Logic for Lawyers

1 Dare to think 9
1.1 The argument 9
1.2 Why should lawyers learn logic? 10
1.3 How to read this book 12
1.4 How to learn logic 13

PART I – INTRODUCTION TO LOGIC FOR LAWYERS 15
2 Pro-et-contra surveys 17
2.1 Bulls**t 17
2.2 Pro-et-contra surveys 18
2.3 How does a pro-et-contra survey work? 18
2.4 Assessment 23
2.5 Clarity and vagueness 25

3 The syllogism 27
3.1 Introduction 27
3.2 Syllogisms 27
3.3 Formal and material truth 30
3.4 The syllogism and the law 31
3.5 Syllogisms and fallacies 37
3.6 Conclusion 38

4 Fallacies 39
4.1 Introduction 39
4.2 Non sequitur (incorrect deduction) 40
4.3 Secundum quid (induction or hasty generalisation) 41
4.4 Post hoc ergo propter hoc 43
4.5 Affirming the consequent (abduction) 44
4.6 Analogy 45
4.7 A contrario 47
4.8 Argumentum e silentio 48
4.9 Hidden premise 48
4.10 Slippery slope 49
4.11 Argumentum ad absurdum 50
4.12 Excluded middle (false dilemma) 50
4.13 Petitio principii (circular reasoning) 51
4.14 Amphiboly 51
4.15 Argumenta ad ‘X’ 52
4.16 Conclusion 55

5 A formal language 57
5.1 Lawyers and language 57
5.2 Syntax, semantics and pragmatics 57
5.3 Truth 59
5.4 Consistency 60
5.5 Validity (and deducibility) 60
5.6 Logical strictness 61

6 Propositional logic 63
6.1 Connectives 63
6.1.1 Conjunction 63
6.1.2 Negation 65
6.1.3 Disjunction 66
6.1.4 Implication 69
6.1.5 Equivalence 73
6.2 More complex formulas 75
6.3 Exhaustiveness 78
6.4 Truth values 79
6.5 Translation and interpretation 82

7 Testing consistency and validity – The tableau method 85
7.1 Introduction 85
7.2 From truth tables to tableaux 85
7.2.1 Conjunction 86
7.2.2 Disjunction 87
7.2.3 Implication 87
7.2.4 Equivalence 88
7.2.5 Negation and composite formulas 88
7.3 More complex formulas 90
7.4 Testing consistency 91
7.4.1 Linking tableaux and closing branches 92
7.4.2 How to read tableaux 93
7.4.3 Astute construction 93
7.4.4 Hidden inconsistencies 95
7.5 Testing validity 95
7.6 Remarks on validity 97
7.6.1 Ex falso sequitur quodlibet 97
7.6.2 The formal nature of validity 98
7.7 The truth table method 99
7.7.1 Consistency test 100
7.7.2 Validity test 101
7.8 Conclusion – what is a good argumentation? 104

8 Logic and rhetoric 105
8.1 Being versus appearing 105
8.2 Means of persuasion 106
8.3 The enthymeme (logos) 108
8.3.1 Persuasion is a dual activity 108
8.3.2 Example from legal practice 110
8.3.3 The moment 111
8.3.4 Final remark about the enthymeme 112
8.4 The logic of persuasion 112
8.4.1 The speaker’s character (ethos) 112
8.4.2 Emotion as a means of persuasion (pathos) 114
8.5 Rhetoric: conclusion 115
8.6 Part I: conclusion 115

PART II – EXTENSIONS AND ALTERNATIVES 117
9 Modern logic 119

10 Predicate logic 121
10.1 Introduction 121
10.2 Vocabulary: predicates and constants, quantifiers and variables 122
10.2.1 Predicates and constants 122
10.2.2 Quantifiers and variables 122
10.3 The discussion domain: sets 125
10.4 Quantifier properties 126
10.4.1 Qualifiers and negation 126
10.4.2 Quantifiers and connectives 128
10.5 More complex sentences 129
10.5.1 Relational predicates 129
10.5.2 Several quantifiers in one proposition 130
10.5.3 Quantifier scope and variable binding 130
10.6 Consistency testing 131
10.7 Validity testing 136
10.8 Validity and consistency of complex sentences 137
10.9 Identity 140
10.10 Conclusion 143

11 Modal logic 145
11.1 Introduction 145
11.2 The Aristotelian square of opposition 145
11.3 Epistemic logic 146
11.4 Deontological logic 147
11.5 Modal logic 149
11.6 Combining modal operators 150
11.7 Part II: conclusion 151

POSTSCRIPT AND APPENDICES 153
12 Postscript – The value of not knowing 155

Appendix I – Truth tables 157
Appendix II – Rules of inference for the tableau method 159
Appendix III – Stepwise testing of consistency and validity using the tableau
method 161
Appendix IV – Rules of inference in natural deduction: propositional logic 163
Appendix V – Rules of inference in natural deduction: predicate logic 175
Appendix VI – Suggestions for further reading 179

Word of thanks 183
References 185
Index 189