: Claude Gratton
: Infinite Regress Arguments
: Springer-Verlag
: 9789048133413
: 1
: CHF 87.50
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: Allgemeines, Lexika
: English
: 211
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Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of using this tool indicate that there is a need for a theory to re-orient our practice.

My general approach tocontribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: (1) How are infinite regresses generated in infinite regress arguments? (2) How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infiniteregress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regressarguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments.

Acknowledgements5
Introduction9
1 What is an Infinite Regress Argument?11
1.1 The General Structure of Infinite Regress Arguments11
1.2 Boundaries of an Infinite Regress Argument15
1.2.1 Boundaries when an Infinite Regress is Vicious16
1.2.2 Boundaries when an Infinite Regress is Benign19
1.3 A Hypothesis About the Nature of Infinite Regresses22
1.4 Testing Hypothesis H 28
1.5 Testing Hypothesis H with Nonconcatenating Regresses31
1.6 Potentially Infinite and Actually Infinite Regresses35
1.7 The Necessary Quantity of Terms and Relations38
1.8 Applications of Hypothesis H to Various Examples41
1.8.1 Plato's Couch41
1.8.2 Teachers Taught by Teachers42
1.8.3 Gods Giving Meaning to Gods43
1.8.4 Maps of Maps45
1.8.5 Lewis Carroll''s ''What the Tortoise Said to Achilles''48
1.9 Logical Functions of Infinite Regresses54
1.9.1 Benign Regresses55
1.9.2 Superfluous Regresses59
1.10 Cogency and Benign Regresses62
2 The Formal and Nonformal Logic of Infinite Concatenating Regresses67
2.1 Recurring Terms, Loops, and Regress Formulas67
2.2 The Relation of Terms and Objects of an Infinite Regress73
2.3 Applications74
2.4 Recurring Terms, Loops, and Infinite Concatenating Regresses78
2.5 Relations and Loops82
2.6 Blocking All Possible Loops85
2.7 Are Irreflexivity, or Asymmetry or Transitivity Necessary to Block Loops?88
2.8 Concatenating Relations in Regress Formulas91
2.9 Directions of Infinite Concatenating Regresses92
2.9.1 The Importance of the Direction of an Infinite Regress93
2.9.2 The Formal Direction of an Infinite Regress94
2.9.3 The Semantic Direction of an Infinite Regress96
2.10 Non-formal Considerations in Regress Formulas97
2.10.1 Relations and Their Implications98
2.10.2 Unstated Properties of Relations and Terms99
2.10.3 Stated Properties of Objects or Conditions in a Regress Formula100
2.10.4 Unstated Properties of Objects Designated by Terms101
2.11 Summary108
2.12 Evaluative Questions109
3 Viciousness111
3.1 Are There Inherently Vicious Regresses?111
3.2 Clark on Viciousness115
3.3 Johnstone and Viciousness117
3.4 Uncompletability and Viciousness121
3.5 Occams Razor: Ontological Extravagance125
3.6 Blocking Vicious Infinite Regresses129
3.6.1 Hume130
3.6.2 Miller133
3.6.3 Laurence and Margolis135
3.6.4 The General form of the Argument for Blocking Regresses137
4 Circular Definitions, Circular Explanations, and Infinite Regresses141
4.1 A Formal Derivation of Infinite Regresses from Circular Definitions141
4.2 Infinitely Many Infinite Regresses144
4.3 Semantic Considerations145
4.4 Regresses Independent of Circularity148
4.5 The Viciousness of Infinite Regresses Entailed by Circular Definitions149
4.6 The Derivation of Infinite Regresses from Circular Explanations152
5 Infinite Regresses and Recurring Questions157
5.1 Recurring Questions and the Derivation of Infinite Regresses159
5.2 Recurring Questions and Vicious Regresses163
6 Infinite Regresses of Recurring Problems and Responses168
6.1 Platos Aviary in the Theatetus169
6.2 McTaggarts Discontinual Regress172
6.3 Mackies Discontinual Regress176
6.4 Armstrongs Continual Regress181
6.5 A Continual Regress in Defense of Cantors Diagonal Method187
6.6 Lehrers Regress of Recurring Possible Problems and Possible Responses191
6.7 Evaluative Questions197
6.8 Summary of the Book198
Appendix A 202
Appendix B 203
References 211
Index1