Reduplication and distributivity in Kannada

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Content REDUPLICATION AND DISTRIBUTIVITY IN KANNADA by Janet Katherine Anderson A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy (Linguistics) December 2012 ii Copyright 2012 Janet Katherine Anderson iii DEDICATION In memory of Jean‐Roger Vergnaud iv ACKNOWLEGEMENTS Audrey, Elena, and Jean‐Roger – The great triumvirate who have seen me through this journey through grad school. Each one has been invaluable, both intellectually and personally. I would not have gotten anywhere without Audrey’s patience and encyclopedic knowledge of all things syntax; Elena’s clear introduction to the fantastic playground that is semantics; and Jean‐Roger’s unbridled innovation. I have greatly missed the marathon discussions with Jean‐Roger, where the whole of syntax was on the table, and the biggest question was “why?” While mentioning my graduate committee, I also must thank Tom Ernst, one of my undergraduate committee members. Tom started this whole journey by introducing me to the beauty of formal inquiry and showing how to tame unruly intuition into a linguistic argument. I am grateful to have such a gifted teacher and mentor as a Plan sponsor. Thanks also to my many speakers, some who were consistently and graciously involved through the whole process, and some who just popped in for a few weeks. Thanks especially to Kishore Kodical for turning me on to Kannada by saying “well, my other language does that…” and for being one of the clearest speakers I have ever had the privilege to have worked with. Thanks to Krithika Rao for cheerfully spending time with me that she could have spent in the lab, and to Vicky Adhikari for his thoughtful analyses. Thanks also to Karthik Dantu, Banashankar Veerad, Pramod Shrikanth, Divya Appana, Arjun Badarinath, Sanjay v Purushotham, and Venkat Paritala. As careful as all of you were, I’m sure I’ve still made many mistakes. Any mistake or confusion is my own. I am deeply grateful for the influence on my personal life of Stephen Tobin, Rob Shanklin, and Frank Wulf. Each of you provided needed support, encouragement, and camaraderie. Life in LA would not have been the same without you, nor would life after LA have fallen into place without you. It was an honor to spend two seasons with the Burlington (Vt.) Police Department. I learned a lot from being with such good, focused, blunt, and opinionated people. Thanks for giving me room to discern what I wanted to do, and not understanding why it was taking me so long to finish school. Thanks especially to Deputy Chief Jennifer Morrison and Sergeant Paul Glynn for being free with advice and making time to talk when I asked. Thanks also to Ofc. Chris Sweeney for daring me to finish my dissertation and move on with life, though you probably don’t remember issuing such a challenge. Finally, thanks to my parents, Sandy and Trudy Anderson, who graciously put up with me and all my ups and downs. Thanks for your encouragement, your faith, and your acceptance. vi TABLE OF CONTENTS 1 Introduction 1 1.1 In The Beginning 1 1.2 Roadmap Of Dissertation 4 1.3 Data Collection Methodology 5 1.4 Sketch Of Kannada Grammar 6 1.4.1 Case Marking, Demonstratives, And Specificity 8 1.4.2 Verbal Domain 10 1.4.3 Embedded Clauses 12 1.4.4 Relativization 13 1.4.5 Adjuncts 13 1.4.6 Wh‐Word Inventory, Wh‐In‐Situ 14 1.5 Reduplication Types 15 1.5.1 Numeral Reduplication (NR) Indicates Distributive Reading 15 1.5.2 Pronoun Reduplication (PR) 18 1.5.3 ‘One’ Reduplication 20 1.5.4 Wh‐Word Reduplication 21 1.5.5 Purely Phonological Reduplication: Echo Word Reduplication 24 2 C‐Command In NR And PR 26 2.1 Matrix Subjects 26 2.1.1 NR In Subjects 26 2.1.2 PR In Subjects 27 2.2 Relative Clauses 29 2.2.1 NR And Relative Clauses 29 2.2.2 PR And Relative Clauses 30 2.3 Ditransitives 31 2.3.1 Nr And Ditransitives 31 2.3.2 Ditransitives And Pronoun Reduplication 35 2.4 Adjuncts And C‐Command 36 2.5 Restrictions On What Can C‐Command The Reduplicant 38 2.5.1 Distributors Must Be Pluralities 38 2.5.2 Possible Antecedents For PR 41 vii 2.6 Generalizations 42 3 The Proposal And Some Alternatives 43 3.1 Option 1: Reduplicant As Bound Item 43 3.1.1 Background: Binding Theory 43 3.1.2 Binding Domains In Kannada 48 3.1.3 Distributivity And Condition A 54 3.1.4 NR As A Reflexive 55 3.1.5 Pronoun Reduplication As An Obligatorily Bound Pronoun 56 3.2 Option 3: Polarity Item Licensing 57 3.3 Option 4: NR Restricts Quantifier’s QR Landing Site 59 3.3.1 Quantifier Types And The Landing Theory Of Scope 60 3.3.2 NR Is Not Just A GQP Disambiguation Strategy 68 4 Semantic Approaches To NR 71 4.1 Background: Pluralities In Semantics 71 4.2 A Basic Example 80 4.3 A Binominal Binding Account Of Distributivity 82 4.3.1 Safir And Stowell’s Semantics For Binominal Each (1988) 82 4.3.2 Spanish Reciprocals And Binominal Each 88 4.3.3 Binding And Movement Approaches For NR 94 4.3.4 Further Support: Case Marking And Dravidian ‘One’ Reduplication96 4.4 Binding, Take 2: Multiplication And A Variable Over Cardinalities 97 4.4.1 Background: Ionin And Matushansky 98 4.4.2 Proposal: An Incomplete Lexical Entry 100 4.4.3 A Problem: Even Distribution 100 4.5 Alternatives 102 4.5.1 D‐Operator 102 4.5.2 A Pragmatic Account 104 5 Other Languages 107 5.1 East Cree 107 5.2 Extensionality And Hungarian Determiner Reduplication (D‐Red) 111 viii 5.3 Korean –Ssik, Choe’s “Anti‐Quantifier” (Choe 1987) 113 6 Conclusion 117 References 118 1 1 Introduction 1.1 In the beginning This dissertation grew out of a brief sketch of numeral reduplication in East Cree that appeared in the work of Marie‐Odile Junker (2000, 2007), which I read for a seminar on numerals taught by Roumi Pancheva. That brief introduction raised more questions than it answered, and Cree speakers being thin on the ground in Southern California, I began researching the phenomenon in a language I did have access to: Kannada, a Dravidian language spoken by many USC grad students from Southern India. The initial question was a simple comparative question of how different languages mark distributivity. In both English and Kannada, distributive sentences involve a relation between two pluralities. For example, consider the following distributive English sentence: (1) Each of the lizards painted three cacti. This sentence relates a set of contextually relevant lizards and several trios of cacti. How many cacti ended up being painted depends on the number of lizards. If the lizards are comprised of just two individuals, say Shoshana and Phil, then (1) would be true iff Shoshana painted three cacti and Phil Painted three cacti. In this context, a maximum of six cacti are painted. 1 On the other hand, if the lizards were a bigger set, say Shoshana, Phil, Orin, Guinevere, Jeff, and Phoebe, a maximum of 18 cacti could have been painted: three for each of the six lizards. The lizards determine the final number of cacti. Distributive sentences consistently show this pattern where one set, which this dissertation calls the distributee, is iterated once for each member of the other set. The set that measures out 2 the distributee is called the distributor. 2 In (1), The lizards are the distributor and the cacti are the distributee. When English marks a sentence as unambiguously distributive, it does so with the word each which (at least some of the time) is associated with the distributor. In Cree and Kannada, Numeral Reduplication (henceforth NR), which marks sentences as unambiguously distributive, is associated with the distributee. (2) Muru huDugi‐jaru jEridu‐jEridu pustaka‐vannu wodidru three girl‐pl two‐two book‐acc read‐past‐pl ‘Each of the three girls read two books.’ In this sentence, the girls are the distributor and the books are the distributee. While the English gloss places each adjacent to the girls, Kannada reduplicates the numeral associated with the books. This dissertation started by asking simply what, if anything, this difference means, especially with respect to the interpretation of quantifiers and the generation of distributive readings. I went at this question heavily influenced by the concept of “anti‐quantifier” 3 proposed in Jae‐Won Choe’s dissertation (Choe 1987). This concept trades on the idea that a distributive quantifier such as each has some sort of requirement that it take wide scope over everything, while anti‐quantifiers require that they be within the scope of some other quantificational element. The introduction of an anti‐quantifier into the pantheon of quantificational stuff was not appealing, not least of which because this categorization that some quantifiers want something in their scope is too strong. While the discussion of Beghelli’s Landing Theory of Scope later in this work will show that some quantifiers, due to the position they select for QR, have larger‐ or smaller‐sized domains of scope, it is not clear that any of these quantifiers care about what is in their scope. If regular old 3 quantifiers don’t actually require a lower‐scope quantifier, then why would these so‐called anti‐quantifiers require that they be in some other quantifier’s scope, and how would that be implemented? Rather than develop the notion of anti‐quantifier further, I looked to other elements of the grammar that already require some c‐commanding element. Because I was looking at reduplication, I was influenced by phonological studies of reduplication that treat the reduplicant as being a morpheme that is partially or fully dependent on its base for its phonological form (McCarthy and Prince 1995) 4 . While reduplicants have syntactic and semantic content, their phonological content is either unspecified entirely or underspecified (e.g., in partial reduplication, especially cases like schm‐ reduplication, part of the reduplicant is specified and the other part is drawn from the base). If phonology allows for a defective phonological form which is dependent on its base for its phonological features, I thought it would be a good idea to explore the possibility that the reduplicant is also underspecified in its denotation. As always, one would hope that the accounts that one builds would be useful cross‐linguistically, not just in languages that employ numeral reduplication. Bringing in English was facilitated by Safir and Stowell’s treatment of ‘binominal’ each as an element that relates two quantificational elements (Safir and Stowell 1988). There is a hope, based on the behavior of binominal each, that rather than the exceptionality that Choe reported for these “anti‐quantifiers,” that on some level, every language works like Kannada, Cree, and the other languages that have such markers of distributees. This is the genesis of the main idea of this dissertation: that the reduplicant induces a distributive reading through a dependency relation and a locality condition – in the spirit 4 of binding. This notion is supported by locality conditions on Numeral reduplication which, when compared with the locality conditions of bound elements in Kannada, bear a very helpful resemblance. 5 In addition, as will be shown in Chapter 2, reduplicated pronouns must be syntactically bound. It would be a nice result if the reduplicant in both Numeral reduplication and pronoun reduplication appealed to binding, bringing a unified account of reduplication in the language that much closer. 1.2 Roadmap of Dissertation The remainder of this chapter is devoted to brief sketches of the methodology used and Kannada grammar. While a full‐scale descriptive grammar is far beyond the scope of this dissertation, the grammatical sketch should give the reader some familiarity with the basic properties of the language, particularly those most relevant to this work. Chapter 2 argues that both NR and Pronoun Reduplication must be in the c‐ command domain of another element Chapter 3 uses the locality conditions that restrict the distribution of NR and PR to argue that the restrictions on their distribution truly are in the spirit of Binding Theory. It also considers some alternatives to a binding approach, including one based on the Landing Theory of Scope (Beghelli 1995). Chapter 4 discusses semantic approaches to deriving a distributive reading through binding, exploring the applicability of Safir and Stowell’s binominal each to Kannada (Safir and Stowell 1988), treating the reduplicated numeral as a complex numeral that contains a variable over cardinalities, and treating the reduplicant as a distributivity maker like Schwartzchild’s D‐operator (Schwarzschild 1996). 5 Chapter 5 is the “further directions” chapter. It discusses similar patterns of data in other languages, including a brief mention of the Cree data that originated this project and the Korean data that inspired Choe’s Anti‐Quantifier work. While there are cross‐linguistic similarities, each work raises its own puzzles. Exploring these puzzles in Kannada, and exploring the contrasts between languages would be invaluable to creating a truly comprehensive account of NR and distributivity. Chapter 6 concludes the dissertation. 1.3 Data Collection Methodology The majority of the data in this work comes from elicitation sessions held at USC between 2008 and Spring 2011, supplemented by elicitation data done in Vermont in the winter of 2011/2012. In Los Angeles, I worked with a variety of Kannada speakers, all graduate students studying at USC, who answered an advertisement in the e‐mail newsletter sent out by the Office of International Students. The two Vermont speakers were members of the University of Vermont Indian Students’ Association; one was a graduate student at UVM and the other had recently received his MS. Since all the speakers had answered a general call for speakers, they self‐selected as speakers of the language, and I further limited participants among the respondents to those who professed to have a strong background of daily Kannada use, preferably as their home language. While most speakers I interviewed reported that they were able to speak languages other than Kannada and English, I did not carefully examine whether or not speaker variation was tied to features in their additional languages. Given that numeral reduplication is available in some, but not all, languages spoken by my consultants, it would be beneficial to a further study of the 6 phenomenon and of Kannada regional variation, to identify the extent to which language contact affects speakers’ use of this strategy. I will leave that for another time. Sessions with speakers employed several task types, including translation, “describe‐the‐scenario,” and felicitousness judgments. The primary mode of elicitation were “describe the scenario” tasks, where the speaker would be tasked with creating a Kannada sentence that would describe felicitously a scenario that was designed to have certain distributive, tense, or agreement issues. Further clarification questions regarding possible ambiguities, alternate word orders, additions or subtractions of particles would then be discussed. Translation tasks were kept to a minimum, due to the difficulty of ensuring that the sentence the speaker presents has the same reading as the English sentence, or, in the case of speakers who were unfamiliar with elicitation tasks, even that the sentence provided would be a natural word order. Felicitousness judgments, where a speaker would be asked if a given Kannada sentence fit as a continuation of summary of a story, were used to confirm sentence judgments and further plumb nuances of readings. 1.4 Sketch of Kannada Grammar Kannada is a nominative‐accusative case‐marking language with an unmarked SOV word order. (3) avaLu ra:manige ondu sveTar koNDaLu she Rama‐dat one sweater buy‐pst‐3sf ‘she bought a sweater for Rama.’ (Sridhar 1990:166) 7 (4) Kannada Case Markers Case suffix example Nominative zero, ‐u huDugi(u) ‘girl.Nom’ pustaka ‘book.nom’ Accusative ‐(v)annu Pustakavannu ‘book.acc’ Dative ‐ige, ‐akke huDugige ‘girl.dat’ pustakakke ‘book.dat’ Genitive ‐a pustaka‐da ‘book.gen’ Locative ‐alli Pustakadalli ‘book.loc’ Instrumental ‐inda pustakadinda ‘book.inst’ Nouns are either animate or inanimate, and take different plural markers depending on class. (5) Inanimate Nouns (Sridhar:198) a. ko:lu(gaLu) ‘stick(s)’ b. mara(gaLu) ‘tree(s)’ (6) Animate Nouns (Sridhar:197) a. huDugi(jaru) ‘girl(s)’ b. huDuga(ru) ‘boy(s)’ Plural marking can also be used as an honorific. (7) –ru as an honorific (Schiffman:24) a. maiSTru ‘teacher’ b. Da:kTru ‘doctor’ c. De:vru ‘god’ 8 Plural morphology comes before Case morphology: (8) Pustaka‐gaL‐annu ‘book‐pl‐acc’ 1.4.1 Case marking, Demonstratives, and Specificity Cursory understanding of how specificity, definiteness, and givenness (and related ideas) interact in Kannada grammar will be useful later when the discussion of quantifier interaction is discussed. Like other languages that lack definite determiners, Kannada employs demonstratives as well as a system of Case‐marker optionality to indicate old and new information as well as uniqueness. (9) nannu pustaka(vannu) wodida I‐nom book‐acc read ‘I read a book.’ (10) Nannu ondu pustaka(vannu) wodida I‐nom one book‐acc read ‘I read one book.’ (11) Nannu i: pustaka(vannu) wodida I‐nom this book‐acc read I read this book.’ Kannada’s system is not especially well understood, and elicitations intended to clarify how exactly each of these pieces affect the readings of a given sentence showed significant variation from speaker to speaker as well as from session to session with the same speaker. Some insight comes from work on Turkish, which uses similar pieces to mark definiteness. In Turkish, the presence of demonstratives correlates with a specific reading, as does the presence of case markers. (12) Referential options for the direct object in preverbal position 9 a. (ben) kitap I oku‐du‐m I book read‐past‐1sg ‘I was book‐reading’ (incorporated) b. (ben) bu kitab‐ı oku‐du‐m I this book‐acc read‐past‐1sg ‘I read this book.’ (demonstrative) c. (ben) kitab‐ı oku‐du‐m I book‐acc read‐past‐1sg ‘I read the book.’ (definite?) d. (ben) bir kitap oku‐du‐m I a book read‐past‐1sg ‘I read a book.’ (indefinite) e. (ben) birkitab‐ı oku‐du‐m I a book‐acc read‐past‐1sg ‘I read a certain book.’ (indefinite specific) (Van Heusinger 2002:255 #18) Similar combinations of determiners and case markers are possible in Kannada, and these have been analyzed as having an effect on the definiteness or specificity of that NP. While it is still not clear precisely what effect the presence or absence of an overt Case marker on the object has on the sentence’s interpretation, it is clear that the use of demonstratives and the numeral ondu ‘one’ parallels the use in Turkish. The similar systems represented by Turkish and Kannada are not the only available options for languages to indicate specificity. For example, Algonkian languages use a proximate/obviative system where, in sentences that contain more than one third person argument, one will bear proximate morphology and the others will bear obviative morphology. The proximate argument is the topic of the sentence or otherwise considered more central than the obviative arguments. The verb will also reflect in their morphology whether the agent or the patient is obviative. (13) Mali ‘‐kis‐ewestuwam‐a‐l peskuw‐ol pomawsuwinuw‐ol Mary 3‐perf‐talk.to‐Dir‐Obv one‐obv person‐obv ‘Mary(prox) spoke to one person (obv).’ (Bruening 2001:38 #37a) 10 The guidelines for proximate and obviative marking are, like the rules for case marker dropping in Kannada, complex. 1.4.2 Verbal Domain 1.4.2.1 Agreement Matrix verbs agree with the nominative argument in person, number, and gender. Agreement markers have different forms in different tenses, although much tense and aspect morphology is handled by aspect markers that go between the verb stem and agreement markers. The aspect markers will be discussed later. (14) Present tense ba:(r)‐ ‘come’ (Schiffman:57) Person Singular Plural 1 Bart‐i:ni Bart‐i:ve 2 Bart‐i:(ya) Bart‐i:ri 3 m Bart‐a:ne polite Bart‐a:re F Bart‐a:Le n Bar‐at:e n Barut‐ve (15) Past tense of ba:(r)‐ ‘come’ (Schiffman:58) Person Singular Plural 1 Bande Bandvu 2 Bande Bandri 3 m Banda Polite Bandru F Bandlu n Bantu n Bandvu 11 Kannada has an extensive inventory of aspect markers. However, because an investigation into the interplay of aspect and distributivity would have gotten very complicated, the data in this dissertation intentionally avoids use of the following aspectual markers. (16) Perfective: biDu (Schiffman:82) avan bid‐biT:a he fall‐perf ‘he fell down’ (17) Change of state: ho:gu (Schiffman:82) anna bend‐ho:gide rice cook‐cos the rice has gotten overcooked.’ (18) Continuity, duration, reciprocal: a:Du (Schiffman:82) avar o:D‐a:Did‐ru they run‐cont‐pl ‘they ran around.’ (19) Attemptive: no:Du (Schiffman:82) avan ka:fi kuDid‐no:Dda he coffee drink‐attempt ‘he tried drinking the coffee, he tasted the coffee.’ (20) Exhaustive: ha:ku (Schiffman:82) avan do:se‐yella tind‐ha:kda he pancake‐all eat‐exh ‘he ate up all the pancakes.’ (21) Perfective: iru (Schiffman:82) band‐id:i:‐ni come‐perf‐1s ‘I have come.’ (22) Progressive: –t:a: iru (Schiffman:82) bar‐ta: id:i:‐ni come‐prog ‐1s ‘I am coming’ 12 (23) Finality: –a:gu (Schiffman:82) avan band‐a:tu he come‐fin ‘he finally came.’ (24) Benefactive: –koDu (Schiffman:82) avan kate bard‐koTTa he story wrote‐ben ‘he wrote the story for someone’s benefit.’ 1.4.2.2 Light Verbs Kannada uses a series of verbs such as ‘go’ and ‘do’ as the main predicate in certain constructions where the verb and a noun together describe the action that is done. (25) VadZaradu kallatanavannu aIda‐kkinta hEtSu mandijaru maDidaru Diamond‐of theft‐acc five‐than more persons did `More than five people did the theft of the diamonds.’ These sorts of constructions are often descriptive of emotional states, as well. (26) Kumar Silla‐lannu santosh goLisidannu Kumar Silla‐acc happy made.ms `Kumar made Silla happy.’ 1.4.2.3 Negation Negation is indicated by the negative affix ‐illa on the verb. (27) Varsha manei‐ana kaTTu‐lilla Varsha house‐acc build‐not `Varsha didn't build a house.’ (28) Anurag [avani‐ge hasivu aguta untu anta] heLulilla Anurag he‐dat hungry happening‐is C said‐not `Anurag1 didn't say he1's hungry.’ 1.4.3 Embedded clauses Embedded clauses are marked with one of a number of markers, the most common of which is anta. 13 (29) Avn bartiini anta heeLda he come.1s anta say.past.1s ‘he said, “I will come.”’ (Schiffman:117) Anta can also be used as a matrix verb meaning say, and is often used to embed quoted speech: (30) Avn bartiini anda he come.fut say.3s ‘he said, “I will come.”’ (Schiffman:117) When anta is used alone, it bears agreement morphology as other verbs do, agreeing with the subject for person and number. 1.4.4 Relativization Relative clauses appear to be head‐final, with the head noun following any relative clause that modifies it. (31) Teja [LakSmi bareda pustakavannu] wodidane Teja Lakshmi wrote book‐acc read `Teja read the book Lakshmi wrote.' Speakers will sometimes express a preference for fronting a relative clause to prevent confusion of the matrix and embedded subjects, as in the following: (32) [LakSmi bareda pustakavannu] Teja wodidane Lakshmi wrote book‐acc Teja read `The book Lakshmi wrote, Teja read.' 1.4.5 Adjuncts Adverbials have a relatively unrestrained distribution in Kannada, although their unmarked position is just after the subject. For example, locations such as manei‐alli ‘at home’ can occur in many positions with respect to the other elements of the sentence: (33) Silla manei‐alli ha:lannu kudidaLu Shilla home‐loc milk drank `Shilla drank milk at home.' 14 a. Silla ha:lannu manei‐alli kudidaLu b. Ha:lannu manei‐alli Silla kudidaLu c. manei‐alli Silla ha:lannu kudidaLu A relatively free distribution of adjuncts is expected, given the cross‐linguistic behavior of adjuncts. 1.4.6 Wh-word inventory, wh-in-situ The majority of wh‐words in Kannada are actually ja‐ or je‐ words, and they occur in‐situ unless moved for focus purposes: (34) Wh‐word inventory a. ja:ru 'who' b. je:nu 'what' c. ja:vaga 'when' d. ja:vudu 'which' e. jelli 'where' f. ja:(tak)ke 'why' g. He:ge: ‘how’ h. jeSTu 'how many' i. jent(a)ha 'what kind' (35) sudha:ma ja:farni‐ge na:Le maida:nadalli ye:nu koDalidda:ne? Sudhama Jaffar‐dat tomorrow playground‐loc what give‐inf‐be‐n.past‐3sm 'What is Sudhama going to give to Jaffar to on the playground?' (Sridhar:10 #37b) (36) sudha:ma ya:ri‐ge na:Le maida:nadalli ka:lceNDannu koDalidda:ne? Sudhama Jaffar‐dat tomorrow playground‐loc football‐acc give‐inf‐be‐n.past‐ 3sm 'Who is Sudhama going to give the football to on the playground tomorrow?' (Sridhar:10 #37c) In negative contexts, wh‐words are used as polarity items. Later in this work, the exhaustive interpretation that reduplication of wh‐words lends to an utterance will be 15 discussed. For now, observe that in negative contexts, reduplicated wh‐words retain their polarity item interpretation (37) Companiu java engineersigu kelasavanu koDalilla. Company what engineers job not:give 'The company didn't hire any engineers.’ (38) Companiu java‐java engineersigu kelasavanu koDalilla. Company what‐what engineers job not:give 'The company didn't hire any engineers, ever.’ (39) Avaru jakjak bITTru anta nanige bekagilla They why why left that me‐to don't want `I don't care why they left.' (About their individual reasons) These reduplicated wh‐words in negative contexts continue to have a negative interpretation. These sentences are a bit stronger or more emphatic than the non‐ reduplicated versions. 1.5 Reduplication Types Kannada uses reduplication in many different ways, not all of which are going to be discussed at length in this dissertation. This section serves as a thumbnail sketch of the major types of reduplication in the language. The next chapter will argue that two of these types, Numeral Redulication (NR) and Pronoun Reduplication (PR) are distinct from the other reduplication strategies in that they both must be within the c‐command domain of another element. 1.5.1 Numeral Reduplication (NR) indicates distributive reading Sentences that contain two pluralities are often ambiguous; they can have either a collective or a distributive reading. This is true for both English and Kannada: (40) Three girls read two books. 16 (41) Muru huDugi‐jaru jEridu pustaka‐vannu wodidru three girl‐pl two book‐acc read‐past‐pl ‘Three girls read two books.’ These sentences are compatible with two situations: one in which there were a total of two books read and another where there were six books read. 6 In English, if one wanted to make clear that one was talking about a situation where six books were read, one would probably add each: (42) Each a. Each of the three girls read two books. b. Three girls each read two books c. Three girls read two books each. Kannada has available to it a quantifier similar to English’s each: prati. Unlike each, prati occurs only adjacent to the distributor. (43) Prati huDugi jEridu pustaka‐vannu wodida each girl two book‐acc read‐past ‘each girl read two books.’ Along with this strategy, as already mentioned,Kannada can also indicate a distributive reading by reduplicating a numeral associated with the distributee: (44) Muru huDugi‐jaru jEridu jEridu pustaka‐vannu wodidru three girl‐pl two two book‐acc read‐past‐pl ‘Three girls read two books each.’ This example is identical to (41) except that the numeral jEridu, ‘two’ is reduplicated. This sentence is compatible only with distributive readings. It is judged false in a context where a total of two books were read a group effort by the three girls. The fact that NR marks the distributee sets this strategy apart from inherently distributive determiners such as English each and every, which mark the distributor when used as determiners. Marking the distributee means that the distributor is unspecified. 17 Unlike English sentences that use each and every, which are unambiguous with regard to their distributor, Kannada NR sentences can be ambiguous. (45) Muru huDugaru aidu huDugijarige muru‐muru huvu koTTu three boys five girls‐dat three‐three flower give ‘Three boys gave three three flowers to five girls.’ The distributee ‘three‐three flowers’ can be in a distributive relation with either the dative argument ‘five girls’ or with the subject, ‘three boys.’ In the first case, the boys (as a group) gave three flowers to every one of the five girls. In the second reading, each one of the boys gave three flowers to a group of five girls. Kannada is also able to identify an understood plurality of events as the distributor rather than a numerically quantified NP. The following exemplifies when such an event reading is the only option; there is no other plurality involved in the sentence: (46) Priya eradu‐eradu ko:tigaLannu noDidalu Priya two monkeys saw ‘Priya saw two‐two monkeys.’ Context would fill in exactly what type of event is acting as the distributor, whether it is every day, or whenever Priya went to the zoo, or simply everywhere she looks. Out of the blue, the sentence is judged somewhat strange, but becomes perfectly fine in an iterative context. The same is not true when the possibility of a plurality of events is removed, as in the following pair of sentences, which specify a particular time for the sighting of monkeys: (47) Priya aidu muvateradakke eradu ko:tigaLannu noDidalu Priya five thirty‐two two monkeys saw Priya saw two monkeys at 5:32. (48) *Priya aidu muvateradakke eraderadu ko:tigaLannu noDidalu Priya five thirty‐two two‐two monkeys saw Priya saw two‐two monkeys at 5:32. 18 While the non‐reduplicative sentence is acceptable, NR in this context is not. The lack of either a plural nominal or a plurality of events in (48) leads to the unacceptability of NR in this sentence. In the following chapter, more will be said about the distribution of NR. While it has been shown here that NR requires some sort of plurality to be acceptable, it will be shown that the plurality must c‐command the reduplicant, and that there are locality conditions on this relation which resemble the locality conditions of Kannada reflexives. One final note before moving on to the next type of reduplication: numerals are the only quantifiers able to undergo this type of reduplication: (49) *Muru huDugijaru {je:lla‐je:lla/kelavu‐kelavu} pustaka‐vannu wodidru three girl‐pl all/some book‐acc read‐past‐pl ‘Three girls each read all/some of the books.’ Non‐reduplicated versions are fine, but reduplication is not possible. 1.5.2 Pronoun Reduplication (PR) Sticking with examples that have a c‐commanding antecedent and a universal quantifier that allows for variable binding (and thus covariation), here are some examples where the subject is the antecedent and the object is a bound variable. In these cases, numeral reduplication serves to disambiguate; a single pronoun may be bound or referential, but a reduplicated pronoun must be bound. (50) Prati huDuga avana baLi Idda ha:vannu noDida. Every boy his side was snake‐acc saw `Every boy1 saw the(/a) snake next to him1/2.' The pronoun in (50) can have either a bound or a referential reading. It is compatible with a scenario where each one of the boys saw a snake next to himself (the 19 bound reading), and it’s also compatible with a scenario where each of them saw a snake next to some other person (the referential reading). When the pronoun is reduplicated, only the bound reading is available. (51) Prati huDuga avana‐avana baLi Idda ha:vannu noDida. Every boy his‐his side was snake‐acc saw `Every boy1 saw the(/a) snake next to him1/*2.' 1.5.2.1 Reduplicated pronouns must have an antecedent While referential pronouns can appear without an antecedent, syntactically bound pronouns require an antecedent within their local domain. If reduplicated pronouns must be syntactically bound, then the Kannada equivalents of the following English sentences should not allow reduplication. (52) Alice kissed her/him/them. (53) The boys kissed her/him/them. In both sentences, the pronoun is too close to the subject of the sentence for syntactic binding to hold in English. 7 In addition, there are gender and number mismatches. These mismatches also apply in Kannada. The prediction is that when there is a mismatch, the bound reading is not possible, and thus reduplication is also not possible. (54) Alice (*ava‐)avanannu noDida. Alice him‐him‐acc saw ‘Alice saw him‐him.’ (55) Hudugaru (*ava‐)avaLannu noDidru boys her‐re‐acc saw ‘The boys saw (her‐)her.’ For numeral reduplication, event readings were able to rescue reduplicants that had no c‐commanding distributor. Adding an iterative adverb such as ‘every day’ was shown in the NR cases to facilitate an event reading. If the two types of reduplication are strictly 20 parallel, one might expect that ‘every day’ would also improve numeral reduplication in cases with no overt antecedent. (56) Alice dIna (*ava‐)avanannu noDida. Alice daily him‐him‐acc saw ‘Alice saw him‐him daily.’ 1.5.3 ‘One’ reduplication Kannada reciprocals take the form of a reduplication of the numeral ‘one,’ with slightly different forms of the numeral for animate and inanimate NPs. (57) Anurag m6ttu Kumar obb‐obar‐annu Kanadinalli nodikondaru Anurag and Kumar one‐one‐acc mirror‐loc saw(pl) ‘Anurag and Kumar saw each other in the mirror.' (58) Bassu ka:ru onda‐kk‐ondu Dikki hoDedavu bus car one‐dat‐one collision hit‐psr‐3npl ‘The bus and car hit each other.’ (Sridhar:#450) In the animate example, Anurag saw Kumar and Kumar saw Anurag. It is not compatible with a scenario where each boy saw himself. Similarly, in the inanimate example, the bus hit the car and the car hit the bus. ‘One’ reduplication differs considerably from reciprocals in English in that it can occur without a clear antecedent. In these cases, the interpretation is much more like each alone, rather than each other. Here are some cases of ‘one’ reduplication being used as a type of determiner: (59) Ondu ondu hudugi Silpa‐ge avara pustaka koTTaru One one girl_1 Shilpa‐dat their_1 book give‐f `Each girl gave Shilpa her (own) book.' (60) Ondu ondu hudugi Silpa‐ge avaLa pustaka koTTaru One one girl Shilpa‐dat her book give‐f `Each girl_1 gave Shilpa her_2 book' 21 In each of these cases, ‘one’reduplication precedes a noun: ‘one‐one boy/girl.’ These cases are not limited to high positions with no c‐commanding DP. The following show objects with determiner‐like ‘one’ reduplication as well: (61) Divya ondu‐ondu hudug6‐nigu praSnei‐gaLu kElidaLu Divya one one boy‐? Question‐pl asked `Divya asked each of the boys the questions (one boy after another) (62) Divya ondu ondu huduganigu bere bere praSnei kElidaLu Divya one one boy.pl.? different different question asked `Divya asked each of the boys different questions.' The ‘each’ interpretation of ‘one’ reduplication can occur in object position without this determiner‐like pattern, as in the following: (63) Ni:mmalli obbobbarige hu:vu kortini Among‐you each‐each‐to flowers give‐1s‐future `I will give flowers to each of you.' 1.5.4 Wh-word Reduplication In addition to reduplicating numerals and pronouns, wh‐words may also reduplicate. Reduplicated wh‐words give the sentence an exhaustive reading, where the answer is expected to be everything that satisfies the requirements of the question. For example, in the following would be answered with a full list of everyone Rohit saw, (64) Rohit jar6‐jar6na noDda Rohit who‐who see? `Who all did Rohit see?' If the wh‐word were not reduplicated, then the answer could have left one of more members of the set of people Rohit saw out. However, it is not required that there be more than one person in the answer to this question, only that there be no other true answers. The full complement of wh‐words can reduplicate, in all positions. 22 (65) jaru‐jaru Rohitanna noDidru who who Rohit‐acc saw‐pl ‘Who‐who saw Rohit?’ (66) jaru‐jaru muru hannu tindru? who who three fruit ate‐pl ‘Who‐who ate three fruits?’ (67) Rohit jaru‐jaru‐ge pustaka‐gaLu kotta Rohit who who book‐pl buy `Who all did Rohit give a book to?' (68) JEn‐jEn bIttu What‐what fell `What all fell?' (69) Varsha jEn‐jEnu kondkondLu Varsha what‐what buy `What all did Varsha buy?' The previous examples have intentionally used only singular NPs to force event readings: multiple events of seeing different people, of buying different things, of giving books of different people. When there is a plural NP in the sentence, this opens the possibilities further, such as in the following case, which allows for either a group gifting by the boys to Sam, or individual boys giving different things to Sam: (70) Hudugaru Sam‐ge jEn‐jEnu koTTru Boys Sam‐to what‐what gave `What all did the boys give Sam?' This is to be expected, as a non‐reduplicated wh‐word would experience this ambiguity as well. The reduplication of adjunct wh‐words brings the relationship between exhaustivity and events to the fore. For reduplication of a wh‐word to be good, there should be an expectation that there can be more than one answer. Speakers report that in the following sentence, the tense/aspect on the verb indicates a single, completed action and they do not accept reduplication of the wh‐word in this context. 23 (71) *Basu javaga‐javaga b6nda? Bus when‐when arrive ‘When‐when did the bus arrive?’ The unacceptability of wh‐reduplication in (71) is expected given that exhaustivity expects more than one possible answer, and when there can only be one (and in this case, because of tense and aspect), reduplication is also weird. Changing the form of the verb to one which allows multiple events of arriving yields a sentence which does allow wh‐ reduplication: (72) Basu javaga‐javaga bartade Bus when when arrive(nonpast) ‘When‐when does the bus arrive?’ Similarly, switching the singular subject for a plural one is not only fine, but allows for answers that vary for each member of the plurality. (73) Hudugijaru javaga‐javaga b6ndru/haDidru Girls when when arrive `When did each of the girls arrive/sing?' This question is likely to be interpreted as asking about the arrival of each girl in the group, although with context, it could be interpreted like the bus example, as asking about a sequence of arrivals of a group of girls travelling together. (74) Hudugijaru jElli‐jElli haDidru Girls where where sing `Where all did the girls sing?' (75) Avaru heNheNge allige hodru They how how there go `How did each of them go there?' (76) Ni:nu java java uri‐ge hodei You where where town‐to went `Which‐which towns did you go to?' If wh‐reduplication is only good in sentences that have some sort of distribution over events going on, then it stands to reason that sentences with wh‐reduplication are 24 able to host numeral reduplication while analogous questions with single wh‐words do not. For example, the following example has no available distributor for the reduplicated numeral. There is no available plural in the sentence, and the sentence is not interpreted as involving multiple events of giving. (77) *Jaru Alice‐ige muru muru huvu koTTru Who Alice‐dat three three flower gave `Who gave Alice three‐three flowers?' Numeral reduplication is acceptable in this sentence when the wh‐word is reduplicated, suggesting that the quantification over events that the reduplication requires is also able to connect with the numeral reduplication. (78) {Jaru‐jaru, jar‐ella} Alice‐ige muru muru huvu koTTru Who‐who who‐all Alice‐dat three three flower gave `Who (exhaustive) gave Alice three‐three flowers?' 1.5.5 Purely Phonological Reduplication: Echo Word Reduplication NR, PR, ‘one’ reduplication, and wh‐word reduplication are the focus of this dissertation as reduplicative phenomena that have a syntactic and semantic component. In addition to these phenomena, Kannada employs other reduplicative strategies which do not fall within the core of the phenomena treated in this dissertation. One such type of reduplication is a partial reduplication that indicates vagueness. The reduplicant takes the form of the second syllable of a bisyllabic word and is suffixed to a fixed syllable. The fixed morpheme is either gi‐ or pa‐. The unmarked form is gi‐, and pa‐ is used when the base’s initial syllable is gi. (79) 𝜎 ! 𝜎 ! 𝑔𝑖𝜎 ! a. Huli gili ‘tigers or other animals (like them)’ b. aaTa giiTa ‘games or other diversions’ 25 c. mane gine ‘houses or other buildings’ d. uuTa giiTa food or other edibles’ (80) 𝜎 ! 𝜎 ! 𝑝𝑎−𝜎 ! a. giLi paLi ‘parrots or other birds’ b. giiTu paaTu ‘lines or other markings’ Schiffman (125) observes that the distribution of gi‐ and pa‐ is not entirely complimentary. When pa‐ is used when it is not phonologically conditioned, he reports that it has a disjunctive interpretation and gives the following examles showing the contrast. His glosses are not consistent in their use of connectives, given that the examples in (79) are glossed as being disjunctive without pa‐. One would expect, that (a) and (c), like the members of (79), would be disjunctive but their glosses are conjunctive. (81) reduplicants, coordination, and disjunction a. uuTa giiTa ‘tigers and other animals’ b. uuTa paaTa ‘tigers or other animals’ c. tiNDi giNDi ‘snacks and other edibles’ d. tiNDi paNDi ‘snacks or other edibles’ In all, this section is little more than a footnote to illustrate that there is more to the world of reduplication in Kannada than the structure‐sensitive, total reduplication strategies that are at issue in this dissertation. In the next chapter, the case will be made that NR and PR both are not only sensitive to the syntactic structure around them, but that they have certain requirements of the structures that contain them, including a requirement that they be within another element’s c‐command domain. 26 2 C-Command in NR and PR This section will use variable binding as its primary diagnostic to determine whether or not c‐command holds between two positions in Kannada. 2.1 Matrix subjects 2.1.1 NR in subjects As previously mentioned, event readings are the only reading available when no plural individual is present in the sentence, as illustrated by the following: (82) Priya erad‐eradu ko:tigaLannu noDidalu Priya two monkeys saw ‘Priya saw two‐two monkeys.’ This sentence can only describe a situation where Priya saw pairs of monkeys everywhere she looked or every time she looked somewhere. A similar effect occurs when the matrix subject is reduplicated. In the following example, the interpretation is necessarily iterative: (83) Ibbibbaru huDugaru haDannu haDidaru Two‐two boys song sang `Two boys sang a song (iteratively).' This example might describe an audition scenario where there are several pairs of boys who all have to sing a song for the judges. Every pair sings its song and then the next pair sings its song. The distributive relation is between the pairs of boys and the events of singing: for every singing event, there were two boys. The relation between the distributor and the distributee in Kannada appears to be determined by surface scope. Even when there is another plurality farther down in the sentence, the reduplicant cannot take inverse scope under that plural NP. 27 (84) Ibbibbaru huDugaru nalku m6gagaLanu noDidru Two‐two boys four monkeys saw‐pl `Every time the four monkeys were seen, they were seen by two boys.' ‘#Each one of the four monkeys was seen by two boys.’ One would correctly predict that when there is a plural NP that c‐commands a subject then distribution over individuals is also possible. Such is the case for the subjects of embedded clauses, which are in the scope of the matrix subject. (85) A:ru hudugaru [muru muru hudugijarannu hu:vu kondukoLalu] he:ladru Six boys three three girls flowers buy‐inf told `Six boys told 3‐3 girls to buy flowers.' This sentence is compatible with a situation where each of the six boys told a different set of three girls to go buy flowers. This reading is compatible with ‘the boys’ acting as the antecedent of the reduplicant. It is important to notice, however that in sentences where there are both an available NP and event to act as a distributor, then it appears that both can be distributors. Consider the following sentence, which has both a plural subject and an adverb that emphasizes iterativity: (86) Ibbaru huDugaru dInaLu nal6ku nal6ku baLEhannu tIndaru two boys daily four four bananas ate 'Two boys ate four bananas daily.' This sentence describes a situation where a total of eight bananas get eaten each day: four by one boy, four by the other. In this sentence, there is a nested distribution. There is distribution of bananas over individuals, and this mapping is distributes over days. 2.1.2 PR in Subjects It is predicted that because matrix subjects inhabit the highest position in a clause’s structure, a pronoun in subject position cannot be syntactically bound by an antecedent 28 lower in the structure. In English, this is illustrated by the lack of covariation possible in the following sentences: (87) *His mother1 kissed every boy1. (88) *He1 said that every boy1 kissed Alice. When the QP is in subject position, it c‐commands the pronoun in object position. This configuration allows variable binding. (89) Every boy1 kissed his1 mother (90) Every boy1 said that he1 kissed Alice. Pronoun reduplication in sentences equivalent to the English cases where the intended antecedent doesn’t c‐command the pronoun: (91) *Avara‐avara ta:i prati huduga‐vannu noDida their‐their mother every boy‐acc saw ‘Their mother1 saw every boy1.’ (92) *Priya‐ge prati hudiga muttu kottalendu avaru‐avaru helidaru. Priya‐dat every boy kiss do‐embedded them‐them say‐pl ‘They‐they1 said that every boy1 kissed Priya.’ If it were simply a matter of getting an antecedent to a position where it could c‐ command the reduplicated pronoun, scrambling might seem like an option. Pronoun reduplication differs from NR in that event readings do not arise. Adding iterative contexts or adverbs like dIna ‘daily’ do not save pronoun reduplication that has no antecedent: (93) *avaru‐avaru dIna hadidru. they‐they daily sang‐pl ‘They sang every day.’ The fact that pronoun reduplication does not occur in matrix subjects is an artifact of c‐command, and is not connected to subject position specifically. As with NR, embedded subjects can be acceptable if there is a c‐commanding antecedent. 29 (94) jella hudugaru avaru‐avaru Priya‐ge muttu kottiddarare endu helidaru all boy‐pl they‐they Priya‐dat kiss do‐pl Comp say‐pl ‘All the boys1 said they1 kissed Priya.’ 2.2 Relative Clauses Showing that matrix subjects cannot host NR or PR while objects and embedded subjects can supports the claim that these reduplicants must be within the c‐command domain of another element, but that is not the only explanation of this distribution. These facts are also compatible with a linear precedence requirement. Looking at examples where the distributor (for NR) or the antecedent (for PR) is within a relative clause allows for these elements to be in a relatively high position, but not one that c‐commands the reduplicant. Because these elements are inside an island, they are not able to QR to even higher positions that would allow them to c‐command the reduplicant. The following sections look at NR and PR and show that neither allow a relation between something within a relative clause and a reduplicant in the matrix clause. 2.2.1 NR and Relative Clauses It has already been shown that subjects can be a distributor for an object in the same clause, and NR is possible in these configurations. Subjects that are not pluralities cannot act as distributors. NR in these cases instead selects a plurality of events as its distributor. Based on these facts, it seems to be the case that the reduplicant looks upward for a plurality. Subjects that are modified by relative clauses provide a useful place to show that the reduplicant is specifically looking for a c‐commanding plurality. Consider the following example: (95) #[The boy who poked two teachers] read three books each. 30 The intended distributive relation is one where the two students is the distributor and the three books is the distributee. If this reading were possible, then the teacher reading the books would have read six books: three for the first student that poked them, and three for the second student. This reading is completely unavailable. The analysis being that the plurality two students is not in a position to c‐command the intended distributee. Because it is embedded within an island, the intended distributor cannot undergo QR to move to a position that would c‐command the distributee. Turning to Kannada, the same distribution is observed. NR is not acceptable in sentences such as the following where pluralities that are embedded within relative clauses that modify atomic subjects. (96) *[i: huduga jeridu maiStru‐annu dZagadidno] muru‐muru pustakavannu wodida this boy two teacher‐acc pinch three‐three book‐acc read ‘The boy that poked two teachers read three books (per teacher).’ If it were the case that the reduplicant were simply looking for any plurality up above it, these examples should be acceptable, but they are not. 2.2.2 PR and Relative clauses A similar point is to be made about PR in relative clauses. Pluralities within relative clauses that modify atomic subjects are not able to bind pronouns in the matrix clause. Reduplicated pronouns are not possible, and while single pronouns are acceptable in these contexts, they have only the referential reading. (97) *[i: huduga prati maiStru‐annu dZagadidno] avanna‐avanna wodida this boy every teacher‐acc pinch him‐him saw ‘The boy who pinched every teacher1 saw him1.’ This distribution is expected if the reduplicant causes the pronoun to require a bound reading, and thus to require a c‐commanding antecedent. Single pronouns, which 31 are able to have a referential reading, are available in a context where the obligatorily bound reduplicated pronouns are not. 2.3 Ditransitives 2.3.1 NR and Ditransitives Ditransitives are a unique syntactic environment in which to explore the QR possibilities of different quantifier types because they are a place where two constituents, both arguments, are relatively low in the structure. When looking at Kannada, this is especially important because of the unavailability or reverse scope readings; as illustrated in the previous section, NR in matrix subject position allows only event readings. A reduplicated subject distributee cannot connect with a distributor in the object position. This suggests that surface c‐command is a relevant property in the availability of NR, and looking at the availability of NR in ditransitives provides another contexts in which c‐command between the intended distributor and the reduplicant can be shown to be a condition of NR. Early accounts of ditransitives entertained several logical possibilities for structural configurations: a tripartite structure, a structure where the two arguments form a constituent together, and a binary branching structure where the first argument first forms a constituent with the verb before taking the second argument. (98) Early generative approaches to ditransitives a. [VP [V ′ V DP1 DP2]] (Oehrle 1976) b. [VP [V ′ V [[ e DP1 ] DP2]]] (Kayne 1981) c. [VP [V ′ [V ′ V DP1] DP2]] (Chomsky and Lasnik 1977, Chomsky 1981) The binding facts presented in (R. Larson 1988) argue for distinct structures for the English Double Object construction and for the Dative construction, both of which have 32 clear asymmetries between the two arguments. In the Double Object construction, the indirect object c‐commands the direct object, and so while the indirect object can bind the direct object, the reverse is not possible: (99) Luis gave [every girl]1 her1 award. (100) *Luis gave her1 [every girl]1’s award. The unavailability of binding in (100) shows that the quantifier every girl is not in a position to c‐command the pronoun her. The reverse relation between the two arguments holds for datives. In the dative construction, the direct object is able to bind the indirect object, but not the reverse: (101) Luis presented [every girl]1 to herself1. (102) *Luis presented herself1 to [every girl]1. These binding facts have been used to argue for particular structures of ditransitives in English. The situation for Kannada has more options than English does, due to the availability of scrambling in this language. Not only are there the two options of which argument is the quantifier and which is the variable, but the linear order of the two arguments can be switched. It is important to notice, though, that although all four orders are possible, variable binding is not available in all four cases. This is to be expected if there is c‐command between the arguments underlyingly. As in the arguments for the structure of ditransitives in English, variable binding should only be possible in structures where the quantifier c‐commands the variable. When the argument which in its base position c‐commands the other argument is the quantifier and the argument that occupies the lower base position contains the variable, the surface word order should not matter. Scrambling should not break the binding relation that is 33 formed before scrambling applies. In the opposite case, when the intended binder for the variable starts out in the position that is c‐commanded by the argument that contains the variable, then scrambling might be able to save the structure by moving the intended binder to a position that c‐commands the variable. According to this line of reasoning, initial data suggests that the dative argument starts out lower than the accusative argument. As predicted, either word order is acceptable when the accusative argument contains the quantifier and the dative contains the variable: (103) Na:nu [prati ondu huv‐annu] [adara florist‐ge] kaLiside I every one flower‐acc its florist‐dat sent 'I sent [every flower] 1 to its 1 florist.' (104) Na:nu [adara florist‐ge] [prati ondu huv‐annu] kaLiside I its florist‐dat every one flower‐acc sent 'I sent [every flower] 1 to its 1 florist.' (105) Kumar [prati huDugana1 pustakavannu] [avana‐ige]1 koTTanu ‘Kumar gave every boy’s book to him.’ (106) ?Kumar [avana‐ige] [prati huDugana pustakavannu] koTTanu ‘Kumar gave every boy’s book to him.’(poetic, requires pauses) If the accusative argument starts out in a position that c‐commands the dative argument, then examples where a variable in the dative argument is bound by a quantifier in the accusative argument should be possible due to the appropriate c‐command relation hold before scrambling has applied. These examples in (104) and (106) show that such binding is possible. Examples where the dative argument binds a variable in the accusative argument are correctly predicted to bad when the accusative argument linearly precedes the dative. While scrambling is able to move the antecedent to a c‐commanding position and thus 34 allows binding, in examples where the variable linearly precedes the quantifier, it at no point is in the domain of that quantifier, so binding cannot take place. (107) Na:nu [prati ondu florist‐ge] 1 [avana1 huv‐annu] kaLiside I every one florist‐dat his flower‐acc sent 'I sent [every florist] 1 his 1 flower.' (108) *Na:nu [avana1 huv‐annu] [prati florist‐ge] 1 kaLiside I his flower‐acc flowers every florist‐dat sent 'I sent his1 flowers to every florist1.' (109) Kumar [prati huDuganige]1 [avana1 pustakavannu] koTTanu ‘Kumar gave every boy his book.’ (110) *Kumar [avana1 pustakavannu] [prati huDuganige]1 koTTanu ‘Kumar gave every boy his book.’ The generalization for all four patterns is that while the preferred order is one where the quantifier precedes the variable, the only case where the variable cannot come first is one where the variable is accusative. This is consistent with the accusative being the higher argument underlyingly. With these structural considerations taken care of, now comes the considerably trickier task of sorting out the NR distribution patterns. As with the binding facts, NR in the accusative argument is acceptable in either order. (111) Kumar [huDugarige] [jEridu‐jEridu praSneigaLannu] kElidanu ‘Kumar asked the boys two‐two questions.’ (112) Kumar [jEridu‐jEridu praSneigaLannu] [huDugarige] kElidanu The structure suggested by the binding facts predicts that sentences where NR is in the accusative argument and precedes the intended distributee in the dative argument will not be acceptable. In fact, both orders were judged to be acceptable: (113) Kumar [jEridu‐jEridu huDugarige] [praSneigaLannu] kElidanu ‘Kumar asked two‐two boys questions.’ 35 (114) Kumar [praSneigaLannu] [jEridu‐jEridu huDugarige] kElidanu ‘Kumar asked questions of two‐two boys.’ This is a puzzle, because this is supposed to be the pair that crucially shows that the c‐command relation rules out (113). However, the most salient reading provided by the speakers for both of these sentences was an event reading. The event reading is one where every time Kumar asked some set of questions, he asked pairs of boys those questions. This reading is very close to the intended reading but differs in that there is no clear mapping between the questions and boys. A distributive reading that distributes pairs of boys over questions would have a question‐to‐pairs of boys mapping. 2.3.2 Ditransitives and Pronoun Reduplication In the NR section on ditransitives, pronoun binding was used as a diagnostic for c‐ command. It was shown that that in general, cases where the pronoun linearly precedes its intended antecedent are less acceptable; the pattern of acceptability was argued to suggest that the basic word order is one where the accusative argument c‐commands the dative argument. The other word orders are derived by scrambling the dative argument above the accusative. Reduplicated pronouns have roughly the same distribution as single pronouns. Examples where the reduplicate pronouns linearly precede their antecedent are unacceptable: (115) Lakshmi [jElla huDugarigu]1 [avar‐avara1 praSnei] kElidalu Laksmi all boys their their question asked ‘Lakshmi asked all the boys1 their1 questions.’ 36 (116) *Lakshmi [avar‐avara1 praSnei] [jElla huDugarigu]1 kElidalu Lakshmi their‐ther question all boys asked ‘Lakshmi asked all the boys1 their1 questions.’ (117) Lakshmi [huDugara1 praSneiannu] [ava‐avarige]1 kElidalu Lakshmi boy’s questions‐acc them‐them‐dat asked ‘Lakshmi asked them the boy’s questions.’ (118) *Lakshmi [ava‐avarige]1 [huDugara1 praSneiannu] kElidalu Lakshmi them‐them‐dat boy’s question‐acc asked ‘Lakshmi asked them the boy’s questions.’ The judgements provided for the case where the dative pronoun precedes an accusative quantifier differ in that these were judged as sompletely unacceptable while the single pronouns and the NR cases were questionable. Still, a basic pattern emerges: (119) Ditransitive patterns: Pronouns PR NR Dat, Acc QP, x OK OK OK x, QP ? * ? Acc, Dat QP, x OK OK OK x, QP * * * 2.4 Adjuncts and c-command Yet another place to look at c‐command and scrambling is with adjuncts. Pronoun binding into and out of adjuncts can indicate c‐command relations: (120) Every girl1 danced because {she1 /her1 brother} won a prize. (121) *She1 danced because {every girl1/every girl1’s brother} won a prize. 37 These binding facts are consistent with the adverbial phrase starting out lower than the matrix subject. While binding is all right when the matrix subject binds a pronoun in the adverbial phrase, when the intended antecedent is in the adverbial phrase and the pronoun is the matrix subject, binding is not acceptable. That is to be expected if the matrix subject c‐commands the adverbial phrase. Fronting the adverbial phrase results in acceptable sentences whether the adverbial phrase contains a pronoun or QP: (122) Because {she1 /her1 brother} won a prize, every girl1 danced. (123) Because every girl1 won a prize, {she1 /her1 brother} danced. The contrast returns when the QP is deeper in the adverbial, as in the following pair (124) Because Alex kissed her1, every girl1 danced. (125) ?*Because Alex kissed every girl1, she1 danced. The second sentence is not good. This makes sense because every girl is too deep int eh structure of the AP to c‐command the pronoun no matter what stage in the derivation binding is paying attention to. However, since there is no systematic study of Kannada adjunction patterns, it’s not a good idea to assume that Kannada always adjoins various types of adjuncts where one might expect if one were following any of the usual adverb models (cf. Cinque 1999, 2004 and Ernst 1984). Nevertheless, assuming such a facile understanding of adjuncts in the language, it is interesting that sentence‐initial adjuncts can have reduplicated pronouns that are bound by something in the matrix clause: (126) Avara(‐avara) adjapakaru Chennai‐jElli Irua karaNa aIdu hudugijaru alli‐ge ho:gguttare Their(‐their) teachers Chennai‐loc stay because five girls there‐to go(3fpl) `Five girls are going to Chennai because their (own) teachers are there.' 38 The acceptability of this sentence suggests that the reduplicated pronoun in the adverbial clause is underlyingly in a position where it is in the c‐command domain of the antecedent, which is in the matrix clause. 2.5 Restrictions on what can c-command the reduplicant 2.5.1 Distributors must be pluralities 8 The fact that NR requires either a plural DP as a distributor or a plurality of events is not surprising; distributivity in general requires distributors to be pluralities. This is also the case with English. In the following examples, no distributive reading arises, and the distributive marker each cannot be present: (127) John ate three apples (*each). (128) Australia gave aid to two countries (*each) It is unsurprising that NR wants pluralities as its distributor, but useful to explore what sorts of pluralities can serve as its distributor. This section shows that any plurality, including universal quantification over worlds, is a possible distributor for NR. Universal quantifiers, modified numerals such as more than five are possible distributors: (129) Prati huDugi jEridu jEridu ga:Di gaLannu toLEDaLu Every girl two two car‐pl‐acc washed `Every girl washed two cars (each).' (130) JElla huDugi‐jaru jEridu jEridu ga:DigaLannu toLEda‐ru all girls two two car‐pl‐acc washed‐pl ‘All the girls washed two cars (each).’ (131) [Aidu kinta {Jaste/kadime} hudugaru] muru muru pustaka wodidru Five than {more/fewer} boys three three book read `More/fewer than five boys read three books each.' (132) i: varSa [ho:da varSa kindlu kaDime hudugaru] muru muru pustaka wodidru This year last year compare fewer boys three three books read `This year, fewer boys than last year read three books each.' 39 Coordinated nominals are also viable distributors. This is especially unsurprising if one takes the view of coordination that it involves universal quantification over the elements in the coordinated set. (133) Naveen matte Ganesh muru muru pustaka takoLdru Naveen and Ganesh three three book took `Naveen and Ganesh bought three‐three books.' Plurals that do not have a quantifier can also be distributors. (134) huDugi‐jaru jEridu jEridu ga:DigaLannu toLEda‐ru girls two two car‐pl‐acc washed‐pl ‘(The) girls washed two cars each.’ In addition to the nominal distributors, there are a variety of event distributors that are possible. Overt adverbials that introduce a plurality of events such as dInaLu ‘daily’ make the event reading more easily accessible, although they are not required if the context is iterative. (135) Rama (dInaLu) nalku nalku m6ngagaLannu noDida Rama daily four four monkeys saw.ms ‘Ram saw four‐four monkeys (every day).’ In addition to temporal adverbs being possible distributors, quantification over worlds, such as in generic sentences, allows NR. In English, generic interpretations can occur with indefinites as well as bare plurals, like rabbits. In order to have a generic interpretation, they must occur in certain sentence types or with adverbs that quantify over worlds. (136) Usually, a rabbit eats carrots. (137) If a rabbit grows wings, something’s wrong. The adverb usually and the conditional require quantification over a set of worlds. The conditional is taken to be universal quantification over contextually relevant worlds, 40 while usually (I suppose) has a lower threshold, and is satisfied when the proposition is true in most contextually relevant worlds. Because generics such as these involve a plurality of worlds, it is predicted that similar generic sentences in Kannada will allow NR. Generic sentences in Kannada are indicated by a morpheme –e on the verb, which Schiffman refers to as a habitual marker (Schiffman 1983:57). (138) MoLagaLu tumba metteige iruttave Rabbits really/more/very soft are `Rabbits are really soft.' (139) TSukigaLu doDDadagi irutave Stars big are `Stars are big.' (140) MoDalane warSada huDugaru Chomsky woditare First year boys Chomsky read `First year boys read Chomsky.' Each of these sentences is a property true of a kind in all relevant worlds. It is possible to use numeral reduplication in such generic sentences, as the following example shows. (141) MoDalane warSada huDugaru (muru)muru pustaka woditare first year boys three three book read `First year boys read three books.' Speakers report that reduplication here feels vacuous, but acceptable. The distribution would be of three books over worlds that have first year boys, which is more or less what a generic is expressing: in all worlds that have first year boys, first year boys read three books in those worlds. 41 2.5.2 Possible Antecedents for PR Singular quantificational antecedents such as prati ‘each’ allow show a contrast in bound and referential readings more clearly than other types of antecedents, but they are not the only type of antecedent. Universal quantifiers such as jella ‘all’ follow the same pattern. (142) Jella huDugaru avara paka ha:vannu noridaru. all boys their side snake saw `All the boys1 saw the snake next to them1/2.' (143) Jella huDugaru avar‐avara paka ha:vannu noridaru. all boys their‐their side snake saw `All the boys1 saw the snake next to them1.' In these two sentences the antecedent and the pronouns are both plural. As in the reduplicated pronoun cases where the antecedent is a plural nominal, in (142), a single pronoun can be either bound or referential. The reduplicated pronoun in (143) must be bound. In this case, because the antecedent is plural, there is the added complexity of a collective reading. A collective reading would be one where the group (as a whole) saw the snake next to the group. This reading is also not available when the pronoun is reduplicated. 9 The sentence is only compatible with a scenario where there were snakes next to each boy, not next to the entire group. Morphological plurals can also act as an antecedent, as can numerically quantified NPs and coordinated names. (144) HuDugaru avara paka ha:vannu noridaru. boys their side snake saw `The boys1 saw the snake next to them1/2.' (145) Muru huDugaru avara paka ha:vannu noridaru. Three boys their side snake saw `Three boys1 saw the snake next to them1/2.' 42 (146) Anurag Kumar avara paka ha:vannu noridaru. Anurag Kumar their side snake saw `[Anurag and Kumar]1 saw the snake next to them1/2.' Non‐reduplicated pronouns can have either a bound reading or a referential one. Reduplicated pronouns have only a bound reading (147) HuDugaru avar‐avara paka ha:vannu noridaru. boys their side snake saw `The boys1 saw the snake next to them1.' (148) Muru huDugaru avar‐avara paka ha:vannu noridaru. Three boys their side snake saw `Three boys1 saw the snake next to them1.' (149) Anurag Kumar avar‐avara paka ha:vannu noridaru. Anurag Kumar their side snake saw `[Anurag and Kumar] 1 saw the snake next to them1.' 2.6 Generalizations A distributor is required. The distributor must be a plurality, and it must either c‐ command the reduplicant or be an event (which is less easily shown to be in a c‐ commanding position, to generally assumed to be). The next chapter, it will be argued that both NR and PR are subject to locality constraints that bear a striking resemblance to the locality conditions of syntactically bound items such as reflexives and pronouns. This is the second half of the argument for unifying NR, PR, and binding under one umbrella, the common c‐command requirement being the first half. Before moving on to making that argument, the next two sections introduce two other reduplicative phenomena that do not have either of these requirements: wh‐word reduplication and echo word reduplication. 43 3 The Proposal and Some Alternatives 3.1 Option 1: Reduplicant as bound item This is the proposal advocated in this dissertation. The reduplicants in both NR and pronoun reduplication are obligatorily, syntactically bound items. Their requirement that they have an appropriate c‐commanding element (for NR, a plurality or event, for Pronoun Reduplication, an antecedent) is can fall within the antecedent requirement within Binding Theory. This is especially straightforward with pronoun reduplication, in that reduplicated pronouns’ distribution is a subset of the distribution of non‐reduplicated pronouns because reduplicated pronouns appear only in contexts where syntactic binding is possible. It is argued that NR parallels the distribution of reflexives in Kannada, and is thus also is subject to Binding Theory. Before presenting these arguments, there is a brief discussion on Binding Theory in general and more specifically about the particular challenges that Kannada imposes on traditional Binding Theory. 3.1.1 Background: Binding Theory Binding Theory is concerned with the distribution of expressions that rely on other parts of the sentence to obtain their reference. These expressions include anaphora such as reflexives and pronouns well as empty categories such as traces and PRO. The goal of this line of research is to create a unified system for all types of dependencies that describes how each element obtains its reference and under what conditions. It is the goal of this work to show that research done on the distribution of bound elements informs the discussion of the behavior of the distributee in distributive relations. Before building that 44 case, though, it is necessary to summarize classical BT to understand where the field has been. After that, a discussion of Kannada’s bound elements within the context of BT will show that Kannada’s prototypical bound elements present a challenge to the dichotomies assumed by BT, even when work on logophors is considered. 3.1.1.1 Binding Theory Binding Theory applies to two types of bound items: pronouns and reflexives. Each has a different distribution, and classical binding theory was initially structured around the observation that, in the basic cases, they are in complementary distribution. Binding theory seeks to provide a model for the structural configuration within which binding can occur as well as the locality conditions that constrain binding of pronouns and reflexives. Pronouns and reflexives differ fundamentally in that reflexives, unlike pronouns, must be bound. In cases where there is no compatible linguistic antecedent, pronouns can happily take discourse reference, while reflexives are unacceptable. (150) He/*himself sang. (151) I saw him/*himself Because pronouns can be present when they are not bound, it is important to be sensitive to whether or not there is covariation when the antecedent is quantificational. In the following, the pronoun can have either a bound or referential reading: (152) Every girl cut her grass. Under the bound reading, every one of the of the contextually relevant girls cut her own grass: Bonnie cut Bonnie’s grass, Kim cut Kim’s grass, Carolynne cut Carolynne’s grass, etc... The referential reading is where all the girls cut one single person’s grass. This reading arises more easily if one’s talking about how Shannon is sick, and her friends 45 wanted to help her out by doing some of the yardwork. When looking at pronoun binding, co‐variation is very important. The lack of co‐variation indicates that binding is not available for a given pronoun. This is important to show that binding does not happen when the reflexive or pronoun is not in the c‐command domain of the intended antecedent. (153) *Himself1 poked Alex1. (154) *He1 said every boy1 was smart. The antecedents do not c‐command their bindees in either case. In the pronoun sentence, the pronoun would be fine under a referential reading, but the lack of covariation shows that the bound reading is not there. The other major component of Binding theory is the notion of locality, meaning and the domains within which an item must be bound or free. It has long been observed that reflexives must be bound locally while pronouns must be free locally. The local domain aspect of BT is intended to provide an explanation for the complementary distribution of reflexives and pronouns. (155) Locality a. Harold1 saw himself1/*him1 b. Harold1 said that Alice saw *himself1/him1. The generalization is characterized as a requirement that reflexives be bound in their local domain while pronouns be free in their local domain. These observations are referred to as Conditions A and B respectively. The definition of local domain in the context of Binding Theory has undergone numerous refinements, the major impetus of which is observed cross‐linguistic variation in the binding possibilities of anaphora. The classic GB formulation of a local domain is this: 46 (156) Governing Category (Chomsky 1981) a. β is a Governing Category for α if β is the minimal category containing α, a governor of α, and a SUBJECT accessible to α. b. SUBJECT=AGR where present, a subject NP otherwise. c. Α is accessbile to β iff α is in the c‐command domain of β and the assignment to α of the index of β would not violate (d) d. *[δ…γ…] where δ and γ bear the same index. This formulation of the binding domain continues to make use of the very important notion of subject, as well as appealing to the tensed/non‐tensed contrast encapsulated in (b) that is intended to cover the contrast in binding in finite and nonfinite clauses. (157) Alice thought she/*herself would win (158) Alice wanted *she/herself to win. Reflexives and pronouns are mostly in complementary distribution, but not entirely. Picture NPs are one case where both can appear in the same context. (159) They saw [their/each other’s pictures]. (Huang 1983) This observation, and similar non‐complementary distribution of reflexives and pronouns in Chinese also led to data that eventually grew into the literature on logophors in Chinese: (160) Zhangsan kanjian‐le ta/ziji de shu Zhangsan see‐asp he self poss book ‘Zhangsan read his/self’s books.’ (Huang 1983) (161) Zhangsan renwei ta/ziji de shu zui hao. Zhangsan think he self poss book most good ‘Zhangsan thinks his/self’s books are the best.’ (Huang 1983) In response to this sort of data, the next major version of the governing category abandoned the role of AGR as a defining feature of a subject: (162) A Governing Category for α is a maximal projection containing both a subject and a lexical category governing α (Chomsky 1986, 169) 47 (163) Α is the domain for β iff α is the smallest IP(TP) containing β and the governor of β. (Hornstein, Nunes, & Grohmann 2005:248) 3.1.1.2 Logophors/long-distance Anaphora and Binding Theory In English, reflexives strictly obey Condition A; their antecedent must be within their governing category. One would like BT and Principles A and B to apply cross‐linguistically, and if this were the case, one would expect that the distribution of pronouns and reflexives be consistent cross‐lingustically. However, certain reflexives such as Mandarin ziji and Icelandic sig have been shown to be bound outside the governing category outlined in BT: (164) Zhangsan shuo Lisi piping‐le ziji (Huang 2001:#16) Zhangsan say Lisi criticized‐asp self ‘Zhangsan1 said that Lisi2 criticized himself1/2.’ (165) Jón1 saði að ég hefði svikið sig1 (Thráinsson 1991:#18) John1 said that I had betrayed self1 ‘John said that I betrayed him.’ In both of these examples, the reflexive’s local domain is defined as being the embedded clause. The embedded clause is the smallest projection that contains both the reflexive and a governor. Condition A’s positive requirement that reflexives be bound in their local domain seems to be violated; if a reflexive must be bound in its local domain, then it stands to reason that the reverse is holds: it should be unacceptable for a reflexive to be bound by something outside the local domain of the reflexive, but the acceptability of these two examples shows that this prediction is not borne out. The options available to explain this long‐distance binding consist of scrapping Condition A entirely or treating it as condition subject to parametric variation, amending the definition of local domain for reflexives to allow for long‐distance binding, or—and this is the road that Huang 2001 chooses—arguing that long‐distance anaphora are distinct from proper reflexives. These logophors may have their own distributional requirements, 48 but those requirements are not to be construed as identical to the requirements of true reflexives. The literature on logophors played a big role in the development of current thinking with regards to binding, particularly when it comes to questioning the universality of the local domain. While the facts of Kannada and Chinese are quite different, these questions opened laid the groundwork for investigation in languages such as Kannada where the domains of different types of bound items appear to be different from the domains predicted by classical Binding Theory, and where the expected complementary distribution is not present. 3.1.2 Binding Domains in Kannada This section describes the locality conditions under which binding occurs in Kannada. As will be shown, Kannada reflexives and pronouns display some apparently exceptional behavior with respect to classical Binding Theory: reflexives can act as logophors and be bound outside of what would be assumed to be their governing category, and pronouns can be bound more locally than Binding Theory would predict. Pronouns in Kannada reflect person and singular/plural. In addition, pronouns are case‐marked depending on their syntactic position. (166) The pronoun system (Schiffman:38) Person Singular Plural 1 Na:nu Na:vu 2 Ni:nu Ni:vu 3m Avanu Avaru 49 3f AvaLu Avaru 3n Adu Avu Kannada pronouns, like other pronouns, may be syntactically bound or have discourse reference. As for reflexives, there are two morphemes that have been analyzed as having reflexive properties in the language: a nominal and a verbal morpheme. These occur independently and together. (167) Ba:gil‐u tere‐du‐koND‐itu door‐nom open‐pp‐refl.pst‐3sn ‘The door self‐opened.’ (Lidz 2004) (168) Raama1 [tannu1 tumba jaaNa anta] heeLuttaane Rama‐nom self very clever come says ‘Rama1 says that self1 is very clever.’ (Amritavalli 2000:57) (169) Kumar tannannu kanadialli noDi‐konD‐anu Kumar self‐acc mirror‐loc sawrefl(ms) `Kumar saw himself in the mirror.' 3.1.2.1 Verbal Reflexive/Valence Changer: koND- Although both morphemes appear in the literature as reflexives, there is reason to believe that koND‐ may actually be a valence‐changing functional item rather than a reflexive (Lidz 2004). Evidence for this analysis comes from Lidz’s careful analysis of the morphology of change of state verbs in Kannada. (170) Basic intransitives a. Barf‐u karg‐it‐tu ice‐nom melt‐pst‐3sn ‘the ice melted’ (Lidz 2004) b. Ba:gil‐u tere‐d‐itu door‐nom open‐pst‐3sn ‘the door opened.’ 50 These verbs also allow koND‐ speakers describe these sentences as describing that something happened by itself, without an external cause. (171) Ba:gil‐u tere‐du‐koND‐itu door‐nom open‐pst‐refl.pst‐3sn ‘the door opened.’ (172) Barf‐u karag‐i‐koND‐itu ice‐nom melt‐pst‐ref.pst‐3sn ‘the ice melted’ (Lidz 2004) Causers 10 in these sentences must be in the dative case: (173) Ga:l‐ige Ba:gil‐u tere‐du‐koND‐itu wind‐dat door‐nom open‐pst‐refl.pst‐3sn ‘because of the wind, the door opened.’ (174) Ga:l‐ige Barf‐u karag‐i‐koND‐itu wind‐dat ice‐nom melt‐pst‐ref.pst‐3sn ‘Because of the wind, the ice melted’ (Lidz 2004:#1) KoND‐ is presented as a morpheme that indicates the presence of little v. It is important that koND not be taken to be a reflexive that has incorporated onto the verb (Kayne 1994). One of the reasons why it is appealing to treat koND‐ as a valence changer of the type Kayne describes is that koND‐ allows the argument whose Case has been absorbed to appear, but as a dative argument. French allows no such co‐occurrence of arguments: (175) Marie se voit (*lui‐même) Marie refl saw herself ‘Marie saw herself herself.’ (176) Hari tann‐annu hogaL‐i‐koND‐a Hari self‐acc praise‐pp‐refl.pst‐3sm ‘Hari praised himself.’ (Lidz 2004) If koND‐ were an argument that had become part of the verb, it would unexpected to have that position again taken up by a lexical, nominal anaphor. 51 3.1.2.2 Lexical Reflexive: Tann- The lexical reflexive tann‐ has several strong restrictions that limit its distribution. It is subject oriented, meaning that its antecedent must be a subject (K. Kim 2006). It also requires a third‐person antecedent. (177) avan‐u1 anita‐ge2 [tann‐a1/*2 kar‐annu] kodalu ishta villa He‐NOM Anita‐DAT self‐GEN car‐ACC to give liking neg ‘He1 does not wish to give his1/her*2 car to Anita2.’ (Sridhar 1976:106) (178) Raama1‐∅ / *naan1‐u/ *niin1‐u [taan1‐u gedda‐nu anta] heeLidaru. Rama.NOM / *I /*you [self‐NOM won‐3SM COMP] said ‘Rama1 said that self1 won.’ (Mohanan and Mohanan 1998) Tann need not be bound locally, and whether it is subject or object of an embedded clause, can look to the matrix subject for its antecedent (179) Raama1 [tann1‐u gedda‐nu anta] heeLidanu Rama‐nom [self‐nom won‐3sm comp] said Rama said that self won.’ (Amritavalli 2000:67) (180) Anurag [Kumar tannannu kanadialli noDi‐an‐Endu] helidanu Anurag [Kumar self‐acc mirror‐in saw‐ms‐embedded] said(ms) `Anurag1 said that Kumar2 saw him1/2 in the mirror.' These examples show that whether tann‐ is an embedded subject or embedded object, it can look outside its clause for its antecedent. As an embedded object, tann‐ can be bound by either the matrix or embedded subject. 3.1.2.3 koND- restricts binding domain of tann- This freedom is reduced when tann‐ co‐occurs with the verbal reflexive koND‐. Although tann‐ can undergo long‐distance binding when it appears alone, its co‐occurrence with the verbal reflexive limits its binding possibilities. (181) Shyaamu2 [raamu1 tann1/*2‐annu hoDe‐du‐koND‐a anta] heel‐id‐a Shyamu Ram self‐acc hit‐pp‐vr.past‐3sm comp say‐past‐3sm ‘Shyamu2 said that Raamu1 hit himself1/*2.’ (Lidz 1996) 52 (182) Anurag2 Kumar1 tannannu1/*2 kanadialli noDi‐koND‐an‐Endu helidanu Anurag Kumar self‐acc mirror‐loc saw‐ref‐ms‐embedded(?) said(ms) `Anurag2 said Kumar1 saw himself1/*2 in the mirror.' In both examples, tann‐ must be bound within its clause, not by the matrix subject. In general, koND‐ appears to restrict binding to its clause. In fact, for most cases where tann‐ is coreferential with the subject, koND‐ is obligatory. In the following example, leaving koND‐ out results in unacceptability. (183) Joon1 tann1‐annu {*civuTi‐danu/civuTi‐koND‐danu} John self‐acc *pinch‐past.3SM/pinch‐vr‐past.3sm ‘John1 pinched himself1.’ (K. Kim 2006:46 #11) The verbal reflexive is not always obligatory; as has already been noted, its presence or absence in an embedded clause affects the domain of tann‐. One could argue that the verbal reflexive is present only when tann is acting as a true reflexive. When tann is acting as a logophor, it does not need the verbal reflexive. Of the examples cited that prohibit the verbal reflexive, all are dative subject sentences. Kim suggests that the verbal reflexive is connected to a little v associated with causation, and these sentences do not have a causer, unlike the active transitive sentences that do employ the verbal reflexive. 3.1.2.3.1 Pronouns bound locally require KoND- Because tann‐ is a third‐person anaphor only, Kannada must use another strategy to describe situations where first and second persons engage in reflexive actions. Kannada uses a combination of koND‐ and pronouns to do this. 11 The following shows how Kannada indicates first person reflexivity: (184) naan1‐u nann1‐annu hoDedu‐koND‐e. I‐nom I‐acc beat.pp‐vr.past‐1s ‘I beat myself.’ (Amritavalli 2000:53) 53 (185) *naan1‐u nann1‐annu hoDe‐de. I‐nom I‐acc beat.pp‐past‐1s ‘I beat myself.’ (Amritavalli 2000:53) In these cases with locally‐bound pronouns, koND‐ is obligatory. It is not clear whether the effect of koND‐ on pronouns’ binding domain simply allows the pronoun to be bound locally or restricts it to a local domain, as it does tann‐. Because this strategy is largely used for first and second pronouns (which have different forms) pronouns will be coreferential with both embedded and matrix subjects regardless: (186) naan1‐u nann1‐annu hoDedu‐(koND)‐alendu nannu1 he:Lde I‐nom I‐acc beat.pp.vr.past‐embedded I‐nom declare‐1s ‘I said that I beat myself.’ Some pronouns used as embedded subjects do appear to lose their ability to take discourse reference when the matrix verb is marked with koND‐ (187) Kumar1 avanu1/2 geddanuendu heeLidanu (188) Kumar1 avanu1/*2 geddanuendu heeLikoNDanu One case where koND does not appear to be required even when pronouns are bound locally is in ditransitives. As a subject‐oriented reflexive, tann‐ is unable to be bound by an object, so local pronoun binding is the only option. (189) Na:n‐u siite1‐yannu avaL1‐ige‐e: toorisi‐de I‐nom Sita‐acc she‐dat‐empha show‐past.1s ‘I showed Sita1 to herself1.’ (Amritavalli 2000:56) The pronoun avaLe‐ in the dative argument is bound by the accusative Sita. That koND‐ is not required here is not surprising within Lidz’s framework, which, because it connects koND to little v, really only makes predictions about koND with regards to the subject/causer/agent in the sentence. 54 3.1.3 Distributivity and Condition A It has been observed since at least Burzio 1981 that distributivity, particularly that arising in English examples using what has been called binominal each, have similar distributional properties to elements that are subject of Condition A of Binding Theory. As with reflexives, locality is a major issue for distributivity. A distributive reading arises in (190), a parallel example to the reflexive binding example (191). (190) The boys read two books each. (191) Harold saw himself in the mirror. The reflexive is bound in its local domain, and the distributee is in a relation with a distributor in the same domain. This is proof of nothing; it could simply be that the distributee is looking for any distributor it can find. The real proof comes with the next pair, where distributivity is unacceptable in the same context in which reflexive binding is impossible: (192) *The boys wanted Alice to buy two books each. (193) *Harold1 wanted me to shave himself1. The local domain of the reflexive in (193) is the embedded clause, and because the matrix subject, which is the intended antecedent, is outside that domain, binding is impossible between those elements. In a very similar configuration, distributivity between the matrix subject and the object of the embedded clause is also impossible. Were it possible, the interpretation would be that every one of the boys wanted Alice to buy two books for himself, possibly different books. Instead, the sentence is just really awkward, a similar awkwardness to sentences where these is no possible distributor, as in the following: 55 (194) *Alice bought two books each Alice cannot be a distributor, because distributors must be pluralities. For the same reasons, Alice cannot be a distributor in (192). The unacceptability of this sentence indicates that distributivity cannot look to the matrix subject for some reason. It is worth exploring the idea that distributivity, like the binding of reflexives, is subject to locality constraints. It would be a neat result if distributivity were not only subject to locality constraints, but sensitive to the same local domains that constrain the distribution and binding of reflexives. 3.1.4 NR as a reflexive If distributivity in general is to be treated as a subject to Condition A, then NR, which marks distributive sentences in Kannada must also be shown to obey Condition A’s locality requirements. The following is a Kannada analog of the English locality example in (192). Like that example, the intended distributive relation is between the matrix subject as the distributor and the embedded object as the distributee. The subject of the embedded clause is not a plurality, so it cannot be a distributor. (195) *Hudugaru Teja‐ge muru‐muru huvu kondukoLalu heLidru boys Teja‐dat three‐three flowers buy‐infinitive said‐pl ‘The boys told Teja to buy three flowers.’ The intended reading where the flowers vary with the individual boys is not possible for this sentence. It is worth noting that this example, which appears to want a local distributive relation for NR, also contains the verbal reflexive koL‐, a variant of the previously discussed koND‐. The verbal reflexive morphemes limit binding of the nominal reflexives to their 56 local domain. If NR parallels the behavior of Kannada reflexives, it is not surprising that NR is limited to a local domain when it co‐occurs with the verbal reflexive. (196) Hudugaru Teja‐ge muru‐muru huvu kondalu heLidru boys Teja‐dat three‐three flowers buy‐infinitive said‐pl ‘The boys told Teja to buy three flowers.’ NR does differ from Kannada reflexives in subject‐orientedness. If NR were subject‐ oriented, then it should not be possible for the girls to be a distributor for the flowers, but this reading is attested: (197) Muru huDugaru aidu huDugijarige muru‐muru huvu koTTu three boys five girls‐dat three‐three flower give ‘Three boys gave three three flowers to five girls.’ The acceptability of non‐subjects as distributors is not especially concerning, if subject‐orientedness is treated as a feature of those particular reflexives rather than of reflexivity on the whole. 3.1.5 Pronoun Reduplication as an obligatorily bound pronoun This section makes the claim that when numerals are reduplicated, they become obligatorily bound variables, unable to have discourse reference. This is the pronoun version of what happens to numerals when they reduplicate: they must be in a relation. The difference is that while NR is subject to condition A, bound pronouns are subject to Condition B. However, reduplicated pronouns cannot have discourse reference, so they lack the escape clause that allows sentences such as the following, in which the pronoun is not syntactically bound: (198) He loves marshmallows. Because pronouns so easily waft from syntactic binding to discourse binding, it can be difficult to discern which is happening in any particular sentence. The presence of 57 covariation is a reliable test for syntactic binding of pronouns. When a pronoun’s reference covaries with its quantificational antecedent, it is syntactically bound. (199) Every boy loves his mother. (200) Because he loves ice cream, every boy bought some at the store. Most cases allow for either a bound or referential reading: (201) Every boy1 saw the snake next to him1/2. The ambiguity between the two readings also exists in Kannada. In the following sentence with a single pronoun, both readings are available. (202) Prati huDuga avana baLi Idda ha:vannu noDida. Every boy his side was snake‐acc saw `Every boy1 saw the(/a?) snake next to him1/2.' It is compatible with a scenario where each one of the boys saw a snake next to himself (the bound reading), and it’s also compatible with a scenario where each of them saw a snake next to some other person (the referential reading). When the pronoun is reduplicated, only the bound reading is available. (203) Prati huDuga avana‐avana baLi Idda ha:vannu noDida. Every boy his‐his side was snake‐acc saw `Every boy1 saw the(/a?) snake next to him1/*2.' 3.2 Option 3: Polarity item licensing The C‐command requirement that NR has is not unique to NR and reflexives. Polarity items, like NR, have a c‐command requirement: they must be within the scope of particular types of quantificational items. 12 Perhaps the most familiar polarity items are negative polarity items, such and English’s anything, anyone, anywhere, and several others. These items are licensed when they are in the scope of negation: (204) Harold didn’t see anything 58 (205) *Harold saw anything. (206) *Anyone saw Harold at the party. (207) Anyone didn’t see Harold at the party. 13 (208) Glenda didn’t think anyone saw Harold at the party. (209) *Glenda thought anyone saw Harold at the party. Like polarity item licensing, NR and pronoun reduplication require c‐commanding distributors or antecedents. In this way, their needs are similar. In addition, it has been shown that, modals can serve as a distributor for NR (they can also license NPIs). However, the two phenomena differ in their sensitivity to intervention effects. It was first observed in (Linebarger 1980; Linebarger 1987) that NPIs do not tolerate quantificational elements intervening between the NPI and their licensor. And argument supporting this comes from the ambiguity that arises from the two levels at which a because‐clause can attach to the matrix clause. In the following, because he was pushed can attach either above or below negation, and that have implications for the sentence’s interpretation. (210) Rico didn’t move because he was pushed (ambiguous) a. CAUSE>NOT: It was because he was pushed that Rico didn’t move. b. NOT>CAUSE: Rico’s having been pushed wasn’t what made him move. Because‐clauses that contain an NPI must be interpreted below negation so the NPI can be in the scope of negation, so the following is unambiguous: (211) Rico didn’t move because anyone pushed him. (not ambiguous) a. #CAUSE>NOT: It was because he was pushed that Rico didn’t move. b. NOT>CAUSE: Rico’s having been pushed wasn’t what made him move. When the NPI is in the matrix clause, the because clause must have wide scope so that it doesn’t intervene between the negative head and the NPI. 59 (212) Rico didn’t budge an inch because he was pushed. (not ambiguous) a. CAUSE>NOT: It was because he was pushed that Rico didn’t move. b. #NOT>CAUSE: Rico’s having been pushed wasn’t what made him move. Assuming that intervention effects of this sort are a general property of licensing, one would expect that NR would experience similar intervention effects when other potential licensors intervene between it and its intended licensor. While it is true that speakers tend to prefer readings where the distributee goes with the closest potential distributor, it is not necessary. Judgments get really complicated, but it doesn’t seem to be the case that an intervening plurality is an absolute barrier (in the non‐technical sense) to using a higher plurality as a distributor. This differs from NPI licensing, where intervention effects do seem to be a barrier. Before moving on, I want to give a nod to Progovac 1994, which argues that NPI licensing is actually binding. If it is the case that NPI licensing and binding can be collapsed, and distributivity can be collapsed with binding, then the distinction between NR and NPI licensing is moot. Exploring the implications of her proposal for NR would be really interesting. 3.3 Option 4: NR restricts quantifier’s QR landing site This option is, in some ways, a modernization of Choe’s Anti‐quantifier proposal, cast in the language of the Landing Theory of Scope (Beghelli 1995; Beghelli and Stowell 1997). The Landing Theory of Scope classifies quantifiers into several types, all of which are argued to select different‐sized domains of quantification. This proposal suggests that reduplication of numerals restricts those QPs to just the smaller domains. 60 3.3.1 Quantifier Types and The Landing Theory of Scope The Landing Theory of Scope, proposed initially in Beghelli 1995 and further described in Beghelli and Stowell 1997, seeks to provide an articulated theory of scope interaction between different types of quantifiers through the creation of a hierarchy of functional projections that each type of quantifier moves to, through QR. This differs from other quantifier scope theories that treat all quantifier types as the same with regard to the landing site for QR, making them unable to account for why certain types of QPs always scope over (or under) other types of QPs. The following section describes the Landing Theory of Scope, how it plays out in English and Kannada, and then how such an account might work. 3.3.1.1 Quantifier Types in English Following Szabolcsi (1997), Beghelli breaks QPs into five distinct types based on their form, meaning, and scopal behavior: (213) Types of Quantifiers: a. GQP—Group‐denoting QP: two rabbits, the rabbits b. CQP —Counting QP: more/less than two rabbits, at most two rabbits, more rabbits than hamsters c. DQP—Distributive QP: each rabbit, every rabbit d. NQP—Negative QP: no rabbit e. WhQP—Wh‐phrases: who, what, which rabbit Beghelli (1995) focuses primarily on the first three types. The behavior of each type of QP is determined both by the semantics of each type and by the selected landing site. Although these two factors are to some extent intertwined, It is the QPs scopal behavior 61 that is most important to the argument of this dissertation, so Beghelli’s proposed semantics for each QP will remain largely unexplored here. DQPs are easily distinguished from CQPs and GQPs because they contain either each or every. DQPs generally take wide scope with respect to other quantifiers, especially when in subject position (which is already quite high in the sentence structure). In the following examples, the subject is a DQP and the objects are indefinite GQPs (a) and a CQP (b). (214) Subject DQP takes wide scope a. Every monkey hugged a rabbit/ two rabbits. b. Every monkey hugged more than three rabbits In this example, the DQP every monkey takes scope over the QPs in object position, so for each individual monkey, there are one, two, or more than three rabbits. DQPs in subject position consistently take scope over most QPs in object position. The exception would be specific GQPs such as the rabbits, which take wide scope over the DQP as shown in (215). (215) Every monkey hugged the rabbits. Beghelli suggests that the specificity of these GQPs allow these QPs to QR to a very high position that no other QP type has access to. Thus, a specific GQP will take scope over every other QP in the sentence, regardless of type. (216) More than two monkeys hugged the rabbits. (217) Two monkeys hugged the rabbits. The specific GQP the rabbits points to a particular group of rabbits, and regardless of the type of the QP in subject position, the only readings available are ones where the other QP is mapped to that one group of rabbits. Looking back at (214), it's clear that object CQPs are not able to scope over a subject DQP. When a DQP is in object position, its ability to take 62 wide scope depends on what type of QP the other QP is. Subject CQPs always take scope over an object DQP, but subject GQPs are ambiguous depending on whether or not they have a specific interpretation. In the following two sentences, the first illustrates the ambiguity that arises when a subject GQP interacts with an object DQP. When the subject GQP is specific, as in (219), the ambiguity does not arise. The specific GQP takes scope over the object DQP. (218) Two rabbits licked every monkey. (219) The rabbits licked every monkey. The specific GQP the rabbits each take scope over the DQP, but the GQP two rabbits can either take wide or narrow scope depending on whether or not is has a specific interpretation. When it takes wide scope, it has a specific interpretation, and when it takes narrow scope, it does not. Except when specificity is a factor, the scope relationship between CQPs and GQPs correlates with their surface position: a subject CQP will take scope over an object GQP, and a subject GQP will take scope over an object CQP. The exception is again with specific GQPs, which obligatorily scope over everything. Specificity is not available for CQPs, which contain modified numerals such as more than three rabbits, fewer rabbits than bears, as many rabbits as Ram could catch. These obligatorily non‐specific QPs are always interpreted in‐situ. They may take scope over CQPs and non‐specific GQPs that they c‐command, although certain types of QPs may still take wider scope. CQPs always take narrow scope with respect to any QP in a higher position. (220) More than three monkeys hugged five rabbits. (221) Five rabbits hugged more than two monkeys. 63 The second example is unambiguous: some group of five rabbits hugged a group of monkeys that consisted of more than two monkeys. The first sentence, however, is ambiguous. If five rabbits is interpreted as specific, then the sentence describes a situation where a group of five rabbits got hugged by some number of monkeys, more than three. If five rabbits is not interpreted as specific, then the monkeys can take scope, and in that case, it describes a situation where five rabbits are such that each one of them hugged more than two monkeys. As a summary, the following shows the scopal relations between types of QPs: (222) Specific GQP ≫ Subject CQP≫DQP≫Non‐specific GQP≫ Object CQP Beghelli argues that this hierarchy of QP scope is best represented as series of functional projections, each of which is a landing site for a particular type of QP. Each type of QP has the scopal possibilities that it does because, when it undergoes QR, it moves to a certain location that places it in a c‐command relationship with the other QPs in the sentence. 64 (223) Functional projections in Beghelli A Target Landing Sites proposal differs significantly from accounts that precede it, derived from May (1977), in which quantifiers adjoin to either IP or VP. Under that analysis, all QPs can adjoin to the same position. While such a system allows for the ambiguity that can arise in a sentence with two QPs, it does so in an unconstrained way, predicting that in any sentence with two quantifiers, either QP can have wide scope. For example, such a system would generate both of the following structures as possible results of QR, even though the second structure represents a reading that is unattested. A Target Landing Sites proposal differs significantly from accounts that precede it, derived from May (1977), in which quantifiers adjoin to either IP or VP. Under that analysis, all QPs can adjoin to the same position. While such a system allows for the abiguity that can arise in a sentence with two QPs, it does so in an unconstrained way, predicting that in any sentence with two quantifiers, either QP can have wide scope. (10) (a) Every monkey kissed a rabbit. (b) [ IP Every monkey 1 [ IP a rabbit 2 [ IP t 1 kissed t 2 ]]] (c) [ IP a rabbit 2 [ IP Every monkey 1 [ IP t 1 kissed t 2 ]]] Because all QPs are treated the same way in this system, there is no expectation to find that particular types of quantifiers have consistent relative scope behavior, nor the capacity to explain that behavior in detail. In contrast, a theory in which each type of quantifier has a particular target for QR makes specific, testable, predictions about the relative scope of quantifiers. In my paper, I considered non-specific GQPs and DQPs. According toBeghelli’s hierarchy of landing sites, he predicts what I reported: that non-secific GQPs take narrow scope with respect to DQPs. I don’t remember his specifically addressing sentences with more than one GQP, but he would probably suggest that one of the GQPs would need to be interpreted as specific, and that GQP would then take wide scope. 3 65 (224) Every monkey kissed more than three rabbits. a. Every monkey ! more than three rabbits ! 𝑡 ! kissed𝑡 ! b. more than three rabbits ! Every monkey ! 𝑡 ! kissed𝑡 ! (225) More than three girls washed every car. a. more than three girls ! every car ! 𝑡 ! washed 𝑡 ! b. every car ! more than three girls ! 𝑡 ! washed 𝑡 ! In the first structure, there is a one‐to‐one mapping of rabbits to monkeys. For every monkey, there is a rabbit that the monkey kissed. The second structure represents a reading where the monkeys kissed some specific group of more than three rabbits. This reading is not attested, but May’s system does not prevent such unattested readings from being generated. In Beghelli’s system, the QP more than three rabbits is a CQP, and because of its quantifier type, its scope is necessarily interpreted in situ, so it must take narrow scope with respect to every monkey. Because every quantifier has to arrive at its own unique landing position, sentences that contain two quantifiers of the same type might seem to pose a problem. In sentences that contain two GQPs, one of the quantifiers is interpreted as specific, and moves to the higher position. (226) Five thieves stole two diamonds a. two diamonds ! five thieves ! 𝑡 ! stole 𝑡 ! b. five thieves ! two diamonds ! 𝑡 ! stole 𝑡 ! A structure like this predicts that when two diamonds is specific, it will assymetrically c‐command the other quantifier in the sentence, so it should not allow reduplication. 66 3.3.1.2 Quantifier Interactions in Kannada This section catalogues the interaction of different quantifier types in Kannada in an effort to support the theory’s application to Kannada. 3.3.1.2.1 Specific GQPs Win Specific GQPs are expected to take scope over all other QPs in a sentence, particularly CQPs, since they are expected to be interpreted in‐situ. The following example shows the interaction between a GQP in object position and a CQP in subject position. If the GQP takes wide scope, then this sentence would be compatible with a scenario where a specific set of diamonds was stolen once by a group of thieves. (227) aIda‐kkinta {hEtSu/kaDime/kammi} kaLLaru vadZara‐vannu kaddaru Five‐than {more/less(proper)/less(informal)} thieves diamond‐acc stole `More/less than five thieves stole the diamonds.' The expected reading is the only reading available. If the CQP were able to take wide scope over the specific GQP then the sentence would also be compatible with a scenario where the same set of diamonds were stolen several times, at least once by each thief. 3.3.1.2.2 Subject CQPs win over everything except specific GQPs Moving down the list of landing sites, the next highest position is occupied by subject CQPs. These QPs are expected to take scope over everything except specific GQPs because they are interpreted in a position higher than the landing site for every type of QP aside from specific GQPs. The following example shows the subject CQP taking scope over a non‐ specific GQP: 67 (228) Aidu kinta {Jaste/kadime} hudugaru muru pustaka wodidru Five than {more/fewer} boys three book read `More/fewer than five boys read three books.' When the CQP has scope over the GQP, there can be three books per boy, as opposed to when the books are specific, and there are only three books. This contrasts with (227), where the GQP is specific, and so multiple stealings are not possible. Similarly, the subject CQP takes scope over a DQP in object position. In this example, the number of boys who read every book is more (or less) than five: (229) Aidu kinta {Jaste/kadime} hudugaru prati pustaka wodidru Five than {more/fewer} boys every book read `More/fewer than five boys read every book.' If the DQP were able to scope over the CQP, then there would be more (or less) than five boys per book, and that is not an available interpretation. 3.3.1.2.3 DQPs win over GQPs DQPs select a landing site above that of non‐specific GQPs and are predicted to consistently take wide scope. In the following example, the non‐specific GQP, the flowers, takes narrow scope with respect to the DQP ‘each boy.’ (230) Prati huDuga aidu huDugijarige muru hu:vu koTTru Each boy five girls‐dat three flowers gave ‘Each boy gave five girls three flowers.' While a subject DQP will unambiguously take scope over a non‐specific GQP in object position, ambiguity is predicted when the positions are reversed: (231) Muru huDugijaru prati gaDijannu toLEdaru Three girls every car wash‐fpl `Three girls washed every car.' In this example, the girls could be interpreted as either specific or non‐specific and thus take either wide or narrow scope with respect to the DQP. 68 3.3.1.2.4 Object CQPs take narrow scope Because CQPs are interpreted in‐situ, object CQPs are predicted to consistently take narrow scope with respect to all other QPs. For example, GQPs will always take wide scope with respect to object CQPs. The following examples only allow readings consistent with the GQP taking wide scope. (232) na:n tSatreigaLu aiwat kinta soLpa kammi pustaka wodidru My students fifty than slightly less book read `My students read just less than 50 books.' (233) jella tSatrigaLu aiwatu kinta kammi pustaka wodidare All students fifty than less book read `All the students read fewer than fifty books.' There are several readings available in these sentences, but the main thing is that there is no reading where ‘fewer than fifty books’ takes wide scope over the other QP. 3.3.2 NR is Not Just a GQP Disambiguation Strategy The Landing Theory of Scope classifies quantifiers according to the quantifier’s requirements for the size of its domain. Some quantifiers, such as DQPs, require relatively large domains, and so when they undergo QR, they move to high positions in the structure. In contrast, other quantifier types have more modest domain requirements and select lower positions for QR. Those quantifiers which select low positions will consistently take narrow scope with respect to quantifiers that select higher QR positions. Given the observation that NR consistently takes narrow scope with respect to other quantifiers, within the context of the Landing Theory of Scope, one might conclude that a reduplicated numeral is a quantifier of a type that takes a very small domain. This is an entirely plausible position considering that the non‐reduplicated form is a GQP, and non‐ specific GQPs take very small domains, much like NR. One could argue that reduplication is 69 a way to disambiguate the GQP; a reduplicated GQP must be non‐specific, while a non‐ reduplicated GQP can be either specific or non‐specific. Treating reduplication as a disambiguating strategy for GQPs would account for why NR always takes narrow scope. Non‐specific GQPs in object positions take narrow scope with respect to every other type of quantifier except for CQPs, which are interpreted in‐situ. Also considering that CQPs also occupy a low QR position, treating reduplication as a special disambiguation strategy provides an explanation why one of the low QPs reduplicates while the other does not: GQPs are ambiguous, but CQPs are not. This is all plausible, but there are several empirical reasons not to go for a disambiguation account of reduplication. NR behaves differently from most quantifiers in that it requires an element that will take scope over it. As has been shown, when there is no quantificational element that can take scope over the reduplicant, reduplication is unacceptable. This contrasts strongly with the behavior of other quantifiers, which have no requirements regarding other quantifiers in the sentence. In particular, non‐reduplicated, non‐specific GQPs are free to occur as the only quantificational element in a sentence. (234) Rama nalku m6ngagaLannu noDida Rama four monkeys saw.ms ‘Ram saw four monkeys.’ Were it the case that NR were a disambiguation strategy, it would be expected that NR would have the same distribution as non‐specific GQPs, and be able to occur without a wide‐scope quantifier, but this is not the case. Reduplicated numerals must be in the scope of another quantifier. This is also apparent when one considers the unacceptability of NR in configurations of quantifiers in which there is another quantifier in the sentence, but that quantifier cannot take scope over the reduplicated numeral. One such example of this 70 is when the intended wide‐scope quantifier occurs within an island. Such a quantifier cannot QR out of the island to c‐command the reduplicated numeral. The disambiguation approach incorrectly predicts that NR would be acceptable in such a case: (235) [Prati vidyarthyannu sipharisida adhyapakanige] yeradu kare bantu every student‐acc recommend professor‐dat two call came ‘The professor who recommended every student received two calls.’ (236) adhyapakanige, sipharisida Prati vidyarthige yeradu yeradu kare bantu professor‐dat recommend every student two two call came ‘The professor who recommended every student got two calls about each student.’ Here, the quantifier prati vidyarthyannu ‘every student is intended to be the wide‐ scope quantifier, and is intended to be the distributor for the reduplicated numeral in matrix object position. However, prati vidyarthyannu is within a relative clause; it does not c‐command the reduplicated numeral from its base position, and it cannot QR out of the relative clause to c‐command the reduplicated numeral. Although the disambiguation account predicts that NR would be acceptable in this example, speakers reject it. 71 4 Semantic Approaches to NR This chapter explores possibilities for a semantic implementation of distributivity that is consonant with the syntactic, binding‐based account proposed in the previous chapter. It begins with a discussion of the requirements of an account that will handle the core NR cases in Kannada and explores the application of Safir and Stowell’s account for English binominal each (Safir and Stowell 1988) to Kannada’s NR sentences. Further support for a binding account of NR comes from a parallel discussion of Arregi’s analysis of Spanish reciprocals (Arregi 2001) within the context of relations between nominals. It is suggested that while reciprocals relate one part of a plurality to another part of that plurality, a distributive function relates one plurality to another in much the same way. That NR and reciprocals can be analyzed as having similar functions lends credence to treating reduplication in Kannada holistically as a binding phenomenon. The last part of the chapter explores several alternatives to this line of inquiry, most of which fail on empirical grounds. 4.1 Background: Pluralities in Semantics Pluralities play a major role in this work, primarily due to their intrinsic role in distributive sentences. As has been noted already, the distributor in a distributive sentence must be a plurality: (237) *Frank sang two songs each. (238) The tenors sang two songs each. 72 In later sections, a connection between distributivity and reciprocals will be explored. One departure point for that analysis is the observation that reciprocals, like the distributee in a distributive relation, require a c‐commanding plurality: (239) *Frank hugged each other. (240) The tenors hugged each other. Thus far, no attempt has been made to define a plurality beyond drawing a distinction between singular and plural NPs. At the intuitive level, that is all there is to it: a plurality is an entity made up of pieces while an atom cannot be further broken down. Singular, named people are atoms; groups of people and things like The Red Sox, the junk in Shannon’s locker, and Brent and Jeff are pluralities. Certain predicates are predisposed to a collective or a distributive reading of pluralities. Verbs like surround or disperse are most compatible with a collective reading. (241) The Occupiers surrounded City Hall. (242) The Occupiers dispersed. Given the size of municipal buildings, it’s unlikely that individual Occupiers would be able to simultaneously be on all sides of City Hall. Similarly, disperse is understood to be true when the members of a group go their separate ways. A distributive reading would probably have individual Occupiers’ cellular structure break down until they disappeared like mist. Other predicates are consistently distributive: (243) The Occupiers were hungry/tired/wet. Being hungry, tired, or wet is a property of individuals. Still other predicates can go either way: (244) Your suitcases exceed the weight limit of 75lbs. 73 This sentence is equally compatible with a collective reading where the total weight of the suitcases exceeds the weight limit but no single suitcase is heavier than 75lbs and a distributive reading where each one of the suitcases is heavier than 75lbs (although this isn’t the conventional use of this utterance). Whether or not a plural NP will be interpreted collectively or distributively depends on the predicate. The fact that the same NPs can have different readings with different predicates shows that the NPs must be able to interact with these predicates as either atoms or pluralities. It is also important to note that atoms, such as single people, are not compatible with predicates that want pluralities and interpret those pluralities collectively: (245) #Steve surrounded City Hall. (246) #Steve dispersed. These examples suggest that something in the denotation of the verbs surround and disperse requires a subject that, while taken as a collective, is comprised of divisible parts. Thus, it’s clear that certain verbs require their arguments to be pluralities. The issue of how a verb does this is tangential to the task at hand; the main point is that, because some verbs require pluralities specifically, that is evidence that pluralities are a real thing. There really are semantic objects that have some level of internal complexity, and that these objects are distinct from atomic individuals. That there are pluralities, and that they are made up of sub‐parts seems clear, there are several ways to describe the parts that make up a plurality. Each specific formulation has its strengths and weaknesses. A first pass at dealing with distributive readings might make use of atomization, a process by which a plurality would be broken up into its constituent atoms. This would 74 make sense for examples where a predicate is true of individual members of a group, such as be tired, or be hungry. (247) The Occupiers were tired/hungry/relieved. What is not so clear in these cases is when the predicate is true of groups of intermediate size; smaller than the plurality as a whole, but larger than single atoms: (248) The quartets are internationally known This example is compatible with a scenario where every quartet under discussion is well‐known as a group, but the individual members have very little name recognition on their own. In addition, it could be the case that at least one member of one of the quartets is a student with no name recognition whatsoever. The quartet that she or he performs with may still be famous, but that player is unknown. The fact that (248) can be true of individual quartets but need not be true of the individuals that make up the quartets suggests that atomization is too strong. Less strong is the notion i‐part, a way of formalizing subsets that make up pluralities. Because i‐parts do not necessarily have to drill down to the atom level, they can be compatible with the quartet example. (249) ≤, i‐part (5, Heim references Link’s “Individual Part”) a. Every individual in D (atom or plurality) is an i‐part of itself. b. Atoms have no proper i‐parts (i.e., no other i‐parts than themselves), whereas pluralities always have two or more proper i‐parts c. Two pluralities are identical iff they have exactly the same atoms as i‐parts. d. One plurality is an i‐part of another plurality iff every i‐part of the former is an i‐part of the latter. According to this definition, i‐parts make up pluralities and they themselves can be comprised of sub‐parts. Similar, but more restrictive definitions of sub‐parts that play a 75 role in accounts of plurality include Covers and Partitions. Covers differ from i‐parts in that they require exhaustive inclusion of all atoms in the plurality in a cover. Partitions go one step further; not only must ever atom be a member of a partition, but atoms can only be a member of one partition. The membership of Covers and i‐parts can overlap. (250) Cover: a family of sets C is a cover of the set X iff a. C is a set of subsets of X b. Every member of X belongs to some set in C c. Ø is not in C (Schwartzchild) (251) Partition: S is a partition of x iff: a. S is a cover of x, and b. ∀𝑧,𝑦∈ 𝑆 𝑧=𝑦∨¬∃𝑎 𝑎≼ ! 𝑧∧𝑎≼ ! 𝑦 (Ionin and Matushansky:#6) Covers and i‐parts, as already noted, are operationally very similar. While i‐parts do not require exhaustivity, nothing in their definition prohibits a plurality from being analyzed as being exhaustively made of i‐parts. (252) 𝑋= 𝑎,𝑏,𝑐,𝑑,𝑒 a. 𝑎,𝑏 , 𝑐,𝑑 , 𝑒 b. 𝑎,𝑏 , 𝑐,𝑑 ,𝑒 Taking the brackets to represent membership in either an i‐part or a cover, (a) is compatible with either covers or i‐parts. The situation in (b) is only compatible with i‐ parts because e is not a member of any sub‐part. The groupings in (a) are also compatible with partitioning because the sub‐parts do not overlap. The following is an acceptable set of covers, but not partitions, of X: (253) 𝑎,𝑏 , 𝑏,𝑐 , 𝑑,𝑒 76 Because b is a member of two covers, this grouping is not compatible with partitioning of X. Which of these ways one uses to define the subsets involved in pluralities will affect the predicted behavior of pluralities. The following relation, called i‐sum, describes how a plurality can be built using either atoms or pluralities. (254) i‐sum: For any 𝑥∈𝐷,𝑦∈𝐷,𝑥⊕𝑦 is the unique 𝑧∈𝐷 such that: a. ∀𝑢 𝑢≤ 𝑥 ∨𝑢≤𝑦→𝑢≤ 𝑧 , and b. ∀𝑧′ ∀𝑢 𝑢≤ 𝑥∨𝑢≤𝑦→𝑢≤ 𝑧 ! → 𝑧≤ 𝑧′ . The i‐sum of x and y, called z, contains the i‐parts of x and y. The plurality z contains no element that is not a member of either x or y. The following derivation puts this definition to work to derive the truth conditions for Tom and Jim are a couple. (255) Tom and Jim are a couple = 1 iff: a. couple and Tom Jim = b. couple 𝜆𝑥 ! .𝜆𝑦 ! .𝑥⊕𝑦 Tom Jim = c. couple Tom⊕Jim = 1 In this example, and is an operator that constructs a plurality from two atoms. If “be a couple” is true of the plurality Tom⊕Jim, then (255) is true. Using coordinated names as a plurality is starting off easy. In the plurality Tom and Jim, the atoms that form the plurality are clear and there is an operator to connect them. With plurals, there is no listing of constituent atoms and no and to create the plurality. The construction of a plurality in these cases is more relevant to the majority of Kannada examples considered in this dissertation, as most of them are numerically quantified, plural NPs. A first pass at providing a denotation for a definite plural would be the following: 77 (256) The boys = The smallest 𝑥∈𝐷 such that ∀𝑦 𝑦∈ boy →𝑦≤ 𝑥 14 This denotation says that the boys is the smallest plurality x for which every y that is a boy is a member of x. It is assumed that somewhere in the DP the boys there is some functional piece that creates a plurality, whether this functional piece is spelled out as –s or the –s is a reflex of the plurality‐making functional item is not a major concern, but for simplicity, the plural morpheme –s will be treated as identical to the item that turns boys into a plurality. (257) The boys = the boy s The plural morpheme takes the predicate boy and creates out of it a set of non‐ atomic individuals, all of whom are boys. (258) boy = λx.boy 𝑥 (259) boys = 𝜆𝑥 ! .𝑥∈ * 𝑦 ! :boy 𝑦 = 1 & boy 𝑥 = 0 The denotation of boys is of type <e,t>, as is the denotation of boy. The star operator is what is doing the work of pluralization; the star operator acts like the and in (255). It creates a set of all the possible concatenations of the atoms that are true of the predicate boy. The final part of the denotation tosses out the atoms. The final result is a predicate boys which is true only of plural individuals that are boys. (260) Let X be a set. The *X is the smallest set that meets the following two conditions: a. 𝑋⊆ *𝑋, and b. ∀𝑦.∀𝑧. 𝑦∈ *𝑋&𝑧∈ *𝑋→𝑦⊕𝑧∈ *𝑋 This definition defines the set *X as one which contains X, all of the members of X, and all the i‐sums of the members of X. To work through an example, consider a set G, made up of the atoms a, b, and c. 78 (261) 𝐺= 𝑎,𝑏,𝑐 (262) *𝐺= 𝑎,𝑏,𝑐, 𝑎⊕𝑏,𝑏⊕𝑐,𝑎⊕𝑐, 𝑎⊕𝑏⊕𝑐 The plural marker takes a predicate and returns another predicate. The function of this expression is to get rid of the atoms in the set that that predicate is true of. (263) Plural 15 = 𝜆𝑓 !,! .𝜆𝑥 ! .𝑥∈ * 𝑦 ! :𝑓 𝑦 = 1 &𝑓 𝑥 = 0 Numeral quantification of boys enforces a given cardinality of the atoms that comprise the set of boys. The numeral combines with boys through predicate modification: (264) two = 𝜆𝑥 ! . 𝑦 ! :𝑦≤ 𝑥&𝑦 is an atom = 2 (265) two boys = 𝜆𝑥 ! . 𝑦 ! :𝑦≤ 𝑥&𝑦 is an atom =2& 𝑥∈ * 𝑧 ! : boy 𝑧 = 1 & boy 𝑧 = 0 The lexical entry for two boys denotes a pluralities of boys made up of just two atoms. The determiner the closes this expression and binds the variable z. (266) the = 𝜆𝑓 !,! .∃!𝑧 st 𝑓 𝑧 = 1 &∀𝑦 ! 𝑓 𝑦 = 1→𝑦≤ 𝑧 The determiner takes a predicate and returns an element of type e: the unique z that satisfies the predicate and for which all individuals y of which the predicate is true are sub‐ parts of z. What this means is that z is the unique set that contains all the pluralities or individuals that satisfy the predicate. In the example the boys, the determiner takes the predicate boys. This will have the result of the boys denoting the unique set that contains just pluralities that are made up only of boys, and it will contain all pluralities of boys. (267) the boys = (268) 𝜆𝑓 !,! .∃!𝑧 ! st 𝑓 𝑧 = 1 &∀𝑦 ! 𝑓 𝑦 = 1→𝑦≤ 𝑧 𝜆𝑥 ! .𝑥∈ * 𝑦 ! : boy 𝑦 = 1 & boy 𝑥 = 0 79 (269) ∃!𝑧 ! st 𝜆𝑥 ! .𝑥∈ * 𝑦 ! : boy 𝑦 = 1 & boy 𝑥 = 0 𝑧 = 1 &∀𝑦 ! 𝜆𝑥 ! .𝑥∈ * 𝑦 ! : boy 𝑦 = 1 & boy 𝑥 = 0 𝑦 = 1→𝑦≤ 𝑧 (270) ∃!𝑧 ! 𝑠𝑡 𝑧∈ * 𝑦 ! : boy 𝑦 = 1 & boy 𝑧 = 0 = 1 &∀𝑦 ! 𝑦∈ * 𝑦 ! : boy 𝑦 = 1 & boy 𝑦 = 0 = 1→𝑦≤ 𝑧 z is a set of non‐atomic individuals made up entirely of boys, and every non‐atomic i‐sum of the set of boys is an i‐part of z. Now that there is a semantics for plurals, it’s possible to look into how they can act as arguments of predicates. Earlier in the section, it was shown that coordinated names can act as the argument of the predicate be a couple. Like that example, the following is not distributive. The boys collectively used the toilet paper up; some boys may have used more than others, but no boy did it all on his own. (271) The boys used up the toilet paper This example is true iff the predicate use up the toilet paper is true of the plural individual made up of boys. This is what the derivation predicts. That a collective predicate has no trouble applying to a plurality is unsurprising. The system creates plural individuals. The question most relevant to the discussion of distributivity is how a predicate with an individual reading is then able to look inside the plural individual and be true of the members of the plural individual, as the following requires: (272) Tom and Jim/The boys are tall. In order to capture this individual reading, the predicate must be able to see into the plurality. Individual readings are true of every member of the plurality. In a sense, a predicate with an individual reading undoes all that the pluralization and numerical 80 quantification has done; while pluralization makes one set out of individuals, the individual reading looks a each individual that makes up the plurality. This plurality‐splitting that occurs in individual readings is incredibly important to distributivity, where sensitivity to sub‐parts of the distributor is what makes the thing work. It is certainly possible to think of the core distributive sentences, such as the following, as ones where the predicate eat three raisins is true of each individual that makes up the boys. (273) The boys (each) ate three raisins. All else being equal, there are several possible places to locate the thing that splits apart the plurality: within the distributor, within the distributee, as an adjunct to the VP, or even as a sentential adjunct. 16 The main approaches explored in this work associate the distributive machinery with the distributee, as will be seen in the following section. Associating distributivity with the distributor is roughly what is assumed with English‐type distributive quantifiers like the each in each boy ate an apple. While this works well for English and for Kannada’s equivalent prati, it’s a bit puzzling why a language might have an alternate strategy where the distributee is marked if it underlyingly is identical to the prati strategy. The VP‐adjunct strategy will also be discussed towards the end of the chapter, when Schwartzchild’s D‐operator is discussed. The major issue with this approach is that it only handles the core distributive cases and cannot handle inverse scope sentences. 4.2 A Basic Example While numerous works explore the myriad puzzles and specialized readings that can affect distributive sentences (Schwarzschild 1996) provides describes of many of these issues), 81 the approach here works from the core cases outward to the periphery. As such, it begins with a discussion of a core case. The following example relates two sets of sets of discrete, countable objects. This is done because many of the puzzles discussed in the literature that arise when events or locations are involved, or when the pluralities participating in the distributive relation in more than one way. Those are all factors to be explored, but they are also complicating factors. In the given example, the distributor is a set of three boys and the distributee is a set of two fruits. (274) Muru hudugaru jer‐jer hannu tIndru Three boys two two fruits ate `Three boys two‐two fruits ate.' For each of the three boys, there are two fruits that boy ate: the first boy ate two, the second boy ate two, and the third boy ate two. In the strongest reading, the reading with no overlap of fruit (which is also the most natural given the telic nature of eating a fruit), there are a total of six fruits that were consumed. As a description of this reading, it would suffice to say that the distributive reading creates iterations of the narrow‐scope item, making one iteration for each member of the wide‐scope item. In this case, there are three sets of two fruits: one pair of fruits for each of the boys. As a description of a basic distributive reading, this is sufficient, but it is more satisfying to build an account of how distributivity relates these two sets to create the interpretation just described. 82 4.3 A Binominal Binding Account of Distributivity 4.3.1 Safir and Stowell’s Semantics for Binominal Each (1988) Safir and Stowell’s paper focuses on a particular usage of the English particle each which comes at the end of sentences, which they call “binominal each.” This type of each, unlike the each that appears adjacent to the distributor (referred to as determiner, or D‐each) or the each that occurs adjacent to the VP (which they call adverbial each), is argued to be a relation between the two nominals that form a distributive relationship. (275) Binominal each a. The boys read two books each b. Fifteen guys watched five movies each. (276) D‐each a. Each boy read two books. b. Five boys read each book. (277) Adverbial each a. The boys each won a prize. b. Fifteen boys each danced the schottische. One major difference between the use of binominal each in the other two types of each is that movement and coordination tests appear to show that binominal each forms a constituent with the distributee, the NP it is adjacent to. (278) Movement tests: a. The men saw one girl each. b. One girl each was seen by the men. c. *How many girls did the men see each? d. *One girl, the men saw each. (279) Coordination test: 83 a. The men saw one girl and five monkeys each. b. ?The men saw one girl each and five monkeys. The other two types do not form a constituent with the distributee. D‐each appears to form a constituent with the distributor, and VP‐each seems to form a constituent with the VP. Not only is binominal each unique in its constituency, it is also unique in have a requirement that there be a distributee. Neither of the other types of each have this restriction. (280) Binominal each requires narrow‐scope NP a. *The men danced each b. The men danced two schottisches each c. *The men danced the schottische each d. Each man danced (the schottische). e. The men each danced (the schottische). While the D‐each and adverbial each examples, (c) and (d), are both acceptable without any distributee, the binominal each example that lacks a distributee is unacceptable. Further, the unacceptability of (b), a binominal each example which has an object, but one than cannot be distributed over another set, shows that binominal each imposes restrictions on what sorts of nominals it will associate with. The other two types of each appear to have no such restrictions. This observation leads into Safir & Stowell’s main claim: that binominal each uniquely is a relation between the two nominals, taking both members of the relation as arguments. This proposal is presented in their lexical entry for binominal each: (281) each =𝜆𝑋.𝜆𝑌.𝜆𝑝 ! !" .∀𝑦<𝑌,𝑝 𝑋 𝑦 = 1 Binominal each takes three arguments: two pluralities and one predicate. The relation says that for every member y of a plurality Y, a predicate p is true of X and y. This 84 encapsulates the interpretation of a distributive sentence such as (282) where every member of the distributor set the boys read two books. (282) The boys read two books each. Binominal each takes the plurality two books as X and the plurality the boys as Y. To be very rough, the desired end result of the calculation is one where the predicate read is true iff every member of the boys read two books: (283) (282) = 1 iff ∀𝑦< the boys , y read two books. This represents a very rough direction in which to head; in fact, deriving this result compositionally requires considerable amounts of movement to get the various DPs in appropriate places for each to be able to take them as its arguments. The following structure has the two nominals that participate in a distributive relation generated close to binominal each and moving to higher positions in the structure. 85 (284) Binominal Each Working from the bottom up, each takes two arguments: it takes the trace of the distributor, the boys, as its internal argument; as its external argument, it takes the trace of the distributee, two books. (285) each 𝑡 ! ! = each 𝑡 ! ! = each 𝑔 1 (286) 𝑡 ! each 𝑡 ! ! = each 𝑔 1 𝑡 ! ! = each 𝑔 1 𝑔 2 Substituting the lexical entry for each given in (281) and applying it to the two arguments results in (287). (287) each 𝑔 1 𝑔 2 = a. 𝜆𝑌.𝜆𝑋.𝜆𝑝 ! !" .∀𝑦<𝑌,𝑝 𝑋 𝑦 = 1 𝑔 1 𝑔 2 = b. 𝜆𝑝 ! !" .∀𝑦<𝑔 1 ,𝑝 𝑔 2 𝑦 = 1 86 At this point, the two pluralities are assignment functions waiting to be assigned when the calculation meets the antecedents of the traces in the positions they raised to. All the expression says so far is that for every member y of g(1), the function p is true of y and g(2). The next level up fills in the function, read. (288) read 𝑡 ! each 𝑡 ! ! = 𝑡 ! each 𝑡 ! ! read = a. 𝜆𝑝 ! !" .∀𝑦<𝑔 1 ,𝑝 𝑔 2 𝑦 = 1 read = b. = 1 iff ∀𝑦<𝑔 1 , read 𝑔 2 𝑦 = 1 c. = 1 iff ∀𝑦<𝑔 1 , 𝜆𝑥.𝜆𝑧.𝑧 read 𝑥 𝑔 2 𝑦 = 1 d. = 1 iff ∀𝑦<𝑔 1 ,𝑦 read 𝑔 2 The expression is now of type t. It is true iff every member of g(1) read g(2). Now the two bound elements, the two pluralities that each relates, must be filled in. Lambda abstraction maps the index 2 to the variable x, which will eventually be bound by the narrow‐scope item, two books. (289) 𝜆𝑥. read 𝑡 ! each 𝑡 ! ! ! ! = 𝜆𝑥.∀𝑦<𝑔 1 ,𝑦 read 𝑥 Before going any further it’s important to sort out the denotation of the plurality two books. (290) contains a useful denotation of two. This denotation takes two predicates as its arguments. One predicate will be the one that determines what kind of thing there is two of: two books, two cats or two flying saucers. The other predicate is the one in (289), which was created in the all the previous steps. (290) two = 𝜆𝑃 !,! .𝜆𝑄 !,! . 𝑢:𝑃 𝑢 = 1 and 𝑄 𝑢 = 1 ≥ 2 This lexical entry says that the number of members of a set, defined as those elements u which satisfy both P and Q, is equal to or greater than two. The following step applies the predicate book to (290), resulting in an expression that says that the number of members of the set of books that are true of Q is greater than or equal to two. 87 (291) two books = two books = a. =𝜆𝑄. 𝑢: books 𝑢 = 1 and 𝑄 𝑢 = 1 ≥ 2 b. =𝜆𝑄. 𝑢: 𝜆𝑧.𝑧 is a book 𝑢 = 1 and 𝑄 𝑢 = 1 ≥ 2 c. =𝜆𝑄. 𝑢:𝑢 is a book and 𝑄 𝑢 = 1 ≥ 2 This expression then takes (289) as its argument. Through functional application, the result is an expression of type t which is true if and only if the number of members of the set of books that were read by every member of the as‐yet unassigned plurality 𝑔 1 is greater than or equal to two. (292) two books 𝜆𝑥.∀𝑦<𝑔 1 ,𝑦 read 𝑥 = a. 𝜆𝑄. 𝑢: 𝜆𝑧.𝑧 is a book 𝑢 = 1 and 𝑄 𝑢 = 1 ≥ 2 𝜆𝑥.∀𝑦< 𝑔 1 ,𝑦 read 𝑥 = b. = 1 iff 𝑢: 𝜆𝑧.𝑧 is a book 𝑢 = 1 and 𝜆𝑥.∀𝑦<𝑔 1 ,𝑦 read 𝑥 𝑢 = 1 ≥ 2 c. = 1 iff 𝑢:𝑢 is a book and ∀𝑦<𝑔 1 ,𝑦 read 𝑢= 1 ≥ 2 The last stage is to give the assignment 𝑔 1 a referent through lambda abstraction. Lambda abstraction introduces the variable z, making the expression again a predicate. (293) 𝜆𝑧. two books 2 read 𝑡 ! each 𝑡 ! !! ! = (294) 𝜆𝑧. 𝑢:𝑢 is a book and ∀𝑦< 𝑧,𝑦 read 𝑢= 1 ≥ 2 (295) 𝜆𝑧. 𝑢:𝑢 is a book and ∀𝑦< 𝑧,𝑦 read 𝑢= 1 ≥ 2 the boys a. = 1 iff 𝑢:𝑢 is a book and ∀𝑦< the boys ,𝑦 read 𝑢= 1 ≥ 2 b. = 1 iff 𝑢:𝑢 is a book and ∀𝑦< the boys ,𝑦 read 𝑢= 1 ≥ 2 This expression is true if and only if the members of the each set of books that were read by individual boys is at least two. The very last stage is to provide a denotation for the plurality the boys. (296) the boys = 𝜄𝑋:𝑋 is the largest plurality of contextually relevant boys This calculation represents formally what intuitively seems to be going on: there are iterations of the narrow‐scope set for each member of the wide‐scope set. In this case, for 88 each member of the set the boys, there is a two‐member set defined as the set of books read by that boy. In a sense, one can think in terms of the iterations covarying with members of the distributor. It is this observation that leads into an exploration of Binding Theory, because covariation is a classic signal of binding. The next section will explore similarities between reciprocals and binominal each with regard to their syntactic and semantic functions. 4.3.2 Spanish Reciprocals and binominal each The idea that binominal each and numeral reduplication should both be affiliated with (if not reduced to) binding grows out of the empirical observation that the restrictions on the distribution of binominal each and numeral reduplication bear a certain resemblance to those of anaphora. As was pointed out in the syntax chapter, observations of the parallelism between the distribution of binominal each and elements that are subject to binding Principle A go back at least to (Burzio 1981). This section explores approaches that allow a unified semantic account of both distributive and reciprocal structures. It takes as its starting point an observation regarding Spanish reciprocals due to Karlos Arregi, who pointed out that reciprocals in that language are composed of two parts: el uno ‘the one’ and al otro ‘the other’ (Arregi 2001). Arregi’s semantics for Spanish reciprocals is much like the semantics proposed for binominal each, except that while binominal each relates two distinct sets to one another, reciprocals map parts of one set to all the other parts of that set. This section draws on an in insight into Spanish reciprocals presented by Karlos Arregi, namely that Spanish reciprocals are comprised of two parts, which not only are morphologically distinct, but also have distinct semantic functions (Arregi 2001). The 89 reciprocal is comprised of an element that splits the antecedent into relevant sub‐parts, and another part that maps the sub‐parts onto the other sub parts. (297) Javier y Marx estuvieron hablando el uno con el otro. Javier and Marx were talking the one with the other ‘Javier and Marx talked with each other.’ (based on Arregi:1 #1) Arregi argues that Spanish reciprocals are comprised of two distinct pieces: el uno and el otro. Analyzing the two parts separately is especially plausible given that they need not be adjacent to one another, and in fact, can even appear separated by an island: (298) Elian e Irena me han dicho que [[el departamento que ha contrado al uno] quiere contratar al otro.] Elian and Irena me have told that the department that has hired to‐the one wants hire to‐the other ‘Elian and Irena told me that the departments that hired each of them want to hire the other.’ (based on Arregi:3 #8) In this example, el uno appears inside a relative clause, and yet el otro is object of the matrix object. This shows that that the two elements may occur separately, and that the two elements need not be in a c‐command relation with each other; however, both elements must be in the domain of the antecedent. Before getting into the detail of Arregi’s proposal, it’s important to take stock of what an account of reciprocals needs to do. Such and account needs to do two things: it needs to break the plural antecedent into sub‐parts, and second, it needs to map those sub‐ parts onto one another. (299) [Alex and Sam]1 love one another1 In this sentence, the plurality Alex and Sam is made up of the two atomic individuals Alex and Sam. For the reciprocal reading where Alex loves Sam and Sam loves Alex, it is crucial that the plurality Alex and Sam not have a collective reading. Such a reading is 90 possible for coordinated names, as the following illustrates, but the reciprocal interpretation does not require that Alex loves herself in addition to loving Sam. (300) Alex and Sam weigh five hundred pounds. The predicate weigh five hundred pounds is unlikely to be true of Alex and Sam individually. It is much more plausible that the weight of both of them together adds up to five hundred pounds. Something in the way a reciprocal works requires an individual reading. This is further shown by the contrast in piano sentences: (301) Piano sentences a. [Alex and Sam]1 lifted a/the/their1 piano. b. [Alex and Sam]1 lifted each other’s1 piano. While (a) is compatible with a group effort to move the piano, (b) is not. It is only with Alex (alone) lifting Sam’s piano and Sam (alone) lifting Alex’s. To do this, a reciprocal account needs a way to break its antecedent into sub‐parts, in much the same way that binominal each needs to break its distributor into sub‐parts. How this might be done will be discussed in a little bit. In addition to excluding the collective reading, a reciprocal account also needs to enforce reciprocality, i.e., that Alex loves Sam and Sam loves Alex. Arregi’s approach employs variable binding to do this. The internal argument of the verb is whoever the external argument isn’t. The following is a sloppy first approximation of this approach: (302) Alex and Sam love one another = 1 iff ∃𝑋. X: Alex, Sam .∀𝑥,𝑥∈ X.𝑥 loves 𝑋−𝑥 This says that there is a plurality X that consists of Alex and Sam, and that for every individual in the set X, x loves everyone in X but themself. Because the plurality in this example is composed of two atoms, it works out that Alex loves Sam and Sam loves Alex. 91 For a plurality with more members, this approach correctly maps one sub‐part to every sub‐part but itself. In the following, the plurality has three members. Given that the reciprocal predicts that that subject acts on every member of the plurality other than itself, the predicted interpretation is one where each girl tuned all the cars but her own. (303) Kim, Krystal, and Kristin tuned each other’s bikes. The prediction is borne out. This sentence is compatible with a scenario where all the bikes got tuned twice. Whatever semantics one uses for reciprocals, it must be weak enough to allow readings where everybody but the owner tuned each bike, rather than there needing to be a particular mapping of one element in the antecedent set to the other (or a specific) element in the antecedent set. (304) Rachael and Rose love one another (305) Rachael and Rose ! 2 the one 𝑡 ! 1 𝑡 ! love an other 1 ∅ ! =1 iff: (306) other 1 ! = 𝜆𝑝.𝜆𝑏.𝑏<𝑝 & 𝑏≠𝑔 1 92 The denotation of other takes a predicate as an argument. In this situation, the argument will turn out to be the plurality Rachel and Rose, but in other contexts it can be any predicate, such as rabbit. (307) Fluffy saw another rabbit. (308) 𝑎𝑛𝑜𝑡ℎ𝑒𝑟 ! rabbit = 𝑎 other rabbit = (309) 𝜆𝑝.𝜆𝑏.𝑏<𝑝 &𝑏≠𝑔 1 𝜆𝑟. rabbit 𝑟 = 𝜆𝑏.𝑏< 𝑟:𝑟 𝑖𝑠 𝑎 𝑟𝑎𝑏𝑏𝑖𝑡 & 𝑏≠𝑔 1 Through existential closure: Through existential closure: (310) ∃𝑏.𝑏< 𝑟:𝑟 𝑖𝑠 𝑎 𝑟𝑎𝑏𝑏𝑖𝑡 & 𝑏≠𝑔 1 (311) see 𝑎𝑛𝑜𝑡ℎ𝑒𝑟 ! 𝑟𝑎𝑏𝑏𝑖𝑡 = 𝜆𝑥.𝜆𝑦.𝑦 sees 𝑥 ∃𝑏.𝑏< 𝑟:𝑟 is a rabbit & 𝑏≠𝑔 1 = 𝜆𝑦.∃𝑏.𝑏< 𝑟:𝑟 is a rabbit & 𝑏≠𝑔 1 𝑠𝑡 𝑦 sees 𝑏 (312) 𝜆𝑦.∃𝑏.𝑏< 𝑟:𝑟 is a rabbit & 𝑏≠𝑔 1 𝑠𝑡 𝑦 sees 𝑏 Fluffy = According to the calculation, Fluffy saw another rabbit is true iff there exists an individual b that is a rabbit and that is distinct from Fluffy such that Fluffy saw b. (312) 𝜆𝑦.∃𝑏.𝑏< 𝑟:𝑟 is a rabbit & 𝑏≠𝑔 1 𝑠𝑡 𝑦 sees 𝑏 Fluffy = ∃𝑏.𝑏< 𝑟:𝑟 is a rabbit & 𝑏≠ Fluffy 𝑠𝑡 Fluffy sees 𝑏 According to the calculation, Fluffy saw another rabbit is true iff there exists an individual b that is a rabbit and that is distinct from Fluffy such that Fluffy saw b. According to the calculation, Fluffy saw another rabbit is true iff there exists an individual b that is a rabbit and that is distinct from Fluffy such that Fluffy saw b. The same process is in force in the use of other in one another in this system, but instead of inputting a predicate like is‐a‐rabbit, the argument of other is a null element bound by the plurality that is the antecedent of the reciprocal. At this stage, the denotation 93 of other ∅ ! is a predicate that is satisfied by an individual that is a member of the plurality g(2) and which is not identical to g(1). (313) other 1 ! ∅ ! ! = 𝜆𝑝.𝜆𝑏.𝑏<𝑝 & 𝑏≠𝑔 1 𝑔 2 = As before, existential closure applies: As before, existential closure applies: (314) ∃𝑏.𝑏<𝑔 2 & 𝑏≠𝑔 1 (315) love ∃𝑏.𝑏<𝑔 2 & 𝑏≠𝑔 1 = 𝜆𝑥.𝜆𝑦.𝑦 loves 𝑥 ∃𝑏.𝑏<𝑔 2 & 𝑏≠𝑔 1 = 𝜆𝑦.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑔 1 𝑠𝑡 𝑦 loves 𝑏 (316) 𝜆𝑦.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑔 1 𝑠𝑡 𝑦 loves 𝑏 ! 𝑡 ! ! = By lambda extraction, m takes assignment function 1. (316) 𝜆𝑦.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑔 1 𝑠𝑡 𝑦 loves 𝑏 ! 𝑡 ! ! = 𝜆𝑦.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑔 1 𝑠𝑡 𝑦 loves 𝑏 ! 𝑔 1 = ∃𝑏.𝑏<𝑔 2 &𝑏≠𝑔 1 𝑠𝑡 𝑔 1 loves 𝑏 By lambda extraction, m takes assignment function 1. By lambda extraction, m takes assignment function 1. (317) 𝜆𝑚.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑚 𝑠𝑡 𝑚 loves 𝑥 The constituent that will bind m is the following: (318) 𝑡ℎ𝑒 𝑜𝑛𝑒 𝑡 ! ! = ∃!𝑟.𝑟< g 2 (319) 𝜆𝑚.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑚 𝑠𝑡 𝑚 loves 𝑏 ∃!𝑟.𝑟< g 2 = Through lambda extraction, z takes assignment function 2. (319) 𝜆𝑚.∃𝑏.𝑏<𝑔 2 &𝑏≠𝑚 𝑠𝑡 𝑚 loves 𝑏 ∃!𝑟.𝑟< g 2 = ∃!𝑟.∃𝑏.𝑟<𝑔 2 & 𝑏<𝑔 2 &𝑏≠ 𝑟 𝑠𝑡 𝑟 loves 𝑏 Through lambda extraction, z takes assignment function 2. Through lambda extraction, z takes assignment function 2. (320) 𝜆𝑧.∃!𝑟.∃𝑏.𝑟< 𝑧 & 𝑏< 𝑧 &𝑏≠ 𝑟 𝑠𝑡 𝑟 loves 𝑏= 94 (321) 𝜆𝑧.∃!𝑟.∃𝑏.𝑟< 𝑧 & 𝑏< 𝑧 &𝑏≠ 𝑟 𝑠𝑡 𝑟 loves 𝑏 Rachel, Rose = ∃!𝑟.∃𝑏.𝑟< Rachel, Rose & 𝑏< Rachel, Rose & 𝑏≠ 𝑟 𝑠𝑡 𝑟 loves 𝑏 According to this calculation, the sentence Rachel and Rose love one another is true iff there exist an r that is a member of the plurality Rachel and Rose and there is a b that is a member of the plurality Rachel and Rose, b and r are distinct, and r loves b. 4.3.3 Binding and Movement approaches for NR As they have been described so far, both binominal each and reciprocals have several similar properties. First, they both have some process of breaking a plurality into sub‐ parts. Second, they both relate those sub‐parts to something else. This is where they differ. In reciprocals, each sub‐part of the set is related to the other sub‐parts, but in binominal each, iterations of the narrow‐scope item are mapped onto each sub‐part of the wide‐scope item. Although these two phenomena use different relations, the fact that they both employ set‐splitters and relations is enough to try to put the two together. This intuition is further fed by Kannada’s use of reduplication for both distributivity and bound pronouns, again showing a relationship between distributivity and binding. (322) Muru hudugaru jeru‐jeru hannu tIndru Three boys two two fruits ate `Three boys two‐two fruits ate.' The proposal is that the reduplicant in both cases is the function that breaks the wide‐scope item into parts. In these examples, it breaks the boys into individual boys. The reduplicant’s attachment to different things results in the use of different relations: the distributive relation in one, and the bound relation in the other. 95 The structure for English binominal each is expected to transfer over to Kannada, with some word‐order details that need to be derived. One possibility is that the reduplicant moves up to two fruits before that whole complex raises to a position that will be spelled out before the verb. (323) eat two fruits RED 3 boys (324) RED = 𝜆𝑋.𝜆𝑌.𝜆𝑝 ! !" .∀𝑦<𝑌,𝑝 𝑋 𝑦 = 1 (325) 𝑡 ! RED 𝑡 ! = 𝜆𝑋.𝜆𝑌.𝜆𝑝 ! !" .∀𝑦<𝑌,𝑝 𝑋 𝑦 = 1 𝑔 1 𝑔 2 = 𝜆𝑝 ! !" .∀𝑦<𝑔 1 ,𝑝 𝑔 2 𝑦 = 1 (326) 𝜆𝑝 ! !" .∀𝑦<𝑔 1 ,𝑝 𝑔 2 𝑦 = 1 wash (327) two fruits = 𝑊𝑜𝑟𝑘 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑖𝑠. (326) 𝜆𝑝 ! !" .∀𝑦<𝑔 1 ,𝑝 𝑔 2 𝑦 = 1 wash =∀𝑦<𝑔 1 , eat 𝑔 2 𝑦 = 1 (327) two fruits = 𝑊𝑜𝑟𝑘 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑖𝑠. (327) two fruits = 𝑊𝑜𝑟𝑘 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑖𝑠. (328) 𝜆𝑥.∀𝑦<𝑔 1 ,𝑦 eats 𝑥= 1 (329) 𝜆𝑥.∀𝑦<𝑔 1 ,𝑦 eats 𝑥= 1 two fruits =∀𝑦<𝑔 1 ,𝑦 eats two fruits 96 (330) 𝜆𝑧.∀𝑦< 𝑧,𝑦 eats two fruits (330) 𝜆𝑧.∀𝑦< 𝑧,𝑦 eats two fruits (331) 𝜆𝑧.∀𝑦< 𝑧,𝑦 eats two fruits three boys 4.3.4 Further Support: Case Marking and Dravidian ‘one’ reduplication Subbãrão and Evaert 2012 provides data that suggests that ‘one’ reduplication in other Dravidian languages is composed of iterations of ‘one’ that bear different case markers. One iteration has the case marker of the antecedent while the other bears the case marker of the reflexive’s position. One such example is the following, from Tamil: (332) avaN‐ukku avaN‐ai avaN‐ukk‐e: piTikkavillai (Tamil) he‐dat self‐acc self‐dat‐emph didn’t like ‘He didn’t like himself.’ (Subbãrão #17) The antecedent is a dative subject, and so one of the iterations of one is marked with the dative case marker ‐ukk. The first iteration of ‘one’ bears the accusative case marker, which agrees with the position that the reflexive holds. That this sentence uses a dative subject is important, because the nominative case marker is a zero morpheme in Dravidian languages: (333) va:LLu okaLLa‐ni okaLLu poguDu‐konn‐a:ru (Telugu) they one.pl‐acc one.pl.nom praise‐vrec‐pst‐3pl ‘They praised each other.’(Subbãrão:#1) The double case marking on reflexives can also occur when the reflexive agrees with an object, such as a dative: (334) abba:yilu amma:yil‐ki okkaLLa‐ki okkaLLa‐ni paricayam ce:se:ru boys girl‐dat one‐dat one‐acc introduction did The boys introduced the girls1 to each other1.’ (Subbãrão:#23) Much the same pattern appears in formal Kannada, as represented by Sridhar’s grammar. Like Subbãrão’s Telugu and Tamil data, in formal Kannada the case marker 97 appears on the first iteration of ‘one.’ Speakers reported that in speech, either iteration could host the case marker. (335) Bassu ka:ru onda‐kk‐ondu Dikki hoDedavu bus car one‐dat‐one collision hit‐psr‐3npl ‘The bus and car hit each other.’ (Sridhar:#450) The two iterations of ‘one’ can also host different case markers. If Subbãrão’s approach, which argues that the first iteration bears the antecedent’s case, is true, the following Kannada example is problematic because there is no ablative NP in the sentence that the reflexive can be using as its antecedent. In fact, it calls into question whether or not ‘one’ reduplication is a real reciprocal, since reciprocals must be bound in their governing category. (336) I: ro:ga obbar‐ind‐obbar‐ige bahu be:ga haraDuttide this disease one‐hum‐abl‐one‐hum‐dat very quickly spread‐n.past‐cont‐3sn ‘This disease is spreading quickly from one to the other.’ (Sridhar:#454) Whether or not ‘one’ reduplication is a reciprocal, the observation that Dravidian ‘one’ reduplication treats the two iterations on ‘one’ separately with respect to case agreement provides support for adoption of Arregi’s approach to reciprocals, especially as done here, in the context of distributivity. Since the idea is to say that numeral reduplication encapsulates the relation between two different sets, it is not surprising that the one part associated with the distributor bear some marking that reflects that and the part that is associated with the distributee reflects its identity as being associated with the distributee. 4.4 Binding, Take 2: Multiplication and a variable over cardinalities Schwartzchild’s initial intuition was that a distributive reading is best represented as iterations of the lower‐scope item (in his case, the VP) for every relevant sub‐part of the 98 wide‐scope element. His approach locates the operator in a position that takes scope over the entire VP, and creates a relation between iterations of the VP and individuals. Although such an approach naturally incorporates a distribution over events reading, it is not without its problems, not the least of which being that such an account cannot handle a case of reverse scope, where an element inside the VP takes wide scope over the subject. One alternative view that does not have this problem locates the distributive operator within the narrow‐scope DP. This is a good thing because this allows the distributive operator to take scope only over the DP that participates in the distributive relation, which means that such an approach would be able to account for a reading where all the girls were nominated for the same two awards, but each girl was nominated by a different group of lizards. (337) Five lizards nominated every girl for two awards. This approach marks the narrow‐scope DP and creates iterations of that DP for each member of the wide‐scope DP. The mechanics of this approach draw heavily on the proposal for multiplicative numerals in (Ionin and Matushansky 2006), which will be described in the next section. 4.4.1 Background: Ionin and Matushansky Ionin and Matushansky’s paper on complex numerals introduces a semantics for multiplicative numerals, i.e., two hundred, which derives the cardinality of these number by multiplying one component number with another. 17 99 (338) The Two Hundred Books This structure shows that the numeral two takes as its argument the already numerically quantified hundred books. What this does is create two iterations of a set of hundred books. (339) Two hundred books a. book = 𝜆𝑏 ! .book 𝑏 b. hundred = 𝜆𝑃 !,! .𝜆𝑥 ! .𝜆𝑆 !,! . 𝛱 𝑆 𝑥 ∧ 𝑆 = 100∧∀𝑠∈ 𝑆 𝑃 𝑠 The denotation here of hundred makes use of partitions, represented by the symbol 𝛱. A partition is a way of dividing up the members of a set so that the members of the set are only ever members of one sub‐group at a time. The use of partitions here serves to make sure that hundred books denotes exactly a hundred books and not at least a hundred books. An alternative way to count the members of the set S would be with covers, which do not require exclusive membership. Because one individual can be a member of more than one cover, while there may still be 100 covers, they may not be 100 individuals in the set. Using partitions is a way to make sure that there are 100 individuals in the set. 100 (340) 𝛱 𝑆 𝑥 = 1 iff S is a cover of x, and ∀𝑧,𝑦∈ 𝑆 𝑧=𝑦∨¬∃𝑎 𝑎≼ ! 𝑧∧𝑎≼ ! 𝑦 (forbidding that cells of the partition overlap ensures tht no element is counted twice) (Ionin and Matushansky:#6) (341) A set of individuals C is a cover of a plural individual X iff X is the sum of all the members of C: ⊔𝐶=𝑋 (Ionin and Matushansky:#7) (342) hundred books = 𝜆𝑥 ! .𝜆𝑆 !,! . 𝛱 𝑆 𝑥 ∧ 𝑆 = 100∧∀𝑠∈ 𝑆 book 𝑠 The denotation of two is added to hundred books through predicate modification. (343) two = 𝜆𝑃 !,! .𝜆𝑥 ! .𝜆𝑆 !,! . 𝛱 𝑆 𝑥 ∧ 𝑆 = 2∧∀𝑠∈ 𝑆 𝑃 𝑠 (344) two hundred books = 𝜆𝑥 ! .∃𝑆 𝛱 𝑆 𝑥 ∧ 𝑆 = 2∧∀𝑠∈ 𝑆∃𝑆′𝛱 𝑆′ 𝑥 ∧ 𝑆 ! = 100∧∀𝑠∈ 𝑆 ! book 𝑠′ 4.4.2 Proposal: an incomplete lexical entry (345) RED two books a. book = 𝜆𝑏 ! .book 𝑏 b. two = 𝜆𝑃 !,! .𝜆𝑥 ! .𝜆𝑆 !,! . Cover 𝑆 𝑥 ∧ 𝑆 = 2∧∀𝑠∈ 𝑆 𝑃 𝑠 c. RED = 𝜆𝑃 !,! .𝜆𝑥 ! .𝜆𝑆 !,! . Cover 𝑆 𝑥 ∧ 𝑆 =𝑔 1 ∧∀𝑠∈ 𝑆 𝑃 𝑠 d. RED two books = 𝜆𝑥 ! .∃𝑆 Cover 𝑆 𝑠 ∧ 𝑆 =𝑔 1 ∧∀𝑠∈ 𝑆∃𝑆′ Cover 𝑆′ 𝑥 ∧ 𝑆 ! = 2∧∀𝑠∈ 𝑆 ! book 𝑠′ Two differences from the original denotation of numerals: • introduction of a variable (g(1)) • using covers rather than partitions. Covers allow for overlap readings, which is necessary for distributivity, but undesirable for an account of numerals. 4.4.3 A Problem: Even distribution As already described, native speakers report that the total number of fruits that were eaten in the scenario described in (346) is 12. (346) Three boys at four‐four fruits. 101 The multiplicative account of NR in Kannada correctly derives 12 as the maximum number of apples, but the interpretation described by the multiplicative account turns out not to be strong enough to accurately reflect speakers’ judgments of this sentence. Consider the following scenario: (347) Mike, Brent, and Lance were given a fruit basket, and each of them ate some of the fruit. Mike really likes kumquats, so he ate nine of them. Brent doesn’t like fruit much at all, so he only ate one orange. Lance ate two plums. In this scenario, a total of 12 fruits were eaten, and each fruit was eaten by one of the three boys. It is argued that the multiplicative account would predict that (346) would be true in this situation, but native speakers judge it to be false. Native speakers report that (346) is true only in a situation where the boys all ate equal numbers of fruits; they each have to have eaten four. The multiplicative account, however, is not strong enough to ensure that each boy eat four, only that the total number of fruits is reached. (348) Red 3 four fruits = 𝜆𝑥 ! .∃𝑆 Cover 𝑆 𝑠 ∧ 𝑆 = 3∧∀𝑠∈ 𝑆,∃𝑆′ Cover 𝑆′ 𝑥 ∧ 𝑆 ! = 2∧∀𝑠∈ 𝑆 ! ,𝑠′ is a fruit This expression creates three sets of four fruits, but it does not link them to the three boys. Since it’s based on Ionin and Matushansky’s semantics for multiplicative numerals, it’s not really designed to do such a thing; given what they were trying to account for, keeping the three sets of distinct would not have been desirable. In this case, however, the only way to ensure that every boy ate the same number of fruits is to formally link each boy with his own set of four fruits. This would add a level of complexity to the system. In addition to the part of the lexical entry that multiplies the sets of four fruits by three, there must also be a portion that individuates the group of three boys and then maps each individual with a set. I’m not sure what that would look like, but considering that it ends up 102 needing to do precisely what the other types of distributive particles need to do, and it does it in two steps rather than in one lexical entry, it seems like this isn’t the best solution to the problem. 4.5 Alternatives 4.5.1 D-Operator 4.5.1.1 How D works Schwartzchild’s account is kind of similar to this alternative semantics idea, because the denotation of a distributive sentence ends up being a universal quantification over alternatives, but it uses a different formalism, and the operator that generates alternatives applies to the VP rather than the wide‐scope item in the distributive sentence. Schwartzchild employs a distributive operator that applies to predicates. This operator takes the predicate, and then says that for whatever external argument the predicate has, the predicate is true of any singularities that make up that external argument. I’ll work through one of his examples, but I’m translating it into lambda notation because that’s what I’m most comfortable with. (349) John and Mary moved the car. (350) 𝐽𝑜ℎ𝑛 𝑎𝑛𝑑 𝑀𝑎𝑟𝑦 𝐷 𝑚𝑜𝑣𝑒𝑑 𝑡ℎ𝑒 𝑐𝑎𝑟 The operator D, which applies to the VP move the car is what makes the sentence distributive. (351) 𝐷 = 𝜆𝑝 !" .𝜆𝑋 ! .∀𝑥<𝑋 𝑝 𝑥 The distributive operator takes a predicate and an external argument (X). The external argument should be made up of more than one element, and there is a universal 103 quantification over the elements in X. All elements x in the plural X satisfy the predicate. In effect, both John moved the car and Mary moved the car are true. (352) 𝐷 move the car = 𝜆𝑝 !" .𝜆𝑋 ! .∀𝑥<𝑋,𝑝 𝑥 𝜆𝑦.𝑦 moved the car (353) 𝜆𝑋 ! .∀𝑥<𝑋,𝑥 moved the car Now, we have a statement that says that moved the car is true of all individuals that make up X. The next step is to fill in what exactly X is. In this example, the members of X are spelled out: John and Mary. (354) 𝜆𝑋 ! .∀𝑥<𝑋 𝑥 moved the car John∧Mary = (355) ∀𝑥< John, Mary 𝑥 moved the car This statement says that both of the members in the set 𝐽𝑜ℎ𝑛,𝑀𝑎𝑟𝑦 moved the car, and that the predicate is true of them as individuals (this important, because otherwise, this would be a group reading). 4.5.1.2 What about when the wide-scope element is in the VP, though? At the moment, I’m content to think that Schwartzchild’s D works for Kannada numeral reduplication, but it hits a major snag when I try to use it for certain English distributve sentences, when the wide‐scope element is in the VP and takes scope over the external argument. (356) Three boys painted each of the (three) cars. 18 Schwartzchild’s examples generally involve the subject taking scope over (depending on how one looks at it) either the VP or the object in the VP. In this sentence, it is the object, the two cars, that takes scope over the boys. 104 (357) Adam, Ben, and Charlie painted the Prius. David, Ed, and Frank painted the Leaf. George, Henry, and Ian painted the Tesla. Given that Schwartzchild’s D applies to the VP, the object in the VP is expected to remain constant, and the external argument varies. What this example shows is covariation of the external object with each individual object. This is something that just can’t happen with Schwartzchild’s D. (358) ∀𝑥.𝑥∈ three boys 𝑥 painted three cars This expression describes a situation where each one of the members of a set of three boys independently painted three cars, like in the following. (359) Adam painted the Volt, the Leaf and the Tesla Ben painted the Impala, the Caprice, and the Charger Charlie painted the 911, the XJS and the Gallardo This isn’t at all what the sentence in (357) is supposed to mean. The only solution is to divorce the distributivity operator from the VP, making D work quite differently. 4.5.2 A Pragmatic Account This approach takes a wildly different tack from the other accounts considered in this dissertation. Rather than assuming that the reduplication is a syntactic phenomenon that has semantic import, a pragmatic account suggests that the pragmatic reasoning triggered by reduplication sets in motion a semantic process that has certain syntactic requirements. In effect, this approach is the mirror opposite of the primary proposal of this dissertation. PR is the best place to start. Consider an example such as the following: (360) Every boy saw the snake next to him. 105 The pronoun in this example can have either a bound or a referential reading. When the pronoun is reduplicated, it has only the bound reading. Reduplication serves as a disambiguation strategy, limiting the possibilities of interpretation. NR is also a disambiguating strategy. Sentences that contain two pluralities in the appropriate syntactic relation may have either a distributive or collective interpretation. Repetition of the distributee’s numeral disambiguates the sentence, and gets rid of the collective reading. Why would it be the case that reduplication serves as a disambiguation strategy? Grice’s manner maxim directs the speaker to, among other things, be brief in speech. The quantity maxim directs the speaker to “make your contribution as informative as is required (for the current purposes of the exchange)” (Grice 1967). The two in conjunction suggest that the repetition of the pronoun must serve some purpose beyond that which the non‐reduplicated pronoun serves. Considering the manner maxim’s directive to avoid ambiguity, it is reasonable to interpret the contribution of the repeated pronoun as a marker that reduces ambiguity. Why do the disambiguation strategies disambiguate in the direction that they do? It is also logically possible that PR would force a referential reading, or that NR would force a collective reading. The answer goes back to the directive to be as informative as possible. In both cases, reduplication disambiguates in favor of the more marked reading: pronouns are bound only when they need to be; they are happily free whenever there is no antecedent for them. According to this pragmatic approach, the syntactic constraints that limit the distribution of NR and PR are not syntactic or semantic requirements of the reduplicant, 106 but simply properties of the readings they generate. The fact that a reduplicated pronoun must be within the c‐command domain of an antecedent is derived from the fact that it cannot have a referential reading, and relies on an antecedent for its reference. The fact that a reduplicated numeral must be within the c‐command domain of a plurality is similarly derived from its having a distributive reading: distributive readings are necessarily relations between pluralities that are in a c‐command relation. Further support for a pragmatic approach to reduplication in Kannada comes from its ability to incorporate wh‐reduplication, which has seemed like an outlier in its lack of a c‐command requirement. However, the exhaustivity of wh‐reduplication, following Mary Byram‐Washburn’s work on the exhaustivity of it‐clefts, can be argued to be an implicature in much the same way that she argues that the exhaustivity in it‐clefts is pragmatically derived. Finally, it goes well with the intuition of native speakers that reduplication has some interplay with emphasis or focus. Speakers frequently make reference to emphasis when describing the difference between a reduplicated and non‐reduplicated sentence, saying that there is more emphasis on a reduplicated pronoun or numeral. All of this said, there is one major problem with a pragmatic account: implicatures must be cancellable. This is one of the primary defining features of an implicature. If numeral reduplication or pronoun reduplication disambiguate through pragmatic reasoning, then that reasoning, like the reasoning that derives other implicatures, should be able to be cancelled. It is not. Sentences with reduplicated numerals are distributive; reduplicated pronouns are bound. 107 5 Other Languages Several languages have phenomena with properties similar to the distributivity data explored in this dissertation. Due to each phenomenon’s particular mix of parallels to and contrasts with the Kannada data, they provide unique insights into the potential cross‐ linguistic applicability of the account explored here for Kannada. This section is intentionally a simple catalog of phenomena which could prove fruitful when explored in greater detail in further comparative work. 5.1 East Cree This project originally started with a course paper on numeral reduplication in East Cree, as described in the work of Marie‐Odile Junker. Reduplication of numerals associated with objects looks similar to the patterns found in Kannada: (361) (Na:‐)neu wa:pimin‐h chi: muwe‐uch anchi:awa:shich (RED‐)4 apples‐obvpl past eat.TA‐3pl children ‘The children ate four apples each.’ (Junker 2007:#25‐26) When the numeral ‘four’ is reduplicated, the sentence has a distributive reading in which the children are the distributor and the apples are the distributee. East Cree also allows reduplication of numerals associated with subjects, and as in Kannada, this triggers a distributive reading over events (362) na:‐neu awa:sh‐ich chi: mi:chisu‐uch Red‐4 child‐pl past eat.AI‐3pl ‘The children ate in groups of four.’ (Junker 2007:#33b) Even the individuating ‘one’ reduplication found in Kannada appears in East Cree. (363) pa:h‐peyakw wa:pimin‐h chi: muweuch anchi: awa:sh‐ich Red‐one apple‐obv past 3.eat.Tad d child‐pl ‘The children ate one apple each.’ (Junker 2007:#30) 108 (364) Pa:h‐peyakw awa:sh‐ich chi: muweuch wa:pimin‐h red‐one child‐pl past 3.eat.Tad apple‐obv.pl ‘Each of the children ate a/some apples.’ (Junker 2007:#31) As in Kannada, East Cree ‘one’ reduplication at first appears to associate with either distributee or distributor. However the gloss provided for the second example suggests that the distributive relation is actually between events of apple‐eating and children, rather than between children and apples. Numerals may attach to East Cree verbs, indicating that an action is being done in particular groupings. (365) Singular (Junker 2000:#13a) a. Mi:chisu: eat.AI.3 ‘s/he is eating’ b. Peyaku‐mi:chisu: one‐eat.AI.3 ‘S/he is eating alone.’ (366) Plural (Junker 2000:#13b) c. Mi:chisu:ch eat.AI.3pl ‘they are eating.’ d. Peya‐mi:chisu:ch one‐eat.AI.3pl ‘they are eating alone.’ e. Pa‐peya‐mi:chisu:ch one‐one‐eat.AI.3pl ‘they are eating one at a time.’ These reduplication patterns may be part of a larger pattern of reduplication indicating iterativity. In East Cree, partial reduplication of verb stems indicates continuous or repetitive action: (367) (Wa‐)uchipitam ‘she pulls continuously.’ (Junker 2007:#13) 109 A telic action like stopping or opening is done repetitively when its verbal form is reduplicated. (368) chipih‐chipihchipayu: red‐stop ‘s/he/it stopped and started, continuously.’ Other verbs, when reduplicated, have more of a stative feel: (369) Pa‐paka:simu: Red‐swim.AI‐3 ‘s/he always swims, s/he swims all the time.’ (Junker 2000:#3) (370) Wa‐uchima:u‐u Red‐chief.AI‐3 ‘He gives orders, does the work of a chief.’ (Junker 2007:#17) Proulx (2005) observes that repetitive reduplication of verbs exist in several different Algoquian languages. Fox, another Central Algonquian language, is reported to have two distinct types of verbal root reduplication that both indicate iterativity. CV reduplication indicates ongoing repetition of the action, while in CVCV reduplication, the action is repeated intermittently: (371) Na:‐nakiškawe:wa Red‐meet.3s.subj.3pobj ‘S/he continually meets them.’ (Proulx 2005:#5) (372) Naki‐nakiškawe:wa Red‐meet.3s.subj.3pobj ‘S/he meets them one after another.’ If all these reduplication types (numeral reduplication associated with nominals, reduplication of nominals that are affixed to the verb, and verbal reduplication) are all part of one continuum of iterative phenomena, how do these patterns fit with the binding story presented for Kannada? 110 If habitual readings can be treated as iterations of an action for every salient event, then verbal reduplication giving rise to a habitual reading falls squarely within the domain of a reduplicant that relates a distributor (salient events) with a distributee (some action) The interpretation of numerals that are attached to verbs is reported to be very similar to the event readings that arise NR is associated with a nominal but there is no nominal distributor, as in the following Kannada example: (373) Ibbibbaru huDugaru haDannu haDidaru Two‐two boys song sang `Two boys sang a song (iteratively).' The structure proposed for Kannada transparently predicts that this example will distribute boys over events. The numeral is associated with the boys, and the only possible distributor present in the sentence is a quantifier over events. I would like to know more about the parameters of this type of numeral reduplication. Can this type of reduplication in Cree associate with a plural subject, as in the following? (374) The boys four‐four‐ate. This example, if allowed by Cree, should be compatible with event readings where either some relevant group of boys split into groups of four and ate at once, or that the groups of four boys ate group by group. Either way, it is distributing groups of four boys over eating events. If this is possible, the question then is how the numeral comes to measure out the plurality of boys. One way that it could do this would rely on Algonquian languages’ pronominal argument structure: 19 since the verb in Algonquian languages is claimed to have incorporated pronouns, perhaps the numerals actually are adjacent to, and able to quantify over, a particular nominal. 111 One way to test this is to see if inputting a nominal that cannot be broken into the specified number of pieces would result in unacceptability: (375) Bob and George four‐four‐ate. The use of a two‐member conjunction in this example should rule out an event reading that requires the event to be done by four people since there are not four people to do the eating. It’s not clear that a PAH‐based analysis would assume that the reduplicant would be strongly associated with the subject, if the subject is not an appropriate distributor. It might be possible for the reduplicant to associate with a plurality in object position and distribute events over the object. This is the sort of reading that emerges in Kannada in sentences such as the following, where the object numeral is reduplicated but the subject is not a plurality: (376) Rama nalku‐nalku m6ngagaLannu noDida Rama four‐four monkeys saw.ms ‘Ram saw four‐four monkeys.’ Unlike Kannada, however, Cree would need to resort to an event reading in certain cases where the subject is a plurality, but it is not divisible by the numeral affix attached to the verb. 5.2 Extensionality and Hungarian determiner reduplication (D-Red) Hungarian allows reduplication of a variety of determiners. This reduplication, like NR in Kannada, signals a distributive reading. (377) Minden gyerek olvasott egy‐egy/hét‐hét könyvet every child read a‐a / seven‐seven book‐acc ‘Every child read a/seven book(s).’ (Farkas:#1) 112 (378) Minden gyerek más‐más könyvet olvasott Every child different‐different book‐acc read Every child read a different book. (Farkas:#2) (379) Minden gyerek külön‐ külön szobán aludt. Every child separate‐separate room slept ‘every child slept in a different room.’ (Farkas:#3) Farkas connects this phenomenon with reduplication of temporal adverbials, which signal an iterative interpretation: (380) A gyerek fel‐fel ébredt. The child up‐up woke ‘The child kept waking up.’ (Farkas:#55) Without reduplication, this sentence would refer to a single event of waking up, but with reduplication, the interpretation is that woke up multiple times. Farkas argues that both D‐Red and temporal adverbial reduplication are tied to iterativity, making the observation that D‐reduplication needs to be in the domain of a potential distributor. She further makes the observation that although distributors may be inviduals or events, they may not be worlds, as shown in the two following examples, where the reduplicant would be dependent on universal quantification over worlds introduced by a counterfactual and a modal: (381) *Ha a tanár megbetegedne, helyettesítené egy‐egy szülö. if the professor sick.cond.III replace cond.III a‐a parent ‘If the teacher were sick, a parent would replace him.’ (Farkas:#40) (382) Mari kell találkozzon egy‐egy párizsi tanárral. Mary must meet a‐a Parisian professor‐with ‘Mary must meet a professor from Paris.’ (Farkas:#41) Reduplication of the indefinite article egy ‘one’ and reduplication of other cardinals are distinct phenomena, supported by the observation that ‘one’ reduplication is possible in the following sentence, but no other reduplicated cardinal may occur in this context: 113 (383) Ahányszor egy‐egy/*két‐két hires személy meglátogatta a várost elvitték a kastélyba Whenever one‐one/two‐two person visited the town they‐took‐him the castle‐ to ‘Whenever one/two famous persons visited the town they took him to the castle.’ (Farkas:#47/50) Farkas argues that Hungarian wh‐word reduplication can act as distributor (in her terminology, it contributes the domain variable). She supports this by observing that, like English D‐each, reduplicated wh‐words appear to need some sort of quantificational element in their domain: (384) Ki‐ki leült a székére /egy‐egy székre who‐who sat‐down thechair.their.on/a‐a chair ‘Everybody sat down on their chair/a chair.’ (Farkas:#52) (385) *ki‐ki leült. who‐who sat‐down ‘Everybody sat down.’ (Farkas:#53) (386) Each child bought a book. (387) *Each child was intelligent. The parallelism between the Hungarian and English examples is a little tricky. The most important factor is that in (387), the predicate be intelligent is not telic, like buying a book, so there cannot be multiple events of being intelligent. Thus, each child cannot distribute over events, as it would in an English sentence closer to (385): (388) Each child sat. This sentence, unlike the Hungarian sentence, is fine. Ostensibly this is because there can be multiple sitting events in (388) but not in (385). 5.3 Korean –ssik, Choe’s “Anti-quantifier” (Choe 1987) Choe builds his case for what he calls “anti‐quantifiers” on data found in an earlier work (Y. H. Kim 1985). “Anti‐quantifiers” are quantificatinal elements that must be in the scope of 114 another quantifier. He argues that sentence‐final each in English (which, following (Safir and Stowell 1988), has been called binominal each in this dissertation) and the morpheme ‐ ssik in Korean, both share this property. Binominal each’s properties have already been explored, so this section will briefly introduce the basic Korean facts. Like NR, ‐ssik is associated with the distributee. In this case, the children are the distributor and the balloons are the distributee. (389) Emma‐ka [ai tul]‐eke [phwungsen‐hana‐ssik]‐ul sacwu‐essta mommy‐nom child‐pl‐to balloon‐one‐ssik‐acc bought ‘Mommy bought each child a balloon.’ (Choe:45 #4) ‐Ssik is most frequently associated with an accusative argument, but occasionally it can appear in a nominative argument. In this case, it is still the distributee: (390) [hyengsa‐twu‐myeng‐ssik]‐i yonguicha‐tul]‐ul ccoch‐ko‐iss‐ta detective‐two‐cl‐ssik‐nom suspect‐pl‐acc chase‐prog ‘two detectives are chasing each suspect.’ (Choe:50 #15) Korean contrasts with Kannada in that this sentence has not only an event reading (which Choe says is the preferred reading, and which is the only reading in Kannada), but also an inverse scope reading. In that reading, the number of detectives is two times however many suspects there are. Sentences that lack a lexical plurality to serve as the distributor of the –ssik‐marked argument have an event reading, as do similar Kannada sentences: (391) na‐nun [phwungsen‐hana‐ssik‐ul] sa‐ess‐ta I‐top balloon‐one‐ssik‐acc bought ‘I bought one balloon (each time/place/day…)’ (Choe:52 #18) While NR seems to prefer the closest available distributor, it is (in the absences of koND‐) able to look outside of its clause for its distributor, if need be. This is not the case 115 for –ssik, which is stubbornly clause‐bound. The the unavailability of the distributive reading in the following show that –ssik cannot look up or down out of its clause: (392) Chemwen‐tul‐I [John‐I Mary‐hanthese phwungsen‐hana‐ssik‐ul sa‐ess‐ta]‐ko malha‐ess‐ta clerk‐pl‐nom John‐nom Mary‐from balloon‐one‐ssik‐acc‐bought C said ‘??Store clerks said that John has bought a balloon each from Mary.’ (Choe:55 #22) (393) John‐I ai‐hanmyeng‐ssik‐eykey [emma‐tul‐I ku sosik‐ul Mary‐eykey cenhay‐ess‐ ta]‐ko malha‐ess‐ta John‐nom child‐one‐ssik‐dat mother‐pl‐nom the news‐acc Mary‐to told C said ‘??John told a child each that Mothers told the news to Mary.’ (Choe:57#25) For the most part, this is all reminiscent of the Kannada data, with the exception of the acceptability of inverse scope readings and Korean’s clause‐boundedness. In addition to these somewhat familiar constructions, ‐ssik is also used in what Y.H. Kim called “Phrasal Quantifiers.” These are one constituent that is made of two parts: a numeral followed by the distributee NP bearing –ssik. (394) chwulyenca seys‐I [hana‐ey noray han‐kok‐ssik‐ul] pwul‐ess‐ta performer three‐Nom one‐ey song one‐CL‐ssik‐Acc sang ‘Three performers sang one song each.’ (Choe:139 #5) Topicalization shows that this phrasal quantifier must be moved as a constituent: (395) [Hana‐ey noray han‐kok‐ssik‐ul] chwulyenca seys‐i pwul‐ess‐ta (Choe:140 #8a) (396) *Hana‐ey chwulyenca seys‐i noray han‐kok‐ssik‐ul pwul‐ess‐ta (Choe:140 #8b) While this example might appear reminiscent of Kannada NR, it differs in that the numerals can differ. When the performers sing in pairs, the second numeral is twul ‘two.’ 20 (397) chwulyenca‐tul‐i [twul‐ey noray han‐kok‐ssik‐ul] pwul‐ess‐ta Performer‐pl‐nom two‐ey song one‐cl‐acc sang ‘The performers sang a song per group of two.’ (Choe:141 #10) The plurality is broken into pairs, and the songs are mapped to each of the pairs. While NR doesn’t do this, the Korean strategy of placing the numerals associated with 116 distributor and distributee together in one constituent is reminiscent of Safir and Stowell’s binominal each, which places both distributee and distributor as arguments of each. Further exploration of this structure and its similarities to binominal each would be really interesting: what evidence is there of movement, for instance? Why does Korean seem to allow the numeral to be left behind? 117 6 Conclusion This dissertation has looked primarily at Numeral Reduplication and Pronoun reduplication in Kannada and argued that an account in the spirit of binding which appeals to Binding Theory’s Condition A applies to NR, and that reduplication of pronouns prevents the pronouns from taking discourse reference. Connecting distributivity and binding is an effort that dates way back, and the existence of similar phenomena in many language families suggests that some treatment of items that specifically mark the distributee is a worthwhile cross‐linguistic endeavor. If the same approach can also encapsulate obligatorily bound pronouns, all the better. 118 References Amritavalli, Rita. 2000. Lexical Anaphors and Pronouns in Kannada. In Lexical Anaphors and Pronouns in Selected South Asian Languages: A Principled Typology, ed. B. Lust et al., 49‐112. Berlin: Mouton de Gruyter. Amritavalli, Rita, and K. A. Jayaseelan 2005. Finiteness and Negation in Dravidian. In The Oxford Handbook of Comparative Syntax, eds. Guglielmo Cinque and Richard S. Kayne. 178-220. Oxford: Oxford University Press. Arregi, Karlos. 2001. Spanish reciprocals. Talk presented at MIT/UConn/UMass Semantics Workshop. Barss, Andrew, and Howard Lasnik. 1986. A Note on Anaphora and Double Objects. Linguistic Inquiry 17 (2): 347-254. 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New York, NY: Oxford University Press. 1 The scenario where six cacti are painted represents the strongest distributive reading, but it is also possible for the sets of cacti to overlap partially or even totally. The sentence is still true in a scenario where Shoshana painted three cacti blue but later, Phil decided that he would rather have red cacti and painted the same three cacti over again. Overlapping readings occur with predicates where the event can overlap or be done again, such as painting, washing, seeing, and singing. Once can remove the possibility for overlapping readings by using predicates like eat a raisin, where telicity of the verb combined with the smallness of the object make it unlikely that the predicate could be repeated (compare (1) with each boy ate two raisins) 2 Distributivity literature has employed many pairs of terms for these sets. Works following Choe 1987 use the terms Key and Share for distributor and distributee respectively. Some works, especially those following a quantifier interaction type approach such as Liu (1990), Beghelli and Stowell (1997), may refer to the distributor as having wide scope over the distributee. In Safir and Stowell (1988), which is exclusively about sentence‐ 124 final each in English, the distributor is the R(ange)‐NP and the distributee is the D(istributing)‐NP. 3 Choe’s choice of terminology makes very little sense from a semantics perspective, and in fact, this term exists in semantics to mean something else entirely. 4 McCarthy and Prince 2005 is the seminal work on reduplication in Optimality Theory. The field, of course, extends both before and after this work. 5 That distributivity shows distributional properties similar to elements that are subject to Condition A goes back to at least Burzio 1981. 6 This characterization oversimplifies things. For one, there are a host of readings where only two books were read that differ in exactly which books were read by which girls: did they do it all together, or did one girl read most of the books and the other two just picked up the last couple chapters? The other issue is that, in a reading where there were two books read per girl, it is not necessary that there actually be six distinct books that got read. It could be that every one of the girls read “My side of the Mountain” and one other. That situation is consistent with these sentences, but it is a special, weaker case of distributive readings. 7 The locality conditions on pronouns in Kannada do allow binding in this configuration, but the pronouns must match in gender and number. 8 This section will assume a naïve working definition of plurality that defines plurality simply as an entity made up of more than one part. For a more rigorous description of pluralities, including a semantic description of pluralities, see the discussion of pluralities in the semantics chapter. 125 9 Although seeing is something done individually, so I can’t speak to whether the seeing was individual or collective. 10 The situation of causers is actually a little more complicated than this. Lidz observes that the two verbs used here belong to two different classes with respect to causers when koND‐ is not present. Verbs of the ‘melt’ type require a causative verbal morpheme in order to have a causer, while verbs of the ‘open’ type cannot have the causative morpheme. Lidz’s approach to the function of koND‐ is built to handle not just the facts peculiar to koND‐, but also how it interacts with the argument structure of these two types of verbs. 11 Similar behavior has been observed for Norwegian SE, which can be bound locally when the verb is inherently reflexive: (i) Max wast zich Max washes SE ‘Max washes SE.’ (ii) Max schaamt zich Max shames SE ‘Max is ashamed.’ (Reinhart & Reuland: 666 #19) 12 This may be a bit of a mischaracterization. Since Ladusaw (1979), a major theme in the literature of NPIs concerns their distribution in downward‐entailing contexts such as yes‐no questions and conditionals. However, even in these contexts, NPIs are within the scope of a downward‐entailing quantifier, if not a negative one. It’s not a matter of the c‐ command requirement weakening, as opening up what categories are able to license NPIs. 126 13 This is ok when negation takes wide scope, like “not everyone saw Harold, just you.” 14 This definition should be tempered by a restriction regarding contextual relevance. Otherwise, this definition would pick out every boy in the universe. 15 This definition of plural might be the source of the “non‐atomic distributivity” problem that Heim mentions on pg. 21. She seems to assume that this denotation operates on atoms exclusively, and thus the denotation of ‘two couple+pl’ will be undefined because applying PL to will result in a set of i‐sums that is everything but pairs of people, because PL is *S‐S. Applying two to couples is a problem because the cardinality of atoms in couples must be more than two. This is a really bad result, but you can skirt it if you do not build cardinality into the denotation of couple. Although you would think that you would want to, given that couples are made up of two people, consider The Hitchhiker’s Guide to the Galaxy, which is a trilogy in five parts. Surely, that shows the tripartite nature of a trilogy is not part of the denotation of ‘trilogy.’ 16 This last option, adjoining the distributive machinery to a full clause, is not explored in depth in this work. Such an approach might consist of a function that takes the clause and returns a distributive reading of the clause. However, this would be difficult to implement in a constrained way, especially in a clause where there were multiple pluralities, any of which could be distributor or distributee. While ambiguity is welcome in many cases, one would have to build into the denotation of the distributive adjunct a c‐ command requirement lest it return a distributive reading for a non‐distributive utterance that contains two pluralities like the lizard that ate three buttons owns two cars. It would be 127 preferable instead to have the c‐command requirement be derived from something rather than stipulated. 17 It is important to distinguish multiplicative numerals, such as two hundred, from addidtive numerals, which are composed of one numeral added to another, such as fifty‐six. In addition, numerals may also be a mixture of the two typles, such as two hundred fifty‐six. Additive numerals are treated differently in their paper, and this work uses exclusively their work on multiplicative numerals. 18 It would have been nice to have named the boys, but that actually doesn’t let me show my point because the problem really only arises when the narrow‐scope items vary with the wide‐scope item. With a sentence like Adam and Ben painted each of the three cars, the sentence is true in the same situations as Adam and Ben each painted the three cars. This is simply an effect of the overlap of sets, and the effect I’m going for only shows up when the sets are able to not overlap. 19 The pronominal argument hypothesis (Jelinek 1984) was proposed to provide an account for the relatively free word order of Algonquian langauges. The idea is that the actual argument positions in Algonquian languages are occupied by pronouns which incorporate into the verb. Depending on who one’s reading, these pronouns may or may not be spelled out as inflectional morphology. The NPs in the sentence are adjoined to the structure and can appear in more or less any order so long as they are able to bind the pronominal arguments. 128 20 It’s not clear from Choe’s text whether the performers are singing in pairs or they are singing to pairs of audience members. Regardless, it is a case of distribution of songs over pairs of something.

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Core Title Reduplication and distributivity in Kannada

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Linguistics

Publication Date 11/30/2012

Defense Date 05/08/2012

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

Tag binding theory,Dravidian,Kannada,OAI-PMH Harvest,reduplication,semantics

Language English

Advisor Li, Yen-Hui Audrey (committee chair), Easwaran, Kenny (committee member), Guerzoni, Elena (committee member)

Creator Email frooblie@gmail.com,jkanders@alumni.usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-123596

Unique identifier UC11292365

Identifier usctheses-c3-123596 (legacy record id)

Legacy Identifier etd-AndersonJa-1374.pdf

Dmrecord 123596

Document Type Dissertation

Rights Anderson, Janet Katherine

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Abstract (if available)

Abstract Reduplication of numerals and pronouns in Kannada is shown to be subject to locality conditions similar to those constraining binding. This dissertation explores an account of distributivity which exploits the similarity to binding, arguing that the source of the distributive reading in Numeral Reduplication is a bound element.