VAGUENESS AND ITS BOUNDARIES: A PEIRCEAN THEORY OF VAGUENESS David Wells Agler Submitted to the faculty of the University Graduate School in partial fulfillment of the requirements for the degree Master of Arts in the Department of Philosophy, Indiana University January 2010 Accepted by the Faculty of Indiana University, in partial fulfillment of the requirements for the degree of Master of Arts. _____________________________ Cornelis de Waal, Ph.D., Chair _____________________________ André De Tienne Ph.D. Master’s Thesis Committee _____________________________ Nathan R. Houser, Ph.D. ii Acknowledgments The amount of assistance I have received in writing this M.A. thesis has been overwhelming. First and foremost, I would like to thank my thesis chair Cornelis de Waal. His patience in receiving drafts of chapters over the last few years and his ability to offer critical and nuanced suggestions on the content of each draft were indispensible for completing this work. I am in debt to him for his loyal and continued guidance. The two remaining members of my committee also provided substantial assistance. I would like to thank André De Tienne for sparking my initial interest in Peirce, for his sustained professional support, and for leveling a number of weighty objections at the very foundation of my project. Finally, Nathan Houser deserves special mention for I first began to take interest in the logic and semantics of vagueness in a seminar he taught on Charles S. Peirce. His comments on a later draft were helpful in developing this text into a readable thesis. A number of other individuals deserve special thanks. Vincent Colapietro offered a number of useful remarks on organization as well as practical advice for expediting the completion of this work. In discussion, Emily Grosholz offered a number of useful comments on intuitionism, Leibniz, and the relation between excluded middle and the principle of non-contradiction. After the oral defense of this work, Irving H. Anellis offered a number of suggestions on how to develop my historical study of vagueness, specifically with respect to Frege, Russell, and the work of Jean van Heijenoort. Toby Svoboda made a number of useful comments on chapters 1, 2, 3, and 6. His demand for clarity concerning borderline cases in chapter 6 was especially helpful in my writing of that chapter. Daniel Brunson read and commented upon chapters 1 and 6, and suggested that I consider the notion of hysteresis in trying to block the paradox. Marco Annoni drew my attention to Peirce’s letter to James on Royce’s logic and offered useful lessons from his own attempt to demolish the sorites. Masato Ishida made a number of helpful remarks about the axiom of choice and the relation of Peirce’s existential graphs to vagueness. Jill Loveall proofread drafts of chapters, provided consistent support as I wrote the bulk of the thesis, and patiently listened as I tried to determine whether or not ‘John is tall’ is true or false. Jessica Trock drew a number of illustrations for graphs I used in an early draft of chapter 5 but they have subsequently been omitted. I owe Benjamin Peltz a heartfelt iii thanks for commenting on chapters 1 and 6, and for helping me clarify my project in its initial stages. Special thanks to Joy Lynn Bala and Chris Nemirow for providing me a place to stay while I wrote the bulk of chapter 4 at the University of Southern California. Finally, I owe thanks to my parents, the Institution for American Thought, particularly the Peirce Edition Project, and the philosophy departments at IUPUI and The Pennsylvania State University. Working as a research assistant at the Peirce Project in 2006–2007 made it possible for convenient access to Peirce’s manuscript material and learning to write drafts for critical annotations fostered a familiarity with certain details of Peirce’s work that would have no doubt been overlooked in the normal course of graduate study. My parents have remained consistently positive that I would finish this work even when other academic research and duties suggested that it would be unlikely. Without past and current financial and academic support from each of the above, the content of this work would have remained hopelessly vague. iv ABSTRACT VAGUENESS AND ITS BOUNDARIES: A PEIRCEAN THEORY OF VAGUENESS David Wells Agler Many theories of vagueness employ question-begging assumptions about the semantic boundaries between truth and falsity. This thesis defends a theory of vagueness put forward by Charles S. Peirce and argues for a novel solution to the sorites paradox based upon his work. Contrary to widespread opinion, I argue that Peirce distinguished borderline vagueness from other related forms of indeterminacy, e.g. indefiniteness, generality, unspecificity, uninformativity, etc. By clarifying Peirce’s conception of borderline vagueness, I argue for a solution to the sorites paradox based upon his logical semantics. In addition, I argue for this theory against the epistemic theory of vagueness, which makes controversial claims concerning the sharp semantic boundary between truth and falsity, and against the supervaluationist theory of vagueness, which is committed to the in principle impossibility of sharp semantics boundaries for propositions with vague terms. Cornelis de Waal, Ph.D., Chair v TABLE OF CONTENTS Chapter 1: An Introduction to Vagueness and the Sorites .................................................1 0. Introduction .............................................................................................................1 1. Depicting Vagueness ...............................................................................................1 2. Two Formulations of the Sorites ..............................................................................5 2.1. The Many Modus Ponens Sorites ..........................................................................5 2.2. Sorites with the Universally Quantified Premise....................................................7 3. General Solutions.....................................................................................................7 4. Originality and Major Claims of the Thesis ............................................................ 10 Chapter 2: A Historical Sketch of the Sorites Paradox ................................................... 12 0. Introduction ........................................................................................................... 12 1. Zeno, Abraham, and Eubulides .............................................................................. 12 2. Chrysippus and the Stoics ...................................................................................... 13 3. Galen ..................................................................................................................... 18 4. After Antiquity: Medievals & Lorenzo Valla ......................................................... 21 5. Three Moderns: Locke, Leibniz, & Hume .............................................................. 23 6. A Prelude to the Rise of Modern Logic: Early 19th Century Discussion .................. 29 7. Conclusion ............................................................................................................. 35 Chapter 3: The Epistemic Theory of Vagueness ............................................................. 36 0. Introduction ........................................................................................................... 36 1. The History of the Epistemic View of Vagueness................................................... 37 2. Semantic Optimism................................................................................................ 37 3. Vagueness as Ignorance and Inexact Knowledge .................................................... 38 4. What Determines Sharp Boundaries? ..................................................................... 43 vi 4.1. Omniscient Speakers ........................................................................................... 44 4.2. Nature ................................................................................................................. 47 4.3. The Argument from Meaning and Use: Williamson’s Master Argument ............. 48 4.3.1 Vagueness and the T-schema ............................................................................ 49 4.3.2. Excluded Middle and Bivalence ....................................................................... 51 5. Conclusion ............................................................................................................. 51 Chapter 4: Supervaluationism ........................................................................................ 53 0. Supervaluationism: An Introduction ....................................................................... 53 1. The History of the Supervaluational View of Vagueness ........................................ 54 2. Supervaluationism: The Basics .............................................................................. 55 3. Objections.............................................................................................................. 61 3.1 Supervaluationism and Validity ........................................................................... 61 3.2. Vagueifiers ......................................................................................................... 62 3.3. No Truth-Functionality, the Argument from Upper-case Letters .......................... 64 3.4.