NUMBER AND INDIVIDUATION A DISSERTATION SUBMITTED TO THE DEPARTMENT OF LINGUISTICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Scott Grimm August 2012 Abstract This dissertation investigates the semantic foundations of nominal countability. Standard accounts are typically concerned with a binary distinction between countable words (dog/ dogs) and non-countable words (water). This dissertation examines this issue from the perspective of languages with richer grammatical number systems. I develop a typological generalization that countability is a scalar phenomenon and propose new techniques to formally model these facets of nominal semantics by augmenting standard mereological accounts with topological relations. Languages such as Welsh or Maltese grammatically recognize what I call aggregate nouns—nouns which designate entities that habitually come together, such as insects (ants) or granular substances (sand). These nouns are grammatically distinct from both non- countable nouns and countable nouns with a singular/plural contrast, instead they display a collective/singulative contrast. These grammatical number systems vividly demonstrate how a binary countable/non-countable distinction oversimplifies the typological space. I argue from the data from Welsh and Maltese, and even more complex fieldwork data from the Gur language Dagaare, that countability is a scalar phenomenon. I propose that the morphosyntactic organization of grammatical number systems re- flects the semantic organization of noun types according to the degree of individuation of their referents. Nouns of different types are individuated to different degrees and can ac- cordingly be ordered along a scale of individuation: substances < granular aggregates < collectives < individual entities. Noun types which are less individuated are on the lower end of the scale and are cross-linguistically less likely to signal grammatical number, while the converse holds for highly individuated noun types. Understanding morphosyntactic number categories in light of a scale of individuation avoids the difficulties binary accounts iv face, since languages may divide up the scale of individuation into any number of classes and at different points. For instance, languages with a collective/singulative recognize a grammatical number category corresponding to the middle region of the scale. At the same time, the proposal provides a predictive framework for how grammatical number systems are organized: the contrasts being made are common across languages, and, as a corollary, the endpoints of the scale (substances and individual entities) are predicted to be stable across languages. I show that this view of countability also answers many of the standard criticisms of accounts where a noun’s meaning determines its grammatical behavior with respect to number marking. I explore the implications of this broader typological view for formal semantic treat- ments of countability. Standard mereological accounts turn out to be not sufficiently expres- sive to model the aggregate nouns nor the grammatical number systems which distinguish them. I enrich the standard mereology framework with topological connection relations, resulting in the more expressive “mereotopology”. Through using different connection re- lations, this framework is able to represent aggregate nouns and the ways in which entities may come together. Consequently, this framework is able to deliver analyses of particular grammatical number systems, such as Welsh. In addition, this more expressive framework resolves several recalcitrant problems noted for many treatments of countability, such as the “minimal parts” problem discussed in relation to nouns such as sand or furniture which, while non-countable, still have minimal pieces. v Acknowledgements This dissertation has benefitted from a large number of people who have advised me, pro- vided insights and criticisms, and who have generally helped me to develop as a linguist. First and foremost, I would like to thank my dissertation advisor Beth Levin. She has given me guidance in matters large and small throughout my time at Stanford—practically every aspect of my graduate career has benefitted from her advice. She has also been an ideal advisor for me. She has a rare ability to make the right suggestion at the right time, simul- taneously leaving much freedom in how to follow up on the suggestion. I have learned an enormous amount working with her. For this, and much more, I am grateful. The other members of my committee have had a similarly large influence on my de- velopment. Paul Kiparsky’s breadth and depth of knowledge has been a source of awe for me throughout my graduate career. Many of the most thrilling intellectual moments of my graduate studies occurred in his classes and in meetings with him. In the context of this dissertation, he has been particularly helpful in both drawing my attention to many portions of my thinking which needed clarity as well as to encouraging me to always re- late my proposals to the big questions. Chris Potts has provided me with extremely useful counsel during the course of this dissertation, and also advised me on projects concern- ing plurality that led up to the dissertation. I have consistently enjoyed being exposed to his infectious enthusiasm for innovative approaches in linguistics and have learned much about semantics, among many other things, through our interactions. I met Donka Farkas through various Bay Area semantics events and it has been a true privilege to have her as part of my committee. I am grateful to her for all the insights she has shared with me about plurals, markedness and semantic theory during our meetings on the idyllic UC Santa Cruz campus. I would also like to thank Tom Wasow for his participation in my dissertation vi defense and for much valuable advice throughout my time at Stanford. This dissertation grew out of my fascination with the Dagaare inverse number marking system. Arto Anttila and Adams Bodomo introduced me to the problem during my first year at Stanford and have provided encouragement for my work on it ever since. Thanks to Adams Bodomo, I got into contact with Mark Ali at the University of Education in Winneba, Ghana. Mark Ali devoted an enormous amount of time to working with me on Dagaare during two trips to Ghana—simply put, this dissertation would not have come into being without him. I can never thank him enough for his generosity, insight, and friendship. As my dissertation research progressed, I gained much from conversations with Dave Barner, Jade Comfort, Cleo Condoravdi, Hana Filip, Jeff Good, Peggy Li, John Lucy, Frank Seifart, and Henriette¨ de Swart. I would also like to thank the members of the “Mass- Count Collective”: David Clausen, Alex Djalali, Sven Lauer, and Tania Rojas-Esponda. Our weekly meetings during Spring Quarter of 2010 shaped many aspects of my thinking which became foundational for this dissertation. During the final phase, Nadine Borchardt, Dan Lassiter, Tania Rojas-Esponda, and Middy Tice provided proof-reading and many valuable comments. Part of the research for this dissertation was carried out during stays in Berlin, Germany. My first stay was as a guest researcher at Zentrum fur¨ Allgemeine Sprachwissenschaft (ZAS). I would like to thank Manfred Krifka and Barbara Stiebels for arranging for that stay, as well as providing me with office space on a subsequent visit, as well as to thank my ZAS colleagues for such a stimulating environment. I also would like to thank Tom Guldemann¨ for supporting me during a second stay in Berlin as a Deutscher Akademis- cher Austauschdienst (DAAD) scholar at Humboldt University. During these stays, I had the pleasure of engaging with the vibrant linguistics community in Berlin. In particular, I would like to thank Laura Downing, Ines Fielder, Gudrun Miehe, Anne Schwarz, Ker- stin Schwabe, Stephanie Solt, Uli Sauerland, Frank Seifart, Tonjes Veenstra, and Malte Zimmermann. A large part of the richness of my graduate experience has been of course due to my fel- low students. I would like to thank my cohort with whom I have spent a most enjoyable six years: Matthew Adams, Uriel Cohen Priva, Marie-Catherine de Marneffe, Jason Grafmiller, and Tyler Schnoebelen. Marie-Catherine deserves special mention: office-mate, frequent vii co-author, and friend, she has also single-handedly prevented my French from falling into total ruin during the last six years. Merci! During my time at Stanford, I have over- lapped with many other students who have provided me with stimulating conversations about linguistics as well as good times. Inbal Arnon, Lucas Champollion, Liz Coppock, Alex Djalali, Itamar Francez, Roey Gafter, Lauren Hall-Lew, Philip Hofmeister, Andrew Koontz-Garboden, Tatiana Nikitina, Lis Norcliffe, Nola Stephens, and Hal Tily—thank you all. I gratefully acknowledge the financial support I have received for the research under- taken in this dissertation: a National Science Foundation Dissertation Improvement Grant (Grant No. 1023289, P.I. Beth Levin), a Stanford Center for African Studies Summer Fel- lowship, a Graduate Research Opportunity Grant from Stanford University and a Deutscher Akademischer Austauschdienst (DAAD) Visiting Scholar Grant. Finally, I would like to thank my family who has provided me with a constant source of love and all manners of support during the various stages of my life. I am especially grateful to my parents who