{"Affiliation":[{"label":"Affiliation","value":"Arts, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Linguistics, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"Aggregated Source Repository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Assis Navarro, Michel","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"Date Available","value":"2024-08-29T18:18:33Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"Date Issued","value":"2024","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree (Theses)","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"Degree Grantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"This thesis investigates the semantics of nominal countability and scope properties of bare nouns (BNs) in Kaingang (J\u00ea, Brazil). The analysis given here ties together these two phenomena by showing that the scope patterns of BNs in Kaingang, and across languages, are contingent on properties underlying countability distinctions. My main claim is that quantization underlies the count interpretation of Kaingang BNs and their variable-scope effects. The thesis also explores the theoretical and typological implications of this analysis. First, I address countability in Kaingang. The main claim is that all Kaingang nouns are count nouns. This hypothesis is supported by several morphosyntactic and semantic properties of nouns in the language. For instance, Kaingang allows numerals and other count quantity expressions to combine directly with individual and substance nouns, and in quantity judgement tasks comparisons with both types of nouns are cardinality-based. I analyze this generalized counting strategy as an effect of the lexical semantics of nouns. Building on Krifka\u2019s approach (1989, 2007), I argue that all Kaingang nouns are lexically quantized, i.e., they are equipped with a context-sensitive counting function that measures quantities in terms of individual- or portion-units. Second, I examine the scope behavior of BNs in Kaingang and its relevance to the study of variation in the scope of BNs across languages. I show that Kaingang BNs exhibit variable scope in relation to other operators. Using a type-shifting framework (Partee 1986; Krifka 2003), I analyse Kaingang indefinite BNs as predicate NPs mapped into arguments via a choice function type-shifter (CF) which gets existentially closed at any level in the clausal spine (Reinhart 1997). I argue that the difference in scope properties between variable-scope BNs and narrowest-scope BNs is linked to the quantized\/cumulative opposition of the predicates they express: the former are quantized predicates, while the latter are cumulative ones. I claim that variable-scope BNs and narrowest-scope BNs are created by two distinct type-shifters: the former by a CF operator and the latter by Krifka\u2019s \u2203 operator (Krifka 2003). I further propose that both operators are sensitive to the quantized\/cumulative opposition and model this sensitivity via presuppositions carried by them.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"Digital Resource Original Record","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/89098?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"Full Text","value":" i QUANTIZATION AND QUANTIFICATION: COUNTABILITY AND SCOPE OF BARE NOUNS IN KAINGANG AND BEYOND by Michel Assis Navarro B.A., State University of Maring\u00e1, 2008 M.A., University of S\u00e3o Paulo, 2012 Ph.D., University of S\u00e3o Paulo, 2017 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Linguistics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2024 \u00a9 Michel Assis Navarro, 2024 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Quantization and Quantification: Countability and Scope of Bare Nouns in Kaingang and Beyond submitted by Michel Assis Navarro in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Linguistics. Examining Committee: Hotze Rullmann, Professor, Linguistics, UBC Supervisor Lisa Matthewson, Professor, Linguistics, UBC Supervisory Committee Member Marcin Morzycki, Professor, Linguistics, UBC Supervisory Committee Member Henry Davis, Professor, Linguistics, UBC University Examiner Ori Simchen, Professor, Philosophy, UBC University Examiner Jenny Doetjes, Professor, Centre for Linguistics, Leiden University External Examiner iii Abstract This thesis investigates the semantics of nominal countability and scope properties of bare nouns (BNs) in Kaingang (J\u00ea, Brazil). The analysis given here ties together these two phenomena by showing that the scope patterns of BNs in Kaingang, and across languages, are contingent on properties underlying countability distinctions. My main claim is that quantization underlies the count interpretation of Kaingang BNs and their variable-scope effects. The thesis also explores the theoretical and typological implications of this analysis. First, I address countability in Kaingang. The main claim is that all Kaingang nouns are count nouns. This hypothesis is supported by several morphosyntactic and semantic properties of nouns in the language. For instance, Kaingang allows numerals and other count quantity expressions to combine directly with individual and substance nouns, and in quantity judgement tasks comparisons with both types of nouns are cardinality-based. I analyze this generalized counting strategy as an effect of the lexical semantics of nouns. Building on Krifka\u2019s approach (1989, 2007), I argue that all Kaingang nouns are lexically quantized, i.e., they are equipped with a context-sensitive counting function that measures quantities in terms of individual- or portion-units. Second, I examine the scope behavior of BNs in Kaingang and its relevance to the study of variation in the scope of BNs across languages. I show that Kaingang BNs exhibit variable scope in relation to other operators. Using a type-shifting framework (Partee 1986; Krifka 2003), I analyse Kaingang indefinite BNs as predicate NPs mapped into arguments via a choice function type-shifter (CF) which gets existentially closed at any level in the clausal spine (Reinhart 1997). I argue that the difference in scope properties between variable-scope BNs and narrowest-scope BNs is linked to the quantized\/cumulative opposition of the predicates they express: the former are quantized predicates, while the latter are cumulative ones. I claim that variable-scope BNs and narrowest-scope BNs are created by two distinct type-shifters: the former by a CF operator and the latter by Krifka\u2019s \u2203 operator (Krifka 2003). I further propose that both operators are sensitive to the quantized\/cumulative opposition and model this sensitivity via presuppositions carried by them. iv Lay Summary The main goal of this thesis is to investigate countability (in particular, the count\/mass opposition) and the scope properties of argumental bare nouns in Kaingang, a J\u00ea language spoken in southeastern and southern Brazil by the Kaingang people. Kaingang is an understudied Indigenous language spoken by about 20,000 people, mostly living in four states of Brazil: S\u00e3o Paulo, Paran\u00e1, Santa Catarina, and Rio Grande do Sul. Argumental BNs are nouns that can occur in argument positions, i.e., in subject or object positions, without any elements such as determiners, number morphemes, or classifiers. In this thesis I show that Kaingang (bare) nouns are number neutral, i.e., they make no semantic distinction between singular and plural interpretations, and I claim that they are all count nouns. This is the first systematic analysis of BNs in Kaingang, focusing on countability and scope, and the first study of both phenomena in the language from the perspective of formal semantics. This dissertation gives a unified analysis of these properties using the semantic concept of \u201cquantization\u201d. v Preface This thesis is original work by the author. I wrote all chapters in it. Some of the content of this thesis has been presented at conferences. Large parts of Chapter 4 were published in the journal Glossa: A journal of general linguistics 9(1), in 2024, under the title \u2018Nominal Countability in Kaingang and Beyond\u2019. A version of Chapter 5 is currently under review by a journal. Ethics approval for this research was granted by the UBC Research Ethics Board (REB) \u23af\tH21-01808. vi Table of Contents Abstract .......................................................................................................................................... iii Lay Summary ................................................................................................................................. iv Preface ............................................................................................................................................. v Table of Contents ........................................................................................................................... vi List of Tables .................................................................................................................................. x List of Figures ................................................................................................................................ xi Abbreviations ............................................................................................................................... xiii Acknowledgments ......................................................................................................................... xv Dedication ................................................................................................................................... xvii Chapter 1: Introduction ................................................................................................................... 1 1.1 Preamble ......................................................................................................................... 1 1.2 An overview of empirical and theoretical proposals ...................................................... 1 1.3 Structure of the thesis ...................................................................................................... 8 Chapter 2: The People and their Language ................................................................................... 10 2.1 Introduction ................................................................................................................... 10 2.2 The people and their lands ............................................................................................ 10 2.3 The language ................................................................................................................. 16 2.4 Kaingang grammar ........................................................................................................ 20 2.4.1 Phonology ................................................................................................................ 21 2.4.2 The pronoun system ................................................................................................. 26 2.4.3 Word order ............................................................................................................... 30 2.4.4 The case system ....................................................................................................... 33 vii 2.4.5 A brief note on relative clauses ............................................................................... 34 2.4.6 Bare noun distribution ............................................................................................. 36 2.5 Number and number neutrality ..................................................................................... 38 2.6 (In)definite and generic interpretations ......................................................................... 42 2.6.1 Indefinite interpretation ........................................................................................... 42 2.6.2 Definite interpretation .............................................................................................. 46 2.6.3 Generic interpretation .............................................................................................. 48 2.7 Numerals ....................................................................................................................... 49 2.8 Other quantity words ..................................................................................................... 50 2.9 Verbal number .............................................................................................................. 52 2.10 Fieldwork methodology ................................................................................................ 55 Chapter 3: Mereology-based and Type-shifting Approaches ....................................................... 62 3.1 Introduction ................................................................................................................... 62 3.2 Mereology-based semantics .......................................................................................... 62 3.2.1 Link\u2019s two-domain theory: atomic vs. nonatomic predicates .................................. 63 3.2.2 A note on plurals ...................................................................................................... 70 3.2.3 Krifka\u2019s undetermined mereology: quantized vs. cumulative predicates ................ 74 3.2.4 Object mass nouns, fence-type count nouns, and doublets ...................................... 79 3.3 Type-shifting semantics ................................................................................................ 82 Chapter 4: Nominal Countability in Kaingang and Beyond ......................................................... 92 4.1 Introduction ................................................................................................................... 92 4.2 Concrete units all over the place ................................................................................... 93 4.2.1 Numerals .................................................................................................................. 93 4.2.2 Quantity words ........................................................................................................ 97 4.2.3 Count adjectives .................................................................................................... 102 4.2.4 Plural pronouns ...................................................................................................... 104 4.2.5 Reciprocals ............................................................................................................ 105 viii 4.3 Quantity comparisons ................................................................................................. 108 4.3.1 M\u1ebd \u2018more\u2019 .............................................................................................................. 108 4.3.2 E \u2018many\u2019 ................................................................................................................ 112 4.3.3 M\u00e1g \u2018big\u2019 ............................................................................................................... 114 4.4 A brief note on container words .................................................................................. 117 4.5 The analysis ................................................................................................................ 121 4.5.1 The semantics of Kaingang nouns ......................................................................... 121 4.5.2 Extending the analysis to Yudja ............................................................................ 134 4.6 A challenge for the analysis ........................................................................................ 139 4.7 Crosslinguistic\/typological and other theoretical contributions ................................. 145 Chapter 5: Scope Effects of Bare Nouns in Kaingang and their Crosslinguistic Implications ... 148 5.1 Introduction ................................................................................................................. 148 5.2 Scope taking ................................................................................................................ 150 5.2.1 Negation ................................................................................................................. 150 5.2.2 Intensional verbs .................................................................................................... 155 5.2.3 Universal quantifier ............................................................................................... 157 5.2.4 If-clauses ................................................................................................................ 159 5.2.5 Frequency adverbials ............................................................................................. 162 5.2.6 Intermediate scope ................................................................................................. 163 5.2.7 Substance bare nouns ............................................................................................. 167 5.3 Type-shifting approaches to narrowest-scope BNs .................................................... 169 5.3.1 Chierchia\u2019s kind-based analysis ............................................................................ 170 5.3.2 Krifka\u2019s predicate-based analysis .......................................................................... 175 5.4 A choice function analysis of Kaingang BNs ............................................................. 178 5.4.1 Background on choice functions ........................................................................... 178 5.4.2 The analysis ........................................................................................................... 180 5.5 Bare noun denotations and scope ................................................................................ 193 5.5.1 Scope and the quantized\/cumulative distinction ................................................... 193 ix 5.5.2 A note on Hebrew bare singulars .......................................................................... 199 Chapter 6: Conclusion ................................................................................................................. 205 Bibliography ............................................................................................................................... 209 x List of Tables Table 1: Macro-J\u00ea family. ............................................................................................................ 18 Table 2: The dialects of Kaingang. .............................................................................................. 20 Table 3: Kaingang consonants. .................................................................................................... 21 Table 4: Consonant-orthography correspondences. ..................................................................... 23 Table 5: Oral vowels. ................................................................................................................... 23 Table 6: Nasal vowels. ................................................................................................................. 24 Table 7: Vowel-orthography correspondences. ........................................................................... 25 Table 8: Personal pronouns. ......................................................................................................... 26 Table 9: Kaingang bare noun interpretations. .............................................................................. 49 Table 10: Semantic properties of nouns. ...................................................................................... 69 Table 11: Substance bare nouns. ................................................................................................ 108 Table 12: Stimulus nouns. .......................................................................................................... 109 Table 13: Enriched nominal type-shifting inventory. ................................................................ 192 Table 14: Scope of indefinite bare nouns across languages. ...................................................... 197 xi List of Figures Figure 1: Federal units of Brazil. ................................................................................................. 13 Figure 2: Current official Kaingang lands. .................................................................................. 14 Figure 3: The Indigenous land of Rio das Cobras. ...................................................................... 15 Figure 4: Territorial distribution of language families. ............................................................... 17 Figure 5: Territorial distribution of the Macro-J\u00ea languages. ...................................................... 19 Figure 6: renhte \u2018milk\u2019. ................................................................................................................ 57 Figure 7: v\u1ebdnh kuri \u2018flour\u2019. .......................................................................................................... 58 Figure 8: Building houses. ........................................................................................................... 59 Figure 9: Intermediate reading scenario. ..................................................................................... 60 Figure 10: Atomic join-semilattice structure (individuals). ......................................................... 66 Figure 11: Atomic join-semilattice structure (stuff\/matter). ........................................................ 66 Figure 12: Inclusive versus exclusive plurals. ............................................................................. 73 Figure 13: Quantized set. ............................................................................................................. 75 Figure 14: Cumulative set. ........................................................................................................... 75 Figure 15: Type-shifting inventory. ............................................................................................. 84 Figure 16: The kitchen scenario. .................................................................................................. 96 Figure 17: The puddles of blood scenario. ................................................................................ 105 Figure 18: The puddles of water scenario. ................................................................................. 106 Figure 19: The piles of flour scenario. ....................................................................................... 107 Figure 20: renhte \u2018milk\u2019. ............................................................................................................ 110 Figure 21: v\u1ebdnh kuri \u2018flour\u2019. ...................................................................................................... 110 Figure 22: n\u0129gja \u2018bench\u2019. ........................................................................................................... 111 Figure 23: kakan\u1ebd \u2018fruit\u2019. ........................................................................................................... 111 Figure 24: v\u00e3fe \u2018string\u2019. .............................................................................................................. 111 Figure 25: kur \u2018fabric\u2019. ............................................................................................................... 112 Figure 26: v\u1ebdnh kuri \u2018flour\u2019. ...................................................................................................... 113 Figure 27: v\u1ebdnh kuri \u2018flour. ........................................................................................................ 115 Figure 28: kur \u2018fabric\u2019. ............................................................................................................... 115 xii Figure 29: kakan\u1ebd \u2018fruit\u2019. ........................................................................................................... 115 Figure 30: kyv\u00e9nh \u2018blood\u2019. ......................................................................................................... 116 Figure 31: renhte \u2018milk\u2019. ............................................................................................................ 117 Figure 32: The two-bucket scenario. ......................................................................................... 119 Figure 33: The one-bucket scenario. .......................................................................................... 119 Figure 34: The two-bottle scenario. ........................................................................................... 120 Figure 35: The kitchen scenario. ............................................................................................... 127 Figure 36: kyv\u00e9nh \u2018blood\u2019. ......................................................................................................... 139 Figure 37: kakan\u1ebd \u2018fruit\u2019. ........................................................................................................... 139 Figure 38: F\u00f3gt\u1ebd goes fishing. ................................................................................................... 151 Figure 39: F\u00f3gt\u1ebd goes fishing. ................................................................................................... 151 Figure 40: Building one house. .................................................................................................. 158 Figure 41: Building houses. ....................................................................................................... 158 Figure 42: Wide scope context. ................................................................................................. 164 Figure 43: Intermediate scope context. ...................................................................................... 164 Figure 44: Narrow scope context. .............................................................................................. 165 Figure 45: Puddles of blood. ...................................................................................................... 168 Figure 46: Intermediate scope context. ...................................................................................... 191 xiii Abbreviations 1PL first-person plural 1SG first-person singular 1P.PL first-person possessive plural 1P.SG first-person possessive singular 2PL second-person plural 2SG second-person singular 2P.PL second-person possessive plural 2P.SG second-person possessive singular 3 third person 3PL.F third-person plural feminine 3PL.M third-person plural masculine 3SG.F third-person singular feminine 3SG.M third-person singular masculine 3P.PL.F third-person possessive plural feminine 3P.PL.M third-person possessive plural masculine 3P.SG.F third-person possessive singular feminine 3P.SG.M third-person possessive singular masculine ABS absolutive ACC accusative ASP aspect CL classifier DAT dative ERG ergative FUT future HAB habitual MOD modal NEG negation NOM nominative xiv PFV perfective Q question marker RECP reciprocal RED reduplication TOP topic xv Acknowledgments To begin, I would like to express my deepest appreciation to the Kaingang consultants who generously shared their knowledge of the Kaingang language with me and provided the core data in this thesis: Darci F\u00f3gt\u1ebd Bernardo, Cristielly Pak\u00f3j Bandeira, and Danusa K\u00f3rig Bernardo Fernandes. I would like to extend my sincere thanks to my friend Cristina Bandeira, who introduced me to the Indigenous territory of Rio das Cobras, its community and consultants. Many thanks to the Kaingang community of Rio das Cobras for welcoming me over these years. To my supervisor, Hotze Rullmann, I am extremely grateful to you for your constant guidance, insightful thoughts, suggestions, and valuable comments throughout my Ph.D. They had an immeasurable impact on the progression of my research. Without your supervision, encouragement, and our discussions, I would not have made it this far. Moreover, thank you for being a model of a researcher and a professor to look up to. I also owe a huge debt of gratitude to the other members on my committee. Thanks to Lisa Matthewson, an extraordinaire linguist. Your insightful comments and lovely encouragement helped me to polish and improve this thesis considerably. The research paths you have opened in the semantics of indigenous languages are a compass for everyone in the field. Thanks to Marcin Morzycki for your thoughtful comments and suggestions. I am also grateful to you for always pushing me to think harder about the theoretical implications of my analyses. My thinking and research have immeasurably benefited from all our discussions. Many thanks to my university examiners, Henry Davis and Ori Simchen, for your insightful comments on this work. It greatly benefited from them. Special thanks to Henry Davis for teaching me a lot about the syntax-semantics interface and for making a better writer out of me. Your energy and sharp mind are admirable. I am also extremely grateful to Jenny Doetjes, the external examiner, for all your thoughtful comments. They have improved this work considerably. I would also like to thank the UBC Semantics Reading Group for giving me not only the opportunity to present and discuss my works, but also the chance to learn from the great works of professors and graduate students in the department. I wish to thank all my professors at UBC during my Ph.D. I cannot measure how much I have learned from you over these years. Many thanks to the Department of Linguistics at UBC for xvi its welcoming atmosphere and for hosting a vibrant community of linguists and students committed to uncovering the principles and rules underlying the structures of natural languages, in particular under-represented languages. I must also thank Amy Rose Deal, Roberta Pires de Oliveira, and Suzi Lima for discussing the core data in this work with me and providing valuable comments and suggestions. To my fellow graduate students, thank you for the laughs, discussions, and encouragement. I would particularly like to extend my sincere thanks to Alexander Angsongna and Raine Salles for all their tips and help on how to better navigate the not always calm waters of a Ph.D. in linguistics at UBC. Special thanks to Alexander Angsongna, a great linguist and friend, for our long conversations, often accompanied by good craft beer, as well as for the chance to try the delicious and diverse food of Ghana. Thanks to my parents and sisters for all their love and emotional support. Often our mutual affection and care have overcome our physical distance over these years. Financially, my Ph.D. was supported by the Four-Year Fellowship (4YF) and the Linguistics Department at UBC. Thanks to UBC and the department for funding my Ph.D. xvii Dedication To the Kaingang people and my parents. xviii Language is an instrument for the expression of propositional contents. (Donald Davidson in \u201cThe Emergence of Thought\u201d, p. 130.) The central fact from which semanticists start is that a certain body of discourse is significant: it is effectively used for the expression and transmission of thoughts. The semanticist seeks to account for this remarkable fact. (Gareth Evans in \u201cThe Varieties of Reference\u201d, p. 23.) 1 Chapter 1: Introduction 1.1 Preamble This thesis addresses the semantics of nominal countability and the scope properties of bare nouns (BNs) in Kaingang, a J\u00ea language spoken in southeastern and southern Brazil by the Kaingang people. Kaingang is an understudied Indigenous language spoken by about 20,000 people, mostly living in four states of Brazil: S\u00e3o Paulo, Paran\u00e1, Santa Catarina, and Rio Grande do Sul. This is the first systematic investigation of bare nouns in Kaingang, focusing on countability (in particular, the count\/mass distinction) and scope, and the first study of both phenomena in the language from the perspective of formal semantics. The analysis offered in this thesis ties together these two phenomena by showing that the scope patterns of BNs in Kaingang, and across languages, are contingent on semantic properties underlying countability distinctions in the nominal domain. My main claim is that quantization underlies the count interpretation of Kaingang (bare) nouns and their variable-scope effects, i.e., the fact that, as indefinites, they can take narrow, intermediate or wide scope. The dissertation also explores the theoretical and typological implications of this analysis. Thus, with this work, I intend to contribute not only to the understanding of semantic variation in the encoding of countability and the scope of BNs across languages, but also to their systematic correlation. I hope this thesis will be of interest not only to semanticists, field linguists, and typologists, but also to psycholinguists, philosophers of language, and anybody curious about the phenomena of countability and scope in natural languages. And, of course, I hope that the research reported in this dissertation will benefit the Kaingang people by contributing to the documentation and description of their language, and will be of use for linguists working on Kaingang and other J\u00ea languages. 1.2 An overview of empirical and theoretical proposals 2 A number of typological studies on nominal countability across languages have shown that languages vary in the way their grammars encode countability distinctions and the count\/mass opposition (Doetjes 1997, 2012, 2017; Chierchia 1998a, b, 2010). In broad outline, there are at least five types of language. The first type (instantiated by English) has the following properties: generally classifiers are not required; some nouns, the so-called count nouns (e.g., girl, tree, child, mountain), can undergo plural inflection (e.g., girls, tree, children, mountains) and are allowed to directly combine with numerals (e.g., two trees, eleven children) and other count quantity expressions (e.g., many trees, few children). Other nouns, the so-called mass nouns (e.g., water, blood, flour, furniture, luggage), cannot inflect for number or combine directly with numerals or other count quantity expressions. In order to create countable constructions containing such nouns, mass\/count languages require that a measure term (e.g., liter, pound, kilo, piece) or container term (e.g., cup, bottle, bucket) be inserted between the numeral (or other count quantity expression) and the mass noun (e.g., one liter of blood, four kilos of flour, seven pieces of furniture). Another type of languages are the so-called classifier languages. Mandarin is an example of this type. These languages lack number morphology in the nominal domain and require the intervention of classifiers between nouns and numerals, as shown in (1) and (2) (Krifka 1995; Chierchia 1998b; Cheng & Sybesma 1999). (1) a. li\u01ceng zh\u0101ng zhu\u014dzi b. *li\u01ceng zhu\u014dzi two CL table two tables \u2018two pieces of tables\u2019 \u2018two tables\u2019 (Adapted from Chierchia 1998b: 354) (2) a. y\u00ed l\u00ec m\u01d0 b. *y\u00ed m\u01d0 one CL rice one rice \u2018one grain of rice\u2019 (Adapted from Chierchia 1998b: 354) A third type of languages are those like D\u00ebne S\u0173\u0142in\u00e9 (Athapaskan) and Tagalog (Austronesian), which are non-classifier languages whose nouns do not inflect for number (Schachter & Otanes 1972; Wilhelm 2008). In these languages count nouns can directly combine with numerals, while 3 mass nouns require the insertion of classifiers to form counting constructions with numerals. These facts are illustrated in (3) and (4) with D\u00ebne S\u0173\u0142in\u00e9. (3) a. sol\u00e1ghe k\u2019\u00e1sba b. sol\u00e1ghe dz\u00f3\u0142 five chicken five ball \u2018five chickens\u2019 \u2018five balls\u2019 (Wilhelm 2008: 46) (4) a. sol\u00e1ghe ned\u00e1dhi b\u00ebr b. *sol\u00e1ghe b\u00ebr five pounds meat five meat \u2018five pounds of meat\u2019 (Wilhelm 2008: 47) There is also a \u201chybrid\u201d type of language like Mi\u2019gmaq (Algonquian), in which some numerals require the presence of a classifier, while others don\u2019t. In Mi\u2019gmaq, numerals up to five combine directly with nouns, while numerals from six onward require an intervening classifier (Bale & Coon 2014). Finally, there is a particularly interesting type of language in which all nouns can have a count meaning, and as such can directly combine with numerals and other count quantity expressions. This type of languages, which can be called generalized non-classifier languages, is exemplified by Hopi (Whorf 1956), Yudja (Tupi), a Brazilian Indigenous language (Lima 2014a, b), and Kaingang, as will be demonstrated in detail in Chapter 4.1 Through the replication of various morphosyntactic and semantic tests for countability distinctions in the nominal domain (Bloomfield 1933; Doetjes 1997; Barner & Snedeker 2005; Rothstein 2010, 2017; Pires de Oliveira & Rothstein 2011; Lima 2014a, b; Lima & Rothstein 2020), I show in Chapter 4 that in Kaingang nouns that refer to both sets of individuals and substances are interpreted as count nouns. By way of illustration, take substance nouns in Kaingang, which, like other nouns in the language, don\u2019t inflect for number. As opposed to other 1 The types of languages listed above by no means exhaust the inventory of available variations. Other types of languages will be mentioned in Chapters 3 and 4. 4 (more familiar) non-classifier languages, Kaingang allows substance nouns to combine directly with numerals in non-conventionalized packaging contexts, as given in (5) with the noun kyv\u00e9nh \u2018blood\u2019, as well as in contexts where the portions counted can vary in shape, size, and containers, as shown in (6) with the noun goj \u2018water\u2019. (5) Context: On the way home from school three drops of blood dripped from F\u00f3gt\u1ebd\u2019s nose. Kyv\u00e9nh t\u00e3gt\u0169 v\u1ef9 n\u00e3g ke \u2205. blood three NOM drip PFV \u2018Three drops of blood dripped.\u2019 (6) Context: F\u00f3gt\u1ebd entered the kitchen and saw one gallon of water on the floor, one glass full of water on the table, and one puddle of water on the floor. F\u00f3gt\u1ebd v\u1ef9 goj t\u00e3gt\u0169-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM water three-ACC see PFV \u2018F\u00f3gt\u1ebd saw three portions of water.\u2019 Likewise, Kaingang substance nouns can directly combine with the count quantity word e \u2018many\u2019, which is always interpreted as expressing a large number of units, as shown in (7). The infelicity of the sentence in (7) in context B is due to the fact that it doesn\u2019t contain multiple portion-units. (7) \u2713Context A: There were many puddles of blood in front of a building. F\u00f3gt\u1ebd saw them. \u2717Context B: There was a large puddle of blood in front of a building. F\u00f3gt\u1ebd saw it. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh e-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many puddles of blood.\u2019 5 Further evidence that substance (bare) nouns in Kaingang can be used to count portion-units comes from the fact they can be the antecedents for reciprocals, as exemplified in (8) with the noun goj \u2018water\u2019. (8) Context: After the rain there were separate puddles of water on the floor. You notice that they are similar in shape and size. Goj t\u00f3g jagn\u1ebd-\u2205 h\u00e3 n\u1ef9t\u0129. water TOP RECP-ACC similar ASP \u2018Some\/the puddles of water look like each other.\u2019 Additionally, in quantity judgement tasks (Barner & Snedeker 2005), the default interpretations of Kaingang comparative constructions with both individual and substance nouns are cardinality-based. For instance, the three Kaingang speakers who were the main language consultants for this dissertation considered sentence (9) felicitous in a scenario where Maria has more portion-units of milk than Pak\u00f3j has, although the total combined volume of Pak\u00f3j\u2019s portions of milk is larger than the total combined volume of Maria\u2019s portions. In other words, the speakers evaluated the substance noun renhte in (9) along the dimension of number, rather than volume. This fact constitutes evidence that Kaingang substance nouns are interpreted in comparative constructions in the same way that count nouns in mass\/count languages are interpreted. (9) Maria v\u1ef9 renhte m\u1ebd n\u0129 Pak\u00f3j ve k\u1ef9. Maria NOM milk more ASP Pak\u00f3j than \u2018Maria has more milk than Pak\u00f3j.\u2019 Findings like those above indicate that in Kaingang there are no morphosyntactic or semantic features that distinguish count nouns from mass nouns. In this regard, as will be demonstrated in detail in Chapter 4, there is compelling evidence in support of two connected hypotheses: (i) that Kaingang doesn\u2019t encode the count\/mass distinction in its nominal grammar, and (ii) that this is so because all Kaingang nouns are count nouns. 6 Thus, based on my findings, and motivated by crosslinguistic evidence, I analyze this pervasive count interpretation of Kaingang nouns as a direct effect of the lexical meaning of root nouns. Building on Krifka\u2019s approach (1986, 1989, 2007, 2008), which grounds the count\/mass distinction in two disjoint semantic properties of predicates, namely quantization and cumulativity, I argue that all Kaingang nouns are interpreted as count because they are born quantized. Kaingang nouns are lexically equipped with a context-sensitive built-in quantizing function that measures quantities in terms of individual- or portion-units, i.e., that provides the units for counting. This analysis, as will be shown in Chapter 4, contributes extensive and detailed new crosslinguistic evidence in support of two important, but still controversial, hypotheses put forward by some previous researchers in the literature on nominal countability: (i) that the mass\/count distinction in the nominal domain isn\u2019t a language universal (Wiltschko 2012), and (ii) that the defining property of count nouns is quantization, rather than atomicity (Krifka 1989, 2007). The second main topic addressed in this thesis is the scope patterns of Kaingang bare nouns under their indefinite interpretation. Kaingang is a generalized bare noun language, i.e., nouns can occur in argument positions without any functional elements such as determiners, number morphemes, or classifiers. In Chapter 5, I show that Kaingang BNs have unrestricted distribution (i.e., they can appear in all argument positions) and exhibit variable scope in relation to other clause-mate operators, such as negation, intensional verbs, if-clauses, universal quantifiers, and frequency adverbials. In other words, Kaingang BNs can have wide, narrow, and even intermediate scope with respect to other operators. Take the scope interaction of the bare noun pir\u00e3 \u2018fish\u2019 and the sentential negation t\u0169 \u2018not\u2019 in (10a), for instance. This sentence can be true in a scenario where F\u00f3gt\u1ebd didn\u2019t catch any fish, i.e., under the interpretation where pir\u00e3 displays narrow scope with respect to negation, as paraphrased in (10b). Moreover, sentence (10a) can be true in a scenario where there is at least one fish that F\u00f3gt\u1ebd didn\u2019t catch, but there are also fish he did catch. This indicates that the BN can scope over negation, as paraphrased in (10c). (10) a. F\u00f3gt\u1ebd v\u1ef9 pir\u00e3-\u2205 sam \u2205 t\u0169 n\u0129. F\u00f3gt\u1ebd NOM fish-ACC catch PFV NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t catch a fish.\u2019 7 b. There isn\u2019t a fish x, such that F\u00f3gt\u1ebd caught x. c. There is a fish x, such that F\u00f3gt\u1ebd didn\u2019t catch x. The variable-scope effects exhibited by Kaingang BNs, along with Hebrew BNs (Dayal 2004, Tonciulescu 2009) and Malagasy BNs (Paul 2016), contrast with the well-known obligatory narrow scope of (plural, mass, or number-neutral) BNs attested in a wide range of typologically diverse languages. Some of these are English (Carlson 1977a, b), Haitian Creole (Deprez 2005), Hindi (Dayal 2004), Indonesian (Chung 2000), Mandarin (Cheng & Sybesma 1999; Rullmann & You 2006), Russian (Dayal 2004), and Teotitl\u00e1n del Valle Zapotec (Deal & Nee 2018), among many others. Interestingly, the wide scope reading of Kaingang bare nouns is also available with substance bare nouns when they are used to talk about portions of substances. For instance, (11a) is felicitous in the context in (11). The lack of contradiction in the coordination of the negative statement with its affirmative counterpart in (11a) reveals that the BN goj \u2018water\u2019 can scope over negation, as represented in (11b). (11) \u2713Context: You live alone. On Monday you filled the clay filter with water before bed. The next morning you notice that the filter is only half full of water, despite the fact that you didn\u2019t drink any water during the night. You find it has a small crack. You conclude: a. Goj v\u1ef9 pa ja n\u0129, h\u00e3ra goj v\u1ef9 pa ja t\u0169 n\u0129. water NOM leak ASP ASP but water NOM leak ASP NEG ASP \u2018Some portion of water leaked out, but some portion of water didn\u2019t leak out.\u2019 b. There is a portion of water x that leaked out, but there is a portion of water y that didn\u2019t leak out. Adopting a type-shifting framework (Partee 1986; Chierchia 1998b; Krifka 2003; Dayal 2004), I analyse Kaingang indefinite bare nouns as predicate NPs mapped onto arguments via a covert choice function type-shifter (CF) which (just like English indefinites under Reinhart\u2019s 1997, 2006 analysis) can get existentially closed at any level in the clausal spine. As a result, Kaingang bare 8 nouns provide evidence that a choice function is not always associated with a syntactic determiner (D) and hence that it belongs to the inventory of covert type-shifters occurring in natural languages. Linking the two main phenomena under investigation in this dissertation, I argue that the difference in scope properties across languages between variable-scope bare nouns and narrowest-scope bare nouns is linked to the quantized\/cumulative opposition of the predicates they express: the former are quantized predicates, while the latter are cumulative ones. This means that the scope patterns of BNs are dependent on the properties of the predicates they express. I propose that variable-scope BNs and narrowest-scope BNs are created by two distinct covert type-shifters: the former by a choice function operator and the latter by Krifka\u2019s \u2203 operator (Krifka 2003). Additionally, I argue that both operators are sensitive to the quantized\/cumulative opposition, and I model this sensitivity via presuppositions introduced by these operators. Krifka\u2019s \u2203 type-shifter, which always gives rise to narrowest-scope interpretations, carries the presupposition that the BN it applies to is cumulative. In contrast, the choice function type-shifter, which creates variable-scope readings, presupposes that the BN it targets is quantized. Thus, the indefinite interpretation and variable-scope effects of bare nouns in languages like Kaingang arise from the interaction of three semantic factors: quantization, a CF type-shifter, and existential closure of the choice function variable. In Chapter 5, I discuss the theoretical and typological consequences of this analysis in more detail, and show that it correctly predicts the variation in scope properties of bare nouns in a number of typologically distinct languages. 1.3 Structure of the thesis This thesis is structured as follows. Chapter 2 offers some information about the Kaingang people, their language, and my fieldwork methodology. First, it introduces the reader to the Kaingang people and their ethnic territories in southeastern and southern Brazil. Second, it addresses some facts about the Kaingang language: family, number of speakers, dialects, and aspects of its grammar. The properties of Kaingang grammar laid out in Chapter 2 are the following ones: its phonetic inventory, syllable structure, word order, case system, relative clauses, pronoun system, the distribution and interpretation of bare nouns, constructions with numerals and other quantity expressions, and verbal number. Third, the chapter discusses the methodology I used in my fieldwork for eliciting the data presented in the thesis. 9 Chapter 3 introduces the two main semantic theories that form the theoretical foundation of this thesis: mereology-based and type-shifting semantics. It focuses on two main approaches to mereology-based semantics: Link\u2019s (1983, 1998) two-domain theory, which accounts for the count\/mass distinction in terms of the notions of atomic vs. nonatomic nouns, and Krifka\u2019s (1986, 1989, 2007, 2008) quantization approach, which accounts for it in terms of the quantized\/cumulative opposition. There I also discuss the empirical advantages of Krifka\u2019s approach over Link\u2019s by particularly highlighting the broader explanatory scope of the former. Subsequently, the chapter addresses Partee\u2019s (1986) type-shifting approach to the semantics of nominals. It shows how the flexible type-shifting mechanisms that she proposed as a way to relate the different meanings of nominals to each other have allowed semanticists to account for variation in the interpretations of bare nouns within a single language and across languages (Chierchia 1998b; Krifka 2003; Dayal 2004, among others). Chapter 4 examines the phenomenon of nominal countability in Kaingang. As already mentioned in this introduction, based on a number of diagnostic tests, Chapter 4 provides compelling evidence that Kaingang nouns exhibit a generalized count interpretation, i.e., that all nouns are count nouns. I analyze Kaingang nouns as lexically quantized predicates due to a context-sensitive quantizing function incorporated into their root denotations, which provides the units for counting. It is argued that such an account is not only empirically supported by the pervasive count interpretation of Kaingang nouns, but also motivated by crosslinguistic evidence. Chapter 5 investigates the scope behavior of Kaingang bare nouns. It presents data on the scope interaction of Kaingang BNs with respect to other semantic operators in the clause, such as negation, intensional verbs, if-clauses, universal quantifiers, and frequency adverbials; these diagnostics show that Kaingang BNs can have narrow, intermediate and wide scope. I treat Kaingang BNs as predicate NPs that shift to an argument type via a covert choice function f existentially closed at any level. It is shown that this treatment of Kaingang BNs accounts for both their existential force and variable-scope effects. In addition, a necessary link is posited between the availability or lack of choice function BNs and properties of the predicates expressed by bare nouns. This is modeled by making the nominal type-shifters that create indefinite readings of BNs sensitive to the quantized\/cumulative opposition. Both Chapters 4 and 5 discuss the theoretical and typological consequences of the analyses advanced in them. Finally, Chapter 6 summarizes the main conclusions, and suggests paths for future research. 10 Chapter 2: The People and their Language 2.1 Introduction In this chapter, I present a general outline of the Kaingang people and their language. In section 2.2, I provide some information about the Kaingang people: population, the states in Brazil where they live, their territories, etc. In section 2.3, I lay out some facts about the Kaingang language. I begin with an outline of the Indigenous language families of Brazil, focusing on the linguistic family to which Kaingang belongs, namely, the J\u00ea family; then I briefly outline the number of Kaingang speakers and the attested regional dialects of Kaingang. In section 2.4, I offer some background information about Kaingang grammar: its phonetic inventory, syllable structure, word order, case system, relative clauses, pronoun system, the distribution and interpretation of bare nouns, constructions with numerals and other quantity expressions, as well as verbal number. Particular attention will be given to the distribution and interpretation of Kaingang bare nouns, due to their special pertinence for the understanding of the close link between the pervasive count interpretation of Kaingang bare nouns and their scope properties. I show, for instance, that Kaingang bare nouns are number neutral, have an unrestricted distribution, and can have (in)definite and generic readings. To conclude this chapter, in section 2.5, I discuss the methodology employed in this study. 2.2 The people and their lands The Kaingang people are a Brazilian Indigenous group from southeastern and southern Brazil. According to the 2010 Brazilian Census, their population is estimated to be around 37,400 people, mostly living in four states: S\u00e3o Paulo, Paran\u00e1, Santa Catarina, and Rio Grande do Sul (Instituto Brasileiro de Geografia e Estat\u00edstica \u23af IBGE 2012). Despite centuries of all sorts of colonial and state violence perpetrated against the Kaingang people (invasion and theft of their lands by settlers, forced displacement and territorial restriction, forced labor, forced religious conversion, torture, diseases, assassinations, and massacres), nowadays they represent the third largest Indigenous 11 group in Brazil, among a total of 305 groups. The Kaingang people are only outnumbered by the Guarani Kaiow\u00e1, with a population of around 43,000 people, and the Tikuna, with a population of 46,000 people. In addition, the Kaingang people make up more than half of the entire population of J\u00ea peoples, which is formed by 22 ethnic groups (IBGE 2012). Currently, most of the Kaingangs live in more than 30 territories. Nearly all these lands are officially recognized by the Brazilian state as Indigenous territories or are in the process of recognition. These lands combined \u201cencompass just over 250 thousand hectares\u201d (Fernandes & de G\u00f3es 2018: 3), constituting a reduced dimension of the Kaingang ancestral territory, formed by plains, rivers, mountains, and forests along the Southern Plateau of Brazil.2 From the first contact with European colonizers in the 18th century until the first half of the 20th century, the Kaingang people experienced a systematic reduction of their territories (Fernandes & de G\u00f3es 2018). The first official recognition of some of the Kaingang territories occurred in the early 20th century, under the First Brazilian Republic, through decrees issued by the states of Paran\u00e1 and Rio Grande do Sul. Nevertheless, in the 1940s, under the Vargas era, the federal government initiated a new cycle of drastic reduction of the Kaingang lands, scaling down the size of the already reduced lands recognized in the beginning of the century. According to Tommasino (1995), as a result of this neo-colonial enterprise of the Brazilian state, an agreement established in 1949 between the state government of Paran\u00e1 and the federal government, represented by the Indian Protection Service (SPI), forced upon the Kaingang people a reduction of 90% of their territory in the state.3 Nevertheless, in the mid 1970s the Kaingang people, giving new impetus to their long struggle for self-determination, initiated the retaking of some of their ancestral territories through direct actions. In the context of a dictatorship showing the first signs of wear, and the emergence of new social movements, the Kaingang people conducted a number of reoccupations of their lands, in particular those they lost in the 1940s, in some cases through open confrontation with land settlers and government authorities. In the early 1980s, as a result of the Kaingang pressure combined with the new political atmosphere of the country, which was heading towards its redemocratization, the federal 2 The presence of J\u00ea groups in southern Brazil dates back at least 3,000 years (Urban 1992). 3 The Indian Protection Service was a federal agency created in 1910 by the Brazilian government during a period in which it promoted new fronts of economic expansion. It aimed at \u201cprotecting\u201d and \u201cintegrating\u201d Indigenous peoples into Brazilian society. It was dismantled in 1967. 12 government began to demarcate the Kaingang lands. They also began to provide welfare policies demanded by the Kaingang people, such as access to public education, health care, etc. A significant number of the current Kaingang lands were recognized between the 1980s and 1990s, showing that the reappropriation movement that started in the mid 1970s was a determining factor in bringing about their official demarcations.4 The Kaingang people up to the present day continue their enduring struggle for the right to their territories in the form of reappropriation processes. There are a number of families living in territories retaken in the last two decades, putting constant pressure on federal authorities to recognize these lands as Indigenous territories of the Kaingang people. Figure 1 displays a map of the federal units of Brazil, with the southeastern and southern states where the Kaingang people live encircled, i.e., S\u00e3o Paulo, Paran\u00e1, Santa Catarina, and Rio Grande do Sul. 4 For case studies about the Kaingang people retaking some of their ancestral lands, see Castro (2011) and Gurski (2022). For a study about the first conflicts between colonizers and the Kaingang people, see Amoroso et al. (2003); for a history of the Kaingang people in Paran\u00e1, see Mota (1994). For an overview of the Kaingang people\u2019s struggle to defend and retake their territories from the 18th century to the second decade of the 21st century, see Fernandes & Go\u00e9s (2018). 13 Figure 1: Federal units of Brazil. Source: The Brazilian Institute of Geography and Statistics (IBGE). 5 The map in Figure 2 shows the distribution of the current Kaingang lands recognized by the Brazilian government. Each land in the map is numbered and its corresponding name can be seen in the list on the right side of the map. 5 Available at: https:\/\/www.ibge.gov.br\/ 14 Figure 2: Current official Kaingang lands. Source: The National Indian Foundation (FUNAI)\/Socioenvironmental Institute (ISA). 6 The bulk of the data for this study originated from fieldwork conducted in the recognized Kaingang territory of Rio das Cobras, in the state of Paran\u00e1 in southern Brazil. The largest Indigenous territory of Paran\u00e1, Rio das Cobras is located on the left bank of the Guarani River, crossed by the Uni\u00e3o and Rio das Cobras Rivers, tributaries of the Igua\u00e7u River, near the municipalities of Nova 6 Available at: https:\/\/img.socioambiental.org\/v\/publico\/kaingang\/kaingang_mapa_val.jpg.html 15 Laranjeiras and Espig\u00e3o Alto do Igua\u00e7u. The encircled red triangle numbered 11 in Figure 2 shows the geographic location of Rio das Cobras. The land of Rio das Cobras was registered as an Indigenous territory in 1901 by decree no 6, issued by the government of Paran\u00e1 (Fernandes & de G\u00f3es 2018). As a result of the 1949 agreement between the federal and state governments, which, as mentioned above, arbitrated the size of the Kaingang territories, the area of Rio das Cobras was delimited at 12,600 hectares. 7 However, in 1969 this territory expanded to 19,106.9 hectares, and currently it has a total area of 18,681 hectares, declared by the National Indian Foundation (FUNAI) in 1984 and then officially demarcated in 1991.8 The territory encompasses the villages of Trevo, Vila Nova, Sede, Campo do Dia, Taquara, Lebre, Encruzilhada, Jacutinga, Pinhal, Vila Paulista, and Miss\u00e3o. Rio das Cobras is inhabited by the Kaingang and Guarani peoples, with a population of approximately 3,112 people according to the 2022 Brazilian Census (IBGE 2023). The source of the majority of the families\u2019 income is based on family farming and handicraft sales. The map in Figure 3 shows the current limits of the territory. Figure 3: The Indigenous land of Rio das Cobras. Source: Brazilian Federal Register, decree n\u00ba 90.744 of December 20, 1984 (Gurski 2022). 7 For a detailed study of the Kaingang people\u2019s fight for the recognition of Rio das Cobras as an Indigenous land and the long processes of its official demarcation, see Gurski (2022). 8 FUNAI is the Brazilian governmental protection agency for the rights of the Indigenous peoples of Brazil. One of its roles is to demarcate Indigenous lands. It was created in 1967, after SPI was abolished. 16 2.3 The language There are approximately 180 Indigenous languages spoken in Brazil, which can be divided into 19 language families. Tupi and Macro-J\u00ea form the two largest families. The former consists of 20 subfamilies, with an approximate total of 45 languages, while the latter has 9 subfamilies, with an approximate total of 30 languages. The other language families are Aruak, Karib, Pano, Tukano, Araw\u00e1, Katukina, Mak\u00fa, Nambikw\u00e1ra, Tixapakura, Yanom\u00e1mi, B\u00f3ra, Guaikuru, M\u00fara, Sam\u00fako, Chiquito, Japot\u00ed, and Wit\u00f3to. Approximately 40 languages haven\u2019t yet been classified as members of any families, and some of them are considered language isolates. The map in Figure 4 shows the distribution of Brazilian Indigenous language families over the Brazilian territory. 17 Figure 4: Territorial distribution of language families. Source: Socio-environmental Institute (2009).9 Kaingang is an Indigenous language of the J\u00ea family, the largest subfamily of the Macro-J\u00ea family, with a total of 18 languages, spread over most of the Brazilian territory. Kaingang is the language of the Kaingang people, spoken in southeastern and southern Brazil. According to the federal census of 2010 (IBGE 2012), Kaingang has approximately 20,000 speakers. It is the J\u00ea language with the largest number of speakers and the third most spoken Indigenous language in Brazil, only 9 Available at: https:\/\/img.socioambiental.org\/v\/publico\/pibmirim\/linguas\/linguasmed.jpg.html 18 outnumbered by Tupi-Guarani (26,500 speakers) and Tikuna (34,000 speakers). Of the 180 Brazilian Indigenous languages, only five have more than 10,000 speakers. The other two are Xavante (13,300), also a J\u00ea language, and Yanomami (12,700). Table 1 lists all languages of the Macro-J\u00ea family, and their respective subfamilies. Table 1: Macro-J\u00ea family. Source: 2010 Federal Census (IBGE 2012). The map in Figure 5 shows the territorial distribution of 28 languages of the Macro-J\u00ea family over the Brazilian territory. Macro-J\u00ea (Sub)families Languages Bor\u00f3ro Bor\u00f3ro; Umut\u00edna Guat\u00f3 Guat\u00f3 J\u00ea Apinay\u00e9; Kanela; Gavi\u00e3o Krikat\u00eaj\u00ea; Gavi\u00e3o Parkat\u00eaj\u00ea; Gavi\u00e3o Pukobi\u00ea; Krah\u00f4; Krikat\u00ed; Timbira; Kaingang; Kayap\u00f3 (Memb\u00eagokr\u00ea); Krenaka; Kis\u00eadj\u00ea; Panar\u00e1; Tapay\u00fana; Xacriab\u00e1; Xavante; Xer\u00e9nte; Xokleng Karaj\u00e1 Karaj\u00e1; Java\u00e9 Kren\u00e1k Kren\u00e1k Maxakali Maxakali; Pataxo H\u00e1-H\u00e1-H\u00e1 Ofay\u00e9 Ofay\u00e9 Rikbaktsa Rikbaktsa-Canoeirosa Yat\u00ea Funi-\u00f4 19 Figure 5: Territorial distribution of the Macro-J\u00ea languages. Source: Tabosa (2014). Wiesemann (1971, 2002) identifies five dialects of the Kaingang language: the S\u00e3o Paulo dialect, the Paran\u00e1 dialect, and the Central, Southwestern and Southeastern dialects. The geographic localization of each dialect is specified in Table 2. 20 Table 2: The dialects of Kaingang. Source: Wiesemann (2002: 8). The current orthographic system of Kaingang was developed between 1958 and 1966 by Wiesemann and a group of native speakers of the language (Silva 1996; Wiesemann 2002). The group had speakers of all the dialects above, and the meetings to determine the orthography occurred in the territory of Rio das Cobras. This joint work also culminated in a Kaingang-Portuguese\/Portuguese-Kaingang dictionary (Wiesemann 1971), which decades later received an updated version, containing a short grammar (Wiesemann 2002). 2.4 Kaingang grammar In this section I introduce some components of Kaingang grammar. The main purpose here is to equip the reader with the information required to interpret the data in Chapters 4 and 5. In this regard, the present section includes the following information about Kaingang grammar: phoneme inventory, syllable structure, word order, case system, pronoun system, the distribution and interpretation of bare nouns, numerals, and quantity expressions like all, some, many, few, and more. As pointed out in the introduction of this chapter, I will particularly focus on the distribution Dialects Location S\u00e3o Paulo dialect Spoken in the north of the Paranapanema River in the state of S\u00e3o Paulo. Paran\u00e1 dialect Spoken in the area between the Paranapanema and Igua\u00e7u Rivers. Central dialect Spoken in the area between the Igua\u00e7u and Uruguay Rivers. Southwestern dialect Spoken south of the Uruguay River and west of the Passo Fundo River. Southeastern dialect Spoken south of the Uruguay River and east of the Passo Fundo River. 21 and interpretation of Kaingang bare nouns, given their special relevance for the discussion about the interplay between nominal countability and the scope properties of bare nouns. 2.4.1 Phonology 2.4.1.1 Consonants Kaingang has 14 consonants, of which 8 are occlusive phonemes (\/p\/, \/t\/, \/k\/, \/\u0294\/, \/m\/, \/n\/, \/\u0272\/, and \/\u014b\/) and 6 continuant phonemes (\/\u027e\/, \/\u0278\/, \/w\/, \/\u0283\/, \/h\/, and \/j\/), as listed in Table 3 (Kindell 1972, 2008 [1961]; Wiesemann 1972; Cavalcante 1987; D\u2019Angelis 1998).10 Bilabial Alveolar Post alveolar Palatal Velar Glottal Plosive p t k \u0294 Nasal m n \u0272 \u014b Tap or flap \u027e Fricative \u0278 \u0283 h Approximant j w voiced labial-velar approximant Table 3: Kaingang consonants. Sources: Adapted from Wiesemann (1972: 39) and Kindell (2008 [1961]: 2). The voiceless occlusives occur only as onsets of syllables, while the voiced occlusives appear as onsets and codas, as illustrated in (12). 10 Each nasal consonant has a series of allophones. It is still a topic of debate among phonologists what phonotactic constraints are governing their manifestations. This issue is beyond the scope of this dissertation. For a list of the allophones in Kaingang and a description of the phonological environments where they occur, see Findell (1972, 2008 [1961]) and D\u2019Angelis (1998); for an in-depth formal analysis of the phonological processes triggering the allophones of the nasal consonants, see D\u2019Angelis (1998). 22 (12) a. \/p\u0254\/ [p\u0254] \u2018stone\u2019 b. \/ki\/ [ki] \u2018in\u2019 c. \/\u014b\u00e3m\/ [\u014b\u00e3m] \u2018break\u2019 d. \/m\u00e3n\/ [m\u00e3n] \u2018again\u2019 e. \/ta\/ [ta] \u2018rain\u2019 f. \/\u0294e\/ [\u0294e] \u2018many\u2019 g. \/\u0272\u0259\u0303\u0272\/ [\u0272\u0259\u0237\u0272\u0303] \u2018squeeze\u2019 h. \/n\u00f5\u014b\/ [n\u00f5\u014b] \u2018remove\u2019 (Kindell 2008 [1961]: 2) As for the voiceless and voiced continuants, they only occur as onsets, as exemplified in (13). (13) a. \/\u0278e\/ [\u0278e] \u2018stomach\u2019 b. \/\u0283i\/ [\u0283i] \u2018elderly\u2019 c. \/hi\/ [hi] \u2018she\/her\u2019 d. \/w\u0254\/ [w\u0254] \u2018no\u2019 e. \/\u027ee\/ [\u0259\u027ee] \u2018grass\u2019 f. \/j\u0259\/ [j\u0259] \u2018bee\u2019 (Kindell 2008 [1961]: 3) Table 4 relates the consonant sounds to their corresponding orthographic representations. 23 Phonemes Orthography \/p\/ p \/m\/ m \/ \u0278 \/ f \/t\/ t \/n\/ n \/\u0272\/ nh \/\u027e\/ r \/\u0283\/ s \/k\/ k \/\u014b\/ g \/\u0294\/ \u2032 \/h\/ h \/w\/ v Table 4: Consonant-orthography correspondences. Source: Adapted from Gon\u00e7alves (2011: 10). 2.4.1.2 Vowels There are 15 vowel sounds in Kaingang, of which 9 are oral sounds (\/i\/, \/\u0268\/, \/u\/, \/e\/, \/\u025b\/, \/\u0259\/, \/o\/, \/\u0254\/, and \/a\/) and 6 are nasal sounds (\/\u0129\/, \/\u0094\/\u0303, \/\u025b\/\u0303 \/\u00e3\/, \/\u0254\u0303\/, and \/\u0169\/). Tables 5 and 6 illustrate their distribution with respect to height and backness. Front Central Back High i \u0268 u Mid e, \u025b \u0259 o, \u0254 Low a Table 5: Oral vowels. Source: Adapted from D\u2019Angelis (2007: 92). 24 Front Central Back High \u0129 \u0094 \u0303 \u0169 Mid \u025b \u0303 \u0254\u0303 Low \u00e3 Table 6: Nasal vowels. Source: Adapted from D\u2019Angelis (2007: 92). In (14) below I offer examples of oral vowels as nuclei of one-syllable words.11 (14) a. \/ti\/ [ti] \u2018he\/him\u2019 b. \/j\u0268\/ [j\u0268] \u2018next to\u2019 c. \/\u0294e\/ [\u0294e] \u2018many\u2019 d. \/tu\/ [tu] \u2018carry\u2019 e. \/ta\/ [ta] \u2018rain\u2019 f. \/m\u025b\/ [mb\u025b] \u2018sheep\u2019 g. \/t\u0254\/ [t\u0254] \u2018say\u2019 h. \/t\u0259\/ [t\u0259] \u2018there\u2019 1. \/\u027eo\u027e\/ [\u027eo\u027e] \u2018round\u2019 (Adapted from D\u2019Angelis 2007: 88 and Kindell 2008 [1961]: 5) Examples of nasal vowels as nuclei of one-syllable words are given in (15). (15) a. \/t\u0129\/ [t\u0129] \u2018go\u2019 b. \/h\u0094m\u0303\/ [h\u0094b\u0303m] \u2018frog\u2019 c. \/t\u0169\/ [t\u0169] \u2018not\u2019 d. \/n\u025bn\u0303\/ [n\u025bn\u0303] \u2018bush\u2019 11 For an inventory of the allophones of the Kaingang vowels see Kindell (1972, 2008 [1961] and Wiesemann (1972). 25 e. \/n\u0254\u0303n\/ [n\u0254\u0303n] \u2018forest\u2019 f. \/pr\u00e3\/ [pr\u00e3] \u2018bite\u2019 (Adapted from D\u2019Angelis 2007: 88 and Kindell 2008 [1961]: 6) The correspondence between the vowels and their orthography is illustrated in Table 7. Phonemes Orthography \/i\/ i \/\u0129\/ \u0129 \/e\/ e \/\u0259\/ \u00e1 \/\u025b\/ \u00e9 \/\u025b\/\u0303 \u1ebd \/a\/ a \/\u00e3\/ \u00e3 \/\u0268\/ y \/\u0094\/\u0303 \u1ef9 \/u\/ u \/\u0169\/ \u0169 \/o\/ o \/\u0254\/ \u00f3 \/\u0254\u0303\/ \u00e3 Table 7: Vowel-orthography correspondences. Source: Adapted from Gon\u00e7alves (2011: 11). 2.4.1.3 Syllable structure Kaingang includes 6 syllable structures: V, VC, CV, CCV, CVC, and CCVC. In (16) each pattern is illustrated with a word (Gon\u00e7alves 2011). 26 (16) a. V \u00e3 \u20182SG\u2019 b. VC \u0129n \u2018house\u2019 c. CV ta \u2018rain\u2019 d. CCV mr\u00e9 \u2018with, and\u2019 e. CVC f\u00f3g \u2018non-indigenous person\u2019 f. CCVC kr\u0129g \u2018star\u2019 2.4.2 The pronoun system Table 8 lists the inventory of Kaingang personal pronouns, which are free morphemes. Person Number Singular Plural 1 inh \u1ebdg 2 \u00e3 \u00e3jag 3 MASCULINE ti ag FEMININE fi fag Table 8: Personal pronouns. Source: Adapted from Tabosa (2014: 109). As Table 8 shows, the Kaingang pronoun system encodes grammatical number. More specifically, it expresses the singular\/plural distinction, with each person having a singular and a plural form. Additionally, the third person pronouns encode grammatical gender, with masculine and feminine forms. 27 The sentences in (17\u23af20) illustrate occurrences of the personal pronouns in subject and object positions.12,13 (17) a. \u00c3-\u2205 v\u00e9 inh \u2205. 2SG-ACC see 1SG PFV \u2018I saw you (singular).\u2019 b. \u00c3jag-\u2205 v\u00e9g \u1ebdg \u2205. 2PL-ACC see 1PL PFV \u2018We saw you (plural).\u2019 (18) a. Inh-\u2205 v\u00e9 \u00e3 \u2205. 1SG-ACC see 2SG PFV \u2018You (singular) saw me.\u2019 b. \u1ebcg-\u2205 v\u00e9 \u00e3jag \u2205. 2PL-ACC see 1PL PFV \u2018You (plural) saw us.\u2019 (19) a. Ti-\u2205 v\u00e9 inh \u2205. 3SG.M-ACC see 1SG PFV \u2018I saw him.\u2019 12 Along with Nascimento\u2019s (1995) syntactic analysis of aspect in Kaingang, I assume a zero perfective marker (\u2205) that follows the verbs in clauses which are not overtly marked for viewpoint aspect. For further works on aspect in Kaingang, see Almeida (2008); Gon\u00e7alves (2011); Nascimento (2012). 13 Kaingang nominals are marked with case. The case system of Kaingang will be discussed in section 2.4.4. For consistency, I am following the previous literature in assuming null case markers (represented as \u2205) in instances where there is no apparent case marker on the surface, but no important theoretical issues in my analysis hinge on this assumption. 28 b. Fi-\u2205 v\u00e9 inh \u2205. 3SG.F-ACC see 1SG PFV \u2018I saw her.\u2019 c. Ag-\u2205 v\u00e9 inh \u2205. 3PL.M see 1SG PFV \u2018I saw them (masculine).\u2019 d. Fag-\u2205 v\u00e9 inh \u2205. 3PL.F see 1SG PFV \u2018I saw them (feminine).\u2019 (20) a. Inh-\u2205 v\u00e9 ti \u2205. 1SG-ACC see 3SG.M PFV \u2018He saw me.\u2019 b. Inh-\u2205 v\u00e9 fi \u2205. 1SG-ACC see 3SG.F PFV \u2018She saw me.\u2019 c. Inh-\u2205 v\u00e9 ag \u2205. 1SG-ACC see 3PL.M PFV \u2018They (masculine) saw me.\u2019 d. Inh-\u2205 v\u00e9 fag \u2205. 1SG-ACC see 3PL.F PFV \u2018They (feminine) saw me.\u2019 Kaingang possessive pronouns are homophonous with personal pronouns; they always immediately precede the possessed noun phrase, as illustrated in (21) and (22), where the constituents inh pratu \u2018my plate\u2019 and fi k\u00f3sin \u2018her son\u2019 occur in subject and object positions. 29 (21) a. Inh pratu-\u2205 v\u1ef9 g\u00f3v \u2205. 1P.SG plate-ACC NOM break PFV \u2018My plate broke.\u2019 (Tabosa 2006: 69) b. F\u00f3gt\u1ebd v\u1ef9 inh pratu-\u2205 g\u00e3m \u2205. F\u00f3gt\u1ebd NOM 1P.SG plate-ACC break PFV \u2018F\u00f3gt\u1ebd broke my plate.\u2019 (Adapted from Tabosa 2006: 69) (22) a. Fi k\u00f3sin v\u1ef9 F\u00f3gt\u1ebd-\u2205 v\u00e9 \u2205. 3P.SG.F son NOM F\u00f3gt\u1ebd-ACC see PFV \u2018Her son saw F\u00f3gt\u1ebd.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 fi k\u00f3sin-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM 3P.SG.F son-ACC see PFV \u2018F\u00f3gt\u1ebd saw her son.\u2019 Kaingang also has one reflexive and one reciprocal pronoun. The reflexive pronoun is v\u1ebdnh \u2018myself\/ourselves\/yourself\/yourselves\/himself\/herself\/themselves\u2019, as shown in (23a\u23afd), while the reciprocal pronoun is jagn\u1ebd \u2018each other\u2019, as given in (24a\u23afb).14 (23) a. Goj t\u00e1 v\u1ebdnh-\u2205 \u1ebdg kyp\u00e9 \u2205. water there REFL-ACC 1PL bath PFV \u2018We bathed ourselves in the water.\u2019 (Adapted from Abreu 2009: 86) 14 I am following the previous literature in assuming that t\u00f3g is a topic marker (Wiesemann 2002). However, no important theoretical issues in my analysis hinge on this assumption. 30 b. Goj ki v\u1ebdnh-\u2205 \u00e3jag kyp\u00e9 \u2205. water in REFL-ACC 2PL bath PFV \u2018You bathed yourselves in the water.\u2019 (Adapted from Abreu 2009: 86) c. V\u1ebdnh-\u2205 rem fi \u2205. REFL-ACC comb 3SG.F PFV \u2018She combed herself.\u2019 (Adapted from Abreu 2009: 85) d. V\u1ebdnh-\u2205 kyp\u00e9 fag t\u0129. REFL-ACC bath 3PL.F HAB \u2018They (feminine) bathed themselves.\u2019 (Adapted from Abreu 2009: 86) (24) a. Fag t\u00f3g jagn\u1ebd-\u2205 ve h\u00e3 n\u0129. 3PL.F TOP RECP-ACC look similar ASP \u2018They (feminine) look like each other.\u2019 b. Ag t\u00f3g jagn\u1ebd-\u2205 to kyn\u223ckyr \u2205. 3PL.M TOP RECP-ACC to RED\u223cbark PFV \u2018They (masculine) barked at each other.\u2019 2.4.3 Word order The default word order in Kaingang is SOV, as illustrated in (25\u23af27), which contain constructions with proper nouns, as in (25), pronouns, as in (26), and bare nouns, as in (27).15 15 Is\u1ef9 in (26) is the agglutinated form of the first-person pronoun inh \u2018I\u2019 and the nominative marker v\u1ef9 (Almeida 2008). 31 (25) F\u00f3gt\u1ebd v\u1ef9 Pedro-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM Pedro-ACC see PFV \u2018F\u00f3gt\u1ebd saw Pedro.\u2019 (26) Is\u1ef9 ti-\u2205 v\u00e9 \u2205. 1.SG.NOM 3SG.M-ACC see PFV \u2018I saw him.\u2019 (27) G\u0129r v\u1ef9 \u0129n-\u2205 v\u00e9 \u2205. child NOM house-ACC see PFV \u2018A\/some\/the child(ren) saw a\/some\/the house(s).\u2019 In constructions with indirect objects, the default order is S IO DO V, as given in (28). (28) F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u1ef9 garinh-\u2205 f\u1ebdg \u2205. F\u00f3gt\u1ebd NOM child DAT hen-ACC give PFV \u2018F\u00f3gt\u1ebd gave a\/some\/the hen(s) to a\/some\/the child(ren).\u2019 A strict constraint on the word order is that O has to precede V. Subjects usually come at the beginning (resulting in SOV as the most common word order), unless they are pronouns that are not followed by the nominative case marker, in which case they usually follow the verb, as already exemplified in (17\u23af20), and also shown in (29\u23af31). (29) \u0128n-\u2205 v\u00e9 fi \u2205. house-ACC see 3SG.F PFV \u2018She saw a\/some\/the house(s).\u2019 (30) Ti-\u2205 v\u00e9 \u00e3 \u2205. 3SG.M-ACC see 2SG PFV \u2018You saw him.\u2019 32 (31) G\u00e3r-\u2205 f\u00e3n \u1ebdg \u2205. corn-ACC harvest 1PL PFV \u2018We harvested corn.\u2019 (Adapted from Abreu 2009: 42) Note that while pronominal subjects display a flexible distribution, direct objects always immediately precede verbs. Indeed, speakers systematically reject objects \u23af\twhether proper names, bare nouns, or pronouns \u23af\tin any position other than right before the verb, as shown in (32\u23af34), which indicates that the OV order is quite rigid in Kaingang. (32) a. ??F\u00f3gt\u1ebd-\u2205 g\u0129r v\u1ef9 v\u00e9 \u2205. F\u00f3gt\u1ebd-ACC child NOM see PFV \u2018A\/some\/the child(ren) saw F\u00f3gt\u1ebd.\u2019 b. ??G\u0129r v\u1ef9 v\u00e9 F\u00f3gt\u1ebd-\u2205 \u2205 child NOM see F\u00f3gt\u1ebd-ACC PFV \u2018A\/some\/the child(ren) saw F\u00f3gt\u1ebd.\u2019 (33) a. ??Fi-\u2205 F\u00f3gt\u1ebd v\u1ef9 v\u00e9 \u2205. 3SG.F-ACC F\u00f3gt\u1ebd NOM see PFV \u2018F\u00f3gt\u1ebd saw her.\u2019 b. ??F\u00f3gt\u1ebd v\u1ef9 v\u00e9 fi-\u2205 \u2205. F\u00f3gt\u1ebd NOM see 3SG.F-ACC PFV \u2018F\u00f3gt\u1ebd saw her.\u2019 (34) a. ??\u0128n-\u2205 g\u0129r v\u1ef9 v\u00e9 \u2205. house-ACC child NOM see PFV \u2018A\/some\/the child(ren) saw a\/some\/the house(s).\u2019 33 b. ??G\u0129r v\u1ef9 v\u00e9 \u0129n-\u2205 \u2205. child NOM see house-ACC PFV \u2018A\/some\/the child(ren) saw a\/some\/the house(s).\u2019 2.4.4 The case system Kaingang is a language with split ergativity i.e., some constructions display a nominative-accusative system, while others show an ergative-absolutive system (Wiesemann 2002; Nascimento 1995). According to Jolkesky and Santos (2008), Tabosa and Santos (2013), and Tabosa (2014), simple and main clauses in Kaingang usually exhibit a nominative-accusative pattern, whereas embedded clauses have an ergative-absolutive pattern. In nominative-accusative clauses subjects of (in)transitive verbs are immediately followed by the nominative marker v\u1ef9. In contrast, direct objects, which always precede the verb, lack an overt case marker. Following Tabosa and Santos (2013) and Tabosa (2014), I assume that direct objects have a zero accusative marker. These facts are illustrated with the simple clauses in (35) and (36) and the complex clause containing an embedded relative clause in (37). (35) F\u00f3gt\u1ebd v\u1ef9 jun \u2205. F\u00f3gt\u1ebd NOM arrive PFV \u2018F\u00f3gt\u1ebd arrived.\u2019 (36) Kanhg\u00e1g v\u1ef9 \u0129n-\u2205 han \u2205. Kaingang NOM house-ACC build PFV \u2018A\/some\/the Kaingang(s) built a\/some\/the house(s).\u2019 (37) [Kanhg\u00e1g t\u1ef9 \u0129n-\u2205 han m\u0169] v\u1ef9 Pedro-\u2205 v\u00e9 \u2205. Kaingang ERG house-ABS build ASP NOM Pedro-ACC see PFV \u2018A\/some\/the Kaingang(s) who built a\/some\/the house(s) saw Pedro.\u2019 In ergative\/absolutive clauses, subjects of transitive verbs are followed by the ergative particle t\u1ef9, while objects of transitive verbs and non-pronominal subjects of intransitive verbs, which 34 immediately precede the verb, have a zero absolutive marker. This pattern is shown in the embedded clauses in (37\u23af39).16 (38) [G\u0129r-\u2205 v\u1ebdnhg\u00e3g m\u0169] v\u1ef9 pr\u1ebdr \u2205. kid-ABS run ASP NOM scream PFV \u2018A\/some\/the child(ren) who ran screamed.\u2019 (Adapted from Tabosa 2014: 116) (39) Pedro v\u1ef9 [f\u00f3g t\u1ef9 ti jyryryn-\u2205 p\u00e9jun ja]-\u2205 Pedro NOM non.indigenous.person ERG 3P.SG.M car-ABS steal ASP -ACC to jykr\u00e9n n\u0129. think ASP \u2018Pedro thinks that a\/some\/the non-indigenous person(s) stole his car.\u2019 2.4.5 A brief note on relative clauses There are many pieces of morphosyntactic evidence for claiming that relative clauses (RCs) in Kaingang are internally headed (IHRCs). For instance, the internal structure of an RC is similar to that of simple clauses. That is, like simple sentences, their default word order is SOV, as the minimal pair (40a\u23afb) and (41a\u23afb) show. Moreover, RCs in Kaingang lack an overt relativizer, as given in (40b) and (41b). (40) Simple clause a. Kanhg\u00e1g v\u1ef9 \u0129n-\u2205 han \u2205. Kaingang NOM house-ACC build PFV \u2018A\/some\/the Kaingang(s) built a\/some\/the house(s).\u2019 (Adapted from Navarro 2020: 03) 16 The grammatical status of the markers v\u1ef9 and t\u1ef9, as well as their syntactic positions, are still open issues and require further research. For consistency, I am following the descriptive literature in this respect, as indicated in the present section. No important theoretical issues in my analysis hinge on this decision. 35 IHRC b. [RC Kanhg\u00e1g t\u1ef9 \u0129n-\u2205 han m\u0169] v\u1ef9 kute \u2205. Kaingang ERG house-ABS build ASP NOM fall PFV \u2018A\/some\/the Kaingang(s) who built a\/some\/the house(s) fell down.\u2019 \u2018A\/some\/the house(s) that a\/some\/the Kaingang(s) built fell down.\u2019 (Adapted from Navarro 2020: 03) (41) Simple clause a. Pedro v\u1ef9 \u0129n-\u2205 v\u00e9 \u2205. Pedro NOM house-ACC see PFV \u2018Pedro saw a\/some\/the house(s). (Adapted from Navarro 2020: 03) IHRC b. Pedro v\u1ef9 [RC Kanhg\u00e1g t\u1ef9 \u0129n-\u2205 han m\u0169]-\u2205 v\u00e9 \u2205. Pedro NOM Kaingang ERG house-ABS build ASP -ACC see PFV \u2018Pedro saw a\/some\/the Kaingang(s) who built a\/some\/the house(s).\u2019 \u2018Pedro saw a\/some\/the house(s) that a\/some\/the Kaingang(s) built.\u2019 (Adapted from Navarro 2020: 03) (40a) is a simple clause with the bare noun kanhg\u00e1g \u2018Kaingang\u2019 as the subject of the verb and the bare noun \u0129n \u2018house\u2019 as the object. The complex clause (40b) contains (40a) as its IHRC. Consequently, as the subject argument of the main verb kute \u2018fall\u2019, the IHRC receives the nominative case marker v\u1ef9. As for the simple clause in (41a), it has a proper name as subject and the bare noun \u0129n \u2018house\u2019 as the object. The complex clause (41b) contains (40a) as its IHRC, which is the object of the main verb v\u00e9 \u2018see\u2019. Likewise, it mirrors the default position of objects in simple clauses, i.e., immediately preceding the verb. Importantly, one salient property of IHRCs in Kaingang is that, due to the lack of a relativising element and to the fact that their constituents reflect the linear order of simple clauses, they can be ambiguous with respect to which constituent is the relativized head, as the alternative 36 translations above demonstrate. Namely, in (40b) and (41b) the bare nouns kanhg\u00e1g \u2018Kaingang\u2019 and \u0129n \u2018house\u2019 can function as the relativized head of the IHRCs. Based on this fact, Tabosa (2014) hypothesizes that such an ambiguity can be resolved contextually or intonationally. It is likely that context and prosody are involved in disambiguating which constituent of a relative clause is the head. However, especially with regard to intonation, there has not yet been any investigation of this phenomenon when it comes to relativization. So, for the time being I remain neutral with respect to the role of prosody in this regard. For descriptive works on Kaingang relative clauses, see Jolkesky & Santos (2008), Tabosa & Santos (2013), and Tabosa (2014). For a formal analysis of their syntax and semantics, see Navarro (2020). 2.4.6 Bare noun distribution Kaingang is a generalized bare noun language, i.e., its nouns can occur in any argument position without any functional elements such as determiners, number morphemes, or classifiers. This is to say that Kaingang BNs have an unrestricted distribution: they can be external and internal arguments. This is shown in (42\u23af45) with the individual-denoting nouns g\u0129r \u2018child\u2019, \u0129n \u2018house\u2019, and j\u00e3nka \u2018necklace\u2019. (42) G\u0129r v\u1ef9 j\u00e3n \u2205. [external argument] child NOM sing PFV \u2018A\/some\/the child(ren) sang.\u2019 (43) G\u0129r v\u1ef9 kute \u2205. [internal argument] child NOM fall PFV \u2018A\/some\/the child(ren) fell down.\u2019 (44) G\u0129r v\u1ef9 \u0129n-\u2205 v\u00e9 \u2205. child NOM house-ACC see PFV \u2018A\/some\/ the child(ren) saw a\/some\/the house(s).\u2019 37 (45) F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u1ef9 j\u00e3nka-\u2205 f\u1ebdg \u2205. F\u00f3gt\u1ebd NOM child DAT necklace-ACC give PFV \u2018F\u00f3gt\u1ebd gave a\/some\/the necklace(s) to a\/some\/the child(ren).\u2019 Similarly, (46\u23af48) illustrate the unrestricted distribution in argument positions of the substance nouns s\u00f3v \u2018mud\u2019, kyv\u00e9nh \u2018blood\u2019, and goj \u2018water\u2019, respectively. (46) S\u00f3v v\u1ef9 \u0129n-\u2205 k\u00f3k\u00e9 \u2205. [external argument] mud NOM house-ACC destroy PFV \u2018A\/some\/the portion(s) of mud destroyed a\/some\/the house(s).\u2019 (47) Kyv\u00e9nh v\u1ef9 n\u00e3g ke \u2205. blood NOM drip PFV \u2018A\/some\/the drop(s) of blood dripped.\u2019 (48) F\u00f3gt\u1ebd v\u1ef9 goj-\u2205 kron \u2205. [internal argument] F\u00f3gt\u1ebd NOM water-ACC drink PFV \u2018F\u00f3gt\u1ebd drank a\/some\/the bottle(s) of water.\u2019 Additionally, both individual and substance bare nouns can appear in predicative position. This is exemplified in (49) and (50). (49) F\u00f3gt\u1ebd v\u1ef9 t\u1ef9 kanhg\u00e1g n\u0129. F\u00f3gt\u1ebd NOM PRED Kaingang ASP \u2018F\u00f3gt\u1ebd is a Kaingang.\u2019 (50) Kanhk\u00e3 v\u1ef9 t\u1ef9 goj n\u1ef9. cloud NOM PRED water ASP \u2018Clouds are water.\u2019 38 Note that the predicative marker t\u1ef9 is homophonous with the ergative particle. The particle t\u1ef9 is obligatory in constructions like (49) and (50). It always immediately precedes bare nouns in predicative position. As a predicative marker, it can co-occur with the nominative marker v\u1ef9. 2.5 Number and number neutrality Nouns in Kaingang, whether animate or inanimate, lack number inflection and semantically are number neutral. As such, BNs can be used to refer to singularities or pluralities. This is illustrated in (51\u23af53), where singular and plural pronouns anaphorically refer to the antecedent animate bare nouns f\u00f3g \u2018non-indigenous person\u2019 and kasor \u2018dog\u2019 in subject and object positions.17As will be shown in detail in section 2.6, Kaingang BNs can have definite and indefinite interpretations.18 17 In Corbett\u2019s (2000) terminology such nouns express what he calls \u2018general number\u2019. 18 Third-person pronouns can immediately follow nouns, thereby enforcing a singular or plural interpretation of the nominal argument, as given in (i). (i) G\u0129r ti\/ag v\u1ef9 F\u00f3gt\u1ebd-\u2205 v\u00e9 \u2205. child 3SG.M\/3PL.M NOM F\u00f3gt\u1ebd-ACC see PFV \u2018Child\/children saw F\u00f3gt\u1ebd.\u2019 The semantics of such constructions and their categorial status are topics still open for further investigation. It may be the case that the subject NP in (i) is left-dislocated to the initial position of the clause, thus co-referring with the pronouns. Or it may be the case that the pronoun is a D head that takes the preceding noun as a complement and forms a constituent with it. At this point, I don\u2019t have enough evidence to decide between these two options. Navarro (2012) hypothesizes that configurations like g\u0129r ti\/ag, in addition to providing number and gender information, give rise to domain restrictions and definite readings. However, the evidence provided there supporting the claim that they have definite interpretation is still inconclusive, requiring further research. Given the current lack of a better understanding of them, these constructions will not be discussed in this dissertation. This is a topic to explore in future research. 39 (51) R\u00e3ket\u00e1 f\u00f3g1 v\u1ef9 \u1ebdg jam\u00e3 m\u0129 k\u00e3tig \u2205. yesterday non.indigenous.person NOM 1P.PL village inside come PFV \u2018Yesterday a\/some\/the non-indigenous person(s)1 came to our village.\u2019 Ti1\/ag1 t\u00f3g p\u00e3\u2032i \u0129n t\u00e1 n\u0169r \u2205. 3SG.M\/3PL.M TOP chief house inside sleep PFV \u2018He1\/they1 slept in the chief\u2019s house.\u2019 (52) R\u00e3k\u00e9t\u00e1 inh fenht\u00e1 t\u00e1 f\u00f3g1 v\u00e9 \u2205. yesterday 1SG party there non.indigenous.person see PFV \u2018Yesterday I saw a\/some\/the non-indigenous person(s)1 at the party.\u2019 Ti1\/Ag1-\u2205 ki kanhr\u00f3 inh. 3SG.M\/3PL.M-ACC know 1SG \u2018I know him1\/them1.\u2019 (53) R\u00e3ket\u00e1 kasor1 v\u1ef9 m\u0129g-\u2205 v\u00e9 \u2205, yesterday dog NOM jaguar-ACC see PFV \u2018Yesterday a\/some\/the dog(s) saw a\/some\/the jaguar(s).\u2019 K\u1ef9 ti1\/ag1 t\u00f3g m\u0129g to kyn\u223ckyr \u2205. then 3SG.M\/3PL.M TOP jaguar to RED\u223cbark PFV \u2018He\/they barked at a\/some\/the jaguar(s).\u2019 The discourse fragment in (54) exemplifies the number-neutral interpretation of inanimate nouns with the noun p\u00f3 \u2018stone\u2019. 40 (54) P\u00f31 v\u1ef9 kon\u1ebd nor-\u2205 g\u00e3m \u2205. stone NOM eye hole-ACC break PFV \u2018A\/some\/the stone(s) broke a\/some\/the window(s).\u2019 M\u00e1g ti1 j\u1ebd. big 3SG.M ASP \u2018It is big.\u2019 M\u00e1g ag1 n\u1ef9t\u0129. big 3PL.M ASP \u2018They are big.\u2019 Because bare nouns are number neutral, they can provide the discourse set for (multiple) indefinites in subsequent clauses, as shown in (55\u23af57). That is, such a set can contain multiple individuals. (55) G\u0129r v\u1ef9 jun \u2205. child NOM arrive PFV \u2018A\/some\/the children arrived.\u2019 \u0168 v\u1ef9 t\u00e9j j\u1ebd j\u00e3vo \u0169 v\u1ef9 rur j\u1ebd. some NOM tall ASP and some NOM short ASP \u2018One is tall and one is short.\u2019 (56) R\u00e3ket\u00e1 kasor v\u1ef9 m\u0129g-\u2205 v\u00e9 \u2205. yesterday dog NOM jaguar-ACC see PFV \u2018Yesterday a\/some\/the dog(s) saw a\/some\/the jaguar(s)\u2019. \u0168 v\u1ef9 kyr \u2205 j\u00e3vo \u0169 v\u1ef9 r\u00e3m ke \u2205. some NOM bark PFV and some NOM run PFV \u2018One barked and one ran away.\u2019 41 (57) P\u00f3 v\u1ef9 kon\u1ebd nor-\u2205 g\u00e3m \u2205. stone NOM eye hole-ACC break PFV \u2018A\/some\/the stone(s) broke a\/some\/the window(s).\u2019 \u0168 v\u1ef9 m\u00e1g j\u1ebd j\u00e3vo \u0169 v\u1ef9 s\u0129 j\u1ebd. some NOM big ASP and some NOM small ASP \u2018One is big and one is small.\u2019 Further evidence that Kaingang BNs can refer to pluralities comes from their ability to co-occur with collective predicates, such as get together, surround, and encircle, which semantically select for plural subjects. This is exemplified in (58\u23af60). (58) G\u0129r v\u1ef9 v\u1ebdnh m\u00e3n \u2205. child NOM get.together PFV \u2018Some\/the children got together.\u2019 (59) G\u0129r v\u1ef9 ka-\u2205 g\u0129n \u2205. child NOM tree-ACC surround PFV \u2018Some\/the children surrounded a\/some\/the tree(s).\u2019 (60) N\u0129gja v\u1ef9 ka-\u2205 m\u00e3n ror n\u1ef9t\u0129. chair NOM tree-ACC encircle PFV \u2018Some\/the chairs encircle a\/some\/the tree(s).\u2019 Another piece of evidence for the number neutrality of Kaingang bare nouns comes from the fact that they can be antecedents for reciprocals, which select for pluralities. This is illustrated in (61\u23af64) with the reciprocal VPs look like each other, play with each other, bark at each other, and stand in front of each other, respectively. 42 (61) G\u0129r v\u1ef9 jagn\u1ebd-\u2205 v\u00e9 h\u00e3 n\u0129. child NOM RECP-ACC look similar ASP \u2018Some\/the children look like each other.\u2019 (62) G\u0129r v\u1ef9 jagn\u1ebd mr\u00e9 ka-nhin\u223cnhir. child NOM RECP with RED\u223cplay \u2018Some\/the children played with each other.\u2019 (63) Kasor v\u1ef9 jagn\u1ebd to kyn\u223ckyr dog NOM RECP DAT RED\u223cbark \u2018Some\/the dogs barked at each other.\u2019 (64) Ka v\u1ef9 jagn\u1ebd kato j\u1ebd. tree NOM RECP in.front.of ASP \u2018Some\/the trees stand in front of each other.\u2019 2.6 (In)definite and generic interpretations In what follows, I provide evidence that Kaingang bare nouns can have indefinite, definite, and generic interpretations. Given that in Chapter 5 I will focus on the scope properties of Kaingang BNs under their indefinite interpretation, I provide several examples of indefinite interpretations before I offer instances of definite and generic readings. Most of the data in this section replicate diagnostic tests found in Matthewson (1999). 2.6.1 Indefinite interpretation A first piece of evidence that an indefinite interpretation is available is that Kaingang BNs don\u2019t entail or presuppose familiarity, i.e., they can be used to introduce novel discourse referents that can subsequently be referred to by an anaphoric pronoun. This is exemplified in the (fragments of) narratives in (65) and (66). 43 (65) Is\u1ef9 \u00e3 m\u1ef9 g\u0129r1 to k\u00e3m\u00e9n ke v\u1ebd. 1SG.NOM 2SG DAT child tell.story FUT ASP \u2018I will tell you a story about a child1.\u2019 V\u00e3nh k\u00e3m\u0129 fi1 t\u00f3g t\u0129g n\u0129\u2026 bush through 3SG.F TOP walk ASP \u2018She1 was walking in the bush\u2026\u2019 (66) Is\u1ef9 m\u0129g1 k\u00e3m\u00e9n ke. 1SG.NOM jaguar tell.story FUT \u2018I will tell a story about a jaguar1.\u2019 N\u1ebdn k\u00e3m\u0129 fi1 t\u00f3g v\u1ebdnhv\u00e3g t\u0129\u2026 forest through 3SG.F TOP run HAB \u2018She1 was running in the forest\u2026\u2019 Secondly, Kaingang BNs are accepted in utterance contexts in which uniqueness is not satisfied. This is illustrated in (67\u23af69), where the bare nouns kr\u0129g \u2018star\u2019, g\u0129r \u2018child\u2019, and kanhg\u00e1g \u2018Kaingang\u2019 can all be used in non-unique scenarios. (67) Context: You and a friend are looking at a cloudy night sky. Suddenly a star appears. You say: Hav\u00e9 kr\u0129g v\u1ebdnh ven \u2205.\tlook star appear PFV \u2018Look, a star appeared.\u2019 44 (68) Context: There are three children in the house. One of them is sleeping. The other two are playing. I enter the house speaking aloud. You admonish me: Kum\u1ebdr h\u00e3 v\u0129, g\u0129r n\u0169r n\u1ef9. slow word child sleep ASP \u2018Talk quietly, a child is sleeping.\u2019 (69) Context: There are many Kaingangs in the house and one of them is singing. Kanhg\u00e1g e v\u1ef9 \u0129n ki n\u1ef9t\u0129 j\u00e3vo kanhg\u00e1g j\u00e3n m\u0169. Kaingang many NOM house in ASP and Kaingang sing ASP \u2018There are many Kaingangs in the house and a Kaingang is singing.\u2019 Thirdly, Kaingang BNs are accepted in conjoined sentences containing incompatible predicates. Although speakers show a preference for interpreting two occurrences of the same bare noun in a sentence as co-referring, especially in out-of-the-blue statements, they do not always enforce it. The fact that (70\u23af72) do not sound contradictory constitutes further evidence that Kaingang BNs do not require uniqueness, since each occurrence of the BN g\u0129r \u2018child\u2019 picks out a different referent. (70) Context: There are two children in the house: Pedro and Sandro. Pedro is sleeping and Sandro is playing. G\u0129r v\u1ef9 n\u0169r n\u1ef9 h\u00e3ra g\u0129r v\u1ef9 kanhir j\u1ebd. child NOM sleep ASP but child NOM play ASP \u2018A child is sleeping, but a child is playing.\u2019 45 (71) Context: Your neighbour had two kids: Pedro and Sandro. Pedro is alive but Sandro is dead. G\u0129r r\u0129r n\u1ef9 h\u00e3ra g\u0129r ter j\u00e1 n\u0129. child alive ASP but child die ASP ASP \u2018A child is alive but a child is dead.\u2019 (72) Context: You made two chairs. Yesterday one of them broke and the other didn\u2019t. N\u0129gja mr\u00e1j \u2205, h\u00e3ra n\u0129gja mr\u00e1j \u2205 t\u0169 n\u0129. chair break PFV but chair break PFV NEG ASP \u2018A chair broke, but a chair didn\u2019t break.\u2019 The availability of indefinite readings of Kaingang BNs is also made explicit by sluicing-like constructions in the language, which, like genuine sluicing cases in English, can be used as a test for indefiniteness (Matthewson 1999). In (73) and (74), the bare nouns m\u0129g \u2018jaguar\u2019 and f\u00f3g \u2018non-indigenous person\u2019, both behaving as antecedents to elided coreferential constituents, are interpreted as non-specific indefinites. That is, (73) and (74) portray the speaker as not having any jaguar or non-indigenous person in mind.19 (73) Context: You know that a jaguar attacked F\u00f3gt\u1ebd, but don\u2019t know which jaguar did it. You tell me: M\u0129g v\u1ef9 F\u00f3gt\u1ebd m\u00e3 \u2205, h\u00e3ra inh ki kagt\u0129g n\u0129. jaguar NOM F\u00f3gt\u1ebd attack PFV, but 1SG not.know ASP \u2018A jaguar attacked F\u00f3gt\u1ebd, but I don\u2019t know which.\u2019 19 I\u2019m cautious to call the sentences in (73) and (74) genuine sluicing cases because they lack a wh-remnant preceding the ellipsis site. In all attempts to elicit sluicing constructions (through discourse contexts or translations of sluicing sentences in Brazilian Portuguese) consultants always provided the construction \u2026h\u00e3ra inh ki kagt\u0129g n\u0129 as in (73) and (74). Despite this, I opted to include the sentences in (73) and (74) because they illustrate existential readings of bare nouns. 46 (74) F\u00f3gt\u1ebd v\u1ef9 f\u00f3g kan\u1ebdg m\u0169, h\u00e3ra inh ki kagt\u0129g n\u0129. F\u00f3gt\u1ebd NOM non.indigenous.person look.for ASP but 1SG not.know ASP \u2018F\u00f3gt\u1ebd is looking for a non-indigenous person, but I don\u2019t know who.\u2019 2.6.2 Definite interpretation Kaingang BNs can also display abilities associated with definite nominals. BNs, for instance, can be used anaphorically, i.e., to refer to familiar discourse referents in a narrative, as laid out in (75\u23af78) with the bare nouns g\u0129r \u2018child\u2019, m\u0129g \u2018jaguar\u2019, and kasor \u2018dog\u2019, respectively. (75) R\u00e3ket\u00e1 g\u0129r1 v\u1ef9 mur \u2205 jam\u00e3 ki. yesterday child NOM born PFV village in \u2018Yesterday a child1 was born in the village.\u2019 G\u0129r1 t\u00f3g m\u00e1g n\u0129. child TOP big ASP \u2018The child1 is big.\u2019 (76) Is\u1ef9 \u00e3 m\u1ef9 g\u0129r1 to k\u00e3m\u00e9n ke v\u1ebd. 1SG.NOM 2SG DAT child tell.story FUT ASP \u2018I will tell you a story about a child1.\u2019 V\u00e3nh k\u00e3m\u0129 g\u0129r1 t\u00f3g t\u0129g n\u0129\u2026 bush through child TOP walk ASP \u2018The child1 was walking in the bush\u2026\u2019 47 (77) Is\u1ef9 m\u0129g1 k\u00e3m\u00e9n ke. 1SG.NOM jaguar tell.story FUT \u2018I will tell a story about a jaguar1.\u2019 N\u1ebdn k\u00e3m\u0129 m\u0129g1 t\u00f3g v\u1ebdnhv\u00e3g t\u0129\u2026 forest through jaguar TOP run HAB \u2018The jaguar1 was running in the forest\u2026\u2019 (78) R\u00e3ket\u00e1 kasor1 v\u1ef9 m\u0129g2-\u2205 v\u00e9 \u2205. yesterday dog NOM jaguar-ACC see PFV \u2018Yesterday a dog1 saw a jaguar2\u2019. K\u1ef9 kasor1 t\u00f3g m\u0129g2 to kyr \u2205. then dog TOP jaguar DAT bark PFV \u2018The dog1 barked at the jaguar2.\u2019 Kaingang bare nouns are also felicitous in unique contexts, i.e., they can be used to refer to unique discourse referents, as shown in (79\u23af81) with the bare nouns r\u00e3 \u2018sun\u2019, kanhk\u00e3 \u2018sky\u2019, and kys\u00e3 ror \u2018full moon\u2019, respectively. (79) R\u00e3 v\u1ef9 jur m\u0169 ha. sun NOM come ASP now \u2018The sun is rising now.\u2019 (Adapted from Wiesemann 2002: 35) (80) Kanhk\u00e3 v\u1ef9 g\u00f3g m\u0169 ha. sky NOM cloudy ASP now \u2018The sky is getting cloudy now.\u2019 (Adapted from Wiesemann 2002: 39) 48 (81) Kys\u00e3 ror t\u1ef9 ga t\u00e1 jun ke k\u1ef9 \u2205 t\u00f3g \u00e9h\u00e9 n\u0129. moon round ERG earth there arrive FUT when 3 TOP large ASP \u2018When the full moon appears in the earth it is large.\u2019 (Adapted from Wiesemann 2002: 59) 2.6.3 Generic interpretation Furthermore, Kaingang BNs can get generic readings when they occur in so-called characterizing sentences (Krifka et al. 1995). This is illustrated in (82\u23af84) with the bare nouns kanhg\u00e1g \u2018Kaingang\u2019, m\u0129g \u2018jaguar\u2019, hinh \u2018armadillo\u2019, and goj \u2018water\u2019. (82) Kanhg\u00e1g v\u1ef9 kanhr\u00f3 n\u0129. Kaingang NOM intelligent ASP \u2018Kaingangs are intelligent.\u2019 (83) M\u0129g v\u1ef9 hinh to h\u00e1 n\u0129. jaguar NOM armadillo like ASP \u2018Jaguars like armadillos.\u2019 (84) Goj v\u1ef9 r\u1ef9g k\u1ef9 v\u00e3nv\u00f3r t\u0129. water NOM heat when boil HAB \u2018Water boils when heated.\u2019 The availability of kind-readings of Kaingang BNs, or lack thereof, is still an open question. So far, I haven\u2019t identified any strictly kind-level predicates, such as be extinct, invent, or discover, which would provide a conclusive test for kind-referring expressions (Krifka et al. 1995). Thus, Table 9 summarizes the (un)attested interpretations of Kaingang bare nouns. 49 Yes No Indefinite reading \u2713 Definite reading \u2713 Generic reading \u2713 Kind reading ? ? Table 9: Kaingang bare noun interpretations. 2.7 Numerals Kaingang is not a classifier language: numerals can combine with count nouns without any accompanying classifier, as shown in (85\u23af91), which display (in)animate nouns modified by numerals. Also, because Kaingang nouns don\u2019t inflect for number, they don\u2019t require any morphological exponent of number information in order to combine with numerals. (85) G\u0129r t\u00e3gt\u0169 v\u1ef9 jun~jun \u2205. child three NOM RED~arrive PFV \u2018Three children arrived.\u2019 (86) F\u00f3gt\u1ebd v\u1ef9 g\u0129r r\u00e9gre-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child two-ACC see PFV \u2018F\u00f3gt\u1ebd saw two children.\u2019 (87) Kasor t\u00e3gt\u0169 v\u1ef9 kyn\u223ckyr \u2205. dog three NOM RED\u223cbark PFV \u2018Three dogs barked.\u2019 (88) F\u00f3gt\u1ebd v\u1ef9 m\u0129g r\u00e9gre-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM jaguar two-ACC see PFV \u2018F\u00f3gt\u1ebd saw two jaguars.\u2019 50 (89) Hav\u00e9 kr\u0129g pir v\u1ef9 v\u1ebdnh ven \u2205. look star one NOM appear PFV \u2018Look, one star appeared.\u2019 (90) F\u00f3gt\u1ebd v\u1ef9 n\u0129gja t\u00e3gt\u0169-\u2205 kaj\u00e3m \u2205. F\u00f3gt\u1ebd NOM chair three-ACC buy PFV \u2018F\u00f3gt\u1ebd bought three chairs.\u2019 (91) F\u00f3gt\u1ebd v\u1ef9 g\u0129r r\u00e9gre m\u1ef9 garinh pir-\u2205 f\u1ebdg \u2205. F\u00f3gt\u1ebd NOM child two to hen one-ACC give PFV \u2018F\u00f3gt\u1ebd gave one hen to two children.\u2019 Note that in the constructions above, which contain nouns modified by numerals in subject and object positions, the numeral always immediately follows the noun. Numeral+noun order is ungrammatical in Kaingang, as given in (92) and (93). (92) *T\u00e3gt\u0169 g\u0129r v\u1ef9 jun~jun \u2205. three child NOM RED~arrive PFV \u2018Three children arrived.\u2019 (93) *F\u00f3gt\u1ebd v\u1ef9 r\u00e9gre m\u0129g-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM three jaguar-ACC see PFV \u2018F\u00f3gt\u1ebd saw three jaguars.\u2019 2.8 Other quantity words Apart from numerals, Kaingang has at least five quantity words: kar \u2018all\u2019, \u0169 \u2018some\u2019, e \u2018many\u2019, pipir \u2018few\u2019, and m\u1ebd \u2018more\u2019. Like numerals, all these terms can directly combine with nouns, as illustrated with the noun g\u0129r \u2018child\u2019 in (94\u23af98). 51 (94) a. G\u0129r kar v\u1ef9 j\u00e3n~j\u00e3n \u2205. child all NOM RED~sing PFV \u2018All the children sang.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 g\u0129r kar-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child all-ACC see PFV \u2018F\u00f3gt\u1ebd saw all the children.\u2019 (95) a. G\u0129r \u0169 v\u1ef9 j\u00e3n~j\u00e3n \u2205. child some NOM RED~sing PFV \u2018Some child(ren) sang.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 g\u0129r \u0169-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child some-ACC see PFV \u2018F\u00f3gt\u1ebd saw some child(ren).\u2019 (96) a. G\u0129r e v\u1ef9 j\u00e3n~j\u00e3n \u2205. child many NOM RED~sing PFV \u2018Many children sang.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 g\u0129r e-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many children.\u2019 (97) a. G\u0129r pipir v\u1ef9 j\u00e3n~j\u00e3n \u2205. child few NOM RED~sing PFV \u2018Few children sang.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 g\u0129r pipir-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child few-ACC see PFV \u2018F\u00f3gt\u1ebd saw few children.\u2019 52 (98) F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u1ebd n\u0129 Pedro ve k\u1ef9. F\u00f3gt\u1ebd NOM child more ASP Pedro than \u2018F\u00f3gt\u1ebd has more children than Pedro.\u2019 Just like numerals, the quantity terms necessarily follow the noun they combine with, i.e., they are precluded from preceding them, as shown in (99) and (100). (99) a. *Kar\/ \u0169\/e\/pipir g\u0129r v\u1ef9 j\u00e3n~j\u00e3n \u2205. All\/some\/many\/few child NOM RED~sing PFV \u2018All\/some\/many\/few child(ren) sang.\u2019 b. *F\u00f3gt\u1ebd v\u1ef9 kar\/ \u0169\/e\/pipir g\u0129r-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM all\/some\/many\/few child- ACC see PFV \u2018F\u00f3gt\u1ebd saw all\/some\/many\/few child(ren).\u2019 (100) *F\u00f3gt\u1ebd v\u1ef9 m\u1ebd g\u0129r n\u0129 Pedro ve k\u1ef9. F\u00f3gt\u1ebd NOM more child ASP Pedro than \u2018F\u00f3gt\u1ebd has more children than Pedro.\u2019 The distribution and interpretation of Kaingang numerals, as well as of most of the quantity expressions introduced in this section, will be discussed in more detail in Chapter 4, in the context of the investigation of nominal countability in the language. There I will show that quantity expressions interact in the same way with individual and substance nouns. 2.9 Verbal number In addition to personal pronouns, many verbs in Kaingang also encode number (Henry 1948; Wiesemann 1971, 2002; Cavalcante 1987; D\u2019Angelis 2004). Such verbs contrast a singular and a plural form. In Kaingang, verbal plurality does not express agreement between the verb and its arguments. Instead, the plural form of verb indicates a multiplicity of events, which can 53 involve a single or multiple participants (Henry 1948; D\u2019Angelis 2004). This phenomenon is called pluractionality in the literature (Cusic 1981; Newman 1990, 2012; Lasersohn 1995; Ojeda 1998; Matthewson 2000; Yu 2003; M\u00fcller & Sanchez 2008, 2021; Ward 2012; Mattiola 2019; Zimmermann 2021). In Kaingang pluractionality can be indicated by verbal reduplication, prefixation, infixation, or a suppletive form, as illustrated in (101\u23af104). (101) Reduplication Singular Plural a. jun junjun \u2018arrive\u2019 b. j\u00e3n j\u00e3nj\u00e3n \u2018sing\u2019 c. n\u1ebdm n\u1ebdmn\u1ebdm \u2018roast\u2019 d. han hynhan \u2018make\/build\u2019 e. gren gringren \u2018dance\u2019 f. kanhin kanhinnhin \u2018play\u2019 (102) Prefixation Singular Plural a. ter k\u00e3gter \u2018die\u2019 b. t\u00e9n k\u00e3gt\u00e9n \u2018kill\u2019 c. grin pugrin \u2018roll\u2019 d. g\u00f3nh p\u00e3g\u00f3nh \u2018to give water\u2019 (103) Suppletion Singular Plural a. m\u00e3n g\u00e9 \u2018carry (short things)\u2019 b. kut\u1ebdm pan \u2018drop\u2019 c. k\u00e3r\u00e3g gem \u2018make someone come in\u2019 d. n\u0129m vin \u2018give (not long things)\u2019 54 (104) Infixation Singular Plural a. kuj\u00e9n kugj\u00e9n \u2018extend\u2019 b. n\u0129f\u00e9nh n\u0129gf\u00e9nh \u2018close\u2019 c. j\u00e3ti j\u00e3gti \u2018dream\u2019 d. pasa pagsa \u2018walk around\u2019 Cavalcante (1987) shows that the default syllable pattern of the verbal reduplicant is CVC, as given in (101a\u23aff). Moreover, he demonstrates that reduplicants can be prefixed to the root of monosyllabic verbs, as given in (101a\u23afe), or can be infixed to the stressed syllable of the basic verb form, as in (101f). Evidence that reduplication in (101a\u23afe) constitutes prefixation, according to Cavalcante (1987) and Salanova (2011), comes from the fact that some verbal reduplicants exhibit vowel raising, as illustrated in (101d,\te). (102a\u23afd) exemplify cases of pluractional forms created by inserting non-reduplicant prefixes. Infixation is illustrated in (104a\u23afd) by cases in which the nasal velar phoneme \/\u014b\/ is inserted before the last syllable of the basic verb form. For a detailed description and analysis of the phonological processes involved in the expression of verbal plurality in Kaingang see Cavalcante (1987). To illustrate some of the available interpretations of pluractional forms of Kaingang verbs, take the reduplicated versions of the intransitive verb j\u00e3n \u2018sing\u2019 in sentences (105) and (106), for instance. (105) F\u00f3gt\u1ebd v\u1ef9 j\u00e3n~j\u00e3n \u2205. F\u00f3gt\u1ebd NOM RED~sing PFV \u2018F\u00f3gt\u1ebd sang (repeatedly).\u2019 Iterative meaning (106) G\u0129r v\u1ef9 j\u00e3n~j\u00e3n \u2205. child NOM RED~sing PFV \u2018A\/the child sang (repeatedly).\u2019 Iterative meaning \u2018Some\/the children sang.\u2019 Multiple-participants meaning 55 In (105) the verbal root j\u00e3n \u2018sing\u2019 is reduplicated in order to indicate that the singular individual denoted by the proper name F\u00f3gt\u1ebd sang more than once, i.e., to express the iteration of events of singing. This means that whenever the subject of a plural verb is singular, sentences like (105) can give rise to iterative readings involving a single participant. As for sentence (106), which contains as subject the number-neutral bare noun g\u0129r \u2018child\u2019, it can have a number of readings. Like (105), it can mean that a single child sang repeatedly. In addition, (106) can have a meaning which involves multiple participants. For instance, it can be true in a situation in which each child in a group of children sang separately or in a scenario in which some children sang together, whereas others sang individually. The information offered above suffices for the purpose of showing that Kaingang encodes morphological number in its verbal domain. However, it is important to conclude this section by saying that further research on the meaning of verbal number in Kaingang is still needed. The semantic mechanisms underlying the full range of its available readings have not been yet explored. For example, a crucial question still to be addressed is whether the different ways of morphologically marking pluractionality \u23af i.e., via reduplication, prefixation, suppletion or infixation \u23af express different pluractional readings.20 2.10 Fieldwork methodology All the data for this study originated from three periods of fieldwork that took place between 2022 and 2024. Each fieldwork period lasted for about a month and was conducted in the Kaingang territory of Rio das Cobras, in the state of Paran\u00e1 in southern Brazil. The data were collected by the author through direct elicitation with three native speakers of Kaingang, aged 25, 43, and 46 20 A preliminary attempt at a formal investigation of pluractionality in Kaingang was outlined in my first qualifying paper (Navarro 2020). The results of the paper and the questions it raised became the starting point for an ongoing project on verbal plurality in Kaingang, funded by the Jacob Research Funds (JRF). With this project I intend to reach an overarching understanding of verbal number in Kaingang and its interaction with the nominal domain from a formal semantic perspective, as well as to contribute to the study of variations in the meaning of pluractionality across languages. But this is research in progress that goes beyond the scope of this dissertation. 56 years old. All of them are speakers of the Paran\u00e1 dialect, and fluently bilingual in Brazilian Portuguese. The principal elicitation methodology used in this study was the acceptability judgment task (Matthewson 2004; Bochnak & Matthewson 2020). In this task, consultants are presented with a context paired with a well-formed sentence of the language under investigation, and then asked to judge whether the sentence is accepted in that context. This method relies on either truth-value or felicity judgments. The discourse contexts against which sentences were judged were presented either verbally or non-verbally. The latter technique involved language-independent single images or storyboards (Matthewson 2004, 2012; Barner & Snedeker 2005; Krifka 2011; Bochnak & Matthewson 2020; Bohnemeyer 2015; Burton & Matthewson 2015). Following Matthewson\u2019s (2004, 2012) methodological advice, in order to reduce the chance of speakers imagining alternative contexts when hearing a sentence in the target language before a context is provided, I always first presented the context, explained it, and only then provided the Kaingang sentence. Verbal contexts were presented in Brazilian Portuguese and mostly used to represent contexts that are too complex to illustrate with pictures. For instance, to test whether bare nouns could have wide scope with respect to if-clauses (see Chapter 5), sentence (107a) was paired with the context below. (107) \u2713Context: There will be many Kaingangs at the party. You are the party singer. If a particular Kaingang (named F\u00f3gt\u1ebd) arrives there, you will sing the song Gar\u00e7om. You tell me:21 a. F\u00e9nhta ki kanhg\u00e1g-\u2205 jun m\u0169ra, s\u00f3g Gar\u00e7om j\u00e3n party at Kaingang-ABS arrive if 1SG.TOP Gar\u00e7om sing ke m\u0169. FUT ASP \u2018If a Kaingang arrives at the party, I will sing Gar\u00e7om.\u2019 21 Gar\u00e7om \u2018The Waiter\u2019 is a popular Brazilian love song. 57 b. There is a Kaingang x, such that if x arrives at the party, I will sing Gar\u00e7om. The fact that all the three speakers accepted sentence (107a) in the context above indicates that the bare noun kanhg\u00e1g \u2018Kaingang\u2019 in the antecedent of a conditional clause can be used to refer to a specific individual. This can be explained, for instance, by saying that the bare noun is interpreted as scoping over the if-clause, as captured by the paraphrase in (107b). I used single images to design contexts that are easily representable through static pictures (see Chapter 4). For instance, single images were used to investigate the availability of cardinality evaluations of substance nouns like renhte \u2018milk\u2019, v\u1ebdnh kuri \u2018flour\u2019, etc., in comparison constructions (Barner & Snedeker 2005; Lima 2014a, b). The consultants were shown pictures of real-world objects and substances. Each picture contained a collection of one or two portions of a substance side-by-side with another collection of portions of the same substance, as illustrated in Figures 6\tand\t7 with pictures of portions of milk and flour. The quantities on the left side of the pictures were presented as belonging to one person and those on the right side to another one. After showing these stimuli pictures to each consultant, they were asked the target comparative questions in (108) and (109). Figure 6: renhte \u2018milk\u2019. 58 Figure 7: v\u1ebdnh kuri \u2018flour\u2019. (108) \u0168 n\u1ef9 t\u1ef9 renhte m\u1ebd n\u0129? some Q ERG milk more ASP \u2018Who has more milk?\u2019 (109) \u0168 n\u1ef9 t\u1ef9 v\u1ebdnh kuri m\u1ebd n\u0129? some Q ERG flour more ASP \u2018Who has more flour?\u2019 If the speakers\u2019 evaluations are that Maria has more milk and flour than Pak\u00f3j in the scenarios depicted in Figures 6\tand\t7, despite the fact that in both situations the total volumes of milk and flour that Pak\u00f3j has exceed the ones that Maria has, these indicate that the Kaingang speakers can interpret substance nouns along the number dimension, since Maria has more portions of milk and flour than Pak\u00f3j. Moreover, if the finding is that the speakers systematically count the number of portions in their comparative judgements containing substance nouns, this at least suggests that the predominant interpretation of Kaingang substance nouns is cardinality-based, rather than volume-based. Similarly, in the elicitation sessions for Chapter 5, I employed single images to test the availability of a narrow scope reading of a bare noun like \u0129n \u2018house\u2019 under the universal quantifier kar \u2018all\u2019. For example, sentence (110) was paired with the context depicted in Figure 8, where each non-indigenous person built a different house. The distributive reading shown in Figure 8 is only available if the BN takes scope under the universal quantifier. 59 Figure 8: Building houses. (110) F\u00f3g kar v\u1ef9 \u0129n-\u2205 han \u2205. non.indigenous.person all NOM house-ACC make ASP \u2018All non-indigenous persons built a house.\u2019 Finally, I also employed storyboards (Burton & Matthewson 2015) to elicit acceptability judgements. This procedure consists of representing a context \u201cthrough a series of pictures that tell a story\u201d (Bochnak & Matthewson 2020: 269). To test the availability of intermediate scope readings of Kaingang bare nouns, for instance, speakers were presented with the storyboard depicted in Figure 9 and then shown sentence (111a), which contains the bare noun \u0129n \u2018house\u2019 and two occurrences of the universal quantifier kar \u2018all\u2019 (see Chapter 5). The context depicted in Figure 9 contains three chiefs, six non-indigenous persons, and three houses. Each house was built 60 by a distinct pair of non-indigenous persons and each chief likes one of the pairs. Crucially, each non-indigenous person is a member of just one of the pairs. Figure 9: Intermediate reading scenario. (111) a. P\u00e3\u00b4i kar v\u1ef9 f\u00f3g kar t\u1ef9 \u0129n-\u2205 han chief all NOM non.indigenous.person all ERG house-ABS make m\u0169 to h\u00e1 n\u0129. ASP like ASP \u2018All chiefs like all non-indigenous persons that built a house.\u2019 b. For every chief x, there is a house y, such that x likes every non-indigenous person z that built y. The fact that the three speakers considered (111a) felicitous as a description of Figure 9 suggests, as I discuss in detail in Chapter 5, that Kaingang bare nouns can receive intermediate scope readings, as represented in (111b). 61 Thus, in this subsection I have discussed the elicitation method employed in this research, namely the acceptability judgment task. Each technique of pairing a sentence of the target language with a verbal or non-verbal discourse context that was used in this study has been illustrated with at least one example. 62 Chapter 3: Mereology-based and Type-shifting Approaches 3.1 Introduction In this chapter, I introduce the two main background theories of this thesis, namely mereology-based semantics and type-shifting semantics. In section 3.2, I discuss the mereology-based theories of Link (1983, 1998) and Krifka (1986, 1989, 2007, 2008). I start off with Link\u2019s double domain theory, which introduced mereology into formal semantics as a tool to model countability distinctions in natural language, and laid the foundation for what became a productive theoretical framework. Subsequently, I focus on Krifka\u2019s approach, which, by introducing the semantic notion of quantization, as well as avoiding the commitment to a two-domain ontology, offered important solutions to problems engendered by Link\u2019s theory, in particular those in connection with its reliance on atomicity. Indeed, as will be shown in Chapter 4, Krifka\u2019s theory, with minor changes, successfully provides the core formal tools and concepts to analyse nominal countability in languages like Kaingang, whose nouns display a pervasive count interpretation. In section 3.3, I discuss Partee\u2019s (1986) type-shifting theory of nominal phrases. The flexible type-shifting mechanisms that she proposed as a way to relate the different meanings of nominals have allowed semanticists to account for attested variation in the interpretations of bare nouns in a language or across languages (Chierchia 1998b; Krifka 2003; Dayal 2004, among others). As will be shown in Chapter 5, my analysis of the semantics of Kaingang bare nouns, in particular of their variable-scope effects, draws on a type-shifting framework. Further, I show there that there is an interaction between mereological properties of (bare) nouns across languages and their available scope effects. The analyses in Chapters 4 and 5 will demonstrate that my adoption of both Krifka\u2019s framework and type-shifting semantics is empirically motivated by evidence from Kaingang. 3.2 Mereology-based semantics 63 3.2.1 Link\u2019s two-domain theory: atomic vs. nonatomic predicates Link (1983) provides the first mereology-based analysis of the count\/mass and singular\/plural oppositions in the nominal domain. His analysis of mass and plural nouns has a two-fold aim: to capture (i) the similarities between the denotations of mass and plural nouns, and (ii) the differences between the denotations of mass and count nouns. The analysis is empirically motivated by certain intuitions that speakers have about entailment relations that seem to depend on the part-whole structures of the denotations of nouns. For example, take prototypical mass and plural nouns like water and linguists in (112a\u23afc) and (113a\u23afc). Link (1983), following Quine (1960), claims that the inferences from (112a\u23afb) to (112c) and from (113a\u23afb) to (113c) indicate that mass and plural nouns share the property of cumulative reference: if water is true of two things, then it is also true of their sum, and if linguists is true of Lisa and Hotze, as well as of Marcin and Henry, then linguists is true of their sum. (112) a. The liquid in Lisa\u2019s mug is water. b. The liquid in Hotze\u2019s mug is water. c. \u21d2 The liquid in Lisa\u2019s mug and the liquid in Hotze\u2019s mug are water. (113) a. Hotze and Lisa are linguists. b. Marcin and Henry are linguists. c. \u21d2 Hotze, Lisa, Marcin and Henry are linguists. In contrast, the fact that (114a\u23afb) don\u2019t entail (114c) indicates that English singular count nouns are non-cumulative. (114) a. Lisa is a linguist. b. Hotze is a linguist. c. \u21cf Lisa and Hotze is\/are a linguist. 64 Link (1993, 1998) designs the domain of (concrete) entities in the denotation of nouns as a structured set with a join-semilattice (without the null element), i.e., as an algebraic structure that represents their part-whole relations. As such, the mereological sum operation \u2294 is assumed as the basic notion, and the part relation \u2291 is derived from it. Formally, a join-semilattice is a structure \u27e8E, \u2294\u27e9, where E is a set of entities and \u2294 is the sum operation on E (Champollion & Krifka 2016). Hence, if a \u220a E and b \u220a E, then a\u2294b \u220a E. The definition of binary sum is given in (115), while the definitions of part and proper part are laid out in (116) and (117), respectively.22 (115) x\u2294y \u225d \u2294{x,y} (Adapted from Champollion 2015: 11) (116) x \u2291 y \u225d x\u2294y = y (x is part of y iff the sum of x and y is identical to y.) (Adapted from Krifka 2007: 7) (117) x \u228f y \u225d x \u2291 y \u2227 \u00ac(x = y) (x is a proper part of y iff x is part of y and x is distinct from y.) (Adapted from Krifka 2007: 7) Another important notion in mereology theories is overlap, which applies to objects that share parts. Usually, overlap is defined on the basis of the part relation \u2291, as stated in (118). (118) x\t\u25cb y \u225d \u2203z[z \u2291 x \u2227 z \u2291 y] (x and y overlap iff they have a part z in common.) (Adapted from Krifka 2007: 7) 22 The part relation is reflexive, transitive and antisymmetric. 65 In Link\u2019s approach (1983, 1998), the defining property that distinguishes count nouns from mass nouns is atomicity. That is, the count\/mass opposition is based on an ontological distinction between atomic and non-atomic join-semilattice structures. While count nouns are constrained to be interpreted in an atomic domain, mass nouns are interpreted in a non-atomic domain (or one that is non-specified with respect to atomicity). In a mereology-based semantics, atoms can be defined absolutely, as given in (119), or relative to a predicate P, as defined in (120). (119) ATOM(x) \u225d \u00ac\u2203y[y \u228f x] (x is an atom iff x has no proper part.) (Adapted from Krifka 2007: 10) (120) ATOM(P)(x) \u225d P(x) \u2227 \u00ac\u2203y[y \u228f x \u2227 P(y)] (x is an atom relative to a predicate P iff P holds of x and there isn\u2019t a proper part of x of which P also holds.) (Adapted from Krifka 2007: 10) Thus, given (119) and (120), an atomic predicate can be defined as in (121). (121) ATOMIC(P) \u225d \u2200x[P(x) \u2192 \u2203y[y \u2291 x \u2227 ATOM(P)(y)] (A predicate P is atomic iff for every x that is P, there is a part of x that is an atom in P.) (Adapted from Krifka 1989: 78) Link (1983, 1998) models the denotation of plural and mass terms as belonging to two ontologically disjoint domains: the former a domain De of individuals that contains both atomic and plural individuals (e.g., ordinary individuals like Peter and Mary, as well as their sum) and the latter a non-atomic domain Dm of stuff\/matter (e.g., substances like water and blood). The distinction between the two domains can be informally exemplified as follows: while the parts of a cat aren\u2019t cats, the portions of the water in my glass now are also water, at least down to an unspecified granularity. This entails that as individuated entities, one cat in my bedroom and 66 another cat in my kitchen assemble to two cats. In contrast, if I add a quantity of water to the amount of water already in my glass, the result isn\u2019t two quantities of water, but a single amount. In a join-semilattice representation, the atoms are the elements at the bottom, the intermediary sums form the middle of the structure, and the total sum constitutes the top element of the lattice (a.k.a. the supremum), as illustrated in Figure 10. Figure 10: Atomic join-semilattice structure (individuals). The atomic join-semilattice in Figure 10 ensures that, because a, b, and c are individuals, any sums of them are also individuals. For instance, assume that our domain of entities contains three individuals as its atoms: hotze, lisa, and marcin. Since this domain is closed under mereological sum, the plural individuals hotze\u2294lisa, hotze\u2294marcin, lisa\u2294marcin, and hotze\u2294lisa\u2294marcin are also in the domain. As for the domain of stuff\/matter, it is modeled as a non-atomic semilattice. For instance, a domain containing portions of the substance water can be represented as in Figure 11, where \u2018wrn\u2019 stands for a portion of water, the dots at the bottom represent the non-atomicity of the structure, and the other dots indicate a domain of non-inherently discrete entities. Figure 11: Atomic join-semilattice structure (stuff\/matter). 67 In Link\u2019s theory, plural and mass nouns denote join-semilattice structures like in Figures 10 and 11, respectively, and as such share the property of cumulative reference, given that both structures are closed under mereological sum. Formally, cumulativity is defined as a higher-order property of predicates, as given in (122). (122) CUM(P) \u225d \u2200x\u2200y[P(x) \u2227 P(y) \u2192 P(x\u2294y)] (A predicate P is cumulative iff whenever P holds of two entities, it also holds of their sum.) (Adapted from Krifka 1989: 78) While mass nouns are inherently cumulative, as represented in the lexical entry for water in (123), plural nouns get their cumulative interpretation via their plural morphology. (123) \u27e6water\u27e7 = {\u2026wr1, \u2026wr2, \u2026 wr3, wr1\u2294wr2, wr1\u2294wr3, wr2\u2294wrn, wr1\u2294wr2\u2294wr3} Link treats pluralization of count nouns as a logical operation on the domain of individuals. Singular count nouns denote sets of atoms, i.e., the bottom of semilattices such as in Figure 10. Plural count nouns are modeled as denoting sets of atoms and their mereological sums. Such sets are formed via the * operator, conceived of as the algebraic closure of a set under sum formation, as laid out in (124). (124) *P = {x: \u2203P\u2019: P\u2019 \u2260 \u2205 \u2227 P\u2019 \u2286 P \u2227 x = \u2294P\u2019} (*P is the set that contains all the sums of entities in P) (Adapted from Champollion & Krifka 2016: 526) The * operator applies to the denotation of a predicate P and returns a set that contains any sum of entities in the denotation of P. Let\u2019s assume that P denotes the set {a, b, c}. As a result, the algebraic closure of P is *P = {a, b, c, a\u2294b, b\u2294c, a\u2294c, a\u2294b\u2294c}. The set created by the * operator encompasses all members of P and their sums. The application of the * operator to any predicate creates cumulative reference. For instance, in a toy model in which the set of linguists is exhausted by the 68 atoms hotze, lisa, and marcin, the singular noun linguist has the extension illustrated in (125), while the plural linguists denotes the algebraic closure of linguist via *, as represented in (126). (125) \u27e6linguist\u27e7 = {hotze, lisa, marcin} (126) \u27e6linguist-s\u27e7 = *\u27e6linguist\u27e7 = {hotze, lisa, marcin, hotze\u2294lisa, hotze\u2294marcin, lisa\u2294marcin, hotze\u2294lisa\u2294marcin} Thus, plural formation results in an atomic join-semilattice structure. This means that plural nouns, on the one hand, share the cumulativity property with mass nouns, and, on the other hand, share atomicity with singular count nouns. Therefore, in Link\u2019s algebraic semantics, a noun is countable if it is atomic, whereas a noun is uncountable if it lacks atomicity. The non-atomic cumulative denotation of substance mass nouns has also been associated with divisive reference (Cheng 1973). A predicate is divisive if and only if whenever it is true of an entity, it is also true of its parts, as defined in (127). (127) DIV(P) \u225d \u2200x[P(x) \u2192 \u2200y [y \u228f x \u2192 P(y)]] (P is divisive iff whenever it holds of x, it also holds of every y that is a proper part of x) (Adapted from Champollion & Krifka 2016: 525) Basically, if a mass noun like water expresses a divisive predicate it entails that whenever a portion of substance falls under water, the parts of the portion also fall under water. Note that the definitions of cumulativity in (122) and divisiveness in (127) show that while the former is an upward closure property, the latter is a downward one. Thus, the picture that emerges from a Link-inspired double-domain theory that incorporates the divisive property into its framework is as follows. The count\/mass distinction in the nominal domain is based on the atomic\/non-atomic denotation of nouns. Singular count nouns denote non-cumulative atomic sets, plural count nouns denote cumulative atomic sets, and mass nouns denote divisive and non-atomic cumulative sets. Table 10 below represents these nouns in relation to the semantic properties assigned to them. 69 Singular count nouns Plural count nouns Mass nouns Atomic \u2713 \u2713 \u2717 Cumulative \u2717 \u2713 \u2713 Divisive \u2717 \u2717 \u2713 Table 10: Semantic properties of nouns. However, the picture isn\u2019t as neat as suggested by Table 10. The assumptions, on the one hand, that the defining property of count nouns is atomicity, and, on the other hand, that divisiveness holds of all mass nouns, have both faced several challenges. Let\u2019s start with divisiveness. Some authors (Quine 1960; Gillon 1992; Chierchia 2010) argue that taking mass nouns to be divisive leads to the so-called \u2018minimal-parts problem\u2019. Not even prototypical (substance) mass nouns like water seem to exhibit strong divisiveness, if we assume, following chemistry, that water denotes quantities of H2O molecules. This being so, the minimal parts of water are individual molecules of H2O, which entails that neither a molecule of H nor a molecule of O are themselves water.23 It is easy to see how the same problem can also hold for other mass nouns, such as blood, flour, sugar, etc.24 The reliance on atomicity as the characteristic property of count nouns runs into at least two problems. First, count nouns like fence, twig, sequence, rope, wall, etc., are divisive at least down to a certain point (Rothstein 2010). Subparts of a rope can still be ropes and a fence or wall can be constituted by parts that are also fences or walls. Additionally, for most fence-type nouns, what counts as one discrete individual is context-sensitive. In this regard, linking the count semantics 23 Importantly, in spite of proposing a double domain approach in which count nouns take their denotation from an atomic domain and mass nouns from a non-atomic one, Link (1983) prefers to assume a neutral stance with respect to the divisive property, in order to circumvent the minimal parts problem. 24 Some authors have attempted to tackle the minimal parts problem. For example, Champollion (2010, 2017) offers an alternative definition of the divisive property that includes a \u201cgranular parameter\u201d which constrains the application of a predicate to the parts of an entity only down to a certain (contextual) threshold. 70 of this class of nouns to inherently atomic reference is problematic, for it falls short of explaining their (contextual) malleability regarding what constitutes one individual in their denotations. Second, object mass nouns (as coined by Barner & Snedeker 2005) like furniture, luggage, kitchenware, jewellery, clothing, etc., despite being mass, denote discrete objects (and their sums), which, in Link\u2019s framework, have to be modeled as atoms (Barner & Snedeker 2005, Krifka 2007, Rothstein 2010, 2017). Therefore, fence-type count nouns and object mass nouns constitute evidence that atomicity is neither necessary nor sufficient for nouns to be countable.25 3.2.2 A note on plurals Since Link (1983) there have been two main competing views on the denotation of plural nouns, the exclusive theory and the inclusive theory. The exclusive approach claims that plurals mean \u2018two or more\u2019, i.e., that a condition of the form |x| > 1 is part of the meaning of plural count nouns (Link 1983; Roberts 1990; Chierchia 1998b). That is, the denotations of plurals subtract the atomic individuals, hence containing only their sums, as illustrated below: (128) \u27e6linguist-s\u27e7 = *\u27e6linguist\u27e7 \u2212 \u27e6linguist\u27e7 = {hotze\u2294lisa, hotze\u2294henry, lisa\u2294henry, hotze\u2294lisa\u2294henry} 25 Some authors also adopt a one-domain atomistic mereology. For example, in Chierchia (2010, 2021) both count and non-count nouns take their denotations from an atomic domain. Non-count nouns differ from count nouns because the entities at the bottom of their semilattices are \u201cvague\u201d atoms. As such, they cannot be directly counted, thus requiring classifiers or measure\/container terms to specify the countable atoms. For Chierchia, while prototypical count nouns like child and dog have stable atoms in their denotation, i.e., their individuals are constant across contexts, prototypical mass nouns denote atoms that are highly context-dependent, e.g., what counts as one unit that falls under blood can change from context to context: it can be a drop of blood, a liter of blood, a puddle of blood, a stain or a bag of blood, etc. Although this analysis can provide an account of the uncountable nature of substance nouns in languages like English, I don\u2019t see how the notion of \u201cvague atoms\u201d can be extended to object mass nouns like furniture and luggage, which, like count nouns, seem to have stable atoms in their denotation. For a detailed formal implementation of this analysis, see Cherchia (2010, 2021). For an earlier atomistic approach, see Bach (1986). 71 Thus, for the exclusive approach plural and singular forms of count nouns denote disjoint sets. This analysis of plurals is mainly motivated by existential readings of bare plurals in English episodic sentences like (129). (129) Linguists sang at the party. Sentence (129) implies that more than one linguist sang at the party. So much so that the bare plural in (129) seems to be replaceable, salva veritate, by some linguists, as in (130). (130) Some linguists sang at the party. Both sentences can be paraphrased as (131), which explicitly states the \u2018two or more\u2019 condition argued to be a part of the semantic contribution of (bare) plural nouns:26 (131) Two or more linguists sang at the party. This analysis has been challenged by a number of authors (Krifka 1986, 1989; Sauerland 2003; Sauerland et al. 2005; Spector 2007; Zweig 2009, Alexiadou 2019). All of them share the inclusive view of plurals, i.e., that plurals mean \u2018one or more\u2019. In other words, plural nouns denote the algebraic closure of singular nouns, as discussed in section 3.2.1. In the literature, this view is also called the number-neutral theory of plurals. That is, plural nouns are morphologically plural, but semantically unspecified for number. The most convincing arguments in support of the claim that atoms cannot be erased from the denotation of plurals are put forward by Krifka (1986, 1989) and Sauerland (2003). They rely on evidence drawn from downward-entailing and question contexts. Consider (132), the negation of (129). (132) No linguists sang at the party. 26 Examples (129\u23af131) are adapted from Zweig (2009). 72 The exclusive theory wrongly predicts that (132) is true in a scenario in which only one linguist sang. However, sentence (132) is false in such a situation. On the other hand, the available reading is predicted by the inclusive account. (132) is false in the scenario mentioned because plurals include atoms. The same phenomenon holds in questions. Consider the question in (133) and the respective answers. (133) A: Did linguists sing at the party? B: #No, (just) one. B. Yes, one. (Adapted from Zweig 2009: 362) Again, the exclusive view makes the wrong prediction. In a context where just one linguist sang, the negative answer, which is clearly infelicitous, would be predicted to be fine. In contrast, the inclusive approach predicts the felicitousness of the affirmative answer. Because plurals contain the atoms of their singular counterparts, i.e., because their denotations aren\u2019t disjoint, that one linguist sang at the part is a sufficient condition for the felicity of the affirmative answer. Now consider the contrast between (133) and (134) below, which contains a quantified plural. (134) A: Did two or more linguists sing at the party? B. No, (just) one. B. #Yes, one. (Adapted from Zweig 2009: 354) In (134) the judgments about the responses are inverted. B\u2019s negative answer is the felicitous one. This strongly indicates, along with (133), that the condition |x| > 1 is introduced in A\u2019s question by the operator two or more (Zweig 2009). Hence it is not a constitutive part of the meaning of plurals. 73 Krifka (1986, 1989) and Sauerland (2003) both claim that an affirmative sentence like (129) is infelicitous in a context in which only one linguist sang because of pragmatic competition between the use of singular and plural forms of count nouns. Strictly speaking, when speakers intend to make singular reference, both forms enter into competition, and the singular noun, by being the more specific or marked form (because it excludes sums), blocks the use of the plural noun.27 The structure in Figure 12 illustrates the semilattices of exclusive and inclusive denotations of plurals. Figure 12: Inclusive versus exclusive plurals. Recently, the analysis of plurals as having number-neutral meaning has been proposed as a universal, i.e., as being present in all languages that encode the singular-plural contrast in their count nouns. Yatsushiro et al. (2017) and Alexiadou (2019) provide compelling crosslinguistic data in support of the theory.28 If this generalization is correct, it can be the case that the main differentiation between plurals and number-neutral nouns (i.e., nouns that don\u2019t inflect for number and which can be used to refer to singularities and their sums) boils down to the presence or absence of an implicature. Whereas languages that encode the singular\/plural distinction give rise 27 In Sauerland\u2019s (2003) analysis count singulars carry the presupposition that their extension contains only atoms, while plurals are presuppositionless. There is a blocking effect that enforces the use of singular nouns over plurals when the referents are atomic individuals. This mechanism is regulated by a version of Heim\u2019s Maximize Presupposition (Heim 1991). It ensures that plurals are felicitous only when the referents are sums. 28 For experimental investigations of the inclusive reading of plurals, see Sauerland et al. (2005) and Yatsushiro et al. (2017). 74 to an implicature in virtue of being a system in which there is a competition between the two forms, number-neutral languages do not trigger this implicature, since they are divested of the singular\/plural distinction. 3.2.3 Krifka\u2019s undetermined mereology: quantized vs. cumulative predicates Krifka (1986, 1989, 2007) proposes a single-domain mereology that is undetermined with respect to atomicity, i.e., it is a framework in which \u201cwe do not have to commit ourselves to an atomic or non-atomic conception of the world.\u201d (Krifka 1989: 81). As will be shown in this section, this approach allows him to model the count\/mass and the singular\/plural oppositions in a way that solves the problems engendered by an analysis that relies on atomicity to model countability distinctions in the nominal domain. In his theory, as will be discussed below, the essential property that guarantees grammatical counting is not atomicity, but quantization.29 Krifka (1986,1989, 2007) claims that the mass\/count distinction is grounded in two second-order semantic properties: quantization and cumulativity. A predicate P is quantized if and only if whenever P holds of something, it doesn\u2019t hold of any of its proper parts, as formally stated in (135). (135) QUANT(P) \u225d \u2200x\u2200y[P(x) \u2227 P(y) \u2192 \u00ac(y \u228f x)] (Adapted from Krifka 1989: 78) Thus, quantization contrasts with cumulativity. As treated in section 3.2.1, a predicate is cumulative if and only if whenever it holds of two entities, it also holds of their sum, as defined in (122), repeated here as (136) for comparison. (136) CUM(P) \u225d \u2200x\u2200y[P(x) \u2227 P(y) \u2192 P(x\u2294y)] (Adapted from Krifka 1989: 78) 29 For an alternative treatment of the mass\/count distinction that also doesn\u2019t rely on the notion of atomicity, see Landman (2016, 2020, 2021) and De Vries & Tsoulas (2024). Their analyses employ the notions of overlap versus disjointness to account for the distinction. 75 Crucially, (135) and (136) are mutually exclusive.30 The blue circles in the structure in Figure 13 form a quantized set, while those in Figure 14 constitute a cumulative set. Figure 13: Quantized set. Source: Krifka (2007: 8). Figure 14: Cumulative set. Source: Krifka (2007: 8). Prototypical examples of quantized predicates in mass\/count languages such as English are constructions formed by the combination of numerals and count nouns (e.g., one child) or with measure constructions (e.g., two liters of blood). As such, the constituent one child expresses a quantized predicate that is true of each individual child, but not of their proper parts or sums, while four liters of blood holds of sums of liters of blood with cardinality 4, but not of their proper parts. As for cumulative predicates, their prototypical instances are substance mass nouns like blood, which denote a set closed under sum formation, i.e., a join-semilattice structure. Count nouns are modeled by Krifka as two-place predicates which contain a measure function defined on a domain of entities structured by a complete join-semilattice. In this approach, 30 Quantized predicates are neither cumulative nor divisive. 76 the \u201cbuilt-in modes of dividing reference\u201d (Quine 1960: 91) encoded by count nouns are accomplished by an additive measure function from entities to numbers (Krifka 1986, 1989), which provides a unit of measurement. Additive measure functions can also be expressed by classifiers or measure terms such as head-of, kilo-of, liter-of, etc. Formally, Krifka defines an additive measure function as follows: (137) \u03bc is an additive measure function with respect to \u2294 iff \u03bc maps entities to numbers such that: \u00ac x \u25cb y \u2192 [\u03bc(x\u2294y) = \u03bc(x) +\t\u03bc(y)]. (Krifka 2008: 2) The definition in (137) states that a measure function \u03bc is additive whenever the application of the function to the concatenation (mereological sum) of two non-overlapping entities is identical to the arithmetical sum of the application of the function to each entity. As Filip and Sutton (2017) put it, \u201can additive measure function tracks the part structure of the entities it measures\u201d (Filip & Sutton 2017: 343). It follows from (137) that \u201cif two objects have a weight of 2 and 3 kg respectively, then their concatenation has the weight of 5 kg\u201d (Krifka 1989: 79). Similarly, a measure function like head-of is additive because the concatenation of two head of cattle and four head of cattle results in six head of cattle. Further examples of additive measure functions are pounds, meters, calories, etc. In contrast, there are also non-additive measure functions. Take degrees Celsius, for instance. If objects a and b have a temperature of 20 and 30 degrees Celsius, respectively, their concatenation doesn\u2019t result in a temperature of 50 degrees Celsius. Krifka treats counting as a special type of measuring, one whose units of measurement are concrete individuals or portions of a substance. In classifier languages, the additive measure function that provides concrete units is denoted by sortal classifiers, which must apply to cumulative nouns in order to derive countable constructions, which then can combine with numerals. As for mass\/count languages, count nouns are lexically born with this counting function, while mass nouns lack them. Krifka names the built-in counting function of count nouns NU, standing for \u2018natural-unit\u2019 (1986, 1989, 2007, 2008), or OU, standing for \u2018object-unit\u2019 (1995). It is modeled as an additive 77 function \u03bc that expresses a relation between quantities of P and a number n, as given in (138). NU measures P in terms of concrete units of counting. (138) NU(P\u27e8e,t\u27e9)(xe) = n Mass nouns like blood are treated as one-place predicates, namely as functions of type \u27e8e,t\u27e9 that lack a built-in measure function, as illustrated in (139). In contrast, count nouns like child or nominal constructions like liter of blood are treated as two-place relations between numbers and entities, i.e., as functions of type \u27e8n,\u27e8e,t\u27e9\u27e9, as shown in (140) and (141), respectively. (139) \u27e6blood\u27e7 = \u03bbx[BLOOD(x)] (140) \u27e6child\u27e7 = \u03bbn\u03bbx[CHILD(x) \u2227 NU(CHILD)(x) = n] (141) \u27e6liter-of\u27e7(\u27e6blood\u27e7) = (\u03bbP\u03bbn\u03bbx[P(x) \u2227 LITER(P)(x) = n])(\u03bbx[BLOOD (x)]) = \u03bbn\u03bbx[BLOOD (x) \u2227 LITER(BLOOD)(x) = n] Note that in (141) the measure term liter-of is a modifier containing the measure function LITER. It applies to the cumulative predicate blood and maps it into a two-place relation between numbers and entities, thus giving rise to a countable construction. Therefore, under this approach, there are two semantic criteria for the applicability of nouns: one qualitative and one quantitative. The qualitative criterion is associated with the descriptive content of a noun \u23af semantically represented by BLOOD(x) and CHILD(x) in (139) and (140) \u23af while the quantitative criterion is associated with the measure function NU, which determines what counts as \u201cone natural unit\u201d in the denotation of a count noun. Hence, the difference between count nouns and mass nouns is that whereas count nouns have a qualitative and a quantitative criterion of application, mass nouns have only a qualitative one. Numerals are treated as arguments of nouns or constructions containing measure functions, saturating the n variable introduced by them. So, when (140), a function from a number to a predicate, applies to the number 4, the result is a set of pluralities of children with cardinality 4, as 78 laid out in (142).31 In its turn, when (139) applies to 4 it gives rise to a quantized set of pluralities of liters of blood with cardinality 4, as given in (143). As a consequence, no proper parts of the pluralities that fall under four children and four liters of blood also fall under these predicates. (142) \u27e6child\u27e7(\u27e6four\u27e7) = (\u03bbn\u03bbx[CHILD (x) \u2227 NU(CHILD)(x) = n])(4) = \u03bbx[CHILD(x) \u2227 NU(CHILD)(x) = 4] (143) \u27e6liter-of-blood\u27e7(\u27e6four\u27e7) = (\u03bbn\u03bbx[BLOOD (x) \u2227 LITER(BLOOD)(x) = n])(4) = \u03bbx[BLOOD(x) \u2227 LITER(BLOOD)(x) = 4] In languages that allow semantically singular bare nouns, like Czech, bare singulars display the same quantized denotation as nominals containing the numeral one. Krifka claims (2003: 193) that such BNs \u201chave a singular operator SG\u2026[that] operates on the noun stem.\u201d Its role is to resolve the cardinality of the n variable of the noun to 1, as illustrated in (144) with the singular noun pes \u2018dog\u2019. (144) \u27e6NumP pes\u27e7 = \u03bbx[DOG(x) \u2227 NU(DOG)(x) = 1] (Adapted from Krifka 2003: 194) As for languages that have semantically plural bare nominals, like English, plural markers signal the existential closure of the number argument n, creating cumulative reference, as in (145). (145) \u27e6dog-s\u27e7 = \u03bbx\u2203n[DOG(x) \u2227 NU(DOG)(x) = n] As for the selection of singular or plural forms of nouns when combined with numerals, it is enforced by syntactic agreement, since cardinals can only form a constituent with predicates 31 Krifka (1995) also proposes an alternative analysis, according to which in non-classifier languages the measure function NU\/OU is part of the meaning of numerals, whereas in classifier languages numerals combine first with classifiers. In my analysis of Kaingang nouns, I adopt the view in Krifka (1989, 2007), i.e., that count nouns incorporate a measure function in their semantics. For a defense of the theory that classifiers combine with numerals, see Wilhelm (2008) and Bale & Coon (2014). 79 containing an unsaturated number variable. So, while the plural -s in bare plurals in English has a meaning, its role in numeral+plural noun configurations is strictly syntactic (Krifka 2003, 2007). Evidence for plural inflection as agreement comes from plural agreement with decimal fractions in English, as given in (146), and languages where numerals greater than one obligatorily combine with singular nouns, like Turkish, Hungarian, and Welsh (Mittendorf & Sadler 2005; Ionin & Matushansky 2006; Krifka 2003, 2007). (147a\u23afc) illustrate the phenomenon of numeral+singular noun in Turkish. (146) American households have, on average, zero point seven cats\/*cat and one point zero dogs\/ *dog. (Krifka 2003: 192) (147) a. \u00e7okuk \/ \u00e7okuk-lar (Turkish) child \/ child.PL \u2018child \/ children\u2019 b. d\u00f6rt \u00e7okuk five child \u2018five children\u2019 c. *d\u00f6rt \u00e7okuk-lar five child. PL \u2018five children\u2019 (Adapted from Krifka 2007: 25) 3.2.4 Object mass nouns, fence-type count nouns, and doublets Like substance mass nouns, object mass nouns such as furniture, luggage, mail, etc., are inherently cumulative, i.e., they don\u2019t come with a built-in measure function, and in order to combine with numerals they require intervening measure terms like piece(s)-of. Therefore, object mass nouns are not countable and resist pluralization not because they lack discrete objects in their denotations, 80 but because they are not quantized, i.e., they lack a measure function providing the number variable that can be saturated by a number or existentially closed. As such, furniture has the denotation in (148), piece(s) of furniture the denotations in (149) and (150), and four pieces of furniture the one in (151). (148) \u27e6furniture\u27e7 = \u03bbx[FURNITURE(x)] (149) \u27e6piece of furniture\u27e7 = \u03bbn\u03bbx[FURNITURE(x) \u2227 PIECE(FURNITURE)(x) = n] (150) \u27e6piece-s of furniture\u27e7 = \u03bbx\u2203n[FURNITURE(x) \u2227 PIECE(FURNITURE)(x) = n] (151) \u27e6four pieces of furniture\u27e7 = \u03bbx[FURNITURE(x) \u2227 PIECE(FURNITURE)(x) = 4] In a nutshell, object mass nouns, on the one hand, share cumulativity with prototypical mass nouns, and, on the other hand, share atomicity with prototypical count nouns. As for count nouns like fence, wall, table, rope, bouquet, etc., which denote objects whose proper parts are also in their denotation, at least down to a certain threshold, these don\u2019t pose an unbridgeable challenge to Krifka\u2019s analysis. He attributes the impression that fence-type count nouns have a non-quantized nature to the fact that what counts as a unit in their denotation is partially determined by the context. As he puts it, it is the \u201ccontext dependence of count nouns [that] explains the apparent non-quantization of nouns like fence, wall, hedge, bouquet\u201d (Krifka 2007: 35). 32 So, he proposes to represent the context-dependence of the built-in quantizing functions of fence-type count nouns via the subscript C, which relativizes the counting units to each context, as given in the lexical entry for fence in (152). (152) \u27e6fence\u27e7 = \u03bbn\u03bbx[FENCE(x) \u2227 NUC(FENCE)(x) = n] 32 An in-depth discussion of fence-type nouns can be found in Rothstein (2010, 2017). Her theory establishes a distinction between \u2018natural atomicity\u2019 and \u2018semantic atomicity\u2019. Natural atoms are inherently discrete entities, while semantic atoms are defined as atoms relative to contexts. In her analysis all count nouns denote sets of semantic atoms. The atoms associated with prototypical count nouns usually coincide with natural atoms, while those in the denotation of fence-type count nouns, due to their context sensitivity, do not. 81 (Adapted from Krifka 2007: 35) It is important to underline that quantization as defined in (135) doesn\u2019t entail disjointness, which is the opposite of overlap, as Filip and Sutton (2017) point out. This means that quantization applies to certain predicates that contain overlapping units in their denotations. Consider a predicate P that denotes the set {hotze\u2294lisa, marcin\u2294hotze, hotze\u2294nina}. Although P is non-disjoint, for its sums of cardinality 2 overlap in the individual hotze, it is quantized, since none of the sums is part of any of the others. This consequence is empirically welcome, and specially appropriate for nouns like fence. For example, despite the fact that one fence overlaps with another fence in the post they share to form a corner, they can fall under the predicate two fences (Filip & Sutton 2017). Hence, these facts indicate that quantization has an explanatory advantage over disjointness. Additionally, Krifka\u2019s theory provides a neat explanation of the denotational semantics of doublets, i.e., near synonymous pairs of nouns in which one member is mass, but the other is count, like change\/coins, mail\/letters, footwear\/shoes, etc. Link\u2019s theory, due to its ontological assumptions, inevitably entails the view that the denotations of these pairs of nouns are taken from two disjoint domains, in spite of the fact that doublets get their reference from a shared domain. In contrast, in Krifka\u2019s theory, the main difference between the nouns in each pair doesn\u2019t derive from ontology but from the higher-order properties of the predicates they express, namely from the quantized\/cumulative opposition. While their mass version is inherently cumulative, and hence lacks the quantizing function NU, which provides the n variable to be saturated by numerals, their count version comes with NU, and hence can directly combine with numerals and be pluralized. The pair mail\/letters in (153a\u23afb) illustrates the lexical entries of doublets: (153) a. \u27e6mail\u27e7 = \u03bbx[MAIL(x)] b. \u27e6letter\u27e7 = \u03bbn\u03bbx[LETTER(x) \u2227 NUC(LETTER)(x) = n] (Adapted from Krifka 2007: 35) In Chapter 4, I will revisit the \u201cspecial\u201d meanings of fence-type count nouns, as well as of object mass nouns, in connection with the Kaingang data, and claim that both types of nouns provide additional empirical motivation for my analysis of Kaingang nouns. 82 3.3 Type-shifting semantics The type-shifting analysis of nominal constructions advanced by Partee (1986) emerged as an attempt to integrate two conflicting theories of the semantics of noun phrases: Montague Grammar, in particular its version in the paper \u201cThe proper treatment of quantification in ordinary English\u201d (Montague 1973, 1974) \u23af henceforth PTQ \u23af and Kamp\u2019s (1981) and Heim\u2019s (1982) approaches.33 In PTQ, Montague designs a grammar for a fragment of English in which every syntactic category is uniformly associated with only one semantic type. That is, in PTQ there is a rigid one-to-one correspondence between the syntactic categories of constituents and their semantic types. All nominal constructions are uniformly modeled as generalized quantifiers (GQs), i.e., they denote sets of sets and as such are all of type \u27e8\u27e8e,t\u27e9,t\u27e9. One great merit of this approach is that it accounts for the possibility of coordinating a proper name and a generalized quantifier, as in Hotze and every student, without abandoning the assumption that only constituents of the same type can be coordinated. The proper name Hotze is modeled as a GQ with the semantics in (154a), i.e., as denoting the set of all sets that have hotze as a member. As such, its coordination with the quantificational NP every student, which has the semantics in (154b), i.e., of a nominal denoting the set of all sets that have the set of students as a subset, generates as output the constituent in (154c), which is also a GQ.34,35 (154) a. \u27e6hotze\u27e7 = \u03bbP[P(hotze)] b. \u27e6every student\u27e7 = \u03bbP\u2200x[STUDENT(x) \u2192 P(x)] c. \u27e6hotze and every student\u27e7 = \u03bbP[P(hotze) \u2227 \u2200x[STUDENT(x) \u2192 P(x)]] 33 For an overview of Partee\u2019s theory, see Hendriks (2020). 34 In the PTQ framework all members of a syntactic category are always associated with the highest type \u201cthat is needed for some expression in that category\u201d (Hendriks 2020: 4). This strategy is known as \u201cgeneralizing to the worst case\u201d. 35 For an elucidating introduction to the semantics of PTQ in particular and Montague grammar in general see v2, ch.6 of Gamut (1991). 83 In contrast, Kamp\u2019s and Heim\u2019s semantics distinguish among quantificational, referential, and predicative NPs. Both authors claim that the uniform treatment of all NPs\/DPs as generalized quantifiers distorts their semantics. They draw this conclusion based on English constructions which suggest that expressions under the NP\/DP category do not show a uniform semantic interpretation. Take, for instance, discourse anaphora. While proper names and (in)definite descriptions license singular pronouns as discourse anaphors, as illustrated in (155a), quantified nominals like every student, no student, and more than one student don\u2019t, as shown in (155b). (155) a. Hotze\/the student\/a student walked in. He looked happy. b. Every student\/no student\/more than one student walked in. *He looked happy. (Adapted from Partee 1986: 119) The constructions in (155a\u23afb), therefore, suggest that only nominals of type e can be the antecedent for a singular pronoun in discourse. As for the interpretation of (in)definite nominals as predicates, this is supported by constructions with verbs such as consider and become, which allow both AP and NP complements, as well as their coordination, as given in (156a\u23afc).36 (156) a. Lisa considers Hotze competent in experimental phonetics. b. Hotze considers Lisa an\/the authority on forensic linguistics. c. Marcin considers Hotze competent in experimental phonetics and an\/the authority on forensic linguistics. (Adapted from Partee 1986: 119) In Partee\u2019s framework the different meanings of nominal phrases are related to each other via a number of type-shifting mechanisms. There are three available semantic types associated with nominals: e (individuals), \u27e8e,t\u27e9 (functions from individuals to truth-values), and \u27e8\u27e8e,t\u27e9,t\u27e9 (functions from functions of type \u27e8e,t\u27e9 to truth-values). Referential interpretations of nominals are associated 36 Partee (1986) treats nominals introduced by determiners as NPs. 84 with a denotation of type e, predicate interpretations with type \u27e8e,t\u27e9, and quantificational ones with type \u27e8\u27e8e,t\u27e9,t\u27e9. In this flexible type-driven theory, nominal phrases can be mapped onto more than one semantic type. In other words, the type-shifting principles proposed by Partee allow for a one-to-many correspondence between syntactic categories and semantic types. Basically, what a type-shifting operator does is to map one type into another. The rationale is to start with the simplest type available for a syntactic category and, when needed, apply certain type-shifting mechanisms to it so as to give rise to the higher types that the category can express. Partee\u2019s inventory of type-shifting mechanisms, which she suggests are potentially universal, is represented in the triangular diagram in Figure 15, followed by a specification of the meaning of each operation in (157): Figure 15: Type-shifting inventory. Source: Partee (1986: 121). (157) a. LIFT: e \u21d2 \u27e8\u27e8e,t\u27e9,t\u27e9 LIFT(a) = \u03bbP[P(a)] b. LOWER: \u27e8\u27e8e,t\u27e9,t\u27e9 \u21d2 e LOWER(\u03bbP[P(a)]) = a c. ident: e \u21d2 \u27e8e,t\u27e9 a \u21d2 \u03bb\ud835\udc65[\ud835\udc65 = a] 85 d. iota: \u27e8e,t\u27e9 \u21d2 e P \u21d2 \u03b9x[P(x)] e. nom: \u27e8e,t\u27e9 \u21d2 e P \u21d2 \u2229P (Chierchia 1984, 1998b) f. pred: e \u21d2 \u27e8e,t\u27e9 k \u21d2 \u222ak (Chierchia 1984, 1998b) g. THE: \u27e8e,t\u27e9 \u21d2 \u27e8\u27e8e,t\u27e9,t\u27e9 P \u21d2 \u03bbQ\u2203\ud835\udc65\u2200\ud835\udc66[P(\ud835\udc66) \u21d4 y = x \u2227 Q(x)] h. A: \u27e8e,t\u27e9 \u21d2 \u27e8\u27e8e,t\u27e9,t\u27e9 P \u21d2 \u03bbQ\u2203x[P(x) \u2227 Q(x)] i. BE: \u27e8\u27e8e,t\u27e9,t\u27e9 \u21d2 \u27e8e,t\u27e9 \u03bbP\u03bbx[{x} \u220a P} \u21d2 P (Adapted from Partee 1986: 121) The LIFT and LOWER mechanisms relate the referential and quantificational readings of nominals. An e-type nominal is mapped onto a GQ via LIFT, and inversely a GQ is mapped into e via LOWER. For instance, in the constituent Hotze and every student the proper name Hotze is lifted to the GQ \u03bbP[P(hotze)] in order to display the same type as its conjunct-mate every student. The iota, ident, nom, and pred functions relate predicates and nominals of type e. Ident is a function from e to \u27e8e,t\u27e9, mapping any element onto its singleton set. That is, it is a function from an individual a onto the set of all entities identical to a. The iota operator selects the unique member of a set denoted by a predicate. This is to say that \u03b9 applies to a predicate P if and only if there is a unique individual that falls under P. The \u03b9-operator presupposes existence and uniqueness. Some authors treat \u03b9 as the meaning of the English definite article (Strawson 1950; Heim & Kratzer 1998; Chierchia 1998b). Nom (\u2229) and pred (\u222a) are the intensional counterparts of iota and ident. They are crucial operations in Chierchia\u2019s semantics of nominalizations and bare nouns (Chierchia 1984, 1998b). \u2229 maps properties into kinds, while \u222a maps kinds onto the set of their instantiations in a world of evaluation. Both operators depend on an ontology that includes kinds, as a sort of (abstract) individual, in the universe of discourse. In a simplified extensional version of the intensional language used by Chierchia, as given in (157e\u23aff), \u2229 applies to a set of individuals and their sums and maps it into a kind, whereas \u222a applies to a kind and returns as value a set of the individuals and sums thereof that instantiate the kind. (For expository purposes, the present thesis, whenever possible, will always opt for an extensional over an intensional language.) 86 Predicates and GQs are related by three operations: THE, A, and BE. The operator THE maps a predicate onto a GQ. It asserts existence and uniqueness. In PTQ, THE is the meaning of the English definite article the. The operator A turns a predicate into an existential GQ. That is, A is the \u2203-closure of a predicate. In PTQ, A is the meaning of the indefinite article a. As for BE, it is the inverse operation of THE and \u2203, i.e., it maps a GQ into a predicate. In PTQ, BE is the meaning of the verb be in copular constructions like be Hotze, be a linguist, etc. In Partee\u2019s model it is generalized to predicative interpretations of nominals other than those in copula constructions, as in sentences like (156a\u23afc) above. Type-shifting mechanisms have shown to be extremely useful tools for empirically adequate semantic theories of argument formation across languages, in particular for tackling the different meanings of bare nouns (Chierchia 1998b; Krifka 2003; Dayal 2004). Take two available interpretations of English bare plurals, for instance. In the episodic sentence in (158) dogs has an existential reading, while in a sentence with the kind-level predicate be extinct like (159) dogs has a kind reading. (158) Dogs are barking. Reading: Some dogs are barking. (159) Dogs are extinct. Reading: The kind\/species dog is extinct. Avoiding for now the details of how distinct theories treat these readings, and which basic denotations they assign to English bare plurals, the meanings of dogs in (158) and (159) can be accounted for by using some of the type-shifting mechanisms in (157). In Chapter 5, Chierchia\u2019s (1998b) and Krifka\u2019s (2003) theories of bare noun interpretations will be discussed in connection with my analysis of indefinite bare nouns in Kaingang. More specifically, I will focus on how their theories derive the existential force of bare nouns on their indefinite readings, as well as how they account for their scope properties. For expository reasons, in this background section I will abstract away from issues of number morphology. First, let\u2019s assume, for the sake of illustration, that bare nouns start off as predicates \u23af or properties in an intensional language (Krifka 2003). Hence, the indefinite reading of dogs in 87 (158) can be associated with the operation A in (157h), i.e., it can be derived by existential closure of the predicate dogs, as given in (160). (160) A: dogs\u27e8e,t\u27e9 \u21d2 \u2203[dogs]\u27e8\u27e8e,t\u27e9,t\u27e9 = \u03bbQ\u2203x[DOG(x) \u2227 Q(x)] As for the kind reading of dogs, it can be accomplished via nom in (157e), that is, by applying \u2229 to the denotation of dogs, mapping it onto the kind DOG, as illustrated in (161). (161) nom: dogs\u27e8e,t\u27e9 \u21d2 \u2229dogse Alternatively, let\u2019s suppose that bare plurals are kind-denoting terms (Chierchia 1998b). In this regard, dogs doesn\u2019t need to be type-shifted to get the reading in (159): it can immediately combine with the verbal predicate be extinct, which selects for kind arguments. In contrast, to receive an existential reading, dogs has to go through a two-step type-shifting procedure. First, it is mapped into the instantiations of the kind DOG, i.e., to the set of dogs and their sums, which then becomes the input for \u2203-closure, as stated in (162). (162) pred: \u2229dogse \u21d2 \u222a\u2229dogs\u27e8e,t\u27e9 \/ A: \u222a\u2229dogs \u21d2 \u2203[\u222a\u2229dogs] \u27e8\u27e8e,t\u27e9,t\u27e9 = \u03bbQ\u2203x[DOG(x) \u2227 Q(x)] step 1 step 2 In determinerless languages such as Mandarin, Hindi, and Russian (Chierchia 1998b; Dayal 2004), bare nouns display a wider range of interpretations, including, for instance, a definite reading. Consider Mandarin, a language in which all nouns are uninflected for number and have a number-neutral meaning. In sentence (163), the number-neutral bare noun xi\u00f3ng \u2018bear\u2019 has a definite or indefinite interpretation. (163) W\u00f2 k\u00e0njii\u00e0n xi\u00f3ng le. I see bear ASP \u2018I saw a\/some\/the bear(s).\u2019 (Adapted from Chierchia 1998b: 354) 88 Again, a type-shifting approach provides the means to model the definite reading of a bare noun. If the bare noun is a predicate, the procedure is straightforward: the iota operator applies to the denotation of xi\u00f3ng \u2018bear\u2019 and maps it onto the unique individual that falls under xi\u00f3ng (in a given context), as in (164). (164) iota: BEAR\u27e8e,t\u27e9 \u21d2 \u03b9BEARe = \u03b9x[BEAR(x)] On the other hand, if the basic denotation of xi\u00f3ng \u2018bear\u2019 is a kind, a two-step procedure is required: first pred applies to the kind BEAR, mapping it into the set of its instantiations, then iota applies to this set and selects one of its members, as laid out in (165). (165) Pred: \u2229BEARe \u21d2 \u222a\u2229BEAR\u27e8e,t\u27e9 \/ iota: \u222a\u2229BEAR \u27e8e,t\u27e9 \u21d2 \u03b9[\u222a\u2229BEAR]e = \u03b9x[\u222a\u2229BEAR(x)] step 1 step 2 A number of authors argue that type-shifting rules don\u2019t apply freely, but that they are a last-resort device to resolve type and sortal mismatches that can emerge in semantic derivations (Chierchia 1998b; Krifka 2003; Dayal 2004). In other words, type-shifting operations are a repair mechanism that precludes interpretations from crashing, shifting the type of a constituent in order to allow functional application (FA) to apply and hence for semantic derivation to proceed. On the assumption that bare plurals are predicates, in sentence (158) the verbal predicate be barking selects only for an individual. So, to repair the type-mismatch between two predicates, i.e., dogs(x) and be-barking(x), given that English BNs lack a definite reading, dogs is shifted to a generalized quantifier via \u2203-closure. As a result, the verbal predicate can be the argument of the GQ, thus allowing functional application to occur, as given in (166). (166) Dogs are barking. a. [dogs [are barking]] b. \u27e6dogs\u27e8e,t\u27e9\u27e7, \u27e6are barking\u27e8e,t\u27e9\u27e7 type mismatch (FA fails) 89 c. \u2203\u27e6dogs\u27e7\u27e8\u27e8e,t\u27e9,t\u27e9, \u27e6are barking\u27e8e,t\u27e9\u27e7 type-shifting by \u2203 d. (\u03bbP\u2203x [DOG(x) \u2227 P(x)])(\u03bbx[BE-BARKING(x)]) by \u03bb-conversion e. \u2203x[DOG(x) \u2227 BE-BARKING(x)] FA (Adapted from Krifka 2003: 195\u23af6) Alternatively, on the assumption that bare plurals are kind-denoting expressions, (158) gives rise to a sortal mismatch. The predicate be barking fails to apply to the kind-denoting term dogs because it selects for concrete individuals as its argument, while kinds are abstract individuals. To repair this, dogs can be type-shifted to the set of its instantiations and then existentially closed. Hence, once it has been type-shifted to a generalized quantifier, dogs can now apply to be barking via functional application, as shown in (167). (167) Dogs are barking. a. [dogs [are barking]] b. \u27e6dogse\u27e7, \u27e6are barking\u27e8e,t\u27e9\u27e7 sortal mismatch c. (\u22c3\u2229DOG)(\u03bbx[ARE-BARKING (x)]) type-shifting by \u22c3 and \u2203\t d. \u2203x[\u22c3\u2229DOG \u2227 ARE-BARKING(x)] by FA Another principle adopted by many as regulating the application of type-shifting rules is Chierchia\u2019s Blocking Principle (Chierchia 1998b). This principle says that a covert type-shifting operation can apply in a language only if there isn\u2019t an overt determiner that expresses the same operation. That is, it constrains the application of a covert type-shifter through the presence or lack of an overt type-shifter. Chierchia\u2019s principle is stated in (168). 90 (168) Blocking Principle (\u2018Type Shifting as Last Resort\u2019) For any type shifting operation \ud835\udf0f and any X: * \ud835\udf0f(X) if there is a determiner D such that for any X in its domain, D(X) = \ud835\udf0f(X) (Chierchia 1998b: 360) Thus, the fact that bare nouns in languages like English and Hebrew (Chierchia 1998b; Dayal 2004; Tonciulescu 2009) lack a definite interpretation can result from (168), given that these languages have a definite determiner. The Blocking Principle predicts that in determinerless languages bare nouns will display both indefinite and definite readings. This is borne out by languages like Mandarin, Hindi, and Russian (Chierchia 1998b; Dayal 2004). A number of nominal type-shifting operations other than those in the diagram in Figure 13 have been proposed. Some interesting operations are those that track the join-semilattice structure of the (sub)domains of entities from which (bare) nouns take their denotation, as pointed out by Hendriks (2020). For instance, Chierchia\u2019s kind-formation operator \u2229 is only defined for cumulative predicates, i.e., for sets closed under sum formation, while the instantiation set operator \u22c3, as the inverse of \u22c3, maps a kind into a cumulative set (Chierchia 1998b). Another fine example of this kind of type-shifter is Landman\u2019s group formation operator \u2191 (Landman 1989, 2000), designed to account for the meaning of group nouns like team, committee, party, etc. The idea is that groups are a particular kind of individual (\u201cimpure atoms\u201d). They are derived from sums via the application of \u2191. A third example is the set of covert type-shifters proposed by Pelletier and Schubert (2002), which contains type-shifters that map mass predicates into count predicates, or vice-versa, as well as type-shifters that convert mass predicates into e-type mass terms, or vice-versa To conclude, it is important to underline that although the inventory of nominal type-shifters in Partee\u2019s diagram is in principle intended to be universally available, it is an empirical matter which subset of them is exploited by any particular language, and whether any new operators need to be added to the \u201cuniversal\u201d catalog. In Chapter 5, for instance, I will argue that Kaingang bare 91 nouns provide evidence that the list of covert type-shifters needs to be enriched with a new member, namely a choice function, in order to account for the available scope properties of indefinite bare nouns across languages. Additionally, I will claim that the covert type-shifters that give rise to indefinite readings are sensitive to the quantized and cumulative properties of the predicates they target. 92 Chapter 4: Nominal Countability in Kaingang and Beyond 4.1 Introduction In this chapter, I examine the semantics of nominal countability in Kaingang. I show that Kaingang neither encodes a grammatical opposition nor a semantic distinction between count and non-count nouns. I argue that Kaingang parallels Yudja (Lima 2014a, b), a Tupi language, when it comes to countability in the nominal domain. Namely, in Kaingang both individual and substance nouns are interpreted as count nouns. This finding suggests that the generalized count interpretation of nouns is not an idiosyncrasy of Yudja. However, contrary to Lima\u2019s analysis (Lima 2014a, b) of Yudja, according to which the count meaning of Yudja nouns is derived via a covert morphological operation, my main hypothesis is that all Kaingang nouns are inherently count. This claim is based on the replication of various morphosyntactic and semantic tests found in the literature (Bloomfield 1933; Barner & Snedeker 2005; Doetjes 1997; Rothstein 2010, 2017; Pires de Oliveira & Rothstein 2011; Lima 2014a, b; Lima & Rothstein 2020). First, Kaingang allows numerals to combine directly with individual- and substance-denoting nouns. For substance nouns, even non-conventionalized portion-units can be counted. Second, count quantity expressions freely combine with both types of nouns. For example, the quantity words e \u2018many\u2019 and pipir \u2018few\u2019, whether forming a constituent with an individual noun or a substance noun, always trigger the cardinal interpretation of a large\/small number of concrete units. Third, bare substance nouns can also appear in constructions with count adjectives and be the antecedents of plural pronouns and reciprocals. In addition, the application of Barner & Snedeker\u2019s (2005) quantity judgement tasks shows that in comparative constructions with substance nouns Kaingang speakers not only access cardinality-based readings, but they also consistently privilege them. That is, the default evaluation of Kaingang substance nouns is based on cardinality. I analyze this pervasive counting strategy in Kaingang as a direct effect of the lexical meaning of root nouns in the language. Drawing on Krifka\u2019s approach (1986,1989, 2007, 2008), my hypothesis is that all nouns come from the lexicon already equipped with a context-sensitive 93 built-in counting function that, depending upon the type of noun, measures quantities in terms of individual or portion-units. This amounts to saying that all nouns in Kaingang are born quantized. This chapter is structured as follows. In sections 4.2, 4.3, and 4.4 I present the data supporting the main hypothesis of this chapter. Section 4.5 contains my analysis of the generalized count meaning of Kaingang nouns. In section 4.5.1, I treat all nouns in Kaingang as lexically quantized due to a context-sensitive quantizing function incorporated into their root denotations, which provides the units for counting. I argue that such an analysis is not only supported by the pervasive count interpretation of Kaingang nouns, but also motivated by crosslinguistic evidence. In the same section, I show that a treatment of count nouns as quantized predicates with a built-in measure function \u00e0 la Krifka\u2019s NU (natural-unit) is compatible with modeling them as being of type \u27e8e,t\u27e9, rather than a relation between numbers and sets, as in Krifka\u2019s work. With this solution, I intend to show that Kaingang bare nouns can be used to refer to pluralities picked out from the denotation of quantized nouns, which means that plural readings of bare nouns uninflected for number don\u2019t need cumulative reference at the N(P) or NumP level. In section 4.5.2, I briefly discuss Lima\u2019s (2014a, b) analysis of Yudja. I show that analysing Kaingang and Yudja count nouns as quantized predicates, rather than (derived) atomic cumulative ones, as Lima advocates for Yudja, has the explanatory advantage of allowing a crosslinguistic generalization about the semantics of count nouns. In section 4.6, I deal with one potential challenge to my analysis. This challenge comes from a version of the quantity judgement test: one in which two individual- or portion-units, differing in volume, are compared. The initial explanation that suggests itself is that speakers allow evaluations along the volume dimension in these scenarios. However, I propose a reinterpretation of these data which makes them compatible with a cardinality judgement. In section 4.7, I highlight some contributions of the findings in this thesis for the study of crosslinguistic variation in the expression of nominal countability. Finally, in section 4.8 I offer my conclusions. 4.2 Concrete units all over the place 4.2.1 Numerals 94 As demonstrated in Chapter 2, section 2.7, Kaingang is a non-classifier language. That is, Kaingang allows numerals to combine with count nouns without any intervening classifier or measure construction, as illustrated in (169a\u23afc). (169) a. G\u0129r t\u00e3gt\u0169 v\u1ef9 jun~jun \u2205. (= (85)) child three NOM RED~arrive PFV \u2018Three children arrived.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 g\u0129r r\u00e9gre-\u2205 v\u00e9 \u2205. (= (86)) F\u00f3gt\u1ebd NOM child two-ACC see PFV \u2018F\u00f3gt\u1ebd saw two children.\u2019 c. F\u00f3gt\u1ebd v\u1ef9 g\u0129r r\u00e9gre m\u1ef9 garinh pir-\u2205 f\u1ebdg \u2205. (= ( 91)) F\u00f3gt\u1ebd NOM child two DAT hen one-ACC give PFV \u2018F\u00f3gt\u1ebd gave one hen to two children.\u2019 Like in familiar non-classifier languages, Kaingang numerals are compatible with substance nouns when the latter are coerced to refer to conventional packages, as in (170), or in subkind\/taxonomic interpretations, as in (171). (170) Context: F\u00f3gt\u1ebd drank the 3 bottles of water that were in the fridge. F\u00f3gt\u1ebd v\u1ef9 goj t\u00e3gt\u0169-\u2205 kron \u2205. F\u00f3gt\u1ebd NOM water three-ACC drink PFV \u2018F\u00f3gt\u1ebd drank three bottles of water.\u2019 (171) Context: You are telling a doctor what blood types there are in your family. \u1ebcg \u0129n t\u00e1 \u1ebdg v\u1ef9 kyv\u00e9nh r\u00e9gre n\u1ef9t\u0129: A kar O. 1P.PL house there 1PL NOM blood two ASP: A then O \u2018In our house we have two kinds of blood: A and O.\u2019 95 However, Kaingang departs from familiar non-classifier languages by allowing numerals to combine directly with substance nouns even when they are interpreted as referring to non-conventionalized portion-units. This is shown in (172\u2013176). (172) Context: You enter the kitchen and notice that there are three puddles of water on the floor. \u1ebcgn\u00e9nh j\u00e3f\u00e3 ki t\u00f3g goj t\u00e3gt\u0169 n\u0129. kitchen in TOP water three ASP \u2018There are three puddles of water in the kitchen.\u2019 (173) Context: On the way home from school F\u00f3gt\u1ebd\u2019s nose dripped three drops of blood. Kyv\u00e9nh t\u00e3gt\u0169 v\u1ef9 n\u00e3g ke \u2205. blood three NOM drip PFV \u2018Three drops of blood dripped.\u2019 (Adapted from Lima 2014a: 58) (174) Context: F\u00f3gt\u1ebd saw three puddles of blood on the floor. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh t\u00e3gt\u0169-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood three-ACC see PFV \u2018F\u00f3gt\u1ebd saw three puddles of blood.\u2019 (175) Context: Pak\u00f3j took a bucket full of sand from her house to Maria\u2019s. On the way she spilled three portions of sand on the floor. Pak\u00f3j v\u1ef9 r\u1ef9nhr\u1ef9j t\u00e3gt\u0169-\u2205 kuj\u1ebdn \u2205. Pak\u00f3j NOM sand three-ACC spill PFV \u2018Pak\u00f3j spilt three portions of sand.\u2019 96 (176) Context: Your son walks into the kitchen wearing a shirt with two stains of mud on it. You tell him: \u00d3r\u00e9 r\u00e9gre t\u00f3g ti kam\u0129sa t\u00f3 sa. mud two TOP 3.P.SG.M shirt on hang \u2018There are two stains of mud hanging on your shirt.\u2019 In (172), the counted portions are puddles of water. In (173) and (174) the units are drops and puddles of blood, respectively, while in (175) they constitute portions of sand and in (176) stains of mud. In all cases the portions are contextually supplied and don\u2019t correspond to conventionalized units. Furthermore, the portions counted in a situation can vary in shape, size, and containers, as given in the context in (177), depicted in Figure 16. Together with the possibility of directly counting (non-)conventional units, the felicity of the sentence in (177) in the context below indicates that the \u2018unitizing\u2019 semantics of Kaingang nouns should be extremely general.37 (177) Context: F\u00f3gt\u1ebd entered the kitchen and saw one gallon of water on the floor, one glass full of water on the table, and one puddle of water on the floor. Figure 16: The kitchen scenario. F\u00f3gt\u1ebd v\u1ef9 goj t\u00e3gt\u0169-\u2205 v\u00e9 \u2205. (= (6)) F\u00f3gt\u1ebd NOM water three-ACC see PFV \u2018F\u00f3gt\u1ebd saw three portions of water.\u2019 37 I am indebted to Suzi Lima (p.c.) for suggesting this test to me. 97 In sum, the data above show that in Kaingang numerals directly modify individual and substance nouns. The availability of substance noun+numeral constructions in contexts that supply non-conventional portions constitutes one piece of evidence that substance nouns in Kaingang can be interpreted as referring to individuated portions. 4.2.2 Quantity words In many mass\/count languages there are quantity words which select for particular types of nouns. For instance, in English, (a) little, less and much combine only with substance mass nouns, as shown in (178a\u23afb), whereas (a) few, many, and several require count nouns, as laid out in (179a\u23afb). The availability of this distinction in the distribution of quantity words is often used as one diagnostic test for the existence of the mass\/count distinction in a language (Bloomfield 1933; Doetjes 1997, 2012). (178) a. There is little\/less\/much water\/blood in the kitchen. b. *There is (a)few\/many\/several water\/blood in the kitchen. (179) a. There are (a)few\/many\/several students\/chairs in the room. b. *There are little\/less\/much students\/chairs in the room. Kaingang has at least five quantity words: kar \u2018all\u2019, \u0169 \u2018some\u2019, e \u2018many\u2019, pipir \u2018few\u2019, and m\u1ebd \u2018more\u2019. All these terms are compatible with individual and substance nouns, as illustrated by the minimal pairs in (180\u23af188), where the quantity words immediately follow the nouns in subject and object positions. (180) a. G\u0129r kar v\u1ef9 j\u00e3n~j\u00e3n \u2205. (= (94a)) child all NOM RED~sing PFV \u2018All the children sang.\u2019 98 b. Goj kar v\u1ef9 ror n\u1ef9t\u0129. water all NOM round ASP \u2018All portions of water are round.\u2019 (181) a. F\u00f3gt\u1ebd v\u1ef9 g\u0129r kar-\u2205 v\u00e9 \u2205. (= (94b)) F\u00f3gt\u1ebd NOM child all-ACC see PFV \u2018F\u00f3gt\u1ebd saw all the children.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh kar-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood all-ACC see PFV \u2018F\u00f3gt\u1ebd saw all portions of blood.\u2019 (182) a. G\u0129r \u0169 v\u1ef9 j\u00e3n~j\u00e3n \u2205. (= (95a)) child some NOM RED~sing PFV \u2018Some child(ren) sang.\u2019 b. Goj \u0169 v\u1ef9 ror n\u1ef9t\u0129. water some NOM round ASP \u2018Some portions of water are round.\u2019 (183) a. F\u00f3gt\u1ebd v\u1ef9 g\u0129r \u0169-\u2205 v\u00e9 \u2205. (= (95b)) F\u00f3gt\u1ebd NOM child some-ACC see PFV \u2018F\u00f3gt\u1ebd saw some child(ren).\u2019 b. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh \u0169-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood some-ACC see PFV \u2018F\u00f3gt\u1ebd saw some portion(s) of blood.\u2019 (184) a. G\u0129r e v\u1ef9 j\u00e3n~j\u00e3n \u2205. (= (96a)) child many NOM RED~sing PFV \u2018Many children sang.\u2019 99 b. Goj e v\u1ef9 ror n\u1ef9t\u0129. water many NOM round ASP \u2018Many portions of water are round.\u2019 (185) a. F\u00f3gt\u1ebd v\u1ef9 g\u0129r e-\u2205 v\u00e9 \u2205. (= (96b)) F\u00f3gt\u1ebd NOM child many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many children.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh e-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many portions of blood.\u2019 (186) a. G\u0129r pipir v\u1ef9 j\u00e3n~j\u00e3n \u2205. (= (97a)) child few NOM RED~sing PFV \u2018Few children sang.\u2019 b. Goj pipir v\u1ef9 ror n\u1ef9t\u0129. water few NOM round ASP \u2018Few portions of water are round.\u2019 (187) a. F\u00f3gt\u1ebd v\u1ef9 g\u0129r pipir-\u2205 v\u00e9 \u2205. (= (97b)) F\u00f3gt\u1ebd NOM child few-ACC see PFV \u2018F\u00f3gt\u1ebd saw few children.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh pipir-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood few-ACC see PFV \u2018F\u00f3gt\u1ebd saw few portions of blood.\u2019 100 (188) a. F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u1ebd n\u0129 Pedro ve k\u1ef9. (= (98a)) F\u00f3gt\u1ebd NOM child more ASP Pedro than \u2018F\u00f3gt\u1ebd has more children than Pedro.\u2019 b. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh m\u1ebd n\u0129 Pedro ve k\u1ef9. F\u00f3gt\u1ebd NOM blood more ASP Pedro than \u2018F\u00f3gt\u1ebd has more portions of blood than Pedro.\u2019 The quantity expression e \u2018many\u2019, for instance, always preserves its cardinal interpretation of a large number of units, irrespective of the noun it combines with. When combined with a substance noun the large number will be of portions, as exemplified in (189). The infelicity of the sentence in (189) in context B results from the fact that this scenario doesn\u2019t provide multiple portion-units for e to quantify over. (189) \u2713Context A: There were many puddles of blood in front of a building. F\u00f3gt\u1ebd saw them. \u2717Context B: There was a large puddle of blood in front of a building. F\u00f3gt\u1ebd saw it. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh e-\u2205 v\u00e9 \u2205. (= (7)) F\u00f3gt\u1ebd NOM blood many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many puddles of blood.\u2019 To describe a context like B, the adjective m\u00e1g \u2018big\u2019 is used instead, as in (190). (190) F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh m\u00e1g-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood big-ACC see PFV \u2018F\u00f3gt\u1ebd saw a\/some\/the big (puddle(s) of) blood.\u2019 Note that due to the number neutrality of the noun kyv\u00e9nh, (190) can also mean that F\u00f3gt\u1ebd saw more than one big puddle of blood. As expected, the adjective m\u00e1g isn\u2019t in complementary distribution with e. Both can occur in the same nominal construction, always triggering the meaning of a large number of big individuals or portions, as given in (191) and (192). 101 (191) F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u00e1g e-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM child big many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many big children.\u2019 (192) F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh m\u00e1g e-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood big many-ACC see PFV \u2018F\u00f3gt\u1ebd saw many big puddles of blood.\u2019 The same pattern is displayed by pipir \u2018few\u2019. Whether it combines with individual nouns, as in (186a), or with substance nouns, as in (193) and (194), it consistently means a small number of individuated units. (193) \u2713Context A: F\u00f3gt\u1ebd accidently cut his left foot, and a few drops of blood dripped. \u2717Context B: F\u00f3gt\u1ebd accidently cut his left foot, and one single drop of blood dripped. Kyv\u00e9nh pipir v\u1ef9 n\u00e3g ke \u2205. blood few NOM drip PFV \u2018Few drops of blood dripped.\u2019 (194) \u2713Context A: There are two puddles of blood in front of a building. F\u00f3gt\u1ebd saw them. \u2717Context B: There is a single puddle of blood in front of a building. F\u00f3gt\u1ebd saw it. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh pipir-\u2205 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood few-ACC see PFV \u2018F\u00f3gt\u1ebd saw few puddles of blood.\u2019 To describe a situation where a small portion of blood dripped, the count adjective s\u0129 \u2018small\u2019 is used instead. This is shown in (195). 102 (195) Kyv\u00e9nh s\u0129 v\u1ef9 n\u00e3g ke \u2205. blood small NOM drip PFV \u2018A\/some\/the small drop(s) of blood dripped.\u2019 The sentence in (195) can also be used to describe a situation with small units of blood, due to the number neutrality of the noun. Just as e \u2018many\u2019 and m\u00e1g \u2018big\u2019 can co-occur, pipir \u2018few\u2019 is not in complementary distribution with s\u0129. Pipir can participate in a noun phrase headed by a noun already modified by s\u0129 \u2018small\u2019, as in (196) and (197). (196) G\u0129r s\u0129 pippir v\u1ef9 jun~jun \u2205. child small few NOM RED~arrive PFV \u2018Few small children arrived.\u2019 (197) Kyv\u00e9nh s\u0129 pipir v\u1ef9 n\u00e3g ke \u2205. blood small few NOM drip PFV \u2018Few small drops of blood dripped.\u2019 Summarizing, the data in this subsection demonstrate that quantity words in Kaingang are compatible with individual and substance nouns. Particularly, they show that the quantity terms e \u2018many\u2019 and pipir \u2018few\u2019 are associated with a cardinality interpretation even when combined with substance nouns. 4.2.3 Count adjectives As already foreshadowed in section 4.2.2, substance nouns can occur with adjectives which hold of each singularity in the extension of a noun. In other words, Kaingang substance nouns can be modified by adjectives which denote properties of individuated entities, such as m\u00e1g \u2018big\u2019, s\u0129 \u2018small\u2019, and ror \u2018round\u2019. Because these adjectives mostly select for count nouns, Deal (2017) refers to them as \u2018count adjectives\u2019, whereas Schwarzschild (2011) calls them \u2018stubbornly distributive adjectives\u2019. Consider the minimal pairs below: 103 (198) a. n\u0129gja m\u00e1g chair big \u2018big chair(s)\u2019 b. kyv\u00e9nh m\u00e1g blood big \u2018big portion(s) of blood\u2019 (199) a. n\u0129gja s\u0129 chair small \u2018small chair(s)\u2019 b. kyv\u00e9nh s\u0129 blood small \u2018small portion(s) of blood\u2019 (200) a. n\u0129gja ror chair round \u2018round chair(s)\u2019 b. kyv\u00e9nh ror blood round \u2018round portion(s) of blood\u2019 In addition, these adjectives can also appear as predicative adjectives in constructions whose subjects are substance bare nouns. Sentences (201) and (202) illustrate this fact with bare individual nouns, while (203) and (204) illustrate it with substance bare nouns. (201) G\u0129r v\u1ef9 m\u00e1g n\u1ef9t\u0129. child NOM big ASP \u2018Some\/the children are big.\u2019 104 (202) N\u0129gja v\u1ef9 ror n\u1ef9t\u0129. chair NOM big ASP \u2018Some\/the chairs are round.\u2019 (203) Context: You notice that some drops of blood on the floor are round. Kyv\u00e9nh v\u1ef9 ror n\u1ef9t\u0129. blood NOM round ASP \u2018Some\/the drops of blood are round.\u2019 (204) Context: You notice that some drops of blood on the floor are big. Kyv\u00e9nh v\u1ef9 m\u00e1g n\u1ef9t\u0129. blood NOM big ASP \u2018Some\/the drops of blood are big.\u2019 Importantly, in (203) and (204), the properties of being round and big distribute to each portion-unit of blood referred to by the bare noun. 4.2.4 Plural pronouns Further evidence that substance bare nouns in Kaingang can be used to refer to portion-units comes from the fact that a third-person plural pronoun can anaphorically refer to a sum of portion-units denoted by a substance bare noun. This is laid out in (205). 105 (205) Context: There are some puddles of blood in front of F\u00f3gt\u1ebd\u2019s house and he saw them. Figure 17: The puddles of blood scenario. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh1 v\u00e9 \u2205. F\u00f3gt\u1ebd NOM blood see PFV. \u2018F\u00f3gt\u1ebd saw some\/the puddles of blood1.\u2019 M\u00e1g ag1 n\u1ef9t\u0129. big 3PPL.M ASP \u2018They1 are big.\u2019 The discourse fragment in (205) is felicitous in the context above, depicted in Figure 17. In it the third-person plural pronoun ag \u2018they (masculine)\u2019 picks out the sum of three puddles of blood denoted by the bare noun kyv\u00e9nh \u2018blood\u2019 in the previous sentence. Also note that the use of the count adjective in predicative position in the second sentence gives rise to a reading in which the property of being big is asserted of each of the portion-units of blood in the context above. 4.2.5 Reciprocals Just like individual-denoting bare nouns, as in (206), bare substance nouns can be the antecedents for reciprocals, as in (207\u23af209). 106 (206) G\u0129r v\u1ef9 jagn\u1ebd h\u00e3 n\u0129. child NOM RECP similar ASP \u2018Some\/the children look like each other.\u2019 (207) Context: After the rain there were separate puddles of water on the ground. You notice that they are similar in shape and size. Figure 18: The puddles of water scenario. Goj t\u00f3g jagn\u1ebd h\u00e3 n\u1ef9t\u0129. (= (8)) water TOP RECP similar ASP \u2018The puddles of water look like each other.\u2019 (208) Context: A clay bench has cracked into three pieces. You notice that they are similar in shape and size. \u00d3r\u00e9 t\u00f3g jagn\u1ebd h\u00e3 n\u1ef9t\u0129. clay TOP RECP similar ASP \u2018The pieces of clay look like each other.\u2019 107 (209) Context: There are three piles of flour on the table. You notice that they are similar in shape and size. Figure 19: The piles of flour scenario. V\u1ebdnh kuri t\u00f3g mesa kri jagn\u1ebd h\u00e3 n\u1ef9t\u0129. flour TOP table on RECP similar ASP \u2018The piles of flour on the table look like each other.\u2019 The constructions with substance nouns above involve the application of their reciprocal VPs to a plurality containing unitized portions of a substance, each of which bears the reciprocal relation of being similar to all the others. The felicity of (207\u2013209) in the contexts above shows that their subject bare nouns are interpreted as denoting sets of contextually salient portion-units of water, clay, and flour, respectively. Thus, Table 11 summarizes the findings about Kaingang (bare) substance nouns above. 108 Yes No Combine directly with numerals \u2713 Combine directly with count quantity terms \u2713 Modified by count adjectives \u2713 Antecedents for plural pronouns \u2713 Antecedents for reciprocals \u2713 Table 11: Substance bare nouns. 4.3 Quantity comparisons 4.3.1 M\u1ebd \u2018more\u2019 In languages that encode the mass\/count distinction, count nouns are primarily compared based on cardinality, whereas substance mass nouns are evaluated based on volume\/weight (Barner & Snedeker 2005). In English, for instance, the comparative sentence (210a) asserts that the cardinality of Pedro\u2019s children is greater than the cardinality of Roberta\u2019s children. In contrast, sentence (210b) means that the overall volume of flour that Roberta has is greater than the overall volume of flour that Pedro has. (210) a. Pedro has more children than Roberta. b. Roberta has more flour than Pedro. Accordingly, depending on the noun replacing N in comparative constructions of the type X has more N than Y, speakers will privilege judgements along the number or volume dimensions. The Kaingang data laid out so far support the thesis that all nouns can be interpreted as count nouns and as such denote sets of counting units. This gives rise to the prediction that speakers will privilege number-based interpretations of all nouns in comparative constructions. 109 To test this prediction, Barner and Snedeker\u2019s (2005) quantity judgement tasks were applied. The consultants were shown pictures of real-world objects and substances. Each picture contained a collection of one or two objects or portions of a substance side-by-side with another collection of multiple objects of the same category or portions of the same substance. The quantities on the left side of the pictures were presented as belonging to one person and those on the right side to another one. Importantly, the total volume of the objects\/portions on the left always exceeded those on the right, whereas the objects\/portions on the right outnumbered those on the left. After showing these stimuli pictures to each consultant, they were asked the target comparative question in (211a) containing the quantity expression m\u1ebd \u2018more\u2019, where N was replaced by an individual or substance noun, and then requested to provide one of the two possible answers in (211b). (211) a. \u0168 n\u1ef9 t\u1ef9 N m\u1ebd n\u0129? some Q ERG N more ASP \u2018Who has more N?\u2019 b. Pak\u00f3j\/Maria v\u1ef9 N m\u1ebd n\u0129 Maria\/Pak\u00f3j ve k\u1ef9. Pak\u00f3j\/Maria NOM N more ASP Maria\/Pak\u00f3j than \u2018Pak\u00f3j\/Maria has more N than Maria\/Pak\u00f3j.\u2019 Stimuli were designed with six nouns of each type, as listed in Table 12. Individual-denoting nouns Substance-denoting nouns g\u0129r \u2018child\u2019 kasor \u2018dog\u2019 ka \u2018tree\u2019 kakan\u1ebd \u2018fruit\u2019 kur \u2018clothes\/clothing\u2019 n\u0129gja \u2018bench\/chair\/stool\u2019 goj \u2018water\u2019 kyv\u00e9nh \u2018blood\u2019 renhte \u2018milk\u2019 v\u1ebdnh kuri \u2018flour\u2019 kur \u2018fabric\u201938 v\u00e3fe \u2018string\u2019 Table 12: Stimulus nouns. 38 The noun kur is ambiguous; it means clothes\/clothing or fabric. This fact justifies the occurrence of kur in both lists. 110 Note that although the nouns kur \u2018fabric\u2019 and v\u00e3fe \u2018string\u2019 do not denote substances, I heuristically include them in the substance nouns category because cross-linguistically they are often treated as mass nouns compared in terms of volume\/size (Deal 2017). Figures 20\u201325 display six instances of the visual stimuli provided in the comparative tasks. Figure 20: renhte \u2018milk\u2019. Figure 21: v\u1ebdnh kuri \u2018flour\u2019. 111 Figure 22: n\u0129gja \u2018bench\u2019. Figure 23: kakan\u1ebd \u2018fruit\u2019. Figure 24: v\u00e3fe \u2018string\u2019. 112 Figure 25: kur \u2018fabric\u2019. In accordance with the prediction, speakers systematically compared all nouns along the number dimension. Thus, even in scenarios containing substances, like in Figure 20, and a target question like in (212a), there were no volume-based interpretations. (212) a. \u0168 n\u1ef9 t\u1ef9 renhte m\u1ebd n\u0129? (= (108)) some Q ERG milk more ASP \u2018Who has more milk?\u2019 b. Maria v\u1ef9 renhte m\u1ebd n\u0129 Pak\u00f3j ve k\u1ef9. Maria NOM milk more ASP Pak\u00f3j than \u2018Maria has more milk than Pak\u00f3j.\u2019 Although the volume of the portion of milk on the left of Figure 20 is larger than the total volume of the three drops on the right, the speakers without hesitation counted the number of portions. That is, in a context where the portion of milk on the left edge belongs to Pak\u00f3j, while all the other portions to Maria, the three consultants, when asked (212a), responded that Maria had more milk, as given in (212b). As a result, these findings offer further supporting evidence that all nouns in Kaingang are interpreted as count nouns. 4.3.2 E \u2018many\u2019 113 Given the count meaning of e \u2018many\u2019, particularly when it combines with substance nouns, one immediate prediction is that when exposed to the same battery of visual stimuli exemplified in Figures 20\u201325 and then asked the question (213a), speakers will offer a cardinality-based judgement. Thus, to test this, the consultants were shown most of the pictures that were used with the sentences in (211a\u23afb). In this task, after having been shown a picture exhibiting on its left side a collection of one or two objects\/portions and on its right side three or more objects\/portions, the consultants were exposed to the target sentences in (213a\u23afb). (213) a. \u0168 n\u1ef9 N e n\u0129? some Q N many ASP \u2018Who has many N?\u2019 b. Pak\u00f3j\/Maria v\u1ef9 N e n\u0129. Pak\u00f3j\/Maria NOM N many ASP \u2018Pak\u00f3j\/Maria has many N.\u2019 Once more the consultants\u2019 responses were as predicted, i.e., they systematically associated e with a cardinality interpretation, whether it applied to individual or substance nouns. For instance, in a context like the one depicted in Figure 26, when asked (214a), the speakers systematically provided a cardinality-based evaluation, i.e., they asserted that Maria has many portions of flour, as given in (214b). Figure 26: v\u1ebdnh kuri \u2018flour\u2019. 114 (214) a. \u0168 n\u1ef9 v\u1ebdnh kuri e n\u0129? some Q flour many ASP \u2018Who has many portions of flour?\u2019 b. Maria v\u1ef9 v\u1ebdnh kuri e n\u0129. Maria NOM flour many ASP \u2018Maria has many portions of flour.\u2019 Hence, the findings above add evidence in support of the main hypothesis of this study, i.e., that all nouns in Kaingang are interpreted as count nouns. 4.3.3 M\u00e1g \u2018big\u2019 If substance nouns denote sets of portion-units and m\u00e1g \u2018big\u2019 is a count predicate, we predict that in quantity tasks m\u00e1g will be interpreted as a property assigned to individual- or portion-units. This diagnostic test was first proposed by Lima (2014a, b), as part of her study of countability in Yudja. To investigate this prediction, I again used the number-neutral nouns in Table 12. The visual stimuli were constituted by pictures containing on the left side one big object or portion of a substance and on the right side multiple objects of the same category or portions of the same substance. In (215) below is the question employed, followed by the two opposing responses. (215) a. \u0168 n\u1ef9 N m\u00e1g n\u0129? some Q N big ASP \u2018Who has a big N?\u2019 b. Pak\u00f3j\/Maria v\u1ef9 N m\u00e1g n\u0129. Pak\u00f3j\/Maria NOM N big ASP \u2018Pak\u00f3j\/Maria has a big N.\u2019 For illustration, I lay out in Figures 27\u201330 four samples of the pictures used as stimuli. 115 Figure 27: v\u1ebdnh kuri \u2018flour. Figure 28: kur \u2018fabric\u2019. Figure 29: kakan\u1ebd \u2018fruit\u2019. 116 Figure 30: kyv\u00e9nh \u2018blood\u2019. The prediction that m\u00e1g primarily would be attributed to the single object or portion on the left side of each picture was confirmed. Therefore, this result offers further evidence in support of the thesis that, like individual nouns, substance nouns in Kaingang provide units for counting. This prediction was further shown to be upheld even in a scenario where the total volume of the multiple portions of a substance exceeds the volume of the single portion on the left edge of the picture. In such a scenario the speakers compared the sizes of individuated portions, not their overall volume. For instance, in a situation where the portion of milk on the left edge belongs to Pak\u00f3j, while all the other portions to Maria, as displayed in Figure 31, the default response of the consultants, when asked (216a), was that Pak\u00f3j had a big unit of milk, as given in (216b).39 39 Two out of the three consulted speakers said that Maria could be considered to have a bigger quantity of milk as long as we imagine that all the units are brought together to form a big portion. I believe that the possibility of such an interpretation doesn\u2019t conclusively show that m\u00e1g can also mean \u2018a large quantity\u2019, for this reading can be made available by an imagined shift of context on the part of the speakers. In other words, imagining a different context where the several small portions are gathered to form a portion-unit which is bigger than the one on the left in Figure 31 can be attributed to world knowledge about the nature of substances, rather than be taken as evidence for the ambiguity or vagueness of m\u00e1g. 117 Figure 31: renhte \u2018milk\u2019. (216) a. \u0168 n\u1ef9 renhte m\u00e1g n\u0129? some Q milk big ASP \u2018Who has a big (portion of) milk?\u2019 b. Pak\u00f3j v\u1ef9 renhte m\u00e1g n\u0129. Pak\u00f3j NOM milk big ASP \u2018Pak\u00f3j has a big portion of milk.\u2019 4.4 A brief note on container words Kaingang allows for the optional use of container phrases in constructions with numerals and substance nouns. In such configurations container words like runja \u2018bucket\u2019 and kej \u2018basket\u2019 are complements of a locative, like in Yudja (Lima 2014a, 2016), or of a postposition of instrument. For example, the container noun runja \u2018bucket\u2019 in (218a\u23afb) is the complement of the same postpositions as in (217a\u23afb). (217) a. \u0128n ki g\u0129r t\u00f3g n\u1ef9t\u0129. house inside child TOP ASP \u2018Some\/the children are in a\/some\/the house(s).\u2019 118 b. F\u00f3gt\u1ebd v\u1ef9 n\u0129gja mraj ka t\u1ef9. F\u00f3gt\u1ebd NOM chair break stick with \u2018F\u00f3gt\u1ebd broke a\/some\/the chair(s) with a\/some\/the stick(s).\u2019 (218) a. F\u00f3gt\u1ebd v\u1ef9 runja ki r\u1ef9nhr\u1ef9j r\u00e9gre-\u2205 tat\u0129n \u2205. F\u00f3gt\u1ebd NOM bucket inside sand two-ACC carry PFV \u2018F\u00f3gt\u1ebd carried two portions of sand in a\/some\/the bucket(s).\u2019 b. F\u00f3gt\u1ebd v\u1ef9 runja t\u1ef9 r\u1ef9nhr\u1ef9j r\u00e9gre-\u2205 tat\u0129n \u2205. F\u00f3gt\u1ebd NOM bucket with sand two-ACC carry PFV \u2018F\u00f3gt\u1ebd carried two portions of sand with a\/some\/the bucket(s).\u2019 Note that in (218a\u23afb) the container phrases runja ki \u2018in bucket(s)\u2019 and runja t\u1ef9 \u2018with bucket(s)\u2019 don\u2019t occur between the numeral r\u00e9gre \u2018two\u2019 and the substance noun r\u1ef9nhr\u1ef9j \u2018sand\u2019. Constructions in which a container phrase intervenes between the numeral and the noun are ruled out in Kaingang, as illustrated in (219a\u23afb). (219) a. ??F\u00f3gt\u1ebd v\u1ef9 goj runja ki r\u00e9gre tat\u0129n \u2205. F\u00f3gt\u1ebd NOM water bucket inside two carry PFV \u2018F\u00f3gt\u1ebd carried two buckets of water.\u2019 b. ??F\u00f3gt\u1ebd v\u1ef9 goj runja t\u1ef9 r\u00e9gre tat\u0129n \u2205. F\u00f3gt\u1ebd NOM water bucket with two carry PFV \u2018F\u00f3gt\u1ebd carried two buckets of water.\u2019 Thus, the syntactic configuration in (218a\u23afb) and the consultants\u2019 rejection of (219a\u23afb) suggest that container phrases in Kaingang are adjuncts. Like in English, in Kaingang and Yudja container phrases can be interpreted as providing the units for counting. However, as opposed to English, in Kaingang and Yudja container phrases can also have a locative meaning. That is, sentences like (218a\u23afb) can be interpreted as referring 119 to locations where already individuated units are placed. 40 To illustrate this point, consider sentence (220) and the three contexts below. (220) F\u00f3gt\u1ebd v\u1ef9 runja ki\/t\u1ef9 goj r\u00e9gre-\u2205 tat\u0129n \u2205. F\u00f3gt\u1ebd NOM bucket inside\/with water two-ACC carry PFV \u2018F\u00f3gt\u1ebd carried two portions of water inside\/with a\/some\/the bucket(s).\u2019 \u2713Context A: F\u00f3gt\u1ebd carried two buckets with water. Figure 32: The two-bucket scenario. \u2713Context B: F\u00f3gt\u1ebd poured two bottles of water in a bucket and carried it. Figure 33: The one-bucket scenario. 40 Like in English, in Yudja container phrases can also have a measuring interpretation. It is still unclear whether a measuring interpretation of Kaingang container phrases is also available. For an in-depth discussion of container phrases in Yudja and all their available interpretations, see Lima (2014a, 2016). 120 \u2713Context C: F\u00f3gt\u1ebd put two closed bottles full of water in a bucket and carried it. Figure 34: The two-bottle scenario. The sentence in (220) is felicitous in all the three scenarios above. One crucial element common to all of them is that the quantity of water carried can be mapped onto two concrete portions of water. In context A, depicted in Figure 32, the two portions are individuated by two buckets, i.e., units and buckets coincide. In context B, depicted in Figure 33, although the quantity of water carried isn\u2019t individuated inside the bucket, it can be traced back in time to two concrete bottles that partitioned the quantity into two counting units. As for context C, depicted in Figure 34, in it the container phrase is interpreted as just indicating the receptacle where the concrete counting units individuated by the two bottles are placed, i.e., the bucket is neither used to individuate nor to measure the portions. The felicity of the sentence in (220) in context C, hence, shows that Kaingang container phrases can also have a locative interpretation, i.e., one that indicates where concrete counting units are located. Accordingly, the fact that Kaingang container phrases are adjuncts and that they cannot intervene between numerals and (substance) nouns, as well as the fact that the interpretation of constructions like the one in (220) does not always associate the units with the receptacles denoted by the container nouns, are quite compatible with an analysis of Kaingang substance nouns as count nouns that denote portion-units. Summarizing, this section has provided a set of morphosyntactic and semantic pieces of evidence showing that individual and substance nouns in Kaingang pattern alike in the counting system of the language, i.e., there are no morphosyntactic or semantic features that distinguish them in this domain. These findings support the hypothesis that all nouns in Kaingang are interpreted as count. Like individual nouns, substance nouns denote counting units not only when combined with numerals and other quantity words, or in comparative constructions, but also when 121 they appear bare, as evidenced in the examples with reciprocals and count adjectives. As a result, the individuating mechanism involved in the count interpretation of Kaingang nouns cannot be attributed to numerals and quantity expressions. Thus, the only thesis that seems to be supported by the facts is that the operation supplying the individual- or portion-units must already be encoded in the nouns themselves. The conclusion is that all nouns are inherently count in Kaingang, i.e., they enter derivations already vested with a count meaning. In section 4.5, I provide a semantic analysis of this lexical property shared by all Kaingang nouns. 4.5 The analysis 4.5.1 The semantics of Kaingang nouns Based on the number neutrality and pervasive count meaning of Kaingang bare nouns, it can be tempting, at first blush, to analyse individual and substance nouns in the language as cumulative atomic predicates, i.e., as exhibiting join-semilattice denotations with atoms at the bottom. Basically, in such an approach individuals and portions are modeled as atomic entities, and the denotations of nouns are treated as sets of atoms closed under sum formation. As discussed in Chapter 3, in a mereology-based semantics atoms can be defined absolutely, as defined in (221), or relative to a predicate, as laid out in (222). (221) ATOM(x) \u225d \u00ac\u2203y[y \u228f x] (= (119)) (x is an atom iff it has no proper part.) (Krifka 2007: 10) (222) ATOM(P)(x) \u225d P(x) \u2227 \u00ac\u2203y[y \u228f x \u2227 P(y)] (= (120)) (x is an atom relative to a predicate P iff there isn\u2019t a proper part of x of which P also holds.) (Krifka 2007: 10) 122 In turn, on the basis of (221) and (222), an atomic predicate can be characterized as in (223). (223) ATOMIC(P) \u225d \u2200x[P(x) \u2192 \u2203y[y \u2291 x \u2227 ATOM(P)(y)] (= (121)) (A predicate P is atomic iff for every x that is P, there is a part of x that is an atom in P.) (Adapted from Krifka 1989: 78) Note that ATOMIC(P) is true of both non-cumulative and cumulative atomic predicates. In other words, ATOMIC(P) applies to nouns that denote sets of atoms, namely (prototypical) singular nouns, as well as those that denote sets of atoms and their sums, i.e., plural nouns. As a result, on the assumption that atomicity is sufficient for nouns to be countable, an analysis of Kaingang nouns as cumulative atomic predicates would explain their count interpretation. Nevertheless, it turns out that there is compelling crosslinguistic evidence indicating that atomicity is not the defining property of count nouns (Krifka 2007; Rothstein 2010, 2017). One piece of evidence comes from object mass nouns like furniture, luggage, kitchenware, jewellery, clothing, etc. Although these nouns have atoms in their denotations, and thereby can pattern in certain ways with count nouns \u2212\t by allowing cardinal-based evaluations in comparative constructions and combining with count adjectives (Barner & Snedeker 2005) \u2212\t this isn\u2019t sufficient for them to be vested with the morphosyntax of count nouns. For example, in English object mass nouns can neither inflect for number nor directly combine with numerals and other count quantity expressions. Barner and Snedeker (2005) and Bale and Barner (2009) argue based on experimental tests that the availability of cardinality-based readings of object mass nouns in quantity comparisons is evidence in support of an analysis of object mass nouns as semantically count, but morphosyntactically mass. The authors go further and claim that this class of nouns always triggers cardinality-based interpretations. But some studies have challenged this view (Rothstein 2016, 2017; Rothstein & Pires de Oliveira 2016). They demonstrate that object mass nouns can also be interpreted along other dimensions, such as weight and volume, and that this flexibility is context dependent. For instance, if (224a) is uttered \u201cin the context of choosing a moving truck, the volume of the furniture is relevant and not the number\u201d (Rothstein 2017: 122). As such, (224a) can be true in a scenario where Bill has five pieces of furniture and John just three pieces, provided that the 123 totality of John\u2019s pieces of furniture occupies more space in a truck than Bill\u2019s. Importantly, this is not the case with (224b), which is judged false in a scenario such as the one above. This indicates, as Rothstein observes (2017), that pieces of furniture, as opposed to furniture, always forces a number-based reading. (224) a. John has more furniture than Bill, so he should use the larger moving truck. b. John has more pieces of furniture than Bill. (Rothstein 2017: 122) These cases hence reveal that the semantics of object mass nouns and singular count nouns in English differ. The cardinality-based evaluation of object mass nouns in comparisons seems to be favored by perceptual salience of the objects in their denotations. However, due to their mass meaning, they don\u2019t impose any measuring dimension, leaving it for the context to arbitrate (Rothstein 2017). I believe Krifka\u2019s theory (1989, 2007) offers a neat explanation of this flexible behavior of object mass nouns. They share atomicity with English prototypical count nouns and cumulativity with substance nouns. But, by lacking the quantized nature of count nouns, the cardinality dimension can\u2019t be the only one available for them in comparison tasks.41 A second piece of evidence that atomicity is not the defining property of count nouns, as Rothstein (2010, 2017) points out, involves count nouns such as rope, fence, wall, bouquet, table, etc. These nouns are non-atomic. Subparts of a rope can still be ropes, a fence or wall can be constituted by parts that are also fences or walls, and two bouquets or tables can be joined to form one bouquet or table. What counts as one fence or wall is context-sensitive, i.e., it can vary across utterance contexts. Without further specification, linking the count semantics of this class of nouns to atomic reference would be problematic, for it falls short of explaining their malleability regarding what constitutes one unit in their denotations. Accordingly, on the basis of the generalized count interpretation of Kaingang nouns and motivated by the crosslinguistic evidence above, I consider Krifka\u2019s (1986, 1989, 2007) emphasis on the quantized\/cumulative opposition better suited for explaining the semantics of the 41 For a crosslinguistic perspective on object mass nouns, see Rothstein (2016). 124 count\/mass distinction than the atomic\/non-atomic opposition, as discussed in detail in Chapter 3. This is embedded in the machinery of his theory, which offers, I hope to demonstrate, an efficient toolbox for dealing with a language like Kaingang, where all nouns exhibit a count meaning. Quantization and cumulativity, as laid out in Chapter 3, are properties of predicates. A predicate is quantized if and only if whenever it is true of entities a and b, neither can be a proper part of the other. In English, quantized predicates are constructions such as two dogs, five tables, three liters of water, seven portions of flour, etc. On the other hand, a predicate is cumulative if and only if whenever it is true of entities a and b, it is also true of their sum. Examples of cumulative predicates are substance mass nouns like blood, milk, etc., and object mass nouns like furniture, luggage, etc. For expository reasons, the formal definitions of quantized and cumulative predicates introduced in Chapter 2 are repeated here as (225) and (226), respectively. (225) QUANT(P) \u225d\t\u2200x\u2200y[P(x) \u2227 P(y) \u2192 \u00ac(y \u228f x)] (= (135)) (A predicate P is quantized iff whenever P holds of something, it doesn\u2019t hold of any its proper parts.) (Adapted from Krifka 1989: 78) (226) CUM(P) \u225d \u2200x\u2200y[P(x) \u2227 P(y) \u2192 P(x\u2294y)] (= (122)) (A predicate P is cumulative iff whenever P holds of two entities, it also holds of their sum.) (Adapted from Krifka 1989: 78) In Krifka\u2019s framework (1986, 1989, 2007, 2008) counting is a special type of measuring, one whose units of measurement are individuals or portions of a substance. Count nouns carry a built-in counting function NU (\u2018natural-unit\u2019), which expresses a relation between quantities of a predicate P and a number n, as given in (138), repeated here as (227). This quantizing function measures P in terms of concrete units of counting. (227) NU(P\u27e8e,t\u27e9)(xe) = n 125 English count nouns like child are modeled as two-place relations between numbers and entities, i.e., as functions of type \u27e8n,\u27e8e,t\u27e9\u27e9, as given in (140), repeated here as (228). As such, by providing a number variable n to be saturated by numbers, they are allowed to directly combine with numerals, hence giving rise to quantized constructions. (228) \u27e6child\u27e7 = \u03bbn\u03bbx[CHILD(x) \u2227 NU(CHILD)(x) = n] On the other hand, mass nouns like blood and furniture express one-place predicates, i.e., they are functions of type \u27e8e,t\u27e9 which lack a built-in measure function, as illustrated in (139) and (148), repeated here as (229a\u23afb). As a result, they are precluded from directly combining with numerals because, lacking a measure function, they don\u2019t supply a number variable to be saturated by numbers. In this regard, an intervening measure construction like liter-of, piece-of, etc., must first apply to these cumulative nouns in order to derive countable constructions \u23af\tand hence counting units \u23af which then can form a constituent with numerals, as given in (141) and (149), repeated here as (230a\u23afb). (229) a. \u27e6blood\u27e7 = \u03bbx[BLOOD(x)] b. \u27e6furniture\u27e7 = \u03bbx[FURNITURE(x)] (230) a. \u27e6liter-of\u27e7(\u27e6blood\u27e7) = (\u03bbP\u03bbn\u03bbx[P(x) \u2227 LITER(P)(x) = n])(\u03bbx[BLOOD (x)]) = \u03bbn\u03bbx[BLOOD (x) \u2227 LITER(BLOOD)(x) = n] b. \u27e6piece of\tfurniture\u27e7 = \u03bbn\u03bbx[FURNITURE(x) \u2227 PIECE(FURNITURE)(x) = n] Thus, building on Krifka\u2019s approach, I propose to analyse the generalized counting strategy in Kaingang as a direct effect of the lexical meaning of nouns. Kaingang nouns are predicates that come from the lexicon already equipped with a context-sensitive built-in additive function \u00e0 la Krifka (1986, 1989, 2007, 2008) which maps entities (individuals or portions) into numbers. Because all nouns have this quantizing function as part of their lexical meaning, they are already born quantized, which means that Kaingang root nouns are specified as being count. 126 I assume that nouns give semantic information on the type of units in their denotations (Quine 1960). This is modeled as encoded in the counting functions of Kaingang nouns. To indicate this information, I label the counting function of individual nouns IUC (individual-units), given in (231), whereas the one of substance nouns is tagged PUC (portion-units), laid out in (232). (231) IUC(P\u27e8e,t\u27e9)(xe) = n (IU measures P in context C in terms of individual-units.) (232) PUC(P\u27e8e,t\u27e9)(xe) = n (PU measures P in context C in terms of portion-units.) Taking g\u0129r \u2018child\u2019 and kyv\u00e9nh \u2018blood\u2019 as illustrative nouns, the lexical entries in (233) and (234) are assigned to Kaingang root nouns. The term \u2018root nouns\u2019 refers to the members of the open-class vocabulary categorized as nouns. The use of the symbol \u221a to represent roots is a standard notation in Distributive Morphology (Marantz 1997, 2001). (233) \u27e6>g\u0129r\t\u27e7 = \u03bbx[CHILD(x) \u2227 IUC(CHILD)(x) = n] (234) \u27e6>kyv\u00e9nh \u27e7 = \u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = n] Individual root nouns such as (233) denote sets of individual-units, whereas substance root nouns like (234) denote sets of portion-units. Their inherent counting function expresses a relation between quantities and a number, represented by the free variable n.42 The subscripted C in IU\/PU encodes the context-dependence of what counts as one unit (Krifka 2007 Rothstein 2010). Under the analysis advanced here, the parameter of interpretation C provides the partition of the noun denotation by supplying the contextually salient individuals or portions to be accessed by the counting function IU\/PU. The incorporation of C into the counting function thus allows us to represent the crucial role of utterance contexts in deriving the sets of portion-units in the denotation 42 A discussion of n as a free variable is given on pages 127\u23af131. 127 of substance nouns, which easily varies across contexts. For instance, if the sentence in (235) is uttered in the context depicted in Figure 35, the set of units in the denotation of quantized goj \u2018water\u2019 will include the individuated portions (which are distinct in size and shape) in the gallon, in the glass, and forming the puddle, but exclude their proper parts. As a result, only the three (spatially) salient portions will be counted. (235) Context: Pak\u00f3j entered the kitchen and saw one gallon of water on the floor, one glass full of water on the table, and one puddle of water on the floor. Figure 35: The kitchen scenario. F\u00f3gt\u1ebd v\u1ef9 goj t\u00e3gt\u0169-\u2205 v\u00e9 \u2205. (= (177)) F\u00f3gt\u1ebd NOM water three-ACC see PFV \u2018F\u00f3gt\u1ebd saw three portions of water.\u2019 Thus, by making PU sensitive to the context of utterance, we neatly capture the instability of substance count noun denotations, for portions are modeled as contextual units. Moreover, the analysis shows that it is the \u201ccontext dependence of count nouns [that] explains the apparent non-quantization of nouns like fence, wall, hedge, bouquet\u201d (Krifka 2007: 35), as well as of substance count nouns in Kaingang. As for count nouns that denote sets of stable individuals, like g\u0129r \u2018child\u2019 and f\u00f3g \u2018non-indigenous person\u2019, the sets of individuals will be constant for every context C. Observe that in (233) and (234) the number variable n is left free. I treat its value as contextually supplied, rather than saturated by a number argument. This departure from Krifka\u2019s analysis not only allows cumulative and quantized predicates to be of the same type, i.e., \u27e8e,t\u27e9, but it also prevents quantized nouns from gaining a cumulative denotation in an early stage of the derivation via existential closure of n at the N(P) or NumP level, i.e., before they are converted 128 into bare noun arguments. This analysis shows that Kaingang bare nouns can be used to refer to pluralities selected from the denotation of quantized nouns, which indicates that plural interpretations of bare nouns uninflected for number don\u2019t need cumulative reference at the N(P) or NumP level. Thus, given the contextual dependence of quantized nouns in Kaingang and fence-type nouns in languages like English, a definition of contextually quantized predicates can be stated in which QUANT(P) is relativized to a context C and an assignment function g, as given in (236). (236) Definition quantization relative to a context and an assignment function: \u27e6QUANT(P)\u27e7C,g = 1 iffdef \u2200d1,d2 \u2208 D [d1 \u2208 \u27e6P\u27e7C,g \u2227 d2 \u2208 \u27e6P\u27e7C,g \u2192 \u27e6y \u228f\tx\u27e7C,g[x \u2192 d1, y \u2192 d2] = 0] (A predicate P is quantized relative to a context C and an assignment function g iff whenever P holds in C of an entity in the domain, it doesn\u2019t hold of any its proper parts in C.) Definition (236) makes sure that the context C is kept constant when assessing the part-whole relation, so whatever value it picks out for the n variable of a quantized P, it stays fixed. (236) is a particular case of definition (225), stated in a more formal way in order to take into account the role of the context.43 A note of caution is in order here. It is important not to call individuals and portions \u201catoms\u201d because they have parthood structures and as such clearly don\u2019t fall under (221), namely, the absolute definition of atoms. I can\u2019t see how definition (221) could be true of the entities of our daily experience. However, once the semantics of fence-type and substance count nouns is linked to context sensitivity in the way proposed above, it follows from this that the contextual units of quantized predicates coincide with Rothstein\u2019s contextual atoms, i.e., atoms relative to contexts (see Chapter 3). As a result, ATOM(P)(x), as defined in (222), is true of the entities that are 43 Given (236), a context-independent definition of QUANT(P)\tcan be laid out as follows: (i) \u27e6QUANT(P)\u27e7 = 1 iffdef for any C and assignment g, \u27e6QUANT(P)\u27e7C,g = 1 In (i) a predicate P is quantized in an absolute sense if it is quantized relative to any context C and assignment function g. I would like to thank Hotze Rullmann (p.c) for suggesting (236) and (i) to me. 129 (contextual) units in the denotation of Kaingang nouns. Note that this doesn\u2019t contradict the claim that \u201cthe essential feature [of count nouns] is quantization, not atomicity\u201d (Krifka 2007: 28). Although QUANT(P) entails ATOMIC(P), as defined in (223), the reverse direction of the entailment doesn\u2019t hold. So far I\u2019ve said what the BN roots denote, now I turn to how they combine with other elements in sentences. To implement this analysis, I represent Kaingang indefinite bare nouns in argument position as existentially bound choice functions.44 In prose, a choice function f maps a non-empty set onto one of its elements, which means that it\u2019s a function of type \u27e8\u27e8e,t\u27e9,e\u27e9. For instance, f applies to a quantized substance bare noun like kyv\u00e9nh \u2018blood\u2019 and selects one of the portion-units that consist of blood. Let us take the context in (237) below as an example. The salient drops of blood in this context have cardinality 3. Given that I treat contexts of utterance as supplying the value of the free variable n, in the context below n turns out to be 3. That is, under this analysis, the n variable can be saturated by the cardinality of the portion-units that are contextually salient. As a result, the bare noun kyv\u00e9nh in (237) denotes a quantized set with pluralities of cardinality 3 as elements, as given in (238a). Therefore, if, in this context, the choice function picks out the salient plurality of portions of blood with cardinality 3, e.g., the one that is encircled in (238a) and represented in (238b), then the sentence in (237) will be true. 44 This representation of indefinite bare nouns as choice functions isn\u2019t merely posited to oil the wheels of the analysis above. The choice function theory of indefinites, introduced by Reinhart (1997) and Winter (1997), was specially designed to account for the exceptional scope behavior of indefinites with respect to syntactic islands such as if-clauses. The main empirical advantage of a choice function analysis is that it explains the scope interaction of indefinites with respect to other operators without resorting to movement, given that LF movement has been shown to make incorrect predictions for indefinites. The existential closure of choice functions at any level captures their interpretations. Given that Kaingang indefinite bare nouns scopally interact with other operators such as negation, intensional verbs, and if-clauses, as well as exhibiting intermediate scope readings, treating them as contributing an existentially closed choice function is an empirically motivated solution. The scope data for Kaingang will be discussed in Chapter 5. 130 (237) Context: You notice that some drops of blood [a total of 3 drops] fell from F\u00f3gt\u1ebd\u2019s nose. Kyv\u00e9nh v\u1ef9 n\u00e3g ke \u2205. blood NOM drip PFV \u2018Some drops of blood dripped.\u2019 (238) a. \u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = 3] = {b1\u2294b2\u2294b3, b4\u2294b5\u2294b6, \u2026,b20\u2294b21\u2294b23, \u2026} b. f(\u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = 3]) = b20\u2294b21\u229423 In (239), I provide a compositional semantics of the truth conditions of the sentence in (236), abstracting away from tense and aspect. (239) \u27e6S\u27e7 = 1\u2194 \u2203f [DRIP(f(\u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = 3]))] \u2203f DRIP(f(\u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = 3])) f(\u27e6NP kyv\u00e9nh\u27e7) \u27e6VP n\u00e3g ke\u27e7 = \u03bbx[DRIP(x)] \u03bbP[f(P)] \u27e6NP kyv\u00e9nh\u27e7 = \u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = 3] Note that the analysis implemented in (237\u23af239) accounts for the plural interpretation of Kaingang bare nouns without associating it with a cumulative denotation. The contextual saturation of the n variable allowed us to demonstrate that in principle plural interpretations of bare nouns are not incompatible with assigning them a quantized denotation. In this regard, it is easy to see how the same analysis can be extended to contexts in which Kaingang bare nouns get a singular interpretation. In such scenarios the salient individual or portion is a singularity. As a consequence, the n variable will be saturated by 1. Thus, in the analysis illustrated in (237\u23af239), by the time that 131 a Kaingang bare noun is type-shifted to an argument, it expresses a predicate which contains an unbound variable n, and hence is quantized relative to any contextual assignment of a value to n.45 Alternatively, if we assume that the number-neutral meaning of Kaingang bare nouns necessarily relies on cumulative reference, this idea can be implemented by existentially binding the free variable n. This resource, as Krifka (1989) shows, gives rise to a cumulative interpretation. However, this is accomplished not at the root or NP\/NumP level, but at a higher syntactic level after the quantized noun is inserted in the syntactic derivation. For concreteness, let us assume that this existential closure takes place at the level of the clause. By contrast, in languages that contain plural bare nouns, such as English, it is the plural morpheme on the noun itself that introduces \u2203-closure. Given that the number neutrality of Kaingang bare nouns is not associated with plural morphology, it can be assumed that the number variable n is unselectively bound by the existential operator that also binds the choice function variable f. Thus, the cumulative reading of Kaingang bare nouns arises whenever the structure in (240) occurs at the clausal level (where \u2018\u03bcC\u2019 stands for the contextual measure function, either IUC or PUC). (240) \u2203f,n\u2026[f(\u03bbx[P(x) \u2227 \u03bcC(P)(x) = n]))]... Thus, the approach proposed above envisages two possible ways of resolving the free variable n of Kaingang bare nouns, namely contextual saturation or existential closure. Each of these 45 The analysis proposed above isn\u2019t incompatible with the interpretation of Kaingang bare nouns in sentences like (i) and (ii), which portray the speaker as not having any specific number in mind. (i) I saw children, but I don\u2019t know how many. (ii) Do you have children? The fact that the context provides the number which saturates the n variable doesn\u2019t need to entail that the speaker always has a specific number in mind when uttering sentences with a quantized bare noun. In this regard, a parallel can be drawn with questions like What time is it?, which are used to request information about the time, a phenomenon which has a specific number in every context. I propose that something similar occur when a Kaingang speaker utters sentences like (i) and (ii). Although the contexts in which they are uttered provide a value for the number variable n, the speaker doesn\u2019t know what that value is. Particularly, in yes\/no questions like (ii), the cardinality of the bare noun is highly dependent on contextual facts about the addressee: for instance, if they have one child, then the contextual cardinality is resolved to 1, while if they have none, then the cardinality is 0. I am indebted to Hotze Rullmann (p.c) for calling my attention to this interesting parallel. 132 mechanisms brings about its own semantic effects. The former always gives rise to a quantized bare noun with a contextually specified cardinality, while the latter leads to cumulative reference at the clause level (but not at the root level). Thus far both mechanisms are equally consistent with the Kaingang data. Only further research on the semantics of Kaingang bare nouns may provide supporting evidence to decide between the two strategies. One immediate consequence of treating quantized nouns as predicates of type \u27e8e,t\u27e9 is that numerals in Kaingang cannot denote arguments for the n variable, for whenever they combine with a noun n represents a free variable. To tackle this, I propose to model Kaingang numerals as predicate modifiers with a cardinality presupposition whose satisfaction depends upon the contextual value of the number variable n within quantized predicates. To illustrate this, (241a\u23afb) give the lexical entry of the numerals r\u00e9gre \u2018two\u2019 and t\u00e3gt\u0169 \u2018three\u2019. (241) a. \u27e6r\u00e9gre\u27e7 = \u03bbP\u27e8e,t\u27e9 \u03bbxe: \u2200x[P(x) \u2192 IUC\/PUC(P)(x) = 2].P(x) b. \u27e6t\u00e3gt\u0169\u27e7 = \u03bbP\u27e8e,t\u27e9 \u03bbxe: \u2200x[P(x) \u2192 IUC\/PUC(P)(x) = 3].P(x) Under this theoretical solution, the cardinality presupposition targets the number within the measure function. It introduces the condition that the predicate modified by a numeral must display a certain contextual cardinality. The idea is that a numeral is only defined if its presupposition is satisfied by the contextually supplied number for the n variable of the noun it combines with. Given the lexical entries in (241a\u23afb), hence, one-place quantized predicates become arguments of numerals. By functional application of the denotation of a numeral to a quantized predicate another quantized predicate is then created, but now with a cardinality presupposition passed on by the numeral. The schematic tree in (242) illustrates this procedure with the constituent kyv\u00e9nh t\u00e3gt\u0169 \u2018three portions of blood\u2019. 133 (242) \u27e6\ud835\udefc\u27e8e,t\u27e9\u27e7 = \u03bbx: \u2200x[P(x) \u2192 PUC(P)(x) = 3].[BLOOD(x) \u2227 PUC(BLOOD)(x) = n] \u27e6t\u00e3gt\u0169 \u27e8\u27e8e,t\u27e9, \u27e8e,t\u27e9\u27e9 \u27e7 = \u03bbP\u03bbx: \u2200x[P(x) \u2192 PUC(P)(x) = 3].P(x) \u27e6NP\u27e8e,t\u27e9\u27e7 = \u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = n] \u27e6>kyv\u00e9nh\t\u27e7 = \u03bbx[BLOOD(x) \u2227 PUC(BLOOD)(x) = n] In (242) the NP denotation encodes the quantized nature of the noun, along with its \u27e8e,t\u27e9 type, and as such it is ready to be the argument of the numeral, which, as a predicate modifier, i.e., an expression of type \u27e8\u27e8e,t\u27e9,\u27e8e,t\u27e9\u27e9, applies to the NP and generates another predicate. At this stage, the presupposition of the numeral is projected into the derived predicate.46 The analysis outlined in (241a\u23afb) and (242) obviously is not intended to be an exhaustive account of numerals in the language. It was set forth in this thesis, first and foremost, to show that it is in principle possible to provide a compositional treatment of a noun+numeral constituent in Kaingang when quantized nouns are represented as predicates of type \u27e8e,t\u27e9 containing in their internal structure a counting function modeled along the lines of Krifka.47 To summarize, the analysis advanced here treats all nouns in Kaingang as lexically count. Nouns express quantized predicates of type \u27e8e,t\u27e9 containing a built-in counting function that measures quantities in terms of individual- or portion-units. The context-sensitivity of what counts as a unit is incorporated into the analysis by treating the quantizing function as context-dependent. This guarantees that the units are evaluated relative to the utterance context. Further, the number variable of the counting function is left free, allowing its value to be contextually supplied and hence ensuring that the noun is quantized relative to any contextual assignment of a value to n. This solution shows that individual and substance nouns in Kaingang can still be quantized at the point at which they are converted into bare noun arguments with an indefinite interpretation, unlike English bare plurals, which have cumulative reference. That is, Kaingang BNs can be quantized 46 One could raise the issue that the account above entails a presupposition failure for numerals in out-of-the-blue statements. I don\u2019t think this is a real problem for the analysis, because of the pervasiveness of presupposition accommodation. The presupposition can be accommodated by leaving it up to the hearer to imagine a context compatible with the presupposition. 47 The presuppositional analysis of numerals can be extended to vague quantity words like e \u2018many\u2019, by assuming that they carry the presupposition that the contextually supplied value of n is a large number. 134 even when they refer to pluralities. In turn, by representing indefinite bare nouns as introducing a choice function, I have shown that pluralities can be selected from the extension of quantized nouns whenever their contextual cardinality is > 1. In addition, I have shown that the number-neutral meaning of bare nouns can alternatively be analysed as arising at the clause level from the option of unselectively binding the number variable via the existential operator that also binds the choice function variable. 4.5.2 Extending the analysis to Yudja In this section, I shall first briefly discuss Lima\u2019s (2014a, b) analysis of Yudja nouns. By doing so I aim to highlight what I consider to be the explanatory advantage of an alternative approach that treats the count nature of nouns in Yudja as resulting from a quantized denotation. In Yudja nouns are number neutral, can be bare in all argument positions, and allow (in)definite or kind readings. Numerals can combine directly with individual and substance nouns. Substance nouns are modified by numerals even when used to refer to non-conventionalized portion-units, as in (243). (243) Txab\u00efu apeta pe\u223cpe\u223cpe. (Yudja) three blood drip\u223cRED \u2018Three drops of blood dripped.\u2019 (Lima 2014a: 58) Quantity words also select for substance nouns, in most cases triggering a cardinal interpretation. In (244) itx\u00efb\u00ef \u2018many\u2019 exhibits the cardinal reading of a large number of contextually supplied portion-units of water. (244) Itx\u00efb\u00ef y\u2019a a\u2019i. (Yudja) many water here \u2018There are many portions of water here.\u2019 (Lima 2014b: 535) 135 Quantity judgement experiments show that Yudja speakers strongly favor a number-based evaluation of substance nouns in comparative constructions (Lima 2014a, b). In scenarios, for instance, containing a collection of one or two portions of flour side-by-side with another collection of multiple portions of the same substance, the majority of Yudja speakers responded to the stimuli sentences (245) and (246) \u2212 which contain the quantity expressions bitu \u2018more\u2019 and itx\u00efb\u00ef \u2018many\u2019, respectively \u2212 by choosing the collection with a greater number of portion-units of flour, regardless of their total volume. To be precise, in comparisons containing itx\u00efb\u00ef \u2018many\u2019 all adult speakers offered a number interpretation of the stimulus substance nouns. (245) Ma de bitu asa dju a\u2019au? (Yudja) who more flour have \u2018Who has more flour?\u2019 (Lima 2014a: 120) (246) Ma de itx\u00efb\u00ef asa dju a\u2019au? (Yudja) who many flour have \u2018Who has many portions of flour?\u2019 (Lima 2014a: 183) Based on the pervasive count interpretation of individual and substance nouns in Yudja, which parallels the Kaingang data I have reported in this chapter, Lima (2014a, b) claims that all nouns in Yudja are countable. However, she offers an analysis that differs from mine. She proposes a semantics for Yudja nouns in which root nouns denote kinds, as illustrated in the lexical entry of asa \u2018flour\u2019 in (247), where FLOUR in capital letters is a standard notation for kinds. (247) \u27e6\u221aasa\t\u27e7 = FLOUR (Adapted from Lima 2014a: 100) As for the predicate meaning of nouns, Lima (2014a, b) proposes that it is morphologically derived by combining the root with a silent operator, called KO (kind-to-object), which maps a kind \u201cto a property that is true of atomic individuals and their sums\u201d (Lima 2014a: 100). More precisely, it 136 applies to a kind k and returns \u201ca number neutral property of atomic individuals and their sums who are members of k\u201d (Lima 2014b: 537), as in (248a\u23afb).48 (248) a. KO = \u03bbk: k \u220a K. \u03bbx. AT*(x)(k) b. KO(\u27e6\u221aasa\t\u27e7) = \u03bbx. AT*(x)(FLOUR) (Adapted from Lima 2014a: 100) Note that (248b) is the derived denotation of asa, i.e., a set of atomic and sum realizations of the kind FLOUR. Although Lima doesn\u2019t represent the context in (248a\u23afb), she claims that the atoms of substance nouns are spatially specified.49 By having an atomic join-semilattice denotation, (248b) is cumulative, i.e., a set which is closed under sum formation, as already observed by Deal (2017). Consequently, (248b) is not a quantized predicate, although it contains (contextually determined) atomic parts. This reveals that in Lima\u2019s approach the property ensuring that all nouns are countable is atomicity, and not quantization, as on my account. However, although Lima\u2019s analysis can apply specifically to Yudja, it falls short of allowing for generalization to other languages. As discussed in Chapter 3 and section 4.5, there is convincing crosslinguistic evidence that denoting a set of atoms and their sums, i.e., having cumulative atomic reference, doesn\u2019t guarantee that a noun is count. This is attested by object mass nouns (like furniture) in mass\/count languages, which denote an atomic join-semilattice structure. Further evidence that a sum denotation with atoms as parts doesn\u2019t ensure that a noun is lexically count can also come from classifier languages. For instance, Doetjes (1997) and Cheng et al. (2008) propose that Mandarin encodes a parts-based distinction, rather than a sums-based one. Roughly speaking, all Mandarin nouns are cumulative, and their main division is between atomic and non- 48 Lima\u2019s analysis of Yudja nouns is formulated in an intensional language, where a world variable is part of the lexical entries. KO maps a kind into a property, i.e., into a set of atoms and their sums in a world of evaluation w. KO contains a function AT* \u201cthat maps an individual x, a world w and a kind k to the truth value 1 if and only if x is the sum of atomic parts of k(w)\u201d (Lima 2014b: 537). For expository purposes, (247) and (248a\u23afb) are simplified extensional versions of the original denotations. 49 To model portions as atoms, Lima (2014a, b) relies on mereotopological notions (Casati & Varzi 1999) such as (self)-connectedness and maximal self-connected portions. Drops of blood, portions of sand, etc., are represented as atoms whose individuations are spatially specified. 137 atomic join-semilattice denotations. If such an analysis is on the right track, it can be interpreted as showing that Mandarin distinguishes atomic from non-atomic mass nouns, but not count nouns from mass nouns. Indeed, if across languages being a count noun means being quantized, and if numerals (and other count quantity expressions) only select for quantized constructions, to maintain the semantics in (247) and (248a\u23afb) we then would have to complement it with one of two options. We could stipulate a covert counting function that applies to Yudja substance nouns and turns them into quantized predicates, which then can be complements of numerals, as Deal (2017) proposes. Or we could treat the counting function as part of the lexical meaning of Yudja numerals (and other count quantity expressions), along the lines of Wilhelm\u2019s (2008) analysis of D\u00ebne S\u0173\u0142in\u00e9, an Athapaskan language. However, either option would undermine Lima\u2019s claim that all Yudja nouns can be interpreted as count nouns. Rather, I believe that my account of Kaingang nouns as inherently quantized predicates of type \u27e8e,t\u27e9 can be extended to Yudja nouns. In this way, I propose to eliminate the operator KO and replace the lexical entry of a (substance) noun like asa in (247) by (249), analogous to my analysis of Kaingang. (249) \u27e6\u221aasa \u27e7 = \u03bbx[FLOUR(x) \u2227 PUC(FLOUR)(x) = n] In (249) asa is a root noun of type \u27e8e,t\u27e9 with a context-sensitive counting function as part of its lexical meaning. PUC maps a quantity of flour onto a number n of contextually specified portion-units of flour. Thus, just like Kaingang nouns, the count nature of Yudja nouns arises from their quantized semantics. Concerning the number neutrality of Yudja bare nouns, like in Kaingang, it does not need to be associated with a lexical cumulative denotation, as shown in section 4.5. In (249) the number variable is left free, which means that it can be contextually resolved or bound by \u2203-closure. The latter strategy gives rise to cumulative reference at the phrasal level, not for the root noun. That is, 138 a cumulative denotation can perfectly well result from a semantic operation applying at a higher syntactic level after the root noun is inserted in the syntactic derivation.50 As a hypothetical exercise, I posit that the kind interpretation of Yudja bare nouns is derived via a type-shifting operation triggered by a type mismatch between their lexical denotation as predicates and that of kind-level predicates, which require a kind argument. It can be modeled as a three-step mechanism. First, the n variable is existentially closed at the NP layer. That is, the quantized denotation of the root noun is projected to the NP layer, where the n variable is then targeted by \u2203. Secondly, the \u2203-binder above the root is demoted to a position after the x argument.51 The resulting predicate then has cumulative reference. Finally, Chierchia\u2019s (1998b) kind-shifting operator \u22c2 applies to this predicate and maps it onto a kind, as illustrated below. (250) a. \u27e6\u221aasa \u27e7 = \u03bbx[FLOUR(x) \u2227 PUC(FLOUR)(x) = n] b. [\u2203]\u27e6\u221aasa \u27e7 = \u03bbx\u2203n[FLOUR(x) \u2227 PUC(FLOUR)(x) = n] by \u2203-closure and demoting of \u2203\t c. \u22c2\u03bbx\u2203n[FLOUR(x) \u2227 PUC(FLOUR)(x) = n] = FLOUR by the kind-shifting operator \u22c2 Note that in (250b) I allow Yudja to differ from Kaingang with respect to how the existential closure of the n variable occurs. In (250b) \u2203 must only bind n, as opposed to Kaingang, in which \u2203 unselectively binds a choice function variable and n. Such differences in the way that \u2203-closure is implemented are not a problem for the analysis. How the existential binding of n is accomplished may very well vary across languages. Crucially, in (250a\u23afc) I adopt the approach in Krifka (2003), where bare nouns are predicates (or properties in their intensional version) and can be shifted to kinds in appropriate contexts via the \u22c2 operator, as opposed to the approach of Krifka (1995), where nouns start out as kind-denoting expressions. It is still unclear, as mentioned in Chapter 2, whether Kaingang bare nouns can also be used to refer to kinds. 50 Note that the analysis of Yudja nouns in (249) forces us to treat Yudja numerals the same way we analysed Kaingang numerals. However, this point is not essential here. The lexical entry for nouns like asa \u2018flour\u2019 could denote a relation between numbers and predicates, as in Krifka (1989, 2007). What is crucial here is to treat Yudja nouns as having built-in quantizing functions. Either account can accomplish this requirement. 51 For previous use of the demoting mechanism in the literature, see Chung & Ladusaw (2003). 139 In the next section, I deal with a potential challenge to the claim that all nouns in Yudja and Kaingang are count nouns. 4.6 A challenge for the analysis Data from a version of the quantity judgement tasks may at first glance pose a challenge to the thesis that all nouns in Kaingang and Yudja are inherently count. It comes from scenarios exhibiting pictures of two portions of the same substance\/entity, differing in volume, as shown in Figure 36 and 37. Figure 36: kyv\u00e9nh \u2018blood\u2019. Figure 37: kakan\u1ebd \u2018fruit\u2019. When shown the single-unit situations above followed by the stimuli questions in (251) and (252), two out of the three Kaingang consultants said that neither one had more quantities of blood or 140 fruit, because the units are numerically identical, whereas one speaker pointed to the unit with the larger volume.52 (251) \u0168 n\u1ef9 t\u1ef9 kyv\u00e9nh m\u1ebd n\u0129? some Q ERG blood more ASP \u2018Who has more blood?\u2019 (252) \u0168 n\u1ef9 t\u1ef9 kakan\u1ebd m\u1ebd n\u0129? some Q ERG fruit more ASP \u2018Who has more fruit?\u2019 The immediate stance is to interpret the larger unit answer as a case of assessment along the volume dimension. On the assumption that a volume interpretation is associated with a mass denotation, one then can argue that there are constructions in Kaingang and Yudja where substance nouns are not quantized and as such cannot be inherently count, so that their count interpretation must involve a silent unitizing operator. As a result, although languages like Kaingang and Yudja morphosyntactically don\u2019t encode the mass\/count distinction, the volume evaluation attested in quantity judgments of single-unit scenarios would suggest that a semantic distinction is available. This is basically Deal\u2019s (2017) reanalysis of Yudja nouns as sharing the semantics she assigns to Nez Perce, a Sahaptian language. That is, Yudja individual nouns are lexically quantized, while substance nouns are born with a mass denotation, which then is mapped onto a quantized one via Deal\u2019s (2017) silent atomization operator.53 52 In single-unit scenarios, most Yudja consultants (Lima 2014a) offered a volume interpretation of substance nouns modified by bitu \u2018more\u2019. 53 Doetjes (2021b) offers an alternative explanation of the Yudja data. She argues that the availability of volume readings in single-unit situations in Yudja is due to the meaning of the quantity word bitu \u2018more\u2019, rather than the semantics of the noun. Volume readings would demonstrate that the quantity expression bitu, like its English counterpart more, doesn\u2019t necessarily trigger a comparison in terms of number, i.e., that it would allow interpretations along other quantity measures, like volume, whenever the context favors them. Thus, whereas itx\u00efb\u00ef \u2018many\u2019 is a count quantity expression, always triggering a number interpretation of the noun it combines with, bitu doesn\u2019t impose such a restriction. According to Doetjes (2021b), count quantity expressions like itx\u00efb\u00ef and many presuppose countability, 141 I don\u2019t think that the availability of a volume-like interpretation for some speakers constitutes conclusive evidence against lexically quantized substance nouns. Instead, it could be accommodated by a coercion-based mechanism that licenses a mass interpretation of count nouns which maps individuals onto their proper parts, along the lines of Lewis\u2019s Universal Grinder operation (Pelletier 1975; Cheng et al. 2008; Rothstein 2017). This operation was introduced to account for constructions like (253) and (254), where the count nouns dog and car are coerced to denote the stuff individuals are made up of. Strictly speaking, it\u2019s in principle possible to offer an analysis of the Yudja and Kaingang data that posits a count-to-mass interpretation shift triggered by (comparison) scenarios that coerce nouns into a mass reading.54 (253) After the accident there was dog all over the highway. (254) Too many people are driving too much car these days. (Moravcsik 2017: 440) while bitu and more are presuppositionless with respect to the dimension of evaluation. She dubs the latter \u2018non-count quantity expressions\u2019. So far, the data from Kaingang suggest that e \u2018many\u2019 and m\u1ebd \u2018more\u2019 are count quantity expression, like Yudja itx\u00efb\u00ef and English many. However, further research about the meaning of e and m\u1ebd needs to be conducted before a formal analysis of these quantity expressions can be proposed. 54 Cheng et al. (2008) offer a coercion theory of the grinding phenomenon. Based on the absence of grinding interpretations of certain individual-denoting nouns in Mandarin (particularly animal-denoting nouns), they argue that there is crosslinguistic variation in the coercion mechanisms triggering stuff interpretations. In English the trigger is syntactic. Since only mass nouns can occur as bare singulars, the grinding reading of count nouns like dog is a last resort to resolve the mismatch between their count meaning and the non-count syntactic contexts in which they are used, i.e., when they appear bare (without numerals or determiners) and lacking plural markers. In contrast, in Mandarin there isn\u2019t such a syntactic mismatch, for all its nouns can appear bare. In Mandarin, the available grinding readings, according to them, are triggered by world knowledge. As for the existence of Mandarin individual-denoting nouns that don\u2019t allow a shift to stuff interpretations, like zh\u016b \u2018pig\u2019, this is attributed to lexical competition. \u201cThe availability of forms with r\u00f2u \u2018flesh, meat\u2019 [such as the compound zh\u016br\u00f2u \u2018pork\u2019] blocks the possibility of forcing a mass reading onto words such as zh\u016b \u2018pig\u2019\u201d (Cheng et al. 2008: 57). The conditions underlying the availability (or lack thereof) of coerced-mass readings of individual nouns in Kaingang is a topic for future investigation. 142 However, I will not follow this path here. Rather, in a hypothetical fashion, I will tackle the apparent problem raised by single-portion situations. I propose to reinterpret them in a manner that makes the option for the larger unit compatible with a cardinality judgement. For exposition, let us focus on a substance noun like kyv\u00e9nh \u2018blood\u2019. The idea is that Kaingang speakers can conclude that the single unit on the left side of Figure 36 is larger than the one on the right side by drawing an interpretation that uses the smaller portion as a parameter-unit of comparison on the basis of which they partition the larger portion. This is achieved by reasoning that the larger portion can be partitioned into two or more units, one of which, at least, is of the same size as the one displayed by the smaller portion. I claim that this partition reading is a last-resort interpretation of comparisons triggered by single-portion scenarios. Strictly speaking, one of the three Kaingang speakers resorted to it to enforce a cardinality reading in these scenarios. In set theory talk, a partition of a set can be defined as in (255). (255) Y is a partition of a set A iff: i. Y is a set of subsets of A. ii. Every member of A belongs to a set in Y. iii. \u2205 does not belong to Y. iv. No two members of Y overlap. v. \u222aY = A (Adapted from Schwarzschild 1996: 64) I propose to extend the notion of a partition above to proper parts of an individual or portion, as laid out in (257). (256) is the definition of proper parthood. (256) x \u228f y \u225d x \u2291 y \u2227 \u00ac(x = y) (= (117)) (x is a proper part of y iff x is part of y and x is distinct from y.) (Adapted from Krifka 2007: 7) 143 (257) Y is a partition of an individual\/portion-unit x \u2212 PART(Y)(x) \u2212 iff: i. Y is a set of proper parts of x. ii. Every proper part of x belongs to Y. iii. No two members of Y overlap. iv. \u2294Y = x Thus, the partition-based reasoning that makes available a cardinality interpretation of (258), given the context depicted in Figure 36 above, is formalized in (259). Crucially, (259) doesn\u2019t represent the truth conditions of (258). (259) is just a formal representation, cast in a long formula, of an interpretation derived via a pragmatic reasoning that underlies the cardinality judgement of (258) in single-unit contexts. (258) Pak\u00f3j v\u1ef9 kyv\u00e9nh m\u1ebd n\u0129 Maria ve k\u1ef9. Pak\u00f3j NOM blood more ASP Maria than \u2018Pak\u00f3j has more blood than Maria.\u2019 (259) \u2203x\u2203y\u2203Y\u2203z1\u2026\u2203zn[BLOOD-OF-PAK\u00d3J(x) \u2227 PUC(BLOOD-OF-PAK\u00d3J)(x) = 1 \u2227 BLOOD-OF-MARIA(y) \u2227 PUC(BLOOD-OF-MARIA)(y) = 1 \u2227 PART(Y)(x) \u2227 (z1 \u220a Y) \u2227 (zn \u220a Y) \u2227 \u00ac(z1 = zn) \u2227 (SAME-SIZE(z1, y) \u2228\u2026\u2228 SAME-SIZE(zn, y))]. Notice that in (259) the minimal cardinality requirement on the partition is two, as indicated by the existentially bound variables z1 and zn and the negation of identity, expressed by \u00ac(z1 = zn). This allows flexibility in the ways a unit can be partitioned, the cardinality of the partition, and the sizes of its cells, so long as the partition contains at least one unit-cell with the same size of the unit that serves as the parameter of comparison. This last condition is ensured by the disjunction(s) of the two-place predicate SAME-SIZE. Importantly, (259) does not involve evaluating the overall size of the partition. Sameness of size between one unit of the partition and the parameter-unit is sufficient for opting for the larger portion. I propose that the speaker arrives at the interpretation in (259) via the following pragmatic steps involving Grice\u2019s cooperative principle (Grice 1975). 144 (260) a. The interlocutor asks a question that implies there should be a cardinality difference between two quantities of context-dependent portion-units of blood. b. However, the most contextually salient portion-units result in a cardinality of 1 for both quantities. c. The consultant wants to be cooperative. d. The consultant adjusts the parameter of interpretation C to one that leads to a cardinality difference between the two quantities, e.g., by partitioning the larger portion-unit of blood. As for the comparison involving the individual-denoting noun kakan\u1ebd \u2018fruit\u2019, it is easy to see how the same rationale in (260) can also be carried over to this case to give rise to an interpretation like (259). Importantly, there were no volume-like comparisons in single-unit scenarios with nouns denoting animate beings and artefacts, such as g\u0129r \u2018child\u2019 and n\u0129gja \u2018bench\u2019, respectively. That is, in single-unit scenarios with these nouns the three speakers stated that it wouldn\u2019t make sense to ask the question \u0168 n\u1ef9 t\u1ef9 g\u0129r\/n\u0129gja m\u1ebd n\u0129? \u2018Who has more children\/benches?\u2019, given that both persons had the same quantity of children\/benches. The possibility for some speakers of a partition interpretation like in (259) of Kaingang substance nouns and nouns like kakan\u1ebd \u2018fruit\u2019 in single-unit contexts can be attributed to language-independent factors involving world perception\/knowledge. Because the \u2018minimal\u2019 parts of a blood-unit or fruit-unit that are still considered blood or fruits can go down to quite small parts (particularly in the case of blood), contextually larger units in the extension of kyv\u00e9nh \u2018blood\u2019 or kakan\u1ebd \u2018fruit\u2019 become privileged candidates to be partitioned in scenarios where the cardinality of the quantities under comparison is 1. Thus, by suggesting the alternative interpretation modeled in (259) and (260), which relies on the notion of a partition set imposed on the larger portion of a single-unit scenario, I think I have shown that the assessment of one of the speakers is not in principle incompatible with a cardinality-based comparison. (259) can be used to rescue nouns from a mass-like interpretation. In short, partitions of the larger individuals or portions of single-unit situations can be portrayed as a pragmatic strategy at the disposal of Kaingang speakers to make available, whenever it is 145 relevant for communicative purposes, an alternative cardinal assessment that circumvents the numerical identity of these scenarios. 4.7 Crosslinguistic\/typological and other theoretical contributions The growing body of work on nominal countability across understudied languages in the last fifteen years shows that there is significant variation in the ways that languages encode the mass\/count distinction in their nominal domain (Deal 2017; Davis 2014; Gillon 2010; Lima 2014a, b; Lima & Rothstein 2020; Mathieu 2012; Wilhelm 2008; Wiltschko 2012; among others). Some of these studies, as pointed out by Lima and Rothstein (2020), have challenged two core assumptions in earlier typological approaches, such as in Greenberg (1974) and Chierchia (1998b). First, the assumption that in mass\/count languages mass nouns cannot be directly modified by numerals, unless they undergo conventionalized packaging or receive a taxonomic reading, doesn\u2019t always hold. Deal (2017) demonstrates that this is not the case for Nez Perce. All Nez Perce nouns combine with numerals without the intervention of classifiers. The morphosyntactic realization of the mass\/count distinction shows up in plural marking on adjectives when they interact with quantifiers. In a constituent like [Q[Adj+noun]], adjectives must be pluralized when combined with individual nouns, but not with substance nouns. A second challenged assumption is the idea that in mass\/count languages where nouns inflect for number count nouns can be pluralized, while mass nouns cannot. There are a number of languages that pluralize mass nouns. For instance, Innu-aimun (Gillon 2010) and Ojibwe (Mathieu 2012), both Algonquian languages, allow mass nouns to inflect for number. Recent studies, all carried out as part of a typological research project on countability in Brazilian Indigenous languages coordinated by Suzi Lima and Susan Rothstein, have also shown that some languages which encode the mass\/count distinction can pluralize (substance) mass nouns. Such languages are Teneteh\u00e1ra (Chamorro & Duarte 2020) and Sakurabiat (Galucio & Costa 2020), both Tupi languages, Terena (Sanchez-Mendes et al. 2020), an Arawakan language, as well as Taurepang (Costa 2020a) and Ye\u2032kwana (Costa 2020b), both Cariban languages. Importantly, in Sakurabiat, Taurepang, and Ye\u2032kwana the pluralization of substance nouns gives rise to a plurality of portions reading, rather than an abundance one. Rothstein (2021) analyses plural substance nouns in Sakurabiat, Taurepang, and Ye\u2032kwana as denoting a contextually specified set of discrete portions 146 closed under sum formation. Interestingly, these nouns are not countable, despite their portion readings. This fact provides further crosslinguistic evidence that having discrete entities in their denotations isn\u2019t a sufficient condition for nouns to be countable. In order to be so, they have to be quantized. Kaingang provides some important contributions to the understanding of nominal countability across languages. One relevant contribution is that Kaingang joins Yudja (Lima 2014a, b) as evidence that the mass\/count distinction isn\u2019t a language universal in the nominal domain. This is so because the data assembled in the present chapter show that Kaingang, like Yudja, lacks any morphosyntactic or semantic properties associated with the mass\/count distinction. Such crosslinguistic commonalities indicate that the opposition between mass and count nouns plays no role in these languages.55 Another contribution of Kaingang relates to mismatches between the linguistic encoding of countability and the conceptual or perceptual distinction between substance and objects. As discussed in Chapter 3 and in this chapter mass\/count languages that contain object mass nouns like furniture, luggage, etc., demonstrate not only that there are asymmetries in the mapping from the substance\/object opposition to the grammar of the mass\/count distinction, but they also tell us that atomicity isn\u2019t a sufficient condition for a noun to be count (Krifka 2007, Rothstein 2010, 2017). If my analysis is correct, Kaingang and Yudja indicate that the asymmetry is stronger, since even substance nouns can be lexically count. The existence of inherently count substance nouns, together with fence-type count nouns (Rothstein 2017), shows that atomicity isn\u2019t even a necessary condition for a noun to be count. In other words, Kaingang and Yudja provide further evidence that the grammatical encoding of the mass\/count distinction is independent of the ontological or conceptual opposition between substance and object. Let me end this section with the typological picture that emerges from the two Krifka-inspired generalizations suggested in this chapter. The first generalization is the view that the count meaning of Kaingang and Yudja nouns, associated with the crosslinguistic facts above, constitutes evidence that the defining property of grammatical counting is quantization. The second 55 According to Wiltschko (2012), Halkomelem (Salish) challenges the universality of the count\/mass distinction (Wiltschko 2012). However, I should mention here that, to my knowledge, the quantity judgement test hasn\u2019t been applied to Halkomelem. In addition, Davis (2014) argues that Wiltschko's empirical arguments are not compelling, and that no such claim can be made about Halkomelem. 147 generalization is that one semantic source of variation in relation to the count\/mass opposition in the nominal domain is lexical and derived from the quantized\/cumulative distinction.56 Placed on a scale of nominal countability, classifier languages like Mandarin fall on one extreme as languages where all nouns are inherently cumulative, and as such lack a quantizing function. This type of language encodes a parts-based distinction, i.e., they distinguish atomic from non-atomic mass nouns. In these languages the count interpretation is associated with classifiers, which apply to nouns and map their cumulative denotation onto quantized ones. On the other extreme of the scale is the type of language where all nouns are lexically quantized, such as Yudja and Kaingang. In these languages a cumulative denotation is derived via existential closure of the number variable of their nouns. Somewhere between these two poles reside the so-called mass\/count languages, such as English. These languages lexically encode the cumulative\/quantized distinction, i.e., they differentiate inherently cumulative nouns from nouns containing a built-in quantizing function. 56 For an in-depth discussion of other sources of variation in the domain of the count\/mass distinction, in particular with respect to the types of quantity expressions (e.g., count vs. non-count quantity expressions), see Doetjes (2021b, c). In these works, the author investigates the ways in which quantity expressions, within a single language or across languages, semantically interact with each other and with the types of nouns and constructions they combine with. 148 Chapter 5: Scope Effects of Bare Nouns in Kaingang and their Crosslinguistic Implications 5.1 Introduction This chapter offers a semantic analysis of the scope behavior of bare nouns (BNs) in Kaingang and discusses its relevance to semantic variation in the scope patterns of BNs across languages. As demonstrated in Chapter 2, Kaingang is a generalized bare noun language, i.e., nouns can occur in any argument position without any functional elements such as determiners, number morphemes, or classifiers. Based on a range of evidence, I demonstrate that under indefinite readings Kaingang BNs take variable scope with respect to other semantic operators like negation, intensional verbs, if-clauses, universal quantifiers, and frequency adverbials. Interestingly, the variable-scope effects exhibited by Kaingang BNs, along with Hebrew BNs (Dayal 2004; Tonciulescu 2009) and Malagasy BNs (Paul 2016), contrast with the obligatory narrow scope of (plural, mass, or number-neutral) BNs attested in a wide range of geographically distant or genetically unrelated languages. Among these languages are, for instance, English (Carlson 1977a, b), Haitian Creole (Deprez 2005), Hindi (Dayal 2004), Indonesian (Chung 2000), Mandarin (Cheng & Sybesma 1999; Rullmann & You 2006), Russian (Dayal 2004), and Teotitl\u00e1n del Valle Zapotec (Deal & Nee 2018). Adopting a type-shifting framework (Partee 1986; Chierchia 1998b; Krifka 2003; Dayal 2004), I claim that the indefinite interpretation of Kaingang BNs is associated with a choice function operator (CF). Kaingang BNs are analysed as predicate NPs mapped onto arguments via a choice function type-shifter. Their existential force and scope interactions with other operators arise from existential closure of the choice function at any level in the clausal spine, as in Reinhart\u2019s (1997, 2006) analysis of English indefinites. Independent evidence that a choice function can be a type-shifter in Kaingang, rather than be associated with an unpronounced determiner, as proposed for Malagasy (Paul 2016), comes from the syntactic distribution of Kaingang BNs. On the assumption that null determiners must be syntactically licensed (Contreras 1986; Chierchia 1998b; Longobardi 1994, 2001; Paul 2016, 149 among others), if Kaingang BNs had a null determiner, we would expect restrictions on their distribution (e.g., they would be ruled out as external arguments). However, Kaingang BNs with indefinite interpretations appear in any argument position. As a result, they provide compelling evidence that a choice function is not always bound to Ds and hence that it also belongs to the natural language inventory of covert type-shifters. I also discuss what I consider to be a necessary condition for the possibility of a CF interpretation of argumental BNs. I argue that the quantized\/cumulative distinction in bare noun denotations plays a crucial role in determining two closely related phenomena: (i) when a CF can access a bare noun; and (ii) the variation in scope properties of BNs across languages. The idea is that the difference in scope properties observed across languages between variable-scope BNs and narrowest-scope BNs is closely linked to the quantized\/cumulative opposition: the former are quantized predicates, while the latter are cumulative. In turn, I propose that variable-scope BNs and narrowest-scope BNs are created by two distinct covert type-shifters: the former by a CF operator, whereas the latter by Krifka\u2019s \u2203 operator (Krifka 2003). I claim thus that both type-shifters are sensitive to algebraic properties of the nominal predicates they target. According to the analysis proposed in this chapter, the choice function type-shifter, which can create variable scope readings, carries the presupposition that the BNs it applies to are quantized. In contrast, Krifka\u2019s \u2203 type-shifter, which always gives rise to narrowest-scope interpretations, presupposes that the BNs it applies to are cumulative. I show that from this analysis arises a typology that captures the semantic variation in scope behavior of bare nouns attested across languages. This chapter is structured as follows. In section 5.2, I present the core data on the scope interactions of Kaingang BNs with respect to other semantic operators in the clause, such as negation, intensional verbs, if-clauses, universal quantifiers, and frequency adverbials. In section 5.3, I consider two main type-shifting accounts of the obligatory narrow scope of plural or number-neutral BNs attested across many languages, namely Chierchia\u2019s neo-Carlsonian kind-based approach (Chierchia 1998b) and Krifka\u2019s predicate-based analysis (Krifka 2003). I show that the latter analysis has an explanatory advantage over the former, since it also accounts for languages in which BNs have narrowest-scope indefinite readings, but lack kind readings, i.e., languages in which indefinite readings of BNs cannot be derived from a kind denotation. 150 In section 5.4, I present my analysis of the Kaingang data. I represent Kaingang BNs under their indefinite reading as predicates that shift to an argument type via a covert choice function f existentially closed at any level in the clause. I show that this treatment of Kaingang BNs accounts for both their existential force and variable-scope effects. Section 5.5 proposes a link between the availability or lack of choice function bare nouns and the quantized\/cumulative opposition of bare noun denotations. This is accomplished by making the nominal type-shifters that create indefinite readings of bare nouns sensitive to these higher order properties of predicates. This solution, which can be seen as a synthesis of my choice function analysis of Kaingang bare nouns with Krifka\u2019s (2003) account of narrowest-scope bare nouns, is then shown to correctly predict the variation in scope properties of bare nouns across languages. 5.2 Scope taking This section lays out the data on the variable-scope effects of Kaingang bare nouns. I demonstrate that under an indefinite interpretation Kaingang BNs scope under or over other operators. Furthermore, I show that intermediate scope readings are also possible, e.g., Kaingang BNs can scope between two operators. 5.2.1 Negation First let us look at scope interactions between BNs and negation. To examine the availability of wide and narrow scope readings of the BN pir\u00e3 \u2018fish\u2019 with respect to negation in sentence (261a), consultants were shown the storyboard scenarios in Figures 38 and 39. Figure 38 is available for free download from the webpage of The Scope Fieldwork Project (Bruening 2008).57 Figure 39 is an adapted version of Figure 38 in which we erased the fish to create a scenario for the narrow scope reading.58 57 Available at: https:\/\/udel.edu\/~bruening\/scopeproject\/scopeproject.html 58 Figure 38 was previously used in Navarro & Nederveen (2022). That paper investigated the semantics of the indefinite determiner re in Secwepemcts\u00edn, a Salish language. 151 Figure 38: F\u00f3gt\u1ebd goes fishing. Figure 39: F\u00f3gt\u1ebd goes fishing. 152 (261) a. F\u00f3gt\u1ebd v\u1ef9 pir\u00e3-\u2205 sam \u2205 t\u0169 n\u0129. (= (10a)) F\u00f3gt\u1ebd NOM fish-ACC catch PFV NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t catch a fish.\u2019 b. \u2203x[FISH(x) \u2227 \u00ac[CATCH(x)(F\u00d3GT\u1ebc)]] c. \u00ac[\u2203x[FISH(x) \u2227 CATCH(x)(F\u00d3GT\u1ebc)]] Both readings for the BN in (261a) are available. The wide scope interpretation was tested through the storyboard depicted in Figure 38, where one fish isn\u2019t caught. This reading is shown in (261b), where the existential quantifier scopes over the negation. This conclusion is further strengthened by the fact that anaphoric binding is possible, i.e., the BN pir\u00e3 in (261a) can be the antecedent to the pronoun ti \u2018he\/him\u2019, as shown in (262). (262) F\u00f3gt\u1ebd v\u1ef9 pir-\u22051 sam \u2205 t\u0169 n\u0129. F\u00f3gt\u1ebd NOM fish-ACC catch PFV NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t catch a fish1.\u2019 Ti1 t\u00f3g goj k\u00e3 h\u00e1 t\u00e1 n\u0129. 3SG.M TOP river inside ASP there ASP \u2018It1 is there in the river.\u2019 The possibility of a wide scope reading is further supported by the fact that speakers allow the conjunction of (261a) with its affirmative counterpart. Thus, (263a) did not result in a contradiction because the BN pir\u00e3 can have wide scope with respect to negation, as captured in (263b). 153 (263) a. F\u00f3gt\u1ebd v\u1ef9 pir\u00e3-\u2205 sam \u2205 h\u00e3ra \u2205 t\u00f3g pir\u00e3-\u2205 sam F\u00f3gt\u1ebd NOM fish-ACC catch PFV but 3 TOP fish-ACC catch \u2205\t t\u0169 n\u0129. PFV NEG ASP \u2018F\u00f3gt\u1ebd caught a fish, but he didn\u2019t catch a fish.\u2019 Consultant\u2019s comment: \u201cThat\u2019s right, because first he caught fishes and then he didn\u2019t catch one fish.\u201d b. \u2203x[FISH(x) \u2227 CATCH(x)(F\u00d3GT\u1ebc)] \u2227 \u2203x[FISH(x) \u2227 \u00ac[CATCH(x)(F\u00d3GT\u1ebc)]] Sentence (261a) is also true in the scenario depicted in Figure 39, where there aren\u2019t any fish in the pictures. This shows that the BN pir\u00e3 can also have narrow scope with respect to negation, as paraphrased in (261c). This conclusion receives further support from the fact that (261a) can be followed by a sentence that explicitly denies the existence of any fish in the river, as in (264). (264) F\u00f3gt\u1ebd v\u1ef9 pir\u00e3 sam \u2205 t\u0169 n\u0129. F\u00f3gt\u1ebd NOM fish catch PFV NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t catch a fish.\u2019 Goj ki pir\u00e3 t\u0169 n\u0129. river in fish NEG ASP \u2018There are no fish in the river.\u2019 Note that the BN pir\u00e3 \u2018fish\u2019 in (261\u23af264) is in object position, i.e., it is the internal argument of the verb sam \u2018catch\u2019. The availability of the wide scope interpretation of bare nouns as external arguments was also attested. This is illustrated by sentences (265a) and (266a), which contain the bare nouns g\u0129r \u2018child\u2019 and kanhg\u00e1g \u2018Kaingang\u2019, respectively. 154 (265) \u2713Context: Yesterday at the party there were two children. One sang and the other did not. a. G\u0129r v\u1ef9 j\u00e3n \u2205, h\u00e3ra g\u0129r v\u1ef9 j\u00e3n \u2205\t t\u0169 n\u0129. child NOM sing PFV, but child NOM sing PFV NEG ASP \u2018A child sang, but a child didn\u2019t sing.\u2019 b. \u2203x[CHILD(x) \u2227 SING(x)] \u2227 \u2203x[CHILD(x) \u2227 \u00ac[SING(x)]] (266) \u2713Context: F\u00f3gt\u1ebd and Jo\u00e3o, both Kaingangs, went to the city. There F\u00f3gt\u1ebd saw Pedro, but Jo\u00e3o didn\u2019t see Pedro. a. Kanhg\u00e1g v\u1ef9 Pedro-\u2205 v\u00e9 \u2205, Kaingang NOM Pedro-ACC see PFV, \u2018A Kaingang saw Pedro,\u2019 h\u00e3ra kanhg\u00e1g v\u1ef9 Pedro-\u2205 v\u00e9g \u2205 t\u0169 n\u0129. but Kaingang NOM Pedro-ACC see PFV NEG ASP \u2018but a Kaingang didn\u2019t see Pedro.\u2019 \tb. \u2203x[KAINGANG(x) \u2227 SEE(PEDRO)(x)] \u2227 \u2203x[KAINGANG(x) \u2227 \u00ac[SEE(PEDRO)(x)]] In sentence (265a) the BN g\u0129r \u2018child\u2019 is the subject of the intransitive verb j\u00e3n \u2018sing\u2019, whereas the BN kanhg\u00e1g \u2018Kaingang\u2019 in sentence (266a) is the subject of the transitive verb v\u00e9(g) \u2018see\u2019. The felicity of construction (265a) in the context in (265), i.e., the fact that it doesn\u2019t necessarily give rise to a contradiction, indicates that g\u0129r \u2018child\u2019 can be interpreted in the second conjunct as an indefinite BN that scopes over the negation particle t\u0169 \u2018not\u2019, as paraphrased in (265b). Analogously, sentence (266a) was accepted by the speakers in a scenario in which only one of the two Kaingangs saw Pedro. Again, this shows that (266a) allows for an interpretation in which the subject indefinite BN kanhg\u00e1g in the second conjunct scopes over negation, as represented in (266b). 155 5.2.2 Intensional verbs Variable-scope effects of Kaingang bare nouns are also attested with respect to intensional verbs. This is illustrated by sentence (267a), in which the BN f\u00f3g \u2018non-indigenous person\u2019 scopally interacts with the opaque verb s\u00f3r \u2018want\u2019. (267) \u2713Context A: Many non-indigenous persons will be at the party. F\u00f3gt\u1ebd wants to see a particular non-indigenous person (named Carlos) there. \u2713Context B: F\u00f3gt\u1ebd wants to see any non-indigenous person this week, whoever they are. a. F\u00f3gt\u1ebd t\u00f3g f\u00f3g v\u00e9 s\u00f3r m\u0169. F\u00f3gt\u1ebd TOP non.indigenous.person see want ASP \u2018F\u00f3gt\u1ebd wants to see a non-indigenous person.\u2019 b. \u2203x[NON-INDIGENOUS-PERSON(x) \u2227\tWANT [SEE(x)(F\u00d3GT\u1ebc)]] c. WANT [\u2203x[NON-INDIGENOUS-PERSON(x) \u2227 SEE(x)(F\u00d3GT\u1ebc)]] Sentence (267a) is felicitous in both scenarios. The wide scope reading of the bare noun f\u00f3g \u2018non-indigenous person\u2019 is verified by context A, and the narrow scope reading by context B. (267b) represents the transparent reading of the bare noun in (267a), while (267c) its opaque interpretation. One consequence of the wide scope interpretation of the BN f\u00f3g in (267a) is that it allows the BN to be anaphorically referred to by a third-person pronoun, as shown in (268). 156 (268) F\u00f3gt\u1ebd t\u00f3g f\u00f3g1 v\u00e9 s\u00f3r m\u0169. F\u00f3gt\u1ebd TOP non.indigenous.person see want ASP \u2018F\u00f3gt\u1ebd wants to see a non-indigenous person1.\u2019 F\u00e9nhta k\u00e3 ti1 j\u1ebdnh ke m\u0169. party inside 3SG.M ASP FUT ASP \u2018He1 will be at the party.\u2019 The same scope patterns hold for the interplay between BNs and the intensional verb kan\u1ebdg \u2018look for\u2019. This is shown in (269) below. (269) \u2713Context A: Many non-indigenous persons are at the party. You are looking for a particular non-indigenous person (named Carlos) there. You tell me: \u2713Context B: You are painting your own house, and you are looking for any non-indigenous person to help you; anyone will be fine. You tell me: a. Is\u1ef9 f\u00f3g kan\u1ebdg m\u0169. 1SG.NOM non.indigenous.person look.for ASP \u2018I\u2019m looking for a non-indigenous person.\u2019 b. \u2203 > LOOK-FOR c. LOOK-FOR > \u2203 The wide scope reading of the bare noun f\u00f3g \u2018non-indigenous person\u2019 with respect to the intensional verb kan\u1ebdg \u2018look for\u2019 makes sentence (269a) true in context A. In contrast, the narrow scope interpretation of f\u00f3g makes (269a) true in context B. Again, in context A the BN f\u00f3g can be anaphorically referred to by a third-person pronoun, as given in (270). 157 (270) Is\u1ef9 f\u00f3g1 kan\u1ebdg m\u0169. 1SG.NOM non.indigenous.person look.for ASP \u2018I\u2019m looking for a non-indigenous person1.\u2019 F\u00e9nhta k\u00e3 ti1 j\u1ebd. party inside 3SG.M ASP \u2018He1 is at the party.\u2019 In sum, the fact that sentences (267a\u23af270) were accepted in the discourse contexts provided above shows that Kaingang BNs scopally interact with intensional verbs, making available wide and narrow scope interpretations. 5.2.3 Universal quantifier Kaingang bare nouns also display scope interactions with respect to the universal quantifier kar \u2018all\u2019. In sentence (271a), the BN \u0129n \u2018house\u2019 can have wide and narrow scope readings. The former reading is exemplified through the context depicted in Figure 40, and the latter through the context depicted in Figure 41. (271a) is accepted in both scenarios.59 59 The scenario depicted in Figure 40 contains three houses in order to exclude the definite reading of the bare noun. 158 Figure 40: Building one house. Figure 41: Building houses. 159 (271) a. F\u00f3g kar v\u1ef9 \u0129n-\u2205 han \u2205. (= (110)) non.indigenous.person all NOM house-ACC make PFV \u2018All non-indigenous persons built a house.\u2019 b. \u2203y[HOUSE(y) \u2227 \u2200x[NON-INDIGENOUS-PERSON(x) \u2192 MAKE(y)(x)]] c. \u2200x[NON-INDIGENOUS-PERSON(x) \u2192 \u2203y[HOUSE(y) \u2227 MAKE(y)(x)]] Paraphrase (271b) represents the interpretation of sentence (271a) in which the BN scopes over the universal quantifier, i.e., there is one house built by all the non-indigenous persons. In contrast, (271c) captures the reading in which the universal quantifier outscopes the BN, i.e., each non-indigenous person builds a (potentially) different house.60 5.2.4 If-clauses 60 A cautionary observation is important here. Sentence (271a) per se constitutes only weak evidence of the variable scope of Kaingang BNs. This is so because of entailment relations. Predicate logic shows that in sentences containing an existential and a universal quantifier the wide-scope reading of the existential entails its narrow-scope reading, as stated in the implication in (i). (i) [\u2203y\u2200x[P(x)(y)]] \u2192 \u2200x\u2203y[P(x)(y)] (Reichenbach 1966 [1947], 22, \u00a720: 101) Based on the logical truth in (i), one can argue that sentences like Every man loves a woman are not scopally ambiguous, since in them the wide-scope reading would entail the narrow-scope one. In other words, any context that makes the wide-scope reading of the indefinite true, would also make the narrow-scope reading true. Considerations about the entailment relation in (i) mean that examples like (271a), as well as those involving frequency adverbials (which will be discussed below), may not, in and of themselves, constitute compelling evidence in support of the claim that Kaingang BNs exhibit variable scope. Nevertheless, the fact that BNs scopally interact with negation (as shown above) and if-clauses, as well as the fact that they receive intermediate readings (as will be shown below), strongly suggest that in clauses like (271a) the same phenomenon occurs. In other words, in light of a set of compelling cases of variable scope taking, (271a) can be seen as providing secondary evidence for this fact. For a discussion of this phenomenon, as well as examples of contexts that make wide scope readings true, but narrow scope readings false, see Abusch (1994). 160 Sentence (272a) can have two interpretations, depending on whether the bare noun kanhg\u00e1g \u2018Kaingang\u2019 scopes over the if-clause or under it. The variable-scope effects of bare nouns in if-clauses are revealed through contexts A and B. Context A makes sentence (272a) true under the interpretation in which the BN scopes over the if-clause, as paraphrased in (272b). In this context the indefinite BN kanhg\u00e1g has a wide scope interpretation. The same sentence is also true in context B, i.e., under the interpretation in which the BN displays narrow scope with respect to the if-clauses. The narrow scope interpretation is represented in (272c). (272) \u2713Context A: There will be many Kaingangs at the party. You are the party singer. If a particular Kaingang (named F\u00f3gt\u1ebd) arrives there, you will sing the song Gar\u00e7om. You tell me: \u2713Context B: You are the party singer. If any Kaingang arrives at the party, whoever they are, you will sing the song Gar\u00e7om. You tell me: a. F\u00e9nhta ki kanhg\u00e1g jun m\u0169ra, s\u00f3g Gar\u00e7om-\u2205\t j\u00e3n party at Kaingang arrive if 1SG.TOP Gar\u00e7om-ACC sing ke m\u0169. (= (107a)) FUT ASP \u2018If a Kaingang arrives at the party, I will sing Gar\u00e7om.\u2019 b. \u2203x[KAINGANG(x) \u2227 [ARRIVE(x) \u2192 SING(GAR\u00c7OM)(SPEAKER)]] c. [\u2203x[KAINGANG(x) \u2227 ARRIVE(x)]] \u2192 SING(GAR\u00c7OM)(SPEAKER) In sentence (272a) the BN kanhg\u00e1g is the subject of the antecedent clause. The same scope interplay was verified when the BN occurs in object position. This is laid out in (273a) below. 161 (273) \u2713Context A: There will be many Kaingangs at the party. You are the party singer. If you see a particular Kaingang (named F\u00f3gt\u1ebd) at the party, you will sing the song Gar\u00e7om. You tell me: \u2713Context B: You are the party singer. If you see any Kaingang at the party, whoever they are, you will sing the song Gar\u00e7om. You tell me: a. Is\u1ef9 kanhg\u00e1g-\u2205 v\u00e9g m\u0169ra, s\u00f3g Gar\u00e7om-\u2205\t j\u00e3n 1SG.NOM Kaingang-ACC see if, 1SG.TOP Gar\u00e7om-ACC sing ke m\u0169. FUT ASP \u2018If I see a Kaingang, I will sing Gar\u00e7om.\u2019 b. \u2203 > IF c. IF > \u2203 Thus, the felicity of sentences (272a) and (273a) in contexts A and B above demonstrates that Kaingang BNs also scopally interact with if-clauses. Importantly, the variable scope behavior exhibited by Kaingang BNs in the conditional clauses above contrasts with universally quantified phrases, which cannot scope over if-clauses. Sentence (274a) illustrates this fact. The quantified phrase f\u00f3g kar \u2018all non-indigenous person(s)\u2019 cannot take scope over the conditional m\u0169ra \u2018if\u2019, as attested by the fact that (274a) is felicitous in context A, although not in context B. That is, (274a) cannot mean that for every non-indigenous person x, if x goes to the party, then the speaker will sing Gar\u00e7om. (274) \u2713Context A: There will be a party in the village, and you will be the singer. Three non-indigenous persons were invited. If all of them go there, you will sing Gar\u00e7om. \u2717Context B: There will be a party in the village, and you will be the singer. Three non-indigenous persons were invited. If any one of them goes here, you will sing Gar\u00e7om. 162 a. F\u00e9nhta ki f\u00f3g kar jun m\u0169ra, s\u00f3g Gar\u00e7om Party at non.indigenous.person all arrive if, 1SG.TOP Gar\u00e7om j\u00e3n ke m\u0169. sing FUT ASP \u2018If all non-indigenous persons arrive at the party, I will sing Gar\u00e7om.\u2019 b. IF > \u2200 c. *\u2200 > IF Thus, the fact that kar phrases cannot outscope if-clauses indicates that conditional clauses with m\u0169ra \u2018if\u2019 create syntactic islands. Consequently, the wide scope readings of Kaingang BNs with respect to mur\u00e3 show that they are island-insensitive and as such have \u201cexceptional\u201d wide scope, behaving in this respect like English indefinite DPs headed by a (Fodor & Sag 1982; Ludlow & Neale 1991; Abusch 1994; Reinhart 1997). 5.2.5 Frequency adverbials Kaingang BNs also exhibit variable-scope effects with respect to frequency adverbials. This is illustrated in (275). The wide scope of f\u00f3g \u2018non-indigenous person\u2019 in relation to pr\u1ef9g kar \u2018every year\u2019 gives rise to a reading in which the same non-indigenous person visits the village every year. Consultants accepted (275a) in context A, which supports the wide scope reading of the BN, represented in (275b). The narrow scope reading of the BN, captured in (275c), is also available. That is, (275a) is felicitous in context B, where a different person visited the village each year. (275) \u2713 Context A: Carlos, a non-indigenous person, visits your village every year, and Marcos, also a non-indigenous person, visits it every other year. \u2713 Context B: Pedro, a non-indigenous person, visited your village in 2020. Sandro, a non-indigenous person, visited your village in 2021. Jo\u00e3o, a non-indigenous person, visited your village in 2022. Alberto, a non-indigenous person, visited your village in 2023. 163 a. F\u00f3g v\u1ef9 pr\u1ef9g kar ki jam\u00e3 m\u0129 k\u00e3t\u0129g t\u0129. non.indigenous.person NOM year all in village inside visit HAB \u2018A non-indigenous person visits the village every year.\u2019 b. \u2203y[NON-INDIGENOUS-PERSON(y) \u2227 \u2200t[YEAR(t) \u2192 VISIT-THE-VILLAGE-IN(t)(y)]] c. \u2200t[YEAR(t) \u2192 \u2203y[NON-INDIGENOUS-PERSON(y) \u2227 VISIT-THE-VILLAGE-IN(t)(y)]] Sentence (276a) is another case of scope interactions with frequency adverbials. (276a) is felicitous in contexts A and B. The wide scope reading of the BN s\u1ebdsi \u2018bird\u2019 with respect to the adverbial p\u1ebd han \u2018many times\u2019 is attested by context A, and the narrow scope reading by context B. (276) \u2713 Context A: There are many birds in your backyard. Yesterday, a particular sparrow entered your house many times in the morning. \u2713 Context B: At 8 am a sparrow entered your house; at 9 am a bem-te-vi entered your house; at 10 am a pigeon entered your house; at 11am a quero-quero entered your house. a. S\u1ebdsi v\u1ef9 kus\u00e3 ki \u0129n k\u00e3-ra~r\u00e3 \u2205 p\u1ebd han. bird NOM morning in house RED~enter PFV many make \u2018A bird entered the house many times in the morning.\u2019 b. \u2203 > MANY-TIMES c. MANY-TIMES > \u2203 5.2.6 Intermediate scope Kaingang bare nouns can interact with two universal quantifiers in a sentence, giving rise not only to wide and narrow scope readings, but also to intermediate scope, i.e., an interpretation in which the bare noun scopes between two operators. Thus, sentence (277a) can be true in the three contexts depicted by the storyboards below. 164 Figure 42: Wide scope context. Figure 43: Intermediate scope context. 165 Figure 44: Narrow scope context. (277) a. P\u00e3\u00b4i kar v\u1ef9 f\u00f3g kar t\u1ef9 \u0129n-\u2205 han chief all NOM non.indigenous.person all ERG house-ABS make m\u0169 to h\u00e1 n\u0129. (= (111a)) ASP like ASP \u2018All chiefs like all non-indigenous persons that built a house.\u2019 b. There is a house y, such that every chief x likes every non-indigenous person z that built y. \u2713 \u2203 > \u2200 > \u2200 c. For every chief x, there is a house y, such that x likes every non-indigenous person z that built y. \u2713 \u2200 > \u2203 > \u2200\t d. For every chief x and every non-indigenous person z, if z built a house y, then x likes z. \u2713 \u2200 > \u2200 > \u2203 Consultant\u2019s comment (while laughing): \u201cI found it interesting because the same sentence works in all the situations.\u201d 166 The discourse context depicted in Figure 42 makes true an interpretation of sentence (277a) in which the BN \u0129n \u2018house\u2019 displays widest scope, as represented in (277b). In this context there is a single house made by all the non-indigenous persons together, and every chief likes all the house builders. The intermediate scope reading, paraphrased in (277c), was verified by the acceptance of (277a) in the context exhibited in Figure 43, where the houses covary with the number of chiefs, but not with the number of non-indigenous persons. That is, the context depicted in Figure 43 contains three chiefs, six non-indigenous persons, and three houses. Each house was built by a distinct pair of non-indigenous persons and each chief likes one of the pairs. Crucially, each non-indigenous person is a member of just one of the pairs. In turn, the narrow scope reading, represented in (277d), is attested by the scenario in Figure 44, where the houses covary with each non-indigenous person, i.e., there are as many houses as non-indigenous persons, and each chief likes all the house builders. Sentence (277a) is also felicitous in this context. Another piece of evidence for intermediate readings of Kaingang BNs comes from conditional clauses like (278a), where the BN f\u00f3g \u2018non-indigenous person\u2019 scopally interacts with the universal quantifier kar and the conditional m\u0169ra \u2018if\u2019.61 (278) \u2713Context A: F\u00f3gt\u1ebd, Pak\u00f3j, and K\u00f3rig will give a party. They invited three non-indigenous persons: Sandro, Lisa, and Fl\u00e1vio. F\u00f3gt\u1ebd, Pak\u00f3j, and K\u00f3rig will be happy if Sandro arrives at the party. They don\u2019t care about the others. \u2713Context B: F\u00f3gt\u1ebd, Pak\u00f3j, and K\u00f3rig will give a party. They invited three non-indigenous persons: Sandro, Lisa, and Fl\u00e1vio. F\u00f3gt\u1ebd will be happy will if Sandro arrives, Pak\u00f3j if Lisa arrives, and Maria if K\u00f3rig arrives. \u2713Context C: If any non-indigenous person arrives at the party, F\u00f3gt\u1ebd, Pak\u00f3j, and K\u00f3rig will be happy. 61 Sentence (278a) was tested with only one of the consultants. 167 a. Kanhg\u00e1g kar v\u1ef9 m\u1ef9s\u00e9r j\u1ebd ke m\u0169 f\u00f3g Kaingang all NOM happy ASP FUT ASP non.indigenous.person jun m\u0169ra. arrive if \u2018All Kaingangs will be happy if a non-indigenous person arrives.\u2019 b. There is a non-indigenous person y such that every Kaingang x will be happy if y arrives. (wide scope) c. For every Kaingang x there is a non-indigenous person y such that x will be happy if y arrives. (intermediate scope) d. Every Kaingang x will be happy if any non-indigenous person y arrives. (narrow scope) The fact that sentence (278a) is true in context A indicates that it allows the reading paraphrased in (278b), where the BN scopes over both the if-clause and the universal quantifier. The felicity of (278a) in context B shows that it can also have the reading captured in (278c), where the BN scopes between the other two operators. In turn, the acceptance of (278a) in context C suggests that it can display the reading represented in (278d), in which the BN has narrow scope. 5.2.7 Substance bare nouns Substance BNs in Kaingang, like goj \u2018water\u2019 and kyv\u00e9nh \u2018blood\u2019, also display variable scope taking. As expected, given the attested obligatory narrow scope readings of substance BNs across languages, the Kaingang BN goj can scope under another operator in the clause, as shown in (279a\u23afb). (279) a. F\u00f3gt\u1ebd v\u1ef9 goj-\u2205 kron \u2205 t\u0169 n\u0129. F\u00f3gt\u1ebd NOM water-ACC drank PFV NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t drink any water.\u2019 168 b. \u2713\u00ac > \u2203\t As for the wide scope readings of Kaingang substance bare nouns, they are available when substance BNs are used to talk about individuated portions of a substance. Sentences (280a) and (281a) illustrate this point with the substance (bare) nouns goj \u2018water\u2019 and kyv\u00e9nh \u2018blood\u2019, respectively. Note that the context in (281) is depicted in Figure 45. (280) \u2713Context: You live alone. Monday you filled the clay filter with water before bed. The next morning you notice that the filter is only half full of water, despite the fact that you didn\u2019t drink any water during the night. You find it has a small crack. You conclude: a. Goj v\u1ef9 pa ja n\u0129, h\u00e3ra goj v\u1ef9 pa ja t\u0169 n\u0129. (= (11a)) water NOM leak ASP ASP but water NOM leak ASP NEG ASP \u2018Some portion of water leaked out, but some portion of water didn\u2019t leak out.\u2019 b. \u2203x[PORTION-OF-WATER(x) \u2227 LEAK-OUT(x)] \u2227 \u2203x[PORTION-OF-WATER(x) \u2227 \u00ac[LEAK-OUT(x)]] (281) \u2713Context: There is one puddle of blood in front of your house and one in the backyard. F\u00f3gt\u1ebd sees the puddle of blood in front of the house but doesn\u2019t notice the one in the backyard. Figure 45: Puddles of blood. 169 a. F\u00f3gt\u1ebd v\u1ef9 kyv\u00e9nh-\u2205 v\u00e9 \u2205, F\u00f3gt\u1ebd NOM blood-ACC see PFV \u2018F\u00f3gt\u1ebd saw a puddle of blood,\u2019 h\u00e3ra \u2205 t\u00f3g kyv\u00e9nh-\u2205\t v\u00e9g \u2205 t\u0169 n\u0129. but 3 TOP blood-ACC see PFV NEG ASP \u2018but he didn\u2019t see a puddle of blood.\u2019 b. \u2203x[PUDDLE-OF-BLOOD(x) \u2227 [SEE(x)(F\u00d3GT\u1ebc)]] \u2227 \u2203x[PUDDLE-OF-BLOOD (x) \u2227 \u00ac[SEE(x)(F\u00d3GT\u1ebc)]] Sentences (280a) and (281a) are felicitous in the contexts above. The lack of contradiction in the conjunction of negative statements with their affirmative counterparts shows that the BNs goj \u2018water\u2019 and kyv\u00e9nh \u2018blood\u2019 under indefinite readings can scope over negation, as represented in (280b) and (281b). 5.3 Type-shifting approaches to narrowest-scope BNs The scope ambiguities exhibited by Kaingang BNs contrast with the obligatory narrow scope of (plural, mass, or number-neutral) BNs observed in a wide range of typologically distinct languages. These include English (Carlson 1977), Haitian Creole (Deprez 2005), Hindi (Dayal 2004), Indonesian (Chung 2000), Mandarin (Cheng & Sybesma 1999; Rullmann & You 2006), Russian (Dayal 2004), and Teotitl\u00e1n del Valle Zapotec (Deal & Nee 2016), among others. Before offering my type-shifting analysis of the scope properties of Kaingang BNs, I consider in this section two main competing type-shifting accounts of obligatory narrow scope bare nouns, namely Chierchia\u2019s neo-Carlsonian kind-based approach (Chierchia 1998b) and Krifka\u2019s predicate-based analysis (Krifka 2003).62 I will claim that Krifka\u2019s analysis has one 62 Krifka (2003) offers an intensional analysis. BNs are modeled as denoting properties, i.e., functions from worlds to predicates. For the sake of simplicity, I present an extensional version of his approach, which models bare nouns as predicates. The extensional version offered here keeps intact the explanatory power of Krifka\u2019s original version. 170 important empirical advantage over Chierchia\u2019s: it can also account for obligatory narrow scope bare nouns in languages in which they lack kind readings, like Romanian (Dobrovie-Sorin & Beyssade 2012). 5.3.1 Chierchia\u2019s kind-based analysis Since Carlson\u2019s (1977a, b) seminal work on the semantics of English bare plurals, it has been shown that in a number of languages bare plurals or number-neutral BNs contrast with indefinites headed by a determiner in their scope properties. Genuine indefinites usually display variable scope interactions in relation to other operators, as shown in the English examples in (282). (282) a. Alex didn\u2019t read a book. (\u2713\u2203 > \u00ac \/ \u2713\u00ac > \u2203) b. Alex wants to read a book. (\u2713\u2203 > WANT \/ \u2713WANT > \u2203) In contrast, BNs always take narrow scope with respect to other operators in the clause, as illustrated in (283\u23af285) with English, Mandarin, and Hindi bare nouns, respectively.63 (283) a. Hotze didn\u2019t read books. (*\u2203 > \u00ac \/ \u2713\u00ac> \u2203) b. Hotze wants to read books. (*\u2203 > WANT \/ \u2713WANT > \u2203) 63 For views that challenge the claim that (English) bare nouns have obligatory narrow scope, see Kratzer (1980) and Le Bruyn & de Swart (2022). These approaches will not be discussed in this thesis. 171 (284) Mandarin (Number-neutral bare noun) Mini xiang gen nianqing de xinlixuejia antan. Minnie wish with young MOD psychiatrist talk \u2018Minnie wants to talk to psychiatrist(s).\u2019 (*\u2203 > WANT \/ \u2713 WANT > \u2203) (Adapted from Rullmann & You 2006) (285) Hindi (Bare plural) Kamre meN cuuhee nahiiN haiN. room in mice not are \u2018There aren\u2019t any mice in the room.\u2019 (*\u2203 > \u00ac \/ \u2713\u00ac> \u2203) (Adapted from Dayal 2004: 404) In the spirit of Carlson\u2019s analysis of English BNs, Chierchia (1998b) argues for a uniform treatment of narrowest-scope bare nouns across languages as kind-denoting expressions. His analysis heavily relies on languages like English, Mandarin, and Hindi, which allow for kind interpretations of their bare nouns, as illustrated in (286\u23af288), in addition to existential readings, as shown above. (286) Dogs are extinct. (287) Mandarin Gou juezhong le. dog extinct ASP \u2018Dogs are extinct.\u2019 (Dayal 2004: 402) 172 (288) Hindi Kutte yehaaN aam hain. dogs here common are \u2018Dogs are common here.\u2019 (Dayal 2004: 402) Chierchia (1998b) devises an interpretation mechanism named derived kind predication (DKP), defined in (289), which derives the existential force that BNs display in episodic sentences, while simultaneously ensuring their narrowest-scope property. DKP is a repair strategy that applies whenever BNs, which are treated as referring to kinds, combine with verbal predicates that only select for ordinary objects as arguments. To adjust the sortal mismatch between a BN and a predicate that doesn\u2019t apply to kinds, DKP introduces an existential quantifier that binds a variable ranging over instances of the kind denoted by the bare noun. Importantly, the existential quantification over instances of a kind is made available because DKP contains the reverse operation of the kind-forming operator \u22c2, i.e., the instantiation operator \u22c3. The former maps a property into its kind, as stated in (290a), while the latter maps a kind into the set of all individuals that instantiate it, i.e., the set comprising the singular individuals and their sums, as defined in (290b).64 (289) Derived Kind Predication If P applies to objects and k denotes a kind, then P(k) = \u2203x[x \u2264 \u22c3k \u2227 P(x)] (Chierchia 1998b: 364) (290) a. \u2229P = \u03bbw \u03b9x[Pw(x)] c. \u22c3k = \u03bbw\u03bbx[x \u2264 kw] (Adapted from Chierchia 1998b: 350\u23af351) 64 The iota in (290a) is a maximality operator that maps P onto the maximal sum of all entities that are P in an evaluation world. For Chierchia (1998b), this maximal sum is identified with the kind. 173 In (291a\u23afb), we illustrate how DKP applies in the derivation of the truth conditions of the English sentence Dogs are barking. (291) Dogs are barking. a. [dogs [are barking]] b. (\u03bbx[ARE-BARKING (x)])( \u2229DOG) sortal mismatch c. \u2203x [x \u2264 \u22c3\u2229DOG \u2227 ARE-BARKING(x)] by DKP (Adapted from Chierchia 1998b: 364) In (291b) the abstract individual \u2229DOG, i.e., the \u2018dog kind\u2019, cannot be the argument of the stage-level predicate ARE-BARKING, which applies only to concrete dogs. To repair this sortal mismatch, DKP first applies the type-shifter \u22c3 to \u2229DOG, mapping the latter into the set of its instantiations (the set of dogs), and then introduces existential quantification over them. This leads to the desired truth conditions in (291c), which state that there is at least one instantiation of \u2229DOG that is barking. By assuming that DKP is only derived locally, i.e., when it is triggered by the sortal mismatch between an object-selecting predicate and a kind argument, Chierchia guarantees that the existential binding inherent to DKP is always inserted under any other clause-mate operator. That is, DKP gives rise only to narrow scope readings of bare nouns, as in (292), which contains the negative counterpart of Dogs are barking. (292) Dogs aren\u2019t barking. a. [dogs \u03bb1 [not [t1 are barking]]] b. \u03bbx1 \u27e6[not [t1 are barking]]\u27e7 (\u27e6dogs\u27e7) d. \u00acARE-BARKING(\u2229DOG) sortal mismatch d. \u00ac\u2203x [\u22c3\u2229DOG(x) \u2227 ARE-BARKING(x)] by DKP 174 In (292a) the kind-denoting BN, which is assumed to be base-generated below negation, moves above it. However, as Dayal (2013) points out, since dogs is an expression of type e, it \u201cgets lowered to the argument position of the negative predicate\u201d (Dayal 2013: 53). As such, when the sortal mismatch occurs in (292c), triggering DKP, the existential operator is necessarily inserted under the scope of negation. This mechanism gives rise to a narrow scope reading of the bare noun, as captured in (292d). In other words, negation ends up applying to a structure derived via the DKP rule, i.e., one already containing \u2203-closure of the variable ranging over instances of the kind. Chierchia\u2019s kind-based analysis of the existential interpretation of BNs accounts for languages whose BNs can get kind readings. In these languages BNs are compatible with kind-level predicates, as shown in (286\u23af288). However, as Dobrovie-Sorin & Beyssade (2012) observe, this approach is problematic for languages in which BNs lack generic readings, but have indefinite interpretations, such as Romanian and Italian. Crucially, in such languages indefinite BNs also have obligatory narrow scope with respect to other operators. The examples in (293a\u23afb) and (294) illustrate this in Romanian. Its bare plurals are incompatible with kind- or individual-level predicates, as in (293a\u23afb), but still display narrowest-scope readings in episodic sentences, as in (294). (293) Romanian a. *\u00cen Rom\u00e2nia sunt pe cale de dispari\u021bie ur\u0219i. in Romania are on way to disappearance bears \u2018In Romania bears are becoming extinct.\u2019 b. *Lui Ion \u00eei plac pra\u0103jituri. DAT Ion him.DAT appeal cakes \u2018Ion likes cakes.\u2019 (Dobrovie-Sorin & Beyssade 2012: 52) 175 (294) Romanian N-am citit romane. NEG-have-1SG read novels \u2018I haven\u2019t read novels.\u2019 (*\u2203 > \u00ac \/ \u00ac > \u2203) (Dobrovie-Sorin & Beyssade 2012: 47) Languages like Romanian provide evidence that their bare plurals are not kind-denoting expressions. Consequently, as Dobrovie-Sorin and Beyssade (2012) highlight, their indefinite interpretations and obligatory narrow scope cannot be derived via DKP.65 5.3.2 Krifka\u2019s predicate-based analysis Krifka (2003) also proposes that all argumental BNs have a uniform basic denotation. However, instead of denoting kinds, BNs are predicates that can be shifted to kind or (in)definite readings via covert type-shift operations. The kind interpretation arises via Chierchia\u2019s down operator (\u2229), definite readings involve the iota operator (\u03b9), and indefinite interpretations are associated with the existential operator (\u2203). The first two type-shifters turn predicates into arguments of type e, whereas \u2203 gives rise to generalized quantifiers. As standardly assumed in a type-shifting framework, nominal type-shifts are repair mechanisms that lead to interpretable structures. They come into play in order to allow functional application (FA) whenever it fails due to a type-mismatch between an argument and a predicate. By assuming that the type-shifting of a bare noun always occurs locally, i.e., \u201cwhen the mismatch between the bare NP and the verbal predicate becomes apparent\u201d (Krifka 2003: 196), Krifka\u2019s analysis ensures that the existential operator associated with the indefinite reading of a BN is structurally introduced under other semantic operators. That is, it predicts that bare nouns under an indefinite interpretation always get a narrow scope reading. 65 Dobrovie-Sorin and Beyssade (2012) analyses obligatory narrow-scope BNs as generalized existential quantifiers ranging over amounts of individuals or substances. The authors don\u2019t discuss variable-scope bare nouns. 176 To illustrate how this is accomplished, let us first observe the (partial) derivation of the affirmative sentence in (295). (295) Dogs are barking. a. [dogs [are barking]] b. \u27e6dogs\u27e7, \u27e6are barking\u27e7 type mismatch (FA fails) c. \u2203\u27e6dogs\u27e7(\u27e6are barking\u27e7) type-shifting by \u2203 d. (\u03bbP\u2203x [DOG(x) \u2227 P(x)])(\u03bbx[BE-BARKING(x)]) e. \u2203x[DOG(x) \u2227 BE-BARKING(x)] by FA (Adapted from Krifka 2003: 195\u23af6) The configuration in (295b) is uninterpretable because the predicate requires arguments of type e, i.e., individuals, and not predicates. This type mismatch is repaired by applying the \u2203 type-shifter to the denotation of dogs. As such, the predicate in (295c\u23afd) becomes the argument of a generalized quantifier, allowing FA to occur. As output, we get the desired truth conditions in (295e). Assuming that a nominal type-shifter is always inserted at the level of the type mismatch, in a negative sentence \u2203 will necessarily appear under negation. This is shown below through the derivation of the truth conditions of the negative sentence in (296). (296) Dogs aren\u2019t barking. a. \u27e6[dogs \u03bb1 [aren\u2019t [t1 barking]]]\u27e7\t b. \u03bb1[\u27e6aren\u2019t t1 barking\u27e7](\u27e6dogs\u27e7) c. \u03bbx1[\u27e6aren\u2019t\u27e7 t1\u2192 x1 \u27e6t1 barking\u27e7t1\u2192 x1](\u27e6dogs\u27e7) d. \u03bbx1[\u03bbp[\u00acp](\u27e6t1\u27e7 t1\u2192 x1, \u27e6barking\u27e7t1\u2192 x1)](\u27e6dogs\u27e7) e. \u03bbx1[\u03bbp[\u00acp](x1, \u03bbx[BE-BARKING(x)])](\u27e6dogs\u27e7) f. (\u03bbp[\u00acp])(\u27e6dogs\u27e7, \u03bbx[BE-BARKING(x)) type mismatch (FA fails) 177 g. (\u03bbp[\u00acp])(\u2203\u27e6dogs\u27e7)(\u03bbx[BE-BARKING(x)]) type-shifting by \u2203\t h. (\u03bbp[\u00acp])(\u03bbP\u2203x[DOG(x) \u2227 P(x)])(\u03bbx[BE-BARKING(x)]) i. (\u03bbp[\u00acp])(\u2203x[DOG(x) \u2227 BE-BARKING(x)]) by FA j. \u00ac\u2203x[DOG(x) \u2227 BE-BARKING(x)] by FA (Adapted from Krifka 2003: 196) In (296a) the predicate dogs \u201cis moved above negation\u201d (Krifka 2003: 196), leaving behind a trace of the same type, i.e., of type \u27e8e,t\u27e9.66 In consequence, it gets semantically reconstructed to its argument position via lambda conversion. In (296f) a type-clash occurs, since the verbal predicate only applies to a subject argument of type e, i.e., the application of \u03bbx[BE-BARKING(x)] to \u27e6dogs\u27e7 fails. Then, in order to repair this, a type-shifting operation is triggered in (296g): \u2203 applies to the predicate denotation of dogs, resulting in a generalized quantifier. Subsequently, via functional application of \u2203\u27e6dogs\u27e7 to the verbal predicate we get the existential sentence, which is then the argument of negation. The final step leads to interpretation (296j), in which negation scopes over the existential quantifier, as desired. Krifka\u2019s analysis exhibits a generality that Chierchia\u2019s lacks. The DKP mechanism proposed by Chierchia, as shown above, depends on a treatment of BNs as denoting kinds. This approach faces the problem of not accounting for narrow-scope BNs in languages where BNs cannot have kind readings. In contrast, Krifka\u2019s analysis of BNs as predicates, with their nominal interpretations resulting from type-shifting operations, accommodates both types of narrow-scope bare noun languages: those in which BNs can refer to kinds and those in which they cannot.67 66 In fact, Krifka (2003) is neutral with regard to the type of the trace left behind by the raised bare noun. However, I assume here that bare nouns, as predicates, leave a trace of their types, i.e., of type \u27e8e,t\u27e9. I prefer to adopt this in order to make explicit the semantics behind the reconstruction mechanism. 67 There are other important semantic analyses of the phenomenon of obligatory narrow scope of BNs across languages. For instance, there is van Geenhoven\u2019s (1998) analysis, which originates from the study of incorporation in West Greenlandic. By establishing a connection between narrow scope, object BNs and (pseudo-)incorporation, she proposes an analysis in which the existential quantifier binding the variable supplied by the (object) bare nouns is built-in in the denotation of verbal predicates. There is also Diesing\u2019s (1992) syntactic-semantic approach. Her analysis posits a VP-level existential closure of the bare noun variables. This is ensured by positing a syntactic rule that attaches 178 However, given that both analyses are designed to account for obligatory narrow-scope BNs, neither of them can be used to accommodate the scope properties exhibited by Kaingang BNs. As shown in section 5.2, Kaingang bare nouns display variable-scope effects. In section 5.4, I will propose an analysis of Kaingang indefinite bare nouns as predicate NPs type-shifted to arguments of type e via a covert choice function type-shifter. Their variable scope properties will be associated with existential closure of the CF variable at any level in the clause. Then, in section 5.5, I will link the distinction between variable-scope BNs and narrowest-scope BNs to the quantized\/cumulative opposition of the predicates they express. Variable-scope BNs and narrowest-scope BNs are created by two distinct covert type-shifters: the former by a CF operator and the latter by Krifka\u2019s \u2203 operator (Krifka 2003). With this I intend to show how my theory, by incorporating Krifka\u2019s type-shifting analysis of narrowest-scope BNs, accounts for the attested crosslinguistic scope patterns of indefinite bare nouns. 5.4 A choice function analysis of Kaingang BNs 5.4.1 Background on choice functions The choice function theory of indefinites, introduced by Reinhart (1997, 2006), Winter (1997, 2001), and Kratzer (1998), was designed to account for the exceptional scope behavior of indefinites with respect to syntactic islands such as if-clauses. Since Fodor and Sag (1982), it has been observed that while quantified DPs such as every linguist obey scope islands, indefinite DPs such as a linguist are insensitive to them. To illustrate this contrast, the conditional sentence in (297a) can have a reading in which a linguist, the subject of the antecedent clause, scopes over the if-clause, i.e., one in which a specific linguist arrives at the party, whereas in (298a) this possibility is ruled out for every linguist. That is, (298a) cannot mean that for every linguist x, if x arrives at the party, then the speaker will be happy. \u2203 to the left boundary of the VP.\t Both approaches predict that (object) bare nouns are always interpreted under the scope of another operator. 179 (297) a. If a linguist arrives at the party, I will be happy. b. \u2713IF > \u2203\t c. \u2713\u2203\t> IF (298) a. If every linguist arrives at the party, I will be happy. b. \u2713IF > \u2200\t\tc. *\u2200\t> IF The main advantage of a CF approach is that it models the scope interactions of indefinites with respect to other operators, including if-clauses, without positing any special sort of LF movement distinct from the syntactic movement common to all genuine quantified DPs, which cannot violate island constraints. By assuming that indefinites can introduce choice functions that are existentially closed at any level in the clause, Reinhart (1997, 2006) shows that the scope ambiguity of sentences like (297a) can be captured with indefinites interpreted in situ, i.e., without resorting to an exceptional sort of movement insensitive to islands. In prose, a choice function f applies to a non-empty set and maps it into one of its elements, i.e., it is a function of type \u27e8\u27e8e,t\u27e9,e\u27e9. For instance, in (297a) above the choice function f denoted by a applies to the predicate linguist and yields one of the individuals falling under it, as shown in (299). (299) \u27e6DPe \u27e7 = f(LINGUIST) D NP \u27e6a\u27e8\u27e8e,t\u27e9,e\u27e9\u27e7 = \u03bbP[f(P)] \u27e6linguist \u27e8e,t\u27e9\u27e7 = \u03bbx[LINGUIST(x)] The indefinite DP a linguist is an argument of type e. Its existential force and variable-scope effects derive from the binding of the choice function variable via \u2203-closure at different locations in the clausal spine. This allows us to represent both available readings of (297a) as in (300a\u23afb). 180 (300) a. [\u2203f [CH(f ) \u2227 ARRIVE(f(LINGUIST))]] \u2192 WILL-BE-HAPPY(SPEAKER) \u2018If there is a choice function f, such that the linguist selected by f arrives, then I will be happy.\u2019 b. \u2203f [CH(f ) \u2227 [ARRIVE(f(LINGUIST)) \u2192 WILL-BE-HAPPY(SPEAKER)]] \u2018There is a choice function f, such that if the linguist selected by f arrives, then I will be happy.\u2019 In both readings the indefinite is kept in situ. The narrow scope reading in (297a) results from the existential closure of the CF variable under the scope of the if-clause, as captured in (300a), whereas the wide scope reading, exhibited in (300b), arises from the existential binding of the CF outside the if-clause. 5.4.2 The analysis All CF analyses of indefinites treat choice functions as bound to the presence of an (overt or null) determiner (Reinhart 1997, 2006; Winter 1997, 2001; Kratzer 1998; Matthewson 1999; Lyon 2011; Paul 2016). However, if we adopt the view that null Ds must be syntactically licensed (Contreras 1986; Longobardi 1994, 2001; Chierchia 1998b; Paul 2016), the Kaingang data shows that choice functions don\u2019t need to be always linked to the presence of a D. In what follows I make two claims about the semantics of Kaingang bare nouns. First, based on the variable scope properties of Kaingang indefinite BNs and their insensitivity to islands, I propose that they are interpreted by means of a choice function type-shifter. Second, as in Reinhart (1997, 2006), I associate the source of their existential force and variable-scope effects with existential binding of the choice function variable at different levels. There is indirect evidence that Kaingang argumental BNs don\u2019t project a full-fledged DP and, consequently, that their choice functions cannot be introduced by a null determiner, as proposed for Malagasy (Paul 2016). This evidence comes from the unrestricted syntactic distribution of Kaingang BNs shown in Chapter 2, i.e., from the fact that bare nouns can occur as internal and external arguments, as given in (301\u23af304). 181 (301) G\u0129r v\u1ef9 j\u00e3n \u2205. (= (42)) child NOM sing PFV \u2018A\/some\/the child(ren) sang.\u2019 (302) G\u0129r v\u1ef9 kute \u2205. (= (43)) child NOM fall PFV \u2018A\/some\/the child(ren) fell down.\u2019 (303) G\u0129r v\u1ef9 \u0129n-\u2205 v\u00e9 \u2205. (= (44)) child NOM house-ACC see PFV \u2018A\/some\/ the child(ren) saw a\/some\/the house(s).\u2019 (304) F\u00f3gt\u1ebd v\u1ef9 g\u0129r m\u1ef9 j\u00e3nka-\u2205 f\u1ebdg \u2205. (= (45)) F\u00f3gt\u1ebd NOM child DAT necklace-ACC give PFV \u2018F\u00f3gt\u1ebd gave a\/some\/the necklace(s) to a\/some\/the child(ren).\u2019 In the literature on the distribution and interpretation of bare arguments, many authors have claimed that null determiners need to be licensed by a lexical head (Contreras 1986, Longobardi 1994; Chierchia 1998b; Paul 2016). For instance, in languages in which BNs have a restricted distribution, i.e., appear only as internal arguments, such as Italian and Malagasy, null determiners are licensed by V heads, and external bare arguments are ruled out because \u201cthere is no suitable head that can act as a licenser\u201d (Chierchia 1998b: 356). For Chierchia (1998b) and Paul (2016), it follows from that that languages which allow BNs as external arguments, such as English, Mandarin, Pirah\u00e3 (Muran) (Salles 2023), and Kaingang, constitute evidence that arguments aren\u2019t always DPs, as opposed to the DP hypothesis (Abney 1987; Longobardi 1994, 2001; Bernstein 2001; Alexiadou et al. 2007, among others), according to which the DPhood of arguments is a language universal. In this regard, in light of their unrestricted distribution, English bare plurals in argument positions can be NumPs \u23af if we assume that number is a functional category \u23af and 182 number-neutral BNs in Mandarin and Kaingang are genuine bare NPs.68 Under standard type-shifting theories (Partee 1986; Chierchia 1998b; Krifka 2003; Dayal 2004), in this type of language argumental BNs undergo type-shift operations that turn them into referential arguments via \ud835\udea4 or \u2229, or into generalized quantifiers via \u2203. Thus, assuming that null Ds require syntactic licensing, and that the unrestricted argument distribution of number-neutral BNs in Kaingang constitutes evidence that they are NPs, I propose that their indefinite interpretation involves a choice function type-shifter driven by general principles of type shifting (Partee 1986; Chierchia 1998b). Kaingang BNs start as predicates, i.e., as constituents of type \u27e8e,t\u27e9, and get mapped into arguments of type e via the CF operator, as given in (305) with the BN g\u0129r \u2018child\u2019. (305) f: G\u0128R \u21d2 f(G\u0128R) The type-shifter in (305) is triggered by type-mismatch: the combination of nominal predicates with verbal predicates that require arguments of type e results in an uninterpretable structure. So, the choice function type-shifter rescues the derivation from a type-clash by making it interpretable. This is illustrated in (306). (306) G\u0129r v\u1ef9 j\u00e3n \u2205. child NOM sing PFV \u2018A child(ren) sang.\u2019 a. \u03bbx[SING(x)], \u03bbx[CHILD(x)] type-mismatch b. (\u03bbx[SING(x)])(f(CHILD)) by CF type-shift c. SING(f(CHILD)) by FA d. \u2203f [CH(f ) \u2227 [SING(f(CHILD))]] by \u2203-closure of f 68 For a defense, in the syntactic literature, of the claim that NPs can be arguments, see Bo\u0161kovi\u0107 (2005, 2009, 2016) and Bruening (2009, 2020). 183 The type mismatch in (306a) between the BN g\u0129r \u2018child\u2019 and the verbal predicate j\u00e3n \u2018sing\u2019 gets repaired in (306b\u23afc) by type-shifting g\u0129r into a type e argument containing a choice function variable, to which then j\u00e3n \u2018sing\u2019 applies, resulting in the interpretable configuration in (306c). Finally, in (306d) the CF variable is bound by the existential quantifier. In (307) I summarize the steps that led me to the claim that Kaingang bare nouns are predicate NPs mapped onto arguments via a choice function type-shifter. (307) a. Kaingang bare nouns with indefinite readings have unrestricted distribution. b. Null determiners must be syntactically licensed. c. There isn\u2019t a licenser of null Ds in external argument positions. d. Bare nouns that can occur in an external argument position are NPs. e. Kaingang bare nouns with indefinite readings are NPs. By a\u23afd f. Indefinite NPs are predicates that get interpreted by choice function type-shifter. g. Bare NPs that have variable-scope effects and are island insensitive get their interpretation via a choice function existentially closed at any level. h. Kaingang bare nouns have variable-scope effects and are island insensitive. i. Therefore, Kaingang bare nouns are predicate NPs shifted to arguments via a choice function type-shifter. \t \t \t \t \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tBy f\u23afh Let us now look at how the choice function analysis accounts for the variable scope readings of Kaingang bare nouns with respect to other operators. Recall from section 5.2 that Kaingang bare nouns can display narrow, wide, and intermediate scope readings. I first address the scope interplay between bare nouns and negation. Sentence (308a) exhibits scope ambiguity. According to the choice function analysis I propose, the representation in (308b) corresponds to the wide scope reading of the BN pir\u00e3 \u2018fish\u2019 with respect to negation, and (308c) corresponds to the narrow scope reading. 184 (308) a. F\u00f3gt\u1ebd v\u1ef9 pir\u00e3-\u2205 sam t\u0169 n\u0129. (= (10a)) F\u00f3gt\u1ebd NOM fish-ACC catch NEG ASP \u2018F\u00f3gt\u1ebd didn\u2019t catch a fish.\u2019 b. \u2203f [CH(f ) \u2227 \u00ac[CATCH(f(FISH))(F\u00d3GT\u1ebc)]] \u2018There is a choice function f, such that F\u00f3gt\u1ebd didn\u2019t catch the fish selected by f.\u2019 c. \u00ac\u2203f [CH(f ) \u2227 CATCH(f(FISH))(F\u00d3GT\u1ebc)] \u2018It is not the case that there is a choice function f, such that F\u00f3gt\u1ebd caught the fish selected by f. The analysis correctly predicts both readings. The existential closure of the choice function variable above negation captures the interpretation in which a specific fish wasn\u2019t caught. In contrast, the existential closure of the choice function under negation gives rise to the interpretation in which no fish were caught. The different levels of \u2203-closure in (308a\u23afb) are schematized in (309a\u23afb). (309) a. Wide scope b. Narrow scope 185 Likewise, the CF analysis captures the scope interaction between a BN like f\u00f3g \u2018non-indigenous person\u2019 and an intensional verb like s\u00f3r \u2018want\u2019, as shown in (310a\u23afc). (310) a. F\u00f3gt\u1ebd t\u00f3g f\u00f3g v\u00e9 s\u00f3r m\u0169. (= (267a)) F\u00f3gt\u1ebd TOP non.indigenous.person see want ASP \u2018F\u00f3gt\u1ebd wants to see a non-indigenous person.\u2019 b. \u2203f [CH(f ) \u2227 WANT [(SEE(f(NON-INDIGENOUS-PERSON))(F\u00d3GT\u1ebc)]] c. WANT [\u2203f [CH(f ) \u2227 SEE(f(NON-INDIGENOUS-PERSON))(F\u00d3GT\u1ebc)]] Again, the bare noun f\u00f3g, which includes a choice function, is interpreted in situ in both readings. Representation (310b) corresponds to the wide scope reading, while (310c) corresponds to the narrow scope reading. The treatment of Kaingang BNs as involving existentially closed CFs also explains their \u201cexceptional\u201d scope behaviour in relation to if-clauses. The bare noun kanhg\u00e1g \u2018Kaingang\u2019 in sentence (311a) doesn\u2019t violate the island created by m\u0169ra \u2018if\u2019 in its wide scope reading. As shown in (311b), to derive this reading it suffices that the choice function variable of the in situ bare noun gets bound by \u2203 outside the scope of the if-clause. As for the narrow scope reading, it is accomplished via existential closure within the if-clause, as in (311c). (311) a. F\u00e9nhta ki kanhg\u00e1g jun m\u0169ra, s\u00f3g Gar\u00e7om-\u2205 j\u00e3n Party at Kaingang arrive if, 1 SG.TOP Gar\u00e7om-ACC sing ke m\u0169. (= (107a)) FUT ASP \u2018If a Kaingang arrives at the party, I will sing Gar\u00e7om.\u2019 b. \u2203f [CH(f ) \u2227 [ARRIVE-AT-THE-PARTY(f(KAINGANG)) \u2192 WILL-SING-GAR\u00c7OM(S.)]] \u2018There is a choice function f, such that if the Kaingang selected by f arrives at the party, then the speaker will sing Gar\u00e7om.\u2019 186 c. [\u2203f [CH(f ) \u2227 ARRIVE-AT-THE-PARTY(f(KAINGANG))]] \u2192 WILL-SING-GAR\u00c7OM(S.) \u2018If there is a choice function f, such that the Kaingang selected by f arrives at the party, then the speaker will sing Gar\u00e7om.\u2019 The choice function approach also straightforwardly predicts the available scope readings of BNs with respect to the universal quantifier kar \u2018all\u2019. The wide scope reading of the bare noun in sentence (312a) is represented in (312b), while the narrow scope in (312c). (312) a. F\u00f3g kar v\u1ef9 \u0129n-\u2205 han \u2205. (= (110)) non.indigenous.person all NOM house-ACC make ASP \u2018All non-indigenous persons built a house.\u2019 b. \u2203f [CH(f ) \u2227 \u2200x[NON-INDIGENOUS-PERSON(x) \u2192 BUILD(f (HOUSE))(x)]] \u2018There is a choice function f, such that every non-indigenous person x built the house selected by f.\u2019 c. \u2200x[NON-INDIGENOUS-PERSON(x) \u2192 \u2203f [CH(f ) \u2227 BUILD(f (HOUSE))(x)]] \u2018For every non-indigenous person x, there is a (potentially different) choice function f, such that x built the house selected by f.\u2019 Thus, the scope interaction between \u2203 and the universal quantifier determines the differences in the scope readings of the bare noun. Similarly, the analysis correctly predicts the scope ambiguity of sentences containing a BN and a frequency adverbial. The wide and narrow scope readings of the BN s\u1ebdsi \u2018bird\u2019 in sentence (313a) are illustrated in (313b) and (313c), respectively. (313) a. S\u1ebdsi v\u1ef9 kus\u00e3 ki \u0129n k\u00e3-ra~r\u00e3 p\u1ebd han. (= (274a)) bird NOM morning in house RED~enter many make \u2018A bird entered the house many times in the morning.\u2019 187 b. \u2203f [CH(f ) \u2227 MANY-TIMESin-the-morning [ENTER(THE-HOUSE)(f(BIRD))]] \u2018There is a choice function f, such that many times in the morning the bird selected by f entered the house.\u2019 c. MANY-TIMESin-the-morning [\u2203f [CH(f ) \u2227 ENTER(THE-HOUSE)(f(BIRD))]] \u2018Many times in the morning there was a (potentially different) choice function f, such that the bird selected by f entered the house.\u2019 Furthermore, the choice function analysis proposed here, by assuming existential closure of the choice function variable at any level, correctly predicts that Kaingang BNs can scopally interact with more than one operator in a clause. A BN can display intermediate scope in a sentence containing two occurrences of the universal quantifier kar \u2018all\u2019, in addition to wide and narrow scope readings. This is shown in sentence (314a). (314) a. P\u00e3\u00b4i kar v\u1ef9 f\u00f3g kar t\u1ef9 \u0129n-\u2205 han chief all NOM non.indigenous.person all ERG house-ABS make m\u0169 to h\u00e1 n\u0129. (= (111a)) ASP like ASP \u2018All chiefs like all non-indigenous persons that built a house.\u2019 b. \u2203f [CH(f ) \u2227 \u2200x[CHIEF(x) \u2192 \u2200z[NON-INDIGENOUS-PERSON(z) \u2227 BUILD(f(HOUSE))(z) \u2192 LIKE(z)(x)]]] \u2018There is a choice function f, such that every chief x likes every non-indigenous person z that built the house selected by f.\u2019 c. \u2200x[CHIEF(x) \u2192 \u2203f [CH(f ) \u2227 \u2200z[NON-INDIGENOUS-PERSON (z) \u2227 BUILD(f(HOUSE))(z) \u2192 LIKE(z)(x)]]] \u2018For every chief x there is a choice function f, such that x likes every non-indigenous person z that built the house selected by f.\u2019 188 d. \u2200x[CHIEF(x) \u2192 \u2200z[NON-INDIGENOUS-PERSON (z) \u2192 \u2203f [CH(f ) \u2227 BUILD(f(HOUSE))(z)] \u2192 LIKE(z)(x)]]] \u2018For every chief x, for every non-indigenous person z such that there is a choice function f and z built the house selected by f, x likes z.\u2019 Note that \u2203-closure of the choice function variable outside the scope of both quantifiers, as in (314b), corresponds to the wide scope reading of the in situ bare NP \u0129n \u2018house, i.e., one in which a specific house is built by every non-indigenous person. The scope configuration that results in this reading is captured in tree (315). (315) Wide scope The intermediate reading is captured in (314c), where \u2203 is between the quantifiers. The interpretation is that the number of houses, but not the number of non-indigenous persons, covaries with the number of chiefs. Tree (316) displays the scope layout that underlies (314c). (316) Intermediate scope 189 In contrast, (314d) corresponds to the narrowest-scope reading, given that \u2203 is introduced under both universal quantifiers. Under this configuration, which is illustrated in tree (317), (314a) means that the number of houses (potentially) covaries with the number of house builders. (317) Narrow scope Before ending the analysis of the intermediate scope of Kaingang bare NPs, it is important to address a possible competing account instigated by Kratzer\u2019s (1998) challenge to the existence of genuine intermediate scope of English indefinites. With this brief discussion, I hope to provide further justification for the claim that Kaingang BNs have bona fide intermediate scope readings. Kratzer (1998) proposes an analysis of indefinite DPs headed by a(n) as ambiguous between a choice function and an existential generalized quantifier. The latter gives rise to nonspecific readings of the indefinite DP, and the former to specific readings. However, in Kratzer\u2019s approach, choice function variables are not bound by an existential quantifier. Instead, they are free variables whose values can be contextually supplied. This proposal, in the spirit of Fodor and Sag (1982), accounts for the wide scope of indefinite DPs headed by a without resorting to existential operators and the notion of scope. Under this analysis, there is no genuine intermediate scope reading of indefinites understood as arising from the interplay between an existential quantifier and two other operators.69 Motivated by the empirical contrast between the lack of an intermediate reading (or its very marginal availability) in sentences like (318), and its (apparent) presence in (319a), Kratzer proposes an account of (319a) in which the intermediate scope of indefinites is in fact a \u201cpseudo-scope\u201d, emerging only when indefinites contain bound pronouns. That is, by getting bound by the 69 Matthewson (1999) shows that St\u2019\u00e1t\u2019imcets (Salish) also lacks intermediate scope readings of its indefinite DPs. She also proposes a choice function analysis of St\u2019\u00e1t\u2019imcets indefinites. 190 quantifier phrase every professor, the pronoun in (319a) forces the set from which the choice function selects one individual to covary with each professor, as shown in (319b). As a result, the CF selects one (potentially different) student from each professor\u2019s set of students. (318) Every professor1 will rejoice if a student of mine2 cheats on the exam. (319) a. Every professor1 will rejoice if a student of his1 cheats on the exam. b. Every professor x will rejoice if f(STUDENT-OF x) cheats on the exam. Based on Kratzer\u2019s successful analysis of minimal pairs such as (318) and (319a), one could argue that the intermediate reading of the Kaingang BN \u0129n \u2018house\u2019 in sentence (314a) is due to an interpretation in which consultants assume that the houses belong to the chiefs. This would induce a reading in which \u0129n carries a null pronoun which then gets bound by the highest quantifier phrase. As a result, Kaingang bare nouns under their wide and intermediate scope readings could be treated as supplying a free choice function variable that never gets existentially bound. However, the BN \u0129n \u2018house\u2019 in (314a) can get an intermediate reading whether the houses belong to the chiefs or not. To test (314a) in a situation that excludes each chief owning one of the houses, the discourse context depicted by Figure 43, repeated below as Figure 46, was shown to one of the consultants accompanied by an oral description specifying that the houses belonged to individuals of whom the chiefs were unaware. The consultant accepted (314a) in such a context, and even commented that it was good in the context because \u201c[the sentence] doesn\u2019t say that the chiefs own the houses.\u201d 191 Figure 46: Intermediate scope context. Thus, an analysis \u00e0 la Reinhart (1997, 2006), which posits existential closure of choice function variables at any level easily accounts for the intermediate scope reading of (314a), as opposed to Kratzer\u2019s. In addition, it offers a unified treatment of the variable-scope effects of indefinite bare nouns as always associated with a choice function interpretation. From these facts, I conclude that Kaingang bare nouns not only constitute further crosslinguistic evidence for the existence of choice function bare nouns, but also for the mechanism of existential closure of choice function variables. Lastly, let us turn to the wide scope reading of Kaingang substance bare nouns. As shown in Chapter 4 and section 5.2.7, substance bare nouns with an indefinite interpretation can be used to talk about portion-units of a substance. In such situations a wide scope reading can arise. This was attested by the possibility of conjoining affirmative statements with their negative counterparts, as illustrated in sentence (320a). The lack of contradiction in (320a), given a proper context, is correctly predicted by the choice function analysis. In (320b), the existential closure of the choice function variable f\u2019, which selects one of the contextual portions of water, scopes over negation. (320) a. Goj v\u1ef9 pa ja n\u0129, h\u00e3ra goj v\u1ef9 pa ja t\u0169 n\u0129. (= (11a)) water NOM leak ASP ASP but water NOM leak ASP NEG ASP \u2018Some portion of water leaked out, but some portion of water didn\u2019t leak out.\u2019 192 b. \u2203f [CH(f ) \u2227 LEAK-OUT(f(PORTION-OF-WATER))] \u2227 \u2203f\u2019[CH(f \u2019) \u2227 \u00ac[LEAK-OUT(f\u2019(PORTION-OF-WATER))]] \u2018There is a choice function f such that the portion of water selected by f leaked out and there is a choice function f\u2019 such that the portion of water selected by f\u2019 didn\u2019t leak out.\u2019 This section has shown that the variable-scope effects of Kaingang BNs are correctly accounted for by a choice function type-shifting analysis that posits existential closure of the choice function variables at distinct levels in the clause. The fact that Kaingang BNs involve a CF operator provides further evidence that there can be type-shifting CFs. In other words, Kaingang BNs show that the natural language stock of covert type-shifters involved in the interpretation of BNs across languages also contains a choice function. In this regard, I propose to enrich the catalog of covert nominal type shifting mechanisms argued for by Partee (1986), Chierchia (1998b), and Krifka (2003), with a CF type-shifter, as given in (d) of Table 13. Operator Operation Interpretation a. iota (\u03b9) \u27e8e,t\u27e9 \u21d2 e P \u21d2 \u03b9x[P(x)] Definite b. nom (\u2229) \u27e8e,t\u27e9 \u21d2 e P \u21d2 \u2229 P Kind-denoting c. pred (\u222a) e \u21d2 \u27e8e,t\u27e9 k \u21d2 \u222ak Instantiation-set d. CF (f) \u27e8e,t\u27e9 \u21d2 e P \u21d2 f(P) Indefinite e. Krifka\u2019s \u2203: (\u2203) \u27e8e,t\u27e9 \u21d2 \u27e8\u27e8e,t\u27e9,t\u27e9 P \u21d2 \u03bbQ\u2203x[P(x) \u2227 Q(x)] Indefinite Table 13: Enriched nominal type-shifting inventory. However, like the other possible interpretations of bare nouns, the choice function reading is not equally available across languages. In fact, most of the attested BN languages don\u2019t allow variable or exceptional scope readings of their BNs, as widely reported by the literature. As discussed in section 5.3.1, in most languages BNs with existential force have obligatory narrow scope readings. These facts call for a theory that explains the unequal availability of choice function BNs across languages. In section 5.5, I will try to address this issue by proposing an 193 analysis which links the accessibility of distinct type shifters to the quantized\/cumulative opposition exhibited by predicate BNs. 5.5 Bare noun denotations and scope In what follows, I address the differences in scope taking of BNs across languages. The main claim here is that there is a necessary link between the scope properties of indefinite BNs and the predicates they express. Variable-scope BNs, whether singular or number neutral, are quantized predicates, whereas narrowest-scope BNs, whether plural, mass, or number neutral, are cumulative predicates. I propose that the type-shifting operators that give rise to indefinite readings of bare NPs, i.e., the choice function operator and Krifka\u2019s narrow scope \u2203 are sensitive to the underlying higher-order quantized\/cumulative distinction observed in predicates, as discussed in Chapters 3 and 4. The former only applies to quantized predicates, while the latter only selects cumulative predicates. I model the constraint on what type of predicates the type-shifters apply to as presuppositional: the choice function carries the presupposition that P is quantized, whereas \u2203 carries the presupposition that P is cumulative. I further show that this analysis leads to a typology that correctly predicts the observed crosslinguistic variation in the scope of bare nouns. 5.5.1 Scope and the quantized\/cumulative distinction By looking at the scope properties of BNs and their predicate denotations across languages, one can notice an interesting systematic correlation between scope and BN denotations. On the one hand, all obligatory narrow scope BNs observed across languages seem to exhibit cumulative reference, i.e., whenever they hold of two things, they also hold of their mereological sum, as discussed in detail in Chapter 3. In number marking non-classifier languages, like English, narrow-scope BNs are plural and mass NPs, whereas in numberless non-classifier languages, like Haitian 194 Creole (Deprez 2005), as well as classifier languages such as Mandarin (Cheng & Sybesma 1999; Rullmann & You 2006), they are all number neutral. 70 On the other hand, all attested variable-scope BNs are quantized predicates, i.e., whenever they hold of something, they don\u2019t hold of its proper parts. In Hebrew, a non-classifier language that encodes nominal number, such BNs are semantically singular (Dayal 2004; Tonciulescu 2009), while in Kaingang, a generalized non-classifier language in which nouns don\u2019t inflect for number, quantized BNs are number neutral. Hebrew is an interesting illustrative case of such a correlation within a single language. In Hebrew both singular and plural BNs can be interpreted as indefinites. Nevertheless, the former display variable-scope effects, while the latter have obligatory narrow scope (Dayal 2004). I will discuss Hebrew BNs in more detail below. In a nutshell, there is evidence that obligatory narrow scope BNs are associated with cumulative reference across languages, and variable-scope taking bare NPs with quantized reference. This crosslinguistic regularity strongly indicates that there must be a causal connection between the scope properties of BNs and the quantized\/cumulative opposition. This phenomenon has been noted before. In their study on the semantics of Mandarin bare nouns, Rullmann and You (2006) speculate that the correlation between cumulative reference and obligatory narrow scope may not be accidental. The authors, however, don\u2019t offer an account of this observed regularity. Before proceeding, I should emphasize one important point about the view envisaged here. The analysis in this section is primarily designed to account for the variation in scope behavior of genuine argumental bare NPs, i.e., those that, according to Chierchia (1998b), don\u2019t project a DP layer, and hence don\u2019t require a functional category D to map them into arguments. As discussed in section 5.4.2, such bare NPs are those that have unrestricted syntactic distribution (Chierchia 1998b), and as such can also occur as external arguments, i.e., in a configuration in which a null D cannot be syntactically licensed. Consequently, in order to become arguments, these bare NPs appeal to a strictly semantic mechanism of type-shifting operations. Crucially, in all the languages 70 D\u00ebne S\u0173\u0142in\u00e9 (Athapaskan) is also a non-classifier language in which bare nouns don\u2019t inflect for number (Wilhelm 2008). I opt not to include D\u00ebne S\u0173\u0142in\u00e9 in the typology presented in this section because I don\u2019t know of any study on the scope properties of its bare nouns. 195 mentioned above (i.e., English, Mandarin, Haitian Creole, Hebrew, and Kaingang), BNs with indefinite interpretation can be internal and external arguments. However, if studies on the scope behavior of BNs that project a null D, like in Malagasy (Paul 2016), reveal that they are associated with the quantized\/cumulative opposition in the same way as genuine bare NPs, it may be possible to extend the analysis proposed here to those languages as well, in which case a CF introduced by a covert D is also sensitive to the quantized\/cumulative opposition. Thus, I propose that by making both Krifka\u2019s \u2203 type-shifting operator and a type-shifting choice function sensitive to the algebraic properties of the predicates they operate on, we can explain the crosslinguistic variation in the scope properties of BNs. I claim that Krifka\u2019s \u2203 operator applies only to cumulative bare NPs, whereas the covert choice function operator applies only to quantized ones. On the one hand, narrowest-scope BNs are the product of two semantic factors: cumulativity and Krifka\u2019s \u2203 type-shifting operator; on the other hand, variable-scope BNs result from the interaction of three factors: quantization, the choice function type-shifter, and existential closure of the choice function variable. Therefore, I propose to state this generalization about the type-shifters that give rise to indefinite BNs as the principle given in (321). (321) Type-shifter\/predicate dependence a. The covert choice function type-shifter only applies to quantized predicates. b. Krifka\u2019s \u2203 type-shifter only applies to cumulative predicates. As discussed in section 5.3.2, because Krifka\u2019s \u2203 type-shifter only applies locally, it always gives rise to narrow scope interpretations of the BNs it applies to. Again, as observed across languages, we have good reasons to consider BNs that display obligatory narrow scope as cumulative, whether they are plural, mass, or number neutral. As a result, an analysis that constrains Krifka\u2019s \u2203 operator to apply only to cumulative predicates is supported by empirical evidence. The same holds for the choice function type-shifter. As discussed above, there is crosslinguistic evidence that all variable-scope BNs are quantized. As such, an analysis that treats choice function type-shifters as targeting only quantized BNs is also empirically motivated. I propose to model the sensitivity to the quantized\/cumulative opposition of the two type-shifters associated with indefinite interpretations of bare nouns as presuppositional. I treat the CF 196 type-shifter as carrying the presupposition that P is a quantized predicate, as stated in (322). In contrast, Krifka\u2019s \u2203 operator bears the presupposition that P is a cumulative predicate, as given in (323). The presuppositions are represented in boldface. Basically, QUANT(P) stands for \u2018P is quantized\u2019, while CUM(P) stands for \u2018P is cumulative\u2019. (322) f = \u03bbP: QUANT(P). f(P) Choice function BN (323) \u2203\t= \u03bbP: CUM(P). \u03bbQ\u2203x[P(x) \u2227 Q(x)] Existential BN Thus, (322) targets quantized sets, as shown in (324), whereas (323) targets sets that are closed under sum formation, as given in (325). (324) (325) This analysis allows us to account for the systematic correlation between scope patterns of indefinite BNs and their denotations. Semantically singular BNs and number-neutral BNs in (generalized) non-classifier languages can display variable-scope effects because, due to their quantized reference, they shift to arguments via the CF operator in (322), but not the existential operator in (323). Conversely, plural and mass bare NPs, as well as number-neutral BNs in 197 (non-)classifier languages, have obligatory narrow scope because, due to their cumulative reference, they can be accessed by the existential type-shifter in (323), but not by the choice function in (322). As a result, this analysis gives rise to the typology summarized in Table 14 below. Variable-scope BNs (Semantically singular and number-neutral bare nouns) Narrowest-scope BNs (Plural, mass, and number-neutral bare nouns) f[QUANT(P)] Hebrew (bare singulars), Kaingang (number-neutral BNs) \u2203[CUM(P)] English (plural and mass BNs), Mandarin (number-neutral BNs), Haitian Creole (number-neutral BNs), Hebrew (bare plurals), etc. Table 14: Scope of indefinite bare nouns across languages. According to the typology in Table 14 there are three types of bare noun languages. Type I languages, like Kaingang, have only quantized BNs. It follows from this that their indefinite readings are created by a choice function type-shifter, allowing for variable scope interpretation of their BNs. Type II languages, such as English, Mandarin, and Haitian Creole, have only cumulative BNs. Consequently, their BNs can only get an indefinite reading via Krifka\u2019s \u2203 operator, which enforces narrowest-scope interpretations. Type III languages, like Hebrew, are hybrid: they have cumulative and quantized BNs. Bare plurals and bare mass nouns are cumulative, and as such exhibit only narrow scope, while bare singulars are quantized, hence displaying variable-scope effects. Importantly, the analysis advanced here predicts that there are no languages in which cumulative bare nouns have variable scope or quantized bare nouns have obligatory narrow scope. As far as I know, these types of languages haven\u2019t been attested so far. If this is so, we have then good empirical support for the typology advanced in Table 14. 198 To conclude this section, I\u2019d like to speculate about why the correlation between the type-shifters and the semantics of predicate NPs\/NumPs holds. Let us assume that we have good reasons to think there is a plausible cognitive foundation for the fact that the choice function type-shifter only applies to quantized predicates, while Krifka\u2019s \u2203 operator targets only cumulative predicates. It seems reasonable that in order to single out elements from a set, these have to be perceived as distinct from each other. That is, the cognitive operation of selecting one element from a domain requires that its members be counting units. Most of the data that motivate the choice function analysis provide support for a conjecture along these lines, since they involve noun phrases with quantized nouns. If such a hypothesis is correct, it shows that a choice function is not just a formal tool, but a mechanism in natural language that is sensitive to aspects of cognition. As for Krifka\u2019s \u2203 operator, a plausible cognitive account may unfold as follows. Existentially quantifying over (macro-)objects of our daily experience implies the existence of subparts. In other words, whenever we claim that an element of a set of (macro-)objects exists, we necessarily commit ourselves to the existence of any element it contains as a proper part as well. The sensitivity of Krifka\u2019s \u2203 operator to cumulative predicates is supervenient on this cognitive aspect of existential quantification, which is manifested as a condition on the domain of quantification, i.e., that it must contain sums and their parts. Cumulative predicates, by definition, always satisfy this condition and as such are the most suitable candidates for providing the objects of quantification. In light of the conjecture above, the choice function type-shifter and Krifka\u2019s \u2203 operator can be conceived of as the linguistic counterpart of the cognitive distinction between selecting an entity from a set and claiming the existence of an entity. Such a hypothesis, although it isn\u2019t a strictly logical one, might be cognitively plausible. One interesting question is whether it could be turned into a testable hypothesis within a research project that investigates whether there is a cognitive foundation for the semantic correlation proposed in this chapter. A first step of such research, at least on the empirical side, would be to look at more languages to test the generalization advanced here. Then a next step would be to pursue an explanation for the following two challenging questions at the interface between language and thought: What does it mean to pick one thing cognitively? What does it mean to claim existence cognitively? 199 5.5.2 A note on Hebrew bare singulars As a final point, in what follows I show how my analysis accounts for the hybrid nature of Hebrew, which contains narrowest-scope BNs and variable-scope BNs. Tonciulescu (2009) shows that Hebrew bare singulars can be interpreted as (non-)specific indefinites and as referring to kinds. The sentences in (326a\u23afb) illustrate their indefinite interpretation, while sentence (327) is a case of kind-interpretation. (326) a. Kelev noveax. dog bark \u2018A dog is barking.\u2019 (Adapted from Tonciulescu 2009: 166) b. Raiti namer. saw.1SG tiger \u2018I saw a tiger.\u2019 (Adapted from Tonciulescu 2009: 167) (327) Namer nadir ba-ezor ha-ze. tiger rare in.the.area the-this \u2018The tiger is rare in this area.\u2019 (Adapted from Tonciulescu 2009: 167) As mentioned in the previous section, Hebrew bare singulars have variable scope with respect to other operators in the clause. This is shown in examples (328a) and (329a). (328) a. Dan roce lifgoS koxav kolno\u2019a. Dan wants to.meet star cinema \u2018Dan wants to meet a movie star.\u2019 b. \u2713\u2203 > WANT 200 c. \u2713WANT > \u2203 (Adapted from Dayal 2004: 444) (329) a. Dani mexapes kelev. Dani is.looking.for dog \u2018Dani is looking for a dog.\u2019 b. \u2713\u2203 > LOOK-FOR c. \u2713LOOK-FOR > \u2203 (Adapted from Tonciulescu 2009: 171) Tonciulescu (2009) treats bare singulars as kind-referring expressions, i.e., they are assumed to be of type e. Because bare singulars are of type e they can directly combine with kind-level predicates like nadir \u2018be rare\u2019 in (327) via functional application, i.e., no type-shifting operations are involved in their kind interpretations. As for the indefinite readings of kelev \u2018dog\u2019 in (326a) and namer \u2018tiger\u2019 in (326b), they are derived via Chierchia\u2019s (1998b) DKP mechanism. That is, because the stage-level predicate noveax \u2018is barking\u2019 and raiti \u2018saw\u2019 select only for ordinary objects as arguments, a sortal mismatch arises between the kind-referring bare singulars and the verbal predicates. For this reason, DKP is triggered. For instance, kelev \u2018dog\u2019 in sentence (326a) is first mapped via the instantiation operator \u22c3\tinto a predicate and then existential closure is introduced over instances of the kind denoted by the bare noun. This procedure is given in (330). (330) Kelev noveax. a. [Kelev [noveax]] b. (\u03bbx[IS-BARKING (x)])(DOG) sortal mismatch c. \u2203x [x \u2264 \u22c3DOG \u2227 IS-BARKING(x)] by DKP 201 As for the variable scope behavior of Hebrew bare singulars, Tonciulescu (2009) associates it with two distinct mechanisms. Narrow scope interpretations are derived via DKP, while wide scope readings arise through a choice function and the existential closure of the choice function variable at the sentence level, i.e., it is always introduced above another clause-mate operator. The narrow scope of koxav kolno\u2019a \u2018movie star\u2019 with respect to an intensional verb in (328a), which is created through DKP, is given in (331), while its wide scope interpretation derived via the choice function is displayed in (332). (331) WANT [\u2203x[x \u2264 \u22c3MOVIE-STAR \u2227 MEET(x)(DAN)]] via DKP (332) \u2203f [CH(f ) \u2227 WANT [MEET(f(\u22c3MOVIE-STAR))(DAN)]] via CF Note that both strategies involve one intermediary step: the application of the instantiation operator \u22c3 to the bare singular, by which its kind denotation is mapped into a predicate. In (331), the operator is part of DKP, while in (332) it is introduced independently. But the reason for resorting to \u22c3\tis the same in both cases: to provide a set to which \u2203 and the choice function can apply. However, although the analysis that Tonciulescu offers accounts for the scope ambiguity of Hebrew bare singulars, it faces difficulties once Hebrew bare plurals are brought into the discussion. Doron (2003) and Dayal (2004) show that Hebrew bare plurals, as opposed to bare singulars, have obligatory narrow scope, as given in (333a), the plural version of (328a). (333) a. Dan roce lifgoS koxvey kolno\u2019a. Dan wants to.meet stars cinema \u2018Dan wants to meet movie stars.\u2019 b. *\u2203 > WANT c. \u2713WANT > \u2203 (Adapted from Dayal 2004: 444) 202 Let us suppose that Tonciulescu, in conformity with Chierchia\u2019s (1998b) framework, would welcome a treatment of bare plurals like koxvey kolno\u2019a \u2018movie stars\u2019 in (333a) along the same line she offered for the narrow scope of bare singulars. That is, bare plurals in episodic sentences are also interpreted via DKP. If this is so, why is \u22c3 unavailable as an operation that could also independently apply to bare plurals to make them accessible to a choice function? Since both types of bare nouns are mapped into a predicate via the same operator, in principle there isn\u2019t any semantic constraint that restricts \u22c3 to DKP in the case of bare plurals, but not in the case of bare singulars. In addition to the theoretical challenge posed above to our extended version of Tonciulescu\u2019s analysis, if the theory I advanced in section 5.5.1 is correct, there is an even bigger problem with her approach: CF type-shifters are allowed to apply to cumulative predicates. This is so because they shift predicates generated via the instantiation operator \u22c3, i.e., in set talk, they apply to sets of singularities and their mereological sums. However, a CF type-shifter selects only quantized predicates. I believe that by reinterpreting Hebrew bare singulars in light of the approach in section 5.5, we not only account for the variable scope behavior of the bare singulars, but also explain the narrowest-scope property of Hebrew bare plurals. On top of that, a story can be offered about how to derive the kind reading of Hebrew bare singulars. The analysis runs as follows. I propose to model Hebrew bare singulars as quantized expressions that contain the built-in counting function IU (individual-units), which maps quantities into numbers. Following Krifka\u2019s (2003) treatment of singulars in Czech, I suggest that the cardinality of Hebrew bare singulars is resolved to 1. For this reason, they always denote sets of singularities. This is illustrated in (334) with the bare noun koxav kolno\u2019a\t\u2018movie star\u2019. (334) \u27e6koxav kolno\u2019a\u27e7 = \u03bbx[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = 1] As such, because of their quantized nature, Hebrew bare singulars can shift to arguments via the choice function in (322). Their variable-scope taking then arises through existential closure of the choice function variable, which can be introduced above or under the scope of another operator in the clause. The former option gives rise to the wide scope interpretation of the bare noun in 203 sentence (335a), as given in (335b), whereas the latter option yields the narrow scope reading, as shown in (335c). (335) a. Dan roce lifgoS koxav kolno\u2019a. (= (328a)) Dan wants to.meet star cinema \u2018Dan wants to meet a movie star.\u2019 b. \u2203f [CH(f ) \u2227 WANT [(MEET (f(\u03bbx[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = 1]))(DAN)]] c. WANT [\u2203f [CH(f ) \u2227 MEET(f(\u03bbx[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = 1]))(DAN)]] In contrast, Hebrew bare plurals, like English, are associated with a cumulative denotation derived through existential closure of the n variable signaled by the plural morpheme. This is given in (336). (336) \u27e6koxvey kolno\u2019a\u27e7\t=\t\u03bbx\u2203n[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = n] Consequently, bare plurals are not accessible to choice functions. Their indefinite interpretation arises through Krifka\u2019s \u2203 type-shifter. The output of this, as desired, is an interpretation in which bare plurals always have narrow scope. The available interpretation of a sentence like (333a), for example, is captured by the representation in (337). (337) WANT [\u2203x\u2203n[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = n \u2227\tMEET(x)(DAN)]] As for the kind reading of Hebrew bare singulars, it can be created via two mechanisms. First, Link\u2019s * operator (Link 1983, 1998), which forms a cumulative set out of a set of singularities, applies to (334). Secondly, Chierchia\u2019s kind-forming operator \u22c2 applies to the cumulative predicate created by *, and maps it into the \u2018movie star kind\u2019. This two-step procedure is laid out in (338a\u23afb) below. (338) a. [*](\u27e6NP koxav kolno\u2019a\u27e7) = *\u03bbx[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = 1] by * 204 b. [\u22c2](*\u27e6NP koxav kolno\u2019a\u27e7) = \u22c2*\u03bbx[MOVIE-STAR(x) \u2227 IU(MOVIE-STAR)(x) = 1] by \u22c2 I assume here, along with Chierchia (1998b), that \u22c2 is undefined for sets of singularities, i.e., a kind can only be formed out of cumulative predicates. This condition can also be modeled as a presupposition carried by the kind-forming operator, i.e., the \u22c2 operator carries the presupposition that the predicates it applies are cumulative, as stated in (339). (339) \u22c2 = \u03bbP: CUM(P). \u22c2(P) For this reason, bare singulars in Hebrew must shift from a quantized predicate into a cumulative one before they can be mapped into a kind. Because Hebrew singular bare nouns have a cardinality of 1 and hence lack an unsaturated variable n, cumulative reference cannot emerge via existential closure. However, given that Link\u2019s * operator plays the same semantic role as Krifka\u2019s existential closure of the number variable, we can assume that this operator is covertly available in the nominal domain of Hebrew. In short, it can be seen as a resource which is triggered in order to make bare singulars inputs for kind formation. 205 Chapter 6: Conclusion This thesis has investigated the semantics of nominal countability and the scope properties of bare nouns in Kaingang from the perspective of formal semantics. It provides the first analysis of these phenomena in the language. Based on a wide range of supporting evidence, I have argued that there is a necessary link between these two phenomena, advancing an analysis that treats the variable-scope effects of BNs in Kaingang as resulting from the count nature of Kaingang nouns. The overarching claim proposed in this thesis is that quantization underlies the count interpretation of Kaingang (bare) nouns and their variable-scope effects. An integrated analysis of countability and scope of BNs accounts not only for the Kaingang data, but also allows for a generalization that explains the differences in scope properties of BNs across languages. Regarding nominal countability, we have seen that individual and substance nouns in Kaingang are systematically interpreted as count nouns. Compelling evidence showed that both types of nouns pattern alike regarding the grammar of counting, i.e., there are no morphosyntactic or semantic features that distinguish them in this domain. I have accounted for these findings by arguing that all nouns in Kaingang are lexically count. In the spirit of Krifka\u2019s theory of countability (1986, 1989, 2007, 2008), I model this common feature of all nouns by proposing that they express quantized predicates of type \u27e8e,t\u27e9 equipped with a context-sensitive built-in counting function that measures quantities in terms of individual- or portion-units. Kaingang BNs are quantized relative to any contextual assignment of a value to the number variable n introduced by their built-in counting function. In addition, I have demonstrated that this analysis is not only supported by the Kaingang data, but also by crosslinguistic evidence, in particular by the existence of object mass nouns and fence-type nouns in languages like English. I have also argued that there is an explanatory advantage of the quantization property over atomicity as the defining property of count nouns, by showing that my analysis of Kaingang can be generalized to Yudja (Lima 2014 a, b), a language in which nouns also display a pervasive count interpretation. Finally, if my analysis of Kaingang nouns is correct, it has provided additional crosslinguistic evidence that challenges the common view that the mass\/count distinction in the nominal domain is a language universal. 206 As for the scope of Kaingang bare nouns, through several standard diagnostic tests, I have demonstrated that Kaingang BNs under an indefinite reading have unrestricted distribution and display variable scope with respect to other operators, such as negation, intensional verbs, if-clauses, universal quantifiers, and frequency adverbials. To account for these findings, I have analysed Kaingang bare nouns as predicate NPs which get turned into arguments via a choice function type-shifter. Their existential force and variable scope are treated as arising from existential closure of the choice function variable at any clause boundary, following Reinhart (1997, 2006). In this way, Kaingang BNs reveal that a choice function is not always associated with an overt or null D. This entails that the choice function operator has a place in the inventory of covert type-shifters found in human languages. As for the crosslinguistic differences between narrowest-scope BNs and variable-scope BNs, I have linked these to the quantized\/cumulative opposition. I have provided evidence that the former are cumulative, while the latter are quantized. Having proposed that distinct type-shifters are necessarily associated with narrowest- and variable-scope BNs, I treat them as sensitive to the algebraic properties of the predicates expressed by the BNs they target. I model this via presuppositions carried by the type-shifting operator. The choice function type-shifter available in languages like Kaingang and Hebrew comes with the presupposition that the BN it applies to is quantized. In contrast, Krifka\u2019s narrowest-scope \u2203 type-shifter (Krifka 2003) carries the presupposition that the BN it applies to is cumulative. From this analysis a typology emerges that captures the variation in scope behavior of BNs attested across languages. To conclude this thesis, I would like to mention some paths for future investigation. First, the main claims of this thesis should be tested with a larger number of Kaingang speakers in fieldwork, and ideally also in experimental psycholinguistic studies. Here I have in mind the kind of controlled experimental work conducted by Bale and Snedeker (2005) with a large sample of speakers to investigate the interpretation of English object mass nouns in quantity judgement tasks, as well as the experiments done by Lima (2014a, b, 2016) to examine countability in Yudja. Basically, the idea would be to incorporate the tests I have done in Chapter 4 into more controlled experimental research involving a larger group of Kaingang speakers, possibly including speakers of different dialects of the language. Second, it is important to investigate abstract nouns in Kaingang. Languages like English make a distinction between abstract count nouns (e.g., suggestion, belief, apology) and abstract 207 mass nouns (e.g., advice, knowledge, curiosity). In this regard, if the hypothesis that all nouns in Kaingang are count nouns is correct, its abstract nouns should also be count. A third path of investigation worth pursuing would be to test the crosslinguistic prediction that quantized bare nouns under indefinite readings allow for variable scope, in particular if a bare noun language lacks a lexical realization of a choice function. For instance, if this prediction is correct, Yudja (like Kaingang and Hebrew) should allow its BNs to take variable scope with respect to other clause-mate operators. A fourth line of investigation to be pursued is the interaction between the semantics of Kaingang BNs and verbal number. Recall that in Chapter 2 I showed that Kaingang encodes the singular\/plural distinction in its verbal domain. Many verbs in the language have a basic and a pluractional form, where the latter can arise via prefixation, reduplication, infixation, or suppletion. It is known that plural verbs in Kaingang express a plurality of events, but the whole range of their available readings still needs further investigation. The development of event-based algebraic semantics has allowed linguists to account for longstanding observed similarities between the nominal and verbal domains \u23af in particular, lexical aspect \u23af such as the parallelism between the denotations of count nouns and telic verbs, on the one hand, and mass nouns and atelic verbs, on the other (Bach 1986; Krifka 1992, among others). Some authors have demonstrated that telic verbs and verbal phrases (e.g., fall, make, build, draw a\/the circle) can be modeled as quantized predicates, and atelic ones (e.g., run, sleep, cry, walk, etc) as cumulative predicates (Krifka 1992; Filip 2000, 2001). Most significantly, it has been shown that in some languages the denotation of nominals can affect the telicity of the verbal predicates that contain them. In English, for instance, the combination of the verb eat and the definite nominal the orange in the sentence Michel ate the orange yields a telic interpretation of the verbal predicate. According to Krifka (1992) and Filip (2000, 2001), this is so because ate the orange ends up expressing a quantized predicate, i.e., no proper parts of the event denoted by it is also an event of eating the entire orange. In contrast, the combination of the same verb and the substance bare noun flour in the sentence Michel ate flour gives rise to an atelic interpretation of the verbal predicate. This is so because ate flour is a cumulative predicate, i.e., proper parts of an event of eating flour are still events of eating flour (Krifka 1992; Filip 2001). Thus, in light of these crosslinguistic facts and their bearings on countability, it is extremely relevant to investigate to what degree the meanings of bare nouns, lexical aspect, and pluractionality interact in Kaingang 208 sentences, and hence the semantic role each of these elements plays in determining their truth conditions. 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