| Acknowledgements | 5 |
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| Introduction | 9 |
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| 1 What is an Infinite Regress Argument? | 11 |
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| 1.1 The General Structure of Infinite Regress Arguments | 11 |
| 1.2 Boundaries of an Infinite Regress Argument | 15 |
| 1.2.1 Boundaries when an Infinite Regress is Vicious | 16 |
| 1.2.2 Boundaries when an Infinite Regress is Benign | 19 |
| 1.3 A Hypothesis About the Nature of Infinite Regresses | 22 |
| 1.4 Testing Hypothesis H | 28 |
| 1.5 Testing Hypothesis H with Nonconcatenating Regresses | 31 |
| 1.6 Potentially Infinite and Actually Infinite Regresses | 35 |
| 1.7 The Necessary Quantity of Terms and Relations | 38 |
| 1.8 Applications of Hypothesis H to Various Examples | 41 |
| 1.8.1 Plato's Couch | 41 |
| 1.8.2 Teachers Taught by Teachers | 42 |
| 1.8.3 Gods Giving Meaning to Gods | 43 |
| 1.8.4 Maps of Maps | 45 |
| 1.8.5 Lewis Carroll''s ''What the Tortoise Said to Achilles'' | 48 |
| 1.9 Logical Functions of Infinite Regresses | 54 |
| 1.9.1 Benign Regresses | 55 |
| 1.9.2 Superfluous Regresses | 59 |
| 1.10 Cogency and Benign Regresses | 62 |
| 2 The Formal and Nonformal Logic of Infinite Concatenating Regresses | 67 |
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| 2.1 Recurring Terms, Loops, and Regress Formulas | 67 |
| 2.2 The Relation of Terms and Objects of an Infinite Regress | 73 |
| 2.3 Applications | 74 |
| 2.4 Recurring Terms, Loops, and Infinite Concatenating Regresses | 78 |
| 2.5 Relations and Loops | 82 |
| 2.6 Blocking All Possible Loops | 85 |
| 2.7 Are Irreflexivity, or Asymmetry or Transitivity Necessary to Block Loops? | 88 |
| 2.8 Concatenating Relations in Regress Formulas | 91 |
| 2.9 Directions of Infinite Concatenating Regresses | 92 |
| 2.9.1 The Importance of the Direction of an Infinite Regress | 93 |
| 2.9.2 The Formal Direction of an Infinite Regress | 94 |
| 2.9.3 The Semantic Direction of an Infinite Regress | 96 |
| 2.10 Non-formal Considerations in Regress Formulas | 97 |
| 2.10.1 Relations and Their Implications | 98 |
| 2.10.2 Unstated Properties of Relations and Terms | 99 |
| 2.10.3 Stated Properties of Objects or Conditions in a Regress Formula | 100 |
| 2.10.4 Unstated Properties of Objects Designated by Terms | 101 |
| 2.11 Summary | 108 |
| 2.12 Evaluative Questions | 109 |
| 3 Viciousness | 111 |
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| 3.1 Are There Inherently Vicious Regresses? | 111 |
| 3.2 Clark on Viciousness | 115 |
| 3.3 Johnstone and Viciousness | 117 |
| 3.4 Uncompletability and Viciousness | 121 |
| 3.5 Occams Razor: Ontological Extravagance | 125 |
| 3.6 Blocking Vicious Infinite Regresses | 129 |
| 3.6.1 Hume | 130 |
| 3.6.2 Miller | 133 |
| 3.6.3 Laurence and Margolis | 135 |
| 3.6.4 The General form of the Argument for Blocking Regresses | 137 |
| 4 Circular Definitions, Circular Explanations, and Infinite Regresses | 141 |
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| 4.1 A Formal Derivation of Infinite Regresses from Circular Definitions | 141 |
| 4.2 Infinitely Many Infinite Regresses | 144 |
| 4.3 Semantic Considerations | 145 |
| 4.4 Regresses Independent of Circularity | 148 |
| 4.5 The Viciousness of Infinite Regresses Entailed by Circular Definitions | 149 |
| 4.6 The Derivation of Infinite Regresses from Circular Explanations | 152 |
| 5 Infinite Regresses and Recurring Questions | 157 |
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| 5.1 Recurring Questions and the Derivation of Infinite Regresses | 159 |
| 5.2 Recurring Questions and Vicious Regresses | 163 |
| 6 Infinite Regresses of Recurring Problems and Responses | 168 |
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| 6.1 Platos Aviary in the Theatetus | 169 |
| 6.2 McTaggarts Discontinual Regress | 172 |
| 6.3 Mackies Discontinual Regress | 176 |
| 6.4 Armstrongs Continual Regress | 181 |
| 6.5 A Continual Regress in Defense of Cantors Diagonal Method | 187 |
| 6.6 Lehrers Regress of Recurring Possible Problems and Possible Responses | 191 |
| 6.7 Evaluative Questions | 197 |
| 6.8 Summary of the Book | 198 |
| Appendix A | 202 |
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| Appendix B | 203 |
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| References | 211 |
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| Index | 1 |