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Existence: an Unholy Trinity. an Account of Indeterminate Existence City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 2-2014 Existence: An Unholy Trinity. An account of Indeterminate Existence Salas Sanchez-Bennasar Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/105 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] EXISTENCE: AN UNHOLY TRINITY An Account of Indeterminate Existence by Salas Sanchez-Bennasar A dissertation submitted to the Graduate Faculty in Philosophy in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2014 ©2014 SALAS SANCHEZ-BENNASAR All Rights Reserved ii This manuscript has been read and accepted for the Graduate Faculty in Philosophy in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. __________Arnold Koslow_____________ Date ______________ _____________________________________ Chair of Examining Committee _________Iakovos Vasiliou______________ Date ______________ _____________________________________ Executive Officer __________Graham Priest (Advisor)___________ ____________John Greenwood___________ ____________Rohit Parikh____________ ______________Stewart Shapiro___________ Supervisory Committee THE CITY UNIVERSITY OF NEW YORK iii Abstract EXISTENCE: AN UNHOLY TRINITY An Account of Indeterminate Existence by Salas Sanchez-Bennasar Advisor: Professor Graham Priest What is it for something to exist? This dissertation provides an answer to this question by giving a philosophical theory of existence in which the concept of existence in understood as a complex tri- partite notion. The account of existence defended here is arrived at by taking into consideration past philosophical theories of existence, the everyday and scientific uses of the notion, and also philosophical considerations about the nature of reality. There are three conditions that are central to existence: spatiotemporality, mind-independence, and being a member of the quantificational domain of a true and complete scientific description about the world. To exist is to satisfy all three conditions. It is false that something exists if and only if it for each condition, it fails to satisfy it. And, therefore, we get a third case: if an entity satisfies some but not all of the conditions, then it is neither true nor false that it exists, so what follows is an account of indeterminate existence. For some entities, our best theoretical sharpening of our conception of existence still fails to determine whether they exist or not. iv After arguing for each of the three conditions thoroughly, I strengthen the case for my theory of existence by explaining the consequences of its application. I provide several examples. Finally, I focus on the development of a philosophy of mathematics that takes into account that, given our theory of existence, it is neither true nor false that mathematical entities exist. v ACKNOWLEDGMENTS Working with Graham Priest has been a rich, invigorating and maturing experience without which I would have not been able to complete this work. Graham Priest has been a role model and an enabler of my academic training (and my travels and appreciation of Australian wine) above and beyond the requirements of duty. For all of this, I am forever grateful to him. I also want to thank the two readers of this work, Arnold Koslow and Stewart Shapiro, who read through the chapters and gave me invaluable feedback and advice. Stewart Shapiro’s book Thinking about Mathematics was my introduction to the philosophy of mathematics as an undergraduate in London, many years before I met him in person, so his influence has been formative for me. Working with him in person has made this influence enduring. Overall, the encouragement, insights and patience of my committee make me feel very fortunate. I am also grateful to the rest of the examining committee for agreeing to be part of this project: John Greenwood and Rohit Parikh. I also thank my family, who have helped me throughout the years and have encouraged me, supported me, listened and been there for me: my mother, Marga Bennasar Félix, who was my first philosophy teacher; Ramón Sánchez Ramón, to whom I owe my philosophical up-bringing; Josh Dulberger for his kind care and sharp observations; Ellen Dulberger, for her close and constant support; and Sergeant, who kept me company and grounded me during the writing. vi TABLE OF CONTENTS Abstract iv Acknowledgments vi Introduction 1 0.1. Motivating thoughts 2 0.2. Structure 4 Chapter 1: The Linguistic Condition 9 1.1. The Concept of Existence 10 1.1.1. The Problem of Being, Existence and the Concept of Existence 10 1.1.2. Conditions for Existence 17 1.2. The NeoFregean Project 19 1.2.1. Syntax to Semantics 23 1.2.2. Semantics to Existence 29 1.3. The Quinean Condition 33 1.3.1. Against the Sufficiency of the Condition 38 1.3.1.a. Quine 38 1.3.1.b. Other Arguments: A Plausible Best Theory? 41 1.3.1.c. Other arguments: Indispensability 45 1.3.2. The Necessity of the Condition, Qualified: 49 1.4. The Present Suggestion: The Linguistic Condition 51 vii Chapter 2: The Spatiotemporality Condition 59 2.1. Causal efficacy v. spatiotemporality 60 2.1.1. The Nature of Causation 62 2.1.2. Everything that is Causally Efficacious is Spatiotemporal 67 2.1.2. Everything Spatiotemporal is Causally Efficacious 71 2.1.3. Dropping Causal Efficacy 73 2.2. Everything that Exists is Spatiotemporal 75 2.2.1. Ockham’s Razor 79 2.3. The Criterion is not Sufficient 99 2.3.1. Counterexamples 100 2.3.2. There are Three Aspects of Existence 102 Chapter 3: The Independence Condition 104 3.1. Mind-independence: a definition 105 3.1.1. Mind-Independence v. Objectivity 110 3.2. Mind-Independence is a Necessary Condition for Existence 120 3.2.1. Some positions against realism 123 3.2.2. Objection: Azzouni 136 3.3. Mind-independence is not a sufficient condition for existence 141 3.3.1. Mathematical entities are mind-independent 142 3.3.1.a. Applicability 142 3.3.1.b. Apriority 146 3.3.2. Another counterexample to the sufficiency claim 150 Chapter 4: Application of the theory 153 4.1. Application 154 4.2. Indeterminately existing entities 158 viii 4.3. Objections and replies 169 4.3.1. Indeterminate existence? 169 4.3.2. Possible-world semantics 171 4.3.3. The scarcity of nonexistent entities 176 4.3.4. Azzouni: No criteria for existence 177 4.3.5. Quantifier Variance? 186 4.3.6. Sider Against Vague Existence 188 4.3.7. Fictional Entities 192 Chapter 5: Mathematics 197 5.1. The truth-value of mathematical statements 198 5.1.1. A Semantic Interpretation 201 5.2. Knowledge of mathematics? 211 5.2.1. Math is true 212 5.2.2. Math is neither true nor false 214 5.3. The application of mathematics 215 5.3.1. Applying a neither true nor false discourse 215 5.3.2. Applying a true discourse 229 Concluding thoughts 233 Bibliography 237 ix Chapter 0: Introduction What is there? Quine, “On What There Is” (From a Logical Point of View 1) What is there? Quine claimed that the answer is very easy: Everything. But I don’t think that’s correct. Some things don’t exist. People, trees, Venus and electrons exist. But Indiana Jones, Vulcan and phlogiston don’t exist. And what about numbers and other mathematical entities? What about abstract entities? And intersubjective entities, like money or countries? These questions easily force one into the question: What is existence? What does it mean for something to exist? That is the starting point of this dissertation. The account of existence defended here is arrived at by taking into consideration past philosophical theories of existence, the everyday and scientific uses of the notion, and also philosophical considerations about the nature of reality. The result is a philosophical theory of existence that is an improvement on previous attempts, for it combines valuable insights of many other theories together with current use into one complex account. 1 I argue here that existence is best understood as a tri-partite notion: to exist is to satisfy all three conditions. It is false that something exists if and only if for each condition, it fails to satisfy it. And, therefore, we get a third case: if an entity satisfies some but not all of the conditions, then it is neither true nor false that it exists, so what follows is an also account of indeterminate existence. These are the three conditions for existence: a. Theoretical Commitment: Something is a theoretical commitment if and only if it is part of the quantificational domain of a true and complete scientific description of the world. b. Spatiotemporality: Something is spatiotemporal if and only if it is in space and/or time. c. Mind-independence: Something is mind-independent if and only if it is such that its existence (if it exists) and nature do not depend on what any mind judges it to be. In this introduction I explain in broad strokes how I think about existence, doing my best to motivate the general results. I specify how the dissertation argues for the theory and give a quick run-down of chapters, in order to give the reader a clear roadmap of what’s to come. 0.1. Motivating thoughts There is something peculiar about the question “Do numbers exist?”. Ask the layman and she will probably brush off the question altogether. A common non-philosophical impression is that it is the wrong kind of question to ask about numbers—it is met with bafflement more than anything.
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