Infinite Regress Arguments

Acknowledgements

Introduction

1 What is an Infinite Regress Argument?

1.1 The General Structure of Infinite Regress Arguments

1.2 Boundaries of an Infinite Regress Argument

1.2.1 Boundaries when an Infinite Regress is Vicious

1.2.2 Boundaries when an Infinite Regress is Benign

1.3 A Hypothesis About the Nature of Infinite Regresses

1.4 Testing Hypothesis H

1.5 Testing Hypothesis H with Nonconcatenating Regresses

1.6 Potentially Infinite and Actually Infinite Regresses

1.7 The Necessary Quantity of Terms and Relations

1.8 Applications of Hypothesis H to Various Examples

1.8.1 Plato's Couch

1.8.2 Teachers Taught by Teachers

1.8.3 Gods Giving Meaning to Gods

1.8.4 Maps of Maps

1.8.5 Lewis Carroll''s ''What the Tortoise Said to Achilles''

1.9 Logical Functions of Infinite Regresses

1.9.1 Benign Regresses

1.9.2 Superfluous Regresses

1.10 Cogency and Benign Regresses

2 The Formal and Nonformal Logic of Infinite Concatenating Regresses

2.1 Recurring Terms, Loops, and Regress Formulas

2.2 The Relation of Terms and Objects of an Infinite Regress

2.3 Applications

2.4 Recurring Terms, Loops, and Infinite Concatenating Regresses

2.5 Relations and Loops

2.6 Blocking All Possible Loops

2.7 Are Irreflexivity, or Asymmetry or Transitivity Necessary to Block Loops?

2.8 Concatenating Relations in Regress Formulas

2.9 Directions of Infinite Concatenating Regresses

2.9.1 The Importance of the Direction of an Infinite Regress

2.9.2 The Formal Direction of an Infinite Regress

2.9.3 The Semantic Direction of an Infinite Regress

2.10 Non-formal Considerations in Regress Formulas

2.10.1 Relations and Their Implications

2.10.2 Unstated Properties of Relations and Terms

2.10.3 Stated Properties of Objects or Conditions in a Regress Formula

2.10.4 Unstated Properties of Objects Designated by Terms

2.11 Summary

2.12 Evaluative Questions

3 Viciousness

3.1 Are There Inherently Vicious Regresses?

3.2 Clark on Viciousness

3.3 Johnstone and Viciousness

3.4 Uncompletability and Viciousness

3.5 Occams Razor: Ontological Extravagance

3.6 Blocking Vicious Infinite Regresses

3.6.1 Hume

3.6.2 Miller

3.6.3 Laurence and Margolis

3.6.4 The General form of the Argument for Blocking Regresses

4 Circular Definitions, Circular Explanations, and Infinite Regresses

4.1 A Formal Derivation of Infinite Regresses from Circular Definitions

4.2 Infinitely Many Infinite Regresses

4.3 Semantic Considerations

4.4 Regresses Independent of Circularity

4.5 The Viciousness of Infinite Regresses Entailed by Circular Definitions

4.6 The Derivation of Infinite Regresses from Circular Explanations

5 Infinite Regresses and Recurring Questions

5.1 Recurring Questions and the Derivation of Infinite Regresses

5.2 Recurring Questions and Vicious Regresses

6 Infinite Regresses of Recurring Problems and Responses

6.1 Platos Aviary in the Theatetus

6.2 McTaggarts Discontinual Regress

6.3 Mackies Discontinual Regress

6.4 Armstrongs Continual Regress

6.5 A Continual Regress in Defense of Cantors Diagonal Method

6.6 Lehrers Regress of Recurring Possible Problems and Possible Responses

6.7 Evaluative Questions

6.8 Summary of the Book

Appendix A

Appendix B

References

Index