The Epistemic Lightness of Truth : Deflationism and Its Logic

This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original perspectives on this central and controversial issue, his book will be important for those with a background in logic who are interested in formal truth theories and in current philosophical debates about the deflationary conception of truth. Cover 1 Copyright 5 Contents 6 Acknowledgements 8 Introduction 10 1 Preliminaries 16 1.1 Peano Arithmetic 16 1.2 Model Theory 23 1.3 Conservativity 29 1.4 Truth 31 1.5 Reflection Principles 35 2 Approaches to Truth 37 2.1 Model-Theoretic versus Axiomatic Approach 37 2.1.1 Tarski’s Method 38 2.1.2 Kripke’s Construction 41 2.1.3 Axiomatic Systems 43 2.2 Approaches to Truth: Aims and Assessments 47 2.2.1 Philosophical Aims of Truth Theories 47 2.2.2 Model-Theoretic and Axiomatic Approach: An Assessment 53 Summary 57 Part I Disquotation 58 3 Disquotational Theories 63 3.1 Typed Disquotational Theories 64 3.2 Untyped Disquotation 66 Summary 72 4 Why Do We Need Disquotational Truth? 73 4.1 Expressing Generalisations 75 Summary 82 5 The Generalisation Problem 83 5.1 Horwich’s First Solution 85 5.2 Horwich’s Second Solution 90 Summary 96 Part II Conservativity 98 6 (Non)Conservativity of Disquotation 105 Summary 120 7 CT− and CT: Conservativity Properties 122 Summary 143 8 Other Compositional Truth Theories 144 8.1 The Systems of Kripke-Feferman and Friedman-Sheard 144 8.2 Positive Truth with Internal Induction for Total Formulas 147 Summary 158 9 Conservativity: Philosophical Motivations 160 9.1 Semantic Conservativity 160 9.2 Syntactic Conservativity 171 Summary 187 10 Maximal Conservative Theories 189 Summary 196 11 The Conservativeness Argument 198 11.1 Formulations 201 Conservativeness argument: version 1. 201 Conservativeness argument: version 2. 203 Conservativeness argument: version 3. 204 Conservativeness argument: version 4. 205 11.2 Reactions to the Conservativeness Argument 206 11.2.1 Field’s Rejoinder 207 11.2.2 Tennant’s Solution 213 Summary 217 Part III Reflection Principles 218 12 The Strength of Reflection Principles 222 12.1 Partial Truth Predicates 224 12.2 The Truth of First-Order Logic 226 12.3 Δ0 Induction and the Truth of Propositional Logic 230 12.4 Compositional Axioms and Reflection 241 12.4.1 Typed Framework 241 12.4.2 Untyped Framework 243 Summary 245 13 Deflationism and Truth-Theoretical Strength 247 13.1 Torkel Franzén on Implicit Commitments 250 13.2 Accepting PA – Basic Options 257 13.3 The Reflective Process 262 13.4 Believability and Reflective Commitment 267 13.4.1 Formal Properties of Bel(K) 271 13.4.2 Applications: Reflection and the Generalisation Problem 277 13.5 Perspectives and Refinements 281 Summary 291 Afterword 294 Glossary of Symbols 296 Bibliography 300 Index 308 Machine Generated Contents Note: 1. Preliminaries -- 1.1. Peano Arithmetic -- 1.2. Model Theory -- 1.3. Conservativity -- 1.4. Truth -- 1.5. Reflection Principles -- 2. Approaches To Truth -- 2.1. Model-theoretic Versus Axiomatic Approach -- 2.2. Approaches To Truth: Aims And Assessments -- Pt. I Disquotation -- 3. Disquotational Theories -- 3.1. Typed Disquotational Theories -- 3.2. Untyped Disquotation -- 4. Why Do We Need Disquotational Truth? -- 4.1. Expressing Generalisations -- 5. The Generalisation Problem -- 5.1. Horwich's First Solution -- 5.2. Horwich's Second Solution -- Pt. Ii Conservativity -- 6. (non)conservativity Of Disquotation -- 7. Ct- And Ct: Conservativity Properties -- 8. Other Compositional Truth Theories -- 8.1. The Systems Of Kripke-feferman And Friedman-sheard -- 8.2. Positive Truth With Internal Induction For Total Formulas -- 9. Conservativity: Philosophical Motivations -- 9.1. Semantic Conservativity -- 9.2. Syntactic Conservativity -- 10. Maximal Conservative Theories -- 11. The Conservativeness Argument -- 11.1. Formulations -- 11.2. Reactions To The Conservativeness Argument -- Pt. Iii Reflection Principles -- 12. The Strength Of Reflection Principles -- 12.1. Partial Truth Predicates -- 12.2. The Truth Of First-order Logic -- 12.3. Ao Induction And The Truth Of Propositional Logic -- 12.4. Compositional Axioms And Reflection -- 13. Deflationism And Truth-theoretical Strength -- 13.1. Torkel Franzen On Implicit Commitments -- 13.2. Accepting Pa -- Basic Options -- 13.3. The Reflective Process -- 13.4. Believability And Reflective Commitment -- 13.5. Perspectives And Refinements. Cezary Cieśliński (university Of Warsaw). Includes Bibliographical References (pages 285-291) And Index. Providing an up-to-date discussion and defence of deflationism about truth, addressing recent philosophical developments in axiomatic truth theories and evaluating the notion of the innocence of truth, this volume will benefit both students and scholars of philosophy, particularly those interested in logic and in conceptions of truth.