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Exploring the Easy Road to Nominalism University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses October 2018 EXPLORING THE EASY ROAD TO NOMINALISM Jordan Kroll University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Metaphysics Commons, and the Philosophy of Language Commons Recommended Citation Kroll, Jordan, "EXPLORING THE EASY ROAD TO NOMINALISM" (2018). Doctoral Dissertations. 1363. https://doi.org/10.7275/12744857 https://scholarworks.umass.edu/dissertations_2/1363 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. EXPLORING THE EASY ROAD TO NOMINALISM A Dissertation Presented by JORDAN KROLL Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY September 2018 Philosophy © Copyright by Jordan Kroll 2018 All Rights Reserved EXPLORING THE EASY ROAD TO NOMINALISM A Dissertation Presented by JORDAN KROLL Approved as to style and content by: _____________________________________ Phillip Bricker, Chair _____________________________________ Hilary Kornblith, Member _____________________________________ Alejandro Pérez Carballo, Member _____________________________________ Seth Cable, Member ______________________________________ Joseph Levine, Department Head Philosophy DEDICATION To my parents, and my sister, for all their patience and support. ACKNOWLEDGMENTS I would like to thank my advisor Phil Bricker for his careful eye and for his willingness to engage with a project that departs so significantly from his own philosophical convictions. The tone and rigor of my dissertation, if not the views expressed, owe much to Phil. My interest in metaphysics may never have developed were it not for the courses that Phil taught during my first few years at UMass. I would also like to thank my other committee members, Hilary Kornblith, Alejandro Pérez Carballo, and Seth Cable, both for their help on this project and for the courses they’ve taught during my time at UMass. I am tremendously grateful to my friends Bob Gruber, Kim Soland, Miles Tucker, and Aaron Washington for philosophical discussions both serious and silly, for pleasant diversions, and for keeping me sane throughout. And of course to Julie Rose, without whom my time at UMass would have been unimaginably different. I would not have attended UMass at all, let alone written this dissertation, were in not for the philosophical education I received at UBC and UCLA as an undergraduate. I owe a particular debt to Ori Simchen, whose classes on the philosophy of language made me fall in love with technical philosophy. Lastly, I would like to thank my parents and my sister for their unending patience, their love, and their encouragement. I would not have returned to finish this dissertation without their support. v ABSTRACT EXPLORING THE EASY ROAD TO NOMINALISM SEPTEMBER 2018 JORDAN KROLL B.A., UNIVERSITY OF BRITISH COLUMBIA PH.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Phillip Bricker My dissertation is divided into three self-contained chapters, each of which explores some facet of nominalism. The overall aim is to explicate and defend a nominalist approach that recognizes the utility of talking about, or presupposing the existence of, abstract objects even if no such objects exist. The first chapter begins with a question: why is talk about abstract mathematical entities so useful in describing and explaining the physical world? Here is an answer: talk about such entities is useful for describing and explaining the physical world insofar as there is some appropriate structural similarity between them and the target physical system. But this account leads to a problem: there is no guarantee that the world contains a sufficiently rich ontology for the requisite structures to be instantiated. The primary focus of the first chapter is on exploring ways to resolve this problem as it relates to the metaphysics of quantitative properties. In the second chapter I present easy road nominalism, a variant of nominalist that accepts that purported reference to abstract objects is an indispensible part of our best vi scientific theories. The crucial insight of the easy road strategy is that referential discourse can be useful for reasons that have nothing to do with the existence of the entities purportedly being referred to. While I spend some time explaining the core of the easy road strategy, my focus is on applying the easy road strategy to theories of language. I propose that the presupposition that there are abstract linguistic objects plays a crucial role in explaining linguistic behavior, and provides the basis for a nominalistically acceptable account of content. In the third chapter I characterize fictionalism, and examine some of the wide variety of fictionalist theories in the literature. Many fictionalist theories depend crucially on the idea that non-literal utterances of a sentence have different content from literal utterances of that sentence. But I argue that the core fictionalist strategy requires no such thing, and that the prevalence of such views has been driven by assumptions about the role of content and truth that are misplaced. vii TABLE OF CONTENTS Page ACKNOWLEDGMENTS…………………………………………………………. v ABSTRACT……………………………………………………………………….. vi CHAPTER 1. THE PROBLEM OF INSUFFICIENT CONCRETE ONTOLOGY…………… 1 1.1 Structural Similarity and Concrete Ontology.……………………………... 1 1.2 Quantitative Properties…………………………………………………….. 7 1.3 Primitive Ordering and Concatenation…………………………………….. 10 1.4 Why Platonism Doesn’t Help……………………………………………… 13 1.5 Ideology and Explanation………………………………………………….. 16 1.6 Field’s Theory of Quantity………………………………………………… 17 1.7 Armstrong’s Theory of Quantity…………………………………………... 19 1.8 The Mereology of Properties………………………………………………. 31 1.9 Properties, Points, and Dimensions………………………………………... 41 1.10 The Modal Approach……………………………………………………... 45 1.11 Some Concluding Remarks……………………………………………….. 49 2. LANGUAGE WITHOUT ABSTRACT OBJECTS…………………………….. 52 2.1 Introduction………………………………………………………………… 52 2.2 Easy Road Nominalism…………………………………………………….. 55 2.3 Semantic Pretense-Involving Fictionalism………………………………… 65 2.4 Balaguer’s Semantic Fictionalism…………………………………………. 71 2.5 A Theory of Content……………………………………………………….. 77 2.6 Reference and Languages………………………………………………….. 86 2.7 Some Concluding Remarks………………………………………………… 91 3. FICTIONALISM, CONTENT, AND EXPLANATION………………………... 97 3.1 Introduction………………………………………………………………… 97 3.2 Fictionalism Characterized………………………………………………… 98 3.3 Modal Fictionalism and Meta-Fictionalism………………………………... 106 3.4 Variants of Content Fictionalism…………………………………………... 121 3.5 Reference to Abstract Objects as a Descriptive Aid……………………….. 126 3.6 Reference to Abstract Objects as an Explanatory Aid……………………... 131 3.7 Fictionalism and Content…………………………………………………... 138 3.8 Fictionalism and Truth……………………………………………………... 149 BIBLIOGRAPHY………………………………………………………………….. 156 viii CHAPTER 1 THE PROBLEM OF INSUFFICIENT CONCRETE ONTOLOGY 1.1 Structural Similarity and Concrete Ontology Science aims to describe and explain the physical world around us. It is rather curious, then, that abstract objects – scientific models, mathematical objects, and so on – play such a prominent role in current scientific practice; talk about abstract objects is arguably indispensable to science (and if not indispensable, so useful as to be practically indispensable). This is puzzling, or at least it would be if we weren’t so accustomed to it. Why is talk about abstract objects so useful in describing and explaining the physical world? Exactly how one answers this question will depend in large part on one’s other philosophical commitments. Platonists accept the existence of abstract objects, and can take talk about models and mathematical objects at face value as truths about a realm of abstract objects. A commitment to platonism does not, in itself, answer our question. Pointing out that mathematics truly describes a realm of abstract objects tells us nothing about why truths about those abstract objects are relevant to describing and explaining the physical world. Truths about one subject matter are not in general relevant to explaining truths about another (e.g. facts about the digestive systems of mice are not in general relevant when explaining the political system in Canada), except when there is some causal connection between the two. But abstract objects are, by definition, causally 1 inert: abstract objects do not causally interact with physical objects. So if truths about abstract mathematical objects are relevant to scientific practice, and the connection is not causal, we are owed an explanation of just what that connection is. What ought the platonist say? Here is a sketch of an answer for the platonist: talk about abstract objects is useful for describing and explaining the physical world insofar as there is some appropriate similarity between the abstract objects being talked about and the target physical system. Talk about abstract scientific models is useful insofar as the model is sufficiently similar in relevant respects to the physical system being modeled. Mathematics is useful because in employing
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