Scope-taking and presupposition satisfaction Julian Grove September 4, 2019 Contents List of figures ................................ iv List of tables................................. v Acknowledgments.............................. vi Abstract.................................... viii 1 Introduction............................... 1 1.1 Presupposition in dynamic semantics.............. 9 1.1.1 Contemporary satisfaction accounts........... 9 1.2 Problems for the satisfaction account.............. 13 1.2.1 Trapped presupposition triggers............. 13 1.2.2 What if presupposition triggers could “QR”? . 18 1.3 What is to come .......................... 22 1.3.1 Static semantics and presupposition projection . 23 1.3.2 Dynamic semantics, presupposition satisfaction, and filtering........................... 24 1.3.3 Why the monadic approach?............... 24 2 Presupposition as semantic definedness ............... 26 2.1 Introduction ............................ 26 2.2 Monads in linguistic semantics.................. 27 2.3 A monad for semantic definedness ............... 31 2.4 Graded monads .......................... 38 2.5 Presuppositions in the metalanguage.............. 41 2.5.1 Introducing sequents................... 42 2.5.2 A semantics of English .................. 44 2.6 Grammar.............................. 46 2.7 Warm-up exercises......................... 47 2.8 Interim conclusions........................ 49 3 Dynamic presupposition satisfaction................. 52 3.1 Introduction ............................ 52 3.2 A dynamic framework....................... 55 3.2.1 Representing information states............. 55 3.2.2 Abstracting over the context............... 60 3.2.3 Taking stock........................ 63 3.3 Discourse update ......................... 64 i 3.3.1 Adding anaphora ..................... 66 3.4 Indefinites ............................. 69 3.4.1 The semantic contribution of indefinites . 69 3.4.2 Anaphora to indefinites.................. 72 3.5 Conclusions ............................ 77 4 Presupposition triggers as scope-takers................ 81 4.1 Introduction ............................ 81 4.2 Filtering............................... 82 4.2.1 Conditionals (na¨ıve version)............... 82 4.2.2 Propositional attitude verbs ............... 95 4.3 Modal subordination .......................109 4.4 Conclusions ............................117 5 Some further applications .......................119 5.1 Introduction ............................119 5.2 Complex anaphora.........................119 5.2.1 Null complement anaphora . 119 5.2.2 Ellipsis ...........................123 5.2.3 Summary..........................125 5.3 Quantification...........................127 6 Conclusions ...............................137 References ..................................140 A The full fragment ............................150 A.1 The simply typed λ-calculus...................150 A.2 Grammar..............................153 A.3 Lexicon...............................156 A.3.1 Determiners ........................159 A.3.2 Nouns............................159 A.3.3 Adjectives .........................159 A.3.4 Verbs ............................160 A.3.5 Copulas, auxiliaries, and the infinitival morpheme . 160 A.3.6 Coordinators and sentential connectives . 160 A.3.7 Names and pronouns...................161 A.3.8 Miscellaneous type shifters . 161 B Proofs...................................162 B.0.1 Equivalence between sets of laws . 162 ii B.0.2 Theorems from the main text . 167 B.0.3 Facts from the main text . 175 iii List of figures 2.1 The Applicative Functor Laws.................. 30 2.2 The Monad Laws.......................... 31 2.3 Illustration of the Applicative Functor Laws.......... 32 2.4 Illustration of the Monad Laws.................. 33 2.5 The Monoid Laws ......................... 40 2.6 The Graded Applicative Functor Laws ............. 41 2.7 The Graded Monad Laws..................... 42 2.8 Static inference rules ....................... 46 3.1 Dynamic inference rules (first take)............... 64 3.2 The anaphora rule......................... 69 3.3 Dynamic inference rules ..................... 80 5.1 Dynamic inference rules for quantification . 131 A.1 Dynamic inference rules .....................153 B.1 The Graded Monad Laws (alternative presentation) . 167 iv List of tables 3.1 Abbreviations ........................... 59 3.2 Abbreviations ........................... 62 3.3 Abbreviations ........................... 64 3.4 Abbreviations ........................... 67 3.5 Abbreviations ........................... 73 4.1 Abbreviations ........................... 83 4.2 Abbreviations ........................... 85 4.3 Abbreviations ........................... 89 4.4 Abbreviations ........................... 98 4.5 Abbreviations ...........................110 5.1 Abbreviations ...........................122 5.2 Abbreviations ...........................134 A.1 Abbreviations ...........................158 v Acknowledgments Thanks first and foremost to Chris Kennedy, my dissertation advisor, who first suggested that I turn these ten pages of scrambled notes into a disser- tation. There is much too much to thank Chris for here beyond that, but I’ll mention a few things. Thanks for the hours (upon hours) of discus- sion on this project over the last couple of years, which helped immensely in guiding my goals, questions, and presentation. Thanks for taking a gen- uine interest in my unformed intuitions and helping me work them out into something useable. Thanks, not least of all, for teaching me so much about semantics. Thanks to Itamar Francez, who helped me turn this seemingly abstract enterprise into a semantics dissertation. I have learned much from talking to Itamar about the issues I report on here, both about what it contributes to semantic theory and about how to better explain the basics. Thanks also for your unwavering support over the years. Thanks to Greg Kobele. I could probably (attempt to) write an entirely separate dissertation about what I have learned from Greg. Thanks for teaching me so much about what linguistics can be and for guiding me in the right direction. Greg’s influence is on every page of this thesis. Thanks to Malte Willer, who joined the committee only at the very end, but who has offered great insight and help with the project. Malte gave great feedback as I presented earlier versions of this work at the Linguistics and Philosophy workshop at the University of Chicago, which has greatly improved my thoughts about and presentation of the material. Many others have played an important role for me during graduate school and the dissertation writing process. Thanks to Karlos Arregi for the many conversations and good times. Thanks to Jason Merchant for teaching me about ellipsis, and for the wonderful seminars. Thanks to Anastasia Gian- nakidou for the support and for taking an interest in my work. Thanks to Alan Yu for the support. A very very special thanks to Chris Barker for read- ing versions of the work presented here, and for offering extremely helpful comments that led to many improvements. Ming Xiang has been such an important force during my time in Chicago. Ming is partly responsible for bringing me here in the first place as her lab manager. Thank you, Ming, for all of the opportunities you have given me, all of the various ways you have supported me over the years, and for teach- ing me so much. Thanks to the many friends who have had this experience with me. To name just a few: Helena Aparicio, Andrea Beltrama, Gallagher Flinn, Katie vi Franich, Emily Hanink, Asia Pietraszko, Eszter Ronai,´ Adam Singerman, and Mike Tabatowski. Special thanks to Matt Teichman, who was the best reading group partner/fellow functional programming fanatic I could ask for. Another thanks to Matt for helping me improve the presentation of chapters one and two. Many thanks to Peet Klecha for the friendship, for the semantics conversations, and for telling me to be cool. My interest in linguistics started some years ago. Thanks to Kyle Rawl- ins, from whom I first learned about left downward entailment, and to Geraldine Legendre, from whom I first learned about Principle C. Many thanks to Paul Smolensky, because of whom I even ever wanted to apply to grad school. Thanks, finally, to my family, and to Ashley. vii Abstract This dissertation argues that presupposition projection and filtering are best understood as arising from certain expressions taking scope over ex- pressions that contain them. According to Barker(2015), an expression takes scope over another containing it “when the larger [(containing)] ex- pression serves as the smaller [(contained)] phrase’s semantic argument.” Specifically, it is argued that presupposition projection occurs when a pre- supposition trigger takes scope over the larger phrase containing it, while presupposition filtering occurs when a presupposition trigger fails to take scope over the larger phrase containing it. Building on the satisfaction account of presupposition put forward by Karttunen(1973) and Heim(1983), this perspective on presupposition is couched within the theory of graded monads, which have recently been pro- posed, in functional programming languages such as Haskell, as a means to structure the composition of functions and arguments which incur side ef- fects. According to this perspective, presupposition projection is regarded as a side effect to the composition of at-issue meaning. A presupposition trigger is then regarded as taking scope when it incurs