If A, Then B: How Logic Shaped the World

Table of Contents......Page 8
Preface......Page 12
Introduction: What Is Logic?......Page 18
The Strange Nature of Logical Validity......Page 19
What Makes a Valid Argument Valid?......Page 23
The Divine-Command Theory of Logic......Page 26
Logic as Culturally Invariant......Page 28
Logic as Timeless and Placeless......Page 31
The Social History of Logic......Page 33
1. The Dawn of Logic......Page 36
The Effect of Geography on the Flow of Ideas......Page 37
The Effect of the Sea Trade......Page 38
Transportation and Civilization......Page 41
Classical Greece as the Extreme Case......Page 43
The Athenian Assembly......Page 45
2. Aristotle: Greatest of the Greek Logicians......Page 50
The Study of Argument in India......Page 52
The Singularity of Aristotle......Page 55
The Effect of the Athenian Assembly......Page 57
The Sophists......Page 59
The Separation of Logic from Rhetoric......Page 62
3. Aristotle\'s System: The Logic of Classification......Page 66
Manipulating Classes......Page 67
The Square of Opposition......Page 71
The Underlying Mystery of the Square......Page 75
Wittgenstein\'s Proposed Solution......Page 82
Wittgenstein\'s Mistake......Page 83
4. Chrysippus and the Stoics: A World of Interlocking Structures......Page 90
The Stoics......Page 91
The Logic of Choice......Page 95
The Nature of Compound Propositions......Page 100
Interlocking Forms of Argument......Page 103
The Laws of Contradiction and Excluded Middle......Page 105
More Interlocking Forms......Page 108
The Basis of Computer Logic......Page 111
5. Logic Versus Anti-Logic: The Laws of Contradiction and Excluded Middle......Page 116
Paradoxes of Truth......Page 117
The Nature of Fuzzy Logic......Page 130
Is Validity Relative?......Page 133
Does Formal Logic Ultimately Depend on Common Sense?......Page 135
6. Logical Fanatics, Circular Reasoning, and Descartes\'s Fundamental Principle......Page 140
The Origins of the Wars of Religion......Page 142
The Importance of Firm Foundations......Page 146
The Logical Complexity of Our Premises......Page 150
The Origins of Formalized Logic and Mathematics......Page 155
The Paradoxes of Formalization......Page 158
The Double Meaning of \"Foundations\"......Page 161
The Outlook of Thomas Kuhn......Page 163
Kuhn\'s Error......Page 165
Competition Between Scientific Theories......Page 167
7. Will the Future Resemble the Past?: Inductive Logic and Scientific Method......Page 174
The Challenge of the New Literature......Page 175
The Triumph of the Vernacular and the Growing Spirit of Equality......Page 177
The Rise of Modern Political Theory......Page 180
The Right of Dissent and the Reliance on Induction......Page 181
Induction as the New Rationality......Page 184
Aristotle\'s Influence on the Medievals......Page 186
The Rational Foundations of Induction......Page 191
The Apparent Irreducibility of Induction......Page 195
The Assumptions of Empirical Science......Page 197
8. Rhetorical Frauds and Sophistical Ploys: Ten Classic Tricks......Page 202
The Battle for Parliamentary Reform......Page 203
Jeremy Bentham and the Legacy of the Enlightenment......Page 206
Bentham\'s Book of Fallacies......Page 208
9. Symbolic Logic and the Digital Future......Page 222
The Impact of the Industrial Revolution......Page 223
The Origins of Symbolic Logic......Page 227
The Logic of Relations......Page 233
The Effect of the New Mathematics......Page 236
The Impact of Quantification......Page 241
Frege\'s New Foundation for Mathematics......Page 244
The Invention of Digital Computing......Page 246
10. Faith and the Limits of Logic: The Last Unanswered Question......Page 252
Abelard\'s Rise to Power......Page 253
Abelard\'s Attack on Faith Without Reason......Page 257
Are Faith and Reason Compatible?......Page 259
The Foundations of Rational Belief......Page 261
Rationality After the Wars of Religion......Page 263
The Vigilance of Reason......Page 265
Appendix: Further Fallacies......Page 268
Notes......Page 290
Bibliography......Page 338
Index......Page 344