Philosophy and probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2013
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVII, 194 S. graph. Darst. |
| ISBN: | 9780199661831 9780199661824 |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PRIFACE ACKNOWLEDGEMENTS LIST 01BOXESANDFIGURES
1. PROBABILITY AND RELATIVE FREQUENCIES
2. PROPENSITIES AND OTHER PHYSICAL PROBABILITIES
3. SUBJECTIVE PROBABILITY
4. SUBJECTIVE AND OBJECTIVE PROBABILITIES
5. THE CLASSICAL AND LOGICAL INTERPRETATIONS
6. THE MAXIMUM ENTROPY PRINCIPLE
APPENDICES
RIFERENCES INDEX
XLII XVI
XVILI
1
33
51
100
113
133
156
182 193
IMAGE 2
DETAILED CONTENTS
PREJACE KILL
ACKNOWLEDGEMENTS XVI
LIST CFBOXESANDFIGURES XVILI
1. PROBABILITY AND RELATIVE FREQUENCIES 1
1.1 INTRODUCTION 1
1.2 VON MISES S RELATIVE FREQUENCY INTERPRETATION 2
1.2.1 PROBABILITY AND MASS PHENOMENA 2
1.2.2 CONVERGENCE OF RELATIVE FREQUENCY 4
1.2.3 RANDOMNESS-THE IMPOSSIBILITY OF A GAMBLING SYSTEM 7 1.2.3.1 WALD
ON COLLECTIVES 9
1.2.3.2 CHURCH S SOLUTION 10
1.2.3.3 RANDOMNESS-KOLMOGOROV AND AFTER 12
1.2.4 OPERATIONS ON COLLECTIVES 14
1.2.5 OBJECTIONS TO VON MISES S INTERPRETATION 17
1.2.5.1 VILLE S OBJECTION(S) 17
1.2.5.2 ELEGANCE (OR THE LACK THEREOF) 19
1.2.5.3 INFINITE LIMITS AND EMPIRICAL CONTENT 20
1.2.5.4 SINGLE-CASE PROBABILITIES AND THE REFERENCE DASS 22 1.3
KOLMOGOROV AND RELATIVE FREQUENCIES 24
1.3.1 RELATIVE FREQUENCIES ASPROBABILITIESTHE KOLMOGOROV AXIOMS 24
1.3.1.1 FREQUENTIST CONDITIONAL PROBABILITY 26
1.3.1.2 INDEPENDENCE 26
1.3.2 THE MEASURE-THEORETIC FRAMEWORK 27
1.3.2.1 MEASURE ZERO 28
1.3.3 DOOB S REINTERPRETATION OF VON MISES 28
1.3.4 VAN FRAASSEN S MODAL FREQUENCY INTERPRETATION 29
1.3.5 PROBLEMS WITH KOLMOGOROVIAN INTERPRETATIONS 30
1.4 FINITE FREQUENCY INTERPRETATIONS 31
1.5 CONDUSION 32
2. PROPENSITIES AND OTHER PHYSICAL PROBABILITIES 33
2.1 ELEMENTS OF A PROPENSITY INTERPRETATION 34
2.1.1 PROB ABILITY ASA DISPOSITION 34
2.1.2 SINGLE-CASE PROBABILITIES 35
IMAGE 3
X DETAILED CONTENTS
2.2 PROBLEMS WITH PROPENSITY INTERPRETATIONS 36
2.2.1 INDETERMINISM AND THE REFERENCE DASS 37
2.2.2 EMPIRICAL CONTENT 38
2.2.3 HUMPHREYS S PARADOX 40
2.2.4 WHY ARE PROPENSITIES PROBABILITIES? 44
2.2.5 ARE PROPENSITIES RELATIVE FREQUENCIES? 45
2.2.6 IS THERE ASEPARATE PROPENSITY INTERPRETATION? 46
2.3 CONDUSION 48
3. SUBJECTIVE PROB ABILITY 51
3.1 INTRODUCTION 51
3.2 DUTCH BOOKARGUMENTS 52
3.2.1 FAIR BETS 54
3.2.2 THE FORMS OFBETS 55
3.2.3 HOW NOT TO BET 57
3.2.4 ADDING UP BETS AND PROBABILITIES 57
3.2.5 CONDITIONAL BETS AND PROBABILITY 59
3.3 THEAPPLICATION OFSUBJECTIVE PROBABILITIES 61
3.3.1 BAYES S THEOREM AND BAYESIAN EPISTEMOLOGY 62
3.3.2 EXAMPLE:BEER 63
3.3.3 DISCONFIRMATION 65
3.3.4 AM I THIS GOOD A BREWER? -FALSIFICATION 66
3.3.5 AM I THIS GOOD A BREWER?- THE DUHEM-QUINE PROBLEM 67 3.3.6 THE
BAYESIAN ACCOUNT OFTHE DUHEM-QUINE PROBLEM 68 3.3.7 OTHER BAYESIAN
SOLUTIONS 72
3.4 PROBLEMS WITH THE DUTCH BOOK ARGUMENT 74
3.4.1 THE LITERAL INTERPRETATION OF THE DUTCH BOOK ARGUMENT 75 3.4.2 THE
AS-IFINTERPRETATION 78
3.4.3 THE LOGICAL INTERPRETATION 80
3.5 PROB ABILITY FROM LIKELIHOOD 82
3.5.1 PROBLEMS WITH PROBABILITIES FROM LIKELIHOOD 85
3.6 PROBABILITIES FROM PREFERENCES 86
3.6.1 PROBLEMS WITH UTILITY THEORY 88
3.7 OTHER ARGUMENTS EQUATING DEGREES OFBELIEF AND PROBABILITY 90 3.8 IS
BAYESIANISM TOO SUBJECTIVE? 91
3.8.1 BAYESIAN LEARNING THEORY 92
3.8.2 CONVERGENCE OF OPINION 92
3.8.3 THE PROBLEM OFINDUCTION 95
3.8.4 DIACHRONIE DUTCH BOOKS 96
3.9 IS BAYESIANISM TOO FLEXIBLE? OR NOT FLEXIBLE ENOUGH? 97
3.10 CONDUSION 99
4. SUBJECTIVE AND OBJECTIVE PROBABILITIES 100
4.1 THE PRINCIPLE OF DIRECT INFERENCE [00
4.2 BETTING ON FREQUENCIES [02
IMAGE 4
DETAILED CONTENTS XL
4.3 THE PRINEIPAL PRINEIPLE 103
4.3.1 HUMEAN SUPERVENIENEE AND BEST SYSTEMS ANALYSES OFLAWS 104
4.3.2 THE BIG BAD BUG AND THE NEW PRINEIPLE 106
4.4 EXEHANGEABILITY 108
4.5 CONCLUSION 112
5. THE CLASSICAL AND LOGICAL INTERPRETATIONS 113
5.1 THE ORIGINS OFPROBABILITY- THE CLASSIEALTHEORY 113
5.1.1 THE RULE OF SUEEESSION 116
5.1.2 THE EONTINUOUS EASE OFTHE PRINEIPLE OFINDIFFERENEE 117 5.2
PROBLEMS WITH THE PRINEIPLE OF INDIFFERENCE 118
5.2.1 PROBLEMS WITH THE RULE OFSUEEESSION 118
5.2.2 THE PARADOXES 119
5.2.2.1 THE DISERETE EASE 119
5.2.2.2 THE PARADOXES-THE EONTINUOUS EASE 120
5.2.2.3 THE PARADOXES OF GEOMETRIE PROBABILITY (BERTRAND S PARADOX) 121
5.2.2.4 LINEAR TRANSFORMATIONS AND THE PRINEIPLE OFINDIFFERENEE 123
5.3 KEYNES S LOGIEAL INTERPRETATION 123
5.3.1 THE DISERETE EASE AND THE JUSTIFIEATION OF THE PR INEIPIE
OFINDIFFERENEE 124
5.3.2 KEYNES ON THE EONTINUOUS EASE 126
5.3.3 KEYNES ON THE RULE OFSUEEESSION 127
5.4 CARNAP 127
5.4.1 THE LOGIEAL FOUNDATIONS OFPROBABILITY 128
5.4.2 THE CONTINUUM OFINDUETIVE METHODS 130
5.5 CONCLUSION 132
6. THE MAXIMUM ENTROPY PRINCIPLE 133
6.1 BITS AND INFORMATION 133
6.2 THE PRINEIPLE OFMAXIMUM ENTROPY 137
6.2.1 THE EONTINUOUS VERSION OFTHE PRINEIPLE OF MAXIMUM ENTROPY 139
6.2.2 MAXIMUM ENTROPY AND THE PARADOXES OF GEOMETRIE PROBABILITY 140
6.2.3 DETERMINATION OF EONTINUOUS PROBABILITIES 143
6.3 MAXIMUM ENTROPY AND THE WINE- WATER PARADOX 144
6.3.1 PROBLEMS WITH THE SOLUTION-DIMENSIONS OR NOT? 144
6.4 LANGUAGE DEPENDENEE 145
6.4.1 THE STATISTIEAL MEEHANIES EOUNTEREXAMPLE 145
6.4.2 CORREETLY APPLYING THE PRINEIPLE? 146
6.4.3 LANGUAGE DEPENDENEE AND ONTOLOGIE AL DEPENDENEE 148 6.4.4 THE
SEOPE OFTHE MAXIMUM ENTROPY PRINEIPLE 149
IMAGE 5
XII DETAILED CONTENTS
6.5 ]USTIFYING THE MAXIMUM ENTROPY PRINCIPLE AS A LOGICAL
CONSTRAINT 6.5.1 MAXIMUM ENTROPY AS IMPOSING CONSISTENCY 6.5.2 PROBLEMS
WITH THE MAXIMUM ENTROPY PRINCIPLE AS CONSISTENCY
6.6 CONCLUSION
APPENDICES
150 150
153 154
156
AO SOME BASICS 156
A.O.L PERCENTAGES 156
A.0.2 KINDS OFNUMBERS 156
A.0.3 SIZES OF SETS-COUNTABLE AND UNCOUNTABLE 156
A.O.4 FUNCTIONS, LIMITS 157
AO.5 LOGARITHMS 157
A.L THE AXIOMS 158
A.L.1 CONDITIONAL PROBABILITY, INDEPENDENCE 159
A.2 MEASURES, PROBABILITY MEASURES 160
A2.1 FIELDS 160
A.2.2 FIELDS,O -FIELDS 162
A.2.3 MEASURES 162
A.2.3.1 MEASURE ZERO 163
A2.4 PROBABILITY MEASURES 163
A.2.4.1 THE PHILOSOPHICAL STATUS OF COUNTABLE ADDITIVITY 163 A.2.5 SOME
USEFUL THEOREMS 165
A.3 RANDOM VARIABLES 165
A.3.1 SUMS OFRANDOM VARIABLES 166
A.3.2 EXPECTATION 167
A.3.3 CONTINUOUS RANDOM VARIABLES 167
A.4 COMBINATORICS 167
A.4.1 PERMUTATIONS 168
A.4.2 COMBINATIONS 169
A.5 LAWS OFLARGE NUMBERS 169
A.5.1 BERNOULLI RANDOM VARIABLES AND THE BINOMIAL DISTRIBUTION 169 A.5.2
LAWS OFLARGE NUMBERS 171
A.5.3 BEHAVIOUR OFTHE BINOMIAL DISTRIBUTION FOR LARGE NUMBERS OFTRIALS
173
A.6 TOPICS IN SUBJECTIVE PROB ABILITY 174
A.6.1 STRICT COHERENCE 174
A6.2 SCORINGRULES 175
A.6.3 AXIOMS FOR QUALITATIVE AND QUANTITATIVE PROBABILITIES 178
A.7 THE DUHEM-QUINE PROBLEM, LANGUAGE, METAPHYSICS 179
A.7.1 A PROBABILISTIC TRANSLATION OFQUINE S PROGRAMME 180
RIFERENCES
INDEX
1R2 193
|
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| indexdate | 2024-07-10T00:38:49Z |
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| isbn | 9780199661831 9780199661824 |
| language | English |
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| spelling | Childers, Timothy Verfasser aut Philosophy and probability Timothy Childers 1. ed. Oxford Oxford Univ. Press 2013 XVII, 194 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Philosophie (DE-588)4045791-6 s DE-604 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026042408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Childers, Timothy Philosophy and probability Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4137007-7 (DE-588)4045791-6 |
| title | Philosophy and probability |
| title_auth | Philosophy and probability |
| title_exact_search | Philosophy and probability |
| title_full | Philosophy and probability Timothy Childers |
| title_fullStr | Philosophy and probability Timothy Childers |
| title_full_unstemmed | Philosophy and probability Timothy Childers |
| title_short | Philosophy and probability |
| title_sort | philosophy and probability |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Wahrscheinlichkeit Philosophie |
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