Preface to Revised Second Edition xiii

Preface to Second Edition xiv

Preface to Revised Edition xv

Acknowledgments xvi

Introduction to Teacher 1

1 A Brief Introduction to Key Terms 5

1.1 Arguments 5

1.1.1 What is a Statement? 6

1.1.2 Premises and Conclusion 6

1.2 Putting Arguments into a Standard Format 7

1.3 Multiple Conclusions 9

1.4 Deductive Validity 10

1.5 Soundness 13

1.6 Missing Premises and Conclusions 13

2 Argument Forms and Propositional Logic 17

2.1 Formal Validity 17

2.2 Quotation Marks 19

2.3 Metalinguistic Variables 21

2.4 Non-formal Validity 23

2.5 The Need for Propositional Logic 24

2.5.1 Symbolic Notation 25

2.6 The Type/Token Distinction 26

3 Conjunction 31

3.1 Logical Conjunction 31

3.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction 33

3.3 Phrasal Logical Conjunctions 34

3.4 Series Decompounding 34

3.5 Using 'Respectively' 35

3.6 Symbolizing Logical Conjunctions 35

4 Negation 42

4.1 Logical Negation 42

4.2 Some Other Negative Expressions 43

4.3 A Point about Methodology 45

4.4 A Point on Ambiguity 45

4.5 Symbolizing Logical Negations 45

4.6 Ambiguity and the Need for Groupers 46

4.7 Review of Symbols 47

4.8 Using 'Without' 48

4.9 Argument Forms Continued 48

4.10 Symbolizing Logical Negations Continued 51

5 Truth Tables 56

5.1 Well-formed Formulas 56

5.2 Scope 57

5.3 Main Connective 58

5.4 Truth Tables 59

5.4.1 Truth Table Analyses of Statements 61

5.4.2 Truth Table Analyses of Arguments 64

6 Disjunction 68

6.1 Logical Disjunction 68

6.2 Disjunction and Negation 69

6.3 Iterations and Groupers 71

6.4 Inclusive versus Exclusive 'Or' 73

6.5 Symbolizing Logical Disjunctions Continued 76

7 Conditionals 79

7.1 Conditionals with Constituent Statements 79

7.2 Conditionals without Constituent Statements 80

7.3 Logical Conditionals 80

7.4 Symbolizing Conditionals in PL 82

7.5 Necessary and Sufficient Conditions 82

7.6 Only If 84

7.7 Unless 86

7.8 Since, Because 88

7.9 Conditionals and Groupers 89


7.10 If and Only If 90

7.11 A Revised Grammar for Well-formedness in PL 91

7.12 Summarizing Truth Tables 99

7.12.1 Validity 99

7.12.2 Contradiction, Tautology, Contingency 102

7.12.3 Consistency 104

7.12.4 Logical Equivalence 105

8 Truth Trees 109

8.1 Reviewing Validity 109

8.2 Tree Trunks and Compound and Atomic Statements 110

8.3 Truth Tree Rules 111

8.3.1 Non-branching Rules 111

8.3.2 Branching Rules 112

8.4 Strategies 114

8.5 Truth Trees and Invalidity 117


8.6 Propositional Logic and Counter-examples (Counter-models) 121

8.7 Logical Properties and Relations Revisited 123

8.7.1 Consistency 123

8.7.2 Contradiction, Tautology, Contingency 124

8.7.3 Logical Equivalence 126

9 Property Predicate Logic 129

9.1 Limits of Propositional Logic 129

9.2 Singular Terms 130

9.3 Property Predicates 132

9.4 Quantifiers 134

9.4.1 Simple Existential Quantifier Statements 135

9.4.