1. Symbolizing Sentences
1.1 Sentences
1.2 Sentential Connectives
1.3 The Form of Molecular Sentences
1.4 Symbolizing Sentences
1.5 The Sentential Connectives and Their Symbols--Or; Not; If . . . then . . .
1.6 Grouping and Parentheses. The Negation of a Molecular Sentence
1.7 Elimination of Some Parentheses
1.8 Summary
2. Logical Inference
2.1 Introduction
2.2 Rules of Inference and Proof
Modus Ponendo Ponens
Proofs
Two-Step Proofs
Double Negation
Modus Tollendo Tollens
More on Negation
Adjunction and Simplification
Disjunctions as Premises
Modus Tollendo Ponens
2.3 Sentential Derivation
2.4 More About Parentheses
2.5 Further Rules of Inference
Law of Addition
Law of Hypothetica Syllogism
Law of Disjunctive Syllogism
Law of Disjunctive Simplification
Commutative Laws
De Morgan's Laws
2.6 Biconditional Sentences
2.7 Summary of Rules of Inference. Table of Rules of Inference
3. Truth and Validity
3.1 Introduction
3.2 Truth Value and Truth-Functional Connectives
Conjunction
Negation
Disjunction
Conditional Sentences
Equivalence: Biconditional Sentences
3.3 Diagrams of Truth Value
3.4 Invalid Conclusions
3.5 Conditional Proof
3.6 Consistency
3.7 Indirect Proof
3.8Summary
4. Truth Tables
4.1 Truth Tables
4.2 Tautologies
4.3 Tautological Implication and Tautological Equivalence
4.4 Summary
5. Terms, Predicates, and Universal Quantifiers
5.1 Introduction
5.2 Terms
5.3 Predicates
5.4 Common Nouns as Predicates
5.5 Atomic Formulas and Variables
5.6 Universal Quantifiers
5.7 Two Standard Forms
6. Universal Specification and Laws of Identity
6.1 One Quantifier
6.2 Two or More Quantifiers
6.3 Logic of Identity
6.4 Truths of Logic
7. A Simple Mathematical System: Axioms for Addition
7.1 Commutative Axiom
7.2 Associative Axiom
7.3 Axiom for Zero
7.4 Axiom for Negative Numbers
8. Universal Generalization
8.1 Theorems with Variables
8.2 Theorems with Universal Quantifiers
Index
First Course in Mathematical Logic
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