Resonance: from probability to epistemology and back
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
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London
Imperial College Press
[2016]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xx, 408 Seiten 24 cm |
| ISBN: | 9781783269204 1783269200 |
Internformat
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| 264 | 4 | |c © 2016 | |
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Datensatz im Suchindex
| _version_ | 1804177006876688384 |
|---|---|
| adam_text | Contents
Preface vii
About the Author ix
1. Introduction 1
1.1 Knowledge ................................................. 1
1.2 Probability................................................ 2
1.3 Summary of the Main Claims............................ . 3
1.3.1 Resonance.......................................... 3
1.3.2 Critique of frequency and subjective philosophies
of probability ..................................... 4
1.3.2.1 Positive philosophical ideas.............. 5
1.3.2.2 Negative philosophical ideas ...... 6
1.3.2.3 Innovative technical ideas................ 8
1.3.3 Scientific laws of probability..................... 8
1.3.4 Statistics and philosophy.......................... 9
1.4 Historical and Social Context............................. 11
1.5 Disclaimers............................................... 13
Philosophy of Probability 17
2. Main Philosophies of Probability 19
2.1 The Classical Theory...................................... 20
2.2 The Logical Theory ....................................... 20
2.3 The Propensity Theory .................................... 22
2.4 The Subjective Theory..................................... 22
XI
23
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27
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31
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34
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42
46
47
48
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57
59
59
61
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65
67
68
69
Contents
2.4.1 Interpreting subjectivity.....................
2.4.2 Verification of probabilistic statements......
2.4.3 Subjectivity as an escape from the shackles
of verification ..............................
2.4.4 The Dutch book argument.......................
2.4.5 The axiomatic system..........................
2.4.6 Identification of probabilities and decisions . . .
2.4.7 The Bayes theorem.............................
2.5 The Frequency Theory..................................
2.6 Summary of Philosophical Theories of Probability . . .
2.7 From Ideas to Theories................................
2.8 Popular Philosophy....................................
2.9 Is There Life Beyond Von Mises and De Finetti? . . . .
Skepticism
3.1 How Do You Prove that You are Not a Camel?............
3.2 Skepticism............................................
3.2.1 Frustration of philosophers...................
3.3 Anything Goes.........................................
3.4 Von Mises’ Brand of Skepticism........................
3.4.1 The smoking gun...............................
3.4.2 Inconsistencies in von Mises’ theory..........
3.5 De Finetti’s Brand of Skepticism......................
3.5.1 How to eat the cake and have it too...........
3.6 On Approximate Theories...............................
3.7 Temperature, Beauty and Probability...................
3.8 Latter Day Subjectivism...............................
The Frequency Philosophy of Probability
4.1 Collective as an Elementary Concept...................
4.2 Applications of Probability Do Not Rely on Collectives .
4.2.1 Stochastic processes..........................
4.2.2 Unlikely events...............................
4.2.3 Graphical communication.......................
4.3 Collectives in Real Life..............................
4.4 Collectives and Symmetry..............................
4.5 Frequency Theory and the Law of Large Numbers . . .
4.6 Why is Mathematics Useful? ...........................
Contents xiii
4.7 Benefits of Imagination and Imaginary Benefits........ 70
4.8 Imaginary Collectives ................................ 71
4.9 Computer Simulations.................................. 72
4.10 Frequency Theory and Individual Events................ 73
4.11 Collectives and Populations................................ 74
4.12 Are All i.i.d. Sequences Collectives? ................ 75
4.13 Are Collectives i.i.d. Sequences?.......................... 76
4.14 Martin-Lof Sequences....................................... 77
5. The Subjective Philosophy of Probability 79
5.1 “Subjective” — A Word with a Subjective Meaning . . 80
5.2 The Subjective Theory of Probability is Objective ... 81
5.3 A Science without Empirical Content........................ 83
5.4 If Probability does not Exist, Everything is Permitted . 84
5.4.1 Creating something out of nothing................... 85
5.4.2 The essence of probability ......................... 86
5.5 De Finetti’s Ultimate Failure......................... . 88
5.5.1 Lazy decision maker................................. 90
5.5.2 Interpreting Dutch book............................ 91
5.5.3 Dutch book with a lapse of time..................... 92
5.5.3.1 The butterfly effect....................... 93
5.5.4 Rule of conditionalization.......................... 94
5.6 All Sequential Decisions are Consistent.................... 95
5.7 Honest Mistakes............................................ 96
5.8 Cohabitation with an Evil Demiurge......................... 98
5.9 Why Bother to Use Probability?............................ 100
5.10 The Dutch Book Argument is Rejected by Bayesians . . 100
5.11 Insurance Against Everything.............................. 101
5.12 No Need to Collect Data................................... 102
5.13 Empty Promises............................................ 103
5.14 The Meaning of Consistency................................ 104
5.15 Interpreting Miracles..................................... 105
5.16 Science, Probability and Subjectivism..................... 107
5.17 Apples and Oranges........................................ 108
5.18 Arbitrage................................................. 109
5.19 Subjective Theory and Atheism............................. 110
5.20 Imagination and Probability............................... Ill
5.21 A Misleading Slogan....................................... 113
xiv Contents
5.22 Axiomatic System as a Magical Trick..................... 114
5.23 The Meaning of Subjectivity ............................ 114
5.24 Probability and Chance.................................. 119
5.25 Conflict Resolution .................................... 122
6. The Logical Philosophy of Probability 125
6.1 Falsifiability.......................................... 125
6.2 Why Do Scientists Ignore the Logical Philosophy
of Probability?......................................... 127
6.3 Probabilities of Propositions and Events................ 128
7. Common Issues 131
7.1 Law Enforcement......................................... 131
7.2 The Value of Extremism.................................. 133
7.3 Common Elements in Frequency and Subjective
Theories................................................ 133
7.4 Common Misconceptions................................... 134
7.5 Shattered Dreams of Perfection.......................... 136
7.6 What Exists?............................................ 137
7.7 Abuse of Language....................................... 137
7.7.1 Expected value................................... 138
7.7.2 Standard deviation............................... 138
7.7.3 Subjective opinions.............................. 138
7.7.4 Optimal Bayesian decisions....................... 138
7.7.5 Confidence intervals............................. 138
7.7.6 Significant difference .......................... 138
7.7.7 Consistency...................................... 139
7.7.8 Objective Bayesian methods....................... 139
7.7.9 Prior............................................ 140
7.7.10 Non-informative prior............................ 140
Epistemology 141
8. Epistemology 143
8.1 The Problem of Induction................................ 143
8.1.1 An ill posed problem............................ 144
8.1.1.1 On intuitively obvious propositions . . 146
8.1.2 Induction is a law of nature .................... 147
Contents xv
8.1.3 Anthropic principle........................... 148
8.2 Resonance............................................. 149
8.2.1 Information and knowledge..................... 149
8.2.2 Resonance complexity.......................... 150
8.2.3 Facts......................................... 151
8.2.4 Learning resonance............................ 153
8.2.5 Resonance level reduction..................... 155
8.2.6 Properties of resonance....................... 156
8.2.7 Physical basis of resonance................... 157
8.2.8 Information and knowledge revisited........... 159
8.2.9 Resonance and subjectivity.................... 160
8.2.10 Raw resonance................................. 161
8.2.11 Resonance and philosophy of Hume.............. 162
8.2.12 Is resonance a new concept?....................... 163
8.3 Consciousness............................................. 164
8.4 Intelligence.............................................. 166
8.4.1 Artificial Intelligence........................... 169
8.4.2 Social Context of Intelligence.................... 170
8.5 Free Will ................................................ 171
8.6 From Philosophy to Science................................ 174
9. Religion 177
10. Science 181
10.1 Science as a Communication System......................... 181
10.2 Some Attributes of Science................................ 184
10.2.1 Interpersonal character........................... 184
10.2.2 The role and limitations of resonance............. 185
10.2.3 Convergence to the truth?......................... 185
10.2.4 Science control................................... 186
10.2.5 Beyond simple induction........................... 186
10.2.6 Science as a web.................................. 187
10.3 Science for Scientists.................................... 187
10.4 Alien Science............................................. 188
10.4.1 A lonely alien.................................. 189
10.5 Sources and Perils of Loyalty............................. 190
10.5.1 Science as an antidote to manipulation............ 193
10.5.2 Dependent information sources..................... 194
xvi Contents
10.6 Falsificationism and Resonance........................... 195
10.7 Falsificationism as a Religion............................ 197
10.7.1 Sainthood in science.............................. 198
10.8 Technology................................................ 200
10.9 Multiple Personality Disorder............................. 200
10.10 Reality, Philosophy and Science.......................... 202
10.11 Decision Making.......................................... 204
10.12 Major Trends in Philosophy of Science.................... 205
10.12.1 Real science — the big picture................... 207
10.12.2 Probabilism and Bayesianism in philosophy
of science...................................... 208
10.12.3 Levels of philosophical analysis................. 210
10.12.4 Position of my theory in philosophy of science . 211
10.13 Circularity.............................................. 213
Science of Probability 215
11. The Science of Probability 217
11.1 Interpretation of (L1)-(L6)............................... 218
11.1.1 Events............................................ 218
11.1.2 Symmetry.......................................... 219
11.1.3 Enforcement....................................... 221
11.1.4 Limits of applicability........................... 221
11.1.5 (LI)—(L6) as a starting point..................... 222
11.1.6 Approximate probabilities ........................ 223
11.1.7 Statistical models................................ 224
11.1.8 The Bayes theorem................................. 225
11.1.9 Probability of past events........................ 225
11.1.10 Purely mathematical independence................. 226
11.1.11 Ruelle’s view of probability..................... 226
11.2 Scientific Verification of (L1)-(L6)...................... 226
11.3 Predictions............................................... 229
11.3.1 Predictions at various reliability levels......... 230
11.3.2 Predictions in existing scientific and philosophical
theories.......................................... 232
11.3.3 Predictions, conditioning and hypothesis tests . 233
11.3.4 Prediction examples............................... 233
Contents xvii
11.3.5 Histograms and image reconstruction.......... 234
11.3.6 Contradictory predictions.................... 236
11.3.7 Multiple predictions......................... 238
11.4 Symmetry, Independence and Resonance............... 242
11.5 Symmetry is Relative ................................ 243
11.6 Moderation is Golden.................................... 244
11.7 Applications of (LI)—(L6): Some Examples ............ 246
11.7.1 Poisson process ................................ 246
11.7.2 Laws (LI)—(L6) as a basis for statistics...... 247
11.7.3 Long run frequencies and (LI)—(L6)............ 247
11.7.4 Life on Mars.................................... 248
11.8 Symmetry and Data....................................... 250
11.9 Probability of a Single Event........................... 251
11.10 On Events that Belong to Two Sequences.................. 252
11.11 Events Are More Fundamental Than Random Variables 253
11.12 Deformed Coins.......................................... 254
11.13 Are Coin Tosses i.i.d. or Exchangeable?................. 256
11.14 Mathematical Foundations of Probability................. 257
11.15 Axioms versus Laws of Science........................... 258
11.16 Objective and Subjective Probabilities.................. 259
11.17 Physical and Epistemic Probabilities.................... 260
11.18 Can Probability Be Explained?........................... 261
11.19 Propensity.............................................. 263
11.20 Countable Additivity.................................... 264
11.21 Yin and Yang............................................ 265
11.22 Are Laws (LI)—(L6) Necessary? .......................... 266
11.23 Quantum Mechanics....................................... 266
11.24 The History of (LI)—(L6) in Philosophy of Probability . 267
11.25 Symmetry and Theories of Probability.................... 268
12. Decision Making 271
12.1 Common Practices........................................ 271
12.2 Decision Making in the Context of (LI)—(L6)............. 272
12.2.1 Maximization of expected gain................... 272
12.2.2 Maximization of expected gain as an axiom ... 275
12.2.3 Stochastic ordering of decisions ............... 275
12.2.4 Generating predictions.......................... 278
12.2.5 Intermediate decision problems.................. 279
xviii Contents
12.3 Decision Making and Resonance ......................... 280
12.4 Events with No Probabilities........................... 282
12.5 Utility.................................................... 284
12.5.1 Variability of utility in time .................... 284
12.5.2 Nonlinearity of utility............................ 285
12.5.3 Utility of non-monetary rewards.................... 287
12.5.4 Unobservable utilities............................. 288
12.5.5 Can utility be objective?.......................... 288
12.5.6 What is the utility of gazillion dollars?.......... 289
12.6 Identification of Decisions and Probabilities.......... 290
13. Frequency Statistics 291
13.1 Confidence Intervals . . .................................. 291
13.1.1 Practical challenges with statistical predictions . 292
13.1.2 Making predictions is necessary.................... 294
13.2 Estimation ................................................ 294
13.2.1 Estimation and (L1)-(L6) 297
13.2.2 Unbiasedness — a concept with a single
application ........................................ 297
13.3 Hypothesis Testing......................................... 299
13.3.1 Hypothesis tests and collectives................... 300
13.3.2 Hypothesis tests and the frequency interpretation
of probability ..................................... 301
13.3.3 Hypothesis testing and (LI)—(L6)................... 301
13.3.3.1 Sequences of hypothesis tests............. 301
13.3.3.2 Single hypothesis test.................... 302
13.4 Hypothesis Testing and (L6) ......................... 303
13.5 Hypothesis Testing and Falsificationism.................... 304
13.6 Does Frequency Statistics Need the Frequency
Philosophy of Probability?................................. 304
14. Bayesian Statistics 307
14.1 Two Faces of Subjectivity.................................. 307
14.1.1 Non-existence versus informal assessment .... 307
14.1.2 Are all probabilities subjective?.................. 308
14.1.3 Conditioning versus individuality.................. 308
14.1.4 Non-existent decisions............................. 309
14.2 Elements of Bayesian Analysis ............................. 309
Contents xix
14.3 Models.................................................. 310
14.3.1 Bayesian models are totally objective.......... 310
14.3.2 Bayesian models are totally subjective............ 311
14.4 Priors................................................... 311
14.4.1 Objective priors ................................. 312
14.4.2 Bayesian statistics as an iterative method .... 313
14.4.3 Truly subjective priors........................ 315
14.5 Resonance at Work..................................... 317
14.6 Data.................................................. 318
14.7 Posteriors............................................ 318
14.7.1 Non-convergence of posterior distributions . . . 319
14.8 Bayesian Statistics and (LI)—(L6)........................ 321
14.9 Spurious Predictions.................................. 321
14.10 Who Needs Subjectivism?.................................. 322
14.11 Preaching to the Converted............................... 323
14.12 Constants and Random Variables........................... 326
14.13 Criminal Trials.......................................... 328
Miscellanea 331
15. On Ideologies 333
15.1 On Ideologies and Their Photo-Negatives.................. 333
15.2 Experimental Statistics — A Missing Science............. 337
15.3 Statistical Time Capsules................................ 340
15.4 Is Statistics a Science? ................................ 341
15.5 Psychoanalytic Interpretation of Philosophy
of Probability........................................... 343
15.6 From Intuition to Science................................ 344
15.7 Science as Service....................................... 346
15.8 The Three Aspects of Probability......................... 347
15.9 Is Probability a Science?................................ 348
15.10 Are Probability and Logic Experimental Sciences? . . . 349
16. Paradoxes, Wagers and Rules 353
16.1 St. Petersburg Paradox .................................. 353
16.2 Pascal’s Wager .......................................... 355
16.2.1 Scientific aspects of Pascal’s wager.............. 356
XX
Contents
16.2.1.1 Two kinds of infinity.................... 356
16.2.1.2 Minor sins............................... 357
16.2.1.3 On the utility of eternal life in hell . . 358
16.2.1.4 Exponential discounting.................. 358
16.2.2 A sociological analysis of Pascal’s wager .... 359
16.3 Cromwell’s Rule .......................................... 361
16.3.1 Cromwell’s rule: practical implementation ... 361
16.3.2 Cromwell’s rule: philosophical problems .... 364
16.4 Principal Principle....................................... 366
16.5 A New Prisoner Paradox.................................... 367
16.5.1 Analysis of the new prisoner paradox.............. 368
16.6 Ellsberg Paradox.......................................... 369
16.7 The Probability of God................................... 372
17. Teaching Probability 375
17.1 Teaching Independence..................................... 378
17.2 Probability and Frequency................................. 379
17.3 Undergraduate Textbooks................................... 380
18. Mathematical Methods of Probability and Statistics 383
18.1 Probability............................................... 383
18.1.1 Law of large numbers, central limit theorem
and large deviations principle ................... 385
18.1.2 Exchangeability and de Finetti’s theorem .... 385
18.2 Frequency Statistics...................................... 386
18.3 Bayesian Statistics....................................... 387
18.4 Contradictory Predictions................................. 388
Bibliography 391
Index
397
|
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| spelling | Burdzy, K. 1957- Verfasser (DE-588)112571977X aut Resonance from probability to epistemology and back Krzysztof Burdzy, University of Washington, USA. London Imperial College Press [2016] © 2016 xx, 408 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Philosophie Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Erkenntnistheorie (DE-588)4070914-0 gnd rswk-swf Probabilities / Philosophy Knowledge, Theory of Wahrscheinlichkeit (DE-588)4137007-7 s Erkenntnistheorie (DE-588)4070914-0 s DE-604 Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029422232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burdzy, K. 1957- Resonance from probability to epistemology and back Philosophie Wahrscheinlichkeit (DE-588)4137007-7 gnd Erkenntnistheorie (DE-588)4070914-0 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4070914-0 |
| title | Resonance from probability to epistemology and back |
| title_auth | Resonance from probability to epistemology and back |
| title_exact_search | Resonance from probability to epistemology and back |
| title_full | Resonance from probability to epistemology and back Krzysztof Burdzy, University of Washington, USA. |
| title_fullStr | Resonance from probability to epistemology and back Krzysztof Burdzy, University of Washington, USA. |
| title_full_unstemmed | Resonance from probability to epistemology and back Krzysztof Burdzy, University of Washington, USA. |
| title_short | Resonance |
| title_sort | resonance from probability to epistemology and back |
| title_sub | from probability to epistemology and back |
| topic | Philosophie Wahrscheinlichkeit (DE-588)4137007-7 gnd Erkenntnistheorie (DE-588)4070914-0 gnd |
| topic_facet | Philosophie Wahrscheinlichkeit Erkenntnistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029422232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT burdzyk resonancefromprobabilitytoepistemologyandback |