Foreword |
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xv | |
Acknowledgment |
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xvii | |
Preface |
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xix | |
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SECTION I Pure Bayesianism |
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Chapter 1 On A Transformative Journey |
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3 | (14) |
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3 | (2) |
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1.2 My Path Towards Bayesianism |
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5 | (1) |
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1.3 A Unified Philosophy Of Knowledge |
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6 | (2) |
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1.4 An Alternative To The Scientific Method |
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8 | (3) |
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11 | (2) |
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1.6 The Goals Of The Book |
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13 | (4) |
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17 | (16) |
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2.1 The Troll Student Puzzle |
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17 | (1) |
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2.2 The Monty Hall Problem |
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18 | (2) |
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2.3 The Trial Of Sally Clark |
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20 | (1) |
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2.4 The Legal Conviction Of Bayesianism |
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21 | (1) |
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22 | (2) |
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2.6 The Components Of Bayes' Rule |
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24 | (2) |
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2.7 Bayes To The Rescue Of Diagnosis |
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26 | (1) |
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2.8 Bayes To The Rescue Of Sally Clark |
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27 | (2) |
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2.9 Bayes To The Rescue Of The Troll Student Problem |
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29 | (1) |
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2.10 A Few Words Of Encouragement |
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30 | (3) |
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Chapter 3 Logically Speaking |
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33 | (16) |
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3.1 Two Thinking Processes |
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33 | (2) |
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35 | (2) |
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37 | (2) |
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3.4 Quantifiers And Predicates |
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39 | (1) |
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3.5 Aristotle's Syllogism Reinterpreted |
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39 | (1) |
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40 | (1) |
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3.7 Platonists Versus Intuitionists |
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41 | (2) |
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43 | (1) |
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44 | (2) |
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3.10 The Cohabitation Of Incompatible Theories |
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46 | (3) |
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Chapter 4 Let's Generalize! |
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49 | (20) |
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4.1 The Scottish Black Sheep |
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49 | (1) |
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4.2 A Brief History Of Epistemology |
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50 | (1) |
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4.3 A Brief History Of Planetology |
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51 | (2) |
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4.4 Science Against Popper? |
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53 | (1) |
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53 | (3) |
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4.6 Statisticians Against The P-Value |
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56 | (2) |
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58 | (2) |
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4.8 What A Statistics Textbook Says |
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60 | (1) |
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4.9 The Equation Of Knowledge |
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61 | (2) |
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63 | (1) |
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64 | (5) |
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Chapter 5 All Hail Prejudices |
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69 | (20) |
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69 | (1) |
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5.2 Prejudices To The Rescue Of Linda* |
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70 | (2) |
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72 | (1) |
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73 | (1) |
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5.5 Prejudices To The Rescue Of Xkcd |
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74 | (1) |
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5.6 Prejudices To The Rescue Of Sally Clark |
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75 | (1) |
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5.7 Prejudices Against Pseudo-Sciences |
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76 | (1) |
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5.8 Prejudices To The Rescue Of Science |
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77 | (3) |
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5.9 The Bayesian Has An Opinion On Everything |
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80 | (3) |
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5.10 Erroneous Prejudices |
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83 | (3) |
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5.11 Prejudices And Moral Questions |
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86 | (3) |
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Chapter 6 The Bayesian Prophets |
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89 | (20) |
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89 | (1) |
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6.2 The Origins Of Probability |
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90 | (1) |
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6.3 The Mysterious Thomas Bayes |
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91 | (1) |
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6.4 Laplace, The Father Of Bayesianism |
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92 | (2) |
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6.5 Laplace's Succession Rule |
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94 | (4) |
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6.6 The Great Bayesian Winter |
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98 | (1) |
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6.7 Bayes To The Rescue Of Allies |
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99 | (2) |
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6.8 Bayesian Islands In A Frequentist Ocean |
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101 | (2) |
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6.9 Bayes To The Rescue Of Practitioners |
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103 | (1) |
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6.10 Bayes `Triumph, At Last!' |
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104 | (1) |
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105 | (4) |
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Chapter 7 Solomonoff's Demon |
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109 | (22) |
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7.1 Neither Human Nor Machine |
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109 | (1) |
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7.2 The Theory Of Computation |
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110 | (2) |
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112 | (1) |
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7.4 The Solomonoff Complexity |
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113 | (3) |
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7.5 The Marriage Of Algorithmic And Probabilities |
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116 | (3) |
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7.6 The Solomonoff Prior* |
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119 | (1) |
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7.7 Bayes To The Rescue Of Solomonoff's Demon* |
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120 | (2) |
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7.8 Solomonoff's Completeness |
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122 | (1) |
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7.9 Solomonoff's Incomputability |
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122 | (2) |
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7.10 Solomonoff's Incompleteness |
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124 | (1) |
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125 | (6) |
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SECTION II Applied Bayesianism |
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Chapter 8 Can You Keep A Secret? |
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131 | (18) |
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131 | (1) |
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132 | (2) |
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134 | (2) |
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136 | (2) |
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8.5 The Privacy Of The Randomized Survey |
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138 | (1) |
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8.6 The Definition Of Differential Privacy* |
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139 | (1) |
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8.7 The Laplacian Mechanism |
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140 | (1) |
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8.8 Robustness To Composition |
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141 | (2) |
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8.9 The Addition Of Privacy Losses |
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143 | (1) |
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8.10 In Practice, It's Not Going Well! |
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144 | (1) |
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8.11 Homomorphic Encryption |
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145 | (4) |
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Chapter 9 Game, Set And Math |
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149 | (18) |
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149 | (2) |
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151 | (1) |
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152 | (3) |
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155 | (1) |
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156 | (2) |
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158 | (1) |
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9.7 Bayesian Mechanism Design* |
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159 | (2) |
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161 | (2) |
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9.9 The Social Consequences Of Bayesianism |
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163 | (4) |
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Chapter 10 Will Darwin Select Bayes? |
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167 | (20) |
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167 | (1) |
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10.2 California's Colored Lizards |
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168 | (1) |
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10.3 The Lotka-Volterra Dynamic* |
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169 | (2) |
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171 | (1) |
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10.5 Make Up Your Own Mind? |
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172 | (1) |
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10.6 Aaronson's Bayesian Debating |
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173 | (2) |
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10.7 Should You Trust A Scientist? |
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175 | (2) |
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10.8 The Argument Of Authority |
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177 | (2) |
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10.9 The Scientific Consensus |
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179 | (1) |
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179 | (2) |
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10.11 The Predictive Power Of Markets |
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181 | (3) |
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184 | (3) |
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Chapter 11 Exponentially Counterintuitive |
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187 | (20) |
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187 | (2) |
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11.2 The Glass Ceiling Of Computation |
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189 | (2) |
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11.3 Exponential Explosion |
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191 | (2) |
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11.4 The Magic Of Arabic Numerals |
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193 | (2) |
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195 | (1) |
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196 | (2) |
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198 | (1) |
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11.8 Bayes Wins A Godel Prize |
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199 | (2) |
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201 | (2) |
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203 | (4) |
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Chapter 12 Ockham Cuts To The Chase |
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207 | (18) |
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207 | (2) |
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12.2 In Football, You Never Know |
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209 | (1) |
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12.3 The Curse Of Overfitting |
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210 | (3) |
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12.4 The Complex Quest Of Simplicity |
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213 | (2) |
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215 | (1) |
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216 | (2) |
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12.7 Tibschirani's Regularization |
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218 | (1) |
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219 | (1) |
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12.9 Bayes To The Rescue Of Overfitting* |
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220 | (2) |
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12.10 Only Bayesian Inferences Are Admissible* |
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222 | (1) |
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12.11 Ockham's Razor As A Bayesian Theorem! |
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223 | (2) |
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Chapter 13 Facts Are Misleading |
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225 | (24) |
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225 | (2) |
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13.2 Correlation Is Not Causality |
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227 | (3) |
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13.3 Let's Search For Confounding Variables! |
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230 | (1) |
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13.4 Regression To The Mean |
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231 | (1) |
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232 | (2) |
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13.6 The Failure Of Endogenous Stratification |
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234 | (2) |
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236 | (2) |
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13.8 Caveats About Randomized Controlled Trials |
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238 | (1) |
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13.9 The Return Of The Scottish Black Sheep |
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239 | (1) |
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240 | (3) |
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243 | (6) |
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SECTION III Pragmatic Bayesianism |
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Chapter 14 Quick And Not Too Dirty |
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249 | (20) |
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14.1 The Mystery Of Primes |
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249 | (2) |
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14.2 The Prime Number Theorem |
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251 | (1) |
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252 | (1) |
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253 | (1) |
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14.5 The Constraints Of Pragmatism |
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254 | (1) |
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14.6 Turing's Learning Machines |
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255 | (3) |
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14.7 Pragmatic Bayesianism |
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258 | (1) |
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14.8 Sublinear Algorithms |
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259 | (3) |
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14.9 Different Thinking Modes |
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262 | (1) |
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14.10 Become Post-Rigorous! |
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263 | (1) |
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14.11 Bayesian Approximations |
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264 | (5) |
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269 | (22) |
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15.1 Fivethirtyeight And The 2016 Us Election |
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269 | (1) |
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15.2 Is Quantum Mechanics Probabilistic? |
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270 | (3) |
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273 | (1) |
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15.4 Unpredictable Deterministic Automata |
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274 | (2) |
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276 | (1) |
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277 | (2) |
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15.7 Shannon's Optimal Compression |
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279 | (1) |
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15.8 Shannon's Redundancy |
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280 | (1) |
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15.9 The Kullback-Leibler Divergence |
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281 | (1) |
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15.10 Proper Scoring Rules |
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282 | (2) |
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15.11 Wasserstein's Metric |
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284 | (1) |
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15.12 Generative Adversarial Networks (Gans) |
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285 | (6) |
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Chapter 16 Down Memory Lane |
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291 | (20) |
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291 | (1) |
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292 | (1) |
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293 | (1) |
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16.4 Efficient Big Data Processing |
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294 | (2) |
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296 | (2) |
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16.6 Our Brains Faced With Big Data |
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298 | (1) |
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16.7 Removing Traumatic Souvenirs |
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299 | (1) |
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300 | (3) |
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16.9 Bayes To The Rescue Of Memory |
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303 | (1) |
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16.10 Shorter And Longer-Term Memories |
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304 | (1) |
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16.11 Recurrent Neural Networks |
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305 | (2) |
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16.12 Attention Mechanisms |
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307 | (1) |
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16.13 What Should Be Taught And Learned? |
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308 | (3) |
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Chapter 17 Let's Sleep On It |
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311 | (24) |
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17.1 Where Do Ideas Come From? |
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311 | (1) |
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17.2 Creative Art By Artificial Intelligences |
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312 | (2) |
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17.3 Latent Dirichlet Allocation (Lda) |
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314 | (1) |
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17.4 The Chinese Restaurant |
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315 | (1) |
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17.5 Monte Carlo Simulations |
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316 | (2) |
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17.6 Stochastic Gradient Descent (Sgd) |
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318 | (1) |
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17.7 Pseudo-Random Numbers |
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319 | (1) |
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320 | (1) |
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17.9 Importance Sampling For Lda |
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321 | (2) |
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323 | (1) |
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17.11 The Boltzmann Machine |
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324 | (2) |
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17.12 Mcmc And Google Pagerank |
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326 | (1) |
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17.13 Metropolis-Hasting Sampling |
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327 | (1) |
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328 | (2) |
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17.15 Mcmc And Cognitive Biases |
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330 | (2) |
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17.16 Constrastive Divergence |
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332 | (3) |
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Chapter 18 The Unreasonable Effectiveness Of Abstraction |
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335 | (20) |
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18.1 Deep Learning Works! |
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335 | (2) |
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337 | (1) |
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18.3 Word Vector Representation |
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338 | (2) |
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18.4 Exponential Expressivity* |
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340 | (1) |
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18.5 The Emergence Of Complexity |
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341 | (2) |
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18.6 The Kolmogorov Sophistication* |
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343 | (1) |
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18.7 Sophistication Is A Solomonoff Map!* |
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344 | (2) |
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18.8 The Bennett Logical Depth |
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346 | (2) |
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18.9 The Depth Of Mathematics |
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348 | (1) |
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18.10 The Concision Of Mathematics |
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349 | (1) |
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18.11 The Modularity Of Mathematics |
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350 | (5) |
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Chapter 19 The Bayesian Brain |
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355 | (20) |
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19.1 The Brain Is Formidable |
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355 | (2) |
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357 | (1) |
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357 | (2) |
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19.4 The Perception Of Motion |
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359 | (1) |
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360 | (2) |
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19.6 The Scandal Of Induction |
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362 | (1) |
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363 | (2) |
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19.8 The Blessing Of Abstraction |
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365 | (1) |
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19.9 The Baby Is A Genius |
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366 | (1) |
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367 | (1) |
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368 | (2) |
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370 | (1) |
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19.13 Nature Versus Nurture |
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371 | (4) |
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SECTION IV Beyond Bayesianism |
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Chapter 20 It's All Fiction |
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375 | (18) |
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375 | (1) |
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376 | (1) |
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377 | (1) |
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378 | (4) |
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20.5 Is Teleology A Scientific Dead End? |
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382 | (3) |
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20.6 The Church-Turing Thesis Versus Reality |
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385 | (2) |
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20.7 Is (Instrumental) Antirealism Useful? |
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387 | (1) |
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20.8 Is There A World Outside Our Brain? |
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388 | (1) |
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20.9 A Cat In A Binary Code? |
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389 | (2) |
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20.10 Solomonoff Demon's Antirealism |
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391 | (2) |
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Chapter 21 Exploring The Origins Of Beliefs |
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393 | (20) |
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21.1 The Scandal Of Divergent Series |
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393 | (2) |
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21.2 But This Is False, Right? |
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395 | (1) |
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396 | (2) |
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398 | (1) |
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21.5 Are We All Potential Monsters? |
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399 | (2) |
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21.6 Stories Over Statistics |
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401 | (2) |
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403 | (1) |
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21.8 The Darwinian Evolution Of Ideologies |
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404 | (3) |
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21.9 Believing Superstitions Can Be Useful |
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407 | (1) |
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21.10 The Magic Of Youtube |
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408 | (2) |
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21.11 The Journey Goes On |
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410 | (3) |
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Chapter 22 Beyond Bayesianism |
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413 | (22) |
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22.1 The Bayesian Has No Moral |
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413 | (1) |
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414 | (2) |
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22.3 Unaware Of Our Morals |
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416 | (3) |
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419 | (2) |
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22.5 The Moral Of The Majority |
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421 | (1) |
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422 | (3) |
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22.7 Should Knowledge Be A Goal? |
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425 | (2) |
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427 | (2) |
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22.9 Bayesian Consequentialism |
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429 | (3) |
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432 | (3) |
Index |
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435 | |