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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

3.8 Summary

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

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

3.8 Summary

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

Library of Congress subject headings for this publication: Logic, Symbolic and mathematical