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Logical Instrumentalism Logical Instrumentalism Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Teresa Kouri ∼6 6 Graduate Program in Philosophy The Ohio State University 2016 Dissertation Committee: Professor Stewart Shapiro, Advisor Professor Chris Pincock Professor Craige Roberts Professor Kevin Scharp Professor Neil Tennant c Teresa Kouri, 2016 Abstract Logic and reasoning go hand in hand. So often, we hear that someone has reasoned poorly about something if they have not reasoned logically, or that an argument is bad because it is not logically valid. To date, research has been devoted to exactly just what types of logical systems are appropriate for guiding our reasoning. Traditionally, classical logic has been the logic suggested as the ideal for this purpose. More recently, non-classical logics have been suggested as alternatives. Even more recently, it has been suggested that multiple logics are reasoning guiding, or none are. So far, no one has addressed the impact that natural language has on our ability to reason well. My project fills this gap. I focus on the relationship between the meaning of the connectives (\and", \or", \not", etc.) in natural language and logic. By assessing what these connectives mean in natural language, we can figure out what they must mean in the formal language in order to guide our reasoning. I show that the connectives do not have a single meaning across all contexts in natural language, and thus there can be no single meaning to the connectives in the formal language which guides our reasoning. This means that the right logic to guide our reasoning depends on our context. My dissertation is divided into five chapters. The first is a literature review. In the second, I examine the classical and non-classical answers to the question \which logic guides our reasoning?" and find them all wanting. In the third chapter, I show that the views that postulate either that there are multiple logics that guide our reasoning or that there are none are flawed for the reason that they do not appropriately account for the relationship between natural language and logic. In the fourth chapter, I show how we can adapt an ii old view to solve this problem. Finally, in the last chapter, I propose a formal reasoning- guiding system that takes natural language into account and defend it from some potential objections. The appendix begins to address a major problem for this type of project. Given what my dissertation shows, we can see how the traditional view on logic guiding reasoning was misguided. However, if we replace the notion of \right logic" with the system I develop, we can reap the same benefits. iii Dedication To my parents, Brian and Vikki, and my husband, Andrew iv Acknowledgements There are a number of people in my life without whom this dissertation would never have come to be. First and foremost, I owe a debt of gratitude to my advisor, Professor Stewart Shapiro. Without his generosity, guidance and encouragement and engaging discussions, I would not be the philosopher I am (and this dissertation would likely not exist). My other dissertation committee members, Professor Chris Pincock, Professor Craige Roberts, Professor Kevin Scharp and Professor Neil Tennant also provided invaluable feedback and support throughout the development of this work. Professor Ben Caplan and Professor Lisa Shabel, having been members of my committees for other exams, also helped this project come to fruition. My colleagues in the graduate student program at Ohio State have been instrumental in my philosophical development. They have always been willing to engage in philosophical discussions on topics of interest to me, and in return to let me hear about their projects and interests. Additionally, colleagues in other departments at Ohio State, and at philosophy departments other than Ohio State have played no small role. Discussions with them, and the resulting feedback about various sections of this project have been unbelievably helpful. Finally, I need to thank my family. My parents, Brian and Vikki Kouri, have always been supportive of my pursuits, even when I told them that I would be in school until my early thirties, and then *maybe* find a job. My brother, Bradley Kouri, has always kept me grounded by asking questions about reality, rather than the lofty ivory tower I sometimes find myself in. My family-in-law, John, Peg, Emily, Paul, Jimmie and Johnny, has so graciously welcomed me into the fold, and always offered a much needed escape from philosophy with cocktails and dinner on their patio. Most importantly, I need to thank my husband Andrew Kissel. Sometimes marrying someone in the same field as you is a v mistake, but in this case it made me a better person and better philosopher. Between our philosophical conversations and his ability to keep me sane, I know I could not have found a better partner, nor a person more critical in my philosophical development. vi Vita 2008 . B.A., Queen's University 2010 . M.A., University of Calgary Publications \A New Interpretation of Carnap's Logical Pluralism," Topoi, online first, August 2016 \Restall's Proof-Theoretic Pluralism and Relevance Logic," Erkenntnis, online first, De- cember 2015 \Ante Rem Structuralism and the No-Naming Constraint," Philosophia Mathematica, 2016, Volume 24, Issue 1, Pages 117-128 \A Reply to Heathcote's \On the Exhaustion of Mathematical Entities by Structures"," Axiomathes, 2015, Volume 25, Issue 3, Pages 345-357 Fields of Study Major Field: Philosophy vii Table of Contents Abstract ............................................................................. ii Dedication ........................................................................... iv Acknowledgements .................................................................. v Vita ................................................................................. vii List of Figures ....................................................................... x 1 Introduction ..................................................................... 1 1.1 Logical Instrumentalism.............................2 1.2 Dissertation Outline...............................4 2 Literature Review ................................................................ 6 2.1 Monism......................................6 2.2 Nihilism......................................9 2.3 Pluralism.....................................9 2.3.1 More than one Logic........................... 10 2.3.2 More than one Correct Logic...................... 11 2.3.3 More than one Correct Logic in a Single Language.......... 15 2.4 Logical Instrumentalism............................. 29 3 Logical Monism from a Pluralist's Perspective .................................... 30 3.1 Why Logic Ought Not to Legislate to Properly Functioning Sciences.... 31 3.2 Logic and Natural Language........................... 32 3.2.1 The Players................................ 32 3.2.2 The Problem............................... 36 3.3 Logic and Mathematics and the Sciences.................... 38 3.3.1 The Players................................ 38 3.3.2 The Problem............................... 42 3.4 Our Next Step.................................. 44 4 Beall and Restall's Logical Pluralism ............................................. 46 4.1 Connective Meanings in Beall and Restall's Logical Pluralism........ 46 4.1.1 Introduction............................... 46 4.1.2 Beall and Restall's Pluralism...................... 47 4.1.3 Overlapping Clauses........................... 48 viii 4.1.4 The Problem............................... 50 4.1.5 Merely Technical Meanings....................... 55 4.1.6 A Possible Solution............................ 56 4.1.7 Conclusion................................ 57 4.1.8 Appendix................................. 57 4.2 Title........................................ 59 4.2.1 Introduction............................... 59 4.2.2 Restall's Proof-Theoretic Pluralism................... 60 4.2.3 No relevance validity........................... 63 4.2.4 Other Admissibility Conditions..................... 66 4.2.5 Conclusion................................ 70 5 Title ............................................................................. 72 5.1 Introduction.................................... 72 5.2 The Traditional Carnapian View........................ 73 5.3 Carnap's Position................................. 74 5.4 The External Question.............................. 76 5.5 Carnap's Agreement............................... 86 5.6 Shapiro's Position................................ 90 5.7 Conclusion.................................... 92 6 Logical Pluralism from a Pragmatic Perspective .................................. 93 6.1 The Intuitions................................... 93 6.1.1 Carnap's and Beall and Restall's Pluralisms.............. 96 6.2 The New System................................. 96 6.2.1 QUD framework............................. 98 6.2.2 A New Theory of Connective Meaning................. 109 6.3 Conclusion.................................... 114 References ...........................................................................115 Appendices ..........................................................................121 A Two Normative Issues for for the Carnapian Pluralist ............................ 121 A.1 Introduction.................................... 121 A.2 How to Choose our Goals............................ 122 A.3
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