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The Foundations of Linguistics : Mathematics, Models, and Structures

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The Foundations of Linguistics : Mathematics, Models, and Structures The Foundations of Linguistics: Mathematics, Models, and Structures This thesis is submittedRyan in partial M. Nefdt fulfilment for the degree of Doctor of Philosophy 2016 THE FOUNDATIONS OF LINGUISTICS: MATHEMATICS, MODELS, AND STRUCTURES Ryan M. Nefdt A Thesis Submitted for the Degree of PhD at the University of St Andrews 2016 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/9584 This item is protected by original copyright This item is licensed under a Creative Commons Licence This page intentionally left blank Contents Abstract vii Acknowledgements viii Preface xii I Three Grades of Mathematical Involvement in Linguistics 1 1 The Mathematisation of Natural Language 2 1.1 Formalisation,Syntactic Mathematisation Structures and Conservativeness . .3 1.2 Hilbert, Bar-Hillel and Chomsky . .4 2 Methodology and Ontology 14 1.3 The Legacy of ....................8 2.1 Linguistic Conceptualism . 15 2.2 Linguistic Platonism . 20 3 Three Grades of Mathematical Involvement 30 2.3 Linguistic Pluralism . 25 3.1 The First Grade: Models and Linguistic Reality . 35 3.2 The Second Grade: Representational Realism . 48 3.3 The Third Grade: Grammars as Mathematical Theories . 57 3.4 Subconclusion . 61 II Methodology in Syntax and Semantics 62 4 Modelling in Syntax 63 4.1 Modelling and Idealisation . 64 4.2 How the Laws of Linguistics Might Lie . 65 4.3 Minimalist Idealisation from ST to Minimalism . 66 4.3.1 Minimal Generation . 68 iv CONTENTS v 5 The Dynamic turn and other Frameworks 77 4.3.2 Isolation . 72 5.1 Other Generative Frameworks . 77 5.2 Modelling Dynamics . 80 5.3 Model-theoretic Syntax and Overgeneralisation . 83 6 Modelling in Semantics 89 5.4 Subconclusion . 87 6.1 Formal Semantics as Applied Mathematics . 89 6.2 Aims, Target and Methods . 91 6.2.1 Semantic Explananda . 91 6.2.2 Target of the Model . 95 6.2.3 Methods and Model Theory . 101 6.3 On the Unreasonable Effectiveness of Semantics . 105 6.4 Predicting Syntactic Felicity in the Real World . 111 6.5 The Syntax-Semantics Interface . 115 6.5.1 Semantics without Semantic Value . 120 6.5.2 Direct Modelling . 123 7 Part Conclusion: Structural Realism 126 6.6 Subconclusion . 125 III Languages and Other Abstract Structures 131 8 Three Desiderata 134 8.1 Linguistic Creativity and Infinity . 134 8.2 Of Tokens and Types . 140 8.3 Realism and Respect . 143 9 Against Platonism 150 8.3.1 Taking Stock . 148 9.1 The Right Kind of ‘Wrong View’ . 151 9.2 Benacerraf’s Dilemma and Respect . 154 10 Ante Rem Realism 159 9.3 Conceptual Distinctness . 156 10.1 Mathematical Structuralism . 159 10.2 Linguistic Structures . 164 10.3 Quasi-Concreteness . 165 10.4 Banishing a Dogma . 171 10.4.1 Types as Archetypes . 174 vi CONTENTS 10.4.2 Types as Wholes . 178 10.4.3 Types and the Representation Relation . 182 Conclusion 191 10.5 Subconclusion . 189 References 194 Abstract The philosophy of linguistics is a rich philosophical domain which encompasses var- ious disciplines. One of the aims of this thesis is to unite theoretical linguistics, the philosophy of language, the philosophy of science (particularly mathematics and modelling) and the ontology of language. Each part of the research presented here targets separate but related goals with the unified aim of bringing greater clarity to the foundations of linguistics from a philosophical perspective. Part I is devoted to the methodology of linguistics in terms of scientific modelling. I argue against both the Conceptualist and Platonist (as well as Pluralist) interpre- tations of linguistic theory by means of three grades of mathematical involvement for linguistic grammars. Part II explores the specific models of syntactic and semantics by an analogy with the harder sciences. In Part III, I develop a novel account of linguistic ontology and in the process comment on the type-token distinction, the role and connection with mathematics and the nature of linguistic objects. In this research, I offer a structural realist interpretation of linguistic methodology with a nuanced structuralist picture for its ontology. This proposal is informed by historical and current work in theoretical linguistics as well as philosophical views on ontology, scientific modelling and mathematics. Acknowledgements I am greatly indebted to Ephraim Glick and Josh Dever for their dedicated and ex- cellent supervision throughout my time at the University of St Andrews, the Arché Research Centre and the University of Texas at Austin. Ephraim looked at countless drafts of various parts of this thesis when they were still in their infancy. His com- ments and criticism were always of an extremely high standard. He has contributed to my development as a philosopher is so many significant ways. His guidance also often extended beyond the theoretical as he provided me with invaluable assistance on practical matters pertaining to the job market and general academic life. Josh was essential to me seeing the bigger picture but also working through the details of specific examples with his characteristic mixture of precision and insight. I also appreciate all the time he made for me at UT Austin. At Arché, I am grateful for the help and guidance of Arché faculty, fellow re- searchers and visitors: Derek Ball, Patrick Greenough, Stephen Read, Andy Egan, Jody Azzouni, Mark Thakkar, Ravi Thakral, Poppy Mankowitz, Claire Field, Matthew McKeever, Matthew Cameron, Asgeir Matthíasson, Bruno Jancinto, Fenner Tanswell and others. I would also like to heartily thank fellow participants of the Foundations of Lin- guistics workshop at the Braunschweig Institute of Technology in 2015. Geoff Pullum, David Pitt, Terry Langendoen, Scott Soames, Andras Kornai, Bob Levine, Christina Behme, Hans Heinrich Lieb and Martin Neef were all helpful in commenting on or reading work that would eventually find its way into this research. I thank David Pitt for additionally going over some of the details of the ontology of natural language with me at Cal. State, LA and enlightening me about the views and opinions of the late Jerrold Katz. I am also especially grateful to Geoff Pullum, at Edinburgh’s es- teemed linguistics department, for his detailed comments on a draft of this manuscript and taking the time to meet with me on several occasions to discuss various aspects of the history of formal syntax and formal language theory generally. He remains a personal hero of mine. During my time at Yale University in 2016, Zoltan Szabó’s advice and support proved excellent, especially for the chapters on semantic modelling and realism. I would also like to thank Kate Stanton for her inimitable assistance on the content of Part I. Lastly at Yale, I would like to thank participants of the Semantics Sem- inar in the philosophy and linguistics departments for their helpful comments on a presentation of my research there. Geoff Poole at the Centre for Research in Linguistics and Language Sciences at the University of Newcastle deserves my thanks for his assistance with some aspects of my analysis of generative syntax, Bernhard Weiss at the Department of Philosophy at the University of Cape Town for his insightful tutelage during my MA degree in philosophy and continued support thereafter, and Reinhard Blutner and Henk Zeevat both of the Institute for Logic, Language and Computation at the University of Amsterdam, where I conducted my MSc in Logic and Linguistics, for the requisite formal training in formal syntax, semantics and optimality theory. Reinhard also guided some of my thoughts on Part II.4. In addition, Jarda Peregrin of the Czech Academy of Sciences was a much needed voice of caution and insight on the connection between structuralism and semantics (particularly of an inferentialist persuasion). At the philosophy department at the University of Michigan, I would like to thank Lawrence Sklar for introducing me to various issues in the philosophy of science and physics and Sarah Moss for my first contact with formal methods (outside of logic) in philosophy and semantics during my year as a research scholar there and subsequent period as a visiting graduate student. I also thank Hans Kamp, at UT Austin, for shedding necessary light on some issues related to early formal semantics and some of the scientific motivations behind Discourse Representation Theory. Finally, to my good friend Tanmay Inamdar at the department of Mathematics at the University of East Anglia, a special thanks for always being receptive to the questions and worries of a philosopher concerning your fields of set theory and mathematical logic respectively. I would like to sincerely thank audiences in St Andrews, Stirling, Edinburgh, Leeds, Newcastle, Lodz, Szklarska Poreba, Amsterdam, Braunschweig, Boston and New Haven in both linguistics and philosophy departments for their useful comments and suggestions during my conference and research travels. Lastly, I would like to thank my sister Taryn, the scientist, for leading the way and my partner, Anastasia, for her fantastic support during the difficult periods of this research. To my parents, Anthea and Gordon, for their eternal support and encouragement without which none of this wonderful journey would have been possible “Generative linguistics isReflections a perplexing on field Chomsky of inquiry when looked at with philosophic issues in mind.” – Sylvain Bromberger, (1989) “On the structuralist perspective, what is an object in a given context depends on what concepts or predicates are in use, and this depends on what concepts or predicates are available.Philosophy It is of through Mathematics: language Structure that we and organize Ontology the world and divide it into objects.” – Stewart Shapiro, (1997) “Thus in the scientists’ use, ’model’ denotes what I would call a model-type.
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