# Book:Irving M. Copi/Symbolic Logic/4th Edition

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## Irving M. Copi:

## Irving M. Copi: *Symbolic Logic*

Published $1973$, **Macmillan**.

### Subject Matter

4th edition of 1954: Irving M. Copi: *Symbolic Logic*

### Contents

- Preface

**$1$ 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 Incompleteness of the Nineteen Rules
- 3.5 The Rule of Conditional Proof
- 3.6 The Rule of Indirect Proof
- 3.7 Proofs of Tautologies
- 3.8 The Strengthened Rule of Conditional Proof
- 3.9 Shorter Truth Table Technique —
*Reductio ad Absurdum*Method

**$4$ Propositional Functions and Quantifiers**- 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 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

**$7$ A Propositional Calculus**- 7.1 Object Language and Metalanguage
- 7.2 Primitive Symbols and Well Formed Formulas
- 7.3 Axioms and Demonstrations
- 7.4 Independence of the Axioms
- 7.5 Development of the Calculus
- 7.6 Deductive Completeness

**$8$ Alternative Systems and Notations**- 8.1 Alternative Systems of Logic
- 8.2 The Hilbert-Ackermann System
- 8.3 The Use of Dots as Brackets
- 8.4 A Parenthesis-Free Notation
- 8.5 The Stroke and Dagger Operators
- 8.6 The Nicod System

**$9$ A First-Order Function Calculus**- 9.1 The New Logistic System $RS_1$
- 9.2 Development of $RS_1$
- 9.3 Duality
- 9.4 $RS_1$ and the 'Natural Deduction' Techniques
- 9.5 Normal Forms
- 9.6 Completeness of $RS_1$
- 9.7 $RS_1$ with Identity

**Appendix A: Normal Forms and Boolean Expansions**

**Appendix B: The Algebra of Classes**

**Appendix C: The Ramified Theory of Types**

**Solutions to Selected Exercises**

**Special Symbols**

**Index**