A Correspondence Theory of Truth by Jay Newhard B.A., University of California, Santa Barbara, 1994 A.M., Brown University, 1997 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Philosophy at Brown University Providence, Rhode Island May 2002 © Copyright 2002 by Jay Newhard This dissertation by Jay Michael Newhard is accepted in its present form by the Department of Philosophy as satisfying the dissertation requirements for the degree of Doctor of Philosophy Date__________ _________________________________ James Van Cleve, Director Recommended to the Graduate Council Date__________ _________________________________ Ernest Sosa, Reader Date__________ _________________________________ Nathan Salmon, Reader Approved by the Graduate Council Date__________ _________________________________ Peder J. Estrup Dean of the Graduate School and Research VITA Jay Newhard was born on 01 October 1967 in Allentown, Pennsylvania. He received a Bachelor of Science degree in Chemical Engineering in 1989, and a Master of Science degree in Chemical Engineering in 1991, both from the Pennsylvania State University. In 1994, he received a Bachelor of Arts degree in Philosophy from the University of California, Santa Barbara. In 1997, he received a Master of Arts degree from Brown University. He has taught at the University of Rhode Island, Augustana College, and Texas Tech University. PREFACE A number of philosophical theories of truth have been developed upon common pre- philosophical intuitions: a correspondence theory claims that true propositions correspond to reality; a coherence theory claims that true propositions cohere with other true propositions; and a pragmatic theory claims that true propositions are those (belief in) which are pragmatically useful. Each of these theories characterizes truth as a substantive property, but faces serious objections which render it apparently untenable. Dissatisfaction with these theories has led to theories developed upon more sophisticated philosophical considerations, foremost among them those that challenge whether truth is a substantive property. According to the simple theory of truth, truth is a property, but is simple, unanalyzable, and unsubstantive. The redundancy theory of truth claims that truth is not a property, and that the truth predicate is at best a grammatical expedient, and otherwise redundant. The disquotational, minimal, and prosentential theories are alike in holding that truth is not a substantive property, if a property at all. Other sophisticated attempts are the revision theory, which claims that truth is inherently circular, and the vagueness theory, which claims that the truth predicate is a vague predicate. The aim of this dissertation is to offer and defend a correspondence theory of truth. I must, therefore, not only show that all of these theories of truth, with the exception of the correspondence theory, are defective; I must also extricate the correspondence theory from the criticisms, now standard, which have been taken as decisive against it. In chapter 1, I examine the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth, and argue of each that it is unsatisfactory. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. The discussion of the correspondence theory in chapter 1 is limited to a presentation of traditional versions of the theory and objections to them. A special problem facing a theory of truth is the Liar Paradox. In chapter 2, I discuss the Liar Paradox and the responses made to it by the above theories. The devastating effects of the Liar Paradox on these theories has led to the development of formal theories of truth, such as the revision theory, Kripke’s theory, and the vagueness theory, also examined in chapter 2. In chapter 3, I present and argue for the indexical correspondence theory of truth (the IC theory), a novel version of the correspondence theory according to which truth is a correspondence property sensitive to semantic context. This context-sensitivity explains why an ungrounded sentence does not express a proposition. Consequently, the IC theory accounts for the similarity between the Liar and Truth-Teller sentences, and provides a philosophically motivated immunity to the Liar Paradox, including empirical versions. Customized versions of the Liar Paradox besetting the IC theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Löb’s Paradox and to Grelling’s Paradox. Arguments similar to those given to defend the IC theory show that with one minor alteration, Kripke’s formal theory may be used to model the IC notion of truth. ACKNOWLEDGEMENTS I wish to thank my committee members James Van Cleve, Ernest Sosa, and Nathan Salmon for their help with this dissertation, and for their ferocious sense of justice in doing philosophy. Special and abounding thanks are due to Gary Gates and Matthew McGrath for their extremely generous and supportive discussions of the topics in this dissertation. Finally, I wish to thank a few friends whose devoted encouragement, sometimes with kind and sincere words, sometimes just from being their tremendous selves, was most certainly essential to completing this project: David R. Lachterman, John Peterson, André Ariew, George S. Newhard, Jason Kawall, Maria Elena Garcia, Max Deutsch, Alisa Hartz, and most lovingly of all, Rebecca Wee. CONTENTS Chapter 1: Theories of Truth 1 Section 1: Intuitions about the Nature of Truth 1 Section 2: Truth-Bearers 5 Section 3: Correspondence Theories of Truth 9 Section 3.1: Three Weak Correspondence Theories of Truth 10 Section 3.2: Three Strong Correspondence Theories of Truth 12 Section 3.3: Conclusions about Correspondence Theories of Truth 19 Section 4: Coherence Theories of Truth 20 Section 5: Pragmatic Theories of Truth 27 Section 6: Epistemic Theories of Truth 33 Section 7: The Simple Theory of Truth 36 Section 8: The Redundancy Theory of Truth 39 Section 9: Frege’s Theory of Truth 46 Section 10: Tarski’s Theory of Truth 51 Section 11: The Disquotational Theory of Truth 62 Section 12: The Minimalist Theory of Truth 85 Section 12.1: Horwich’s Minimalist Theory of Truth 89 Section 12.2: Sosa’s Finite Minimal Theory of Truth 92 Section 12.3: Horwich’s Minimalist Theory of Truth (slight return) 101 Section 13: The Prosentential Theory of Truth 104 Section 14: Deflationism 109 Section 15: Conclusions about Theories of Truth 113 Chapter 2: Truth Paradox 120 Section 16: The Liar Paradox & Truth Paradox 120 Section 17: Responses to Truth Paradox: Substantive Theories 129 Section 17.1: The Correspondence Theory’s Response 129 Section 17.2: The Coherence Theory’s Response 131 Section 17.3: The Pragmatic Theory’s Response 132 Section 17.4: The Epistemic Theory’s Response 133 Section 18: Responses to Truth Paradox: Deflationary Theories 134 Section 18.1: The Simple Theory’s Response 134 Section 18.2: The Redundancy Theory’s Response 135 Section 18.3: The Disquotational Theory’s Response 136 Section 18.4: The Minimalist Theory’s Response 137 Section 18.5: The Finite Minimal Theory’s Response 139 Section 19: Responses to Truth Paradox: Formal Theories 140 Section 19.1: Tarski’s Theory of Truth 140 Section 19.2: Kripke’s Theory of Truth 143 Section 19.3: Vagueness Theories of Truth 151 Section 19.4: The Revision Theory of Truth 157 Section 20: Context Theories of Truth and Their Responses 162 Section 21: Conclusions about Truth Paradox 168 Chapter 3: A Correspondence Theory of Truth 170 Section 22: The Semantics of the Truth Predicate 170 Section 22.1: Simple versus Complex Correspondence Theory of Truth 170 Section 22.2: Propositions, States of Affairs, and Facts 173 Section 22.3: Truth and Falsity 177 Section 22.4: Truth and Indexicality 185 Section 22.5: States of Affairs and Facts (slight return) 188 Section 22.6: Truth, Truth-Value, and Extension Assignments 192 Section 22.7: Löb’s Paradox 198 Section 22.8: Grelling’s Paradox 200 Section 22.9: The Liar Paradox and the Truth-Teller 203 Section 22.10: A Formal Model of the Truth Predicate 211 Section 23: Objections 217 Section 23.1: Admitting States of Affairs and Facts Multiplies Entities Beyond Necessity 217 Section 23.2: Mereological Worries about Facts 219 Section 23.3: A Partially Defined Predicate Does Not Express a Property 221 Section 23.4: Customized Truth Paradoxical Sentences 223 Section 24: Further Challenging Cases 228 Section 24.1: Analyticity 228 Section 24.2: Counterfactuals and Modalities 235 Section 24.3: Logically Complex Propositions 238 Section 24.4: Negative Facts 241 Section 24.5: True Negative Singular Existentials 244 Section 25: Conclusions 250 Bibliography 256 Table 1: Forms of Negation 125 Figure 1: Expression, Denotation, Correspondence, and Advertance 178 CHAPTER 1: THEORIES OF TRUTH Section 1: Intuitions about the Nature of Truth There are several intuitions commonly had about the nature of truth.1 The correspondence intuition is the intuition that true propositions2 accord with, or correspond to, the way that the world is. For example, if the proposition that Raphael is a painter is true, then Raphael is a painter. Further, the correspondence holds both ways: if Raphael is a painter, then the proposition that he is is true. Truth is often a very useful notion. The truth of the proposition that a certain painting I own was painted by Raphael is extremely important in selling it for its proper value, or perhaps refusing to sell it. The truth of the proposition that a certain syringe contains adrenaline and not a coagulant may be critical in saving a life. The intuition that truth is useful is the pragmatic intuition about the nature of truth.