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Ontology, Quantification, and Fundamentality

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Ontology, Quantification, and Fundamentality ONTOLOGY, QUANTIFICATION, AND FUNDAMENTALITY BY JASON THEODORE TURNER A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Philosophy Written under the direction of Theodore Sider and approved by New Brunswick, New Jersey May, 2008 ABSTRACT OF THE DISSERTATION Ontology, Quantification, and Fundamentality by Jason Theodore Turner Dissertation Director: Theodore Sider The structuralist conception of metaphysics holds that it aims to uncover the ultimate structure of reality and explain how the world’s richness and variety are accounted for by that ultimate structure. On this conception, metaphysi- cians produce fundamental theories, the primitive, undefined expressions of which are supposed to ‘carve reality at its joints’, as it were. On this conception, ontological questions are understood as questions about what there is, where the existential quantifier ‘there is’ has a fundamen- tal, joint-carving interpretation. Structuralist orthodoxy holds that there is exactly one fundamental, joint-carving interpretation that an existential quan- tifier could have (cf. Sider 2008: §10). This orthodox assumption could go wrong — either by there being too few fundamental-quantifier interpretations, or by there being too many. In this dissertation I examine the implications of these non-orthodox options. Someone who thinks there are too many fundamental-quantifier interpreta- tions might think this means standard ontological debates are in some sense ii defective of ‘merely verbal’, or she might think instead that the different quan- tifiers show that there are different ‘ways’ or ‘modes’ of being. I argue that the first option runs into problems with a certain sort of realism about logic, but that there is no general problem with the second option, despite its long- standing bad philosophical reputation. I also argue that realism about logic gives us reason to think the dispute between someone who thinks there are many ‘modes of being’ in this sense and someone who thinks there is just one is not itself verbal. Finally, I turn to the case in which there are no fundamen- tal quantifiers, arguing that it brings with it a host of theoretical problems we could avoid with quantifiers. iii Acknowledgements This dissertation was developed on a chapter-by-chapter basis, and I toyed with the idea of doling out thanks in a similar manner. But (with the one or two obvious exceptions noted below), I decided against it: the helpful, insightful, and very often troublingly penetrating comments, conversations, and criticism from those mentioned below often improved and influenced my thinking about these topics in ways that go far beyond the individual chapters they were about. So, without further ado, thanks to Geoff Anders, Josh Armstrong, Eliz- abeth Barnes, Karen Bennett, Sara Bernstein, Ross Cameron, Ben Caplan, Andrew Cortens, Matti Eklund, Carl Fierabend, Michael Glanzberg, Mark Heller, Hud Hudson, Jonathan Ichikawa, Brendan Jackson, Martin Jönnson, Jeff King, Kelby Mason, Kris McDaniel, Andrew McGonigal, Trenton Mer- ricks, Carlos Montemayor, Mark Moffett, Iris Oved, Josh Parsons, Jonathan Schaffer, Michael Schweiger, Brad Skow, Brian Weatherson, Robbie Williams, and Stephanie Wykstra for helpful comments and criticism. Kris McDaniel deserves special thanks in connection with chapter 3, both for convincing me there was an interesting position there to be defended and for helpful conversations, comments, and encouragement on that chap- ter. Thanks also to participants at the 2007 Inland Northwest and Bellingham Summer Philosophy Conferences, who saw earlier incarnations of chapter 3 and, in the process, provided helpful questions and comments. Chapter 4 came into being as the result of an extended conversation with Jonathan Schaffer (begun at one of the aforementioned conferences), so iv special thanks go also to him for pressing me on the issues discussed therein. Of course, extra special thanks go to my committee — Ted Sider, Cian Dorr, John Hawthorne, and Dean Zimmerman — for their extensive efforts, help, and guidance (both philosophical and practical) throughout the process. Ted especially went above and beyond the call of duty, reading more drafts of each chapter than any human should have to stand and frequently helping me work through whatever snag I had most recently encountered. No one could ask for more in a dissertation director. I’m sure there are many others whom I have forgotten: if you are among them, thanks to you, too, with apologies for my poor memory. But one whom I will not forget to thank here is my wife, Starr. Throughout the entire pro- cess, she unfailingly supported me, making time for my research demands, dealing with my sometimes absenteeism, putting up with me and my various dissertation-related stresses, and (against all rational expectations) seeming to even kind of like me. I certainly don’t deserve such wonderful treatment, but I cannot express my gratitude at having had it. v Dedication To Cami and Graham, with apologies for time spent thinking about meta- ontology when I should have been taking you to the park. vi Table of Contents Abstract ..................................... ii Acknowledgements .............................. iv Dedication .................................... vi Table of Contents ................................ vii List of Figures .................................. xii 1. Introduction ................................. 1 1.1. Two Presuppositions ......................... 2 1.2. The Positions to be Examined .................... 6 2. Ontological Variantism .......................... 11 2.1. Two Conceptions of Metaphysics .................. 12 2.1.1. The Ordinarian Conception and Defectiveness ...... 12 2.1.2. The Structuralist Conception ................ 14 2.1.3. The Structuralist and Defectiveness ............ 18 Denying (iii) .......................... 19 Denying (ii) .......................... 21 2.2. Defectiveness for Structuralists ................... 24 2.2.1. Notational Variants ...................... 24 2.2.2. Metaphysical Analysis and Expressive Equivalence . 26 2.2.3. Analyses and Primitiveness ................. 29 2.2.4. Notational Defection ..................... 31 2.3. Logical Realism to the Rescue .................... 32 vii 2.3.1. Structuralism and Logic ................... 32 2.3.2. Logical Realism and Notational Variance ......... 34 2.3.3. The Argument: A First Pass ................. 35 2.3.4. The Argument Generalized ................. 38 The Theories Specified .................... 39 Interpreting the Logical Realism Constraint ....... 41 Two Useful Kinds of Sentences ............... 42 Further Constraints on the Translation Scheme ..... 44 Three Facts About Logic ................... 47 The Argument ........................ 49 2.4. Further Moves for Defectors ..................... 51 2.4.1. Reject a Constraint ...................... 51 2.4.2. Enrich the Languages .................... 53 How to Enrich the Languages and Extend Constancy . 54 Problem 1: The Original Argument can be Resurrected . 57 Problem 2: The Geach-Kaplan Argument ......... 60 2.4.3. Enrich the Logics ....................... 63 3. Ontological Pluralism ........................... 68 3.1. Ontological Pluralism ........................ 69 3.1.1. Pegboards ........................... 69 3.1.2. Fundamentality ........................ 71 3.1.3. Depicting Ontological Structure .............. 74 Depicting Single Ontologies ................. 75 Depicting Multiple Ontologies ............... 76 Sorting ............................. 77 3.1.4. Fundamental Quantifiers .................. 79 viii Criteria for Quantification .................. 79 Counting Quantifiers ..................... 81 3.1.5. The Thesis of Ontological Pluralism ............ 83 3.2. The Disjunctive Quantifier Argument ............... 83 3.2.1. Easy Unrestriction ...................... 85 The Problem .......................... 85 An Objection ......................... 87 3.2.2. Semantic Quantifiers ..................... 88 The Semantic Criterion Revisited .............. 89 Ordinary and Philosophers’ English ............ 89 The Philosophical ‘There Are’ and Fundamentality . 93 Fundamental Quantifiers and the Semantic Criterion . 95 Back to the Argument .................... 97 3.3. The Conjunction Argument ..................... 99 3.4. Van Inwagen’s Counting Argument ................ 102 3.5. The ‘There Can Be Only One’ Argument ............. 104 3.5.1. Empty Names ......................... 107 3.5.2. Names and Free Variables .................. 109 3.5.3. Change of Logic, Change of Subject ............ 110 3.6. The Economy Argument ....................... 112 3.7. Conclusion ............................... 118 4. Pluralism and Logical Truth ....................... 120 4.1. Fundamental Theories and Notational Variants ......... 121 4.1.1. Fundamental Languages and Metaphysical Disputes . 121 4.1.2. Notational Variants ...................... 123 4.1.3. The Worry for Pluralism ................... 124 ix 4.2. How Logical Realism Taught Me to Stop Worrying. ...... 128 4.2.1. The Argument: A First Pass ................. 128 4.2.2. The Argument Generalized ................. 130 4.3. Can We Start Worrying Again? ................... 139 5. Ontological Nihilism ........................... 146 5.1. Ontological Nihilism ......................... 146 5.2. The Need for Paraphrase ...................... 150 5.2.1. The Challenge ........................
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