TRUTH AND ALETHEIC PARADOX by Kevin Scharp AB, Washington University, 1995 MA, University of Wisconsin-Milwaukee, 1998 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2005 UNIVERSITY OF PITTSBURGH FACULTY OF ARTS AND SCIENCES This dissertation was presented by Kevin Scharp It was defended on 9 May 2005 and approved by Anil Gupta, Distinguished Professor of Philosophy, University of Pittsburgh John McDowell, University Professor of Philosophy, University of Pittsburgh Hartry Field, Professor of Philosophy, New York University Dissertation Director: Robert Brandom, Distinguished Service Professor, University of Pittsburgh ii TRUTH AND ALETHEIC PARADOX Kevin Scharp, PhD University of Pittsburgh, 2005 My objective is to provide a theory of truth that is both independently motivated and compatible with the requirement that semantic theories for truth should not demand a substantive distinction between the languages in which they are formulated and those to which they apply. I argue that if a semantic theory for truth does not satisfy this requirement, then it is unacceptable. The central claim of the theory I develop is that truth is an inconsistent concept: the rules for the proper use of truth are incompatible in the sense that they dictate that truth both applies and fails to apply to certain sentences (e.g., those that give rise to the liar and related paradoxes). The most significant challenge for a proponent of an inconsistency theory of truth is producing a plausible theory of inconsistent concepts. On the account I provide, inconsistent concepts are confused concepts. A concept is confused if, in employing it, one is committed to applying it to two or more distinct types of entities without properly distinguishing between them; that is, an employer of a confused concept thinks that two or more distinct entities are identical. I propose a semantic theory for predicates that express confused concepts, and a new many-valued relevance logic on which the semantic theory depends. This semantic theory serves as the basis for my theory of inconsistent concepts. Given this account of inconsistent concepts and my claim that truth is inconsistent, I am committed to the view that truth is confused. I use the semantic theory for confused predicates as a semantic theory for truth. On the account I advance, a proper theory of truth requires a distinction between several different types of truth predicates. I propose an account of each truth predicate, and I advocate using them as consistent replacements for the concept of truth. The result is a team of concepts that does the work of the inconsistent concept of truth without giving rise to paradoxes. iii TABLE OF CONTENTS PREFACE ......................................................................................................................................... IX INTRODUCTION ................................................................................................................................1 1.0 INTERNALIZABLE SEMANTIC THEORIES .................................................................................. 11 1.1 INTRODUCTION .............................................................................................................. 11 1.2 PREVIOUS PROPOSALS ................................................................................................... 17 1.2.1 THE NATURALISM ARGUMENT .......................................................................... 17 1.2.2 THE COMPREHENSIBILITY ARGUMENT .............................................................. 19 1.2.3 EXPRESSIVE CAPACITY ARGUMENTS................................................................. 20 1.3 INTERNALIZABLE SEMANTIC THEORIES ......................................................................... 22 1.3.1 DEFINITIONS ...................................................................................................... 23 1.3.2 EXAMPLE: KRIPKE’S SEMANTIC THEORY .......................................................... 34 1.4 COMPARISONS ............................................................................................................... 42 1.4.1 UNIVERSALITY................................................................................................... 43 1.4.2 SEMANTIC CLOSURE .......................................................................................... 44 1.4.3 SEMANTIC SELF-SUFFICIENCY ........................................................................... 45 1.5 CONCLUSION.................................................................................................................. 47 2.0 INTERNALIZABILITY REQUIREMENTS ...................................................................................... 49 2.1 INTRODUCTION .............................................................................................................. 49 2.2 INTERNALIZABILITY REQUIREMENTS ............................................................................. 50 2.3 STRONG INTERNALIZABILITY......................................................................................... 53 2.3.1 THE ARGUMENT................................................................................................. 54 2.3.2 OBJECTIONS AND REPLIES ................................................................................. 56 2.4 MODERATE INTERNALIZABILITY, TRUTH, AND NATURAL LANGUAGES......................... 68 2.4.1 THE ARGUMENT................................................................................................. 70 2.4.2 OBJECTIONS AND REPLIES ................................................................................. 75 2.5 INDEFINABILITY............................................................................................................. 90 2.6 CONCLUSION.................................................................................................................. 93 3.0 ALETHEIC VENGEANCE........................................................................................................... 96 3.1 INTRODUCTION .............................................................................................................. 96 3.2 WHY IS INTERNALIZABILITY SO HARD?......................................................................... 98 3.2.1 CONSISTENT CONCEPTS AND NAÏVE THEORIES................................................ 101 3.2.2 TRUTH RULES AND PARADOXICALITY ............................................................. 103 3.2.3 REVENGE AND SELF-REFUTATION ................................................................... 105 3.3 TRUTH, INCONSISTENCY, AND INTERNALIZABILITY..................................................... 116 3.4 CONCLUSION................................................................................................................ 123 4.0 A THEORY OF INCONSISTENT CONCEPTS .............................................................................. 124 4.1 INTRODUCTION ............................................................................................................ 124 4.2 INCONSISTENT CONCEPTS ............................................................................................ 124 4.3 POLICIES FOR HANDLING INCONSISTENT CONCEPTS.................................................... 133 iv 4.3.1 THE REINTERPRETATION POLICY..................................................................... 134 4.3.2 THE CONTAINMENT POLICY............................................................................. 135 4.2.3 THE REPLACEMENT POLICY............................................................................. 136 4.4 INCONSISTENT CONCEPTS ARE CONFUSED................................................................... 138 4.5 CONCLUSION................................................................................................................ 140 5.0 A THEORY OF CONFUSION .................................................................................................... 142 5.1 INTRODUCTION ............................................................................................................ 142 5.2 CAMP’S THEORY OF CONFUSION ................................................................................. 142 5.2.1 THE AMBIGUITY CONDITION ........................................................................... 144 5.2.2 THE BELIEF CONDITION................................................................................... 145 5.2.3 THE TRUTH-VALUE CONDITION ...................................................................... 147 5.2.4 THE NORMATIVITY CONDITION ....................................................................... 150 5.2.5 SEMANTIC STANCES......................................................................................... 154 5.3 CAMP’S LOGIC FOR CONFUSED SENTENCES................................................................. 155 5.4 CONCLUSION................................................................................................................ 160 6.0 CONCEPTUAL CONFUSION AND CONCEPTUAL INCONSISTENCY ............................................ 162 6.1 INTRODUCTION ............................................................................................................ 162 6.2 FIRST-ORDER LOGIC FOR CONFUSION ......................................................................... 162 6.2.1 CONDITIONALS ...............................................................................................