooted in more
abstract morpho-syntactic properties of the nouns in question.
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Chapter 3
A Theory of Individuation and Number for the Count-Mass Distinction
In the previous chapter, I surveyed different morpho-syntactic properties along which classes of nouns differed. These asymmetries included number-marking, modification by certain constituents, the choice of
determiner and the type of ellipses available. The overall picture that emerged was one where ‘being count’
is grammatically marked. One of the most compelling pieces of evidence for this was one/otro-substitution,
and the fact that determiners seem to track the noun being count, but no determiner seems to track the noun
being mass. But what does it mean to have ‘count’ grammatical properties? Or vice versa, what does it
mean to lack them? My answer to these questions in this chapter is that individuation and number are at the
core of count-noun syntax. In particular, I propose that ‘count’ and ‘mass’ nouns differ along two critical
dimensions, both of which are syntactically encoded:
• is the nominal root individuated or not?
• is Number projected in the syntax?
With respect to the first question, I propose that the presence of a feature [INDIVIDUATED] on the categorizer, the first syntactic node that an acategorial root adjoins to, is responsible for making discrete individuals
as part of the extension of the root available. This feature is what will enable the root to enter a count syntactic frame including enabling Number to project. It is in Number where [SINGULAR] and [PLURAL] are merged
(Ritter 1991). The contribution of these features is to mark the predicate as singular or plural. [SINGULAR]
58

will have the semantic effect of restricting the denotation of the noun to a singleton set of those discrete individuals (Krifka 1989; Gillon 1992; Rothstein 2004; Harbour 2007, 2011); in contrast, [PLURAL] will restrict
the denotation to non-singletons, i.e. sums of discrete individuals (Link 1983; Krifka 1995; Schwarzschild
1996; Sauerland 2003; Rothstein 2004; Harbour 2007, 2011). What makes a noun ‘count’ is the both being marked for [INDIVIDUATED] and [SINGULAR/PLURAL] (i.e. having Number). I will show that most of the
asymmetries here described fall out from projecting Number, including, but not limited to, modification by
numerals and Stubbornly Distributive adjectives.
In contrast, being ‘mass’ is better understood as the lack of count properties, in particular a Number
projection hosting [SINGULAR/PLURAL]. This claim entails that the while nouns like dregs must have a plural
feature, the location of said feature cannot be the same as in count nouns. The data from noun-noun compounds is strong evidence for the different source of plural-marking. Despite their not having a Number
projection, I will further show that mass nouns differ in whether or not they are marked for [INDIVIDUATED].
That is, while canonical mass nouns and plural mass nouns lack the [INDIVIDUATED] feature, and thus discrete individuals, object mass nouns will be specified as [INDIVIDUATED]. This feature is, I propose, what
they share in common with count nouns.
Unlike plural count nouns, however, object mass nouns will be not singular or plural-marked because
they do not project Number. Instead, they will be composed of a feature that I call [COLLECTIVE]. Such a
feature will be spelled out as -ery, -ment, -age, -ware on a root-by-root basis and be located on an outer head
that competes with Number to satisfy its selectional requirements. The insight is that object mass nouns
are morpho-syntactically complex objects which are built on an individuated constituent. I argue that this
explains why languages have count-object mass doublets (e.g. jewel-jewelry, leaf-foliage or the Spanish
counterparts joya-joyería, hoja-follaje) and why these object mass nouns cannot be plural-marked. Given
that both plural count nouns and object mass nouns are countable, (i.e. measured along a cardinality scale)
59

and they are [INDIVIDUATED]-marked, we can conclude that what makes an NP countable is the presence of
this feature.
In what follows, I spell out the pieces of theory in detail. Then, I move on to argue how the theory derives
the morpho-syntactic asymmetries described and generalizations identified. When relevant, I will also show
that the theory makes important predictions, which I argue are borne out.
3.1 The Proposal
3.1.1 Some necessary basics
I am assuming a generative approach to syntax as outlined by Chomsky (2000, 2001, 2008) and subsequent
work, in tandem with the Distributed Morphology model (Halle and Marantz 1993; Marantz 1997; Embick
and Noyer 2001; Embick 2007, 2010, 2015; Embick and Marantz 2008; Bobaljik 2012; Harley 2014). Under
DM, the terminal nodes provided and manipulated by the syntax are simply bundles of features. These
features may be interpretable or uninterpretable features. The interpretable features will be notated as [F]
and will have semantic import on the terminal that bears them. Uninterpretable features will be noted as
[𝑢F]. 𝑢Fs can themselves be unvalued or inherently valued (Pesetsky and Torrego 2007): [𝑢F:_] ∼ [𝑢F: val].
I further assume that all syntactic operations, including Merge and Move, are feature driven (Svenonius
1994; Adger 2003; Pesetsky and Torrego 2006; Heck and Müller 2007; Müller 2010; Folli and Harley 2020,
a.o.). I will represent c-selectional requirements as [•F•] when relevant. Following Adger (2003, p.67), I
assume that this c-selectional feature is checked under sisterhood: a feature [•F•] on a syntactic object Y is
checked when Y is sister to another syntactic object Z which bears a matching feature 𝐹. I will assume that
movement of a constituent 𝛼 to a position 𝛽 is triggered when an EPP feature is associated with an unvalued
feature; also following Adger (2003), I will represent such a movement-triggering EPP property with a ‘*’
on [𝑢F].
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Following Chomsky (2000) and others, I will assume that there is an operation called Agree between a
probe (with unvalued features) and a goal (with a feature that matches the probe’s). I further assume, as it
has become standard in the literature on Agree, that it involves a two-step process (Benmamoun et al. 2009;
Bhatt and Walkow 2013; Arregi and Nevins 2012; Smith 2021): (i) a matching operation establishing a link
between the probe and the goal; and (ii) a copying operation, according to which the values of F on the goal
are copied onto the unvalued 𝑢F counterparts that have been previously matched.
Lexical categories such as noun, verb, adjective etc. are decomposed into a category-neutral terminal,
i.e. the √ROOT, and a category-determining head, e.g. n, v, a. These two terminals form a complex head
the label of which is provided by the categorizer (Marantz 1997, 2001; Arad 2003; Levinson 2007, 2014;
Embick 2010, 2015; Folli and Harley 2020). From now on, I will represent this complex head as in (1).
(1) Complex head: √ROOT + categorizer x
x/xP
√ROOT x
After spell-out, at PF, the feature bundles on the terminals are mapped to an exponent via Vocabulary
Insertion (VI) rules, which are subject to competition as mediated by the Subset Principle (Kiparsky 1973).
Following the notation from Embick (2015), VI rules have the format in (2).
(2) VI rule format
𝛼[F] ⇔ 𝑋/__𝛽 ‘Map F on 𝛼 to vocabulary item X in the context of 𝛽’
𝛼 is the syntactic category of the terminal; [F] is the relevant feature or feature bundle on the terminal
node; 𝑋, to the right of the bidirectional arrow, represents the phonological form, i.e. the exponent; and the
slash ‘/’ indicates the context of application, which may be more or less specific (see Moskal 2015; Moskal
and Smith 2016).
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3.1.2 The active players: Individuation and number
It is generally assumed in DM-based approaches that there are two distinct domains for the computation of
morphological and semantic processes: an “inner” domain and an “outer” domain. The former is tied to
morphological and lexical irregularity or idiosyncrasies (e.g. idiomatic/inherent meanings, root-suppletion
etc.), and the latter is tied to morphological and semantic regularity (e.g. regular inflection). The consensus
in the literature is that the inner domain is located within the nP, i.e. categorizers and below, whereas the
outer domain is characterized by functional projections above nP, i.e. Number or D, (Marantz 2001, 2013;
Arad 2003; Embick 2010; Harley 2014; Wood 2016, 2023): Figure 3.1.
Figure 3.1: Inner vs. outer domains within nominals
Outer domain
D
Number Inner domain
√ROOT n
I propose that a theory of the count-mass distinction must make reference to at least two types of features,
whose syntactic and semantic contribution must differ: individuation and number. We can think of the
individuation feature as a sort of classificatory feature: when applied to a root, they will determine whether
the root has discrete individuals or not, i.e. atoms.1 As a result, I assume that this feature must be located
within the inner NP domain. In particular, building on insights from Bale and Barner (2009), I propose that
the categorizing n head that roots occur with determines whether the nominalized root, i.e. √ROOT + 𝑛, is or
not individuated. Thus, the categorizing ns that roots may combine with come into two “flavors”, illustrated
in (3).
1
I will refrain from using terms such as ‘atom’ in this part of the dissertation. For now, it is enough to say that the [IND] feature
on n makes discrete units available. In technical semantic terms, this means that n imposes a semi-lattice on the root that is closed
under sum and generated from the set of atoms: if atom = {𝑎, 𝑏, 𝑐}, then ∗atom = {𝑎, 𝑏, 𝑐, 𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐}.In Chapter 4, I provide
formal definitions for atom and individuated semi-lattice.
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(3) Count vs. mass n
a. n[IND(IVIDUATED)]
b. n
One flavor of n is specified as [IND], and the other flavor of n is underspecified. The role of [IND] on
n is to perform individuation, understood as described above. That is, it will make available discrete, i.e.
individually separable and distinct, elements that can be later on counted. In the absence of such a feature, the
nominalized root will simply be underspecified for individuation and will lack separable countable elements.
In a nutshell, [IND] makes the NP countable; lack of [IND] makes the NP non-countable.2
The presence of the [IND] feature on n is conceptually justified. The count-mass distinction is in many
ways idiosyncratic, and generally considered a “lexical” property; [IND] is within the inner nominal domain
identified in Figure 3.1, which is responsible for such idiosyncrasies. What is more, for the class of nouns
that allows a singular-plural contrast, it makes sense that a noun is first set to being count by bearing [IND]
and then number-marked, as opposed to the other way around.
The feature is also empirically justified. First, some roots may appear as count in some contexts or mass
in others, and viceversa, a property that we can attribute to the type of n that the root adjoins to in the syntax.
Second, only count nouns (regardless of their number specification) can undergo one-substitution; having a
feature that is sensitive to the two classes of nouns can facilitate modeling of this ellipsis asymmetry. Third,
determiners are sensitive to the noun being count, thus making [IND] (in addition to Number) a possible goal
for probes on determiners to enter an Agree relation with. Moreover, having this feature helps us establish
a structural and formal parallel between object mass nouns (e.g. jewelry) and count nouns (e.g. jewel);
namely, they both are both individuated, specified as [IND]. Despite this commonality, they must differ in
some respect.
2The presence or absence of [IND] is similar to Borer’s (2005) presence or absence of division: If [IND]/DIV is present, the NP is
countable; if it is absent, the NP is non-countable.
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Besides [IND] on n making the basic distinction between count and mass, I assume that there are two
number features: [SG] for singular and [PL] for plural. The location of number features has been argued to
vary across and within languages (Alexiadou 2004, 2015; Acquaviva 2008, 2016; Wiltschko 2008, 2021;
Kramer 2016; Kouneli 2020), a view commonly referred to as ‘split number’: lexical or idiosyncratic plurals
are located in the inner NP while regular plurals are located in the outer NP domain. Even in languages like
English and Spanish, the encoding of number might vary on structural height depending on the class that
the noun belongs to. Thus, building on the insights from the prior literature and the observations from the
previous chapter, I assume that number features, and specifically plural, might be located on two different
syntactic positions: n and Number. The former will be the source of lexical and idiosyncratic plurality and
need not depend on the n being [IND]. This is for example the source of plural-marking on mass nouns.
In contrast, I assume that the latter head, i.e. Number, which is above n and below D (Ritter 1991; Cowper
2005; Wiltschko 2008; Harbour 2011), is the source of regular singular/plural-marking. This head, I propose,
requires complementation by an nP specified as [IND]. I encode this with the feature [•IND•] on the Number
head.
Despite the differing location, I assume that the meaning of Number features is uniform: [SG] maps a noun
to a singularity, i.e. a singleton set of discrete atoms; [PL] maps the noun to a plurality, i.e. non-singletons
or sums of discrete atoms. Although the contribution of these number features does not differ depending on
the syntactic position, the syntactic (and semantic) input on which they operate will: namely whether the nP
is or not individuated.
Last but not least, I propose that we need an additional feature which I call [COLL(ECTIVE)] which will
be relevant for object mass nouns. Corbett (2000) uses the label ‘collective’ to refer to nouns denoting a
group whose members are conceived of as a unit. He goes on to point out that the members of the collection or group share something in common (what Corbett 2000, p.141 refers to as ‘the cohesion of a group’).
This is intuitively accurate for the case of object mass nouns. For instance, if we think about what it means
64

for something to qualify as ‘jewelry’, we can intuitively say something along these lines: jewelry is a collection/plurality of items that are canonically made from or contain jewels.3 Similarly, ‘footware’ can be
thought of as ‘a collection of items that are worn by someone’s feet’. Given the derivational nature of object
mass nouns and the observation that these nouns are derived from count noun bases (and in some cases verbal
ones), I assume that the feature is located on a nominalizer. However, just like Number, I take n[COLL] to
require complementation by an nP specified as [IND]: [•IND•]. Semantically, the semantic role of this feature
is to create a plurality of sorts.
We can summarize the pieces of the theory outlined here as follows:
• Count NPs are [IND]-marked and [SG/PL]-marked (i.e. they have Number)
• Mass NPs lack Number, but may be [IND]-marked.
• There are two number features: [SG/PL].
• [PL] may be located on n or on Number. This head requires an [IND] complement.
• n[COLL] generates object mass nouns collections (i.e. pluralities) out of [IND] nPs.
• Both n[COLL] and Number select for an [IND] complement.
In what remains of the chapter, I will argue the generalizations presented for count and mass nouns can be
derived by the interaction of these features with other more general properties of nominal morpho-syntax. By
the end of the chapter, we will have the typology of nominal classes that can be summarized as in Table 3.1.
As indicated in the Table 3.1, the three types of mass nouns share in common the fact that they lack
Number. In addition, canonical and plural mass form a natural class with respect to the lack of [IND] on the
3
In the article This Guide to Jewellery Production by Dauvit Alexander, the author, a professional jeweler, states the following:
“Jewellery is broadly defined as “ornament for the body [...] the majority of jewellery can be described as being wearable ornaments,
often made from high-value materials such as precious metals and gemstones” (https://make.works/blog/guide-to-jewellery). Besides, if we look at what is a dictionary definition of ‘jewel’, Cambridge English Dictionary online defines it as follows: ‘a precious
stone that is used to decorate valuable objects’ (https://dictionary.cambridge.org/us/dictionary/english/jewel). Thus, we can think of
the ‘made of/contains jewels’ relation as the cohesion of the jewelry group.
65

Table 3.1: Typology of features for the mass-count distinction
n1 n2 Number Example
Mass canonical Ø * * ‘water’, ‘salt’
plural [PL] * * ‘suds’, ‘dregs’
object [IND] [COLL] * ‘jewelry’, ‘footware’
Count singular [IND] * [SG] ‘jewel’, ‘foot’
plural [IND] * [PL] ‘jewels’, ‘feet’
nominalizer. The approach also captures the similarity between object mass nouns and count nouns: they
are all [IND]. The two classes, however, differ in whether or not they project Number or an additional n layer.
Count nouns project Number and are thus singular or plural-marked; object mass nouns project an additional
nominalizer. These heads seem to be in complementary distribution.
3.2 Analysis
One set of the morpho-syntactic generalizations that need to be accounted for was summarized in Table 2.7,
repeated below. This section is dedicated to these properties. I will start first by establishing the baseline
comparison of the (singular/plural) count vs. canonical mass nouns. Then, I will move on to each of the
other two classes, namely plural mass nouns and object mass nouns.
2.7: Morpho-syntactic properties of all mass & count nouns (final version)
Canonical Mass PL Mass Object Mass Count
SG/PL distinction * * * ✓
Direct modification by numerals * * * ✓
Modification by Stubbornly Distributed Predicates * * ✓ ✓
Number mismatches under ellipsis NA NA NA ✓
one/otro-substitution * * * ✓
66

3.2.1 Count vs. canonical mass
The first asymmetry to be accounted for between count and canonical mass nouns is the availability of overt
plural-marking on the former. I propose that this difference falls out from the fact that count nouns always
project NumP while mass nouns, disregarding the container/kind reading for a moment, never do.4 This is in
line with previous proposals such as Borer (2005a); Harbour (2007, 2011); Dali and Mathieu (2021) among
others for which mass nouns are syntactically more impoverished than count nouns. The basic structure of
count and canonical mass nouns is thus as in (4).
(4) The basic syntactic structure for count and canonical mass nouns
a. Singular/Plural Count
DP
D NumP
Num
[SG/PL]
[•IND•]
nP
√BOOK n
[IND]
b. Canonical Mass
DP
D nP
√WATER n
Count nouns have the structure in (4a). The root adjoins to a categorizing n that is specified as [IND].
This will introduce discrete individuals in the extension of the noun root. Number requires complementation
by [IND], as indicated by the bullet feature, which is satisfied upon merger. Number then projects on top of
nP. This ensures obligatory number marking in count nouns in languages like Spanish or English. Depending
on the feature specification on Num, the noun will be marked singular, e.g. [SG], or plural, e.g. [PL].
The syntax of mass nouns in (4b) is different from that of count nouns in (4a) in two respects. First, the
n is underspecfied for individuation, which entails that no discrete individuals are introduced. Second, mass
nouns lack NumP; and, as a result they cannot be overtly pluralized and maintain their mass interpretation.
4
In Section 4.4.1, I discuss how to account for shifts between the class of count and mass NPs.
67

We can attribute the failure to pluralize to the c-selectional requirement on Number: merger of Number on
top of the underspecified n will not satisfy Number’s c-selectional requirement.
We can attribute modification by certain elements such as numerals and Stubbornly Distributive adjectives to the presence of [IND] and Number. If we look at word order patterns, we observe the following: (i)
Stubbornly Distributive adjectives precede classificatory adjectives, which are adjoined low in the structure
(Alexiadou et al. 2007; Svenonius 2008); (ii) numerals precede both types of adjectives; and Determiners,
including possessors, must precede everything. This is shown in (5) for English.
(5) Word orders
a. D > # > Stubbornly Distributive A > Classificatory A > N
{The/ John’s/ These} five big Spanish books.
b. D > # > Classificatory A > Stubbornly Distributive A > N
* {The/ John’s/ These} five Spanish big books.
c. D > Stubbornly Distributive A > # > Classificatory A > N
* {The/ John’s/ These} big five Spanish books.
d. # > D > Stubbornly Distributive A > Classificatory A > N
* Five {the/ John’s/ these} big Spanish books.
The data in (5) illustrates that the only possible DP-internal word order when there are multiple modifiers and determiners (or D-like elements) must be as in (5a). In fact, any deviation from that order results
in unacceptability. I take the strict order in (5a) to be the result of the structural height at which the different modifiers are introduced. Namely, classificatory adjectives must be introduced lower than Stubbornly
Distributive adjectives, which must be introduced lower than numerals. Determiners, demonstratives and
possessors occupy the highest part of the DP.
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The situation in Spanish is very much the same, with the caveat that adjectives are generally postnominal
while numerals are prenominal. Stubbornly Distributive adjectives have to occur further away from the noun
than classificatory ones. The reversed order is unacceptable. These patterns are shown in (6).
(6) Word orders for Spanish
a. D > # > N > Classificatory A > Stubbornly Distributive A
Lo-s
the.M-PL
cinco
five
libro-s
book.M-PL
españole-s
Spanish-PL
grande-s
big-PL
‘The five big Spanish books’
b. D > # > N > Stubbornly Distributive A > Classificatory A
* Lo-s
the.M-PL
cinco
five
libro-s
book.M-PL
grande-s
big-PL
españole-s
Spanish-PL
‘The five Spanish big books’
While Stubbornly Distributive adjectives are generally postnominal, they may occur prenominally in
which case they must always follow numerals, as in (7). Thus, the word order facts resemble those for
English.
(7) a. D > # > Stubbornly Distributive A > N > Classificatory A
Lo-s
the.M-PL
cinco
five
grande-s
big-PL
libro-s
book.M-PL
españole-s
Spanish-PL
‘The five major Spanish books’
b. D > Stubbornly Distributive A > # > N > Classificatory A
* Lo-s
the.M-PL
grande-s
big-PL
cinco
five
libro-s
book.M-PL
españole-s
Spanish-PL
‘The major five Spanish books’
I take these sets of facts as evidence for the following. Classificatory adjectives are adjoined to the
domain of class, which is the lowest in the structure (Alexiadou et al. 2007; Svenonius 2008; Wiltschko
2014; Dékány 2021), i.e. nP. Given the interaction of Stubbornly Distributive adjectives with number and
69

individuation, I propose that these must be adjoined higher than the lower nP (Cinque 2005, 2010; Svenonius
2008; Deal 2017; Dékány 2021). In particular, when modifying count nouns, they are adjoined to NumP.
Numerals are introduced by their own functional head, which I label here as CARD(inlaity) after Scontras
(2013). Finally, determiners and demonstratives are introduced as D heads, and possessives are located in
D’s specifier position (Abney 1987; Corver 1990). The full DP structure for count nouns is in (8).5
(8) The articulated structure for count nouns
DP
D
{‘the’/‘these’}
CARDP
#P
‘five’
CARD’
CARD
[•Num•]
NumP
AP
‘big’
Num’
Num
[PL]
[•IND•]
nP
APclass
‘Spanish’
n’
√BOOK n
[IND]
Not only does this structure derive the desired word order between DP-internal constituents, but it also
accounts for why Stubbornly Distributed adjectives are unnaceptable with mass nouns: mass nouns lack a
NumP domain and adjunction to that position is therefore precluded. This is very much in line with Deal’s
(2016a; 2017) analysis of Nez Perce: classificatory adjectives are structurally closer to the nominalized root
than Stubbornly Distributed adjectives, which require additional structure making the noun count.6
In addition, it is consistent with the observation that (some) Stubbornly Distributive adjectives require the presence
5
I assume that the postnominal position of adjectives in Spanish in (6) and (7) may be achieved via head movement of the n/nP
to a higher projection, as proposed by Cinque (2005, 2010) for instance; or by assuming that the directionality of adjunction differs
between English and Spanish.
6For Deal (2016a, 2017), this is achieved via a covert functional head above n and below Number, where she assumes PL is
merged.
70

of overt classifiers, whose distribution is sometimes paralleled to that of Number (Borer 2005a; Cowper and
Hall 2014). Examples include Hungarian in (9) from Dékány (2021) or Teochew, Southern Min in (10),
adapted from Biggs and Zhuosi (2022).
(9) Hungarian
a. két
two
nagy
big
szem
CL𝑒𝑦𝑒
alma
apple
‘two big apples’
b. * két
two
szem
CL𝑒𝑦𝑒
nagy
big
alma
apple
Int. ‘two big apples’
c. két
two
vekni
CL𝑙𝑜𝑎𝑓
meleg
warm
kenyér
bread
‘two warm loaves of bread’
d. * két
two
meleg
warm
vekni
CL𝑙𝑜𝑎𝑓
kenyér
bread
Int.: ‘two warm loaves of bread’
(10) Teochew, Southern Min
a. Hi
that
sa
three
go
CL
dua
big
*( -go)
A.CL
gai
N.MOD
tun
candy
‘those three big pieces of candy’
b. Hi
that
sa
three
go
CL
sio
hot
(* -go)
A.CL
gai
N.MOD
tun
candy
‘those three pieces of hot candy’
In both Hungarian it is dimensional adjectives (e.g. size and shape), which are lower than numerals,
that must precede the classifier: (9a) vs. (9b). Others like warm must follow the classifier: (9c) vs. (9d).
Similarly, in Teochew, Southern Min dimensional adjectives require the obligatory presence of the classifier
following the adjective, e.g. (10a); but non-dimensional adjectives are ungrammatical with the classifier, e.g.
(10b). Dimensional adjectives are a very common type of Stubbornly Distributive adjectives, thus data like
(9) and (10) strengthen the argument that there is a structural connection between Number and the position
of these adjectives.
The syntax in (8) is also consistent with analyses that have located numerals higher than Number but
lower than D, e.g. Pancheva (2021, 2022); Toquero-Pérez (2023a). What is more, we can assume that, at
71

least for the languages analyzed here, the CARD head is sensitive to there being a NumP. 7 This requirement
is enforced by the selectional feature [•Num•] on the CARD head.
There is an additional welcome consequence of this structure regarding classificatory adjectives. These
adjectives are acceptable with mass nouns. In fact, when more than one adjective of this class co-occurs, the
order is not fixed, as shown in (11). These facts can be accounted for under the assumption that there are no
ordering restrictions between adjuncts of the same XP (Alexiadou 1997; Cinque 1999), i.e. nP in this case.
(11) a. Mineral sparkling water Sparkling mineral water
b. Agua
water
gasificada
carbonated
mineral
mineral
Agua
water
mineral
mineral
gasificada
carbonated
‘Carbonated mineral water’ ‘Mineral carbonated water’
Before proceeding any further, it is necessary to locate the syntactic position that QAs occupy in the DP.
This will be relevant when discussing ellipsis and one/otro-substitution. With count nouns, QAs must occur
higher than Stubbornly Distributive adjectives, but lower than D given the facts in (12).
(12) Word orders with QAs for count nouns
a. D > QA > Stubbornly Distributive A > N
i. The many big books
ii. Lo-s
the.M-PL
mucho-s
much.M-PL
grande-s
big-PL
libro-s
book.M-PL
‘The many major books’
b. D > Stubbornly Distributive A > QA > N
i. * The big many books
ii. * Lo-s
the.M-PL
grande-s
big-PL
mucho-s
much.M-PL
libro-s
book.M-PL
‘The major many books’
7
In Chapter 5, we will see further evidence from Alasha Mongolian supporting the hypothesis that Stubbornly Distributive
adjectives are located in the NumP domain.
72

c. QA > D > Stubbornly Distributive A > N
i. * Many the big books
ii. * Mucho-s
much.M-PL
lo-s
the.M-PL
grande-s
big-PL
libro-s
book.M-PL
‘Many the major books’
In the case of mass nouns, QAs must enter the structure higher than classificatory adjectives, as in (13).
In Spanish classificatory adjectives are always postnominal, and thus the datapoint has not been included
because it is not relevant.
(13) Word orders with QAs for mass nouns
a. QA > Classificatory A > N
Too much mineral water
b. Classificatory A > QA > N
* Mineral too much water
Considering these distributional facts, we can conclude that QAs are higher than NumP in the case of
count nouns because they must precede Stubbornly distributed adjectives and are sensitve to the noun being
plural-marked. In the case of mass nouns, they must be located higher than the nP level at which classificatory
adjectives are adjoined. I propose that QAs are merged in the specifier position of a Q-head above NumP for
count nouns and above nP for mass nouns. This is schematically represented in (14).
73

(14) The position of QAs
a. Count DPs
DP
D QP
DegP
‘many/muchos’
Q’
Q NumP
...
b. Mass DPs
DP
D QP
DegP
‘much/mucho’
Q’
Q nP
...
The next pieces of data that need to be accounted for involve ellipsis. Namely, we observed that count
nouns allowed deletion of the NP under identity. QAs and numerals determine the boundary of the ellipsis
site, i.e. they are always remnants. The target of the ellipsis and the antecedent of the ellipsis need not match
in number, though. It is generally argued that for ellipsis to allow feature mismatches, the relevant feature
has to be outside of the ellipsis site (Merchant 1999, 2004, 2014; Saab 2010; Bobaljik and Zoca 2011; Lipták
and Saab 2014; Ranero 2021). I assume insights from Merchant (1999), Aelbrecht (2010) and others that
ellipsis marking takes place in the syntax and it is performed by the licensing of a feature [E] to the relevant
node and everything that node dominates.8
Given the syntactic structure advocated for count nouns in this chapter, I propose that the Q or CARD heads
are responsible for licensing ellipsis of their complement. In particular, I propose that there are three possible
ellipsis options depending on (i) what licenses ellipsis, (ii) what constituent is marked for ellipsis, and (iii)
how the ellipsis-marked constituent is exponed at the time of Vocabulary Insertion. The three options, that
I will discuss in turn, are as follows: Option A is the deletion of the Number projection licensed by the
functional head introducing QAs or numerals; Option B is the deletion of nP licensed by the head introducing
8For the purpose of this dissertation, it is not fully relevant how the licensing condition is performed. For Aelbrecht (2010),
for example, the relation between licensor and ellipsis site is established via Agree. For other proposals see Rudin (2019); Ranero
(2021); Stigliano (2022).
74

QAs in its specifier; Option C is the replacement of the [IND]-marked n-head for one in English or otro in
Spanish in the presence of Number. These are summarized in Table 3.2.
Table 3.2: Ellipsis options: licensors, [E]-bearers and exponence
Licensor [E]-bearer Exponent
Option A Q/CARD → NumP → Ø
Option B Q → nP → Ø
Option C Num → n[IND] → one/otro
For Option A, the derivation must proceed as follows. When the licensor, in this case Q or CARD, is
merged into the structure, Num will undergo head movement onto it.9 This is how we ensure that the Num
head is outside of the ellipsis site. The licensor will then assign NumP, and everything NumP dominates,
with an [E] feature. The derivation is shown in (15), where [∗𝑢Num] is a head-movement triggering feature in
the spirit of Adger (2003); Folli and Harley (2020). After spell-out, at PF, anything that bears the [E] feature
will be mapped to a zero morpheme via the VI rule in (15e).
(15) Deriving Number mismatches under ellipsis, e.g. (16) and (20) from Chapter 2
a. The baseline: one book...three books/ un libro...tres libros
Antecedent NumP
...[SG]...
DP
D CARDP
#P
‘3’
CARD’
CARD
[
∗𝑢Num]
NumP
Num
[PL]
nP
√BOOK n
[IND]
b. Head movement of Num onto CARD
9For a proposal in which movement triggering features must be checked or satisfied before ellipsis-triggering features see Stigliano
(2022).
75

Antecedent NumP
...[SG]...
DP
D CARDP
#P
‘3’
CARD’
CARD[
∗𝑢Num]
Num
[PL]
CARD
[
∗𝑢Num]
NumP
𝑡 nP
√BOOK n
[IND]
c. [E] licensing to NumP
Antecedent NumP
...[SG]...
DP
D CARDP
#P
‘3’
CARD’
CARD[
∗𝑢Num]
Num
[PL]
CARD
[
∗𝑢Num]
NumP[E]
𝑡 nP[E]
√BOOK
[E]
n
[E, IND]
d. The structure after spell-out
...
√BOOK
[E]
n
[E, IND]
CARD Num
[PL]
e. Vocabulary Insertion rule for Non-pronunciation of [E]-marked terminals
𝛼[E] ⇔ Ø ‘Map any terminal 𝛼 with the feature [E] to Ø’
As shown in (15a), the antecedent and the target of the ellipsis mismatch in number (e.g. singular vs.
plural). The head-movement triggering feature forces the Num[PL] head to incorporate onto CARD, illustrated
76

in (15b). Next in (15c), CARD licenses the [E] feature to its complement NumP. As a result, anything that NumP
dominates is marked for ellipsis as well. The relevant spelled-out structure, after terminal node linearization,
is in (15d), where the root and n terminals are [E]-marked. At the point of Vocabulary Insertion, any [E]-
marked terminal node will be subject to the general rule in (15e): the root and the n head are exponed as
zeros.
I have illustrated the ellipsis facts with a numeral, but the situation is identical with a QA. The only
difference is that instead of dealing with CARD as a licensor and numerals as remnants, we are dealing with
Q as a licensor and QAs as remnants.
The proposal that what undergoes ellipsis with count nouns is NumP makes the following prediction:
Stubbornly Distributive adjectives in spec,NumP must not survive ellipsis. If anything dominated by NumP
undergoes deletion, and these APs occupy the specifier of NumP they will be no exception. The data in (16)
from English and (17) from Spanish indicate that the prediction is borne out.
(16) Al bought one big book ...
a. and Mary bought {many/ five} big books.
b. * and Mary bought {many/ five} big books.
(17) Juan
Juan
compró
bought
un
one
libro
big
grande
book
...
a. y
and
María
María
compró
bought
{ mucho-s/
much.M-PL
tres}
three
libro-s
book-PL
grande-s
big-PL
‘and María bought {many/ three} big books’
b. * y
and
María
María
compró
bought
{ mucho-s/
much.M-PL
tres}
three
libro-s
book-PL
grande-s
big-PL
‘and María bought {many/ three} big books’
In both English and Spanish, it is possible to utter (16a) and (17a) with the meaning that the ‘many/three
books Mary bought were also big books’. Failure to elide the Stubbornly Distributive adjective results in
ungrammaticality, as the b-counterparts show.
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Turning to mass nouns, they instantiate Option B in Table 3.2. The lack of number mismatches under
ellipsis follows from them not projecting NumP. Nevertheless, mass nouns can undergo ellipsis under identity
when there is a QA like much in the structure. This was shown with examples like English (17) and Spanish
(21) in the previous chapter. Given the proposal, this can be explained if the Q-head that introduces much
in its specifier licenses ellipsis of its nP complement. Evidence for nP ellipsis comes from the fact that
classificatory adjectives cannot survive the ellipsis, as the continuations to (17b) and (21) in (18) and in
(21b) from Chapter 2 respectively indicated. This follows from the proposal: (i) classificatory adjectives are
adjoined to nP, and (ii) any node dominated by the [E]-marked nP is mapped to a zero exponent by the rule
in (15e). The relevant structure is provided in (18) where the shaded parts indicate what undergoes deletion,
or more accurately zero-exponence.
(18) Mass nP ellipsis
DP
D QP
DegP
‘much/mucho’
Q’
Q nP[E]
APClass
‘Spanish’
n’
√WINE n
The last piece of data that needs to be derived concerns one/otro-substitution, i.e. Option C in Table 3.2.
Given the sensitivity of these proforms to the noun being count, and the fact that classificatory adjectives must
survive what is being substituted, I hypothesize that one/otro-substitution targets the n[IND] head. Building
on insights from Harley (2005), I propose that ‘substitution’ is in fact the insertion of a non-zero exponent
on n when a VI rule that is more specific to the one in (15e) wins over. The rule is given in (19).10
(19) 𝑛[E, IND] ⇔ {𝑜𝑛𝑒/ 𝑜𝑡𝑟𝑜}/ Num
10For Harley (2005), the relevant feature on the elided and substituted constituent is [+Identity].
78

‘Map the terminal n terminal node with the bundle [E, IND] to vocabulary item one (in English) and
otro (in Spanish) in the context of Number’
Since the ellipsis site is smaller than in canonical NP-ellipses, I assume that what licenses one/otrosubstitution is the Number head, and what is [E]-marked is the n[IND] head rather than the full nP.11 This
accounts for why classificatory APs, located in Spec,nP, are outside of the domain of one/otro-substitution.
The step-by-step derivation of examples involving one/otro-substitution is provided in (20).
(20) the French book on the table and the Spanish one(s) on the shelf
a. n and the root are a
complex head
DP
D
‘the’
NumP
Num
[SG/PL]
nP
AP
‘Spanish’
n’
n[IND]
√BOOK n
[IND]
b. [E]-licensing to n
DP
D
‘the’
NumP
Num
[SG/PL]
nP
AP
‘Spanish’
n’
n[E, IND]
√BOOK
[E]
n
[E, IND]
c. The structure after
Spell-Out
√BOOK
[E]
n
[E, IND]
Num
[SG/PL]
The structure in (20a) is what the syntax puts together via merger of the different terminals: [n √ROOT]
is a complex head projecting the label n; the classificatory adjective is introduced in the specifier position of
nP; and Number takes the nP as its complement given its complementation requirement. The next step is for
Num to license ellipsis to its complement’s head. As a result, everything dominated by n is [E]-marked: this
includes the n[IND] itself, and the root as shown in (20b).
11There seems to be variation as to whether full XPs or smaller constituents within XP can be targeted for ellipsis. Arguments for
this parametrization can be found in Bošković (2014). It is not unreasonable to think that different heads might have distinct scope
in their availability to license ellipsis: some might license ellipsis of their complement while others might only be able to target the
complement’s head.
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After Spell-Out, and linearization of terminals, the structure is as in (20c) where Num is local to n. Under
the assumption that VI proceeds from the root outwards, the root is mapped to no exponent given the general
rule in (15e) repeated as (21b). However, the locality between n and Num bleeds the application of this more
general rule. Instead, by the Subset Principle, the more specific rule in (19) repeated in (21a) is applied: ‘map
the n specified as [E, IND] to the exponent one (in English) or otro (in Spanish) in the context of Number’.
(21) VI rules for [E]-marked terminals
a. 𝑛[E, IND] ⇔ {𝑜𝑛𝑒/ 𝑜𝑡𝑟𝑜}/ Num
b. 𝛼[E] ⇔ Ø
It is not necessary to relativize the locality between n and Num to a particular feature: [SG] and [PL] feed
one/otro-substitution. If Number is [PL], though, it will be exponed as /-z/ in English or /-s/ in Spanish. In
the sections to follow, I will show that the rule, as formulated in (21a), correctly applies only in the case of
‘count’ nouns.
3.2.2 Plural mass nouns
Now that we have established the basic structure and formal properties of mass nouns, namely lack of [IND]
and as a result lack of NumP, we are in a position to address the syntax of plural mass nouns. I propose that
while plural mass nouns lack both [IND] and NumP, the categorizer that the roots adjoin to in the syntax to
form a complex head is speficied as [PL]. This has already been proposed for plural mass nouns in languages
like Greek (Alexiadou 2004, 2011, 2015; Kouneli 2019). The syntactic structure is represented in (22).12
12I represent Spanish roots lacking theme or class vowels, which I assume following Harris(1991); Embick (2010); Kramer (2015)
are inserted postsyntactically in n, where they bundle with gender features.
80

(22) a. Plural mass nouns in English
DP
D nP
⎧
{
{
{
{
{
{
{
⎨
{
{
{
{
{
{
{
⎩
√DREG
√HOP
√SUD
√BRAIN
...
⎫
}
}
}
}
}
}
}
⎬
}
}
}
}
}
}
}
⎭
n
[PL]
b. Plural mass nouns in Spanish
DP
D nP
⎧
{
{
{
{
{
{
{
⎨
{
{
{
{
{
{
{
⎩
√AGUJET-
√CEL-
√VÍVER-
√BAB-
...
⎫
}
}
}
}
}
}
}
⎬
}
}
}
}
}
}
}
⎭
n
[PL]
As mass nouns, they lack reference to discrete individuals. Besides, since there is no [IND] feature Number
cannot be merged into the structure: the requirement that its complement be marked individuated, i.e. [•IND•],
will not be checked off upon merger resulting in a crash. This is illustrated in (23).
(23) [•IND•] on Num is not checked off via merger
*
Num
[SG/PL]
[•IND•]
nP
{√DREG, √CEL-}
n
[PL]
Furthermore, by virtue of these nouns not having NumP, many of their grammatical restrictions follow.
First, they have no singular/plural distinction and, by that same token, disallow NumP ellipsis with mismatching features. Second, modification is restricted to classificatory adjectives, adjoined to nP. Stubbornly
Distributive adjectives which are adjoined higher than the lowest nP, at least at the NumP level, are unacceptable. Third, the CARD head that introduces numerals in its specifier cannot be merged into the structure
either: this head has a selectional [•Num•] feature that cannot be checked off because NumP is not part of
the structure. Therefore, numerals in Spec,CARDP are unnaceptable with plural mass nouns.
With respect to nP ellipsis, given the three options outlined in Table 3.2, the structure of plural mass
nouns only makes Option B available: Q, merged on top of n, licenses ellipsis of its complement nP. The
81

full nP then undergoes deletion, which in the analysis is mapping to a null exponent. This is shown in (24),
and it is exactly the same as for canonical mass nouns in (18). Zero exponence on the [E]-marked terminals
proceeds via the VI rule in (21b).
(24) a. Plural mass nP ellipsis (English)
DP
D QP
DegP
‘much/ %many’
Q’
Q nP[E]
APClass
‘Spanish’
n’
√HOP n
[PL]
b. Plural mass nP ellipsis (Spanish)
DP
D QP
DegP
‘muchos/tantos’
Q’
Q nP[E]
APClass
‘españoles’
n’
√VÍVER- n
[PL]
One/otro-substitution is precluded. Again this can be explained by the lack of the relevant licensor, i.e.
Number, and the relevant target, i.e. n[IND]. Thus, the configuration that needs to be created for the VI rule
in (21a) to apply is not met.
This analysis of plural mass nouns is consistent with the intuition that “lexical” plural marking is closer
to the root than regular inflectional plural marking (Alexiadou 2004, 2011, 2015; Acquaviva 2008; Kouneli
2019). In other words, despite the feature [PL] being mapped to the same exponent at the point of vocabulary
insertion, the terminal node that bears this feature is structurally and categorially different. This way of modeling the distinction between plural-marking on count nouns and mass nouns has a welcome consequence:
number-marking on noun-noun compounds.
In Section 2.2 of Chapter 2, I discussed the observation that only the head-noun of a count noun-noun
compound can be inflected for number. This restriction is generally attributed to the fact that the non-head
noun may be as large as an nP, but it does not include NumP (Wiltschko 2008; Harley 2009). Thus, the
82

structure for something like police dog(s) or perro(s) policía is as in (25), ignoring head-directionality, where
nP2
is the non-head member of the compound.
(25) noun-noun compound with count non-head
NumP
Num
[SG/PL]
nP1
nP2
‘police/policía’
n’
{√DOG, √PERR-}
n
[IND]
We also observed that when the noun-noun compound has a plural mass noun as a non-head pluralmarking on it survived: dregs filter but *dreg filter, e.g. (46) from Chapter 2, or niño babas ‘kid drooling.PL’
but *niño baba ‘kid drooling’, e.g. (48) from Chapter 2. This fact is predicted if [PL] is not located on Number,
but on n, as I am proposing here. Thus, we can roughly represent the structure of noun-noun compounds as
in (26).
(26) noun-noun compound with plural-mass non-head
NumP
Num
[SG/PL]
nP1
nP2
√ROOT n2
[PL]
n’
√ROOT n
[IND]
There is an additional prediction that the account makes: if the [PL] feature is located on the nominalizer,
plural-marking on the root is not expected to survive when the root adjoins to a different categorizer such as
v or a. The data in Table 3.3 show that this prediction seems to be borne out.
The verbs and adjectives in Table 3.3 are formed on the basis of roots licensed in plural-mass contexts.
Crucially, these verbs and adjectives do not retain the overt plural-marking. That is, it seems that the verb
83

Table 3.3: Verbs and adjectives based on plural mass noun roots
Language Bare Plural Mass Verb Adjective
English fumes to fume/ *to fumes
‘to emit fumes or gas’
fum-y/ *fumes-y
‘full of fumes’
dregs dregg-y/ *dregs-y
‘full of dregs’
hops to hop/ *to hops
‘to flavor with hops’
hopp-y/ *hops-y
‘full of hops’
oats
oat-y/ *oats-y
‘of, like, or containing oats’
Spanish babas
‘drooling’
bab-ar/ *babas-ar
‘to drool’
bab-oso/ *babas-oso
‘drooly’
celos
‘jealousy’
cel-ar/ *celos-ar
‘to distrust’
cel-oso/ *celos-oso
‘jealous’
agujetas
‘muscle sores’
agujet-ear/ *agujetas-ear
‘to suffer from muscle sores’
agujet-eado/ *agujetas-eado
‘suffering from muscle sores’
and the adjective are formed directly on top of a root that has no /-s/. We can takes this as evidence that
plural-marking is the n’s doing rather than being lexically part of root.
A potential exception to the class seems to be suds. As indicated by Merriam-Webster and Collins
dictionaries online, the following forms in (27) are all acceptable. (27a)-(27c) are all taken from the same
source.
(27) a. to suds (transitive) ‘to wash something in suds’
b. to suds (intransitive) ‘to form suds’
c. suds-less ‘without suds’ (https://www.merriam-webster.com/dictionary/suds)
d. suds-y ‘full of suds’ (https://www.collinsdictionary.com/us/dictionary/english/suds)
With the exception of suds, we can take data like the one in Table 3.3 as evidence that the plural marker
is added to the bare root as part of the syntactic derivation. Namely, it encodes nominality, i.e. the root is
labeled as a noun.
84

3.2.3 Object mass nouns
The class of nouns that is left is object mass nouns. An important observation that was extracted at the end of
Section 2.3 in Chapter 2 was that the nouns composing this class were morphologically complex giving rise,
in most cases, to doublets: one being a count noun and the other being an object mass noun. The structural
descriptions that I proposed for the nouns in this class in (69) from Chapter 2 are repeated below.
(69) a. [[√⏟⏟⏟⏟⏟⏟⏟ ROOT COUNT
carpet
] OBJECT MASS ⏟⏟⏟⏟⏟⏟⏟
-ing
] ⇝ ‘collective’
b. [[√⏟⏟⏟⏟⏟⏟⏟ ROOT VERB
carpet
] OBJECT MASS ⏟⏟⏟⏟⏟⏟⏟
-ing
] ⇝ ‘eventive’
In this section, I will concentrate on (69a) only leaving aside the eventive cases. I take the morphological
facts to be too robust to be ignored, and thus I argue for (28):
(28) Object mass nouns, at least on the collective interpretation, are always formed of top of count noun
bases.
Analytically, under the proposal developed in this chapter, (28) entails that object mass nouns are syntactically contain an [IND]-marked nP. That is, first the n that the root combines with must be n[IND]. Then
an additional terminal node is added derivationally on top on this nP layer: the n[IND] is contained, in the
sense of Bobaljik (2012), by this outer head.
Note that structure-wise, i.e. the syntactic position that this additional layer occupies, is very much the
same that Number occupies. This is schematized in (29).
(29) Number
X
>
>
n[IND]
n[IND]
>
>
√ROOT
√ROOT
What is more, the semantic effect that this extra piece of structure contributes is very similar to [PL];
in fact, it is assumed that these nouns denote collections of individuated pluralities (Gillon 1992; Chierchia
1998a, 2010, 2021; Bale and Barner 2009). However, it would be a mistake to call the syntactic terminal X
in (29) Num[PL]. For starters, it is never exponed as [PL]. Second, allomorphy (an suppletion in particular)
85

is conditioned by the features on the terminal nodes, given certain locality requirements, rather than the
vocabulary items themselves. Thus, if this terminal node X was in fact Num[PL] it would trigger the same
types of root suppletion as Num[PL] does. The data in (30)-(32) indicate that this prediction is not borne
out.13
(30) a. √LEAF ⇔ leave/ PL ‘leaves’
b. √LEAF ⇔ foli-/ X ‘*leavage’, ‘foliage’
(31) a. √FOOT ⇔ feet/ PL ‘feet’
b. √FOOT ⇔ foot-/ X ‘*feetware’, ‘footware’
(32) a. √MUEBL- ⇔ mueble/ PL ‘muebles’ (furniturecount.pl)
b. √MUEBL- ⇔ mobil-/ X ‘*muebliario’, ‘mobiliario’ (furnituremass)
In (30), [PL] triggers the insertion of the vocabulary item leave; if we supplant the Number feature with
X, a different vocabulary item is inserted: foli-. A more compelling case is perhaps (31). The root for foot
has a suppletive allomorph in the plural: feet. In contrast, X, responsible for the object mass counterpart,
does not trigger suppletion of the root, which surfaces as the unmarked or elsewhere form, e.g. foot. The
Spanish case in (32) is similar to the leave/foliage contrast: a plural feature does not trigger suppletion of the
root, but the object mass counterpart feature does. The b-form lacks a diphthong and involves metathesis of
the liquid and the vowel, which has shifted in height.
All things considered then, X and Number (specifically [PL]) share a series of properties: they both seem
to have the exact same syntactic distribution, they both may trigger suppletion on the root and they both have
13When looking at the rules, the reader might be wondering where the categorizing n-head is in the contextual specification. For
ease of representation, I have left it out of the formulation of the rules here. The full contextual representation is something like the
following in (v).
(v) √ROOT ⇔ root/ n[IND] ] PL/X]
For now it is just worth mentioning that any theory of allomorphy must account for the fact that Number may trigger allomorphy on
the root past the nominalizer, considering that allomorphy is constrained by locality (Embick 2010; Bobaljik 2012; Moskal 2015;
Bobaljik and Harley 2017; Moskal and Smith 2016). In footnote 17, I discuss two approaches to this: the zero-morph approach
from Embick (2010) and the Hyper-Contextual VI rule approach from Moskal and Smith (2016). I show that either approach can
be made to work with the proposal being developed in this dissertation.
86

a similar semantic contribution. However, X and Number must be different terminal nodes specified with
their own distinct features. Focusing on their distribution, a compelling fact is that they never co-occur. That
is, when Number[PL] is present, X (in its many surface forms) cannot be; and when X is present, Number[PL]
cannot be: jewel-s but not *jewel-s-ery and jewel-ery but not *jewel-ri-es. Based on these facts, I propose
that this is exactly the situation under discussion: X and Number are in complementary distribution, i.e. they
both require their complementation by n[IND].
I propose that the piece I have been calling X so far is a nominalizer n.
14 This n bears a feature I refer to
as [COLL(ECTIVE)]: when given an individuated item 𝛼, it creates a collection (or plurality) of items 𝛽 which
are somehow associated with 𝛼.
15 We can think of this association as Corbett’s (2000) cohesion relation
between the members making up the collection. The structure that object mass nouns have is given in (33).
(33) a. English ‘jewelry’
DP
D nP
n
[COLL]
[•IND•]
nP
√JEWEL n
[IND]
b. Spanish ‘joyería’ (jewelry)
DP
D nP
n
[COLL]
[•IND•]
nP
√JOY- n
[IND]
Locating n[COLL] immediately c-commanding n[IND] is consistent with the observations that this terminal node parallels the distribution of Number. As a result, just like Number can condition allomorphy on the
root, so can n[COLL], i.e. the locality conditions for allomorphy are the exact same. Moreover, just like Number, this head comes equipped with the merge-triggering feature [•IND•]. This feature is a complementation
feature and must be checked-off immediately via merger of n’s complement. Given that both Number and
n have the same complementation feature, which must be obligatorily checked-off by merging the relevant
complement, we can account for the unacceptability of their co-occurrence: merger of n[COLL] will block
14In Section 3.3 I show some evidence for why the [COLL] feature may be located in a nominalizer.
15Chapter 4 is devoted to the formal semantic definition and composition of the noun classes.
87

merger of Number, and viceversa, thus accounting for their complementary distribution. This competition
for merger is illustrated in (34).
(34) Satisfying [•IND•]
a. Competing for merger
Num
[SG/PL]
[•IND•]
n
[COLL]
[•IND•]
nP
√ n
[IND]
b. Merger of n[COLL]
nP
n
[COLL]
[•IND•]
nP
√ n
[IND]
c. Merger of Number
NumP
Num
[SG/PL]
[•IND•]
nP
√ n
[IND]
As illustrated in (34a), Number and n compete for merger. If n is merged as in (34b), it will write off
its complementation feature and project nP, blocking merger of Number. The resulting vocabulary item is
jewelry. If Number is merged instead, as in (34c), its complementation feature will be discharged and NumP
will project; this will result in the insertion of vocabulary item jewel(s). Attempting to iterate Number and n
leads to a crash: only one of the two heads, i.e. the first-merged head, will be able to write its complementation
feature off (Adger 2003; Heck and Müller 2007; Müller 2010). This is schematized in (35).
(35) a. Merge(n, n) > *Merge(Num,n)
*
Num
[SG/PL]
[•IND•] n
[COLL]
[•IND•] √ n
[IND]
b. Merge(Num,n) > *Merge(n, Num)
*
n
[COLL]
[•IND•] Num
[SG/PL]
[•IND•] √ n
[IND]
By virtue of not having a NumP, many of the grammatical properties of this class of nouns follow. For
instance, the obvious one is no singular/plural contrast, which is also unavailable under ellipsis. Second,
88

numeral modification is disallowed. This fact follows from the claim that the CARD head that introduces
numerals in its specifier requires complementation by Number. Since there is no Number in the structure,
merger of CARD is not feature-driven, and the derivation will crash. This is schematized in (36).
(36) Merge(n, n) > *Merge(CARD,n)
*
CARD
[•NUM•]
n
[COLL]
[•IND•] √ n
[IND]
The situtation with Stubbornly Distributive adjectives is different. My argument for why these adjectives
are not allowed with most mass nouns has been that the syntactic structure of these mass nouns is impoverished and does not provide the room for the adjective to be adjoined. In the case of count nouns, that extra
structural piece was Number. Regarding object mass nouns, these are not as syntactically impoverished; in
fact, their structure involves an additional layered nP above the lower domain where classificatory adjectives
are adjoined. That said and given the geometrical similarity between Number and this layered n, I propose
that Stubbornly Distributive adjectives adjoin to the specifier of this outer nP. Besides, if these adjectives
impose a semantic requirement on the noun that they modify, as proposed by Deal (2016a, 2017), namely
that the noun be individuated, that requirement is satisfied.
With respect to ellipsis, lack of NumP entails that only Option B in Table 3.2 is available. Thus, object
mass nouns are no different from the other two subclasses of mass nouns: what undergoes ellipsis is Q’s
complement which is the highest nP (and everything it dominates). The account also explains why Option
C, i.e. one/otro-substitution, is not acceptable with object mass nouns. While it is true that one/otro targets
n[IND] and this head is in fact present in the structure of object mass nouns, the conditions for the VI rule in
(21a) are not met since there is no Number. Thus the rule fails to apply. Besides, there is no Number head
that can license ellipsis of its complement’s head.
89

The hypothesis that object mass nouns are built on top of an individuated nP has a series of welcome
consequences, as I have shown here. There is one trade-off of adopting this decompositional account: not
every object mass noun has a count noun counterpart. This is most clearly seen in English with the example of furniture; but which vocabulary items are missing can be a matter of idiosyncracy across languages.
The question is then what licenses the root to occur in one context (the object mass) but not the other (the
count one). In more or less lexicalist approaches, this is easily captured by the assumption that object mass
noun roots are listed as such in the lexicon: the root √FURNITURE is mapped to a vocabulary item furniture and there is no nominal root √FURNISH (Chierchia 1998a; Bale and Barner 2009; Rothstein 2010). In
DM-style approaches, like the one adopted here, “listedness” and root-specific conditions are grammatically
determined instead.
There are two potential reasons for why a root might not be licensed, i.e. paired up with the relevant
terminal or sets of terminals (Harley and Noyer 1998, 1999, 2000; Acquaviva 2009; Kramer 2015; Ranero
2021): a semantic condition, and a morpho-phonological one. The semantic condition entails that pairing
up a root with a particular terminal leads to uninterpretability. In the case at hand, this would entail that a
root like √FURNISH will lead to a semantic crash if it occurs in the environment in (37).16 The ‘↔’ is meant
to indicate the mapping from structure to interpretation.
(37) [Number[SG/PL] [n[IND] √FURNISH]] ↔ ‘no meaning’
However, one could argue that attributing the gaps to an inability to assign a certain meaning misses the
generalization that I have been attempting to capture all along: object mass nouns are derivationally built on
count nouns.
Instead, I hypothesize that the reason why there are lexical gaps in the paradigm is morpho-phonological:
the relevant root cannot be mapped to an exponent at the point of Vocabulary Insertion in a particular context.
This entails that, in those cases where there is an object mass noun but no count noun counterpart, the root
16Remember the discussion in Section 2.3 in Chapter 2 that furniture shares the same root as surface forms furnish and furnishing.
This lead to the conclusion that √FURNISH is a more accurate representation of what the underlying root might be.
90

can only be licensed in a nominal context where n[COLL] is present. For instance, a root like √FURNISH may
only be exponed in the contexts in (38).
(38) a. √FURNISH ⇔ furnit-/ n[IND] ] n[COLL] ] ‘furniture’
b. √FURNISH ⇔ furnish/ v ‘furnish’
If the contexts in (38) are not met, no vocabulary item will be able to be inserted. As Kramer (2015,
p.54) notes, this way of thinking is very much in line with the Subset Principle: Vocabulary Insertion cannot
proceed if (i) the target contains features that are not present in the syntactic derivation or (ii) the target does
not occur in the relevant context specified by the rule.17
Pushing the licensing condition to the post-syntax, and in particular to the operation of Vocabulary Insertion, entails that certain combinations of (i) nominalizing features, (ii) number features, and (iii) the √ROOT
yield no phonological output.18
17The rule in (38b) is what Moskal and Smith (2016) refer to as ‘Hyper-Contextual’ VI rule: it makes reference to multiple
terminal nodes. One may wonder about the specificity of the rule and whether it is a conceptual and/or an empirical issue. I want to
briefly comment here that it is not. First, any theory of allomorphy has to account for the observation that terminals like Number can
trigger suppletion on the root despite ‘not being strictly local’ and occupying different cyclic domains (or phase cycles, Chomsky
2000, 2001; Marantz 2001; Embick 2010). This can be cashed out by assuming that in contexts where the intervening terminal, in
this case n, is a zero-morpheme then the next higher terminal located in a different cyclic domain can trigger allomorphy on the root.
This is similar to what Embick (2010) proposes and it is schematically represented in (vi).
(vi) a. [[√⏟ROOT n
Cycle A
][Number ⏟Cycle B
]
b. √GOOSE
goose
n]
Ø
Number]
PL
‘geese’
The outer head must have access to the root even if they occupy different cycles. The alternative is Moskal and Smith’s (2016) who
propose, in a nutshell, that allomoprhy on the root can occur as long as it is triggered by the terminal that immediately c-commands
the cyclic head: if n is such a head, Number has then access to the root, which they formulate via VI rules that are hyper-contextsensitive. Given that the location of Number and n[COLL] is structurally identical the same logic applies here. I do not intend to
adjudicate between the two proposals here; what I hope to have shown is that the structural description for the licensing of certain
roots is not only empirically justified but it can be formalized within current theories of allomorphy. Whether it is preferable to do
it via Hyper-Contextual VI rules or via zero-morph exponence (or pruning) is something that I leave open.
18This type of approach raises a series of questions about learnability and variation which I cannot fully answer here. With respect
to learnability, learners have to figure out two things. The first is the arbitrary licensing conditions for the set of roots in the language.
This is not entirely different from the fact that in languages that make grammatical gender distinctions, learners have to figure out
what root goes with what n encoding gender. The second thing they need to figure out is that the distribution of certain roots or
terminal nodes can be highly restricted to very specific contexts. Regarding variation and “listedness”, given the idiosyncrasy of
what is an acceptable root-categorizer pairing, we do not expect the licensing conditions to be universal across languages but rather
arbitrary. While a root-categorizer pair may be available in language A, the same combination may not be available in language B.
This accounts for the variation in the types of gaps we might observe.
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3.2.4 Determiner selection
The last set of generalizations that have to be explained involves the requirement that certain determiners and
quantifiers impose on the NPs. The five determiner classes and the representative vocabulary items for each
class are again repeated below in Table 2.8 and Table 2.1 respectively.
Table 2.8: Restrictions on determiner selection (final version)
Class of Determiner Mass Count
Canonical PL Object SG PL
Class 1: Count-only * * * ✓ ✓
Class 2: SG-count only * * * ✓ *
Class 3: PL-count only * * * * ✓
Class 4: Mass & PL-count ✓ ✓ ✓ * ✓
Class 5: Underspecifed ✓ ✓ ✓ ✓ ✓
Table 2.1: Determiner correspondences English-Spanish based on the count-mass distinction
Classes of Determiners English Spanish
Class 1: Count-only – Todo(s), algún(os), ningún(os), un(os)
Class 2: SG-count only each, a, every cada, cualquier
Class 3: PL-count only several varios
Class 4: Mass and PL-count all, QAs todo el/todos los, QAs
Class 5: Underspecifed the, this/these, some, no el/los, este/estos
In order to account for the restrictions, I am assuming that D/Q heads can be characterized by the features on Table 3.4, with a rough approximation of their semantic import, building on insights from Beghelli
and Stowell (1997) analysis of quantificational determiners and Cowper and Hall (2014) decomposition of
determiners. I am assuming that indefiniteness is the lack of definiteness.
In addition to the inherent features on determiners, I propose that features located in the extended projection of the NP may appear on D-heads. When they do, they must have been copied onto the terminal
during the syntactic derivation, via Agree: D[𝑢F: ]...X[F] → D[𝑢F:F]...X[F]. Determiners and quantifiers,
92

Table 3.4: Inherent features on Determiners
Feature Meaning
[DEF] definite (referentially indexed in the discourse) (Cowper and Hall 2014)
[SPF] specific (denoting a particular individual) (Cowper and Hall 2014)
[PROX] proximal (near the point of attachment)
[DIST] distal (situated away from the point of attachment) (Cowper and Hall 2014)
[UNIV] universal (universal, not necessarily distributed) (Beghelli and Stowell 1997)
[DISTR] distributed (strongly distributed) (Beghelli and Stowell 1997)
[GROUP REF] group reference (existential denoting groups) (Beghelli and Stowell 1997)
as well as other modifiers, that are not heads but occupy specifier positions may also show uniform (phi-
)agreement with the NP and the D-head, i.e. nominal concord. I assume that concord features on these
non-head constituents attach in the form of unvalued features which will receive a matching value. This all
occurs post-syntactically (Bonet 2013; Norris 2014, 2017a,b; Deal 2016b).
3.2.4.1 Determiner Classes 1, 2, 3 & 5.
Leaving determiner Class 4 aside for a moment, in this system, we can summarize the other classes with the
schematic representations in (39).19
(39) a. Class 1: Count-only
DP
D
⎡
⎢
⎢
⎢
⎢
⎣
𝑢Num:SG/PL
𝑢IND:IND
⎤
⎥
⎥
⎥
⎥
⎦
NumP
Num
[SG/PL]
nP
√ROOT n
[IND]
19In order to be as general as possible and provide a unified analysis of determiners for both Spanish and English, I am not
including unvalued gender features on D. Nothing crucial hinges upon this decision. The represenations could be easily enriched
with a [𝑢GEND: ] feature on D. The probing feature will establish a dependency with n, where I assume gender features are located
(Kramer 2015; Kučerová 2018; Adamson and Šereikaitė 2019), and will copy its value onto it.
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b. Class 2: Singular-count only
DP
D
⎡
⎢
⎢
⎢
⎢
⎣
𝑢SG: SG
𝑢IND: IND
⎤
⎥
⎥
⎥
⎥
⎦
NumP
Num
[SG]
nP
√ROOT n
[IND]
c. Class 3: Plural-count only
DP
D
⎡
⎢
⎢
⎢
⎢
⎣
𝑢PL: PL
𝑢IND: IND
⎤
⎥
⎥
⎥
⎥
⎦
NumP
Num
[PL]
nP
√ROOT n
[IND]
d. Class 5: Underspecified
DP
D
Num
[SG]
nP
√ROOT n
e. Class 5: Underspecified (but plural)
DP
D
[𝑢PL: PL]
NumP
Num
[PL]
nP
√ROOT n
[IND]
DP
D
[𝑢PL: PL]
nP
√ROOT n
[PL]
Determiners are sensitive to the features that are available in the extended projection of the noun. Depending on the (unvalued) feature bundle that each determiner bears, what is copied via Agree will differ.
For instance, Classes 1-3 share in common the fact that the determiner is sensitive to individuated properties
as well as number features. However, the classes differ in the granularity of the number feature probes. The
probing feature in Class 1 is satisfied by any feature on the Number head, regardless of whether it is [SG] or
[PL]. The probes on Class 2 and 3 are however relativized to a certain feature specification on Number: [SG]
and [PL] respectively. We can imagine a scenario where a Class 2 D is merged with a Number[PL] head. The
94

probing feature will not be able to establish any Agree-link dependency, and as a result it will be unable to
copy a value onto its probe.
Regarding Class 5, the D head is always underspecified for [IND]. This accounts for why these determiners are acceptable with both any mass noun and (singular and plural) count nouns, e.g. (39d). While the
D head may also be underspecified for Number, some D heads may show sensitivity to plural-marking both
with count and mass nouns: these/those and definite determiners in Spanish. Thus, these Ds may optionally
bear an unvalued plural feature, as illustrated in (39e).
We are now in a position to discuss matters of determiner exponence. Along with the inherent D features
on Table 3.4 and the set of features that each class of D copies in the syntax, the determiners of classes 1, 2,
3 and 5 are spelled out as (40) in English and (41) in Spanish.
(40) VI rules for determiner exponence: English
a. D[UNIV, 𝑢IND: IND, 𝑢SG: SG] ⇔ 𝑒𝑣𝑒𝑟𝑦 Class 2
b. D[DISTR, 𝑢IND: IND, 𝑢SG: SG] ⇔ 𝑒𝑎𝑐ℎ
c. D[𝑢IND: IND, 𝑢SG: SG] ⇔ 𝑎(𝑛)
d. D[GROUP REF, 𝑢IND: IND, 𝑢PL: PL] ⇔ 𝑠𝑒𝑣𝑒𝑟𝑎𝑙 Class 3
e. D[DEF] ⇔ 𝑡ℎ𝑒
f. D[SPF] ⇔ 𝑡ℎ𝑖𝑠
g. D[SPF, DIST] ⇔ 𝑡ℎ𝑎𝑡 Class 5
h. D[SPF, 𝑢PL: PL] ⇔ 𝑡ℎ𝑒𝑠𝑒
i. D[SPF, DIST, 𝑢PL: PL] ⇔ 𝑡ℎ𝑜𝑠𝑒
j. D⇔ 𝑠𝑜𝑚𝑒
k. D[NEG] ⇔ 𝑛𝑜
(41) VI rules for determiner exponence in Spanish
95

a. D[UNIV, 𝑢IND: IND, 𝑢Num: SG/PL] ⇔ 𝑡𝑜𝑑𝑜(𝑠) Class 1
b. D[𝑢IND: IND, 𝑢Num: SG/PL] ⇔ {𝑎𝑙𝑔𝑢𝑛(𝑜𝑠)/𝑢𝑛(𝑜𝑠)}
c. D[NEG, 𝑢IND: IND , 𝑢Num: SG/PL] ⇔ 𝑛𝑖𝑛𝑔𝑢𝑛(𝑜𝑠)
d. D[DISTR, 𝑢IND: IND, 𝑢SG: SG] ⇔ 𝑐𝑎𝑑𝑎 Class 2
e. D[GROUP REF, 𝑢IND: IND, 𝑢PL: PL] ⇔ 𝑣𝑎𝑟𝑖𝑜𝑠 Class 3
f. D[DEF] ⇔ {𝑒𝑙/ 𝑙𝑎} Class 5
g. D[DEF, 𝑢PL: PL] ⇔ {𝑙𝑜𝑠/ 𝑙𝑎𝑠}
h. D[SPF] ⇔ {𝑒𝑠𝑡𝑒/ 𝑒𝑠𝑡𝑎}
i. D[SPF, PROX] ⇔ {𝑒𝑠𝑒/ 𝑒𝑠𝑎}
j. D[SPF, DIST] ⇔ {𝑎𝑞𝑢𝑒𝑙/ 𝑎𝑞𝑢𝑒𝑙𝑙𝑎}
k. D[SPF, 𝑢PL: PL] ⇔ {𝑒𝑠𝑡𝑜𝑠/ 𝑒𝑠𝑡𝑎𝑠}
l. D[SPF, PROX, 𝑢PL: PL] ⇔ {𝑒𝑠𝑜𝑠/ 𝑒𝑠𝑎𝑠}
m. D[SPF, DIST, 𝑢PL: PL] ⇔ {𝑎𝑞𝑢𝑒𝑙𝑙𝑜𝑠/ 𝑎𝑞𝑢𝑒𝑙𝑙𝑎𝑠}
3.2.4.2 Determiner Class 4: all and QAs.
Class 4 presents a challenge to the analysis of the count-mass distinction developed in this chapter. While the
elements of this class only appear with mass nouns (regardless of their subclass) and plural count nouns, these
two groups of nouns do not form a syntactic natural class: there is no common set of features between the
two. There is, however, one other way of linking these two featurally distinct groups of nouns into a natural
class. Both mass and plural count nouns share the semantic property of being cumulative (Quine 1960;
Cheng 1973; Bach 1986b; Krifka 1989; Chierchia 1998b,a, 2010; Borer 2005a, among others): a predicate
𝑃 is cumulative if for every member in 𝑃, their sum is also in 𝑃. The formal definition of cumulativity is in
(42).
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(42) CUM(𝑃) = ∀𝑥[𝑃(𝑥) → ∀𝑦[𝑃(𝑦) → 𝑃(𝑥 ∪ 𝑦)]]
Mass nouns are cumulative because if 𝑥 is water and 𝑦 is also water, then their sum is also water. Similarly,
plural count nouns like books are cumulative because adding books to books is still books. In contrast,
singular count nouns are not cumulative; the sum of two elements in the singular count noun extension is not
in the noun extension: the sum of two book is not a book. That said, we have now a non-syntactic explanation
for what makes Class 4 a natural class: the quantificational determiners of Class 4 require that the NP they
modify be cumulative. We can then encode the cumulative restriction on the (denotation of the) Q head
itself. This is not a novel contribution. Deal (2016a, 2017) reaches the same conclusion when probing the
distribution and properties of similar quantifiers in Nez Perce.
There is a slight difference between the universal quantifiers all in English and todos los ‘all.PL the.PL in
Spanish, and QAs. The universal quantifier seems to occupy a higher position in the DP given that it must
precede determiners and demonstratives. Besides, as originally observed by Sportiche (1988) and subsequent
work after him, the universal can also be stranded in the clause. This is shown in (43) and (44)
(43) a. All the boys have watched the game.
b. The boys have all watched the game.
c. All the water has been drained.
d. The water has all been drained.
(44) a. Todo-s
all.M-PL
lo-s
the.M-PL
chico-s
boy.M-PL
han
have
visto
seen
el
the
partido
game
‘All the boys have watched the game’
b. Lo-s
the.M-PL
chico-s
boy.M-PL
han
have
visto
seen
todo-s
all.M-PL
el
the
partido
game
‘The boys have all watched the game’
c. Toda
all.F
la
the.F
sal
salt.F
se
SE
cayó
dropped
por
over
la
the
mesa
table
‘All the salt was spilled over the table’
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d. La
the.F
sal
salt.F
se
SE
cayó
dropped
toda
all.F
por
over
la
the
mesa
table
‘The salt was all spilled over the table’
Based on these facts, I take Class 4 all and its Spanish counterpart to occupy a specifier position higher
than DP as in (45). In English, the terminal D node that spells out all bears no unvalued features and it is
thus invariant with respect to number-marking. In Spanish, however, if the NP is plural-marked, so must the
Determiner in Spec, QP. Thus, an unvalued [𝑢PL:_] must be inserted post spell-out to ensure concord.20
(45) QP
DP
D
[UNIV]
‘all/todo’
Q’
Q DP
D
([DEF])
...
With respect to QAs, I formulated the empirical generalization in (71) from Chapter 2, repeated below.
In Spanish, the QA must always be plural-marked if there is a plural-feature on the extended projection of
the NP (i.e. plural mass nouns and plural count nouns). In English, the distribution of the more marked-form
many seems more restricted: some speakers of English only accept many with plural count nouns, whereas
others accept it anytime there is a plural feature.
(71) The plural-QA-markedness Generalization
Overt plural marking on the noun
a. forces the QA to be plural-marked in Spanish, and
b. makes it possible for the QA to surface as many in English.
20I have decided to represent Class 4 all and todo(s) as occupying a specifier position of a Q head above the DP. The reason
for this decision is based on the Q-float data and the assumption that intermediate projections such as D’ or Q’ are precluded from
movement (Chomsky 1994, 1995). There is potentially one additional reason why these DPs have to be located in the specifier of
their own projection above DP. In English, possessors generally assumed to be located in Spec,DP (Abney 1987; Corver 1990) must
occur lower than all:
(vii) Kavanaugh and Rodriguez group all John’s maxims as The Sayings of Light and Love.
(https://contemplativehomeschool.com/2015/11/04/the-writings-of-st-john-of-the-cross/)
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While it is in principle possible to hypothesize that there are different lexical items much for mass, many1
for plural count and many2
for plural mass, this comes at the expense of enriching the lexicon and would not
establish any intrinsic relation between the listed items. Variation across speakers of English would amount
to stipulating that while some speakers have the three forms in their inventory, others only have two: much
and many1
. This option would also come at too high a cost if we take into account the cross-linguistic data,
in this case from Spanish:21 QAs track plural-marking if a plural feature is available. This observation has
received empirical support from the work of Wellwood (2018, 2019); Smith (2021); Cleani and ToqueroPérez (2022).22
Taken together, I interpret these facts as evidence for the hypothesis that the surface form of the QA is
sensitive to number marking. In particular, just like muchos is the surface form of a degree morpheme and
(gender and) number features, so is many (except for the gender part). The surface forms mucho and much
are thus the unmarked cases. Under the account developed here this amounts to saying that the DegP that
hosts much/many and their Spanish counterparts may also be specified for a plural feature whose value must
be copied. In the spirit of Bresnan (1973); Hackl (2000); Bobaljik (2012); Wellwood (2015); Dunbar and
Wellwood (2016), I adopt a decompositional approach to QAs according to which positive, comparative and
superlative forms of QAs have the internal structure in (46).
(46) The internal structure of QAs
Deg
Deg
√MEAS Deg
COMPR
COMPR SUP
QAs are composed of a measure root √MEAS and a categorizer Deg. The root is licensed in the context
of this head. This structure, built upon insights from Dunbar and Wellwood (2016), entails that Deg and
21In Chapter 4, I will show further evidence from Greek and Telugu that suggests that the lexical approach is not empirically
supported.
22Cleani and Toquero-Pérez (2022) discuss Norwegian. The language is like English with respect to the positive form of the QA:
it has a much/many distinction. Unlike English, Norwegian also keeps a contrast in the comparative form depending on whether the
noun is or not plural-marked. See Cleani and Toquero-Pérez (2022) for more details.
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√MEAS are always syntactically represented in positive, comparative and superlative forms of QAs.23 Given
the fact that Deg projects, the positive can occur without the COMPR and SUP heads, but the latter two cannot
occur without the former. This is consistent with Bobaljik’s (2012) Containment Hypothesis: the syntactic
representation of the superlative contains the comparative which contains the positive.
We can assume that the underlying structure of an equative is identical to (46) with the only difference
that instead of a COMPR-head, the relevant head is EQ (which does not take SUP as a complement). While in
English, the measure root √MEAS surfaces with the same form as in the positive (including degree questions),
in Spanish, the form that √MEAS surfaces with in equatives and degree questions differs from those in the
positive/comparative/superlative: tanto/cuánto vs. mucho/más. I will assume that these alternations in Spanish are morpho-syntactically conditioned by the local context in which the measure root occurs. Restricting
ourselves to the positive forms, √MEAS surfaces as tan-/cuan- in the context of Deg[D (,WH)] and √MEAS
surfaces as mucho elsewhere.24 The structures are summarized in (47) for English and in (48) for Spanish.
(47) English
a. Positive
Deg ⇔ 𝑚𝑢𝑐ℎ/𝑚𝑎𝑛𝑦
√MEAS Deg
b. Comparative
Deg ⇔ −𝑒𝑟/𝑚𝑜𝑟𝑒
Deg
√MEAS Deg
COMPR
c. Equative
Deg ⇔ 𝑎𝑠 𝑚𝑢𝑐ℎ/𝑚𝑎𝑛𝑦
Deg
√MEAS Deg
EQ
23The difference between the structure in (46) and Dunbar and Wellwood’s (2016) is the extra step in the decomposition: for
Dunbar and Wellwood (2016), the root-Deg compound is collapsed into a single terminal which they label MUCH. The measure
morpheme for them is MUCH, whereas for me the measure morpheme is √MEAS.
24The [D] feature on Deg is intended to indicate a more determiner-like use of tan/tanto. For instance, it is the only Deg-word
that has a wh-counterpart.
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(48) Spanish
a. Positive
Deg ⇔ 𝑚𝑢𝑐ℎ𝑜(𝑠)
√MEAS Deg
b. Comparative
Deg ⇔ más
Deg
√MEAS Deg
COMPR
c. Equative
Deg ⇔ 𝑡𝑎𝑛𝑡𝑜(𝑠)
Deg
√MEAS Deg
[D]
EQ
DegPs are not heads in the extended projection of the NP, but they occupy a specifier position (Zabbal
2005; Kayne 2005; Schwarzschild 2006; Nakanishi 2007). Thus, any unvalued feature spelled-out on the
Deg-head will not have been copied via Agree, but inserted post-Spell-Out. It is at this point, and crucially
before the application of any other post-syntactic operation such as Impoverishment or Vocabulary Insertion, when they will receive a matching value.25 The syntactic representations of DPs containing a QA are
provided in (49) for plural count nouns. For ease of illustration, I will concentrate on the positive form.
(49) Feature copying on QAs: Plural count nouns
a. Insert [𝑢PL] on Deg
DP
D
[𝑢PL: PL]
QP
DegP
√MEAS Deg
[𝑢PL:_]
Q’
Q NumP
Num
[PL]
nP
√ROOT n
[IND]
b. Copy PL value
DP
D
[𝑢PL: PL]
QP
DegP
√MEAS Deg
[𝑢PL: PL]
Q’
Q NumP
Num
[PL]
nP
√ROOT n
[IND]
25I want to emphasize here that I am not committing to any particular account of nominal concord. For an overview of concord
proposals, see Norris (2017a,b). I am simply assuming that the mechanism that underlies the operation of concord is distinct from
the syntactic operation Agree.
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The first step in the (post-syntactic) derivation is to insert an unvalued feature [𝑢PL] on the Deg-head,
e.g. (49a). This feature then gets a PL-value copied via concord as in (49b). At the point of VI, there are
two possible insertion rules in English, formulated in (50). The rule in (50a) is more specific and thus is
applied according to the Subset Principle. In Spanish, there is no suppletion triggered by plural and instead
[PL] surfaces as an affix to the root. The relevant VI rules in Spanish are in (51).
(50) VI rules for √MEAS (English)
a. √MEAS ⇔ 𝑚𝑎𝑛𝑦/ Deg[𝑢PL: PL]
b. √MEAS ⇔ 𝑚𝑢𝑐ℎ
(51) VI rules for √MEAS and Deg (Spanish)
a. √MEAS ⇔ 𝑐𝑢á𝑛/__Deg[D, WH]
b. √MEAS ⇔ 𝑡𝑎𝑛/__Deg[D]
c. √MEAS ⇔ 𝑚𝑢𝑐ℎ𝑜
d. Deg[D, 𝑢PL: PL] ⇔ −𝑡𝑜𝑠
e. Deg[D] ⇔ −𝑡𝑜
f. Deg[𝑢PL: PL] ⇔ −𝑠
In the case of canonical mass nouns and object mass nouns, there is no plural-feature available in the
structure. Thus, there is no need for post-syntactic insertion of [𝑢PL].26 Thus, lack of plural-concord blocks
the application of the more specific rule in (50a) in English, triggering insertion of the elsewhere case: (50b).
In Spanish, the only features that are inserted for concord are gender-features, which I have not included in
the representations. This derivation is shown in (52a).
(52) No PL-feature copying: canonical and object mass nouns
26Even if the concord feature was inserted after Spell-Out, no value will be copied onto it.
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a. canonical mass
DP
D QP
DegP
√MEAS Deg
Q’
Q nP
√ROOT n
b. Object mass
DP
D QP
DegP
√MEAS Deg
Q’
Q nP
n
[COLL]
nP
√ROOT n
[IND]
Regarding plural mass nouns, I propose that the derivation in both languages proceeds exactly as in the
case of plural count nouns in (49): an unvalued plural feature is inserted and it is subject concord. As in
(49b), a value is copied onto this feature. This is shown in the trees in (53).
(53) Feature copying on QAs: Plural mass nouns
a. Insert [𝑢PL] on Deg
DP
D
[𝑢PL: PL]
QP
DegP
√MEAS Deg
[𝑢PL:_]
Q’
Q nP
√ROOT n
[PL]
b. Copy PL value
DP
D
[𝑢PL: PL]
QP
DegP
√MEAS Deg
[𝑢PL: PL]
Q’
Q nP
√ROOT n
[PL]
In the case of Spanish, the VI rules in (51) apply accordingly, thus resulting in overt plural agreement
between the QA and the noun: muchos celos. In the case of English, something else must be said because the
locality between √MEAS and PL on Deg predicts that the rule in (50a) should be triggered univocally, inserting
many in this context. However, there is variation and most speakers seem to prefer the elsewhere case much.
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I propose that we can still maintain the uniform representations and VI rules, while still accounting for the
variation with plural mass nouns if Impoverishment applies before VI. More specifically, an Impoverishment
rule deletes the plural feature on Deg, as in (54).
(54) Deletion rule
Deg[𝑢PL: PL] ⇔Deg✘
❳✘❳✘❳✘ [uPL: PL❳] in the context of plural n
Impoverishment deletes syntactic features on terminals prior to Vocabulary Insertion (Bonet 1991, 2008;
Embick 2010; Arregi and Nevins 2007, 2012, 2013). As a result, more specific VI rules that would be applied
no longer fulfill the insertion conditions determined by the Subset Principle. This triggers the application of
the less specific rule instead. This is precisely the case of much and plural mass nouns under discussion. The
rule in (54) is not universally shared across English speakers. Those speakers who have this rule as part of
their grammar will apply (54) after the plural feature has been copied, shown in (55), which will bleed the VI
rule in (50a). For those speakers who lack the rule altogether, there is no additional step in the post-syntax
and the more specific VI rule in (50a) will win over. This variation can be summarized in Table 3.5.
(55) Impoverishment of PL on Deg
DP
D
[𝑢PL: PL]
QP
DegP
√MEAS Deg
✘
❳✘❳✘❳✘ [𝑢PL: PL❳]
Q’
Q nP
n
[PL]
√ROOT
The analysis of QAs proposed here is consistent with a uniform treatment of QAs across languages that
show sensitivity to plural-marking, as summarized in Table 2.11. Besides, it pushes the variation away from
the lexicon: the surface form of QAs is not lexically determined (Solt 2009, 2015) but morpho-syntactically
so (Bobaljik 2012; Wellwood 2015, 2018; Bale 2016; Smith 2021; Cleani and Toquero-Pérez 2022). This
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Table 3.5: Variation in √MEAS-exponence (English)
Grammar PL-concord Impoverishment VI rule
𝔾𝟙 ✓ ✓ (50b) = much
𝔾𝟚 ✓ * (50a) = many
also has a consequence for thinking about the semantic interpretation of these items. The analysis advocates
for the hypothesis that there is no one-to-one mapping between the surface form of the QA and the dimension
of measurement they introduce in the semantics.
3.3 Variation in the distribution of [COLL] feature
An important piece of the analysis was the [COLL] feature that I proposed is responsible for generating object
mass nouns. But proposing this feature raises several questions. First, it seems that, when given an individuated item 𝛼, [COLL] creates a collection of items 𝛽 which are somehow associated with 𝛼. Object mass nouns
are not the only types of NPs that have been argued to denote collections or similar aggregates. Nouns like
team, committee, government also refer to groups that consist of individual members (Link 1984; Landman
1989a,b; Joosten 2010; Pearson 2011; de Vries 2021).
Second, [COLL] seems to be in many ways similar to [PL] on Number: in terms of their selectional features,
they both require an individuated nP complement; in terms of the semantics, which I have not been yet
discussed in (formal) detail, there must also be similarities between [COLL] and [PL] given that the traditional
view on object mass nouns has assumed that they are inherently plural-marked (Chierchia 1998a; Bale and
Barner 2009; Smith 2021).
Thus, all in all we might wonder (i) whether [COLL] is also responsible for generating group nouns, (ii)
whether it is empirically justified to locate [COLL] on n instead of Number and (iii) whether [COLL] can ever
be located on Number giving rise to languages that have, potentially, [SG/ PL/ COLL] as part of their inventory
of Number features. I will show that object mass nouns and group nouns have a different morpho-syntactic
105

distribution which leads to the conclusion that their underlying syntax must be different too. I will then move
on to argue why [COLL] is part of categorizing heads in languages like English or Spanish, but it might be
located on Number in other languages such as Czech. Thus, just like [PL] can be located on n and Number
so can [COLL].
3.3.1 Group nouns do not have [COLL].
One could hypothesize that NPs that refer to a collection (including groups or object mass) are marked for
[COLL] in the syntax. However, group nouns like team, committee, government do not have the same morphosyntactic distribution as object mass nouns. In fact, group nouns pattern with count nouns with respect to
number-marking, numeral modification, and ellipsis. The relevant data for English is in (56) and the relevant
data in Spanish is in (57).
(56) Group nouns English
a. {Each Spanish team/ Several Spanish teams} will win a competition. (SG/PL-marking)
b. Two Spanish teams will win a competition. (numeral modification)
c. Messi only played for one big Spanish team, but Figo played for two big Spanish teams.
(SG/PL-mismatch)
d. The crowd cheered for the Spanish team and booed the French one. (one-substitution)
(57) Group nouns Spanish
a. Cada
each.M
equipo
team
español
Spanish.M
ganará
win.FUT.3SG
una
a.F
competición.
competition
‘Each Spanish team will win a competition’ (SG-marking)
b. Vario-s
several.M-PL
equipo-s
team-PL
español-es
Spanish.M-PL
ganarán
win.FUT.3PL
una
a.F
competición.
competition
‘Several Spanish teams will wine a competition’ (PL-marking)
106

c. Dos
two
equipo-s
team-PL
español-es
Spanish.M-PL
ganarán
win.FUT.3PL
una
a.F
competición.
competition
‘Two Spanish teams will win a competition’
d. Messi
Messi
solo
only
jugó
played
para
for
un
one
equipo
team
español
Spanish.M
grande,
big
pero
but
Figo
Figo
jugó
played
para
for
dos
two
equipo-s
team-PL
español-es
Spanish.M-PL
grand-es
big-PL
‘Messi only played for one big Spanish team, but Figo played for two big Spanish teams.
(SG/PL-mismatch)
e. La
the
gente
people
animaba
cheered
a
to
este
this
equipo
team
español,
Spanish.M
y
and
abucheaba
booed
a
to
este
this
otro
other.M
francés
french.M
‘The people cheered for this Spanish team and booed this French one’ (otro-substitution)
As also evidenced by both sets of examples, group nouns are compatible with Class 2 determiners each
and cada, and with Class 3 determiners such as several and varios. These are determiners that require
the NP to be count (i.e. [IND, SG/PL]). The relevant data are in (56a) for English and (57a) and (57b) for
Spanish. All these properties indicate that group nouns have the underlying syntax of regular count NPs.
It is also worth noting that if group nouns and object mass nouns were to be treated on a par, we would be
loosing the generalization in (28) (i.e. morphologically complex object mass nouns, at least on the collective
interpretation, are always formed of top of count noun bases).
Besides, while object mass nouns satisfy the semantic property of cumulativity allowing modification
by QAs like much, mucho, more, más, the unmarked form of group nouns does not, as illustrated by the
following examples in (58).
(58) a. * There was {too much/more} team holding a meeting in that room
b. There were {many/more} teams holding a meeting in that room
c. * Había
there.were
{ mucho/
much.M/
más}
more
equipo
team
teniendo
having
una
a
reunión
meeting
en
in
la
the
sala.
room
d. Había
there.were
{ muchos/
much.M-PL/
más}
more
equipo-s
team-PL
teniendo
having
una
a
reunión
meeting
en
in
la
the
sala.
room
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A further difference with object mass nouns is related to agreement patterns with verbs when the group NP
functions as subject. In varieties of British and Canadian English, when they are morphologically unmarked
(e.g. team, committee), group nouns may control singular or plural agreement on the verb Sauerland and
Elbourne (2002); Pearson (2011); Thoms (2019). This is shown in (59) from Thoms (2019). What is more,
when the unmarked group noun in subject position controls plural agreement on the verb, the NP cannot
reconstruct for scope.
(59) a. A Spanish team is likely to win the Champions League. likely>∃
b. A Spanish team are likely to win the Champions League. *likely>∃
While facts like (59b) have been taken as evidence for “semantic agreement” (Wechsler and Zlatić 2003;
Corbett 2006), the conditions under which the group NP controls plural agreement on the verb are syntactically conditioned by movement (Sauerland and Elbourne 2002; Nevins and Anand 2003; Thoms 2019).
In (60), the group NP remains in-situ, assuming analyses of there-existentials such as Chomsky (2000) or
Deal (2009), and only singular agreement is possible. Similar facts seem to obtain in Spanish: group nouns
control plural agreement when the NP undergoes some (A-bar) movement operation (Suñer 2002; FernándezSánchez 2015). The example in (61a) is from (Fernández-Sánchez 2015).
(60) There {was/ *were} a team holding a meeting in the room.
(61) a. Este
this
equipo,
team
yo
I
creo
think
que
that
{ juega/
play.3SG
juegan}
play.3PL
mejor
better
bajo
under
presión.
pressure
‘This team, I think that {plays/ play} better under pressure’
b. Yo
I
creo
think
que
that
este
this
equipo
team
{ juega/*
play.3SG
juegan}
play.3PL
mejor
better
bajo
under
presión.
pressure
‘I think that this team {plays/ play} better under pressure’
None of these facts are possible with object mass nouns which univocally control 3rd person singular
agreement on the verb, regardless of whether the relevant NP has undergone movement or remains in-situ.
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All in all, we can conclude that syntactically group nouns of the team or committee type do not form a natural
class with object mass nouns in terms of the count-mass distinction.
There are also reasons to think that these classes of nouns are not semantically the same. Group nouns
refer to collections that are more than just the sum of their parts (Landman 1989a): for instance, a team is
not only a collection of its individual members, it is also an entity in and of itself. Joosten (2010) refers to
this property as “non-additivity”. On the contrary, an object mass noun is “additive” because it pretty much
refers to the sum of its individual parts; in other words, they denote collections of individual entities or items
which share some relation or property. Related to this is the observation that group nouns and object mass
nouns give rise to different entailment patterns (Joosten 2010). For instance, there is a difference between
the following statements in (62) and (63).
(62) a. The old committee members gathered ↛ the old committee gathered
b. The old committee gathered ↛ the old committee members gathered.
(63) a. John gathered the old chairs and tables → John gathered the old furniture.
b. John gathered the old furniture → John gathered the old chairs and tables.
While being a committee member that is old does not entail, or at least not necessarily, that the committee
itself is old, being a chair and a table that are old does entail that the furniture itself is old. The same patterns
obtain in the other direction as illustrated in (62b) and (63b).
In this section I have shown that group nouns pattern nothing like object mass nouns with respect to
the count-mass asymmetries discussed. In fact, they behave like regular count nouns. While it is true that
semantically, and in some ways syntactically, they are different from regular count nouns such as member, we
cannot ascribe these properties to the [COLL] feature. The feature-based account that I have proposed here is
able to account for most, if not all, morpho-syntactic asymmetries between the class of (count) group nouns
and object mass nouns. It is possible that more is required to formally account for all the special properties
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of these group nouns, both syntactically and semantically; but, as of now, I remain neutral about what that
might be. All that I can do is point the reader to the relevant semantic analyses like Landman (1989a,b, 2004);
Barker (1992); Pearson (2011); Henderson (2017); Zwarts (2020) and syntactic analyses such as Sauerland
and Elbourne (2002); Thoms (2019); Smith (2021) among others.
3.3.2 [COLL] on n or Number
I proposed that the [COLL] feature, at least in languages like English and Spanish, was located on a nominalizing head that is layered on top of the inner-most nominalizing n[IND]. Pretheoretically at least, it is argued
that morphemes generating object mass nouns in these languages are ‘derivational’, rather than ‘inflectional’
(Lieber 2004, 2016; De Belder 2011, 2013; Cohen 2020). In DM-style approaches to morpho-syntax, derivational morphemes are generally represented by categorizing heads and inflectional morphemes correspond
to functional heads such as those encoding number, person, definiteness or case (Marantz 1997, 2001, 2013;
Arad 2003; Embick and Marantz 2008). In this regard, locating [COLL] on n as opposed to Number is consistent with this view.
In addition, the nominalizing status of [COLL] in these languages is supported by the fact that the same
morpheme can create nouns out of other nouns, but also verbs or even adjectives. Some examples are in (64)
and (65) for English
(64) carpeting
a. carpetverb: ‘to cover something with a carpet’
carpetverb+ [COLL] → carpetingnoun: ‘the result of covering something with a carpet’
b. carpetnoun: ‘floor covering made from some fabric’
carpetnoun + [COLL] → carpetingnoun: ‘collection of carpet-related items’
(65) activewear
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activeadjective: ‘engaged in some (physical) activities’
activeadjective+[COLL] → activewearnoun: ‘collection of items worn when engaging in physical
activities’
As observed in the examples above, adding the [COLL] feature can recategorize the base: from v/n/a to
n. In Spanish, similar facts are observed. What is more, adding the [COLL] feature triggers a change in the
grammatical gender and declension class of the base. For instance in (66b), the nominal base is feminine and
spells out declension class 2 (CLS2), e.g. -a, whereas the derived object mass noun is masculine and spells
out declension class 1, e.g. -o.
27 Another example just focusing on gender and declension class changes is
shown in (67).
(66) armamento
a. arm-ar
weapon-INF
√ROOT-v
‘to weapon’
arm-ar
weapon-INF
√ROOT-v
+[COLL]
-n
→ armamento:
weaponry.M.CLS1
‘the result of equipping with weapons’
b. arm-a
weapon-F.CLS2
√ROOT-n
‘(a) weapon’
arma
weapon.F.CLS2
√ROOT-n
+[COLL]
-n
→ armamento:
weaponry.M.CLS1
‘collection of weapon-related items’
(67) a. grad-a
grandstand-F.CLS2
b. grad-erí-o
grandsand-COLL-M.CLS1
‘Collection of grandstands’
27Nouns themselves do not generally spell out gender, but class. That is, the word marker attached to the nominal root is a class
exponent, not a gender marker. For more information about declension classes in Spanish, see Roca (1989); Harris (1991); Kramer
(2015).
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If gender is located on n (Alexiadou 2004; Kramer 2015) and class markers on the noun are also on n
(Oltra-Massuet and Arregi 2005; Kramer 2015; Kučerová 2018), the fact that object mass nouns may undergo
shifts in both class marker exponence and gender is strong evidence for the n-status of the collective feature
in Spanish too.28
We can take these facts as evidence for the proposal that [COLL], responsible for deriving object mass
nouns, is on n at least in the two languages that have been discussed in this dissertation. This is not supposed
to be a universal claim about the syntactic position of [COLL]. After all, features may appear distributed along
different heads within a single language or across languages. In fact, this is the situation with [PL] which
may appear on Number or n in English, Spanish, Amharic (Kramer 2016) or Greek (Alexiadou 2011, 2015;
Kouneli 2019), but also on D in languages like Persian (Ghomeshi 2003). Thus, it would not be surprising
to find [COLL] in a different syntactic position. What is more, given the similarities between [COLL] and [PL],
we might find languages where [COLL] is actually a feature on the Number head instead of the nominalizer.
If that is the case, the theory I have developed in this chapter makes (at least) the predictions in (68).
(68) If [COLL] is on Number,
a. only count noun bases will bear this feature;
b. [COLL]-marked nouns will enable numeral modification; and,
c. [COLL]-marked nouns allow one-substitution.
(68a) is expected if only count nouns project Number; (68b) follows from the hypothesis that the head
introducing numerals selects for Number; (68c) follows from the analysis of one-substitution as insertion of
a vocabulary item one on the individuated n-head in the context of Number. Grimm and Docekal (2021)
report some data from Czech showing that predictions (68a) and (68b) are borne out. They do not discuss
one-substitution in the language, and thus no claims can be made about (68c) based on their data.
28See also Fábregas (2013); Kramer (2015) for evidence that changes in declensional class and gender-marking involve renominalization.
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Grimm and Docekal (2021) report that in Czech a morpheme -í can be affixed to count noun roots resulting in an interpretation that refers to a ‘collection of N’.29 The authors note that this morpheme is not very
productive in the language and its distribution is restricted to a limited set of count nominal roots. In fact, in
their footnote 5, they indicate the following: they surveyed 22 -í-marked nouns, which, the authors report,
comprise the majority of -í-marked nouns in the language.
The example in (69) shows that the count noun root for leaf can either be overtly plural-marked or -ímarked. In addition, they show that if a noun is -í-marked then it cannot be subsequently plural-marked.
This is illustrated in (70). Grimm and Docekal (2021) gloss -í, and its allomorphs, as ‘í’ but I will gloss it as
COLL to indicate its collective contribution to the meaning of the noun.
(69) a. list-y
leaf-M.PL
‘leaves’
b. list-í
leaf-COLL
‘Foliage’
(70) a. list-í-m
leaf-COLL-INSTR
‘foliage’
b. * list-í-mi
leaf-COLL-INSTR.PL
‘foliages’
In this respect, the distribution of -í in Czech seems very similar to that of -ery or -age in English: it
attaches to a count noun stem and it is in complementary distribution with plural-marking. What is more,
when describing the meaning of the -í-marked forms, they note the following: “the meanings of nouns
derived by -í contrast strongly with ordinary plural meanings. [...] [T]he resultant meaning of nouns derived
by -í is not simply a set of, for example, pine trees, but a set in which the members are coherently related”
(Grimm and Docekal 2021, p.93). This semantic contribution resembles what [COLL] is doing for English
and Spanish.
29Grimm and Docekal (2021) indicate that the morpheme -í has several allomorphs such as -oví, which, as far as they are aware,
make no semantic difference. I want to note the following: (i) Grimm and Docekal (2021) do not consistently gloss the gender
on the -í-marked nouns; and, when they do, the gender on the -í-marked nouns seems to change to ‘neuter’ (NT). See Grimm and
Docekal (2021, p.92: ex.10b), included in this dissertation as (72). (ii) Grimm and Docekal (2021) do not always provide a complete
morphological segmentation of the nouns and they do not always provide perfect minimal pairs.
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The fact that only count noun bases are compatible with this -í-marking is consistent with the prediction
in (68a). However, it is not conclusive evidence that -í is spelling out a feature on Number as opposed to
n. The crucial data come from complex numeral modification. Many Slavic languages, Czech included,
have simple cardinal numerals, but also morphologically derived complex cardinal numerals, e.g. Ionin and
Matushansky (2018). The latter are used to talk about kinds, groups and collections. See the contrast in (71)
taken from Grimm and Docekal (2021, p.94: ex.15).
(71) a. tri
three
námoříc-i
sailor-NOM.PL
‘three sailors’ simple cardinal numeral
b. troj-ice
three-GROUP
námořík-ů
sailor-GEN.PL
‘a group of three sailors’ complex cardinal numeral for groups
Simple cardinal numerals like tři ‘three’ in (71a) are morphologically unmarked and, in the case of
numerals 1-4, the NP they modify is nominative and plural-marked. When the numeral is morphologically
marked with -ice as in (71b), (i) the NP is genitive and plural-marked, and (ii) the numeral root shows
suppletion. Besides, complex cardinal numerals marked with -ice give rise to a group interpretation: ‘a
group of X-number of sailors’.
Simple cardinals are ungrammatical as modifiers of -í-marked nouns, as (72) shows. However, Czech
has another complex cardinal numeral which is marked -oje (for numerals 2-3) and -ery (for numerals above
3) and it translates as ‘2/3/4...collections’. We can call this numeral ‘collective cardinal’ and I gloss it as such
(COLL.CARD). Crucially, collective cardinal numerals are grammatical with -í-marked nouns, but ungrammatical with plural-marked nouns such as table as shown in (73).
(72) a. dva
two.M
list-y
leaf-M.PL
‘two leaves’
b. * dvě
two.NT
list-í
leaf-NT.COLL
Lit.: ‘two foliages’
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(73) a. ?? dv-oje
two-COLL.CARD
stol-y
table-PL
‘two sets of tables’
b. dv-oje
two-COLL.CARD
nádob-í
container-COLL
‘two sets of dishes’
As the datapoint in (73b) illustrates, an -í-marked noun such as nádobí ‘dishes’ can be directly modified
by a collective cardinal dvoje ‘two (collective)’. This fact is what makes this subclass of nouns in Czech
different from object mass nouns in English and Spanish. Under the proposal advanced in this dissertation,
direct numeral modification is only possible if Number has been projected: CARD introducing numerals in
its specifier bears a feature [•Number•]. The fact that -í-marked nouns in Czech can be directly modified
by a numeral, in addition to their being formed on top of count nouns stems, is therefore evidence that the
[COLL] feature responsible for generating the ‘collection’ interpretation is located on Number, as schematized
in (74a).
(74) a. [CARDP
[#[uAGR:COLL]
] [CARD’ CARD[•Number•] [NumP Number[COLL, •IND•][nP n[IND] √ROOT]]] = (73b)
b. [CARDP
[#[uAGR:PL]
] [CARD’ CARD[•Number•] [NumP Number[PL, •IND•] [nP n[IND] √ROOT]]] = (72a)
[COLL] is spelled out as /-í/, and it surfaces on the noun. -oje on the numeral can be analyzed as the
result of nominal concord between the numeral and the [COLL] feature on Number (Norris 2014; Ionin and
Matushansky 2018).30 Plural-marked count nouns have a similar underlying structure but differ in the set of
features that they bear on Number, e.g. (74b); as a result, a plural morpheme is exponed on the noun and no
-oje surfaces on the numeral.31
If we were to locate the feature on a layered n instead, as we did for English and Spanish, we would
account for the complementary distribution of [COLL] and [PL] but we would be left with no explanation as
to why numerals can modify [COLL]-marked nouns in Czech but not in English or Spanish. That said, we
30Contrary to the complex numeral in (71b), Grimm and Docekal (2021) claim that both collective and simple cardinal numerals
must agree with the noun they modify in case and number – and given their glossing, gender too. However, this is difficult to
determine given that case and number morphology on the numeral are never mapped to an overt exponent (at least in the examples
they provide).
31Grimm and Docekal (2021, p.97) report that collective cardinals can also modify pluralia tantum nouns and “entities that
typically come together in multiples”. These two other classes of nouns are not -í-marked: brýle ‘glasses’ (pluralia tantum), hranolky
‘French fries’ (multiples).
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can conclude that the location of the [COLL] feature is subject to variation, just like [PL] is (Wiltschko 2021,
for an overview): in some languages, it will be located on n, while in others it will be located on Number.
This is how we account for the variation between Czech and English/Spanish summarized in (75): [COLL] is
a nominalizing feature in English/Spanish, but it is a Number feature in Czech.
(75) a. English/Spanish: n[PL/COLL], Number[SG/PL]
b. Czech: Number[SG/PL/COLL]
3.4 Conclusion
This chapter has focused on setting the bases for the theory of number and individuation that I will develop
throughout the dissertation. At an empirical level, the goal of the chapter has been to provide a formal analysis
of the different asymmetries between the classes of count and mass nouns: number-markedness, modification
by numerals and/or stubbornly distributed adjectives, determiner restrictions, and ellipsis options.
I have proposed that separating the roles of individuation and number helps account for these asymmetries. An important motivation for this analytic move was the Plural-Count Generalization. In particular,
mass nouns may not be specified for individuation and do not project Number. Number, as a dedicated functional projection, is contingent upon the noun being marked for individuation. Many of the asymmetries
between the classes can be derived by virtue of Number not being projected. The conclusions that we arrive
to can be summarized as follows: numerals require Number; (a projection as high as) Number enables modification by Stubbornly Distributive adjectives; and, Number licenses [E]-marking of its complement’s head,
resulting in one/otro-substitution.
There existed two paradoxical cases: plural mass and object mass. The former resemble plural count
nouns in morphological markedness, but nothing else. The latter share with count nouns the fact that they
can be modified by adjectives like large or round. Regarding the first paradox, I have argued that despite
116

them both being plural-marked, there is a structural difference with respect to the source of plural-marking:
n or Number. Plural mass nouns, though, are still unmarked for individuation.
Regarding the second paradox, I put forth the hypothesis that object mass nouns are built on top of an
individuated nP shell. What is more, this layered head in languages like English or Spanish is not Number
or [PL], and it would be a mistake to label it as such. This head is a nominalizer bearing the feature [COLL],
and it is in fact in competition with Number for merger. Therefore, there is nothing lexically special about
this class of nouns: their properties are determined by the syntax. This novel analysis does not only account
for why there are many count-object mass doublets, but also for other properties, including lack of overt
plural-marking, root-allomorphy, and the enabling of adjectival modification. Besides, lacking Number but
being [IND]-marked ensures that the noun has discrete separable units in its extension. This, I will argue in
the next chapter, will be crucial for their symmetrical behavior with count nouns in terms of their semantics.
With respect to the determiners, the analysis sheds light onto the generalization about determiner distribution more generally and the interaction of this class of syntactic objects, number and invidividuation. The
descriptive generalizations in (72) from Chapter 2 can be reformulated in more abstract terms in (76).
(76) a. If a determiner is sensitive to [IND]-marking, it will be also sensitive to Number.
b. If a determiner is sensitive to [PL], it need not be sensitive to [IND].
c. There is no determiner that is exclusively sensitive to the noun being mass.
These facts, in concert with the other properties surveyed, emphasize the hypothesis that there are few, if
any, grammatical markers that track or encode ‘mass’. Rather, being mass is better instantiated by the lack
of count properties. This also brings us back to the situation with QAs. The distribution of the different
forms of QAs is not lexically determined, but grammatically so. QAs across many languages are sensitive to
𝜑-features on the extended projection of the noun that they modify. Plural was such a feature in the case of
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English and Spanish. Thus, the much/many distinction, even in cases where it seems to have been neutralized, is no different than the mucho/muchos distinction in Spanish or the mere/flere ‘moremass/moreplural-count’
distinction in Norwegian (Cleani and Toquero-Pérez 2022): allomorphy on the measure root at the point of
Vocabulary Insertion triggered by a local plural feature. Such a view on QA distribution is not only aligned
with the view that QAs are morpho-syntactically complex (Bresnan 1973; Hackl 2000; Bobaljik 2012; Dunbar and Wellwood 2016), but also with the view that measure morphemes are semantically underspecified
(Wellwood 2015, 2018, 2019). This way of thinking, in concert with the theory of number and individuation
developed, helps us predict the type of alternations that we might observe cross-linguistically and also it will
help us predict when the combination ‘QA + N’ can be interpreted in terms of cardinality uniformly across
languages.
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Chapter 4
Canonical Dimensions of Measurement: when more N means ‘cardinality’
The discussion in Chapter 2 and Chapter 3 was concerned with four syntactic asymmetries observed across
the classes of count and mass nouns. These chapters served to set the descriptive and analytic basis for
what it means to be ‘count’ like book and also ‘mass’, including its different subtypes. There is one more
asymmetry that needs to be addressed and this is concerned with the semantic interpretation of these nouns
when modified by QAs. This chapter focuses on this semantic asymmetry.
It has been observed that the interpretation of canonical and plural mass nouns differs from the interpretation of plural count nouns and object mass nouns, when these are modified by QAs (Solt 2009, 2015; Bale
and Barner 2009). Namely, while the former are interpreted in terms of ‘volume’ or ‘weight’, the latter are
univocally interpreted in terms of ‘cardinality’. See the contrasts in (1) and (2).
(1) Positive QA + Mass NP
a. much coffee VOLUME, WEIGHT
b. much/%many suds VOLUME, WEIGHT
c. much jewelry CARDINALITY, #VOLUME
(2) Positive QA + plural count NP
a. many coffees CARDINALITY, #VOLUME
b. many bubbles CARDINALITY, #VOLUME
c. many jewels CARDINALITY, #VOLUME
This difference in interpretation also survives when the QA surfaces in its comparative form. This is
illustrated in (3) and (4).
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(3) more + Mass NP
a. more coffee VOLUME, WEIGHT
b. more suds VOLUME, WEIGHT
c. more jewelry CARDINALITY, #VOLUME
(4) more + plural count NP
a. more coffees CARDINALITY, #VOLUME
b. more bubbles CARDINALITY, #VOLUME
c. more jewels CARDINALITY, #VOLUME
(Plural) count nouns and object mass nouns are therefore countable: the can be measured along a cardinality scale; the other nouns, i.e. canonical and plural mass nouns, are non-countable. Based on these two
sets of facts, two possible empirical generalizations have been identified: Uniform Dimensionality (Hackl
2000; Solt 2009, 2015; Snyder 2021), and the Cardinality Generalization (Bale and Barner 2009; Wellwood
et al. 2012; Wellwood 2018).1
(5) Uniform Dimensionality (UD)
Many is associated with cardinality, while much is associated with other dimensions.
(6) The Cardinality Generalization
Comparatives with object mass nouns (e.g. furniture, jewelry, footwear, baggage etc.) and all
plural count nouns permit only cardinality-based interpretations.
There is one way to link the two generalizations and subsume the Cardinality Generalization as a subset
of UD. On such a view, comparative morphemes are ambiguous and can be formed on top of two different
positive bases: (i) MUCH + COMPR is spelled out as more and (ii) MANY + COMPR is also spelled out as more.
The former would be underspecified for the dimension of measurement it introduces, whereas the latter will
select for plural count nouns and be univocally associated with the dimension of cardinality. This explanation
conforms to UD.
1The formulation of UD in (5) is taken from Solt (2009). The generalization in (6) is based on the original formulations from
Bale and Barner (2009); Wellwood (2018). As formulated in (6), it is meant to capture the empirical observations and remain neutral
about whether mass nouns like jewelry are inherently plural. Besides, I want to note that none of these authors call the generalization
in (6) ‘the Cardinality Generalization’. Bale and Barner (2009), who made the original observation, do not give it a name; Wellwood
(2018, p.79) calls it ‘Number’ generalization. Since I will be using the label Number for a functional head in the syntax (Ritter 1991),
I will refrain from using this name throughout the dissertation.
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It should be noted that UD is a generalization about surface forms of QAs. Based on the data discussed
in Chapter 2 and the analysis in Chapter 3, it is clear that even for a language like English UD does not make
the right predictions. First of all, plural mass nouns may be modified by many for some speakers (also Smith
2021); and second of all, object mass nouns, which are measured along a cardinality scale, are unacceptable
with many.
Besides, this asymmetry in meaning is more generally observed across languages (Lima 2014; Deal
2016a, 2017; Doetjes 2021), which it makes it a good candidate for a language universal. However, stating
UD as in (5) misses this generalization. In particular, this is so because, as I hypothesized in Section 3.2.4.2,
the surface form of the QA is sensitive to number marking not necessarily semantic interpretation. In fact,
in Spanish if the plural-marked noun is count, then a cardinality interpretation obtains as illustrated by the
contrast in (7a) and (7b) from Cleani and Toquero-Pérez (2022, p.713). If the plural-marked noun is mass,
the QA will still be plural-marked but the dimension of measurement is not cardinality as shown in (8).2
(7) a. tanta
as.much.F
naranja
orange
‘(as) much orange’ #CARDINALITY, VOLUME
b. tanta-s
much.F-PL
naranja-s
orange.PL
‘(as) many oranges’ CARDINALITY, #VOLUME
(8) [ The Spanish government and the US government both sent a provision batch to the affected town:
the former sent a truck with 50 kilos of provisions contained in 5 boxes; the latter sent a red truck
with 50 kilos contained in 10 boxes]
a. El
the
gobierno
government
español
Spanish
mandó
sent
tanto-s
as.much.M-PL
vívere-s
provision-PL
como
like
el
the
americano
american
Lit.: ‘The Spanish government sent as many provisions as the US government’
2
In Section 4.4.2, I will show data from Greek and Telugu. In both languages, the plural-marked form of the QA is used with
plural mass nouns and the interpretation is not in terms of cardinality.
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Int.: The Spanish government sent as {much/ %many} provisions as the US government
#CARDINALITY, VOLUME
b. * ... tanto
as.much.M
vívere-s
provision-PL
como ...
Lit.: ‘much provisions’
Int.: ‘much provisions’
That said, the statement of UD as in (5) entails a one-to-one mapping between surface forms and semantic
interpretation which is not supported by the (cross-linguistic) data. In fact, as I argued in Section 3.2.4.2
in Chapter 3, the distribution of the surface forms of QAs could be predicted based on the availability or
lack-thereof a plural feature. Besides, by virtue of hard-coding the dimension of cardinality as part of the
lexical entry of a putative MANY, and by transitivity its comparative counterpart (e.g. MANY-COMPR), the
generalization disregards the interaction between individuation and number, both of which play a core role
in determining the count properties of nouns.
A different attempt at unifying the two generalizations is made by Cleani and Toquero-Pérez (2022).
Following Wellwood (2015, 2018, 2019), they assume that there is only one underlying and underspecified
measure morpheme MUCH that may have different surface forms and they propose a reformulation of UD as
in (9).
(9) Abstract Uniform Dimensionality (AUD)
If MUCH has (semantic) PL in its scope, the associated dimension of measurement is cardinality.
While their generalization is certainly an improvement over UD and is on the right track to achieve
uniformity, this rests on the assumption that the plural feature on mass nouns such as suds is uninterpretable.
In addition, in order to account for cardinality with object mass nouns, they would probably need to assume
that these nouns, like plural count nouns, have [PL] in their extended projection or are lexically specified as
such. This is a position which I have argued against on empirical grounds in Section 3.2.3 of Chapter 3.
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Thus, the first question that arises at this point is the following:
Q1: What do object mass nouns and plural count nouns have in common that the other subtypes (i.e. canonical mass and plural mass) do not? In other words, what makes the former class countable but the latter
non-countable?
Given the in-depth discussion in Chapter 3, the answer is that both types of nouns share the presence
of an individuating feature. That is, the key to being countable is being marked for individuation. Since
canonical and plural mass nouns are not marked for this feature, they are non-countable. Besides, object
mass nouns and plural count nouns both have an additional feature in their extended projection: [PL], in the
case of count nouns, and [COLL], in the case of object mass nouns. Both of these features are responsible for
creating pluralities.
The second question that arises is formulated below:
Q2: Is it possible to unify both (an empirically accurate version of) UD and the Cardinality Generalization
in (6) into a single generalization?
The answer that I will argue for is that unification is indeed possible and empirically justified. In fact,
under a decompositional approach to QAs like the one adopted in Chapter 3, based on insights from Bobaljik
(2012); Dunbar and Wellwood (2016) according to which comparative and positive forms of QAs stand in a
containment relation, whatever is said about the positive will be true about the comparative. The generalization that I propose is stated as in (10), where √MEAS is the measure root.
(10) The Cardinality Generalization Redux
When Deg, i.e. [√MEAS Deg], has an individuated plurality in its scope, the associated dimension of
measurement is cardinality.
As I will argue, there are (at least) two ways of accomplishing an individuated plurality: by having [PL] or
[COLL] on top of the n[IND] head. When the DegP has either configuration in its syntactic scope, the dimension
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that the measure-root √MEAS will be assigned will be cardinality. I will then show how this generalization
also fares better cross-linguistically than UD by looking at languages like Greek and Telugu.
4.1 Meaning asymmetries
Bale and Barner (2009, p.224: ex.10) observe that the interpretation of the sentences in (11) varies according
to the denotation of the noun phrase.
(11) a. Esme has more chairs than Seymour has tables. CARDINALITY, #VOLUME
b. Esme has more water than Seymour has juice. #CARDINALITY, VOLUME
c. Esme has more rope than Seymour has string. #CARDINALITY, LENGTH
d. Esme has more gold in her ring than Seymour has silver in his necklace. #CARDINALITY, WEIGHT %
The sentence in (11a) has a plural count noun chairs as the object of comparison. What is being compared
is the cardinality of chairs that Esme has and the cardinality of tables that Seymour has. All the other sentences
in (11) involve a mass noun: water/juice, rope/string, gold/silver. In none of these cases is the cardinality
interpretation available: (11b) is comparing Esme’s volume of water to Seymour’s volume of juice; (11c) is
comparing the length of Esme’s rope to the length of Seymour’s string; and, (11d) is comparing the proportion
of gold’s weight in Esme’s ring to the proportion of silver’s weight in Seymour’s necklace (Bale and Schwarz
2019; Bale et al. 2020).
Bale and Barner (2009) conclude that comparative constructions are a reliable diagnostic to classify NPs
as being countable or non-countable. The generalization that arises is that cardinality is the default dimension
of measurement for plural count nouns and object mass nouns. Thus, the distinction is between the nouns
that require measurement by cardinality and those that do not. These observations are not only applicable to
comparatives since, as Solt (2009, 2015) has shown, they can be extended to nouns modified by QAs in their
positive form.
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In this section, I will apply the dimension of measurement diagnostic to the classes of nouns identified in Chapter 3. I will do that by looking at data from Spanish and English, as I did there. I will focus
on the interpretation of the nouns when modified by different forms of QAs, including but not limited to
comparatives.
4.1.1 The interpretation of QAs with plural count and canonical mass nouns
We have already seen in (11) that for canonical count and mass nouns the application of the comparative test
yields the expected asymmetry between the two classes of nouns. Example sentences in (12) illustrate that
the same interpretations are obtained (i) when the context is controlled for and (ii) when the target noun has
a “shifted” interpretation.
(12) a. [Barney has 5 chairs which are small and light. Robin has 2 chairs, but they are large and heavy]
Barney has more chairs than Robin does. CARDINALITY, #VOLUME, #WEIGHT
b. [Barney has 5 gallons of beer stored in a single bottle. Robin has 2 gallons of beer stored in 3
bottles.]
Barney has more beer than Robin does. #CARDINALITY, VOLUME
c. [Barney broke 2 bottles of beer that each held 1 gallon. Robin broke a single bottle of beer that
held a total volume of 5 gallons.]
Barney broke more beers than Robin did. CARDINALITY, #VOLUME
The sentence in (12a) is true in the context where Barney has a greater number of chairs than Robin does
regardless of whether Robin’s chairs are heavier and bigger: 5 chairs > 2 chairs. In (12b), the situation is
different. Robin has a greater number of beer containers than Barney (i.e. 3 > 1), whereas Barney has a
greater volume of beer than Robin (i.e. 5 gallons > 2 gallons). The sentence is true in the context provided
because the comparison is being established in terms of volume, not cardinality. If we pluralize beer and
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make it count with a container interpretation, as in (12c), the opposite holds: the sentence is true because
Barney broke a greater number of beer containers than Robin despite hers being more voluminous.
In addition to comparatives, Solt (2009, 2015) observed that the interpretation of count and mass nouns
can be differentiated by using the following two diagnostics: (i) degree questions; and (ii) equatives.3
According to Solt, degree questions such as (13) force cardinality answers: the addressee can reply to
the question with a number (e.g. 5), indicating numerosity, but not with an amount such as 5𝑘𝑔𝑠 which is
suggestive of ‘volume’ or ‘weight’. However, questions like (14) force a non-cardinality answer.
(13) A: How many potatoes did you buy? B: {5 (potatoes)/ #5kgs}
(14) A: How much potato did you buy? B: {#5 (potatoes)/ 5kgs}
There is a caveat with questions: Cleani and Toquero-Pérez (2022) note that degree questions may not
be a reliable diagnostic and report that across languages speakers tend to readily accept answers like the ones
Solt marks with ‘#’. That is why they are not a conclusive diagnositc on their own.
Likewise, according to Solt (2009, p.62), equatives (e.g. as many/much …as) with a plural count noun
only allow for a cardinality interpretation. If potatoes could be interpreted along a weight scale, the sentence
in (15a) should be interpretable: both Fred and John have a total of 4𝑘𝑔𝑠. However, the sentence is false in
the context provided. The true counterpart is in (15b), which suggests that the only possible dimension of
3To this we could add Snyder’s (2021) anaphoric that much/many. According to Snyder (2021) anaphoric that much/many
can make reference to the either the relevant number in the context and thus enforce a cardinality interpretation or to the relevant
amount and thus enforce a volume or weight interpretation. The difference between anaphorically picking out a cardinality or a
weight/volume is determined by the type of noun: plural count and mass noun, respectively. This is illustrated in (viii) and (ix).
(viii) [John ate 3 potatoes a year]
a. Ash ate that many potatoes a year too.
b. # Ash ate that much potato a year too.
(ix) [John ate 3kgs of potatoes a year]
a. # Ash ate that many potatoes a year too.
b. Ash ate that much potato a year too.
In (viii), that many potatoes is felicitous in the context because the the anaphoric degree expression is making reference to the
number of individual potatoes. In contrast, that much potato in (viii.b) is not felicitous because there is no salient amount/weight of
‘potato stuff’ that is made available in the context. However, in (ix) the opposite situation obtains. I have decided not to illustrate
this diagnositc here, but nothing crucial hinges upon this decision since the result correlates with the other tests. See also Cleani
and Toquero-Pérez (2022).
126

measurement is cardinality: the number of potatoes that Fred has, i.e. 7, is not equal to or greater than the
number that John has, i.e. 10.
(15) [Fred has 7 potatoes weighing 4 kilos in total. John has 10 (smaller) potatoes weighing 4 kilos in
total]
a. # John has as many potatoes as Fred.
b. Fred doesn’t have as many potatoes as John.
If on the contrary, the noun potato is not pluralized, and potato refers to something like ‘potato stuff’
rather than an ‘individual potato’, the dimension of cardinality is not available. In fact, the dimension of
measurement is something like ‘weight’ given the context in (16).
(16) [Fred has 7 potatoes weighing 4 kilos in total. John has 10 (smaller) potatoes weighing 4 kilos in
total]
John has as much potato as Fred.
All these diagnostics indicate that when the noun is a plural count one, it must be interpreted in terms
of cardinality when modified by a QA (both in comparative and positive form). However, when the noun is
mass, cardinality is not available.
Turning to Spanish, the comparative morpheme is más ‘more/-er’ and the standard of comparison may
be introduced by a complementizer que ‘that’ or a preposition de ‘of’. The choice of one standard over the
other depends on whether the constituent inside the standard is a full clause or a Measure Phrase respectively
(Toquero-Pérez 2023b). The interpretation of nominal comparatives in the language is like English. This is
illustrated in (17), using the same contexts as in (12) for English, with clausal comparatives.
(17) a. Barney
Barney
tiene
has
más
more
silla-s
chair-PL
que
that
Robin.
Robin
‘Barney has more chairs than Robin does’ CARDINALITY, #VOLUME, #WEIGHT
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b. Barney
Barney
tiene
has
más
more
cerveza
beer
que
that
Robin.
Robin
‘Barney has more beer than Robin does’ #CARDINALITY, VOLUME
c. Barney
Barney
rompió
broke
más
more
cerveza-s
beer-PL
que
that
Robin.
Robin
‘Barney broke more beers than Robin did’ CARDINALITY, #VOLUME
When the noun is plural and count as in (17a) and (17c) the only possible interpretation is one where the
cardinality of chairs or beer-units is being compared. On the contrary, when the noun is mass and unmarked
for number, as in (17b), a non-cardinality measurement is the only option.
With respect to the positive form of QAs, we have already seen in Chapter 3 that they obligatorily agree
in number and gender with the noun they modify. Thus, the much/many distinction is marked by the presence
or absence of plural agreement on the QA. Before delving into the relevant diagnostic examples, it is worth
reminding ourselves that Spanish has two distinct measure morphemes roughly corresponding to much/many:
tant-M/F-PL ‘as/so much’ and much-M/F-PL ‘much’. The distribution of these two morphemes in the language
is slightly different. This is illustrated in (18)-(19).
(18) Degree Questions
a. { Cuánto-s/
how.much.M-PL/
Qué
what
tanto-s}
as.much.M-PL
niño-s
kid.M-PL
…
Lit.: ‘{How many/ what as many} kids?
Int.: ‘How many kids?
b. * { Cuán
how.as
mucho-s/
much.M-PL/
Qué
what
tan
as
mucho-s}
much.M-PL
niño-s
kid.M-PL
…
Lit.: ‘{How many/ what as many} kids?
Int.: ‘How many kids?
(19) Equatives
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a. tanto-s
as.much.M-PL
niño-s
kid.M-PL
‘as many kids’
b. * Tan
as
mucho-s
much.M-PL
niño-s
kid.M-PL
…
‘As many kids’
Degree questions in (18) and equatives in (19) are all built using tanto/a, and never mucho/a.
4 Mucho/a
is generally found bare, namely in attributive position following a determiner as in (20a), determinerless NPs
as in (20b), in the differential position of a comparative as in (20c) or in predicative position (20d).
(20) a. Hablaron
spoke.3PL
de
of
lo-s
the.M-PL
mucho-s
much.M-PL
niño-s
kid.M-PL
afectados
afected.M.PL
por
by
el
the
conflicto.
conflict
‘They talked about the many children affected by the conflict’ (attributive)
b. Hablaron
spoke.3PL
de
of
mucho-s
much.M-PL
niño-s
kid.M-PL
afectados
afected.M.PL
por
by
el
the
conflicto.
conflict
‘They talked about many children affected by the conflict’ (determinerless)
c. Mucho-s
much.M-PL
más
more
niño-s
kid.M-PL
que
that
niña-s
kid.F-PL
‘Many more boys than girls’ (differential)
d. Los
the
niño-s
kid.M-PL
eran
be.IPFV.3PL
mucho-s
much.M-PL
‘The boys were many’ (predicative)
4With adjectives, tanto/a and the interrogative counterpart are syncopated. This is shown in (x).
(x) a. Mi
my
casa
house
es
is
{* tanta/
as.much.F/
tan}
as
bonita
beautiful
como
like
la
the
tuya.
yours
‘My house is as beautiful as yours is’
b. {* Cuánta/
how.as.much.F/
Cuán/
how.as/
Qué
what
tan}
as
bonita
beautiful.F
es
is
su
his
casa?
house?
‘How beautiful is his house?
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With these facts in mind, we can now look at the interpretation of nouns when modified by QAs like
tanto/a and mucho/a. Starting with degree questions, we observe that generally they only accept answers that
are interpreted along a cardinality scale when the noun is plural count.5 This is shown in (21).
(21) [Manuela goes to the store and buys 100 oranges worth 50lbs. Diego goes to the store and buys 80
oranges worth 50lbs. Manuela asks:]
a. M: Cuánta-s
how.much.F-PL
naranja-s
orange.F-PL
compraste?
bought.2SG
‘How many oranges did you buy?’
b. D: Mucha-s
much.F-PL
naranja-s,
orange.F-PL
pero
but
no
NEG
tanta-s
as.much.F-PL
como
like
tú.
you
De
in
hecho
fact
compré
bought.1SG
80.
80
‘Many oranges, but not as many as you did. In fact, I bought 80.’
c. D: # mucha-s
much.F-PL
libra-s,
pound.F-PL
tanta-s
as.much.F-PL
como
like
tú:
you
también
also
compré
bought.1SG
50
50
libra-s.
pound.F-PL
#‘Many pounds, as many as you did: I also bought 50lbs’
It is possible for Diego to answer the question as in (21b) using muchas to indicate a large unspecified
number of oranges. As the continuation with both the equative and the numeral indicates, the answer is
indeed referring back to the number of oranges and not to the pounds. In fact, Diego cannot answer the
question to refer back to the amount/volume of oranges in pounds, as the alternative answer in (21c) shows.
As opposed to plural count nouns, canonical mass nouns do not receive a cardinality interpretation when
modified by a QA. For example, the question in (22) probes for the weight of oranges in kilos, and not the
individual oranges themselves. In addition, the fact that only the answer in (22b) is felicitous indicates that
what is being compared is not the cardinality of oranges but their weight.
(22) [Manuela has 100 oranges weighing 50kgs in total. Diego has 80 oranges weighing 50kgs total.
Manuela asks:]
5Again, see Cleani and Toquero-Pérez (2022) for some cautionary considerations.
130

a. M: Cuánta
how.much.F
naranja
orange.F
tienes?
have.2SG
‘How much orange do you have?’
b. D: Mucha,
much.F
de
of
hecho
fact
tanta
as.much.F
como
as
tú:
you
50kgs.
50kgs
‘Much orange, in fact as much as you: 50kgs.’
c. D: # Mucha(-s),
much.F-PL
pero
but
no
NEG
tanta(-s)
as.much.F-PL
como
as
tú:
you
80
80
naranja-s.
orange-PL
#‘Much, but not as much as you: 80 oranges’
We can conclude from this subsection that plural count nouns are always interpreted along a cardinality
scale when modified by QAs in both English and Spanish. This is compatible with the discussion in Bale
and Barner (2009) and Solt (2009, 2015).
4.1.2 The interpretation of QAs with plural mass nouns
When describing the morpho-syntactic properties of plural mass nouns, we concluded that these were no
different from canonical mass nouns like water. The only difference was the obligatory plural marker located
on the n. In terms of their interpretation in comparative constructions, we observe that the parallel behavior
with canonical mass nouns also holds. For example, this is shown in (23).
(23) [There are two small heaps of suds in the bathtub, whereas there is a single large heap of suds in the
sink.]
There are more suds in the sink than in the bathtub. #CARDINALITY, VOLUME
(23) is acceptable in a context where what is being measured is the amount or volume of suds covering
the tub or sink. However, if the relevant intended dimension of measurement was cardinality, the sentence
cannot be interpreted as true in the context.
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With respect to the situation with the positive form of the QA, we must be reminded of the variation
across English speakers: some only accept much with plural mass nouns while others also accept many. The
choice of QA does not seem to affect the interpretation. This is shown in (24a) and (24b).
(24) a. A: How {much/ %many} suds are in the sink? B: {a large volume/ #
a large number}
b. There aren’t as {much/ %many} suds in the bathtub as in the sink. #CARDINALITY, VOLUME
The interpretation of plural mass nouns when modified by QAs, regardless of their surface form, is in
terms of volume and not cardinality. Thus, an acceptable answer to the question in (24a) has to make reference
to the volume but not the number; and similarly, the sentence in (24b) is acceptable in the context from (23);
again, the sentence would be unacceptable in that context if the dimension was cardinality.
There are two main points we can draw from these English data. One is that plural mass nouns do not
induce a cardinality interpretation when modified by QAs. The other is that the choice of QA in the positive
form does not have an impact on the dimension of measurement or semantic interpretation. This piece of
data provides support to the analysis developed in Chapter 3 according to which the variation is a matter of
exponence, not lexical properties.
Turning to Spanish, we observe that when plural mass nouns occur in comparative constructions, they
cannot induce cardinality interpretations either. An example is shown in (25).
(25) [The government sent batches of provisions in two different trucks: the blue truck has 50 kilos
contained in 5 boxes; the red truck has 30 kilos contained in 10 boxes]
El
the
camión
truck
azul
blue
llevó
carried
más
more
vívere-s
provision-PL
que
that
el
the
camión
truck
rojo.
red
‘The blue truck carried more provisions than the red one’ #CARDINALITY, VOLUME
The sentence in (25) is acceptable with the interpretation that the blue truck transported a larger volume
of provisions than the red truck did: 50ks > 30kgs. If it was the case that the plural mass noun induced a
132

cardinality interpretation, speakers would reject the sentence on the basis that they would be tracking the
number of the individual boxes of provisions instead: 5 < 10.
The same interpretive results obtain with the positive form of QAs. This is shown with the degree question
in (26a) and the possible answer to the question in (26b).
(26) a. Cuánto-s
how.much.M-PL
vívere-s
provision-PL
llevó
carried
el
the
camión
truck
rojo?
red
‘How much/ %many provisions did the red truck carry?’
b. Mucho-s
much.M-PL
vívere-s,
provision-PL
pero
but
no
NEG
tanto-s
as.much.M-PL
como
like
el
the
azul:
blue
30kgs
30kgs
‘Much/ %Many provisions, but not as much/ %many as the blue one: 30kgs.’
We observe again here that what is being picked out is the volume of provisions in kilograms. Assuming
that both 50kgs and 30kgs are large quantities, both trucks carried a large volume; thus, it is acceptable to
say muchos víveres ‘many provisions’ in (26b). However, since the blue truck carried 50kgs and the red one
only 30kgs, the latter truck did not carry as much.
We must note again that all the positive forms of the QA in Spanish must have obligatory plural-marking
if there is a plural: {cuanto/ mucho/ tanto}-s. These facts, in addition to the variation across English speakers,
suggest that the surface form of QAs and the dimension of measurement that they introduce need to be kept
separate, contrary to what UD in (5) would predict. This conclusion will receive further support from object
mass nouns in the next subsection where the opposite situation obtains: the unmarked form of the QA surfaces
(e.g. much, mucho, tanto) even though the interpretation is a cardinality one.
4.1.3 The interpretation of QAs with object mass nouns
Bale and Barner (2009) observe that mass nouns can be divided into two types depending on the semantic
interpretation they support in comparatives: those that do not allow comparison by number (e.g. water or
133

suds) and those that do (e.g. furniture or jewelry). In particular, they note that the latter type patterns exactly
like plural count nouns in this regard. This is illustrated by the example in (27).6
(27) a. [John bought 5 chairs and a dresser; a total volume of approximately 1.5m3
. Mary bought a
large chair, a big desk and a large sofa; a total volume of approximately 4m3
.]
John has more furniture than than Mary. CARDINALITY, #VOLUME
b. [John owns 4 rings and a bracelet. Mary owns 2 large necklaces and a tiara.]
John owns more jewlery than Mary. CARDINALITY, #VOLUME
The comparison in (27a) is being established in terms of cardinality: John has 6 pieces of furniture
and Mary has 3. Establishing a comparison in terms of volume is unacceptable even if the total of Mary’s
furniture pieces is larger in volume than the total of John’s. Likewise, (27b) is equivalent to ‘John owns more
pieces of jewelry than Mary’ despite the fact that Mary’s are heavier or more voluminous.
If we move outside of the comparative and look at degree questions and equatives, we observe that the
cardinality interpretation prevails in those syntactic contexts as well. An example for each construction is
given in (28) and (29), the context being the same as in (27a).
(28) A: How much furniture did John buy? B: {6 pieces/ #4m3}
(29) Mary doesn’t have as much furniture as John does. CARDINALITY, #VOLUME
As the examples show, it is possible to answer the degree question in (28) with the phrase ‘6 pieces’
which tracks the number of individual furniture items. On the contrary, an answer that refers to the overall
volume, e.g. 4 cubic meters, is unacceptable. Likewise, the equative in (29) is acceptable in the context
provided because the number of furniture items that Mary has is not as numerous as the number of items
that John has. If volume was the relevant dimension of measurement, we would expect the sentence to be
unacceptable.
6The volume of furniture has been calculated using the ‘NAVTRANS Global Relocation Service’ (link). The unit of measurement
is cubic meters.
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As described and discussed in the previous chapter, the QA must be unmarked for number when modifying these nouns. Thus, while object mass nouns pattern like plural count nouns in terms of their semantic
interpretation, they pattern like canonical mass nouns in the choice of QA. This reinforces the hypothesis
that the surface form of the QA is sensitive to a number feature, not semantic interpretation.
The Spanish data are no different. Comparatives with object mass nouns are interpreted in terms of
cardinality, and nothing else. This is shown for the sentence in (30a), which is equivalent to (30b). We can
use the same context as in (27).
(30) a. Juan
Juan
compró
bought
más
more
mobiliario
furniture
que
that
María.
María
‘Juan bought more furniture than María’ CARDINALITY, #VOLUME
b. Juan
Juan
compró
bought
más
more
mueble-s
furniture-PL
que
that
María.
María
‘Juan bought more furniture items than María’ CARDINALITY, #VOLUME
Both sentences in (30) indicate that Juan bought a larger number of furniture items than María did. They
differ with respect to the syntactic properties of the noun involved in the comparison, though: an object mass
noun that resists overt plural marking in (30a) and a count noun that is overtly plural marked in (30b).
The same interpretations are obtained with degree questions and equatives. This is shown in (31).
(31) a. Cuánto
how.much.M
mobiliario
furniture
compró
bought
María?
María
‘How much furniture did María buy?’ CARDINALITY, #VOLUME
b. Mucho
much.M
mobiliario,
furniture
pero
but
no
NEG
tanto
as.much.M
como
like
Juan:
Juan
3
3
piezas.
pieces
‘Much furniture, but not as much as Juan: 3 pieces.’ CARDINALITY, #VOLUME
The question in (31a) is probing the number of furniture pieces that Mary bought. This is supported by
the answer in (31b) which is making specific reference to the cardinality of the pieces. In both cases, the QA
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cannot be plural marked. This is expected given that the object mass noun is not plural-marked, blocking
plural nominal concord inside the DP.
4.2 Taking stock
The data discussed so far conform to the generalizations from Bale and Barner (2009), and subsequent literature after them, that plural count nouns and object mass nouns receive a cardinality interpretation when
modified by QAs. That is, the interpretation of cardinality is restricted to these two subclasses of nouns.
Narrowing it down, the data support the hypothesis that I have been defending all along that the surface form
of the QA is sensitive to plural-marking, not semantic interpretation. The lack of a one-to-one mapping between surface form and semantic interpretation is summarized in Table 4.1, which is a more complete version
of Table 2.11 in chapter 3. The table lists the 4 types of nouns that were previously identified and contains
information about number marking, its relation to the surface form of the QA and the semantic interpretation
associated with the nouns when they occur with these QAs or in comparatives.
Table 4.1: Number marking, choice of QA, and semantic interpretation by noun type (not final)
Lang. Agreement QA form Dimension of measurement
Type of N SG PL Unmarked
(much/mucho)
PL-Marked
(many/muchos)
CARDINALITY OTHER
Canonical Mass English ✓ * ✓ * * ✓
Spanish ✓ * ✓ * * ✓
Object Mass English ✓ * ✓ * ✓ *
Spanish ✓ * ✓ * ✓ *
PL Mass English * ✓ ✓ % * ✓
Spanish * ✓ * ✓ * ✓
PL Count English * ✓ * ✓ ✓ *
Spanish * ✓ * ✓ ✓ *
As shown in Table 4.1, plural-marking on the noun or the QA does not guarantee that the dimension of
measurement will be cardinality. Otherwise, plural mass nouns would form a natural class with plural count
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nouns. The opposite is also not true, as instantiated by object mass nouns: lack of plural-marking on the
noun and QA does not preclude a cardinality interpretation. If that was the case, object mass nouns would
pattern with canonical mass nouns.
At this point we must ask ourselves: in what way(s) do the nouns that are interpreted in terms of cardinality form a natural class? In other words, what makes these nouns countable? The theory of number and
individuation that I developed consisted of 4 features (IND, SG, PL, COLL) and depending which of these features were available in the syntactic representation, nouns are classified into different categories. The theory
proposed argued for the separation of individuation and number. Given the Plural-Count Generalization I
formulated in (70) in Chapter 2, repeated below, we know that number-marking is not a required condition
for count syntax, and also it looks like it is not a requirement for a noun to be countable either (e.g. dregs,
suds). That said, the key element that remains is markedness for individuation. I argue for (32), which is
also consistent with the Plural-Count Generalization that .
(32) The Countability Hypothesis
Being countable means being marked for individuation.
(70) The Plural-Count Generalization
In some languages (e.g. English and Spanish) plural-marking on the noun does not entail count noun
syntax.
The hypothesis in (32) provides an understanding of what countability is, and how it is different from
being count. In particular, it correctly predicts that count NPs are a subset of the NPs that are countable:
{count NPs} ⊂ {count NPs, object mass NPs}. Despite the fact that singular count nouns do not allow QA
modification (e.g. *much book), they can still be counted (i.e. measured along a cardinality scale) via numeral
modification: one book. I take this as evidence for them being countable. The hypothesis also motivates the
separation of individuation from number marking, and more specifically plural-marking: individuation is
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the introduction of discrete individuable elements and plural is responsible for sum-formation. Thus, we can
represent the countability asymmetries in the dependency tree in Figure 4.1.
Figure 4.1: Predicting countability asymmetries
Is n marked [IND]?
No
is n marked [PL]?
No: Canonical mass
(water, sal)
Yes: Plural mass
(dregs, celos)
Yes:
Is there Number?
No: Object mass
[COLL]
(jewelry, joyería)
Yes:
is Number [PL]?
No: Singular count
[SG]
(jewel, joya)
Yes: Plural count
[PL]
(jewels, joyas)
The dependency tree in Figure 4.1 shows that the dividing feature that groups canonical and plural mass
nouns, on the one hand, and object mass and (plural) count nouns, on the other, is [IND] on the nominalizer.
QAs require the constituent they modify to be cumulative. Within the natural class of individuated nouns
identified in fig. 4.1, there are two ways to satisfy this cumulativity requirement, i.e. by denoting a plurality:
via [PL] on Number or [COLL] on n. The general picture that arises from this discussion is that the selection of the dimension of measurement as cardinality when the noun is modified by a QA can be predicted
by the morpho-syntactic make up of the relevant NP.7 Against this background, I propose that the actual
generalization is what I referred to as the Cardinality Generalization Redux, repeated below.
(10) The Cardinality Generalization Redux
When Deg, i.e. [√MEAS Deg], has an individuated plurality in its scope, the associated dimension of
measurement is cardinality.
7The generalization extends beyond the NP given that it also holds at the VP level (Wellwood et al. 2012): Last week John
climbed the mountain {as much as/ more than} Mary did = ‘the number of climbing-the-mountain events with John as an agent are
as large as/larger than the number of climbing-the-mountain events with Mary as an agent’.
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4.3 Analysis
4.3.1 The interpretation of terminal nodes
Roots and categorizers. The decompositional account to syntax adopted in the dissertation entails that
nouns are not simple linguistic expressions but are divided into a root and a categorizing head. Each of
these pieces provides its own semantic content to the derivation. While the semantics of categorizing heads
might be less controversial, i.e. they are functions of some sort: from predicates to predicates (in some cases
introducing thematic relations, i.e. Kratzer 1996), there is no consensus regarding the semantics of roots.
This is so because root meanings are quite flexible; for example the word for braid can refer to a physical
object as in I like Kristen’s braids or an event as in I braided Kristen a necklace. That is, in one case the
root seems to denote an entity or physical object and in the other it denotes a creation event. For some like
Borer (2005a, 2014); Acquaviva (2009), roots are completely void of meaning; for others like Arad (2003);
Levinson (2007, 2014) roots are polysemous depending on the environment they occur in; in a similar vein,
Pross (2019) proposes that roots are simply mappings from a terminal node to a set of concepts that are
compatible with the meaning of the root in a certain (syntactic) context.
What (most of) these proposals share in common, though, is the following two pieces: (i) there must be
some degree of flexibility as to what a root actually means; and (ii) the root is required to occur in the context
of a categorizer.8
In this regard, these pieces are not very different from those that are at play during the
selection of root allomorphs. That is, a root can have different surface forms and the choice of those surface
forms are conditioned by the syntactic context in which the root occurs. We can think of a root as an abstract
form that represents a set of possible vocabulary items associated with that root. This is represented in (33).
(33) √ROOT = {vocabulary item1
; vocabulary item2
; ...vocabulary item𝑛
}
8For example, on the second piece Acquaviva (2009, p.15) writes that roots “have no meanings by themselves but co-occur with
category-assigning heads to form interpretable typed grammatical entities”.
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The vocabulary items in the set are in competition with each other and the one that is selected, i.e. inserted
using DM-terminology, must meet the most specific conditions for insertion. This is formalized with VI rules
such as the ones in (34) where ⇔ is the function that maps the terminal node to its surface form and 𝜅 stands
for a categorizer.
(34) a. √ROOT ⇔ vocabulary item1
/__𝜅1
b. √ROOT ⇔ vocabulary item2
/__𝜅2
...
According to the rules in (34), the terminal node √ROOT is mapped to vocabulary item1
in the context of
head 𝜅1
; it is mapped to vocabulary item2
in the context of head 𝜅2
and so on. We then say that a root is
licensed at PF if it has been assigned a vocabulary item in the relevant syntactic context. If no vocabulary
item that matches the conditions imposed by the rule, the rule is unlicensed. I propose that the assignment
of a meaning to a root is not much different. In particular, building on insights from Pross (2019) and Wood
(2023), I propose that root licensing at LF is assigning a meaning to a root from the set of possible meanings
that the root is associated with in the context of a categorizer.
I start by assuming that semantics maps syntactic terminals to concepts (Pietroski 2010, 2017; Wellwood
2020). Semantic values (in the sense of Heim and Kratzer 1998) are computed over concepts. We can think
of a terminal node root √ROOT as a set of possible concepts that are compatible with the meaning of that root
in a certain syntactic context. We can represent this as in (35).
(35) √ROOT = {CONCEPT1
; CONCEPT2
; CONCEPT3
...CONCEPT𝑛
}
Which concept from the set in (35) is selected depends on the categorizer that the root is local to. In this
regard a √ROOT acts as an index and ‘fetches’ different concepts from the set, e.g. Pietroski (2010), contingent
upon the choice of categorizer. We can represent this as in (36) where ↔ is the mapping function.
(36) a. √ROOT ↔ CONCEPT1/__𝜅1
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b. √ROOT ↔ CONCEPT2/__𝜅2
c. ...
The rules in (36) are to be read as ‘select this CONCEPT for √ROOT in the context of this categorizer 𝜅’. The
fact that the selection of root meanings at LF requires contextual information as in (36) makes it subject to the
Subset Principle (Kiparsky 1973; Halle and Marantz 1993). In this regard, the selection of root-meanings (i)
resembles the selection of root-allomorphs and (ii) it is consistent with the other approaches to the meaning
of roots: the categorizer and the syntax are crucial in root-meaning selection. Given this parallelism across
the interfaces, we can call each of the concepts in the set ‘allosemes’ of the same root. From now on, I will
refer to the mapping rules in (36) as allosemy rules. For more details, see Wood (2023, ch.1).
When it comes to the denotation of count and mass nPs, i.e. [n([IND]) √ROOT], the literature has identified
an ontological difference between “substance terms” and “object terms” (Soja et al. 1991; Chierchia 1994;
Rips and Hespos 2019). We can assume that this ontological difference is reflected in the possible meanings
that a root can be associated with. I label these two possible meanings for a root as STUFF and THING.
9
STUFF is
to be understood as a placeholder for entities denoting “portions of stuff”, “substances”, “liquids” and so on;
THING is to be understood as a placeholder for entities denoting “physical objects”, broadly construed. The
STUFF concept seems to correlate well then with non-individuated meanings of √ROOT, whereas the THING
concept seems to correlate well with the individuated meaning of √ROOT. Thus, I will refer to each meaning
as such.
Suppose then that a root can be associated with the set of concepts in (37). The question is which concept
is selected in which context. I propose that the selection of the relevant concept (or alloseme) is triggered by
the different categorizing n-heads made available by the syntax. In particular, given the hypothesis in (32)
that what makes a noun countable is markedness for individuation, I propose the allosemy rules in (38).
(37) √ROOT = {ROOT-THING; ROOT-STUFF}
9
I am refraining from using the label object because later on I will use this term with a different meaning.
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(38) Allosemy rules for roots in the context of n-heads (un)marked for individuation
a. √ROOT ↔ ROOT-THING/__𝑛[IND]
b. √ROOT ↔ ROOT-STUFF/__𝑛
The √ROOT associated with the concepts in (37) fetches the individuated root-concept, e.g. ROOT-THING,
in the context of n[IND]; otherwise it fetches the non-individuated one, e.g. ROOT-STUFF. To illustrate with a
concrete example, let’s take the root √APPLE. This root is associated with the set of concepts in (39), and the
allosemy rules are in (40).
(39) √APPLE = {APPLE-THING; APPLE-STUFF}
(40) Allosemy rules for √APPLE in the context of n-heads (un)marked for individuation
a. √APPLE ↔ APPLE-THING/__𝑛[IND]
b. √APPLE ↔ APPLE-STUFF/__𝑛
APPLE-THING is the things that count as a discrete or atomic apple or apples and APPLE-STUFF is the portions
of apple-stuff. The former concept is selected in the context of n[IND], the latter is selected otherwise, i.e.
in the context of the n unmarked for [IND]. Given this system, the semantic conditions will be calculated
relative to the extensions of the concepts. That is, what goes into the interpretation function J⋅K (in the sense
of Heim and Kratzer 1998) is the concept selected by the allosemy rules. For example, this is shown with
the model-theoretic denotations in (41) and (42).10
(41) a. JROOT-THINGK = {𝑥: 𝑥 is an atomic thing or sum of atomic things} = {𝑎, 𝑏, 𝑐...𝑎𝑏𝑐}
b. JAPPLE-THINGK = {𝑥: 𝑥 is an atomic apple or sum of atomic apples}
(42) a. JROOT-STUFFK = {𝑥: 𝑥 is a portion of stuff or a sum of portions of stuff} = {𝑎𝑠
, 𝑏𝑠
, 𝑐𝑠
...𝑎𝑏𝑐𝑠
}
10Under this model, syntactic terminals and non-terminals (phrases or full sentences) are complex concepts as well. Extensional,
model-theoretic, semantics then operates on the logical forms of these concepts. Schematically the model looks like in (xi).
(xi) syntax → concepts/thoughts
J⋅K
→world
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b. JAPPLE-STUFFK = {𝑥: 𝑥 is a portion of apple-stuff or a sum of portions of apple-stuff}
To continue with the concrete example of the root √APPLE, the extension of JAPPLE-THINGK is the set in
(41) where each lower case letter a, b, c is an atomic apple for all 𝑛-apples there are in the model and their
join {ab, bc, ac, abc} is the sum of those atomic apples in the model. The extension of JAPPLE-STUFFK is
then the set in (42) where each lower case letter subscripted with 𝑠 (for stuff) is a portion of apple-stuff, for
all 𝑛-portions of apple-stuff in the model. It has no atoms in its extension. For now on, and as a shortcut, I
will use the CONCEPT notation for root-meanings rather than the model-theoretic notation.
Thinking about the selection of root meanings as mappings from a terminal node to a concept unifies the
way licensing works at the interfaces: licensing of a root terminal is the insertion of a form or fetching of
concept, depending on the interface at work, from a set via a mapping rule. Failure to insert a form or fetch
a concept results in the root being unlicensed.
Assuming an algebraic semantics, as established by Link (1983), the concepts denoted by the root √ROOT
in (37) are inherently cumulative (Krifka 1989; Kratzer 2008) via Link’s (1983) ‘*’-operator defined in (43):
the ‘*’-operator maps a set 𝑃 to a set 𝑃
′
that contains any sum of objects contained in 𝑃. I also assuming
that that there is a basic relation ‘≤’, defined in (44), which indicates “unstructured parthood” in the sense of
Champollion (2010); Champollion and Krifka (2016).11
(43) Closure under sum
∗
(𝑃) if ∀𝑥 ∈ 𝑃 → ∃𝑄[𝑄 ⊆ 𝑃 ∧ 𝑥 = ⊔𝑄]
(44) Unstructured Parthood
≤= ∀𝑥∀𝑦, 𝑥 ≤ 𝑦 if and only if (𝑥 ⊔ 𝑦) = 𝑦
11As Champollion and Krifka (2016, p.369) point out, “unstructured parts need not be cognitively salient parts of the whole but
may slice up the whole in arbitrary ways”. If X is a set of horses, X’ is a subset of them (unstructured parthood); if X is a house, X’
is its roof (structured parthood).
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The root concepts will then be predicates that are closed under sum, i.e. a predicate whose extension is a
complete join semi-lattice. However, depending on the featural make-up of the categorizer, the type of join
semi-lattice selected for the root concept will differ. In the spirit of Bale and Barner (2009), I will assume
that there are two types of semi-lattices that are relevant: individuated semi-lattices and non-individuated
ones.12 The crucial component of the individuated semi-lattice is that it has atoms as minimal parts, e.g.
(45). Atoms are the discrete separable units that will enable counting. The definition of ‘atom’ is in (46),
based on Bale and Barner’s (2009, p.238) definition of ‘individual’; and the definition of ‘minimal part’ that
I am assuming is in (47).
(45) Individuated semi-lattice
IND(𝑃) = a predicate 𝑃 is an individuated semi-lattice iff
a. 𝑃 is closed under sum, such that if ‘*’ is the sum closure operation, then 𝑃 = ∗𝑃; and
b. 𝑃 is generated by the set of atoms in 𝑃, such that if atom is the set of atoms in 𝑃, then
𝑃 = ∗atom.
(46) Definition of atom
An object 𝑧 is an atom in a set of objects 𝑃 iff 𝑧 is a minimal part for 𝑃 and for all objects 𝑦 ∈ 𝑃,
either (i) 𝑧 ≤ 𝑦 or (ii) there is no 𝑤 ≤ 𝑧, such that 𝑤 ≤ 𝑦.
(47) Definition of minimal part
∀𝑥[𝑃(𝑥) → ¬∃𝑦[𝑃(𝑦) ∧ 𝑦 < 𝑥]]
‘An object 𝑥 is a minimal part for a set of objects 𝑃 iff for all 𝑥 ∈ 𝑃 it is not the case there is an
object 𝑦, such that 𝑦 ∈ 𝑃 and 𝑦 is a proper part of 𝑥.
12For Bale and Barner (2009), there are two types of non-individuated semi-lattices: a continuous one and a limited one. Both
semi-lattices share the fact that they lack what they call ‘individuals’ in the sense of (46). However, they are different in the while
continuous semi-lattices do not have minimal parts, every member of the limited semi-lattice is composed of minimal parts. For the
purposes of this dissertation, it does not matter whether the semi-lattice that mass noun denotations have is limited (Chierchia 2010)
or continuous (Link 1983). The two-way distinction between individuated and non-individuated is enough.
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As Bale and Barner (2009, p.237) point out, the definition of atom in (46) “guarantees that an individuated
semi-lattice will not have minimal parts that share an [object]”. This seems trivial to see in an individuated
semi-lattice like Figure 4.2 because the minimal parts are the single atoms a, b and c. But, it can be made
clear in Figure 4.3: assuming a simple model with only three members {ab, cd, ef }, ab, cd and ef are the
minimal parts in Figure 4.3. No part of a minimal part can be in another object without all of its parts also
being in that object. In other words, since ab is a a minimal part in Figure 4.3, because no subpart of ab is
in any of the objects without the whole ab also being part of the object, then ab is also an atom.
Figure 4.2: Individuated semi-lattice for thing generated from atoms a, b, c
abc
ab   ac bc
a b c
Figure 4.3: Individuated semi-lattice for thing generated from atoms ab, cd, ef
abcdef
abcd   abef cdef
ab cd ef
In contrast, while non-individuated semi-lattices are also closed under sum and thus have a supremum,
they are not generated from the set of atoms and lack minimal parts. The definition for the non-individuated
semi-lattice is in (48) following Bunt (1979); Gillon (1992); Wellwood (2019).13
(48) Non-individuating semi-lattice.
Non-IND(𝑃) = a predicate 𝑃 is a non-individuated semi-lattice iff
a. 𝑃 is closed under sum, such that if ‘*’ is the sum closure operation, then 𝑃 = ∗𝑃; and
b. for every object 𝑥 that is in 𝑃 there is an object 𝑦 such that 𝑦 is also in 𝑃 and it is a proper part of 𝑥
∗𝑃 ∧ ∀𝑥[𝑃(𝑥) → ∃𝑦[𝑃(𝑦) ∧ 𝑦 < 𝑥]]
13What I call non-individuated in (48) is what Bunt (1979); Gillon (1992); Wellwood (2019) refer to as ‘Anti-Atomic’. The
definition in (48) is similar what Bale and Barner (2009, p.238) refer to as continuous semi-lattice: 𝑃 is continuous if 𝑃 is closed
under sum and 𝑃 has no minimal parts.
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The two types of semi-lattices differ in whether they have atoms as minimal parts (individuated) or no
(non-individuated). Together with the discussion about the concepts that a root is associated with, we can
conclude that ROOT-THING is an individuated semi-lattice whereas ROOT-STUFF is non-individuated. This
different will be crucial in determining whether the dimension of measurement can be resolved as cardinality.
I propose that the different flavors of n that I identified in Chapter 3 select for one of the two types
of semi-lattices on the √ROOT. n underspecified for individuation will select for the non-individuated semilattice with no atomic minimal part, i.e. the ROOT-STUFF alloseme. n takes the ROOT-STUFF alloseme and maps
it to a type ⟨𝑒𝑡⟩-predicate with the condition that the predicate has the property of not being individuated.
In contrast, n[IND] will select for the individuated semi-lattice, i.e. the ROOT-THING alloseme. n[IND] takes
the ROOT-THING alloseme and maps it to a type ⟨𝑒𝑡⟩-predicate with the condition that the predicate has the
property of being individuated. The denotations of these terminal nodes is in (49).
(49) a. J𝑛K = 𝜆𝑃.𝜆𝑥.Non-IND(𝑃)(𝑥)
b. J𝑛[IND]K = 𝜆𝑃.𝜆𝑥.IND(𝑃)(𝑥)
To make things concrete, let’s go back to the root √APPLE in (39). First, the locality of √APPLE and the
underspecified n categorizer triggers the allosemy rule in (40b). This alloseme then saturates n’s 𝑃-argument.
Since the APPLE-STUFF alloseme has no atoms, the non-individuated condition imposed by n is satisfied. This
is shown in (50). On the contrary, the locality of √APPLE and n[IND] triggers the allosemy rule in (40a). This
alloseme then saturates n[IND]’s 𝑃-argument. Given that APPLE-THING has atomic apples and sums of atomic
apples, the individuated condition imposed by the categorizer is satisfied. This is shown in (51).
(50) a. √APPLE ↔ APPLE-STUFF/__𝑛
b. J𝑛 √APPLEK = 𝜆𝑥.Non-IND(APPLE-STUFF)(𝑥) (𝑒.𝑔.{𝑎𝑠
, 𝑏𝑠
, 𝑐𝑠
...𝑎𝑏𝑐𝑠
})
(51) a. √APPLE ↔ APPLE-THING/__𝑛[IND]
b. J𝑛[IND] √APPLEK = 𝜆𝑥.IND(APPLE-THING)(𝑥) (𝑒.𝑔.{𝑎, 𝑏, 𝑐...𝑎𝑏𝑐})
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At the end of the chapter, we will see how this proposal for the meanings of roots and categorizers in
tandem with the syntax developed in chapter 3 has important implications for how we understand shifts
across classes of nouns within and across languages (i.e. what is sometimes referred to as nominal flexibility
or countability shifts, Pelletier 1979; Bunt 1985; Rothstein 2010).14
14Instead of this approach to root meanings via allosemy, one could adopt a strict model-theoretic approach. I will briefly sketch
what that approach would look like here. I thank Deniz Rudin for the discussion to follow. Suppose that a root √ROOT is a higher
order predicate: it is a set of sets or a predicate of predicates. A root √ROOT denotes a set whose members are themselves sets. We
can represent the inventory of meanings of a root as in (xii). Each set within the set in (xii) is a possible meaning associated with the
root and can be represented as in (xiii) where 𝛼 and 𝛽 are variables of any type (i.e. each set corresponds to its own 𝜆-expression).
We can use this notation to refer to a meaning of a root, i.e. one of the possible predicates that the root denotes.
(xii) J√ROOTK = {meaning1
, meaning2 … meaning𝑛
}
(xiii) a. Jmeaning1
K = {𝛼: 𝛼 is meaning1
}
b. Jmeaning2
K = {𝛽: 𝛽 is meaning2
}
Assuming the same ontological difference between object terms and substance terms, let’s suppose that a root may denote thing
and/or stuff, whose denotations are in (xiv): the extension of thing denotes the set in (xiv.a) where each lower case letter a, b, c
is an atomic thing or ab, bc, ac, abc are the sums of atomic things, for all 𝑛-things there are in the model; the extension of stuff
denotes the set in (xiv.b) where each lower case letter subscripted with 𝑠 (for stuff) is a portion of stuff, for all 𝑛-portions of stuff in
the model. The two denotations for the root differ in whether they have atoms or not. The set in (xiv.a) is generated from the set
of atoms and their sums; i.e. the extension of thing is an inherently atomized predicate: it is individuated. The set in (xiv.b) is not
generated from the set of atoms and has no salient individuation criterion: it is non-individuated.
(xiv) J√ROOTK = {thing, stuff}
a. JthingK = {𝑥: 𝑥 is an atomic thing or sum of atomic things} = {𝑎, 𝑏, 𝑐...𝑎𝑏𝑐}
b. JstuffK = {𝑥: 𝑥 is a portion of stuff or sum of portions of stuff} = {𝑎𝑠
, 𝑏𝑠
, 𝑐𝑠
...𝑎𝑏𝑐𝑠
}
Each predicate that the √ROOT denotes is obligatorily licensed in the presence of a categorizer. This is a consequence that the
semantics inherits from the syntax: just like a root requires a categorizer to assign a syntactic label to the node that the root adjoins
to, a root requires a categorizer to select a meaning from the set of possible associated meanings it denotes.
The denotations of the root do not exist in isolation, but they must be appropriately licensed by a categorizer. Thus, the syntax constrains the lexical semantic interpretation of the root. In a model-thoeretic semantics, we can assume that the licensing is
performed via Heim and Kratzer’s (1998) Function Application: the categorizer is a function that will take the root as argument
and select a possible meaning from the set of root denotata that meets some condition. I propose that an n-categorizer takes the
denotation of a root and maps it to a type ⟨𝑒𝑡⟩-predicate making use of the element of that root’s denotation that has the property of
being individuated or not. Starting with n[IND], I propose the denotation in (xv.a).
(xv) a. J𝑛[IND]K = 𝜆𝒫.𝜆𝑥.𝜄𝑃.(IND(𝑃) ∧ 𝑃 ∈ 𝒫)(𝑥)
b. J𝑛[IND] √ROOTK = 𝜆𝑥.𝜄𝑃.(IND(𝑃) ∧ 𝑃 ∈ J√ROOTK)(𝑥)
= 𝜄𝑃.(IND(𝑃) ∧ 𝑃 ∈ J√ROOTK)(JthingK)
The n-head in (xv.a) takes the root as argument and selects the denotation from the root’s denotata that has the property of being
individuated: generated from the set of atoms. The individuation function is defined as in (45). The only denotation that matches
that condition is JthingK. 𝜄’s 𝑃-argument is thus saturated by the thing-predicate.
As opposed to the categorizer in (xv.a), the n categorizer unmarked for individuation features has the denotation in (xvi.a). It
takes the root as argument and selects the denotation from the root’s denotata that has the property of being non-individuated via the
non-individuating function Non-IND, defined as in (48). The only denotation that matches that condition is JstuffK. 𝜄’s 𝑃-argument
is thus saturated by the stuff-predicate.
(xvi) a. J𝑛K = 𝜆𝒫.𝜆𝑥.𝜄𝑃.(Non-IND(𝑃) ∧ 𝑃 ∈ 𝒫)(𝑥)
b. J𝑛 √ROOTK = 𝜆𝑥.𝜄𝑃.(Non-IND(𝑃) ∧ 𝑃 ∈ J√ROOTK)(𝑥)
= 𝜄𝑃.(Non-IND(𝑃) ∧ 𝑃 ∈ J√ROOTK)(JstuffK)
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Singular, plural and collective. In addition to the interpretation of roots and n-terminals, we need to assign
a meaning to the number features and the collective feature that object mass nouns have. The meaning of [SG]
and [PL] are given in (52), after insights from Harbour (2007, 2011, 2014); Wellwood (2018, 2019); Martí
(2020b,a).15
(52) a. J[SG]K = 𝜆𝑃.𝜆𝑥.𝑃(𝑥) ∧ minimal(𝑥)
b. J[PL]K = 𝜆𝑃.𝜆𝑋.∀𝑥[𝑋(𝑥) → (𝑃(𝑥) ∧ ¬minimal(𝑥))]
[SG] maps 𝑃 to a property that only has minimal parts, i.e. the minimal parts that do not share an aggregate. 𝑋 in (52b) is a plural variable; and, [PL] maps 𝑃 to a property of pluralities, every non-minmal part of
which satisfies 𝑃.
16 It is worth noting here that the number features, in particular [PL], do not impose any
individuation requirement on their individual argument. This is meant to capture the observation that plural
does not entail the NP being countable, i.e. individuated. In other words, [PL] is able to compose with a predicate that has an individuated semi-lattice as well as with one that has a non-individuated semi-lattice. The
semantic effects of the number features will differ depending on the type of semi-lattice that their 𝑃-argument
has. When applied to an individuated semi-lattice such as Figure 4.2, [SG] will remove the non-minimal parts
of the lattice, i.e. the sums of atoms: it will return a predicate that is true of atomic minimal parts. When
15For Wellwood (2018, 2019) the denotation of [PL] is as in (xvii). What Wellwood calls an atom in (xvii.b) is what I call a
minimal part. In addition, the denotation of the plural morpheme encodes a presupposition that its first argument be atomic, i.e
composed of single atoms.
(xvii) J[PL]K = 𝜆𝑃: Atomic(P).𝜆𝑋.∀𝑥(𝑋(𝑥) → 𝑃(𝑥))
a. Atomic(𝑃) = a predicate P is Atomic if for all 𝑥 in 𝑃, 𝑥 is an atom
b. atom(𝑥) = for all 𝑥, 𝑥 is an atom if there is no 𝑦 such that 𝑦 < 𝑥
For Harbour (2007, 2011, 2014); Martí (2020b,a), the denotation of the plural morpheme is in (xviii). Again, for them the definition
of the function atom is the same as my definition of minimal part from Bale and Barner (2009).
(xviii) J[PL]K = 𝜆𝑃.𝜆𝑥.𝑃(𝑥) ∧ ¬atom(𝑥)
atom(x) = ¬∃𝑦[𝑦 < 𝑥]
16This meaning of the plural gives rise to exclusive pluralities. As mentioned in Chapter 3 Section 4.4.1, the plural in English (and
also Spanish, e.g.Martí 2008) can be interpreted inclusively (Krifka 1989; Chierchia 1998b; Sauerland 2003) in some environments.
I stay away from this issue here, and assume that whatever is responsible for deriving the inclusive interpretation of the plural is
potentially structurally conditioned (Harbour 2016; Ackema and Neeleman 2018; Martí 2020a). In Chapter 5, I provide an explicit
account of how to derive inclusive plural readings in Alasha Mongolian via allosemy. This account makes a series of welcome
predictions for English too, though it is not free of problems.
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applied to individuated semi-lattices such as Figure 4.2, [PL] will have the opposite effect: it will remove the
minimal parts, thus returning a predicate that is true of atomic non-minimal parts, i.e. the sums of atoms{ab,
ac, bc, abc}. Given that non-individuated semi-lattices have no minimal parts, [SG] is not compatible with
mass nouns. While predicates with non-individuated semi-lattices have sums, [PL] can apply to them but its
application will be vacuous, at most it will remove the smallest subparts in the extension the NP.
Last but not least, I take the meaning of [COLL] to be as in (53). The meaning of this feature is based
on Wellwood’s (2018; 2019) denotation of the additive plural and Tomioka’s (2021, p.492) denotation of
the associative plural: as before, 𝑋 is a plural variable; and 𝑅 is a free relation variable that refers to some
salient association between the members of the plurality and the atomic members of 𝑃. We can think of 𝑅 as
Corbett’s (2000) ‘cohesion of the group’ relation.
(53) J[COLL]K = 𝜆𝑃: IND(𝑃).𝜆𝑋.∀𝑥[𝑋(𝑥) → ∃𝑦[𝑃(𝑦) ∧ minimal(𝑦) ∧ 𝑦 ≠ 𝑥 ∧ 𝑅(𝑥, 𝑦)]]
‘For every 𝑥 among the 𝑋s, there is an atomic minimal 𝑦 in 𝑃 which is different from 𝑥 and stands in
the relation 𝑅 with 𝑥’
Given that the complement of n[COLL] in the syntax is an nP headed by n[IND], I assume that the denotation of the terminal node encodes a presupposition that his first argument be an individuated predicate. This
will ensure that COLL’s 𝑃 argument will be an individuated semi-lattice. Having atoms as minimal parts is
what will enable counting as well. If we think about what it means for something to qualify as ‘jewelry’, for
instance, we can intuitively say something along these lines: jewelry is a collection of items that are typically made from or contain individual jewels. Similarly, ‘footware’ is a collection of items that are worn in
someone’s feet. This is the intuition that the denotation of [COLL] is meant to capture: ‘collection of items’
= 𝑋(𝑥); ‘discrete/individual N’ = IND(𝑃)(𝑦) ∧ minimal(𝑦); ‘made from/worn in, i.e. the cohesion of the N
group’, = 𝑅(𝑥, 𝑦).
We can summarize the pieces of assumed so far as follows:
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• n[IND] selects for a root concept that satisfies the property of being individuated.
• Underspecified n selects for a root concept that satisfies the property of not being individuated.
• Only individuated [n+√ROOT] constituents have atoms as minimal parts which enable counting.
• [SG/PL] restrict the closed-under sum predicate to singletons (minimal parts) or sums (non-minimal
parts).
• [COLL] creates collections (i.e. pluralities) out of individuated predicates and is underspecified for a
cohesion relation between its members.
4.3.2 Some basic derivations
Before moving on to showing how the Cardinality Generalization Redux is derived, we must look at how
the system generates the appropriate interpretations for each class of noun. Starting with count nouns like
jewel(s), the structure generated by the syntax and transferred to the semantic derivation is as in (54).
(54) Singular/Plural Count
D
Num
[SG/PL]
√JEWEL n
[IND]
Given this syntax, and the allosemy rules in conditions in (37) the meaning that will be licensed for the
root is the individuated root-concept JEWEL-THING: the set of all jewel-atoms and their sums, e.g. {a, b, c, ab, bc, ac, abc}.
The unit of individuation is whatever counts as a ‘jewel item’. The categorizer then composes with the selected root-concept, and since the concept is individuated, the condition imposed by the n-head is satisfied.
If Num is [SG], the extension will be restricted to just the jewel-atoms, i.e. the singletons {a, b, c}, as in
(55c); if it is plural, the extension will be restricted to just the jewel-pluralities, i.e. the sums {ab, bc, ac,
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abc}, as in (55d). In other words, a plural-marked count noun is true of pluralities of atomic non-minimal
individual parts. The step-by-step derivation is in (55).
(55) jewel(s) – joya(s)
a. √JEWEL ↔ JEWEL-THING/__n[IND]
b. Jn[IND] √JEWELK = 𝜆𝑥.IND(JEWEL-THING)(𝑥)
c. J[SG]   n[IND] √JEWELK = J[SG]K(J(55𝑏)K) = 𝜆𝑥.IND(JEWEL-THING)(𝑥) ∧ minimal(𝑥)
d. J[PL]   n[IND] √JEWELK = J[PL]K(J(55𝑏)K) =
= 𝜆𝑋.∀𝑥[𝑋(𝑥) → IND(JEWEL-THING)(𝑥) ∧ ¬minimal(𝑥)))]
Moving on to mass nouns, the syntactic structure that the semantic derivation operates on is given in (56).
There is no individuated feature on n, and subsequently no NumP. As a result, the licensed meaning for the
root-concept is WATER-STUFF in (57a), whose extension is a non-individuated semi-lattice. As a result, the
condition imposed by n will, i.e. that the semi-lattice is a non-individuated one, is satisfied: the set of all
portions of water (i.e. all the parts that count as water). The denotation of water in (57) is composed of
(smaller) water parts (e.g. 𝑤1𝑠
, 𝑤2𝑠
) and their sums (e.g. 𝑤1𝑠𝑤2𝑠
). None of these parts are atomic.
(56) Mass
D
√WATER n
(57) water – agua
a. √WATER ↔ WATER-STUFF/__n
b. Jn √WATERK = 𝜆𝑥.Non-IND(WATER-STUFF)(𝑥) {...𝑤1𝑠
, 𝑤2𝑠
, 𝑤1𝑠𝑤2𝑠
...}
Next, if the n is not specified for individuated, but it is plural, the derivation proceeds as in the case
of canonical mass nouns: n selects a STUFF denotation for the root. [PL] will then take this predicate as its
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argument. However, given that there already are no minimal parts in the extension of the predicate, it is
difficult to determine what J[PL]K is restricting the denotation to. We can assume that pluralization of a nonindividuated predicate is trivial.17 The syntactic representation and semantic derivation are in (58) and (59)
respectively.
(58) Plural mass
D
√DREG n
[PL]
(59) dregs or celos ‘jealousy.PL’
a. √DREG ↔ DREG-STUFF/__n
b. Jn[PL] √DREGK = J[PL]K(J𝑛K(JDREGK))
c. J𝑛 DREGK = 𝜆𝑥.Non-IND(DREG-STUFF)(𝑥) =
d. J[PL]K(J(59𝑐)K) = 𝜆𝑋.∀𝑥[𝑋(𝑥) → (Non-IND(DREG-STUFF)(𝑥) ∧ ¬minimal(𝑥))]
Like water, dregs lacks atoms. Unlike water, the denotation of dregs is slightly different in that (59c) is
true of pluralities of non-atomic subparts.
Last but not least, object mass nouns have the syntax in (60). The root has the same semantics as in
(55a) given the locality with n[IND]. After composing with the categorizer as before, the next step in the
derivation is the composition with the [COLL] feature. Since its 𝑃-argument is an individuated predicate, the
presupposition is satisfied. The result is a plurality for every part of which there is an atomic minimal part
(𝑦) which is distinct from the member of the plurality (𝑥) and stands in some relation with that member. The
derivation is provided in (61).
(60) Object mass
17One could imagine that if [PL] has any effect on the nP is the removal of the smallest subparts in the extension of the nP.
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D
n
[COLL]
√JEWEL n
[IND]
(61) jewelry – joyería
a. Jn[IND] √JEWELK = (55𝑏)
b. Jn[COLL]   n[IND] √JEWELK = Jn[COLL]K(J(55𝑏)K) =
= 𝜆𝑋.∀𝑥[𝑋(𝑥) → ∃𝑦[IND(JEWEL-THING)(𝑦) ∧ minimal(𝑦) ∧ 𝑦 ≠ 𝑥 ∧ 𝑅(𝑥, 𝑦)]]
The denotation of jewelry is an individuated semi-lattice that contains pluralities of jewelry items. This
set is composed of single jewelry items, i.e. the atomic minimal parts, and their sums: {a, b, c, ab, bc,
ac, abc}. In the case of jewelry, the 𝑅 variable can be assigned the value of something like ‘made of’
or ‘contains’. The fact that the denotation of jewelry/joyería and jewels/joyas both denote an individuated
plurality, i.e. plurality built generated from the set of atoms, is what allows them to be measured along the
same scale.
4.3.3 Adding QAs into the mix
As outlined in Section 3.2.4.2, I am assuming a decompositional approach to QAs. The underlying structures
for the positive, comparatives and equative QAs was provided in (47) for English and (48) for Spanish in
Chapter 3. For ease of reference, these are repeated in (62) and (63) below, ignoring morpheme linearization.
As indicated in that chapter, I take much, many, mucho, tanto etc. as different allomorphs of the same
underlying measure root √MEAS.
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(62) English
a. Positive
Deg ⇔ 𝑚𝑢𝑐ℎ/𝑚𝑎𝑛𝑦
√MEAS Deg
b. Comparative
Deg ⇔ −𝑒𝑟/𝑚𝑜𝑟𝑒
Deg
√MEAS Deg
COMPR
c. Equative
Deg ⇔ 𝑎𝑠 𝑚𝑢𝑐ℎ/𝑚𝑎𝑛𝑦
Deg
√MEAS Deg
EQ
(63) Spanish
a. Positive
Deg ⇔ 𝑚𝑢𝑐ℎ𝑜(𝑠)
√MEAS Deg
b. Comparative
Deg ⇔ más
Deg
√MEAS Deg
COMPR
c. Equative
Deg ⇔ 𝑡𝑎𝑛𝑡𝑜(𝑠)
Deg
√MEAS Deg
[D]
EQ
Following Wellwood (2015, 2018, 2019), I assume that the measure roots have the denotation in (64),
licensed against the relevant categorizing head Deg. They introduce a variable ranging over measure functions 𝜇. The value of 𝜇 is underspecified and will be determined by the assignment function 𝐴. Thus, 𝐴(𝜇)
is the measure function that 𝐴 assigns to 𝜇. There are some restrictions on the possible dimensions of measurement that 𝐴 can assign to 𝜇, which I assume are constrained by Monotonicity (Schwarzschild 2006;
Nakanishi 2007; Wellwood et al. 2012) defined as in (65).18
(64) J√MEASK
𝐴 = 𝐴(𝜇) ⟨𝛼, 𝑑⟩
(65) Monotonicity Constraint
If two elements (objects, events etc.) 𝑥 and 𝑦 in a domain D stand in a proper subpart-superpart
relation such that 𝑥 < 𝑦, then the measure of the subpart must be strictly smaller than the measure of
the superpart
18In later work, Wellwood (2015, 2018, 2019) departs from the definition of the Monotonicity constraint in (65). For Wellwood,
monotonicity is about structure preservation, not necessarily about part-whole structure preservation.
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∀𝑥, 𝑦 ∈ 𝐷 if 𝑥 < 𝑦 → 𝜇(𝑥) < 𝜇(𝑦)
The Monotonicity Constraint allows 𝜇 to be resolved with dimensions such as DISTANCE, DURATION,
VOLUME, WEIGHT or CARDINALITY: these are all part-whole structure-preserving dimensions. However, it
rules out dimensions such as TEMPERATURE or SPEED which are not part-whole structure preserving.19
The denotation of the Deg head is as in (66), adapted from Hackl (2000). It is a function from measure
functions to a function from degrees to properties of individuals (𝑒), events (𝑣), states (𝑠). The variable 𝛼
indicates the underspecification of the semantic type. I will assume the theory of comparatives and equatives
first proposed by Heim (2001) and later developed by Bhatt and Pancheva (2004, 2007); Toquero-Pérez
(2023b). According to these authors, the comparative and equative morphemes are generalized quantifiers
over degrees, of type ⟨⟨𝑑𝑡⟩, ⟨𝑑𝑡, 𝑡⟩⟩. As generalized quantifiers, they must undergo Quantifier Raising (QR)
to a structurally higher position. It is in this position that the than/as-phrase will be late-merged, saturating
COMPR/EQ’s first argument.
(66) JDegK = 𝜆𝜇⟨𝛼,𝑑⟩.𝜆𝑑.𝜆𝛼.𝜇(𝛼) ≥ 𝑑
(67) a. JCOMPRK = 𝜆𝑃⟨𝑑𝑡⟩.𝜆𝑄⟨𝑑𝑡⟩.𝑀𝐴𝑋(𝑄) > 𝑀𝐴𝑋(𝑃)
b. JEQK = 𝜆𝑃⟨𝑑𝑡⟩.𝜆𝑄⟨𝑑𝑡⟩.𝑀𝐴𝑋(𝑄) ≥ 𝑀𝐴𝑋(𝑃)
The measure root saturates Deg’s first argument. In positive contexts, I will assume that the degree
variable of Deg is existentially bound via existential closure, whereas in equatives and comparatives it is
saturated by a degree-variable that the comparative/equative terminal has left in its launching site as a result
of QR. This variable is then bound via a lambda-abstractor in the terminal’s landing site, as per Heim and
Kratzer (1998).
Building on insights from Wellwood, I take the value that 𝐴 assigns to 𝜇 to be determined via what is
being measured. Crucially, I propose that if the complex Deg head that contains the measure root has an
19One notable documented exception to the Monotonicity Constraint is reported in Toquero-Pérez (2022), where verbal comparatives such as John runs more than Mary can be interpreted in terms of speed in Iberian Spanish. Alexis Wellwood (p.c.) notes that
an expression like more heat would also be considered as a counterexample to the Monotonicity Constraint as stated in (65).
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individuated plurality in its immediate scope in the syntax, then the value of 𝜇 will be affected accordingly:
𝐴(𝜇) →CARDINALITY. The structural description that needs to be met for this is schematized in (68), and the
definition of a CARDINALITY measure function is in (69).20
(68) Structural description for the resolution of 𝜇 as CARDINALITY
Deg
√MUCH Deg {[PL]/[COLL]}
[IND] √ROOT
(69) A CARDINALITY measure function is defined for properties of individuated semi-lattices: when
defined, CARDINALITY(𝛼) = 1 iff
a. 𝛼 is an atom in 𝑃; or
b. for every member/part of 𝛼 there is an atom in 𝑃;
c. and |𝛼| ≥ 𝑑.
4.3.4 Deriving the ‘Cardinality Generalization Redux’
Given the discussion here, we can go back to the examples with QAs from Section 4.1. We can use the
phrases in (70) as an illustration. The bare-letter example is in Spanish, and the prime-letter example is in
English.
(70) a. mucha
much.F
agua
water
a’. much water
b. mucho-s
much.M-PL
celo-s
jealousy-PL
b’. much/%many dregs
c. mucha-s
much.F-PL
joya-s
jewel-PL
c’. many jewels
d. mucha
much.F
joyería
jewelry
d’. much jewelry
20The approach taken to define the CARDINALITY measure function follows insights from Bale and Barner’s (2009) list-approach.
For an alternative approach based on automorphism invariance, see Wellwood (2018, 2019).
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According to the semantics I have attributed to noun phrases, mass nouns such as (70a-a’) have the
denotation in (57). Adding the DegP gives rise to the denotation in (71).
(71) a. Jagua/ waterK = Jn √WATERK = 𝜆𝑥.Non-IND(WATER-STUFF)(𝑥)
b. Jmucha/ muchK = JDegK(J√MUCHK
𝐴) = 𝜆𝑑.𝜆𝛼.𝐴(𝜇)(𝛼) ≥ 𝑑 =
𝜆𝛼.∃𝑑[𝐴(𝜇)(𝛼) ≥ 𝑑]
c. Jmucha agua/ much waterK = J(71𝑏)KJ(71𝑎)K =
𝜆𝑥.∃𝑑[Non-IND(WATER-STUFF)(𝑥) ∧ 𝐴(𝜇)(𝑥) ≥ 𝑑]
The nP water denotes a non-individuated property, which entails that the lattice structure has not been
generated from a set of atoms. The DegP composes with the nP via Predicate Modification (Heim and Kratzer
1998) after existential closure of its degree-argument. 𝜇 ranges over functions of type 𝑒, because JwaterK
belongs to the domain of ‘entities’. The structural conditions for 𝐴 to assign 𝜇 the value of CARDINALITY
are not met; and subsequently the CARDINALITY measure function is not defined: there are no atoms in the
extension of predicate water. 𝐴 must assign a value to 𝜇 that is different from CARDINALITY and still satisfies
the Monotonicity requirement in (65). Such a value is VOLUME or WEIGHT.
21
The same occurs with plural mass nouns like those in (70b-b’). The structural description for 𝐴 to assign
𝜇 the value of CARDINALITY is not met. While they have [PL], they denote a non-individuated predicate which
means that there are no atoms available. In other words, 𝜇 ranges over functions of type 𝑋, that is properties
of pluralities, but there are no atoms in that plurality; and as a result, the CARDINALITY measure function is
not defined. The semantic derivation is in (72).22
21In principle, nothing rules out 𝐴 from assigning 𝜇 a value such as DISTANCE/DURATION. However, these values are never assigned
to these canonical mass nouns and are generally reserved for processes or events. Here I would like to channel Wellwood (2019,
p.49): the domain conditions category mismatches, i.e. type 𝑒 vs. 𝑣 is relevant.
22Rothstein (2021, p.67) speculates that pluralization of non-individuated noun phrases, as in the case of lexical plurals, can
give rise to “instantiations of N which are either large (= abundance reading) or multiplicities of instantiations (= sums of events
or instances)”. Neither of these interpretations are, nevertheless, measuring cardinalities. It is unclear how the semantics of [PL]
alone can derive any of these interpretations, and Rothstein does not provide a formal account either. A possible answer is that
the abundance or multiplicity reading of some plural-marked nouns result from different licensing conditions on the root. In other
words, just like n[IND] licenses a THING meaning for some roots, we can hypothesize that n[PL] licenses a different meaning too.
This would require to enlarge our ontology of root meanings to include a meaning like ABUNDANCE. I will discuss this briefly in
section 4.4.1 when I discuss nominal flexibility.
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(72) a. JdregsK = J(59𝑑)K = 𝜆𝑋.∀𝑥[𝑋(𝑥) → (Non-IND(DREG-STUFF)(𝑥) ∧ ¬minimal(𝑥))]
b. Jmuch/ % many dregsK = J(71𝑏)KJ(72𝑎)K =
= 𝜆𝑋.∃𝑑[∀𝑥[𝑋(𝑥) → (Non-IND(DREG-STUFF)(𝑥) ∧ ¬minimal(𝑥))] ∧ 𝐴(𝜇)(𝑋) ≥ 𝑑]
In the case of plural count nouns, the structural description in (68) is met: both n[IND] and [PL] are in the
c-command domain of Deg. These nouns denote a predicate that is true of pluralities of atomic non-minimal
objects. As in the case of plural mass nouns, when Deg composes with the relevant NP-node via Predicate
Modification, 𝜇 ranges over functions of type 𝑋. However, unlike in the case of plural mass nouns, the
semi-lattice structure that the property of pluralities takes as input is an individuated one: [PL] has mapped a
property of an individuated semi-lattice, i.e. the nP constituent, to a property of pluralities whose members
are only the non-minimal parts, i.e the sums. Thus, for every member of the plurality 𝑋, there is an atom in
the extension of the nP. As a result, 𝐴 can assign 𝜇 the value of CARDINALITY, and the measurement of the
noun phrase is in terms of ‘number’. The step-by-step derivation is shown in (73).
(73) a. Jjewels/ joyasK = J(55𝑑)K = 𝜆𝑋.∀𝑥[𝑋(𝑥) → (IND(JEWEL-THING)(𝑥) ∧ ¬minimal(𝑥))]
b. Jmany jewels/ muchas joyasK = J(71𝑏)KJ(73𝑎)K=
= 𝜆𝑋.∃𝑑[∀𝑥[𝑋(𝑥) → (IND(JEWEL-THING)(𝑥) ∧ ¬minimal(𝑥))] ∧ 𝐴(𝜇)(𝑋) ≥ 𝑑]
𝐴(𝜇) → CARDINALITY
The derivation of object mass nouns proceeds along the same lines as with plural count nouns. The DegP
composed of the measure root and the Deg head c-commands [COLL] and [IND] in the extended projection of
the noun. This is enough to satisfy the structural description in (68). After [COLL] takes the individuated nP
as its argument, satisfying the presuppositional requirement, it returns a property that is true of pluralities for
every part of which there is an atomic minimal part which is distinct from the member among the plurality. As
a result, what 𝜇 ranges over is also a variable of type 𝑋 formed on the basis of an individuated semi-lattice.
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Like in the case of plural count nouns, the value for 𝐴(𝜇) is calculated with respect to this individuated
plurality, resulting in the resolution of 𝜇 as CARDINALITY. The derivation is shown in (74).
(74) a. Jjewelry/ joyeríaK = J(61𝑏)K =
= 𝜆𝑋.∀𝑥[𝑋(𝑥) → ∃𝑦[IND(JEWEL-THING)(𝑦) ∧ minimal(𝑦) ∧ 𝑦 ≠ 𝑥 ∧ 𝑅(𝑥, 𝑦)]]
b. Jmuch jewelry/ mucha joyeríaK = J(71𝑏)KJ(74𝑎)K
= 𝜆𝑋.∃𝑑[∀𝑥[𝑋(𝑥) → ∃𝑦[IND(JEWEL-THING)(𝑦)∧minimal(𝑦)∧𝑦 ≠ 𝑥∧𝑅(𝑥, 𝑦)]]∧𝐴(𝜇)(𝑋) ≥ 𝑑]
𝐴(𝜇) → CARDINALITY
I have illustrated how assigning the value of CARDINALITY to 𝜇 works in the case of positive QAs for
simplicity. The situation is exactly the same in the case of comparatives or equatives, with the exception that
QR of the comparative/equative morpheme and late-merger of their complement is required. I illustrate the
schematic syntactic derivation of sentence like (75) involving a comparative in (76), for the than-P, and (77),
for the matrix clause. The derivation of the equivalent sentence in Spanish proceeds in the exact same way
(Toquero-Pérez 2023b).
(75) Barney bought more jewels than Mary did.
(76) than-Phrase LF:
a. than [TP Mary [vP buy [NP1
[DegP1
√MEAS Deg OP] [N’1
PL IND √JEWEL ]]]].
b. than OP 𝜆𝑑.[TP Mary [vP buy [NP1
[DegP1
√MEAS Deg dOP] [N’1
PL IND √JEWEL ]]]].
c. JNP1
K = 𝜆𝑋.[∀𝑥[𝑋(𝑥) → (IND(JEWEL-THING)(𝑥) ∧ ¬minimal(𝑥))] ∧ 𝐴(𝜇)(𝑋) ≥ 𝑑𝑂𝑃]
(77) Matrix clause LF:
a. [CP [COMPR] 𝜆𝑑.[TP Barney [vP buy [NP2
[DegP2
√MEAS Deg-𝑑COMPR] [N’2
PL IND √JEWEL ]]]]]
b. [CP [COMPR [than-P]] 𝜆𝑑.[TP Barney [vP buy [NP2
[DegP2
√MEAS Deg-𝑑COMPR] [N’2
PL IND √JEWEL
]]]]]
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c. JNP2
K = 𝜆𝑋.[∀𝑥[𝑋(𝑥) → (IND(JEWEL-THING)(𝑥) ∧ ¬minimal(𝑥))] ∧ 𝐴(𝜇)(𝑋) ≥ 𝑑COMPR]
Starting with the than-P in (76), there is movement of a null degree operator (Bresnan 1973; Chomsky
1977) to the left periphery of the clause. This movement leaves a variable in its launching site which is
bound via lambda-abstraction in the operator’s landing site (Heim and Kratzer 1998). Assuming that the TP
node denotes a proposition of type 𝑡, the node resulting from the application of lambda abstraction is a set
of degrees of type ⟨𝑑𝑡⟩. During the semantic composition at the NP1
-level, the Deg head takes the measure
root as its first argument, and then the 𝑑-variable saturates Deg’s second argument. The internal structure of
NP1
in (76b) is identical to the underlying structure of the constituents we have been looking at: the features
[IND] and [PL] are in the scope of the DegP1
. Thus, the denotation of the NP1
, after the N’1
-node composes
with the DegP1
, will be as in (76c). At this point 𝐴 will assign 𝜇 the value of CARDINALITY.
Moving to the matrix clause in (77), the COMPR terminal undergoes QR into the clause (Heim 2001;
Hackl 2000; Bhatt and Pancheva 2004). Analogous to what happened in the than-P, COMPR leaves a variable
of type 𝑑 in its launching site. This variable is then bound by the lambda abstractor created by QR of COMPR,
as in (77a). Again, assuming that the TP node denotes a proposition of type 𝑡, lambda-abstraction will create
a node of type ⟨𝑑𝑡⟩, i.e. a set of degrees. The than-P is then late-merged in the complement position of
COMPR after QR, as in (77b). COMPR takes the than-P as its first argument and the lambda-abstracted TP
node its second argument, extracting the maximal degree in each set and establishing the ordering between
the two. NP2
-internally, the semantic composition proceeds in the exact same way as in the than-P: (i) the
N’2
-node denotes an individuated plurality by virtue of being [PL] and [IND]; (ii) √MEAS saturates Deg’s first
argument, and the 𝑑-variable its second argument; (iii) DegP2
and N’2
compose via Predicate Modification
giving rise to the denotation in (77c). At this point, we can assume that 𝜇 is assigned the relevant value, i.e.
CARDINALITY.
As a result, the dimension of measurement in both matrix and than-P are calculated identically and the
interpretation of the sentence can be paraphrased as follows: “the maximal degree in the set of number of
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jewels bought by Barney is larger than the maximal degree in the set of number of jewels bought by Mary”.
In other words, the total number of jewels that Barney bought exceeds the total number of jewels that Mary
bought. The denotation of the full sentence is schematized in (78).
(78) JBarney bought more jewels than Mary didK =
= 𝑀𝐴𝑋(𝜆𝑑.JBarney bought NP2
K) > 𝑀𝐴𝑋(𝜆𝑑.JMary bought NP1
K)
We have now an explanation for the Cardinality Generalization Redux. If the denotation of the noun
contains atoms, they will allow for number-based measurement, i.e. CARDINALITY. Plural count nouns and
object mass nouns are both mapped from individuated semi-lattices, built from the set of atoms, to pluralities;
whereas canonical mass nouns and plural mass ones are not: the roots of these nouns are mapped to nonindividuated semi-lattices that lack atoms. As a result, the conditions required to ensure measurement in
terms of cardinality are not met. This holds regardless of whether the noun itself is plural-marked and
denotes a property of pluralities. The assignment of the relevant value to 𝜇, and in particular CARDINALITY is
dependent on the structural make-up of the domain that is being measured. That is, the interpretable features
that are made available in the syntax together with the position that the DegP occupies in the structure play
an important role in determining how the dimension of measurement is to be resolved.
4.4 Ramifications of the theory
4.4.1 Shifts between classes
Before concluding this chapter I want to briefly mention what I think it is an advantage of the proposal
developed here. This aspect is related to what is sometimes referred to as ‘countability shifts’ or ‘nominal
flexibility’. For example, canonical mass nouns like beer can occur in count contexts to mean ‘container or
units of’: beers, a beer, 2 beers. Likewise, count nouns may occur in mass contexts, sometimes known as
‘grinding’ contexts (Pelletier 1979): there is dog all over the place.
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There is some analysis that unifies the two types of shifts and relates them to the overall grammatical
properties of the class of nouns they have shifted into. For some like Pelletier (1979); Bunt (1985); Rothstein (2010), the shifts are triggered by the semantics of covert operators that apply to the relevant nominal
predicate. These authors operate largely under lexicalist assumptions and they make an analytic distinction
between roots that are lexically mass and roots that are lexically count.
For others like Borer (2005a); Mathieu (2012), the shifts are syntactically derived: for them, all nominal
roots start out as mass and what determines countability is the projection of a head that divides matter into
countable units, e.g. Division (DIV). As described in the introductory chapter of this dissertation, NPs are
count because they project DIVP; thus, in the absence of DIVP the interpretation of an NP like rock or dog is
a mass one. In contrast, when a mass NP like beer or water is divided by DIV, then a packaging or container
interpretation arises. That is, additional count structure is added on top of a mass NP. The proponents of this
type of approach for languages like English or Spanish parallel the role of DIV to that of a singulativizing
morpheme in languages like Arabic or Welsh (Mathieu 2012; Mathieu and Dali 2021; Dali and Mathieu
2021). Subsequent pluralization is possible, just like pluralization of singulatitves.
We can test whether container-readings of shifted mass nouns involve singulativization. Mathieu and
Dali (2021) note that the plural of the singulative, at least in the languages that they investigate, gives rise to
an exclusive plural interpretation: only reference to sums. In English, it has been observed that plurals are
generally exclusive except in downward entailing contexts and questions, in which case they are inclusive,
i.e. they include both singletons and sums (Krifka 1989; Chierchia 1998a; Sauerland 2003; Sauerland et al.
2005). Thus, if the plural of the singulative is always exclusive regardless of the downward entailingness of
the context (Mathieu and Dali 2021), we predict that beers or waters with a container interpretation will only
make reference to the non-singleton sums of beer/water units. That is, there should be no difference between
the plural interpretation of beers in an upward entailing context and a downward entailing one. As the data
in (79) show, the prediction is not borne out for English.
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(79) a. Barney drank beers at the fair last night. (
✓ ≥2, ∗ ≥1)
b. Barney didn’t drink (any) beers at the fair last night. (
∗ ≥2, ✓ ≥1)
A: Did Barney drink (any) beers at the fair last night?
B: {Yes, one/ #No, one}
While in the upward entailing context in (79a), the bare plural beers refers to two or more beer-units (i.e.
only the sums), the same bare plural noun does not make reference to two or more beers in the other two
contexts. In fact, (79b) is only felicitous if Barney didn’t drink any beers at all; and the question in (79b) can
be answered positively with the numeral one, which denotes a singleton.
The theory that I have proposed so far does not rely on the presence of a covert singulativizing morpheme.
Shifts can be accounted for by pairing a root with a different categorizer. The root must however be licensed,
both semantically and morpho-phonologically. In other words, while the syntax does not preclude a root to
adjoin to different nominalizing ns, at the interfaces the object put together by the syntax must be mapped to
a vocabulary item and an appropriate concept. Under this approach, there is no ‘shifting’ involved, but the
licensing of, or lack thereof, a root in a different syntactic context.
Accounting for shifts. To see how this works, let’s first take the situation of shifted mass nouns into a
container. The root √BEER adjoins to the n[IND] categorizer which individuates the root. As a result, Number
can be merged on top of. If Number is PL, /-s/ will surface on the noun. The semantic effect that plural has
will also be uniform. This is represented in (80).
(80) mass-to-count (container interpretation)
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DP
D NumP
Num
[SG/PL]
[•IND•]
nP
√BEER n
[IND]
When the structure is transferred to the interfaces, the root √BEER is appropriately licensed in this context.
At PF, it is mapped to a vocabulary item beer. At LF, the root is also assigned a meaning that is compatible
with it. Suppose that the root √BEER is associated with the root-concepts in (81), where BEER-THING and
BEER-STUFF. The choice of one concept over the other is determined by the categorizer that the root adjoins
to in the syntax. The LF licensing of the root √BEER in the nominal domain is summarized by the allosemy
rules in (82).
(81) √BEER = {BEER-STUFF, BEER-THING}
(82) a. √BEER ↔ BEER-THING/ n[IND]
b. √BEER ↔ BEER-STUFF
The licensing of (82a) captures the idiomatic interpretation of the root √BEER when it occurs in a count
context, i.e. local to n[IND]. The relevant unit of individuation will be whatever counts as a unit of beer,
i.e. container: a glass or a bottle. The individuated root-concept is selected by the individuating categorizer.
Elsewhere, i.e. when the categorizer is underspecified for individuation features, the BEER-STUFF concept is
licensed.
The same rationale can be applied to the grinding cases of count nouns. But in this case, it is the mirror
process: a root like √DOG will be adjoined to an underspecified n. Since n is not [IND], the nP will not be
marked for individuation; Number cannot project and so all the mass-like properties that ground-count nouns
share with canonical mass follow. The syntax of ‘ground-dog’ is given in (83).23
23In languages that make gender and class inflection distinctions between count and mass nouns, the system predicts that pairing
up the same root 𝛼 with a different categorizer will result in the root bearing a different gender or class exponent. This prediction is
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(83) count-to-mass (grinding)
DP
D nP
√DOG n
At PF, the root is properly licensed because it is able to be mapped to an exponent: dog. At LF, the root
is also properly licensed since it is mapped to a meaning. Obtaining this idiomatic meaning for the root can
also be modeled in terms of root-allosemy conditioned by the categorizer. I represent the relevant allosemy
rules in (85). The most specific allosemy rule in this case is (85a): select the DOG-STUFF concept for the root
in the context of underspecified n; elsewhere, i.e. in the context of n[IND], select the DOG-THING concept (e.g.
the animal).
(84) √DOG = {DOG-STUFF, DOG-THING}
(85) a. √DOG ↔ DOG-STUFF/ n
b. √DOG ↔ DOG-THING
The question that one might be willing to raise now is the following: are there ever attested cases in which
roots (other than √SUD, √DREG, √HOP) adjoin to n[PL]? The answer is yes! These are sometimes referred to
as (i) plurals of extension such as mountains, skies, cliffs, following the nomenclature in Nauta et al. (2022),
and (ii) plurals of abundance such as waters, sands, snows (Alexiadou 2004, 2011; Tsoulas 2006, 2009;
Acquaviva 2008; Kouneli 2019; Rothstein 2021). Nauta et al. (2022) observe that there are slight differences
borne out in Asturian. In Asturian, a root like √FERR ‘iron’ can have a class marker -u or -o. The former signals masculine gender
and appears on count nouns, and the latter is a portmanteaux for masculine mass (Bonet 2013). Postnominal adjectives agree with
the noun in count/mass, while prenominal adjectives agree with the noun in gender. The data and observations are taken from Bonet
(2013, p.178).
(xix) a. fierr{
iron
-u/
-M/
-o}
-M.MASS
‘iron (piece/ material)
b. dur-u
hard-M.
fierr-u
iron-M
ferruños-u
rusty-M
‘hard rusty iron piece’
c. dur-u
hard-M
fierr-o
iron-M.MASS
ferruños-o
rusty-M.MASS
‘hard rusty iron’
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between the two classes of lexical plural nouns, but for our purposes it suffices to show how these two classes
really pattern like the plural-mass nouns discussed in this chapter.
With respect to the former, Nauta et al. (2022) observe that mountains in a sentence like (86a) does not
refer to a plurality of mountain-individuals, but to a mountainous area. What is more, they observe that
these plurals of extension are unacceptable with Class 3 determiners like several which, as we saw, track
individuation and plural number. They also disallow cardinal numeral modification. Both these properties
are shown in (86b). With respect to the other group, i.e. plurals of abundance, these too are incompatible
with several and cardinal numeral modifiers. This is illustrated in (87).
(86) a. We took a hike in the mountains.
b. * We took a hike in {several/ five} mountains.
(87) The snows of the Kilimanjaro, international waters, the sands of the Sahara …
a. * The three/several international waters.
b. * The several snows of the Kilimanjaro.
We can straightforwardly account for the syntactic structure that underlies these two types of exceptional
plurals: they arise when the root adjoins to n[PL] bleeding count structure. As a result, the mass properties
also follow from the syntax in (88).
(88) mass/count-to-plural mass
DP
D nP
{√WATER, √MOUNTAIN}
n
[PL]
We can also model the ‘exceptional’ meanings in terms of the approach to the licensing of root-meanings
developed here. In particular, the plural feature on n can trigger an abundance interpretation of the root. That
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is, the abundance interpretation is root-allosemy condtioned by n[PL]. The allosemy rules can be summarized
as in (90), assuming that a root like √WATER can be associated with the set of concepts in (89).24
(89) √WATER = {WATER-STUFF, WATER-THING, WATER-ABUNDANCE, WATER-EVENT}
(90) a. √WATER ↔ water-thing/ n[IND]
b. √WATER ↔ water-abundance/ n[PL]
c. √WATER ↔ water-event/ v
d. √WATER ↔ water-stuff
We can account for cross-linguistic variation in similar terms. For example, in English roots like √WATER
can be licensed in an individuated and non-individuated context, whereas other roots like √BLOOD cannot.
In contrast, in Nez Perce, both √WATER and √BLOOD can be licensed in either context (Deal 2017); while in
Alasha Mongolian neither root can be licensed in an individuated context. What this means in this model
is that while the syntax can put the relevant terminals together (e.g. the root and n[IND]), the root cannot
be assigned a compatible meaning associated with that root. That is, the relevant root-concept is absent
from the set of root. As a result, there is no allosemy rule that can map the root to such root-concept.
semantic composition fails because the categorizer cannot map the root to the unique root denotation that
meets the individuation criteria. A small typology of languages can be summarized in Table 4.2. A first-pass
generalization is that the most-marked meaning for some roots, i.e. the most specific allosemy rule, is the
one that is not universally available across languages.
The account developed here presents itself as an elegant and parsimonious alternative to covert-shifting
approaches or singulativizing approaches. These seemingly exceptional cases are not so exceptional after
all, and they do not really involve any ‘shifting’ in the syntax (at least in the two languages analyzed here):
24This is not unreasonable given the following observation from Rothstein (2021, p.67) about the relation between overt pluralization and mass noun syntax: “marking the mass noun as plural would draw attention to sums in the denotation of the noun
N, i.e. instantiations of N which are either large (= the abundance reading) or multiplicities of instantiations (= sums of events or
instances).”
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Table 4.2: Variation across-languages in the licensing of root-meanings
Language Form Syntax Root-meaning example
Nez Perce kuus ⇔ [√ROOT n] ↔ WATER-STUFF kuus ‘water’
kuus ⇔ [√ROOT n[IND] ] ↔ WATER-THING 3 kuus ‘3 units of water’
kike’t ⇔ [√ROOT n] ↔ BLOOD-STUFF kike’t ‘blood’
kike’t ⇔ [√ROOT n[IND] ] ↔ BLOOD-THING 2 kike’t ‘2 drops of blood’
English water ⇔ [√ROOT n] ↔ WATER-STUFF water
water ⇔ [√ROOT n[IND] ] ↔ WATER-THING 2 waters
blood ⇔ [√ROOT n] ↔ BLOOD-STUFF blood
blood ⇔ [√ROOT n[IND] ] ↔ # 2 bloods
Alasha Mongolian os ⇔ [√ROOT n] ↔ WATER-STUFF os ‘water’
os ⇔ [√ROOT n[IND] ] ↔ # 2 os ‘2 units of water’
tsos ⇔ [√ROOT n] ↔ BLOOD-STUFF os ‘blood’
tsos ⇔ [√ROOT n[IND] ] ↔ # 2 tsos ‘2 drops of blood’
their syntactic properties follow from the same underlying syntax that makes a noun like book count and a
noun like water or salt mass. The syntax is blind as to whether a root can be adjoined to one categorizer or
another. But this does not entail that any root-categorizer pair will be appropriately licensed at the interfaces
(Harley and Noyer 1998, 1999, 2000; Acquaviva 2009; Harley 2014; Kramer 2015; Pross 2019; Ranero 2021;
Wood 2023): the root must be assigned a vocabulary item and a compatible meaning given the relevant
syntactic context. While we can also account for cross-linguistic variation in this way, the proposal here
does not rule out the fact that some languages might accomplish container and grinding interpretations via
different syntactic operations that are independently available, e.g. singulativization as argued for Arabic or
Welsh (Borer 2005a; Mathieu 2012). Cross-linguistic variation thus results from the way that the syntax puts
terminal nodes together in concert with the satisfaction of the different requirements at the interfaces.
4.4.2 QAs, plural-markedness and the dimension of measurement beyond English and Spanish
The theory that I have advanced, following Wellwood (2015, 2018, 2019), is one where the surface form of
the QA does not correlate with the dimension of measurement that is assigned in the semantic composition.
The generalization that I have put forth is one where the dimension of cardinality is predictable based on the
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interpretable content that certain syntactic terminals are assigned during the semantic computation; namely
an individuated plurality. In addition, I have made explicit the following two claims throughout the dissertation: the surface form of QAs can be sensitive to plural-marking, and being countable means being marked
for individuation which need not entail being plural-marked. This makes the following predictions:
(i) if a language 𝕃 has count and mass nouns both of which are plural-marked they might both trigger
allomorphy or plural agreement on the QA;
(ii) the (plural-)marked form of the QA will only be associated with the dimension of cardinality when the
plural-marked noun is count, marked for individuation.
Both of these were borne out in English and Spanish. In this section, I show that they are also borne out
for Greek and Telugu.
Greek Greek makes a distinction between count and mass nouns. For example, count nouns can be overtly
pluralized and be modified by cardinal numerals as in (91), whereas mass nouns in (92) are only acceptable
in these contexts under a shifted interpretation, i.e. a container reading. The container interpretation comes
out clearly in sentences like (93), from Tsoulas (2009, p.132: ex.7) and from Kouneli (2019, p.239: ex.16b).
(91) Count Nouns in Greek
a. periodik{
magazine
-o/
-SG/
-a}
-PL
‘magazine/ magazines’
b. dio
two
periodik-a
magazine-PL
‘two magazines’
(92) Mass Nouns in Greek
a. ner{
water
-o/
-SG/
-a}
-PL
‘water’ (substance)/ ‘waters’ (containers)
b. dio
two
ner-a
water-PL
‘two waters’ (#
substances/ containers)
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(93) a. Tere
bring
tria
three
ner-a
water-PL
‘Bring three waters’
b. Ipia
drank.1SG
dio
two
bires
beer.PL
prin
before
ligo
a.bit.ACC
‘I drank two beers long ago’
While mass nouns in Greek can appear plural-marked and with numerals under a shifted interpretation,
in which case they pattern with count nouns, there is a subclass of mass nouns that when pluralized do not
give rise to container interpretations. When this occurs, the interpretation that is obtained is sometimes
referred to as an ‘abundance’ interpretation paraphrased as something like ‘a lot of’ according to Acquaviva
(2008); Tsoulas (2009); Alexiadou (2011) or ‘substance scattered/spread over a surface in a disorderly way’
according to Kouneli (2019). As Alexiadou (2011) notes, this ‘abundance’ interpretation is more salient with
verbal predicates like spray, fall, drip, run or gather, as illustrated in (94).
(94) a. ( Ta)
the.PL
ner-a
water-PL
trexun
run.3PL
apo
from
to
the.SG.ACC
tavani
ceiling.SG.ACC
‘A lot of water drips from the ceiling’
b. * Dio
two
ner-a
water-PL
trexun
run.3PL
apo
from
to
the.SG.ACC
tavani
ceiling.SG.ACC
‘Two waters drip from the ceiling’
The data in (94a) shows that the noun agrees in plural number with the determiner and the verb. Evidence
that this type of plural-marked mass noun is in fact mass and not a shifted noun is given in (94b): modification
by a numeral is unacceptable. Further evidence for this comes from Kouneli’s (2019) observation that plurals
of abundance in Greek are also incompatible with Stubbornly Distributive adjectives. The relevant example
is in (95).
(95) # Ta
the.PL
ner-a
water-PL
sto
at.the.SG.ACC
patoma
floor.SG.ACC
in
are.3PL
stroglia.
round.3PL
‘A lot of water on the floor is round’
That said, the generalization is that plurals of abundance in Greek are mass nouns despite being overtly
plural-marked and showing overt plural agreement DP-internally and externally.
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Moving to QAs, Greek is like Spanish: the QAs (at least in their comparative form) agree in phi-features,
including number, with the noun they modify. When the noun is a plural count one, the QA agrees with
it in plural number as in (96a); when the noun is mass and unmarked for number, so is the QA as in (96b).
Crucially, if the mass noun is plural-marked and occurs in an abundance context, the QA is also plural-marked
as in (96c); that is, the surface form of the QA is identical to the one found with plural count nouns in (96a).
(96) Greek plural mass nouns
a. Den
not
exo
have.1SG
ksana-di
again-seen
perissoter-a
more-PL.ACC
periodik-a
magazine-PL.ACC
sto
at.the.SG.ACC
patoma
floor.SG.ACC
‘I have never seen more magazines on the floor’ CARDINALITY, #ABUNDANCE, #VOLUME
b. Ipia
drank.1SG
perissoter-o
more-SG.ACC
ner-o
water-SG.ACC
‘I drank more water’ #CARDINALITY, VOLUME
c. Den
not
exo
have.1SG
ksana-di
again-seen
perissoter{
more
-a/
-PL.ACC/
∗
-o}
-SG.ACC
ner-a
water-PL.ACC
sto
at.the.SG.ACC
patoma
floor.SG.ACC
‘I have never seen more water on the floor’ #CARDINALITY, ABUNDANCE
The example in (96a) involves a plural count noun. The QA perisster- ‘more’ agrees with the noun in
plural number -a. The interpretation of the comparative is in terms of cardinality. The sentence in (96b)
involves a canonical mass noun which is unmarked for number. The form of the QA is also unmarked
perisstero, and the comparison is being established in terms of volume. However, in (96c), the mass noun
nera ‘water’ is plural marked and so is the comparative morpheme. Interestingly, as reported by Tsoulas
(2009); Kouneli (2019) the interpretation that arises is not one where the number of containers of water is
being compared; instead the idiomatic interpretation is something like “I have never seen a larger amount of
water spread over the floor”.
Alexiadou (2011, 2015); Kouneli (2019) both argue that (i) the plural feature in plurals of abundance is
located on the nominalizer n that the root combines with, and (ii) these nouns lack NumP. This is exactly the
same analysis that I have proposed for plural mass nouns in English and Spanish. Besides, like in Spanish,
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the presence of a plural feature in the extended projection of the noun is relevant for concord on nominal
modifiers including QAs. This is just one further example that the surface form of a QA need not be directly
mapped to a certain dimension of measurement. Rather, the form of the QA seems to be sensitive to the
presence or absence of a plural number feature, contrary to what is expected by UD in (5) as proposed by
Solt (2009).
Telugu. Telugu is a Dravidian language spoken in India. The data and judgments in this part have all been
taken from Smith (2021, ch8). Smith (2021) reports that Telugu makes a singular-plural distinction reflected
on the noun and the verb. On the noun, the singular is morphologically unmarked, whereas the plural is
marked by the suffix -lu. This is shown in (97).
(97) Telugu singular/plural agreement
a. kukka
dog
tinn-a-di
eat-PAST-3NM.SG
‘A dog ate’
b. kukka-lu
dog-PL
tinn-aa-ji
eat-PAST-3NM.PL
‘Dogs ate’ (Smith 2021, p.218: ex.346-347)
The class of nouns that make the overt singular-plural distinction are compatible with numeral modifiers. Numerals in the language require the noun to be overtly plural-marked. Besides, these nouns allow
modification by Stubbornly Distributive adjectives. This is all shown in (98).
(98) Modification of plural (count) nouns
a. Raaju
Raaju
muuDu
three
aratipanD-lu
banana-PL
tinn-aa-Du
eat-PAST-3M.SG
‘Raaju ate three bananas’ (Smith 2021, p.218: ex.349)
b. aratipanD-lu
banana-PL
pedda-gaa
big-GA
unn-aa-ji
be-PRES-3.NM.PL
‘The bananas are large’ (Smith 2021, p.220: ex.353a)
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These nouns thus show some hallmark properties of count nouns. In fact, they contrast with those that do
not have a singular-plural distinction, cannot be modified by numerals and are unacceptable with Stubbornly
Distributive adjectives. Smith labels this class as ‘mass’. The relevant examples are given in (99).
(99) Telugu mass nouns
a. * aa
the
abbaaji
boy
isuka-lu
sand-PL
tavvu-tunn-aa-Du
dig-PROG-PRES-3.NM.SG
Int.: ‘The boy is digging sands’ (Smith 2021, p.218: ex.348)
b. * Raaju
Raaju
renDu
two
isuka-lu
sand-PL
konn-aa-Du
dig-PAST-3M.SG
Lit.: ‘Raaju dug two sands’ (int.: ‘Raaju dug two piles of sand’) (Smith 2021, p.219: ex.350)
c. # vendi
silver
pedda-gaa
big-GA
un-di
be-3.NM.SG
Int.: ‘The silver is large’ (Smith 2021, p.220: ex.353b)
In addition to these canonical mass nouns, there is a very restricted set of nouns in the language that are
obligatorily plural-marked and trigger plural agreement with the verb. Nevertheless, they pattern with the
mass nouns in (99); that is, no numeral modification and Stubbornly Distributive adjectives. This is shown
in (100).
(100) Telugu plural mass nouns
a. { nii-LLu/
water-PL/
paa-lu}
milk-PL
{ unn-aa-ji/
be-PRES-3PL/
∗undi}
be-3.NM.SG
‘There is {water/ milk}’ (Smith 2021, p.221: ex.356)
b. * Raaju
Raaju
renDu
two
nii-LLu
water-PL
taag-ææ-Du
drink-PAST-3.M.SG
Int.: ‘Raaju drank two units of water’ (adapted from Smith 2021, p.222: ex.358)
c. # nii-LLu
water-PL
pedda-gaa
big-GA
un-aa-ji
be-PRES-3PL
Int.: ‘The water is large’ (Smith 2021, p.222: ex.359)
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With respect to QAs, the much/many distinction is neutralized but the little/few distinction is not. In other
words, while QA čaala ‘much/many’ occurs with both count and mass nouns as shown in (101), konni ‘few’
occurs with plural count nouns and končam ‘little’ with canonical mass nouns. This is shown in (102).
(101) Raaju
Raaju
čaala
much
{ aratipanD-lu/
banana-PL/
annam}
rice
tinn-aa-Du
eat-PAST-3M.SG
‘Raaju ate {many bananas/ much rice}’ (Smith 2021, p.219: ex.351)
(102) konni vs. končam
a. Raaju
Raaju
konni
few
aratipanD-lu
banana-PL
tinn-aa-Du
eat-PAST-3M.SG
‘Raaju ate few bananas’ (Smith 2021, p.219: ex.352a)
b. Raaju
Raaju
končam
little
uppu
salt
tinn-aa-Du
eat-PAST-3M.SG
‘Raaju ate little salt’ (Smith 2021, p.219: ex.352b)
Smith reports that the interpretation of the nouns modified by QAs also differs. While plural count
nouns modified by konii are measured in terms of cardinality, mass nouns modified by končam are measured
in terms of volume. Thus, the sentence in (102a) can be paraphrased as “the number of bananas Raaju ate is
small” while the one in (102b) can be paraphrased as “the volume of salt that Raaju ate is small”.
If the surface form of the QA determined the dimension of measurement in the semantics, as predicted
by Solt’s (2009) UD, we expect plural mass nouns like nii-LLu ‘water-PL’ or paa-lu ‘milk-PL’ to occur with
končam. However, this is not what the data in (103) show.
(103) aa
the
abbaaji
boy
{ konni/
few/
∗končam}
little
nii-LLu
water-PL
taag-ees-tun-aa-Du
drink-EMPH-PROG-PRES-3.M.PL
Lit.: ‘The boy is drinking {few/ ∗
little} waters’
Int.: ‘The boy is drinking some (volume of) water’ (Smith 2021, p.222: ex.357)
The mass noun in (103) is plural marked and the QA that is acceptable with this plural mass noun is konni.
This is the same surface form that occurred with plural count nouns in (102a). Besides, the interpretation,
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as reported by Smith, is in terms of volume, not cardinality. What do the nouns in (102a) share with those in
(103)? The answer is overt plural-marking, which is compatible with the analysis that plural-marking has an
effect on the surface form of the QA. As a result, we can model the distribution of these surface forms with
the VI rules in (104), in the spirit of Smith (2021, p.231: ex. 369).
(104) a. √KONČAM ⇔ 𝑘𝑜𝑛𝑛𝑖/ Deg[𝑢PL: PL]
b. √KONČAM ⇔ končam
Telugu is like English regarding QA suppletion (e.g. little vs. few) and also like Spanish (i.e. overt-plural
marking on the noun triggers plural concord on QAs). Telugu is, thus, one more case in which the surface
form of the QA is not conditioned by the semantic interpretation that it is assigned, but by the presence of
a plural feature in the extended projection of the noun. The dimension of cardinality is determined by the
presence of an individuated feature, which enables subsequent pluralization. The cross-linguistic patterns of
plural-marking on the noun/verb, the surface form of the QA and the semantic interpretation that the QA is
assigned are summarized in Table 4.3, which is an extended version of Table 4.1.
4.5 Conclusion
This chapter has focused on a semantic asymmetry between some mass nouns and plural count nouns.
Namely, object mass and plural count nouns are interpreted in terms of cardinality when modified by QAs,
while canonical and plural mass nouns are not. This is not a peculiar property of English, but it seems to be
a good candidate for a language universal (see also Lima 2014; Deal 2017; Chierchia 2021; Doetjes 2021,
among others). I started by casting doubt on why a generalization like Uniform Dimensionality in (5) misses
this robust cross-linguistic fact by correlating surface forms of QAs to their semantic interpretation.
I then proposed that the actual generalization need not, and in fact should not, make any reference to
surface forms. The generalization, which I have labeled as the Cardinality Generalization Redux, is more
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Table 4.3: Number marking, choice of QA, and semantic interpretation by noun type
Langs. Agreement QA form Dimension of measurement
Tyep of N SG PL Unmarked PL-Marked CARDINALITY OTHER
Canonical Mass English ✓ * ✓ * * ✓
Spanish ✓ * ✓ * * ✓
Greek ✓ * ✓ * * ✓
Telugu ✓ * ✓ * * ✓
Object Mass English ✓ * ✓ * ✓ *
Spanish ✓ * ✓ * ✓ *
PL Mass English * ✓ ✓ % * ✓
Spanish * ✓ * ✓ * ✓
Greek * ✓ * ✓ * ✓
Telugu * ✓ * ✓ * ✓
PL Count English * ✓ * ✓ ✓ *
Spanish * ✓ * ✓ ✓ *
Greek * ✓ * ✓ ✓ *
Telugu * ✓ * ✓ ✓ *
abstract: the dimension of cardinality is predictable if the domain to be measured denotes an individuated
plurality. Based on the theory of individuation and number that I have developed, this amounts to saying
that the noun must be specified for [IND] in the syntax, and then be either plural or collective-marked. Thus,
the dimension of measurement is determined by the syntactic position of the measure word in concert with
formal features of the target constituent.
I have then gone on to showing that this approach, allows us to capture shifts between classes without the
need to posit covert operations. Roots can be adjoined to different categorizers in the syntax but the root has
to be licensed both at PF (mapped to a vocabulary item) and LF (and assigned an interpretation). At LF, a
root is licensed if the categorizer, which introduces a selection function, can map the root to an appropriate of
denotation from the set denoted by the root: ultimately, this boiled down to whether the root had a thing or a
stuff denotation that n[IND] and n could compose with respectively. If either of those denotations is missing,
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the corresponding meaning for the root will remain unlicensed. I have shown how this system enables us to
account for cross-linguistic variation.
Last but not least, I have articulated how the proposal, in tandem with a decompositional approach to
QAs, allows us to also capture the distribution of the different surface forms of QAs. Surface forms of QAs
may be sensitive to plural-marking, but not semantic interpretation. This is not to say that number features are
the sole triggers of QA allomorphy; there might be other features that contribute to the insertion of different
exponents, such as gender or noun class. The proposal here is compatible with these features being involved
in allomorph selection. The view that there is not a perfect match between phonological form and semantic
interpretation also supports a view of QAs according to which the dimension of measurement that they are
assigned is underspecified (Wellwood 2015, 2018, 2019), rather than lexically determined. This is in turn
compatible with a modular view of the grammar according to which there is no interaction between morphophonological processes such as Vocabulary Insertion and the semantic interpretation of terminal nodes (and
viceversa). In other words, the morpho-phonological system and the semantic system are non-overlapping.
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Chapter 5
Accommodating Number Neutrality: Markedness and Semantic
Interpretation
5.1 Introduction
Languages oftentimes make a morpho-syntactic distinction between singular and plural marking on nouns
or DP internal elements. For example, in Wolof, nouns may occur bare or with a determiner or class marker
which spells-out singular. Plural-marking is not expressed on the noun, but on the determiner or class marker.
This is shown in (1) adapted from (Fong 2023).
(1) Wolof
a. Awa
Awa
defar-na
fix-NA.3SG
oto
car
( b-i)
CM.SG-DEF
‘Awa fixed (the) car’ SG ⇔ {Ø/ b-}
b. Awa
Awa
defar-na
fix-NA.3SG
oto
car
y-i
CM.PL-DEF
‘Awa fixed the cars’ PL ⇔ yAs argued by Fong (2021, 2023), the unmarked form in (1a) makes reference to singularities (i.e. only
atoms), regardles of whether it occurs bare or with the determiner/class marker. In other words, it is exclusively singular. The plural-marked form in (1b) makes reference to exclusive pluralities (i.e. only sums).
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The distinction as to whether what counts as a singularity or plurality, however, does not always align
with morpho-syntactic exponence. Let’s consider the forms in (2) from Western Armenian and those in (3)
from English.
(2) Western Armenian
a. d@gha
boy
SG ⇔ Ø
b. d@gha-ner
boy-PL
PL ⇔ -ner
(3) English
a. boy SG ⇔ Ø
b. boy-s PL ⇔ -S
In Western Armenian, the unmarked form in (2a) can make reference to both atoms and their sums, but
the plural-marked one in (2b) makes exclusive reference to sums (Bale et al. 2011; Bale and Khanjian 2014).
In other words, the unmarked form is number neutral whereas the plural-marked form is exclusively plural.
In English, like in Wolof, the unmarked form boy in (3a) denotes a singularity, but the plural-marked one
is ambiguous: it may denote an exclusive plurality or an inclusive one, i.e. atoms and sums (Krifka 1989;
Sauerland 2003; Sauerland et al. 2005; Spector 2007; Zweig 2009; Farkas and de Swart 2010). As observed
by these authors, the latter interpretation is found in downward entailing environments and questions. From
now on, I will be using the labels U(pward)E(ntailing)C(ontext) and D(ownward)E(ntailing)C(ontext). For
example, this is shown with the contrasts in (4).
(4) a. Ash fostered boys in the cabin.
i. ✓Exclusive: ‘Ash fostered two or more boys’
ii. #Inclusive: ‘Ash fostered one or more boys’
b. Ash didn’t foster boys in the cabin.
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i. #Exclusive: ‘Ash didn’t foster two or more boys’
ii. ✓Inclusive: ‘Ash didn’t foster any boys’
c. If Ash fosters boys, he can apply for food stamps
i. #Exclusive: ‘If Ash fosters two or more boys, he can apply for food stamps’
ii. ✓Inclusive: ‘If Ash fosters any boys, he can apply for food stamps’
The conclusion that we can draw from this is that having a morphological singular-plural distinction
does not guarantee a uniform semantic interpretation. In fact, it seems that there is variation regarding the
denotation of unmarked and plural-marked nouns across languages. This is schematized with the denotation
of nPs that are marked or unmarked for number below.
(5) Unmarked nP that denotes a singleton
J𝑛P-SGK = {𝑎, 𝑏, 𝑐} English, Wolof
(6) Unmarked nP that is number neutral
J𝑛P-ØK = {𝑎, 𝑏, 𝑐, 𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐} Western Armenian
(7) Plural-marked nP that denotes an exclusive plurality
J𝑛P-PLK = {𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐} English (UEC), Western Armenian, Wolof
(8) Plural-marked nP that denotes an inclusive plurality
J𝑛P-PLK = {𝑎, 𝑏, 𝑐, 𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐} English (DEC)
However, variation in the interpretation of nPs that are marked or unmarked for number can be even
more fine-grained. For example, Bylinina and Podobryaev (2020) report that in Barguzin Buriat (Mongolic)
the interpretation of unmarked nouns is sensitive to animacy: unmarked inanimates are number neutral, but
unmarked animates denote a singleton.1 Plural-marked nouns behave like their English counterparts: they
1An overview of the data is beyond the scope of this chapter, though. See Bylinina and Podobryaev (2020) for details.
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can be exclusively or inclusively plural depending on the upward/downward entailingness of the context. In
a nutshell, the differences in morpho-semantic markedness in terms of number that seem to emerge across
languages are summarized in Table 5.1. The labels SNG/PLR refer to the semantic interpretation and not the
phonological form of the noun; thus, SNG refers to a ‘singularity’ or singleton (e.g. 1) and PLR refers to
a ‘plurality’ (e.g. 2 or more). If a noun can refer to both, then we will say the noun is number neutral if
unmarked or inclusively plural if plural-marked.
Table 5.1: The interpretation of number in languages with unmarked and plural-marked forms (to be extended)
Unmarked nP PL-marked nP
SNG PLR SNG PLR
English ✓ * ✓ ✓
Buriat (animate) ✓ * ✓ ✓
Western Armenian ✓ ✓ * ✓
Buriat (inanimate) ✓ ✓ ✓ ✓
In this paper, I focus on the nominal number system in Alasha Mongolian (Mongolic). I provide novel
data from my own fieldwork, a sample of which is illustrated in Table 5.2.
2
Table 5.2: Unmarked and PL-marked bare nouns in Alasha Mongolian
inanimate a. SG PL b. SG PL
nom nom-o:d almort almort-o:d
book book-PL apple apple-PL
‘book(s)’ ‘books’ ‘apple(s)’ ‘apples’
animate c. SG PL d. SG PL
mör mör-ö:d xü xüch-üd
horse horse-PL boy boy-PL
‘horse’ ‘horses’ ‘boy’ ‘boys’
As shown in the idiomatic translation, there is a difference between unmarked inanimate nouns like
nom ‘book’ and almort ‘apple’ and animate ones like xü ‘boy’ and mör ‘horse’: the former are number
2Throughout the paper I will ignore IPA and phonetic transcription. I use the following orthographic conventions that map onto
the corresponding IPA symbols. The conventions for vowels are the following: 𝑎 = [A]; ö = [ø]; ü = [Y]; u = [o/u]; o = [o]; V = [@] or
highly reduced unstressed vowels; small caps V is a placeholder for any vowel. Long vowels are represented with [∶] after the vowel.
The conventions for consonants are as follows: ch = [tS]; j = [dZ]; gh = [G]; sh = [S]; v = [V]; x = [x/X/h]; ng = [N]; w = [w].
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neutral, whereas the latter denote a singularity. The animacy split is neutralized in the plural-marked form:
both animates and inanimates may denote inclusive or exclusive pluralities depending on the polarity of the
context (like English). In addition to the basic paradigm in Table 5.2, adjectives like expensive, heavy, large
force the unmarked inanimate noun to denote a singularity. See (9).
(9) { tam/
big
xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
nom
book
SG: ‘{big/ heavy/ expensive} book’
#PL: ‘{big/ heavy/ expensive} books’
The empirical generalizations presented so far are as follows: (i) unmarked inanimate nPs are number
neutral, unless modified by a subclass of adjectives, in which case they denote a singleton. (ii) Unmarked
animate nPs are always strictly singular. (iii) Plural-marked nPs are ambiguous between denoting an exclusive
plurality (only sums) or an inclusive one (atoms and sums), depending on whether they are embedded in an
upward or downward entailing context. These facts raise the following questions:
Q1. Is there a syntactic difference between unmarked nouns that are number neutral and those that are
strictly singular?
Q2. Where is Number encoded?
Q3. How does the inclusive/exclusive ambiguity in the PL-marked forms emerge?
Q4. What is the relation between the class of adjectives in (9) and Number?
Q5. What is the relation between the morpho-syntax and semantics of number?
I will argue that that the generalizations about the morpho-syntactic expression of number and its semantic interpretation follow directly from the syntactic structure of DPs in the language. In particular, I will
answer the questions as follows:
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A1. I propose that, by adopting the theory of number and individuation developed throughout the dissertation, all (count) nouns are [IND]-marked which makes them underdetermined for number until
Number, which hosts [SG/PL], is merged (Borer 2005a; Harbour 2007, 2011, 2014; Cowper and Hall
2009, 2012; Kramer 2017). Thus, the difference between unmarked nouns that are strictly singular
and those that are number neutral boils down to the presence or absence of Number (see also Kramer
2017; Martí 2020a): animate nouns always project Number, but inanimates need not always do so. I
show that unmarked inanimates may project Number if there is morpho-syntactic evidence to do so:
overt plural-marking, modification by a subclass of adjectives and numerals.
A2. Based on word order facts of DP-internal modifiers, I argue that NumP hosting [SG/PL] features is
located between n and D, and below numerals (Ritter 1991).
A3. The inclusive/exclusive ambiguity is the result of syntactically conditioned allosemy at LF (Arad 2003;
Marantz 2001, 2013; Harley 2014; Wood 2016, 2023). In particular, I argue that an indefinite determiner which is either an NPI or inherently negative triggers an interpretation of [PL] which results in
an inclusive plurality. Elsewhere, [PL] gives rise to exclusive plurals.
A4. The presence of NumP enables modification by the subclass of adjectives in (9). In other words, this
subclass of APs is unacceptable with number neutral nouns, including mass ones.
A5. The results of the analysis paired with cross-linguistic observations about number give rise to a novel
generalization that correlates morphological markedness and semantic interpretation: unmarked forms
must at least contain individual non-overlapping atoms; and plural-marked ones must contain sums of
atoms.
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5.2 Alasha Mongolian: Some background
Mongolian languages are spoken in various regions of Central and Northeast Asia. There is a fair amount
of comprehensive descriptive studies (Poppe 1955, 1970; Binnick 1979, 2011; Janhunen 2012) and also a
growing body of formal morpho-syntactic and semantic literature (Guntsetseg 2016; Fong 2019; Bylinina
and Podobryaev 2020; Gong 2021, 2022; Toquero-Pérez 2023a). None of these works reports data from
the Alashan variety, however. Alasha Mongolian is a variety of Mongolian spoken in the Alxa League
region located in west inner Mongolia.3 The variety is in close proximity to Oirat, also spoken in west inner
Mongolia (Janhunen 2012). The total number of speakers is unknown, and only Wkipedia reports that the
number of Alasha Mongolian speakers is roughly 40,000.4
Like other languges in the Altaic family (Turkish, Sakha, Buriat a.o.), Alasha Mongolian is head final: the
canonical order is SOV (10a), it has postpositions (10b) and adjectives precede the noun they modify (10c).
Moreover, it has a rich case system whose exponents are spelled out in the head noun. Among the relevant
cases, Alasha Mongolian distinguishes ACC(usative), DAT(itve), GEN(itve), INSTR(umental), ABL(ative) and
COMIT(ative). Nominative is typically covert, execept for certain pronouns, nominalized elements or the
subject of relative clauses, (see also Janhunen 2012; Gong 2022, for the same observation in other Mongolian
varieties).5
(10) a. bi
I
BatVr
Batar
xar-sVn
see-PST.PERF
‘I saw Batar’
b. xol-ni
food-GEN
tuxai
about
‘about food’
c. tam
big
nom
book
(
∗
tam)
big
‘big book’
3The data collection took place during the spring of 2022 as part of a field methods class in Los Angeles, California. In addition
to the general class (20 1.5h sessions), there were a total of 8 1h individual sessions. The data were elicited from a single speaker.
4https://en.wikipedia.org/wiki/Alasha_dialect.
5The aspect and tense system of Mongolian is complex and in some cases subject to massive syncretism (Binnick 2011; Janhunen
2012; Gong 2022). The suffix -sVn, in particular, can be used as a perfective aspectual marker, but also as a finite past tense ending.
In non-finite contexts, it is acts as a perfect participle marker. From now on, I will be indicating in the glosses the relevant meaning:
PST.PERF for finite contexts and PERF.PART for the non-finite ones.
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5.3 Core data: unmarked NPs and PL-marked NPs
Nouns in Alasha Mongolian make a morpho-syntactic distinction between a ‘singular’ form and a ‘plural’
one. The ‘singular’ form is morphologically unmarked, i.e. there is no overt singular exponent, whereas
the plural form is spelled-out as /-V:d/. The vowel in the plural morpheme is subject to vowel harmony
conditioned by the noun root.6 A sample of the data was given in Table 5.2, repeated below for convenience.
Table 5.2: Unmarked and PL-marked bare nouns in Alasha Mongolian
inanimate a. SG PL b. SG PL
nom nom-o:d almort almort-o:d
book book-PL apple apple-PL
‘book(s)’ ‘books’ ‘apple(s)’ ‘apples’
animate c. SG PL d. SG PL
mör mör-ö:d xü xüch-üd
horse horse-PL boy boy-PL
‘horse’ ‘horses’ ‘boy’ ‘boys’
As mentioned in the introduction to the chapter, the first empirical observation is that there is an animacy
split in the case of unmarked nouns: inanimates are number neutral whereas animates are strictly singular.
In what follows, I first motivate this distinction for unmarked nouns, and then probe the properties of their
plural-marked forms. After that, I show how each of these forms (unmarked and plural-marked) interact with
DP-internal modifiers such as adjectives and numerals.
Unmarked inanimate nouns. The number neutral interpretation of unmarked inanimate nouns is found in
a wide variety of syntactic contexts. For example in (11a), nom is the complement of the transitive verb onsix
‘to read’ and the sentence is ambiguous between the speaker having read one or several books. The same is
observed when the NP is the complement of a preposition in (11b) or the subject of a copular construction
in (11c):
6The surface forms of Alasha Mongolian inflectional and derivational suffixes are subject to vowel harmony. Given that the
conditions of vowel harmony are not the goal of this paper and the selection of the particular vowel has no semantic effect, I treat
all plural allomorphs as variants of the same underlying form /-V:d/.
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(11) a. bi
I
nom
book
onsh-Vn
read-PST.PERF
SG: ‘I read a book’
PL: ‘I read books’
b. nom-in
book-GEN
tuxai
about
SG: ‘about a book’
PL: ‘about books’
c. nom
book
bol
COP
unte
expensive
SG: ‘A book is expensive’
PL: ‘Books are expensive’
Case marking on the relevant noun does not eliminate number-neutrality. This is observed in (11b)
where nom is overtly marked genitive. (12a) and (12b) show further support for this observation: almort
bears instrumental case, and nom accusative case.
(12) a. bi
I
xan-ig
goat-ACC
almort-or
apple-INSTR
tijil-sVn
feed-PST.PERF
SG: ‘I fed the goat with an apple’
PL: ‘I fed the goat with apples’
b. bi
I
nom-ig
nom-ACC
xotaltin
bought
ap-pa
get-PST
SG: ‘I bought a book’
PL: ‘I bought books’
In addition to these contexts, number neutrality is maintained with overt possessive determiners and is not
sensitive to person restrictions, as illustrated in (13), (in this respect Alasha Mongolian differs from Buriat,
Bylinina and Podobryaev 2020).7
(13) tir
that
xü
boy
{ mi-ni/
1SG-GEN/
chi-ni/
2SG-GEN/
tu-ni}
3SG-GEN
tstsig(-ig)
flower(-ACC)
BatVr-t
Batar-DAT
og-sVn
give-PST.PERF
SG: ‘That/the boy gave Batar {my/your/his/her} flower’
PL: ‘That/the boy gave Batar {my/your/his/her} flowers’
Unmarked inanimate nouns show the typical hallmarks of number neutral nouns cross-linguistically
(Farkas and de Swart 2003, 2010; Bale et al. 2011; Dayal 2011; Bylinina and Podobryaev 2020). For example,
they serve as the antecedent of either a plural or a singular anaphoric pronoun, as shown in (14).
(14) bi
I
nom𝑖
book
xotaltin
bought
ap-pa
get-PST
‘I bought {a book/ books}.
a. in𝑖
3SG
bol
COP
unte
expensive
‘It was expensive’
b. tidgir𝑖
3PL
bol
COP
unte
expensive
‘They were expensive’
7Alasha Mongolian lacks overt articles, but it has a demonstrative system: tir ‘that’ marks definitiness and can be used with the
meaning of ‘the’. Thus, the translation.
186

In addition, the same NP nom is compatible with distributive adjuncts such as nig nigir ‘one by one’ in
(15a). This is not a particular property of nig nigir as the same pattern is observed with other distributive
markers such as tsilgir dülün ‘each other’ in (15b), and adelbas nomin-sangas ‘from different libraries’ in
(15c).
(15) a. BatVr
Batar
nom(-ig)
book-ACC
nig-nig-ir
one-one-INSTR
onsh-wa
read-PST
‘Batar read {*a book/ books} one by one’
b. BatVr
Batar
nom(-ig)
book
teldur-t
shelf-DAT
tsilgir-dülün
each other
tav-o:
place-PST
‘Batar put {*a book/ books} next to each other on the shelf’
c. [Batar is writing his dissertation and needs many books to consult. He requested all the books
he needed via interlibrary loan.]
nom
book
adelbas
different
nom-in-sang-as
book-GEN-warehouse-ABL
ir-be
came-PST
‘{?? a book/ books} arrived from different libraries.’
Int.: Book-1 arrived from library-𝑥, book-2 from library-𝑦 etc.
Apart from showing that unmarked inanimate nouns are number neutral, the data in this section have
important consequences for analytic choices to be made. In particular, the data serve as convincing evidence
against an analysis based on (pseudo-)incorporation (Massam 2001; Dayal 2004). In those languages where
number neutrality is argued to be the result of pseudo-incorporation of the NP (Hungarian, Farkas and de
Swart 2003; Hindi, Dayal 2004; 2011; Turkish, Sağ 2022), only non-case marked nouns remain number
neutral and the number neutral NP must be (lineraly) adjacent to the verb or selecting predicate. None of these
diagnostics hold in Alasha Mongolian. We have seen that case-marked nouns can still be number neutral (e.g.
(11b), (12)) and the NP can be separated from the verb (e.g. (13) in which the possessive direct object tsitsig(-
ig) ‘flower(-ACC)’ is separated from the verb by the indirect object BatVrt ‘Batar-DAT’). Last but not least, as
reported by Dayal (2011), pseudo-incorporated NPs are incompatible with telic predicates under a number
187

neutral interpretation. Again, this does not hold for Alasha Mongolian either (and potentially Mongolic
languages more generally, see Bylinina and Podobryaev 2020): inanimate NPs unmarked for number are
compatible with a number neutral interpretation when the verbal predicate is telic. For example, in (16) the
telicity is marked by the temporal adjunct taun tsakt ‘five hour’ and the restructuring verb dosxix ‘to finish’
(Dowty 1979).
(16) [Batar is an avid reader and has to read LGB, SPE and Barriers for an assignment.]
BatVr
Batar
tau-n
five-ATTR
tsak-t
hour-DAT
nom-ig
book-ACC
ons-ich
read-CONV
dosx-wa
finish-PST
‘Batar finished reading the books in 5h’
Unmarked animate nouns. Unmarked animate NPs such as xü ‘boy’ or mör ‘horse’ receive a strict singular
interpretation. This is shown in (17).
(17) a. bi
I
xü(d-ig)
boy-ACC
dilgur-t
store-DAT
xar-sVn
see-PST.PERF
SG: ‘I saw a boy in the store’
#PL: ‘I saw boys in the store’
b. tir
that
xü
boy
mi-ni
1SG-GEN
tstsig(-ig)
flower(-ACC)
mör-t
horse-DAT
og-sVn
give-PST.PERF
SG: ‘That/the boy gave a horse my flower(s)’
#PL: ‘These/the boys gave horses my flower(s)’
The univocal singular interpretation is maintained regardless of case-marking on the noun or syntactic
position: in (17a) xü is the direct object and may be marked accusative, and in (17b) mör bearing dative case
is the recipient argument.
Besides, the unmarked animate NP in (17a) cannot serve as the antecedent for a plural anaphoric pronoun
as in (18). Likewise, the unmarked animate NP is incompatible with distributive adjuncts like nig nigir or
adelbas nomin-sangas, as illustrated in (19).
188

(18) { tir/*
3SG/
tirgir}xü
3PL
bol
COP
tam.
big
‘(I saw a boy at the store.) {He was/ *They were} big’
(19) a. * bi
I
xü(d-ig)
boy-ACC
nig-nig-ir
one-one-INSTR
xar-sVn
see-PST.PERF
Lit.: ‘I saw a boy one by one’
Int.:‘I saw boys one by one’
b. * xü
boy
adelbas
different
nom-in-sang-as
book-GEN-warehouse-ABL
ir-be
came-PST
Lit.: ‘A boy arrived from different libraries.’
Int.: Batar arrived from library-𝑥, Brian from library-𝑦 etc.
Plural-marked nouns. As shown in Table 5.2, in addition to the unmarked form, all count nouns in Alasha
Mongolian can be inflected for plural number by adding the morpheme -V:d. In an UEC, a sentence like (20)
can only signify that there are two or more apples that the speaker bought. That is, the presence of the -V:d
morpheme on almort induces an exclusive plural interpretation. The same is found with overt plural-marked
animate nouns in (21).
(20) Plural-marked inanimate noun (exclusive plural in UEC)
bi
I
almort-o:d(-ig)
apple-PL-ACC
xotaltin
bought
ab-sVn
get-PST.PERF
‘I bought (2 or more) apples’
(21) Plural-marked animate noun (exclusive plural in UEC)
a. bi
I
xüch-ü:d(-ig)
boy-PL-ACC
dilgur-t
store-DAT
xar-sVn
see-PST.PERF
‘I saw (2 or more) boys in the store’
b. tir
that
xü
boy
mi-ni
1SG-GEN
tstsig(-ig)
flower(-ACC)
mör-ö:d-Vt
horse-PL-DAT
og-sVn
give-PST.PERF
‘That/the boy gave (2 or more) horses my flower(s)’
189

However, in DEC and questions, plural nouns are interpreted inclusively, i.e. atoms and sums. An
example is shown in (22) for inanimates and in (23) for animates.
(22) Plural-marked inanimate noun (inclusive plural in DEC)
bi
I
almort-o:d(-ig)
apple-PL-ACC
xotaltin
bought
ab-sVn-ghue
get-PST.PERF-NEG
‘I didn’t buy (any) apples’
(23) Plural-marked animate noun (inclusive plural in DEC)
bi
I
xüch-ü:d(-ig)
boy-PL-ACC
dilgur-t
store-DAT
xar-sVn-ghue
see-PST.PERF-NEG
‘I didn’t see (any) boys in the store’
In (22) and (23), the negative marker ghue ‘not’ surfaces as a verbal suffix, linearly following tense/aspect
morphemes. (22) is judged false if the speaker bought one apple; (23) is judged false if the speaker saw one
boy at the store. The same pattern observed with negation is also replicated in polar questions. This is shown
in (24) for inanimates and (25) for animates.
(24) A: chi
you
almort-o:d
apple-PL
idi-tVg-o?
eat-HAB-Q.POL
‘Do you typically eat (any) apples?’
B: time:,
yes
nig
one
‘Yes, I (typically) eat one’
# ughue,
NEG
nig
one
‘No, I (typically) eat one.’
(25) A: chi
you
xüch-üd
boy-PL
dilgur-t
store-DAT
xar-tVg-o?
see-HAB-Q.POL
‘Do you typically see (any) boys at the store?’
B: time:,
yes
nig
one
‘Yes, I (typically) see one’
# ughue,
NEG
nig
one
‘No, I (typically) see one.’
190

In both (24) and (25), speaker A uses the plural-marked form of the noun in the question, and speaker B
can answer felicitously by saying “yes, one”. It is infelicitous for B to provide a negative answer.
The effect of (non-)classificatory adjectives. Despite the fact that the number neutral interpretation of
unmarked inanimate NPs seems to have no restrictions based on the syntactic position of the NP, it is however unavailable in one very particular syntactic context: when the unmarked noun is modified by nonclassificatory adjectives occurring in attributive (i.e. prenominal) position. These non-classificatory adjectives are also gradable and include old, big, expensive, heavy etc. Modification by this class of attributive
adjectives forces the unmarked inanimate noun to denote a singleton.
This class, when used attributively, contrasts with what Alexiadou et al. (2007) call “classificatory” adjectives, such as Mongolian, European, scientific or religious. These classificatory adjectives are in turn
non-gradable, and do not block number neutrality.8
(26) and (27) illustrate the contrast between the two
classes of adjectives.9
(26) a. bi
I
{ tam/
big
xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
nom
book
onsh-Vn
read-PST.PERF
SG: ‘I read a {big/ heavy/ expensive} book’
#PL: ‘I read {big/ heavy/ expensive} books’
b. bi
I
{ monghol/
mongolian
shashin-tei/
religion-ADJ
iuvrop}
european
nom
book
onsh-Vn
read-PST.PERF
SG: ‘I read a {Mongolian/ religious/ European} book’
PL: ‘I read {Mongolian/ religious/ European} books’
8While the adjectives in (26a) and (27a) are compatible with degree modifier mash ‘very’, the adjectives in (26b) and (27b) are
marked at best. See (xx). This is as might be expected if the latter can be coerced into a gradable property but such coercion is
marked.
(xx) a. mash
very
{ tam/
big
xunde/
heavy
unte}
expensive
‘very {big/ heavy/ expensive}
b. ?? mash
very
{ monghol/
Mongolian
shashin-tei/
religion-ADJ
iuvrop}
European
‘very {Mongolian/ religious/ European}
9Similar observations between the two classes of AP have been reported for Turkish (Sağ 2022) and Western Armenian (Kalomoiros 2021).
191

(27) a. bi
I
xan-ig
goat-ACC
{ xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
almort-or
apple-INSTR
tijil-sVn
feed-PST.PERF
SG: ‘I fed the goat with a {heavy/ expensive} apple’
#PL: ‘I fed the goat with {heavy/ expensive} apples’
b. bi
I
xan-ig
goat-ACC
{ monghol/
Mongolian
iuvrop}
European
almort-or
apple-INSTR
tijil-sVn
feed-PST.PERF
SG: ‘I fed the goat with a {Mongolian/ European} apple’
PL: ‘I fed the goat with {Mongolian/ European} apples’
Attributive non-classificatory APs have a trivial impact on unmarked animate NPs: they are still strictly
singular as (28) shows.
(28) bi
I
{ tam/
big
xunde-n}
heavy
xü(d-ig)
boy-ACC
dilgur-t
store-DAT
xar-sVn
see-PST
SG: ‘I saw a {big/ heavy} boy in the store’
#PL: ‘I saw {big/ heavy} boys in the store’
Importantly, overt plural marking on the noun can co-occur with non-classificatory AP modifiers. In that
case, the plural morpheme has the expected effect in both upward and downward entailing contexts: in the
former it is interpreted exclusively, while in the latter it is interpreted inclusively. This is shown in (29) for
inanimates and (30) for animates.
(29) a. bi
I
{ tam/
big
xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
nom-o:d
book-PL
onsh-Vn
read-PST.PERF
‘I read (2 or more) {big/ heavy/ expensive} books’ (exclusive plural)
b. bi
I
{ tam/
big
xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
nom-o:d
book-PL
onsh-Vn-ghue
read-PST.PERF-NEG
‘I didn’t read (any) {big/ heavy/ expensive} books’ (inclusive plural)
(30) a. bi
I
{ tam/
big
xunde-n}
heavy-ATTR
xüch-üd(-ig)
boy-PL-ACC
dilgur-t
store-DAT
xar-sVn
see-PST.PERF
‘I saw (2 or more) {big/ heavy} boys in the store’ (exclusive plural)
192

b. bi
I
{ tam/
big
xunde-n}
heavy-ATTR
xüch-üd(-ig)
boy-PL-ACC
dilgur-t
store-DAT
xar-sVn-ghue
see-PST.PERF-NEG
‘I didn’t see (any) {big/ heavy} boys in the store’ (inclusive plural)
Classificatory APs are also compatible with overt plural marking on the noun they modify. An example is
in (31). Once again, the plural is exclusive or inclusive depending on the upward or downward entailingness
of the sentence.
(31) a. shashin-tei
religion-ADJ
nom-o:d
book-PL
‘Religious books’
b. shashin-tei
religion-ADJ
xüch-üd
boy-PL
‘Religious boys’
In addition to gradability and their interaction with number, the two classes of adjectives differ in three respects: (i) the presence of the attributive morpheme /-n/; (ii) NP-internal word order; and (iii) (in)compatibility
with mass nouns. I discuss each of these in turn.
Prenominal non-classificatory adjectives bear a morpheme /-n/, which is labelled in the descriptive grammars as attributive (ATTR) marking, (Janhunen 2012, ch.6). This attributive marker does not surface on
prenominal classificatory APs. Furthermore, it is ungrammatical when it surfaces on both classes of APs
when used predicatively. The difference in attributive marking between the two classes of AP is is illustrated
in (32) and (33).
(32) Attributive marking with non-classificatory APs
a. bi
I
unte*(-n)
expensive-ATTR
nom
book
onsh-Vn
read-PST
SG: ‘I read a expensive book’
#PL: ‘I read expensive books’
b. nom
book
bol
COP
unte(∗
-n)
expensive-ATTR
SG: ‘A book is expensive’
PL: ‘Books are expensive’
(33) Attributive marking with classificatory APs
193

a. bi
I
shashin-tei(∗
-n)
religion-ADJ-ATTR
nom
book
onsh-Vn
read-PST
SG: ‘I read a religious book’
PL: ‘I read religious books’
b. nom
book
bol
COP
shashin-tei(∗
-n)
religion-ADJ-ATTR
SG: ‘A book is religious’
PL: ‘Books are religious’
If the modifier does not end in a vowel, the attributive morpheme is covert. For example, this is shown
in (10c) and (26a) for the adjective tam: ‘big’. In addition, the lack of ATTR-marking on adjectives like
shashintei ‘religious’ in (33) is not conditioned by the morpheme -tei which seems to be an adjectivizing
head. Complex gradable adjectives like fast are built from the root xortots ‘speed’ + -tei and yet they require
ATTR-marking: (34).
(34) xortots-tei-n
speed-ADJ-ATTR
mashin
car
‘fast car’
With respect to NP-internal word order, the two classes of adjectives can co-occur in the same NP. When
that happens, non-classificatory APs must surface to the left of classificatory APs. This is a common pattern across languages (Cinque 2005, 2010; Alexiadou et al. 2007; Svenonius 2008). The opposite order is
ungrammatical, as seen in (35).
(35) ‘expensive religious book’ APnon-Class > APClass > N
a. unte-n
expensive-ATTR
shashin-tei
religion-ADJ
nom
book
b. * shashin-tei
religion-ADJ
unte-n
expensive-ATTR
nom
book
Last but not least, non-classificatory APs are only compatible with count nouns, and are unacceptable
with mass nouns. This is shown in (36). Classificatory APs can modify mass nouns, in contrast, as shown
in (37).
(36) * { tam/
big
xunde-n/
heavy-ATTR
unte-n}
expensive-ATTR
{ tsos/
blood
os}
water
Int.: ‘{Large/ heavy/ expensive} {blood/ water}’
194

(37) { monghol/
Mongolian
iuvrop}
European
{ tsos/
blood
os}
water
This distribution of non-classificatory APs is reminiscent of Schwarzschild’s (2011) observation for
Stubbornly Distributive adjectives (e.g. *large/heavy water).10,11 Thus, we can conclude that while nonclassificatory APs (or at least the ones elicited so far) require the noun to be count and singular/plural, classificatory ones do not.
Numerals. Alasha Mongolian has precise numerals. When used enumeratively, i.e. in a list, they are
uninflected as in (38).
(38) nigV(*-n),
one-ATTR
xoirV(*-n),
two-ATTR
ghorovV(*-n),
three-ATTR
duruvV(*-n),
four-ATTR
tau(*-n)...
five-ATTR
‘one, two, three, four, five... (List)
When they modify a noun, they are prenominal and must be inflected for attributive morphology, i.e. /-n/.
If used predicatively, no attributive marker is spelled-out on the numeral. The difference between attributive
and predicative uses of numerals is illustrated in (39a) and (39b).
(39) a. { nigV-n/
one-ATTR
ghorovV-n/
three-ATTR
dulu-n}
seven-ATTR
almort
apple
‘{one/ three/ seven} apples’ (Attributive)
b. almort
apple
bol
COP
{ ghorovV(*-n)/
three-ATTR
dulu(*-n)
seven-ATTR
}
‘The apples are {three/ seven} (Predicative)
10Schwarzschild (2011) builds on the observations from Quine (1960); McCawley (1979); Chierchia (1998b); Gillon (1999) and
others to establish his generalization.
11In English at least, it is possible to modify mass nouns like water, tea as in (xxi). It is unclear whether water/tea in such examples
have a ‘canonical mass’ interpretation or count one (e.g. expensive containers/types of water). It is also possible to say things like
(xxii) where heavy is modifying a mass noun. However, heavy does not seem to introduce a dimension of weight/volume but rather
‘strength/abundance’.
(xxi) They drink expensive {water/ tea} at home.
(xxii) Heavy perfume
195

When numerals and non-classificatory APs co-occur, numerals must precede the AP. In other words, the
order is always as in (40a), and never as in (40b). In addition, the ATTR morpheme must surface on both the
numeral and the non-classificatory AP. If the ATTR morpheme is absent, the sentence is unacceptable as in
(41).
(40) Numeral > APnon-class > N
a. duruvV-n
four-ATTR
xunde-n
heavy-ATTR
nom
book
b. * xunde-n
heavy-ATTR
duruvV-n
four-ATTR
nom
book
‘Four heavy books’
(41) * duruvV
four
xunde-n
heavy-ATTR
nom
book
‘Four heavy books’
In addition to the attributive marker, numerals and non-classificatory adjectives have in common the
fact that they cannot directly modify mass nouns. The examples in (42) are ungrammatical even in packaging/container or sorting/kind contexts (Bunt 1985; Bach 1986b).12
(42) a. * bi
I
duruvV-n
4-ATTR
os
water
ob-sVn
drink-PST.PERF
‘I drank 4 waters’ (#container, #kind)
b. * bi
I
duruvV-n
4-ATTR
adelbas
different
os
water
abchir-gwa
bring-PST
‘I brought 4 different waters’ (#container, #kind)
With respect to the interaction of numerals and number marking on the noun, we observe that the numerically modified noun must be unmarked, and cannot be inflected for plural. This is shown in (43) for
inanimates and in (44) for animates.
(43) a. { nigV-n/
one-ATTR
ghorovV-n/}
three-ATTR
almort
apple
b. * { nigV-n/
one-ATTR
ghorovV-n/}
three-ATTR
almort-o:d
apple-PL
‘{one/ three} apples’
(44) a. { nigV-n/
one-ATTR
ghorovV-n/}
three-ATTR
xü:
boy
b. * { nigV-n/
one-ATTR
ghorovV-n/}
three-ATTR
xü:ch-ü:d
boy-PL
‘{one/ three} boys’
12The container interpretation can only be obtained with a pseudo-partitive structure. See Toquero-Pérez (2023a).
196

The compatibility of numerals with unmarked animate nouns, which always refer to a singleton (i.e. they
are strictly singular semantically), and their incompatibility with the overt plural morpheme, which makes
reference to pluralities, suggests that the noun in combination with numerals must be semantically singular
rather than number neutral (Krifka 1989, 1995; Ionin and Matushansky 2006, 2018; Pancheva 2021, 2022;
Sağ 2022).
5.4 A novel diagnostic for number neutrality: much/many and unmarked
NPs
5.4.1 Some background
In addition to precise cardinal numerals, many languages also have QAs (e.g. much/many/little/few etc.).
These QAs are restricted in their distribution. For example, some only surface with mass NPs while others
only surface with plural count NPs. English is an example of such a language, as discussed in the previous
chapters (Bresnan 1973; Hackl 2000; Schwarzschild 2006; Bale and Barner 2009; Wellwood et al. 2012).
However, singular count NPs are unacceptable with QAs.
The formal explanation for this restriction, i.e. the fact that singular count NPs are unacceptable with either many or much, is found in the structure of the extension of the relevant NP. Mass and plural count nouns
have cumulative extensions that have a part-whole structure; singular count nouns, on the contrary, lack extensions with such part-whole relations among their elements (Cartwright 1975; Link 1983; Krifka 1989,
1997; Chierchia 1998b, 2010, a.o.). Under the assumption that QAs introduce measure functions whose dimension for measurement must preserve the part-whole structure of the domain (Krifka 1989; Schwarzschild
2006; Bale and Barner 2009; Wellwood et al. 2012), QAs can combine with plural count nouns because they
197

are closed under sum (or some other operation that ensures the existence of plural individuals in the extension). Singular NPs denote singletons and do not have sums of atoms in their extension. Thus, they do not
satisfy the cumulativity requirement.
Alasha Mongolian has QAs which are also sensitive to the mass-count distinction. Similar to English,
ix ‘much’ is only compatible with (unmarked) mass nouns and olin ‘many’ is acceptable with plural count
nouns. This is shown in (45) and (46).13
(45) a. ix
much
{ os/
water
tsos}
blood
‘much {water/ blood}’ VOLUME/WEIGHT, #CARDINALITY
b. * ix
much
xü(ch-ü:d)
boy-PL
‘much {boy/ boy}
(46) a. * olin
many
{ os/
water
tsos}
blood
‘many {water/ blood}’
b. olin
many
xüch-ü:d
boy-PL
‘many boys’ #VOLUME/WEIGHT, CARDINALITY
Like in English, when a canonical mass nouns like water/blood is modified by a QA, the interpretation
is in terms of volume or weight, but not cardinality, as in (45). On the contrary, plural count nouns modified
by QAs are interpreted in terms of cardinality only, e.g. (46).
Focusing only on count nouns, we can use the distribution and interpretation of ix/olin to determine
whether a noun in Alasha Mongolian denotes a plurality or a singleton. In particular, we predict that if
13I will not be discussing the count-mass distinction in Alasha Mongolian. For the purposes of this chapter, we can simply establish
that the language makes the distinction overtly. For example, we have seen that mass nouns cannot be modified by stubbornly
distributive adjectives (36), and be directly modified by numerals as in (42). In addition, they cannot be pluralized either, e.g.
(xxiii).
(xxiii) os
water
– * os-o:d
water-PL
|| tsos
|| blood
– * tsos-o:d
blood-PL
198

nPs unmarked for number are really number neutral and their denotation is as in (6), repeated in (47) for
conveninence, such an nP must be compatible with QAs; however, if the nP is not number neutral, but
strictly singular, the nP must be incompatible with them. These predictions are schematically represented in
(48):
(47) J𝑛PK = {𝑎, 𝑏, 𝑐, 𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐} Number neutral nP
(48) Predictions of the much/many-test for number neutrality
a. If an unmarked count nP is number neutral, e.g. (47), it must be acceptable with QAs.
b. If an unmarked count nP is NOT number neutral, but strictly singular, it cannot be acceptable with
QAs.
c. If an unmarked count nP can be modified by QAs, its interpretation will be along a cardinality
scale.
I now show that the predictions in (48) are borne out in Alasha Mongolian.
5.4.2 Applying the much/many-test to Alasha Mongolian
As shown in (49a), inanimate count nPs like almort, jürj ‘orange’ or nom can be modified by olin when they
are unmarked for number . The interpretation of said nP must be in terms of cardinality: (49a) means “the
cardinality of apples/oranges/books exceeds a contextually determined standard”. Modification by ix is not
acceptable, as shown in (49b).
(49) QA + unmarked inanimate nP
a. olin
many
{ almort/
apple
jürj/
orange
nom}
book
‘many {apples/ oranges/ books}’ #VOLUME/WEIGHT, CARDINALITY
b. * ix
much
nom
book
‘much book’
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In addition, olin is acceptable with (inanimate) nPs that are overtly marked for plural: (50). While
plural-marking is optional for inanimate nPs when modified by olin, that is not the case for animate ones as
illustrated in (51): in fact, if the nP is animate, plural-marking on the noun is required. Crucially, unmarked
animate nPs are unacceptable with olin.
(50) olin + plural-marked inanimate nP
a. olin
many
nom-o:d
book-PL
‘many books’ #VOLUME/WEIGHT, CARDINALITY
b. olin
many
almort-o:d
apple-PL
‘many apples’ #VOLUME/WEIGHT, CARDINALITY
(51) olin + animate nP
a. olin
many
xüch-ü:d
child-PL
‘many children’ #VOLUME/WEIGHT, CARDINALITY
b. * olin
many
xü
child
‘many child’
The data confirm the predictions outlined in (48): unmarked inanimates are grammatical with QA olin
and must be number neutral; unmarked animates are ungrammatical with olin and must therefore be strictly
singular.
5.5 Taking stock and generalizations
Up until this point, I have described the distribution of animate and inanimate nPs that are both unmarked
for number and that are plural-marked in a variety of contexts. The data are summarized in Table 5.3 for
unmarked nPs and in Table 5.4 for plural-marked ones. As before, the labels SNG/PLR refer to the semantic
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interpretation and not the phonological form of the noun: SNG = ‘singularity’ or singleton (e.g. 1); and PLR
= ‘plurality’ (e.g. 2 or more). If a noun can refer to both, then we will say the noun is number neutral
if unmarked or inclusively plural if plural-marked. The labels ‘UEC’ and ‘DEC’ in Table 5.4 stand for
‘Upward Entailing Context’ and ‘Downward Entailing Context’ (including questions), respectively. The
generalizations that emerge from looking at Table 5.3 and Table 5.4 are summarized in (52).
Table 5.3: Number interpretation of unmarked nPs in Alasha Mongolian
nP-case Poss. nP Anaphoric Ref. Non-Class. AP Class AP
SNG PLR SNG PLR SNG PLR SNG PLR SNG PLR
[-animate] ✓ ✓ ✓ ✓ ✓ ✓ ✓ * ✓ ✓
[+animate] ✓ * ✓ * ✓ * ✓ * ✓ *
Table 5.4: Number interpretation of plural-marked nPs in Alasha Mongolian
nP-case Non-Class. AP Class AP
SNG PLR SNG PLR SNG PLR
UEC [-animate] * ✓ * ✓ * ✓
[+animate] * ✓ * ✓ * ✓
DEC [-animte] ✓ ✓ ✓ ✓ ✓ ✓
[+animate] ✓ ✓ ✓ ✓ ✓ ✓
(52) Generalizations about the interpretation of number in Alasha Mongolian
a. Inanimate unmarked nPs are always number neutral unless they are modified by
non-classificatory adjectives in attributive position, in which case they are strictly singular.
b. Animate unmarked nPs are never number neutral, i.e. they are strictly singular.
c. In UEC, plural-marked nPs are always exclusively plural.
d. In DEC, plural-marked nPs are always inclusively plural.
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The generalizations in (52) are very similar to the ones reported by Bylinina and Podobryaev (2020) for
Buriat in table 5.1, with the exception of some micro-variation which I do not discuss here.14 The generalizations indicate that Alasha Mongolian is also different from Western Armenian, as described by Bale et al.
(2011); Bale and Khanjian (2014), in two important respects: (i) the animacy asymmetry and (ii) the fact that
plural-marked NPs are not always exclusive. In fact, Alasha Mongolian is similar to English in this respect,
given that the exclusive/inclusive distinction with plural-marked nouns is conditioned by the veridicality of
the context (Krifka 1989; Sauerland 2003; Sauerland et al. 2005; Zweig 2009).
In addition to these generalizations, we must address the case of numerals. Precise numerals were ungrammatical with overt plural-marked nouns, regardless of their animacy. What is more, the fact that they
are grammatical with unmarked, strictly singular, animate nouns led to the conclusion that they require the
noun to refer to a singurality. This is summarized in (53).
(53) Numerically modified nPs must be unmarked for number and refer to a singularity.
The generalization in (53) distinguishes Alasha Mongolian from languages like Western Armenian where
numerals are compatible with plural-marked nouns and unmarked nouns that are number neutral (Bale et al.
2011; Bale and Khanjian 2014). But it also makes Alasha Mongolian different from English where nouns
modified by numerals higher than one are plural-marked.15
In addition to precise numerals, I surveyed the distribution of QAs ix and olin with different types of
count nPs. This distribution is summarized in Table 5.5, where it is compared to the distribution of cardinal
numerals.
Given the generalizations in (52) that inanimate unmarked nPs are number neutral, but animate ones are
strictly singular we expected only the former to be acceptable with QAs. This is borne out for olin, and
14In Buriat ACC-marked NPs are strictly singular and so are 1𝑠𝑡 and 2𝑛𝑑 person possessed NPs. Bylinina and Podobryaev (2020)
make no distinction with respect to the type of adjectival modification and there is no discussion of the presence of the attributive
marker. They do not discuss numerically modified NPs either.
15In terms of the semantics, there is a debate as to whether numerals in English require the noun they modify to denote a singleton despite morphological markedness (Krifka 1989, 1995; Ionin and Matushansky 2006, 2018; Alexiadou 2019) or a plurality
(Chierchia 1998b, 2010; Bale et al. 2011; Scontras 2013; Martí 2020b, and others). I come back to this question in §5.7.
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Table 5.5: Syntactic distribution of olin and cardinal numerals with count nouns
[-animate] [+animate]
unmarked
(nom ‘book’)
PL-marked
(nom-o:d ‘books’)
unmarked
(xü ‘boy’)
PL-marked
(xüch-üd ‘boys’)
ix ‘much’ * * * *
olin ‘many’ ✓ ✓ * ✓
numerals ✓ * ✓ *
is consistent with the predictions outlined in (48). It is in stark contrast with unmarked animate nPs, which
cannot combine with olin. This is also expected if unmarked animates are strictly singular. ix is not acceptable
with unmarked animates or inanimates, and neither is it acceptable with their plural-marked counterparts.
The distribution of olin does not conform to the plural-QA-markedness generalization according to which the
surface form of QAs is sensitive to plural-marking on the noun. We observed this was the case for English,
Spanish, Greek and Telugu. This could in principle be taken as evidence for Uniform Dimensionality in the
spirit of Solt (2009), in particular because olin+nP gives rise to a cardinality interpretation. However, despite
the fact that this could be a potential generalization, we would be losing all the mileage that we gained from
separating the forms of QAs from their meaning. Instead, it seems that the distribution of ix and olin can
be predicted on a different basis that is neither meaning nor plural-marking on the noun. I propose that the
actual generalization is in (54).16
(54) olin is found when the noun is individuated, whereas ix is found elsewhere.
The generalization is consistent with the observation that count nouns, including number neutral and
plural-marked ones, must be marked for individuation in the syntax (Chapter 3). This is also consistent with
the observation that the dimension of cardinality is assigned when the measure morpheme has an individuated
plurality in its scope. If number neutral nouns denote an individuated semi-lattice, the semantic facts also
follow.
16Smith (2021) reaches a similar conclusion for Purépecha.
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If we compare numerically modified nouns in (43) and (44) to olin-modified nouns, as described in
section 5.4.2, we observe important differences as summarized in the Table 5.5: nouns that are modified
by numerals must be morpho-syntactically unmarked regardless of their animacy, whereas nouns modified
by olin may not. In fact, animates cannot be morpho-syntactically unmarked, but inanimates can. In other
words, we can conclude that while the animacy split for number neutrality is not maintained in cardinal
numeral-noun constructions, it remains in olin-noun constructions. We can take these facts as evidence
that the syntactic and semantic requirements that need to be met for cardinal numeral modification and QA
modification differ.
5.6 Analysis
I propose that the generalizations in (52)-(54), as well as the distribution and interpretation of number in
Alasha Mongolian, can follow directly from the syntactic representation of the DP, and its mapping to the
morphological and semantic interfaces. In particular, under the proposal that (i) an [IND] feature on n selects
the denotation of the root has atoms and sums of atoms, i.e. the individuated one, and (ii) the features on a
Num(ber) head restrict the denotation of the noun to a singleton or a plurality (Cowper 2005; Harbour 2007,
2011, 2014; Cowper and Hall 2009, 2012), the number neutral interpretation of unmarked inanimate nouns
is the result of Num not being projected: if Num is not projected, number features cannot restrict the noun’s
denotation. NumP is projected only when there is morpho-syntactic evidence to do so: plural marking,
non-classificatory APs, numerals. On the contrary, Num is always present when the noun is [ANIMATE].
I show that this analysis of nominal number has welcome consequences for the analysis of numerals as
well. In addition, I propose that the inclusive/exclusive ambiguity of the plural can be derived via semantic
competition or alloseme selection (Arad 2003; Marantz 2001, 2013; Harley 2014; Wood 2016, 2023).
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5.6.1 Setting up the system
One of the generalizations to be accounted for is the fact that inanimate unmarked NPs are number neutral,
whereas their animate counterparts are strictly singular. Following Ritter (1993); Kramer (2015); Wiltschko
and Ritter (2015) I liken animacy to gender and assume that animacy is encoded by the n head. Following
Cowper and Hall (2009), a feature [ANIMATE] on n sorts roots into the class of animate things; in the absence
of the feature, the noun root will be inanimate.
In addition, I assume the theory of number and individuation spelled-out in the previous chapters: (i)
n is the locus of countability or individuation (Bale and Barner 2009; Smith 2021), via the feature [IND];
(ii) n[IND] triggers an individuated interpretation for the root; (iii) but underspecified n triggers a nonindividuated interpretation of the root. This is schematically summarized as in (55), following the notation
introduced in Chapter 4.
(55) a. √ROOT ↔ ROOT-THING/__n[IND]
JROOT-THINGK = {𝑥: 𝑥 is an atomic thing or sum of atomic things} = {𝑎, 𝑏, 𝑐...𝑎𝑏𝑐}
b. √ROOT ↔ ROOT-STUFF/__n
JROOT-STUFFK = {𝑥: 𝑥 is a portion of stuff or a sum of portions of stuff} = {𝑎𝑠
, 𝑏𝑠
, 𝑐𝑠
...𝑎𝑏𝑐𝑠
}
Assuming a simple model in which there are only three members {a, b, c} which are atoms, the extension
of the individuated nominalized root in (55a) is semi-lattice structure in . The relevant definition of ‘atom’
and ‘minimal part’ are the same as in (46) and (47) repeated in (56) and (57) for convenience.
Figure 5.1: Individuated semi-lattice generated from atoms {a, b, c}: extension of [n[IND] √ROOT]
abc
ab   ac bc
a b c
(56) Definition of atom
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An object 𝑧 is an atom in a set of objects 𝑃 iff 𝑧 is a minimal part for 𝑃 and for all objects 𝑦 ∈ 𝑃,
either (i) 𝑧 ≤ 𝑦 or (ii) there is no 𝑤 ≤ 𝑧, such that 𝑤 ≤ 𝑦.
(57) Definition of minimal part
∀𝑥[𝑃(𝑥) → ¬∃𝑦[𝑃(𝑦) ∧ 𝑦 < 𝑥]]
‘An object 𝑥 is a minimal part for a set of objects 𝑃 iff for all 𝑥 ∈ 𝑃 it is not the case there is an
object 𝑦, such that 𝑦 ∈ 𝑃 and 𝑦 is a proper part of 𝑥.
Depending on the combination of [ANIMATE] and [IND] on the nominalizer, we can find the flavors of n
summarized in Table 5.6. The semantic value of the feature bundles in Table 5.6 is given in (58) and (59).
The n-head marked for individuation selects the root concept that has the property of being individuated (i.e.
the root-concept that is generated from the set of atoms): ROOT-THING. The definitions of IND and Non-IND
are repeated in (60).
Table 5.6: Flavors of n in Alasha Mongolian
[IND] [ANIMATE]
animate count ✓ ✓
inanimate count ✓ –
mass – –
(58) Animate count n
a. n[IND, ANIMATE]
b. Jn[IND, ANIMATE]K = 𝜆𝑥.IND(𝑃)(𝑥) ∧ animate(𝑥)
(59) Inanimate count n
a. n[IND]
b. Jn[IND]K = 𝜆𝑥.IND(𝑃)(𝑥) ∧ ¬animate(𝑥)
(60) Individuating function:
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IND(𝑃) = a predicate 𝑃 is an individuated semi-lattice iff
a. 𝑃 is closed under sum, such that if ‘*’ is the sum closure operation, then 𝑃 = ∗𝑃; and
b. 𝑃 is generated by the set of atoms in 𝑃, such that if atom is the set of atoms in 𝑃, then
𝑃 = ∗atom.
In addition to this, I assume that number features are located on a functional head called Num, above n
and below D (Ritter 1991; Cowper 2005; Borer 2005a; Wiltschko 2008; Harbour 2011). This functional head
encodes singular or plural number features: [SG/PL]. These features operate on the individuated semi-lattice
imposed by [IND] on the nP and restrict the denotation of the noun. The meanings of these features are as in
(52) in the previous chapter, repeated in (61).
(61) a. J[SG]K = 𝜆𝑃.𝜆𝑥.𝑃(𝑥) ∧ minimal(𝑥)
b. J[PL]K = 𝜆𝑃.𝜆𝑋.∀𝑥[𝑋(𝑥) → (𝑃(𝑥) ∧ ¬minimal(𝑥))]
In a nutshell, we can say that [SG] = singletons (i.e. the minimal parts; the bottom row of the semi-lattice
in Figure 5.1), and [PL] = non-singletons or pluralities (i.e. the non-minimal parts; everything but the bottom
row of the semi-lattice in Figure 5.1). This is summarized in (62).
(62) a. JnP[IND]
K = Jn[IND]K(J√ROOTK) = IND(ROOT-THING)(𝑥) ∧ (¬)animate(𝑥) {a, b, c, ab, ac, bc, abc}
b. J[SG] nP[IND]
K = J[SG]K(J(62𝑎)K) = IND(ROOT-THING)(𝑥) ∧ (¬)animate(𝑥) ∧ minimal(𝑥)
{a, b, c}
c. J[PL] nP[IND]
K = J[PL]K(J(62𝑎)K) =
= ∀𝑥[𝑋(𝑥) → (IND(ROOT-THING) ∧ (¬)animate(𝑥) ∧ ¬minimal(𝑥))] {ab, ac, bc, abc}
5.6.2 The basic syntactic structure of (count) nouns
Given the theory adopted, projecting NumP entails that the noun will be strictly singular if unmarked or
(exlcusively) plural if plural-marked. This leaves no room for unmarked nouns which are number neutral.
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However, there is a solution within this system, which I adopt here: unmarked nouns which are number
neutral are syntactically impoverished and do not project NumP. If [SG/PL] is absent from the numeration
and thus not represented in the syntax, NumP will not be projected;17 as a result, no number features will
restrict the interpretation of the nP. The hypothesis that unmarked number neutral nouns do not project NumP
receives cross-linguistic support from Amharic (Kramer 2017), Bayso and Fouta Jalon Fula (Corbett 2000;
Harbour 2014; Martí 2020a), and Haitian Creole (Déprez 2005) to name a few. That said, I propose that
the structure of unmarked number neutral nouns in Alasha Mongolian is as given in (63a).18 This structure
differs from the one that unmarked animate nouns have, given in (63b).
(63) The syntax of (unmodified) unmarked count nouns
a. Inanimates = number neutral
DP
nP
√NOM
‘book’
n
[IND]
D
b. Animates = singular
DP
NumP
nP
√XÜ
‘boy’
n
[IND, ANIMATE]
Num
[SG]
D
The two structures for unmarked nouns share the fact that n is specified for individuation. But they differ
in two main respects: (i) animacy class features on n, and (ii) the absence or presence of Num. Inanimate
nouns are underspecified for animacy and lack Num; animate nouns are [ANIMATE] and project NumP by
virtue of being specified as [SG].
This does not mean, however, that inanimate nouns will never project NumP. In fact, these nouns can be
overtly pluralized by -V:d, just like their animate counterparts. We can take this as evidence that whenever
17This follows from the theory of Bare Phrase Structure (Chomsky 1994, 1995) and the framework of Distributed Morphology
(Halle and Marantz 1993): syntactic categories are taken to represent the features that compose them.
18I follow von Heusinger and Kornflit’s (2017) analysis of Altaic nominals and assume that, despite lacking an overt articles,
Alasha Mongolian has DPs.
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the noun is overtly plural, [PL] must be part of the syntactic derivation and NumP must be projected. Pluralmarked nouns, therefore, have the structures in (64a) if inanimate, and in (64b) if animate.
(64) The syntax of Plural-marked nouns
a. Inanimates
DP
NumP
nP
√NOM
‘book’
n
[IND]
Num
[PL]
D
b. Animates
DP
NumP
nP
√XÜ
‘boy’
n
[IND, ANIMATE]
Num
[PL]
D
This has consequences for both PF and LF. When transferred to the PF interface, the terminals or features
are assigned a vocabulary item via a series of Vocabulary Insertion (VI) rules. For Alasha Mongolian, the
relevant VI rules are formulated in (65) for n and in (66) for Num.
(65) VI rules for 𝑛
a. n[IND, ANIMATE] ⇔ Ø
b. n[IND] ⇔ Ø
(66) VI rules for Num
a. Num[SG] ⇔ Ø
b. Num[PL] ⇔ -V:d
As the rules predict, there is no overt exponent for the features on n in the language. Likewise, [SG] is
not mapped to an overt exponent either. Only [PL] has an overt exponent.
In terms of the semantic composition, the syntactic structures also give rise to the desired interpretations.The roots √NOM and √XÜ are associated with the concepts in (67). Each one is appropriately selected
by the categorizer. As a result, the denotation of the nP, before Number, is as in (68): (unmodified) unmarked
inanimate nouns denote book-atoms and their sums (i.e. they are number neutral). When nP composes with
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Number, as in the case of animates, the result is a strictly singular predicate: one that only has book-atoms
in its extension. This is shown for singular xü ‘boy’ in (69).
(67) a. √NOM = {BOOK-THING}
b. √XÜ = {BOY-THING}
(68) J(63𝑎)K = JnomK = Jn[IND]√NOMK =
= 𝜆𝑥IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥) (e.g. {a, b, c, ab, ac, bc, abc})
‘The property of being an atomic book or sum of atomic books’
(69) J(63𝑏)K = J[SG] n[IND]√XÜK
a. Jn[IND]√XÜK = 𝜆𝑥.IND(BOY-THING)(𝑥) ∧ animate(𝑥) (e.g. {a, b, c, ab, ac, bc, abc})
b. J[SG]K(Jn[IND]√XÜK) = 𝜆𝑥.IND(BOY-THING)(𝑥) ∧ animate(𝑥) ∧ minimal(𝑥) (e.g. {a, b, c})
‘The property of being an atomic boy’
In addition, restricting ourselves to the interpretation of the plural in upward entailing contexts, the interpretation for both types of nouns regardless of their animacy features is an exclusive plurality. This is
illustrated with the derivations in (70).
(70) a. J(64𝑎)K = J[PL] n[IND]√NOMK =
= 𝜆𝑋.∀𝑥[𝑋(𝑥) → (IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥) ∧ ¬minimal(𝑥))]
‘The property of being a individuated plurality of (only) sums of books’ (e.g. {ab, ac, bc, abc})
b. J(64𝑏)K = J[PL] n[IND]√XÜK = J[PL]K(Jn[IND]√XÜK) =
= 𝜆𝑋.∀𝑥[𝑋(𝑥) → (IND(BOY-THING)(𝑥) ∧ animate(𝑥) ∧ ¬minimal(𝑥))]
‘The property of being an individuated plurality of (only) sums of boys’ (e.g. {ab, ac, bc, abc})
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5.6.3 Deriving the exclusive/inclusive ambiguity with plural-marked nouns
An immediate consequence of the theory of number adopted is that plural-marked nouns, being [PL], will
be forced to be interpreted always exclusively: [PL] will restrict the denotation of the count noun to the
atomic non-minimal parts. While this is certainly a welcome result in the case of plural-marked nouns in
upward entailing contexts, it makes the wrong prediction when it comes to plural-marked nouns in downward
entailing contexts: they are interpreted inclusively.
One possibility, briefly entertained by Harbour (2014) and described in more detail by Martí (2020a,
p.59), would be to hypothesize that plural-marked nouns are structurally ambiguous between projecting
NumP or not. The difference between exclusive and inclusive plural-marked nouns would be along the
same lines as the difference between unmodified unmarked inanimates and their animate counterparts that I
have proposed here. If [PL] is not present in the derivation, the number neutral denotation of the nP imposed
by the categorizer will be passed along the DP.
However, this solution makes inaccurate morpho-syntactic predictions. In those languages, Alasha Mongolian being one of them, where we observe the exclusive-inclusive ambiguity in the plural, there is no difference in the exponence of the plural morpheme. That is, the same vocabulary item that spells out the [PL]
feature is used, regardless of the interpretation. This is unexpected under this type of structural ambiguity
account: if [PL] is not part of the syntax, it will not be subsequently mapped to a vocabulary item at PF;
and the rule in (66b) will not apply. What we can conclude from this is that whatever is responsible for the
ambiguity need only have a semantic effect leaving the VI rules in (65) intact.
A very popular solution in the literature derives the ambiguity based on Gricean competition in the
pragmatic computation (Krifka 1989; Sauerland 2003; Sauerland et al. 2005; Spector 2007; Zweig 2009).
However, Martí (2020a) has recently argued that these approaches would fail to capture Harbour’s robust
typology of number systems. Martí advocates instead for an account that derives the ambiguity based on the
syntactic structure of the DP and its consequences for LF. In this paper, I will adhere to the spirit of the claims
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made by Martí (2020a) and propose an alternative solution to the ambiguity that is rooted in the architecture
of the DP that is fed to LF, and does not rely on implicature calculation.19 In particular, I propose that the
feature [PL] has two allosemes at LF: an elsewhere alloseme, which is the denotation in (61b), and a marked
alloseme that arises whenever [PL] occurs in the local context of a negative or NPI indefinite determiner. In
what follows, I provide some motivation for the presence of an NPI element in the DP; then, I outline the
standard assumptions for allosemy and finally show how we can use it to derive the ambiguity at hand.
Inclusive plurals and covert any. It has been observed, first by Harbour (2016, ch.6: p.149-150) and
shortly after by Ackema and Neeleman (2018, ch.3: p.81-83), that bare plural NPs interpreted inclusively in
downward entailing contexts are in parallel distribution to plural-marked NPs with NPI any. For example,
the negative English sentences in (71) are truth-conditionally equivalent. Compare these to (72): overt any
in (72b) makes the sentence odd.
(71) a. I didn’t see children.
b. I didn’t see any children.
‘There is not even a child that I saw’
(72) a. I saw children.
b. ?? I saw any children.
‘There is more than one child that I saw’
The same occurs with questions as in (73) and antecedents of conditionals such as (74), which are the
other contexts where the inclusive interpretation is found.
(73) A:
⎧
{
{
{
⎨
{
{
{
⎩
Did you see children in the park?
Did you see any children in the park?
⎫
}
}
}
⎬
}
}
}
⎭
B:
⎧
{
{
{
⎨
{
{
{
⎩
Yes, I saw one
# No, I saw one
⎫
}
}
}
⎬
}
}
}
⎭
19An approach that relies of competition in terms of structurally determined scalar alternatives may be in principle compatible
with the data and the syntactic structures proposed here. That is the approach that Bylinina and Podobryaev (2020) pursue for Buriat.
However, for Bylinina and Podobryaev, [PL] = * whereas for me [PL] ≠ *. Thus, one needs to factor this difference when determining
the set of possible alternatives.
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(74) a. If you have children, you are welcome to board now.
b. If you have any children, you are welcome to board now.
‘Even if you have one child, you can board now’
We must note, in addition, that in English the negative indefinite no triggers an inclusive plural interpretation on the noun. See (75).
(75) a. No children were invited to the party.
b. John has no children with Mary.
These patterns observed for any and plural-marked nouns in English are also found in Alasha Mongolian.
An indefinite determiner yamarch ‘any’ is only found in downward entailing contexts, as the contrast in (76)
shows. (77), which parallels (25), illustrates that yamarch can also be found in questions.
(76) a. * bi
I
yamarch
any
{ nom-o:d/
book-PL/
xüch-üd}
boy-PL
xar-sVn
see-PST.PERF
Lit. ‘I saw any {books/ boys}’
b. bi
I
yamarch
any
{ nom-o:d/
book-PL/
xüch-üd}
boy-PL
xar-sVn-ghue
see-PST.PERF-NEG
‘I didn’t see any {books/ boys}’
(77) A: chi
you
yamarch
any
{ nom-o:d/
book-PL/
xüch-üd}
boy-PL
dilgur-t
store-DAT
xar-tVg-o?
see-HAB-Q.POL
‘Do you typically see any {books/ boys} at the store?’
B: time:,
yes
nig
one
‘Yes, I (typically) see one’
# ughue,
NEG
nig
one
No, I (typically) see one.
Like Harbour (2016) and Ackema and Neeleman (2018), we can conclude from this that there is a covert
counterpart of any that occurs with bare plurals in downward entailing contexts. Furthermore, whenever
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this (overt or covert) any/yamarch is appropriately licensed, it will be responsible for triggering the inclusive
interpretation of the plural. Schematically, we can summarize the rule that triggers the inclusive interpretation
of plural-marked nouns as in (78).
(78) General rule for the interpretation of plural-marked nouns in downward entailing contexts
A plural-marked noun …
a. …is interpreted inclusively if it is c-commanded by a negative indefinite or a properly licensed
NPI at LF.
b. Otherwise, it will be interpreted exclusively.
c. Structural description: {NEG/ NPI} > PL > n √ROOT
I will take the structural description of the rule in (78c) to indicate an interaction between the negative
element and the plural feature. In particular, when the structural description is met, the canonical or unmarked
meaning of the plural will be blocked and a different meaning for the plural will be selected instead. I model
this interaction in terms of allosemy (Marantz 2001, 2013; Arad 2003; Harley 2014; Wood 2016, 2023):
competition for selection of meanings into terminals at LF.
Allosemy: some necessary background. We can think of allosemy as the counterpart of allomorphy but
at LF (Arad 2003; Marantz 2001, 2013; Wood 2016, 2023): mapping from terminals to interpretation is
mediated by Sense Insertion rules. In particular, we can adopt the view that the denotation of functional
heads, which have different flavours or are polysemous, is determined post-syntactically via the syntacticosemantic context. Crucially, the rules that determine the insertion of these meanings will only affect the
semantic output, and have no impact whatsoever in the morphology. This already is a promising result for
the case of the inclusive-exclusive interpretation of the plural because, as we have seen, the plural morpheme
is always mapped to the same exponent.
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The analogue to VI rules are the mapping rules in (79), which are also subject to the Subset Principle
(Kiparsky 1973; Halle and Marantz 1993). I schematically formalize these rules in (79) as established by
Harley (2014); Wood (2016, 2023) and others.
(79) a. X ↔ 𝜆𝜎 … /__Y ‘Interpret X as the 𝜆-expression in the context of Y’
b. X ↔ 𝜆𝜎.𝜆𝜏 … ‘Interpret X as the 𝜆-expression elsewhere’
Whenever the contextual specification for X is met, the rule in (79a) will apply. Otherwise, X will be
interpreted as the default or elsewhere case in (79b).
In thinking about the domain of allosemy, we can apply the same logic as for allomorphy (Embick and
Noyer 2001; Embick 2010; Bobaljik 2012). For instance, for a feature/terminal Y to condition an alloseme
on X, there must be no semantically contentful Z that intervenes between them. By semantically contentful,
I am referring to any meaning other than an identity function. A schematic illustration is given in (80).
(80) Locality conditions for allosemy
a.
X Z
𝜆𝜎
Y
*
b.
X Z
Ø
Y
✓
Given the LF structures in (80), Y cannot condition an alloseme on X in (80a) because Z is contentful.
As a result, the elsewhere rule in (79b) is applied. However, if Z is an identity function represented as ‘Ø’
in (80b), Y and X are local and thus Y can trigger alloseme insertion on X. In other words, the contextual
specification for the rule in (79a) is met, and the rule applies.
When applied to the interpretation of the plural at hand, the structural description in (78c) entails that the
NEG or NPI feature and the Number head hosting the feature [PL] must be local for the former to condition
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an idisyncratic alloseme on [PL]. In other words, NEG or NPI and [PL] must be part of the same extended
projection, and the former must immediately c-command the latter. I turn to the formal details next.
[NEG/NPI] as allosemy triggers on [PL]. I propose that negative-words including NPIs and negative determiners are decomposed into two parts (Collins and Postal 2014): a negative or NPI element and an indefinite
element.20 It should be explicitly remarked that it is crucial for the proposal here that NPIs are distinguished
from non-NPI determiners by a syntactically visible feature. I propose the following decomposition in (81)
and (82).
(81) The features of NPI indefinite determiners
D[NPI]⇔ 𝑎𝑛𝑦/𝑦𝑎𝑚𝑎𝑟𝑐ℎ
(82) The features of negative indefinite determiners
D[NEG]⇔ 𝑛𝑜
While the exact semantic content of the NPI feature in (81), though, is to be yet determined, we can take
its contribution to be in the spirit of Guerzoni (2006): the feature must be licensed at LF against the relevant
negative or downward entailing head. D is the category feature and, as in Section 3.2.4 of Chapter 3, I am
assuming that indefiniteness is lack of a feature [DEF]. The denotations for the two feature bundles are as
given in (83).21
(83) a. JD[NPI]K = 𝜆𝑃.𝜆𝑄.[∃𝑥(𝑃(𝑥) ∧ 𝑄(𝑥))]
b. JD[NEG]K = 𝜆𝑃.𝜆𝑄.¬[∃𝑥(𝑃(𝑥) ∧ 𝑄(𝑥))] (Collins and Postal 2014, ch3.: p.25)
In addition to this, I propose that [PL] has two allosemes. These are captured in the allosemy rules
formulated in (84).
20For Collins and Postal (2014), any = [NEG SOME].
21One might wonder whether it is necessary to have two different feature bundles, and two separate denotations for any/yamarch
and no or whether a negative denotation like the one proposed by Collins and Postal (2014) suffices. In terms of parsimony, having
the same denotation for no and any, as Collins and Postal (2014) do, is an advantage. However, as Y. Sudo (p.c.) points out
such denotation of any/yamarch should not involve negation, as it would predict the wrong truth-conditions in various cases, e.g.
under (semantically interpreted) negation, conditional antecedents, sentences with multiple NPIs, etc. Rather, the denotation of
any/yamarch must be standardly built on a simple existential quantifier (some analyses involve some additional mechanisms on top
of that, e.g. Chierchia 2013). Perhaps a solution to reconcile this issue is to fully endorse Collins and Postal’s proposal according
to which the NEG element that NPIs are decomposed into must raise out of D into the clause. For the purpose of this dissertation, I
remain neutral as to whether such an analysis is needed to account for the plural facts.
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(84) Allosemy rules for [PL]
a. [PL] ↔ 𝜆𝑃.𝑃/__ D{[NPI]/[NEG]}
b. [PL] ↔ 𝜆𝑃.𝜆𝑋.∀𝑥[𝑋(𝑥) → 𝑃(𝑥) ∧ ¬minimal(𝑥)]
Given the rules, [PL] has two allosemes which compete for insertion at LF. The elsewhere case in (84b)
is the default denotation. This denotation will be inserted at LF unless there is a D terminal with the feature
[NPI] or [NEG] in its specified local context. In that case, the elsewhere rule will be blocked in favor of the
more specific rule in (84a). According to this rule, the denotation of [PL] will be that of an identity function.
The syntactic structure that I have proposed for DPs in Alasha Mongolian allows us to locate the feature
bundle for the NPI as realizing D. Thus, in downward entailing contexts, the DP structure that is transferred
to LF is illustrated in (85a) and (85b) for inanimates and animates respectively.
(85) LFs of plural marked nouns in downward entailing contexts
a. nom-o:d ‘book-PL’
DP
√NOM
‘book’
n
[IND]
Num
[PL]
D
[NPI]
b. xüch-ü:d ‘boy-PL’
DP
√XÜ
‘boy’
n
[IND, ANIMATE]
Num
[PL]
D
[NPI]
Importantly, as both LF structures show, the structural description in (78c) for the interpretation of the
plural as inclusive is met: [PL] is the immediate scope of a negative indefinite. This allows for D to trigger
allosemy on [PL], i.e. (84a). In particular, the derivation proceeds as in (86), illustrated with an inanimate
noun. The derivation would be identical for animate nouns, with the exception of the [ANIMATE] feature.
(86) Semantic derivation of nom-o:d in a downward entailing context
a. Jn[IND]K(J√NOMK)
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DP
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
√NOM
BOOK-THING
n
[IND]
𝜆𝑥.IND(𝑃)(𝑥) ∧ ¬animate(𝑥)
Num
[PL]
D
[NPI]
b. D triggers allosemy of (84a) on Num
DP
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
√NOM
BOOK-THING
n
[IND]
𝜆𝑥.IND(𝑃)(𝑥) ∧ ¬animate(𝑥)
Num
[PL]
𝜆𝑃.𝑃
D
[NPI]
c. JNum[PL]K(J[n[IND] √NOM]K)
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DP
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
√NOM
BOOK-THING
n
[IND]
𝜆𝑥.IND(𝑃)(𝑥) ∧ ¬animate(𝑥)
Num
[PL]
𝜆𝑃.𝑃
D
[NPI]
d. JDK(J[Num[PL] n[IND] √NOM]K)
𝜆𝑄.[∃𝑥(IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥) ∧ 𝑄(𝑥))]
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
𝜆𝑥.IND(BOOK-THING)(𝑥) ∧ ¬animate(𝑥)
√NOM
BOOK-THING
n
[IND]
𝜆𝑥.IND(𝑃)(𝑥) ∧ ¬animate(𝑥)
[PL]
𝜆𝑃.𝑃
D
[NPI]
𝜆𝑃.𝜆𝑄.[∃𝑥(𝑃(𝑥) ∧ 𝑄(𝑥))]
The semantic composition proceeds bottom-up, as is standard, by composing the root with the nominalizing n head taking the root as its argument The result in (86a) is an individuated semi-lattice which is number
neutral: the predicate has atoms and and their sums in its extension (e.g. {a, b, c, ab, ac, bc, abc}). The
next step in the derivation is the trigger of allosemy as in (86b): [PL] occurs in the context of D[NPI] which
meets the contextual specification for the allosemy rule in (84a). As a result, and given the Subset Principle,
the insertion of the elsewhere sense for [PL] is blocked. Instead, the more specific rule is applied. According
to this rule, [PL] is an identity function. When composing with the number neutral constituent in (86c), [PL]
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has no effect on it, passing along its denotation to the next higher node. By virtue of [PL] being an identity
function, the extension of the noun still has both atoms and their sums. The last step is the composition of
this just-created node and the determiner head, given in (86d).
The derivation has the desired result which is a plurality that also contains atomic minimal parts. Crucially, the derivation of plural-marked nouns in downward entailing contexts differs from their derivation in
upward entailing contexts regarding the choice of denotation inserted for [PL]. In upward entailing contexts,
as illustrated in (64), there is no NPI or NEG on D; as a result, the application of the context sensitive allosemy
rule in (84a) is blocked. Instead, the elsewhere rule for [PL] is applied, which restricts the extension of the
noun to only sums.
There are some important benefits of deriving the ambiguity in this way. First, the analysis relies on
the syntactic structure that is fed to LF and includes a mechanism responsible for neutralizing non-atomic
plural interpretations. In particular, it captures the insight from the pragmatic competition approaches that
the morpho-syntactic expression of plural-marked nouns remains the same across the board, i.e. [PL] always
projects, and only the meaning is affected. In this respect, it is compatible with the claims made by Martí
(2020a) and presents itself as an alternative to other structural ambiguity accounts. Last but not least, there is
a methodological advantage. Given the strict locality conditions for allosemy and the allosemy rules for [PL],
it only takes a single interpretable feature that intervenes between D and Num to block alloseme selection.
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In other words, the account is “fragile” in that it is easily falsifiable. Like Deal (2019); Erlewine (2020), I
take this aspect to be a virtue of the theory.22
5.6.4 Adding (non-classificatory) APs and numerals into the mix
Up until this point, I have argued that a major difference between animate and inanimate nouns is that the
former always project NumP, but the latter need not. I have argued, though, that it is possible for inanimate
nouns to project NumP if they are overtly plural-marked, for instance. The question that arises now is whether
these nouns can also project NumP when they are unmarked. The way that the system is set up does not
preclude Num to be specified as [SG] when the [IND] noun is not specified for animacy. That is, it must be in
principle possible to find cases where unmarked inanimate nouns like nom are actually not number neutral
but singular. This is the exact situation that we found with non-classificatory APs and numerals. I discuss
APs first.
The case of APs. Non-classificatory APs must precede classificatory ones according to the word order
facts in (35). What is more, the former but not the latter, interact with number information in a non-trivial
manner. In particular, the former belong to the subclass of strongly distributive adjectives. I take this set of
facts to propose the following: classificatory APs are adjoined to the domain of class which is lower in the
structure (Alexiadou et al. 2007; Svenonius 2008; Wiltschko 2014; Dékány 2021), i.e. nP; non-classificatory
22While the allosemy account seems to be empirically well-motivated for Alasha Mongolian and can be extended to English, there
are at least two places where the interpretation of (covert/overt) any and inclusive plurals seems to diverge. I thank Y. Sudo (p.c.)
for this observation. (a) One such case is in the scope of only: since the scope of only is an NPI licensing context, we would expect a
plural-marked NP to receive an inclusive interpretation, but that is arguably incorrect, e.g. (xxiv) is wrongly predicted to not imply
that ‘John has multiple iPhones’.
(xxiv) Only John has iPhones.
(b) In a similar vein, plurals in the scope of every are potentially problematic for the analysis (Farkas and de Swart 2010). A
sentence like (xxv) has a reading that does not entail that every applicant submitted multiple journal articles, but at least some
applicants did. Since the scope of every is not an NPI licensing environment, we would expect an exclusive plural interpretation that
should entail that every applicant submitted multiple journal articles.
(xxv) Every applicant submitted journal articles as part of their job application.
These are problematic if we aim to have a generalized allosemy account for the inclusive/exclusive ambiguity of the plural. At
this point, however, there is little that I can say about them and I will thus leave them for future research.
221

APs are adjoined higher in the DP (Cinque 2005, 2010, 2023; Svenonius 2008; Dékány 2021). In particular,
they are adjoined to NumP. The structure of the DP when both types of APs are present is given in (87a) for
unmarked [SG] nouns, and in (87b) for plural-marked [PL] nouns.
(87) a. unmarked [SG] inanimate noun modified by APs
DP ⇔ unte-n shashin-tei nom ‘expensive religious book’
NumP
APnon-class
unte-n
‘expensive-ATTR’
nP
APClass
shashin-tei
‘religion-ADJ’
√NOM
‘book’
n
[IND]
Num
[SG]
D
b. Plural-marked [PL] inanimate noun modified by APs in upward entailing contexts
DP ⇔ unte-n shashin-tei nom-o:d ‘expensive religious books’
NumP
APnon-class
unte-n
‘expensive-ATTR’
nP
APClass
shashin-tei
‘religion-ADJ’
√NOM
‘book’
n
[IND]
Num
[PL]
D
What we can conclude from the structures is that, once again, the difference between unmarked inanimate
nouns which are number neutral and unmarked inanimate nouns that are strictly singular is the absence or
presence of Num. This difference is, however, obscured by the lack of overt exponents at PF. In fact, given
our VI rules in (66), if Num is [SG], there will be no overt vocabulary item associated with it, which has the
222

same phonological effect as there being no Num: the noun will remain unmarked for number in both cases.
If, on the contrary, the noun is overtly plural-marked, that can only be because Num is [PL].
In terms of the semantics, projecting Num[SG] leads to an interpretive difference between the two types
of unmarked inanimate nouns, though: the noun will be interpreted as a singularity. If Num is [PL], the
inanimate noun will denote an inclusive or exclusive plurality depending on the veridicality of the context.
For example, the semantics of the [SG]-marked DP in (87a) is provided in (89), and the semantics of the
[PL]-marked DP in (87b) is provided in (90). Following a degree-semantics framework (Cresswell 1976; von
Stechow 1984; Heim 2001), I will assume that while classificatory APs do not introduce a degree variable in
the semantics because they are non-gradable, non-classificatory ones do. Their semantics are given in (88).23
(88) a. JuntenK = 𝜆𝑥.∃𝑑[expensive(𝑥) ≥ 𝑑]
b. JshashinteiK = 𝜆𝑥.religious(𝑥)
(89) unten shashintei nom ‘expensive religious book’
a. Jshashintei n[IND] √NOMK = 𝜆𝑥.Jn[IND]√NOMK(𝑥) ∧ religious(𝑥)
b. J[SG] shashintei n[IND] √NOMK = 𝜆𝑥.Jn[IND]√NOMK(𝑥) ∧ minimal(𝑥) ∧ religious(𝑥)
c. Junten [SG] shashintei n[IND] √NOMK =
𝜆𝑥.∃𝑑[Jn[IND]√NOMK(𝑥) ∧ minimal(𝑥) ∧ religious(𝑥) ∧ expensive(𝑥) ≥ 𝑑]
‘The property of being a religious book-atom which is d-expensive’
(90) unten shashintei nom-o:d ‘expensive religious books’ (exclusive plural)
a. Jshashintei n √NOMK = 𝜆𝑥.Jn[IND]√NOMK(𝑥) ∧ religious(𝑥)
b. J[PL] shashintei n √NOMK = 𝜆𝑋.∀𝑥[𝑋(𝑥) → (Jn[IND]√NOMK(𝑥) ∧ ¬minimal(𝑥) ∧ religious(𝑥))]
c. Junten [PL] shashintei n √NOMK =
23Svenonius (2008) observes that classificatory APs, or APs adjoined lower in the extended projection of the noun, are generally
non-gradable across languages. However, see Dékány (2021, ch.2: p.46-47) for some possible counterexamples of gradable APs
that are lower in the structure.
223

= 𝜆𝑋.∃𝑑[∀𝑥[𝑋(𝑥) → (Jn[IND]√NOMK(𝑥) ∧ ¬minimal(𝑥) ∧ religious(𝑥))] ∧ expensive(𝑋) ≥ 𝑑]
‘The property of being a non-atomic individuated plurality of religious books which are
d-expensive’
In both (89) and (90), the nP first composes with the classificatory AP via Predicate Modification (Heim
and Kratzer 1998), and then the output of this operation saturates the first argument of [SG/PL]. Afterwards,
non-classificatory APs compose with the [SG/PL] nP again via Predicate Modification.
This manner and order of semantic composition does not interfere with the allosemy rules for [PL]. It
is important to remember that one of the necessary conditions for allosemy, which was the same as for
allomorphy, was that the two terminals involved were local within the same extended projection. Modifiers,
or elements in specifier position, do not disrupt the locality between two heads. In the structure in (87b),
D and Num satisfy the locality condition as there is no intervening head between them. Thus, in downward
entailing contexts when D is [NPI] and Num is [PL], the Sense Insertion rule in (84a) is predicted to apply.24
The situation in predicative contexts differs due to the fact that the syntactic structure is not as in (87).
For ease of exposition, I assume that predicative adjectives have a Small Clause-like structure (Chomsky
1981; Stowell 1981; Bowers 2001, for an overview). Under this approach, the AP is not part of the extended
projection of the NP and is not adjoined to Num; instead, the unmarked NP has the structure in (63a) (i.e. it
lacks NumP), it is merged in a specifier position and acts as the subject of the predication. As a result, no
number restriction is imposed on the interpretation of the noun. The structure is illustrated in (91), where
the PredP label is used purely pretheoretically.
(91) Predicative AP construction
24Another argument for the application of allosemy comes from the timing of the composition. [PL] must compose with the nP
before the non-classificatory AP does. This entails that a denotation for [PL] must be inserted before the nP saturates its argument.
The timing of operations is therefore as illustrated for unmodified plural nouns in (86): (i) the nP is composed; (ii) D triggers
allosemy on Num and the context specific rule is applied; (iii) Num composes with nP; and (iv) the non-classificatory AP enters the
semantic composition.
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PredP
DP
√NOM + 𝑛[IND]
AP
unte
Pred
The case of cardinal numerals. Numerals modifying nouns must not only precede the noun they modify,
but also any AP-modifiers. In fact, if a (non-classificatory) AP precedes the numeral, the sequence is unacceptable, as shown in (40). Numerals must follow other DP-internal constituents such as possessors, which
are located high in the DP (Gong 2021; Toquero-Pérez 2023a). This is shown in (92).
(92) a. xüch-üd-in
child-PL-GEN
dulu-n
seven-ATTR
xunde-n
heavy-ATTR
nom
book
‘The children’s seven heavy books’ POSS > # > AP > N
b. * dulu-n
seven-ATTR
xüch-üd-in
child-PL-GEN
xunde-n
heavy-ATTR
nom
book
Int.: ‘The children’s seven heavy books’ # > POSS > AP > N
Given the interaction of APs with Number and the fact that they must always follow numerals, I propose
that numerals must be higher than NumP. In other words, NumP is merged in the syntax before numeral
modifiers. In addition, assuming that possessors generally occupy Spec,DP (Abney 1987; Corver 1990),
numerals must be located below D.25 I take this position of numerals to be the specifier of a functional
projection called CARD(inality)P (Scontras 2013, 2014; Martí 2020b; Pancheva 2021, 2022).26 This CARD
head selects only for [•SG•]. The structure for numerically modified NPs is in (93).
(93) #P in Spec,CARDP
25If numerals and APs were adjuncts adjoined to the same projection, e.g. NumP, nothing would in principle prevent a flexible
ordering. There are generally no syntactic selectional requirements for adjuncts (Svenonius 1994; Chomsky 1994, 1995; Adger
2003). The strict ordering in (40) would need to be stipulated.
26Scontras (2013, 2014) and Martí (2020b) assume without independent motivation that Num is merged immediately higher than
CARD. Pancheva (2021, 2022) shows that the position of CARD, which she labels as MEAS, can be above and/or below Num. The
word order facts indicate that CARD must be higher than Num in Alasha Mongolian.
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DP ⇔ dulu-n unte-n N ‘seven expensive N’
CARDP
#P
dulu-n
‘7-ATTR’
NumP
APnon-class
unte-n
‘expensive-ATTR’
nP
√ROOT n
[IND(, ANIMATE)]
Num
[SG]
CARD
[•SG•]
D
The hierarchical structure in (93) derives the word order facts: numerals must precede APs because they
are adjoined to a higher functional projection. In addition, CARD selects for a [SG] complement which rules
out overtly-plural marked nouns.
Semantically, I take the view that numerals themselves denote numbers of type n, as in (94). Thus,
a measure expression is required to compose them with the predicate nominal (Krifka 1989, 1995; Hackl
2000; Scontras 2013, 2014; Martí 2020b; Pancheva 2021, 2022). That is the role of CARD whose meaning is
as in (95a), based on Pancheva’s (2021; 2022) denotation for singular-selecting CARD heads.27
(94) JdulunK = 7
(95) a. JCARDK = 𝜆𝑃⟨𝑒,𝑡⟩.𝜆𝑛.𝜆𝑥.∗𝑃(𝑥) ∧ |𝑥| = 𝑛
b. Jdulun CARD [SG] nPK = 𝜆𝑥.∗
J[SG] nPK(𝑥) ∧ |𝑥| = 7
27Alternatively, one could assign CARD a denotation based on Ionin and Matushansky’s (2006; 2018), ch.2: p.13 semantics for
numerals.
(xxvi) JCARDK = 𝜆𝑃⟨𝑒,𝑡⟩.𝜆𝑛.𝜆𝑥.∃𝑆[Π(𝑆)(𝑥) ∧ |𝑆| = 𝑛 ∧ ∀𝑠 ∈ 𝑆 → 𝑃(𝑠)]
‘A set of individuals S is a partition Π of a plural individual 𝑥 if 𝑥 is the sum of all members of S and the members of S do
not overlap.’
The semantics of CARD introduces a partition, Π, in the body of the function. One of the conditions of the partition is that its
members must not overlap. Plurals are cumulative which entails that the members composing the plurality overlap. As a result, the
condition imposed by the partition rules out the possibility that the nominal argument of the numeral denotes a plurality. The feature
[SG] on Num creates a singularity ensuring the non-overlapping of the members in the extension of the constituent that saturates
CARD’s first argument.
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CARD takes an individuated predicate of atomic individuals, 𝑃, a numeral, 𝑛, and returns a predicate of
atoms and their sums with cardinality 𝑛 via Link’s (1983) ‘*’ operator. In other words, CARD reintroduces
the sums into the extension of the individuated nP consisting only of atomic minimal parts: {𝑎, 𝑏, 𝑐} →
{𝑎, 𝑏, 𝑐, 𝑎𝑏, 𝑎𝑐, 𝑏𝑐, 𝑎𝑏𝑐}.
ATTR-marking on prenominal modifiers. There is one final aspect about non-classificatory APs and numerals that needs to be addressed. This involves ATTR-marking. The attributive marker /-n/ surfaces on these
high modifiers when they occur prenominally, but it does not surface on them in predicative position. While
more work needs to be done to fully understand the distribution of the attributive morpheme in the language,
I speculate that this marker is a reflex of agreement.
As Alexeyenko and Zeijlstra (2020, 2021) and Corver (2021) observe, attributive morphemes across
languages seem to serve the purpose of marking ‘nominality’. By ‘nominality’, I mean that they stand in
a local relation with a noun they directly modify. In some cases, like for example German or Dutch, this
nominality is encoded via the overt exponence of the noun’s 𝜑-features (or at least a subset) such as gender
or number. Against this background, Corver (2021) proposes that the ATTR morpheme on Dutch prenominal
adjectives is the result of spelling out the feature bundle of the noun. The affix is then realized on the AP via
Spec-Head agreement.
We could adopt a similar analysis for ATTR-marking in Alasha Mongolian: -n on modifiers is the result
of nominal concord. As in Chapter 3, I assume that concord features on the relevant non-head constituents
attach in the form of unvalued features which will receive a matching value. This all occurs post-syntactically
(Bonet 2013; Norris 2014, 2017a,b; Deal 2016b). This entails that the heads of non-classificatory APs and
numerals receive an unvalued uninterpretable [𝑢AGR:__] feature post-Spell-Out, where ‘AGR’ represents any
potential 𝜑-feature(s): [IND, SG/PL]. This [𝑢AGR:__] feature will copy a value available in the extended
projection of the NP. In the case of count nouns, which are the class of NPs where these modifiers occur
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prenominally, the unvalued feature on the AP will copy the value [SG/PL] on Num and [IND] on the n. This is
represented in (96).
(96) a. [NumP AP[𝑢AGR∶ ]
[Num’ SG/PL [nP n[IND] √ROOT]]]
b. [NumP AP[𝑢AGR∶SG/PL, IND]
[Num’ SG/PL [nPn[IND] √ROOT]]]
The valued AGR feature in (96b) will then be spelled out as /-n/ at the point of vocabulary insertion if
the stem of the adjective that it affixes to ends in a vowel. When the numeral, projecting a #P, is part of the
derivation, it will also receive an unvalued [𝑢AGR] feature post syntactically. This is shown in (98).
(97) [𝑢AGR:val] ⇔ -n/√A/#-V ‘Map the terminal to -n if the A/# ends in a vowel’
(98) [CARDP #P[𝑢AGR∶SG, IND]
[CARD’ CARD [NumP AP[𝑢AGR∶SG, IND]
[Num’ SG [nP n[IND] √ROOT]]]]]
In predicative contexts, the probe features on APs and #P do not occur DP-internally, e.g. (91). This
entails that no [𝑢AGR] feature is inserted post-syntactically on the adjectival and numeral terminals, thus
precluding concord. The relevant VI rule in (97) does not apply, and no attributive marker is exponed in
predicative contexts.
5.6.5 A note on QA allomorphy and the dimension of measurement
It was observed in Section 5.4.2, that QA olin occurred with inanimate unmarked number neutral nouns such
as nom as well as plural marked nouns nomo:od or xüchü:d. The other QA, e.g. ix, was unacceptable with
either. The descriptive generalization was formulated in(54), repeated below.
(54) olin is found when the noun is individuated, whereas ix is found elsewhere.
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In addition, it was also observed that both unmarked number neutral nouns and overtly plural-marked
nouns were measured along a cardinality scale when modified by olin. I want to propose that these facts can
be accounted for in terms of the proposal here and are consistent with the Cardinality Generalization Redux.
In terms of the distribution, olin cannot be sensitive to plural. That is so because number neutral nouns
do not project Number or have a [PL] in their extended projection. What the two classes of nouns share, to
the exclusion of mass nous, is the [IND]-feature on n. ix, on the contrary, occurs in environments where the
[IND] feature is not available. Thus, we can capture these facts with the VI rules in (99).
(99) VI rules for QAs in Mongolin
a. √IX ⇔ 𝑜𝑙𝑖𝑛/__Deg[𝑢IND: IND]
b. √IX ⇔ 𝑖𝑥
Under the assumption that concord features on modifiers are inserted post-sytactically, the Deg head will
receive a [𝑢IND: __] feature. The feature will receive a value from the individuating nomilalizer. At the point
of Vocabulary Insertion, the rule in (99a) will apply. The other rule, e.g. (99b), will apply elsewhere: when
the noun is unmarked for individuation.
In terms of the semantics and the dimension of measurement, [IND] ensures an individuated semi-lattice
generated from the set of atoms. The denotation of this nP will contain the atomic minimal and non-minimal
parts. This is enough for 𝜇 to be assigned the value of CARDINALITY. The semantic composition is in (100).
(100) Jolin nomK
a. JnPK = Jn[IND]K(J√NOMK) = J(68)K {a, b, c, ab, ac, bc, abc}
b. J√IX DegK
𝐴 = 𝜆𝛼.∃𝑑[𝐴(𝜇)(𝛼) ≥ 𝑑]
c. J[√IX Deg] nPK
𝐴 = 𝜆𝑥.∃𝑑[JnPK(𝑥) ∧ 𝐴(𝜇)(𝑥) ≥ 𝑑]
𝐴(𝜇) → CARDINALITY
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The denotation of the nP in (100a) is true of book atoms and book-sums. When the DegP composes with
the nP via predicate modification, 𝜇 has a variable 𝑥 ranging over an inclusive individuated plurality. The
CARDINALITY function is defined because 𝑥 is an atom in 𝑃 (i.e book).
This is predicted by the Countability Hypothesis from Chapter 4, repeated below. We can go back to our
dependency tree in Figure 4.1, in Chapter 4 and update it with the relevant findings. The new version is given
in Figure 5.2.
(32) The Countability Hypothesis
Being countable means being marked for individuation.
Figure 5.2: Predicting countability asymmetries
Is n marked [IND]?
No:
is n marked [PL]?
No: Canonical mass
(water, sal)
Yes: Plural mass
(dregs, celos)
Yes:
Is there Number?
No:
Is there n[COLL]?
No: Number Neutral
unmarked
(nom, tsitsig)
Yes: Object Mass
[COLL]
(jewelry, joyería)
Yes: is Number [PL]?
No: Singular count
[SG]
(jewel, joya)
Yes: Plural count [PL]
(jewels, joyas)
As correctly predicted by the hypothesis, the nouns plural-count nouns, object mass ones and number
neutral ones are all marked for individuation and are thus countable. The nouns, however, differ in their
morpho-syntactic make-up: unmarked for collective or plural; collective, but not plural-marked; and, pluralmarked, but not collective-marked. This in turn has an effect on the semantic interpretation of each class of
noun. The theory of individuation and number that I have proposed is able to capture the similarities among
classes, but also the aspects with respect to which they differ. Besides, it makes predictions about what we
might find across languages. While singular count nouns are unacceptable with QAs because they do not
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satisfy the cumulativity requirement, they are also marked for individuation and are thus countable: they can
be counted via numeral modification (e.g. one book in English or xoirV-n nom ‘two book’ in Mongolian).
5.7 Conclusion: Broader implications
I started the chapter by positing 5 questions that the data from Alasha Mongolian would help shed light on.
We can now go back to answering each of these questions.
The first question was concerned with the morpho-syntactic structure of unmarked nouns. I have argued that unmarked nouns are syntactically ambiguous. In particular, unmarked number neutral nouns are
syntactically impoverished. The NumP hosting number features is absent and so the noun is underdetermined for number: they are bare count nouns underspecified for number, but IND-marked. Singular-denoting
unmarked nouns must project NumP. This was the case of bare unmarked inanimates and AP/numerically
modified inanimates. The animacy split is neutralized in the plural form because [PL] is part of the derivation projecting NumP. Variation in the interpretation of NPs is thus located in the morpho-syntactic pieces
available within and across languages (see also Deal 2016a, 2017).
An innovation of this chapter is the diagnosing of number neutrality via QAs like many/olin. This is a
significant test since it relies on the mereological structure of the noun. In Alasha Mongolian, olin (‘many’) is
compatible with (inanimate) unmarked NPs, which further supports the analysis that (inanimate) unmarked
NPs in Alasha Mongolia are number neutral and have sums of atoms in their extension (in addition to single atoms). This is a promisingly reliable diagnostic and it opens up the possibility to probe the question
of number neutrality of unmarked NPs in languages like Turkish where arguments have been made in both
directions: Bale et al. (2011) argue for unmarked NPs as number neutral, whereas Sağ (2022) has recently
challenged their arguments. Besides, the analysis of QAs is consistent with the theory developed: the semantic interpretation of QAs conforms the Cardinality Generalization Redux, and it is independent of their
surface form.
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The second question addressed the location of Number in the structure. Based on the data from APs
and numerals, the account supports the traditional view that NumP is located between n and D (Ritter 1991;
Cowper 2005; Cowper and Hall 2009, 2012). Furthermore, it provides empirical evidence for the hypothesis
that Number can be lower than numerals (Pancheva 2021, 2022). This goes against the view that numerals
enter the syntactic derivation and semantic composition before Number does, e.g. Scontras (2013); Martí
(2020b). It also goes against approaches that exclusively locate number higher than D, e.g. Sauerland (2003).
Building on the discussion of numerals, Alasha Mongolian sheds light on the debate as to whether numerals universally combine with (semantically) singular (Ionin and Matushansky 2006, 2018) or plural predicates
(Bale et al. 2011; Bale and Khanjian 2014). For example, Bale et al. (2011) propose a semantic universal
which they call the ‘Strong Thesis’: numeral modification is restrictive, because modification in language
is restrictive. If correct, the Strong Thesis predicts that a semantics for numerals à la Ionin and Matushansky (2006, 2018) is not appropriate; and in fact when numerals combine with bare (unmarked) NPs that is
because these NPs must be number neutral. Given the data from Alasha Mongolian, we can conclude that
while numerals combine with bare unmarked NPs, these NPs are not number neutral. Alasha Mongolian,
thus, casts doubt on the universality of the Strong Thesis: it is too strong, and numerals can in fact compose
with strictly atomic predicates. These facts have also been corroborated by Pancheva (2021, 2022) for Bulgarian. That does not mean, though, that Ionin and Matushansky’s competing alternative – that numerals
universally require singular predicates and that plural morphology is uninterpretable agreement – is not too
strong: plural morphology can be interpretable and need not be the result of agreement.
Languages differ as to whether numerals require the nominal they modify to be a predicate of atomic nonminimal part (i.e pluralities) or a predicate of atomic minimal parts (i.e singularities), and the challenge that
remains is to explicate and model that variation. A promising way to account for such variation is proposed by
Pancheva (2021, 2022). Under the assumption that numerals are introduced by a CARD head in the extended
projection of the noun that c-selects for Number, the variation will stem from the specification of this head
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rather than the numeral itself. For instance, for numerals higher than 1, CARD1 will only be compatible with
[SG] nouns, in which case it will have to introduce a pluralizing function; CARD2 will be compatible with [PL]
predicates and will not have pluralizing semantics. Thus, languages will differ depending on whether they
have CARD1
(Alasha Mongolian, Finnish, Turkish), CARD2
(English) or both (Bulgarian).
With respect to the third question, i.e. the exclusive/inclusive interpretation of the plural morpheme, I
developed an account which locates the ambiguity at the syntax-semantics interface. Namely, just like vocabulary items can compete for insertion at PF given the Subset Principle, so can ‘meanings’ at LF. The
exclusive meaning of the plural is taken to be the default one, which is blocked in the presence of an indefinite NPI or a negative indefinite, which may be overt or covert. While the analysis seems to make many
empirically appropriate predictions for languages that also display the same ambiguity, e.g. English, it also
faces some shortcomings (see footnote 21). However, if the analysis is on the right track, the following parallel emerges across the interfaces: just like languages differ in the inventory of VI rules at PF, so will they
in the inventory of allosemy rules at LF.
The fourth question targeted the relation between APs and Number. The non-classificatory APs discussed
here, which overlap with the class of stubbornly distributive adjectives, do not only require the noun to be
individuated. n is responsible for individuating the nominal root; however, if this was the sole condition
that enabled AP-modification, we would expect number neutral nouns to occur with non-classificatory APs.
However, the fact that they do not signals that this class of modifiers is also sensitive to number and the noun
being minimally atomic or non-minimally so. Since that is the function of Num, then it follows that these
adjectives be adjoined at least as high as Num. In the absence of Num, there will be no structural position for
them to adjoin. The hypothesis that individuated atomic (non-)minimal NPs enable adjunction of this class
of APs receives support from classifier languages like Hungarian (Csirmaz and Dékány 2014; Dékány 2021)
or Teochew, Southern Min (Biggs and Zhuosi 2022). In Hungarian, for instance, non-classificatory APs
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including, but not limited to, size, length, height, weight are adjoined higher than classifiers whose function
issimilar to that of Number. Thus, the pattern that emerges is schematized in (101).
(101) AP{non-classificatory/dimensional} > {Num/ CL} > IND N.
The same logic can be applied for numerals. Only nouns that have atoms can be counted (Chierchia
1998b, 2010, 2021; Borer 2005a; Rothstein 2004, 2010, 2021). Moreover, in Alasha Mongolian, the CARD
head that introduces the numeral in its specifier selects for [SG], in the sense of Adger (2003); Müller (2010).
Therefore, their grammaticality is dependent on their being a NumP in the syntax: merger of CARD fails if
[Num: SG] is absent.
Last but not least, the Alasha Mongolian data have broader implications for theories of number, both in
terms of morpho-syntactic markedness and semantics. First, regarding the morpho-syntax of number and
its relation to the semantics, the data present a complication to analyses in which the singular vs. plural
distinction relies on the presence of uninterpretable number agreement (Ionin and Matushansky 2006, 2018;
Alexiadou 2019). One could perhaps build the argument that /-V:d/ is pure Agree(Num, n) in the case
of inanimates but this would face the challenge of PL-marked animate nouns and PL-marked NPs modified
by non-classificatory adjectives in attributive position. Besides, if the plural morpheme is uninterpretable
agreement, we would need to find an independent explanation for the inclusive/exclusive ambiguity. Instead,
the data supports an approach in which there is a one-to-one mapping from syntax to semantics and to
morphology: the morpho-syntactic expression of number on Num, spelled-out on the head noun, is always
semantically interpretable (see Pancheva 2021, 2022, for Bulgarian).
Furthermore, typologically, Alasha Mongolian patterns with Buriat (Bylinina and Podobryaev 2020) in
that both a subset of unmarked and plural-marked NPs are number neutral, with some restrictions. Given
the cross-linguistic data available, we can divide languages that distinguish between unmarked and plural
marked nouns into four types depending on the interpretation of the unmarked and plural-marked forms.
Type A includes languages in which the unmarked form of the NP is strictly singular (i.e. it denotes a
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singleton) and the plural-marked form is exclusively plural, e.g. Wolof (Fong 2021, 2023); Type B consists of
those languages where the unmarked form is strictly singular, but the plural-marked form may be inclusively
plural, e.g. English (Sauerland 2003; Sauerland et al. 2005; Zweig 2009), Spanish (Martí 2008, 2020a), and
animate nouns in Buriat (Bylinina and Podobryaev 2020) and Alasha Mongolian; Type C concerns languages
like Western Armenian (Bale et al. 2011; Bale and Khanjian 2014) or Brazilian Portuguese (Müller 2002;
Martí 2020a): the unmarked form is number neutral but the plural-marked one is exclusively plural; Type
D groups languages where nouns unmarked for number may be number neutral and so may plural-marked
nouns, e.g. inanimates in Buriat and Alasha Mongolian. These patterns are summarized on table 5.7, which
is an extended version of table 5.1.
28
Table 5.7: The interpretation of number in languages with unmarked and plural-marked forms (final version)
Unmarked NP PL-marked NP
SNG PLR SNG PLR
Type A Wolof ✓ * * ✓
Type B English ✓ * ✓ ✓
Spanish ✓ * ✓ ✓
Buriat[+anim.] ✓ * ✓ ✓
A. Mongolian[+anim.] ✓ * ✓ ✓
Type C W. Armenian ✓ ✓ * ✓
B. Portuguese ✓ ✓ * ✓
Type D Buriat[-anim.] ✓ ✓ ✓ ✓
A. Mongolian[-anim.] ✓ ✓ ✓ ✓
Type E unattested (yet) * ✓ ✓ *
I do not intend to provide an answer as to what is driving the variation between the different language
types. I leave this for future research. I want to indicate, though, that all these language types share two
general features: (i) unmarked forms must include at least single atoms in their extension, (ii) and PL-marked
ones must at least include their sums. In other words, the unmarked form must refer to at least a singleton,
28The ‘*’ means that the relevant morpho-syntactic expression (e.g. unmarked vs. PL-marked) cannot be associated with the
intended interpretation (e.g. SNG = singleton vs. PLR = plurality). If the relevant morpho-syntactic expression can be associated with
one interpertation, a ‘✓’ is assigned. This is so even if this interpretation is determined by certain factors (polarity, modification,
etc.).
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while the PL-marked one must refer to at least an exclusive plurality. We can, thus, formulate the (potentially
universal) generalization in (102):
(102) The morpho-semantic number markedness generalization
If a language makes a morphological distinction between unmarked and plural-marked forms in the
nominal domain,
a. the unmarked form must at least contain individual non-overlapping atoms; and
b. the plural-marked one must at least contain sums of atoms.
If this generalization is correct, it predicts that there should be no language of Type E on Table 5.7:
this would be a language in which unmarked forms of nouns denote exclusive pluralities (e.g. {𝑎𝑏, 𝑏𝑐, 𝑎𝑏𝑐})
whereas their plural-marked counterparts denote a singleton (e.g. {𝑎, 𝑏, 𝑐}). As far as I know, there is no
record of such a language, which is promising evidence for the universality of the generalization. Under the
proposed analysis here, such a language should be ruled out given that [SG] will restrict the denotation of
the noun to the minimal parts, i.e. non-overlapping atoms, while [PL] will restrict the extension of the noun
to the non-minimal atoms, i.e. the sums. In case Number was not projected, the theory predicts that the
result should be an unmarked number neutral noun. In the event that such a language is indeed attested, the
explanation for that pattern would have to be potentially found in the meaning of covert material shifting the
atomic structure of the predicate, obscuring the mapping from the morpho-syntax.29
29One may wonder whether languages with inverse number systems like Dangaare (Grimm 2010, 2012, 2018) or Kipsigis and
Didinga (Kouneli 2017, 2020) are a counterexample to the generalization. These languages have what is referred to as “inherently
plural” nouns: morphologically these nouns are unmarked in the plural, but an overt singulative affix surfaces when the noun is
interpreted as a singleton. Descriptively, the languages do not fit the generalization (because the singular is marked morphologically),
but they could be accommodated within the general insights of the generalization. According to Kouneli (2020), number in these
languages is split between a low position in n, where number is uninterpretable, and a high position in Number, where it is interpreted.
Kouneli argues that the structure of inherently plural nouns is as in (xxvii):
(xxvii) [NumP Num[PL] [nP n[PL] √ROOT]]
The two loci of number for inherently plural nouns in (xxvii) are both [PL], and when this happens a morphological operation called
Obliteration (Arregi and Nevins 2007), taking place before Vocabulary Insertion, deletes the higher number feature in Number if it
is identical to the low number feature in n. In the singular, they are marked because [SG] on Number is mapped to an overt exponent.
I would like to thank Maria Kouneli for discussion of this issue.
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All in all, we can summarize the significance of the study of Alasha Mongolian in 3 classes: (i) the
presence vs. absence of syntactic information may drive not only differences in exponence, but also yield
distinctions in interpretation; what this entails is that number neutrality can be syntactically encoded, rather
than lexically presupposed. Further evidence for this comes from looking at QAs. (ii) Number marking
cannot be reduced to uninterpretable agreement on the NP; instead, variation lies on the location, availability
and interpretation of number features in the nominal extended projection. (iii) Taken together these facts
have consequences for the type of predicates that numerals can combine with: singular predicates or plural
ones.
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Chapter 6
Conclusions
The primary aim of this dissertation has been to understand the grammatical encoding of being count and the
grammatical encoding of countability, by probing the count-mass distinction. At a general level, the countmass distinction raises the following questions that I outlined in the introductory chapter of this dissertation:
• What makes an NP count as opposed to mass?
• What do countable NPs, both count and mass, share in common? (i.e. do they form a natural class in
any way?)
• What determines variation?
We are now in a position to answer those questions and discuss the implications that the answers have for
linguistic theories. Building on insights from the previous literature, I have argued at length that we need to
separate individuation from number-marking. While these are closely related and interact in many non-trivial
ways, each of these pieces has their own morphological, syntactic and semantic import. An important analytic
conclusion that we arrive to by separating the two is that being count and being countable are decomposable
into different sets of elements. In particular, being count means both markedness for individuation and SG/PL
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in the syntax. Constituents that are marked for individuation, regardless of whether they are also numbermarked, display the property of countabilitiy, i.e. being countable. In this chapter I address the questions on
the list above by summarizing and discussing what I think are the key contributions of the dissertation.
6.1 Contributions of the dissertation
At an empirical level, the dissertation provides a comprehensive and theoretically informed description of
the count-mass distinction in English and Spanish. In order to probe what it means for a noun to be count as
opposed to mass, we need to look at the morpho-syntactic properties in (1). Descriptively speaking, being
count means having all the properties in (1). Having none or a restricted subset of these properties means
being mass.
(1) Being count (having count syntax)
a. the noun makes a singular/plural distinction;
b. the noun can be modified by cardinal numerals;
c. the noun can be modified by size/shape adjectives (Stubbornly Distributed adjectives);
d. the noun allows number mismatches under ellipsis;
e. the noun can be a target for one-substitution;
f. the noun is allowed to combine with certain determiners such as every, each or several.
Regarding countability, the key property is listed in (2). Nouns that can be measured along a cardinality
scale are countable, whereas those that cannot are non-countable. While singular count nouns are independently ruled out with measure words such as QAs, they can still be measured in terms of cardinality via
cardinal numerals (and in fact in many languages, the numeral requires the NP it modifies to be unmarked,
i.e. singular, e.g. Alasha Mongolian in Chapter 5 but see also Ionin and Matushansky 2018 for more cases).
(2) Being countable
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The noun allows measurement in terms of ‘cardinality’ when modified by measure expressions (e.g.
more, many or numerals...).
One of the takeaways of the dissertation is that being count is not a grammatical primitive or lexical
property of a certain syntactic category, but it is decomposable into two more abstract grammatical units:
markedness for Individuation and Number. Individuation is a feature that appears on nominal categorizers;
Number is a functional head that hosts number features such as [SG/PL]. These grammatical primitives are
distinct from each other and serve different syntactic, morphological and semantic purposes. A summary of
their functions is in Table 6.1.
Table 6.1: The roles of IND and Number
Syntax Morphology Semantics
IND - Enables Number
- Enables [COLL]
- Class 1,2,3 determiners
- [E]-marked for ellipsis
- Triggers QA-allomorphy
(in Mongolian)
- Undergoes one-substitution
under Number
- Selects for semi-lattices with atoms
and sums of atoms
- Enables measurement in terms of
CARDINALITY
Number - Singular/Plural agreement
- Enables adjectival modification
- Enables CARD hosting numerals
- Class 1,2,3,(4) determiners
- [E]-marked for ellipsis
- Marks [IND] for ellipsis
- Triggers QA-allomorphy
- Triggers Root allomorphy
- Spells out plural-marking
- Restrict the denotation to (non-)minimal parts
At an abstract level, we can now say that what makes a noun count is being marked for both [IND] and
[SG/PL] on Number. Mass nouns, however, are those that lack Number hosting [SG/PL]. But, they may be
[IND]-marked as is the case of object mass nouns. Features such as [PL] may but need not be restricted to the
Number terminal. In fact, they may be located lower in the structure. In that case, they will not be contingent
upon there being an [IND] feature.
In addition, depending on whether only [IND] is part of the derivation, the countability properties of the
noun will also differ. Count nouns (both singular and plural), object mass nouns and number neutral (count)
nouns are all [IND]-marked and enable measurement in terms of cardinality. This is what is expected under
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the Countability hypothesis I formulated in Chapter 4, repeated below. Thus, as summarized in Table 6.1,
the crucial property that distinguishes countable from non-countable nouns is markedness for individuation.
(32) The Countability Hypothesis
Being countable means being marked for individuation.
That said, we can establish a formal typology of noun classes based on their underlying features. This is
shown in Table 6.2.
Table 6.2: NP classes based on their underlying features
n1 n2 Number Ex.
Non-Countable Mass canonical Ø * * ‘water’
plural [PL] * * ‘dregs’
Countable object [IND] [COLL] * ‘jewelry’
Num. neutral unmarked [IND] * * ‘nom’ (book)
Count singular [IND] * [SG] ‘jewel’
plural [IND] * [PL] ‘jewels’
As shown in Table 6.2, all the nouns that are marked for [IND] are countable, regardless of whether they
are count or mass. Thus, it is possible that a noun is syntactically mass or does not project Number and
yet it is countable (e.g. object mass nouns and number-unmarked number neutral nouns). Nouns that are
unmarked for individuation features are non-countable. Looking at Table 6.2 there seems to be a correlation
between being count and being countable that I describe in the generalization in (3).
(3) The Count-Countability Generalization
Being count entails being countable, but being mass does not entail being non-countable.
Focusing on count NPs, they are among the most marked class when it comes to their grammatical
properties. This includes the choice of determiners. There is a restricted set of determiners that are only
acceptable with singular and plural-marked individuated nouns, but there is no single determiner that is
restricted to the domain of nouns unmarked for individuation. That is, a D with an unvalued ‘mass’ feature.
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The proposal in this dissertation is able to explain this fact and it is consistent with the hypothesis that ‘mass’
really means lack of count syntax (Doetjes 1997, 2021; Borer 2005a; Deal 2016a, 2017): water, dregs are
unmarked. For the languages analyzed, it was observed that if a D probes for [IND], it will also probe for
Number, which accounts for the fact that there is no object mass specific determiner. Whether this is a
universal or an area of cross-linguistic variation is an issues for future research. If there is a determiner that
is sensitive to [IND] and this is a feature that object mass nouns share with count nouns, we should expect
that determiner to be compatible with the two types of nouns. The closest that we got to this prediction being
borne out was QA allomorphy in Alasha Mongolian post-concord: olin seems to be conditioned by the nP
being marked for [IND]. Smith (2021) reports similar observations from Purépecha.1
One of the longstanding problems in the literature of the count-mass distinction is the status of object
mass nouns, which largely have mass syntax but some of their properties are co-extensive with the class of
count nouns: adjectival modification and measurement in terms of cardinality. A common solution is to
assume that this class of nouns is lexically different from ‘canonical’ mass, and in fact are identical to plural
count nouns, but they enter the syntax in a mass frame (Chierchia 1998a; Borer 2005a; Bale and Barner 2009;
Smith 2021). By looking at their morphological composition, I concluded that this could not be accurate;
namely, across languages the roots on which object mass nouns are formed are coextensive with count noun
roots. What is more, object mass nouns are morphologically more complex.
My solution to the object mass paradox has been to propose that object mass nouns syntactically contain
an individuated nP layer. Where they differ is in the feature that projects on top of n[IND]: [SG/PL] project
Number in the case of count nouns, whereas [COLL] projects in the case of object mass nouns. In English
and Spanish, I argued that the label of this projection was a nominalizer n which competes with Number
for merger. This provides a natural explanation for the lack of pluralized object mass as well as the lack of
1
In the event that these are rare or unattested, we should not think about this as a weakness of the theory. A similar empirical
situation, I believe, is observed with gender: while determiners may be sensitive to both gender and number, as far as I know
determiners that require the NP goal to have a particular gender (i.e masculine, feminine, neuter) regardless of number marking are
not generally reported. We could think about the potential lack or scarcity of [IND]-only determiners in the same way, in particular
if both gender and individuation features are located on n.
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numeral modification. However, languages might differ as to the location of the [COLL] feature. If it is on
n, no numeral modification is possible (English/Spanish), but if it is on Number we would expect numeral
modification to be allowed. I showed that this prediction is borne out in Czech (Grimm and Docekal 2021),
where the [COLL] feature is spelled out on the noun and numeral modifiers.
This fully decompositional approach to the object mass paradox does not negatively impact the semantics.
In fact it enables to formulate a uniform generalization regarding when ‘QA+N’ can be interpreted in terms
of cardinality. What matters is that the constituent to be measured denotes an individuated plurality. The
generalization entails that as long as the constituent is generated from the set of atoms and has sums of atoms
(though it may contain the single atoms as well), the value of the dimension of measurement is cardinality.
Both object mass nouns and plural count nouns conform to this description. The assignment of the value
as ‘cardinality’ is thus predictable given the syntax in tandem with the semantic properties of the target
constituent. This approach makes more language internal and cross-linguistic predictions than lexicalistbased approaches that correlate a certain surface form to a particular semantic interpretation, e.g. Form1 →
DIMENSION𝐴; Form2 → DIMENSION𝐵. The formulation of the generalization in the more abstract terms (i)
makes it a good candidate for a language universal and (ii) enables us to maintain a modular view of the
grammar (Chomsky 1986, 1995, 2000, 2001, 2008; Halle and Marantz 1993; Marantz 1997, 2001; Arad
2003, among others).
We have been able to accommodate the category of number neutral nouns which are unmarked for number. These nouns like (unmarked) mass nouns, which are generally referred to as being number neutral
(Krifka 1989; Chierchia 1998b), cannot be modified by numerals and stubbornly distributive adjectives, and
are cumulative. However, despite them both being closed under sum, they correspond to different semilattices: countable number neutral nouns are generated from the set of atoms while mass nouns are not. This
is evidenced from the fact that QA+number neutral nP results in a cardinality interpretation. As a result, only
countable number neutral nouns but not mass nouns allow Number to project, if there is morpho-syntactic
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evidence to do so; as a result, when Number is projected, they are turned into regular count nouns and as such
they display all the properties of this class including modification by stubbornly distributive adjectives and
cardinal numerals. What is more the investigation of number neutral NPs sheds light on the restriction for adjectival modification across languages: modification by the class of adjectives that are referred as stubbornly
distributive, at least in the domain of attributive adjectives, is syntactically conditioned. In this respect, the
class resembles cardinal numeral modifiers.
Before concluding, I want to address the status of variation. Languages might differ as to whether Number
is projected and the location of the relevant features. For example, the fact that expression X is count mueble
in one language but mass in another is accounted for by saying that the former expression has Number whereas
the latter does not. Similarly, we can say that the reason the Czech counterparts of English object mass nouns
can be modified by numerals is because [COLL] is a Number feature in the former language but not in the latter.
As a result of there being Number, the functional head that hosts numerals can be merged. In this regard, we
can conclude that variation is syntactic.
However, there is also variation in the domain of nominal flexibility and shifts across classes, e.g. containers, grinding etc. The variation here is much less systematic with some roots being more prone to participate
in the shifts and others being less so. This fact is observed within the same language but also across languages. For instance, in English it is more acceptable to obtain a container interpretation with water than it
is with blood: we ordered two waters for the table vs. ??the doctor ordered two bloods for his patient in the
OR. In Nez Perce, there do not seem to be such restrictions as reported by Deal (2016a, 2017), whereas in
Mongolian the changes are even more restricted than in English. The proposal that I have developed here
provides an answer: it is syntactically conditioned lexical variation. In other words, variation in this domain
results from the way that the syntax puts terminal nodes together in concert with the satisfaction of the different requirements at the interfaces (both PF and LF). A very important part of this variation is the ability
to license roots: the assignment of a vocabulary item for the root in the given syntactic configuration and
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the assignment of a meaning for the root in the given syntactic context. When it comes to root licensing at
LF, we observed that the mass interpretation of a root (i.e. the STUFF concept) was the application of the
elsewhere allosemy rule, i.e. the default, whereas shifting entailed a context sensitive and more marked rule.
The inability to map the root to the more marked concept in that particular syntactic configuration results in
an unlicensed root, which cannot be interpreted during the semantic computation.
6.2 Moving forward
Classifiers. There are many ways in which the count-mass distinction is instantiated cross-linguistically.
Here I have focused on overt number-marking languages, that do not have classifiers. A natural empirical
domain to be probed next is languages that have classifiers. Some examples are Mandarin or Cantonese
(Krifka 1995; Chierchia 1998b; Cheng and Sybesma 1999), Bangla (Dayal 2014; Biswas 2016), or Vietnamese (Simpson and Ngo 2018) to name a few. As observed by Cheng and Sybesma (1999), classifiers in
Mandarin for instance, are sensitive to whether the noun the modify is ‘count’ or ‘mass’. Does this go against
the hypothesis that mass nouns are unmarked? Difficult to say, especially if the ‘mass’ classifier in question
is itself an individuated lexical item that refers to a unit or container (Cowper and Hall 2014). In addition,
these languages have a series of measure expressions and quantificational determiners that seem to be sensitive to the noun being individuated or not (Bale and Gillon 2020): mēi ‘each’ and liáo-liáo-wú-jĩ ‘very few’
are compatible with individuated nouns only. These restrictions seem similar, at least at face value, to what
we observed here, which re indeed syntactic. But only an in-depth investigation of the full nominal system
can shed light on the actual generalizations and how the theory can handle them.
Shifts and nominal flexibility. In Czech, grinding and packaging shifts are unacceptable as reported by
Grimm and Docekal (2021). On the one hand, the situation resembles Alasha Mongolian where packaging
of mass is not acceptable. On the other, Czech differs from both Alasha Mongolian and English because
245

interpreting an otherwise count noun as mass (i.e. grinding) is also precluded. Czech is in fact the mirror
image of Nez Perce (Deal 2016a, 2017) and Yudja (Lima 2014), where roots have a larger degree of flexibility.
Can we maintain the same explanation we gave for English and Spanish? Namely, roots are not properly
licensed at the interfaces and this is what precludes the ‘shifts’. Or is there something structurally different
between the types of languages described?
Individuation, number and measurement in the VP. It has been observed that there exists a parallelism
between mass/count and atelic/telic predicates (Mourelatos 1978; Bach 1986a; Krifka 1989; Borer 2005a,b;
van Geenhoven 2005; Wellwood et al. 2012). On the one hand, telic parallels count and atelic mass; on
the other, number on NPs parallels grammatical aspect on VPs: perfective and progressive involve singular
events whereas imperfective-habitual involves plural events. An immediate question that arises is whether
we can have a uniform theory of individuation and number across domains. In other words, how are the
features {IND, SG, PL, COLL} distributed in the VP and how do they interact with argument structure?
In addition, the grammatical properties of the NP/VP domain being measured affect the choice of dimension of measurement. These properties are summarized in Table 6.3, but see Wellwood et al. (2012) for
more details.
Table 6.3: Dimensions of measurement by NP and VP type
Schwarzschild (2006): NP domain Wellwood et al. (2012): VP domain
Type of NP Dimension of measurement Type of VP Dimension of measurement
canonical mass VOLUME, WEIGHT atelic (homogenous) DURATION, DISTANCE
object mass CARDINALITY atelic (non-homogenous) CARDINALITY
PL-count CARDINALITY IMPF-telic CARDINALITY
SG-count * PERF-telic *
These facts are also important for the Cardinality Generalization Redux. Can we extend the syntactic approach to measure expressions to the VP domain? In particular, if object mass parallel atelic non-homogeneus
activities we would expect their underlying syntax to be the same: {[v/n[COLL]], [v/n[IND]]}. Likewise, plural
246

count and imperfective telic should be composed of the same feature bundles: {[Number[PL]], [v/n[IND]]}.
The goal of answering these questions and verifying the predictions is developing a parsimonious theory is
applicable cross-categorially.
247

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Asset Metadata

Creator Toquero Perez, Luis Miguel (author)

Core Title The grammar of individuation, number and measurement

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Linguistics

Degree Conferral Date 2024-08

Publication Date 06/27/2024

Defense Date 05/31/2024

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag count-mass distinction,English,linguistics,measurement,Mongolian,morphology,noun phrases,number,semantics,Spanish,syntax

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Pancheva, Roumyana (committee chair), Wellwood, Alexis (committee chair), Major, Travis (committee member), Rudin, Deniz (committee member), Uzquiano, Gabriel (committee member)

Creator Email l.toquero@hotmail.com,toquerop@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113997AJ1

Unique identifier UC113997AJ1

Identifier etd-ToqueroPer-13166.pdf (filename)

Legacy Identifier etd-ToqueroPer-13166

Document Type Dissertation

Format theses (aat)

Rights Toquero Perez, Luis Miguel

Internet Media Type application/pdf

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Source 20240701-usctheses-batch-1176 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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