Preface | p. viii |
Symbols and notational conventions | p. ix |
Logic for linguists | p. 1 |
Set theory | p. 3 |
Sets and elements | p. 3 |
Relations between sets | p. 5 |
Operations on sets | p. 6 |
Relations and functions | p. 9 |
Inference and logical analysis of sentences | p. 15 |
Inference | p. 15 |
Logical form | p. 18 |
Sentences and propositions | p. 20 |
Possible worlds and the truth-set of a proposition | p. 22 |
Analytic and synthetic sentences | p. 23 |
Simple and compound sentences | p. 24 |
The depth of the logical analysis | p. 25 |
Propositional logic | p. 26 |
Connectives | p. 26 |
The meaning of the logical connectives | p. 30 |
Negation | p. 30 |
Conjunction | p. 32 |
Disjunction | p. 34 |
Implication | p. 37 |
Equivalence | p. 40 |
How to indicate constituent structure | p. 42 |
The syntax and semantics of propositional calculus | p. 44 |
Syntax | p. 45 |
Semantics | p. 47 |
Tautologies and contradictions | p. 50 |
Truth tables | p. 50 |
Predicate logic | p. 58 |
Extending the logical analysis | p. 58 |
Quantifiers | p. 61 |
Summary of the syntax of predicate logic | p. 71 |
The semantics of predicate logic | p. 72 |
True in all interpretations | p. 77 |
Summary of the semantics of predicate logic | p. 83 |
A formal version of the semantics | p. 84 |
Formal properties of relations | p. 88 |
Reflexivity | p. 88 |
Symmetry | p. 89 |
Transitivity | p. 89 |
Converse | p. 90 |
Structure of the domain and co-domain of relations | p. 90 |
Deduction | p. 96 |
The deductive system | p. 96 |
Deduction rules in everyday conversation | p. 104 |
Modal logic | p. 108 |
Modal operators | p. 108 |
Strict implication | p. 110 |
Other modalities | p. 111 |
Problems connected with scope and identity in modal logic | p. 114 |
'De dicto'--'de re' ambiguities | p. 114 |
Specificity | p. 116 |
Opacity | p. 117 |
Cross-world identification | p. 119 |
Counterfactual sentences | p. 120 |
Tense logic and reference points | p. 121 |
Intensional logic and categorial grammar | p. 125 |
Intensions and extensions | p. 125 |
Intension | p. 127 |
The Fregean principle | p. 130 |
The Fregean principle and categorial grammar | p. 132 |
Categories, intensions and types | p. 136 |
Further extensions | p. 148 |
Second-order predicate logic and predicate operators | p. 148 |
Presuppositions and definite descriptions | p. 149 |
Pragmatic analysis of presuppositions | p. 153 |
The abstraction- or lambda-operator | p. 155 |
Logic for linguists? | p. 158 |
General | p. 158 |
The concept of meaning | p. 158 |
The role of formal languages in analysing natural language | p. 164 |
The limitations of classical logic | p. 168 |
References | p. 172 |
Answers to exercises | p. 175 |
Index | p. 181 |
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