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LOGIC MADE EASY How to Know When Language Deceives You DEBORA H J.BENNET T W • W • NORTON & COMPANY I

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INTRODUCTION: LOGIC IS RARE I 1 The mistakes we make l 3 Logic should be everywhere 1 8 How history can help 19 1 PROOF 29 Consistency is all I ask 29 Proof by contradiction 33 Disproof ... 3 6 I ALL 40 All S are P 42 Vice Versa 42 Familiarity—help or hindrance? 41 Clarity or brevity? 50 7 8 CONTENTS 3 A NOT TANGLES EVERYTHING UP 53 The trouble with not 54 Scope of the negative 5 8 A and E propositions s 9 When no means yes—the "negative pregnant" and double negative 61 k SOME Is PART OR ALL OF ALL 64 Some is existential 6 s Some are; some are not 68 A, E, I, andO JO 5 SYLLOGISMS 73 Sorites, or heap 8s Atmosphere of the "sillygism" 8 8 Knowledge interferes with logic 89 Truth interferes with logic 90 Terminology made simple 91 6 WHEN THINGS ARE IFFY 96 The converse of the conditional 10 8 Causation 11 2 The contrapositive conditional US 7 SYLLOGISMS INVOLVING IF, AND, AND OR 118 Disjunction, an "or" statement 119 Conjunction, an "and" statement 121 Hypothetical syllogisms 124 CONTENTS 9 Common fallacies 130 Diagramming conditional syllogisms 134 8 SERIES SYLLOGISMS 137 9 SYMBOLS THAT EXPRESS OUR THOUGHTS 145 Leibniz's dream comes true: Boolean logic 15 J 10 LOGIC MACHINES AND TRUTH TABLES 160 Reasoning machines 160 Truth tables 16 s True, false, and maybe 1 68 11 FUZZY LOGIC, FALLACIES, AND PARADOXES 173 Shaggy logic 1J3 Fallacies 177 Paradoxes 1 8 J M COMMON LOGIC AND LANGUAGE 192 13 THINKING WELL—TOGETHER 202 Theories of reasoning 210 NOTES 219 REFERENCES 233 ACKNOWLEDGMENTS 243 INDEX 24s [Show More]

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