Long-distance movement, binding, and scope in a continuation grammar Cara Leong Su-Yi An Honours Thesis submitted in part fulfilment of the requirements for the degree of Bachelor of Arts with Honours in English Language Department of English Language and Literature Faculty of Arts and Social Sciences National University of Singapore Singapore 15 April 2019 This Honours Thesis represents my own work and due acknowledgement is given whenever information is derived from other sources. No part of this Honours Thesis has been or is being concurrently submitted for any other qualification at any other university. Cara Leong Su-Yi 15 April 2019 ii ACKNOWLEDGMENTS This thesis would not exist without my advisor, Dr Michael Yoshitaka Er- lewine. All the good ideas herein are mostly due to him; all the bad ones that remain were made less terrible by him. I am tremendously grateful for his discernment, enthusiasm, and fortitude in the face of nonsensical notation. This work has benefited from the insight of my linguist-friends. Thanksto Sharmala Solomon and Lauren Koh for accepting the presupposition that uni- corns exist, and for my knives. Anne Ng dug out years-old essays in service of this paper. Thanks also to Keely New for grammaticality judgments, proof- reading, and documenting the crucial moments after I poured an entire glass of chocolate milk onto my laptop three days before this thesis was due. I probably haven’t said this enough, but I owe almost everything to the friends who have seen me through university. Anne and Shien suffered through the worst of it — I’m ever so grateful. Truly, please. Ellen was there from day one. I miss Nicole and Kimi Raikkonen. Si En has never made a bad suggestion, and introduces me to new ways of thinking every time. Royston once told me my thesis was “interesting within the domain”, which I will take as a compliment any day. Ruizhi walked alongside on the writing journey mostly unironically. Leon planted 2020 dreams. Yuchuan bought me a kaya waffle a week. Darren housed my refrigerated goods and midnight worries. Thank you all for propping me up. Finally, all gratitude to my family — I feel impossibly privileged to be yours. Thanks for providing snacks and not asking how my thesis was going. Words aren’t enough. And to You, an open proposition if ever I knew one — still, always, thank You. iii CONTENTS Acknowledgments iii List of definitions, figures and tables vi Abbreviations vii Abstract viii 1 Introduction 1 2 A continuation grammar 3 2.1 Continuations 3 2.2 Semantic types and syntactic categories 3 2.3 Tower notation 6 2.4 Type-shifting in towers 9 2.4.1 lift 9 2.4.2 lower 13 2.5 Multi-layered towers and inverse scope 14 2.6 Gaps, movement and front 16 2.6.1 Gaps 16 2.6.2 front 17 2.7 The value of a continuation-based framework 19 3 Long-distance movement 20 3.1 The clause-bound scope of quantifiers 20 3.2 Limiting the scope of quantifiers 22 3.2.1 The Tensed Clause Condition 22 3.3 Long-distance movement fails 25 3.4 A solution 28 3.4.1 Adjacency and containment 28 3.4.2 An intermediate gap 29 3.5 Predictions 33 3.5.1 Embedding 34 3.5.2 Reconstructing the narrow scope reading 36 3.6 Summary 40 4 Binding and crossover 42 4.1 Binding variables in the continuation framework 42 4.1.1 Adding a new syntactic category 42 4.1.2 Binding and the Tensed Clause Condition 46 4.2 Short-distance movement 49 4.2.1 Movement without binding 49 4.2.2 Binding from a fronted expression 54 4.2.3 Summary 59 4.3 Long distance binding fails 60 iv 4.3.1 Incorrectly predicting crossover effects 61 4.3.2 Failing to predict crossover effects 64 4.4 Towards a solution 67 4.4.1 The Tensed Clause Condition does not apply 67 4.4.2 Altering the type-shifters 69 4.5 The root of the problem 71 5 Conclusion 73 References 74 v LIST OF DEFINITIONS 1 Tower notation 7 2 Combination schema in the continuation framework 8 3 lift type shifter 10 4 lower type-shifter 13 5 front type-shifter 17 6 Tensed Clause Condition (first version) 23 7 Tensed Clause Condition (second version) 29 8 Pronoun 42 9 bind type-shifter 44 10 prolift type-shifter 47 LIST OF FIGURES 1 Schemata of relationship between functors and arguments 6 2 Schema for composing towers (Barker and Shan 2014) 9 3 Schemata of relationship between functors and arguments 29 LIST OF TABLES 1 Syntactic categories necessary for composing with gapped clauses 60 vi ABBREVIATIONS B&S Barker and Shan 2014 DP determiner phrase QP quantifier phrase QR quantifier raising S sentence TCC Tensed Clause Condition vii ABSTRACT In this thesis, I describe and evaluate the continuation-based account of quan- tifier scope, variable binding and movement presented in Barker and Shan 2014. I show that under this account, it is possible to independently enforce the clause-boundedness of quantifier scope while accounting for movement, treat long-distance movement without variable binding, and deal with vari- able binding in local movement configurations. I also point out that the uniform treatment of scope, movement and binding through continuations makes fundamentally flawed predictions when faced with the combination of clause-bound quantifiers, long-distance movement, and variable binding. Par- ticularly, although the continuation framework claims to account for crossover effects, I show that such an account is lost in long-distance movement config- urations. I suggest that this problem has its roots in operations fundamental to the framework, and thus poses a serious challenge to the validity of the theory. viii CHAPTER 1 INTRODUCTION This thesis concerns itself with the treatment of quantifier scope, movement and variable binding in the semantic framework of Barker and Shan 2014. On this theory, the interplay between linear and scopal relationships is key; such an interaction harkens back to the seminal problem in semantics of quantifier scope ambiguity. May (1977) notes that a single form such as (1) can have two different readings: (1) Some man loves every woman. On one reading, a single man loves all women. On this “surface scope” reading, the exis- tential quantifier phrase (QP) some man is said to take wide scope over the universal QP every woman (∃ > ∀). On the second reading, in which the existential takes narrow scope (∀ > ∃), a potentially different man loves each woman. The availability of this “inverse scope” reading does not seem apparent based on surface word order. A common approach to of quantifier scope ambiguity posits the covert movement of quan- tifiers, or quantifier raising (QR), as an explanation for the availability of inverse scope readings. On this theory, objects are covertly moved to allow them to take scope, such that (1) is covertly analyzed as (2): (2) Logical Form (LF): every woman, some man loves. In contrast, so called “in-situ” theories of scope-taking allow for both surface and inverse scope readings to be obtained without appealing to covert movement. In particular, Partee (1987) introduced the notion of type-shifting to allow for in-situ analyses of inverse scope, while Hendriks (1993)’s Flexible Types analysis suggests multiple denotations for verbs and quantifiers. 1 Against this background, Barker and Shan (2014) — henceforth B&S — present a gram- mar that provides an in-situ analysis of quantifier scope ambiguity (see also Barker 2002; Barker and Shan 2008; Kiselyov and Shan 2014; Shan 2007; Shan and Barker 2006). The chief intuition in their framework, which I call the continuation framework, is that some expressions take their continuations, or the immediate context surrounding them, as ar- guments. Working under this hypothesis, B&S build a fragment that uses continuations to capture the scope-taking behavior of quantifiers. They then extend the use of continu- ations to in-situ analyses of movement and variable binding. In this thesis, I consider issues surrounding such a uniform treatment of scope, binding and movement in the continuation framework, and ultimately show that the continuation framework runs into serious problems when attempting to account for the combination of clause-bounded scope, long-distance movement, and variable binding. Chapter 2 intro- duces the continuation framework and shows how it uses type-shifting to provide an in- situ account of inverse scope and movement. In Chapter 3, I problematize unconstrained scope-taking behavior in the continuation framework and implement a constraint that I term the Tensed Clause Condition to account for the clause-boundedness of quantifiers. In Chapter 4, I turn to B&S’s account of variable binding and its interaction with move- ment. I point out a flaw in the way B&S characterize scopal and linear relationships, and suggest why this flaw may be fatal to the framework. Chapter 5 concludes. 2 CHAPTER 2 A CONTINUATION GRAMMAR In this chapter, I summarize the notational system and operations developed by B&S. I show how the continuation framework provides in-situ accounts of inverse scope and the extraction of expressions from their canonical positions. I then briefly discuss the value of working in the continuation framework. 2.1 Continuations A delimited continuation of an expression is “a portion of the context surrounding [that] expression” (Barker and Shan 2014:1) which represents “the computational future of an expression, i.e. what is about to happen to it” (Shan and Barker 2006:95). For example, the continuation of everyone in John gave everyone a pen is what remains of the clause after everyone is taken out of it: “John gave [ ] a pen”; the continuation of gave everyone a pen in the same sentence is “John [ ]”.