University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Philosophy Dissertations, Theses, & Student Research Philosophy, Department of Spring 4-19-2020 Vagueness and the Logic of the World Zack Garrett University of Nebraska - Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/philosophydiss Part of the Metaphysics Commons, and the Philosophy of Language Commons Garrett, Zack, "Vagueness and the Logic of the World" (2020). Philosophy Dissertations, Theses, & Student Research. 13. https://digitalcommons.unl.edu/philosophydiss/13 This Article is brought to you for free and open access by the Philosophy, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Philosophy Dissertations, Theses, & Student Research by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. VAGUENESS AND THE LOGIC OF THE WORLD by Zack Garrett A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy Major: Philosophy Under the Supervision of Professor Reina Hayaki Lincoln, Nebraska May, 2020 VAGUENESS AND THE LOGIC OF THE WORLD Zack Garrett, Ph.D. University of Nebraska, 2020 Advisor: Reina Hayaki In this dissertation, I argue that vagueness is a metaphysical phenomenon—that properties and objects can be vague—and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, con- textualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable of accommodating meta- physical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysi- cal vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans’1 much-disputed argument that vague iden- tities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better expla- nation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by de- gree theories. 1Evans, 1978. Table of Contents Introductioni 0.1 What is Vagueness?.............................i 0.2 Previews of the Theories.......................... iii 0.2.1 Epistemicism............................ iii 0.2.2 Contextualism............................ iv 0.2.3 Supervaluationism.........................v 0.2.4 Semantic Nihilism......................... vi 0.2.5 Trivalent Theories......................... vi 0.2.6 Degree Theories........................... vii 0.3 Goal...................................... viii 1 The Abductive Argument for Epistemicism1 1.1 Introduction.................................1 1.2 The Arguments for Epistemicism.....................2 1.2.1 Sorensen’s Argument.......................2 1.2.2 Williamson’s Argument......................3 1.2.3 The Epistemic Thesis........................8 1.3 The Structure of Williamson’s Argument................9 1.4 How Virtuous is Epistemicism?...................... 10 1.4.1 Intentional Vagueness....................... 14 1.5 Vagueness as a Metaphysical Phenomenon............... 16 1.6 The Weight of Simplicity.......................... 17 1.6.1 Semantic Nihilism......................... 18 2 Context and Vagueness 20 2.1 What is Contextualism?.......................... 21 2.1.1 Three Questions........................... 23 2.2 Ellipses.................................... 26 2.2.1 Is There a Sorites Argument Immune to Context Shifts?.... 28 2.3 A Complete Theory............................. 29 2.3.1 Individual Cases.......................... 29 2.3.2 Psychological and Epistemological Explanations of Individual Cases................................. 29 2.3.3 The Need for an Answer to the Semantic Question....... 30 2.3.4 Consistency with other Theories................. 31 2.4 Contextualism as a Springboard...................... 32 2.4.1 Framework............................. 32 2.4.2 The Multi-Range Theory...................... 33 2.4.3 Relativized Truth.......................... 35 2.4.4 Higher-Order Vagueness..................... 37 2.4.5 Vagueness All the Way Down................... 38 2.4.6 Ordinary Truth........................... 39 2.4.7 Vagueness in the World...................... 40 3 Precisifications 41 3.1 Supervaluationism............................. 41 3.1.1 Objection: Disjunctions and Existential Generalizations.... 44 3.1.2 Objection: Permissible Precisifications.............. 46 3.1.3 Objection: Incomplete Precisifications.............. 47 3.1.4 Quick Summary.......................... 48 3.2 Semantic Nihilism.............................. 49 3.2.1 Is Semantic Nihilism Self-Defeating?............... 51 3.2.2 Braun and Sider’s Nihilism.................... 53 3.2.3 Objection: The Vagueness of ‘Truth-Apt’............ 55 3.2.4 Objection: Metaphysical Vagueness............... 56 3.2.5 Objection: Borderline Approximate Truth............ 57 3.2.6 Simplicity.............................. 57 3.2.7 Quick Summary.......................... 58 3.3 Expressivism................................. 58 3.3.1 Objection: Plurivaluationism Revisited............. 60 3.3.2 Objection: Higher-Order Vagueness............... 62 3.3.3 Quick Summary.......................... 63 4 The Possibility of Vagueness in the World 64 4.1 What Does Vagueness in the World Look Like?............. 65 4.1.1 Vagueness in Property Instantiation............... 66 4.1.2 Vagueness in Existence....................... 66 4.1.3 That These are Metaphysical................... 67 4.2 Argument for the Possibility of Vagueness in the World........ 68 4.2.1 An Argument from Ordinary Objects.............. 68 4.2.2 The Gunky Vague World..................... 70 4.2.3 Indeterminacy at the Bottom................... 72 4.3 The Argument against Vague Identities................. 74 4.3.1 The Argument........................... 75 4.3.2 Do We Need to Respond to Evans?................ 76 4.4 Problems with the Evans Argument................... 78 4.4.1 Indeterminate Existence...................... 78 4.4.2 Some Remarks on Leibniz’s Law................. 79 4.4.3 The Failure of Lambda Abstraction................ 80 4.4.4 Higher-Order Objection...................... 82 4.5 Other Responses............................... 83 4.5.1 Bruce Johnsen............................ 83 4.5.2 E.J. Lowe............................... 85 4.5.3 Peter van Inwagen......................... 86 4.6 Concluding Remarks............................ 89 5 The Logic of States of Affairs 91 5.1 States of Affairs and Indeterminacy.................... 92 5.1.1 Obtaining-Values.......................... 93 5.1.2 Consequence............................ 94 5.2 Sentential Logic............................... 95 5.2.1 The Atomic Elements....................... 95 5.2.2 On Choosing Definitions..................... 96 5.2.3 Tautologies and Contradictions.................. 97 5.2.4 Negation............................... 98 5.2.5 Conjunction............................. 102 5.2.6 Disjunction............................. 105 5.2.7 Quick Summary.......................... 108 5.2.8 Conditionals............................. 108 5.2.9 Biconditionals............................ 111 5.2.10 The Operators in the Metalanguage............... 112 5.3 Quantificational Logic........................... 113 5.3.1 The Domain............................. 113 5.3.2 Universal Quantification...................... 113 5.3.3 Existential Quantification..................... 116 5.3.4 Note on Indeterminate Existence................. 118 5.4 Modal Logic................................. 118 5.4.1 Necessity.............................. 118 5.4.2 Possibility.............................. 119 5.4.3 Equivalences............................ 119 5.4.4 Metaphysical Possibility...................... 119 5.5 Higher-Order Vagueness.......................... 120 5.5.1 The Operators............................ 121 5.5.2 Tripartite Division......................... 122 5.5.3 Indeterminately Indeterminate.................. 123 5.5.4 Is this Really Trivalent?...................... 125 5.6 Advantages................................. 125 6 Degree Theories 128 6.1 An Argument for Degrees......................... 129 6.2 Degree-Functional Semantics....................... 133 6.2.1 Some Approaches to Validity................... 134 6.2.2 Solving the Sorites Paradox.................... 136 6.2.3 Smith’s Approach to Validity................... 138 A Problem.............................. 140 6.3 Non-degree-functional Approach..................... 142 6.3.1 Edgington’s Semantics....................... 142 6.3.2 Objections to Degree-Functionality................ 143 6.3.3 Smith’s Response.........................