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Tables of Contents for Truthlikeness for Multidimensional, Quantitative Cognitive Problems
Chapter/Section Title
Page #
Page Count
PREFACE
ix
CHAPTER 1. INTRODUCTION
1
18
1.1. A Preparatory Example: Electrorheological Fluids
2
4
1.2. Physical Systems and State Spaces
6
5
1.3. Partial Truths, Approximately True Statements, and ad verum Approximations
11
3
1.4. The Concept of Verisimilitude
14
5
CHAPTER 2. ON COMPETING THEORIES OF VERISIMILITUDE AND ON EVALUATING THEM
19
33
2.1. Explications and some Problems in Evaluating them
19
4
2.2. The Proposals of Popper and their Modifications
23
4
2.3. Some Other Proposals
27
4
2.4. The Similarity Approach to Truthlikeness
31
4
2.5. Different Intuitions and Desiderate in the Similarly Approach to Truthlikeness
35
4
2.6. Should the theory of Verisimilitude be a Methodological Tool?
39
13
CHAPTER 3. THE PROBLEMS OF ARBITRARINESS AND VAGUENESS
52
24
3.1. On Miller's Results and on Generalizing them
53
6
3.2. An n-dimensional Analogue for Miller's Theorem
59
2
3.3. The Naturalist Strategy for Dealing with Miller's Problem
61
8
3.4. Problems of Vagueness and Wittgensteinian Bounds
69
2
3.5. Appendix: Proof of Theorem 3.1.
71
5
CHAPTER 4. THE MEASURES OF VERISIMILITUDE OF THE SIMILARITY APPROACH
76
50
4.1. Introduction
76
3
4.2. Some Difficulties
79
6
4.3. Some Desiderata
85
5
4.4. Generalizing the Average Measure
90
3
4.5. The measure Vsyh space as an Analogy of the min-sum-measure
93
4
4.6. The Measures Vs YG
97
11
4.7. The Relationship between the Measures VsYh space and VsYG
108
1
4.8. Appendix: Proofs of theorems 4.1.-4.6.
109
17
CHAPTER 5. VERISILITUDE AND THE STANDARD STRUCTURALIST FRAMEWORK
126
29
5.1. The Structuralist Framework of BMS
127
6
5.2. The Modifications Recently Proposed by Moulines and Straub
133
2
5.3. Against Uniformities
135
3
5.4. Comparing Theoretical Accounts Expressing Partial Truths in the BMS Framework
138
8
5.5. Why Approximately True, False Theoretical Accounts Cannot be Compared in the BMS Framework
146
4
5.6. Appendix: Proofs of Theorems 5.1.-5.4.
150
5
CHAPTER 6. THE STRUCTURALIST DEFINITIONS OF VERISIMILITUDE
155
26
6.1. The Naive and the Refined Definition
156
5
6.2. Some Counter-examples and a Modification to the Refined Definition
161
7
6.3. Applying the Refined Definition to the Problem of Descriptive Verisimilitude
168
3
6.4. The Methodological Rules of the Structuralist Theory of Verisimilitude
171
7
6.5. Appendix: Proof of Theorem 6.1.
178
3
CHAPTER 7. GALILEO, ARISTOTLE, AND SOME DIFFICULTIES WITH QUANTITATIVE LAWS
181
12
7.1. Aristotle, Galileo, and the Probelm of Fall
182
1
7.2. Comparing the Degrees of Verisimilitude of Aristotle's and Galileo's Theoreis of Fall
183
5
7.3. The Difficulty in Generalizing the Metric: Some Elementary Stochastics
188
5
CHAPTER 8. CONCLUDING REMARKS
193
3
NOTES
196
15
REFERENCES
211
8
INDEX OF NAMES
219
3
INDEX OF SUBJECTS
222