# Book:Irving M. Copi/Symbolic Logic/5th Edition

## Irving M. Copi: Symbolic Logic

Published $1979$, Prentice Hall

ISBN 0-02324-980-3.

### Subject Matter

5th edition of 1954: Irving M. Copi: 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—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 ($\mathbf{ZF}$)—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