Predictive Simplicity (eBook)

Front Cover 1
Predictive Simplicity: Induction Exhum'd 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 12
Part I: The Evolution of the Problem 16
Section 1: The Justification of Induction 18
Chapter 1. Hume's Problem 18
1 The scope of induction 18
2 The point of justification 20
3 Major lines of progress 22
Notes 25
Chapter 2. The Inductivist Solution 26
1 Braithwaite's approach 27
2 Black's approach 29
3 Reasons for the failure of the inductive approach 31
Notes 32
Chapter 3. The Pragmatic Vindication 33
1 Reichenbach's vindication 33
2 Salmon's modifications 35
3 Criticisms of the pragmatic approach 36
4 Reasons for the failure of the pragmatic approach 41
Notes 42
Chapter 4. The Dissolution of the Problem 43
1 The analyticity of the reasonableness of induction 43
2 Strawson's claims 44
3 The analyticity of reasonableness and the naturalistic fallacy 45
4 Goodman's analogy with the justification of deduction 49
Notes 50
Section 2: The Characterization of Induction 52
Chapter 5. Goodman's New Riddle and the Justification of Induction 52
1 The new riddle 52
2 The effect of the new riddle on solutions to Hume's problem 53
Notes 56
Chapter 6. A Closer Look at Goodman's New Riddle 58
1 Five conditions necessary to a solution 58
2 Goodman's own solution 62
3 Suggestions for a positive approach 64
Notes 65
Part II: The Resolution of the Problem 68
Section 3: An Account of Simplicity 70
Chapter 7. Simplicity: Raw 70
1 Simplicity as testability 70
2 Prior accounts of testability 71
3 A new account of testability 73
4 A more systematic treatment 74
5 The definition of simplicity 78
6 Several examples 78
7 Simplicity, logical strength, emergent properties, natural kinds 81
Notes 83
Chapter 8. Simplicity: Refined 84
1 Simplicity orderings 84
2 A preliminary distinction 85
3 The revised account 86
4 The simplicity of mathematical relationships 87
5 An extension of the account of simplicity to cases of dimension 89
6 Several examples involving considerations of dimension 91
7 A conflict of standards 92
8 Some more substantive results 94
9 Concluding remarks 97
Notes 98
Section 4: The Explication of Induction 100
Chapter 9. Induction as Simplicity 100
1 The scope of this definition 100
2 Goodman's new riddle 101
3 Some remarks on induction and projectibility 106
Notes 106
Chapter 10. Induction Justified 107
1 The gist of the justification 107
2 Some preliminaries 107
3 The justification 110
4 Coarse graining 112
5 A modification of Hempel's special consequence condition 117
6 Response to objections 119
7 Remarks on the nature of this justification 122
Notes 124
Section 5: Some Implications of Induction 125
Chapter 11. Inductive Logic and Confirmation 125
1 Inductive logic as opposed to probability theory and mathematical statistics 125
2 A non-probabilistic component of inductive logic – simplicity 127
3 A probabilistic component of inductive logic – evidential support 129
4 The paradoxes of confirmation 138
Notes 143
Chapter 12. The Consilience of Inductions 147
1 Arguments that theories are dispensible 148
2 An account of inductive systematization 151
3 The impossibility of a purely probabilistic account of consilience 154
4 The importance of consilience 157
Notes 158
Chapter 13. The Resilience of Induction 160
1 Popper's criticisms of the inductivist program 160
2 An inductivist critique of Popper's program 164
3 An inductivist critique of Lakatos's modifications 165
4 Replies to 'incommensurabilist' programs 169
Notes 172
Chapter 14. A Logic of Scientific Discovery 174
1 The role of simplicity 174
2 The role of confirmation 179
3 Combined considerations 180
Notes 183
Appendix: A Measure of Statistical Simplicity 185
1 A measure of statistical simplicity 186
2 The maximum-entropy principle 188
3 The interpretation of the maximum-entropy principle 191
4 The resolution of the incompatibility between the maximum-entropy principle and Bayesian conditionalization 193
5 The justification of particular prior probability distributions 194
Notes 199
REFERENCES 202
NAME INDEX 208
SUBJECT INDEX 210