Book:Irving M. Copi/Symbolic Logic/Fifth Edition

Subject Matter

 * Symbolic Logic

Contents

 * 1 Introduction: Logic and Language
 * 1.1 What Is Logic?
 * 1.2 The Nature of Argument
 * 1.3 Truth and Validity
 * 1.4 Symbolic Logic


 * 2 Arguments Containing Compound Statements
 * 2.1 Simple and Compound Statements
 * 2.2 Conditional Statements
 * 2.3 Argument Forms and Truth Tables
 * 2.4 Statement Forms


 * 3 The Method of Deduction
 * 3.1 Formal Proof of Validity
 * 3.2 The Rule of Replacement
 * 3.3 Proving Invalidity
 * 3.4 The Rule of Conditional Proof
 * 3.5 The Rule of Indirect Proof
 * 3.6 Proofs of Tautologies
 * 3.7 The Strengthened Rule of Conditional Proof
 * 3.8 Shorter Truth Table Technique&mdash;Reductio ad Absurdum Method


 * 4 Quantification Theory
 * 4.1 Singular Propositions and General Propositions
 * 4.2 Proving Validity: Preliminary Quantification Rules
 * 4.3 Proving Invalidity
 * 4.4 Multiply-General Propositions
 * 4.5 Quantification Rules
 * 4.6 More on Proving Invalidity
 * 4.7 Logical Truths Involving Quantifiers


 * 5 The Logic of Relations
 * 5.1 Symbolizing Relations
 * 5.2 Arguments Involving Relations
 * 5.3 Some Attributes of Relations
 * 5.4 Identity and the Definite Description
 * 5.5 Predicate Variables and Attributes of Attributes


 * 6 Deductive Systems
 * 6.1 Definition and Deduction
 * 6.2 Euclidean Geometry
 * 6.3 Formal Deductive Systems
 * 6.4 Attributes of Formal Deductive Systems
 * 6.5 Logistic Systems


 * 7 Set Theory
 * 7.1 The Algebra of Classes
 * 7.2 Axioms for Class Algebra
 * 7.3 Zermelo-Fraenkel Set Theory ($\mathbf{ZF}$)&mdash;The First Six Axioms
 * 7.4 Relations and Functions
 * 7.5 Natural Numbers and the Axiom of Infinity
 * 7.6 Cardinal Numbers and the Choice Axiom
 * 7.7 Ordinal Numbers and the Axioms of Replacement and Regularity


 * 8 A Propositional Calculus
 * 8.1 Object Language and Metalanguage
 * 8.2 Primitive Symbols and Well Formed Formulas
 * 8.3 Axioms and Demonstrations
 * 8.4 Independence of the Axioms
 * 8.5 Development of the Calculus
 * 8.6 Deductive Completeness


 * 9 Alternative Systems and Notations
 * 9.1 Alternative Systems of Logic
 * 9.2 The Hilbert-Ackermann System
 * 9.3 The Use of Dots as Brackets
 * 9.4 A Parenthesis-Free Notation
 * 9.5 The Stroke and Dagger Operators
 * 9.6 The Nicod System


 * 10 A First-Order Function Calculus
 * 10.1 The New Logistic System $\mathrm{RS}_1$
 * 10.2 The Development of $\mathrm{RS}_1$
 * 10.3 Duality
 * 10.4 $\mathrm{RS}_1$ and the 'Natural Deduction' Techniques
 * 10.5 Normal Forms
 * 10.6 Completeness of $\mathrm{RS}_1$
 * 10.7 $\mathrm{RS}_1$ with Identity
 * 10.8 First-Order Logic Including $\mathbf{ZF}$ Set Theory


 * Appendix A: Incompleteness of the Nineteen Rules
 * Appendix B: Normal Forms and Boolean Expansions
 * Appendix C: The Ramified Theory of Types
 * Solutions to Selected Exercises
 * Special Symbols
 * Index