The Logic Manual

includes index and biblioraphy

1 Sets, Relations, and Arguments 5 1.1 Sets 5 1.2 Binary Relations 7 1.3 Functions 14 1.4 Non-binary Relations 16 1.5 Arguments, Validity, and Contradictions 17 1.6 Syntax, Semantics, and Pragmatics 24 2 Syntax and Semantics of Prepositional Logic 27 2.1 Quotation 27 2.2 The Syntax of the Language of Prepositional Logic 29 2.3 Rules for Dropping Brackets 31 2.4 The Semantics of Prepositional Logic 34 3 Formalization in Prepositional Logic 52 3.1 Truth-Functionality 53 3.2 Logical Form 57 3.3 From Logical Form to Formal Language 62 3.4 Ambiguity 64 3.5 The Standard Connectives 66 3.6 Natural Language and Prepositional Logic 68 4 The Syntax of Predicate Logic 74 4.1 Predicates and Quantification 74 4.2 The Sentences of ¿2 82 4.3 Free and Bound Occurrences of Variables 85 4.4 Notational Conventions 87 4.5 Formalization 88 5 The Semantics of Predicate Logic 94 5.1 Structures 95 5.2 Truth 100 5.3 Validity, Logical Truths, and Contradictions 108 5.4 Counterexamples no 6 Natural Deduction 116 6.1 Prepositional Logic 118 6.2 Predicate Logic 130 7 Formalization in Predicate Logic 143 7.1 Adequacy 143 7.2 Ambiguity 147 7.3 Extensionality 152 7.4 Predicate Logic and Arguments in English 157 8 Identity and Definite Descriptions 166 8.1 Qualitative and Numerical Identity 166 8.2 The Syntax of ¿= 167 8.3 The Semantics of ¿= 168 8.4 Proof Rules for Identity 171 8.5 Uses of Identity 174 8.6 Identity as a Logical Constant 183