CONTENTS
Preface = ⅷ
Symbols and notational conventions = ⅸ
1. Logic for linguists = 1
2. Set theory = 3
2.1 Sets and elements = 3
2.2 Relations between sets = 5
2.3 Operations on sets = 6
2.4 Relations and functions = 9
3. Inference and logical analysis of sentences = 15
3.1 Inference = 15
3.2 Logical form = 18
3.3 Sentences and propositions = 20
3.4 Possible worlds and the truth-set of a proposition = 22
3.5 Analytic and synthetic sentences = 23
3.6 Simple and compound sentences = 24
3.7 The depth of the logical analysis = 25
4. Prepositional logic = 26
4.1 Connectives = 26
4.2 The meaning of the logical connectives = 30
4.2.1 Negation = 30
4.2.2 Conjunction = 32
4.2.3 Disjunction = 34
4.2.4 Implication = 37
4.2.5 Equivalence = 40
4.3 How to indicate constituent structure = 42
4.4 The syntax and semantics of prepositional calculus = 44
4.5 Syntax = 45
4.6 Semantics = 47
4.7 Tautologies and contradictions = 50
4.8 Truth tables = 50
5. Predicate logic = 58
5.1 Extending the logical analysis = 58
5.2 Quantifiers = 61
5.3 Summary of the syntax of predicate logic = 71
5.4 The semantics of predicate logic = 72
5.5 True in all interpretations = 77
5.6 Summary of the semantics of predicate logic = 83
5.7 A formal version of the semantics = 84
5.8 Formal properties of relations = 88
5.8.1 Reflexivity = 88
5.8.2 Symmetry = 89
5.8.3 Transitivity = 89
5.8.4 Converse = 90
5.8.5 Structure of the domain and co-domain of relations = 90
6. Deduction = 96
6.1 The deductive system = 96
6.2 Deduction rules in everyday conversation = 104
7. Modal logic = 108
7.1 Modal operators = 108
7.2 Strict implication = 110
7.3 Other modalities = 111
7.4 Problems connected with scope and identity in modal logic = 114
7.4.1 'De dicto'-'de re' ambiguities = 114
7.4.2 Specificity = 116
7.4.3 Opacity = 117
7.4.4 Cross-world identification = 119
7.5 Counter factual sentences = 120
7.6 Tense logic and reference points = 121
8. Intensional logic and categorial grammar = 125
8.1 Intensions and extensions = 125
8.2 Intension = 127
8.3 The Fregean principle = 130
8.4 The Fregean principle and categorial grammar = 132
8.5 Categories, intensions and types = 136
9. Further extensions = 148
9.1 Second-order predicate logic and predicate operators = 148
9.2 Presuppositions and definite descriptions = 149
9.3 Pragmatic analysis of presuppositions = 153
9.4 The abstraction- or lambda-operator = 155
10. Logic for linguists? = 158
10.1 General = 158
10.2 The concept of meaning = 158
10.3 The role of formal languages in analysing natural language = 164
10.4 The limitations of classical logic = 168
References = 172
Answers to exercises = 175
Index = 181
