America has become a society devoid of understanding of the power of logic and numbers. All too often, we rely on our intuition or on empty statistics to formulate opinions about ourselves and our world. As a result of inadequate schooling in the art of reasoning, we have become a people unable to make truly logical decisions, intimidated by numbers, and too passive to reverse this disturbing trend. The Power of Logical Thinking addresses these concerns, illustrating how you can reason better, how numbers are used against you, and how your vote may be affected. Marilyn vos Savant writes, "We can't trust out intuitions, our statisticians, or our politicians. The 1992 presidential campaign is a case in point. Numbers were used, abused, and misused by the candidates as never before in the history of our country. Voters were easily manipulated, setting a precedent for years to come. Will it happen again? Or will we be more prepared for future elections?" Part One of The Power of Logical Thinking explains the most provocative of the counterintuitive problems that Marilyn vos Savant has encountered in recent years, such as the now classic "Monty Hall Dilemma," the improbability of winning the lottery, and much more. Part Two shows how statistics have quietly become a tool of persuasion instead of education. In addition to exploring puzzles and paradoxes, these sections explains the underlying reasoning to help you answer questions such as which surgery should you choose? what are your odds of having breast cancer? do drug-testing and AIDS-testing give you yes/no answers? In Part Three, vos Savant illustrates how our votes are affected, with examples of selective logic, specious reasoning, and outright sophistry collected from the campaigns of Bill Clinton, George Bush, and Ross Perot.
| Acknowledgments | ||
| Introduction | ||
| 1 | Lessons Set in Everyday Life | 3 |
| The Monty Hall Dilemma | 5 | |
| The Psychological Component | 16 | |
| Probability Problems | 17 | |
| Logic Loops | 29 | |
| Average Traps | 32 | |
| 2 | Lessons Set in Dollars | 38 |
| Economic Illiteracy | 39 | |
| Choosing a Raise | 40 | |
| Renting a Room | 43 | |
| Dysfunctional Dollars | 46 | |
| The Lottery | 47 | |
| An Impossible Average Classroom | 56 | |
| A True Paradox | 58 | |
| 3 | Misunderstanding Statistics | 63 |
| Normal Distributions | 64 | |
| Mean, Median, and Mode | 65 | |
| Numb Numbers | 70 | |
| Facts About Fallacies | 75 | |
| Fallacies about Facts | 84 | |
| 4 | Why We Lead Ourselves Down the Garden Path | 91 |
| Subjective Math and Logic | 92 | |
| About the Appendix | 95 | |
| 5 | How Even Our Health Is Affected | 96 |
| Drug Testing and AIDS Testing | 97 | |
| Screening for Breast Cancer | 103 | |
| Questions We Should Ask | 106 | |
| 6 | The Election of 1992 (The Advent of the "Reign of Error") | 113 |
| The Worst Economic Record in Fifty Years? | 116 | |
| The Tax Cut in Arkansas? | 121 | |
| Helping the Rich at the Expense of the Poor? | 122 | |
| The Top One Percent Got 60 Percent of the Growth? | 127 | |
| Save Social Security with a Cutoff in Benefits? | 133 | |
| The Declining Job Base? | 135 | |
| There's Something Wrong With Our Tax Code? | 137 | |
| Put Everything on Hold Until the Deficit is Slain? | 140 | |
| Raising Taxes on Only the Rich is a Fraudulent Claim? | 143 | |
| The Deficit Will be Cut in Half? | 144 | |
| Arkansas Led the Nation? | 146 | |
| A Plan to Create Eight Million New Jobs? | 147 | |
| Government Mandates Don't Cost Money? | 149 | |
| George Bush Was a Hypocrite? | 150 | |
| Capping Is the Same as Slicing? | 152 | |
| Everyone Should Earn More than Average? | 153 | |
| A Tax Break for Millionaires? | 155 | |
| Job-Seekers Should Move to Arkansas? | 157 | |
| Bush Refused to Increase Taxes? | 159 | |
| Our Wages Have Dropped From First to 13th? | 160 | |
| Forty Million Americans Don't Have Health Insurance? | 161 | |
| The First Decline in Industrial Production Ever? | 162 | |
| We're Working Harder for Less Money? | 164 | |
| Sources | 168 | |
| Appendix: The Monty Hall Dilemma | 169 | |
| Index | 197 | |
| About the Author | 204 |
Overview
America has become a society devoid of understanding of the power of logic and numbers. All too often, we rely on our intuition or on empty statistics to formulate opinions about ourselves and our world. As a result of inadequate schooling in the art of reasoning, we have become a people unable to make truly logical decisions, intimidated by numbers, and too passive to reverse this disturbing trend. The Power of Logical Thinking addresses these concerns, illustrating how you can reason better, how numbers are ...