Preface xi

What Is Logic? 1

Chapter One 3

1.1 Introducing Formal Logic 4

1.2 Constants and Relations 7

1.3 Quantifiers and Variables 9

1.4 Introducing Informal Logic 11

1.5 Conclusions 13

1.6 Dialects of Logic 15

Chapter Two 18

2.1 Formal Inference 19

2.2 Informal Inference 21

2.3 Diagramming Arguments 25

2.4 Saying No 32

2.5 Metalogic 35

Chapter Three 37

3.1 Basic Sentential 37

3.2 Truth Tables 43

3.3 English to Sentential 50

3.4 Negating Statements 56

3.5 Rebutting Premises 59

3.6 Computer Logic 65

Chapter Four 69

4.1 Validity 69

4.2 The Logic of English 73

4.3 Negating Conditionals 76

4.4 Rebutting Inferences 80

4.5 The Logic of Sets 87

Chapter Five 94

5.1 Well-formed Formulas 94

5.2 The Shortcut Method 101

5.3 Local and Global 108

5.4 More on Trees 111

5.5 Rebutting Everything 115

5.6 Polish Logic 122

Chapter Six 129

6.1 Predicate 130

6.2 English to Predicate 139

6.3 Reading Between the Lines 145

6.4 Multi-valued Logic 153


Chapter Seven 162

7.1 Universes 162

7.2 Syllogisms 167

7.3 Validity 172

7.4 Diagramming Your Argument 176

7.5 Inductive Logic 187

Chapter Eight 192

8.1 Predicate Wffs 192

8.2 Outlining Your Argument 196

8.3 The Logic of Chance 205

Chapter Nine 213

9.1 Simple Deduction 213

9.2 Simple Strategy 221

9.3 Writing Your Argument 227

9.4 Basic Modal Logic 234

Chapter Ten 240

10.1 Sentential Deduction 240

10.2 Sentential Strategy 250

10.3 Arguing with Yourself 263

10.4 Sophisticated Modal Logic 279

Chapter Eleven 287

11.1 Predicate Deduction 287

11.2 Predicate Strategy 296

11.3 Why We Argue 306

11.4 Presidential Debating 310

11.5 The Logic of Paradox 315

Chapter Twelve 327

12.1 Deduction with Identity 327

12.2 Deduction, FMTYEWTK 332

12.3 Parliamentary Debating 336

12.4 Cathy, A Decade On 338

12.5 Incomplete Logic 343

What is Logic? 349

Answers to Odd-Numbered Exercises 350

Index 384