Irving M. CopiUniversity of Hawaii

Carl CohenUniversity of Michigan

withDaniel E. Flage

James Madison University

E S S E N T I A L S of L O G I C

Upper Saddle River, New Jersey 07458

S E C O N D E D I T I O N

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Library of Congress Cataloging-in-Publication DataCopi, Irving M.

Essentials of logic / Irving M. Copi, Carl Cohen.—2nd ed.p. cm.

Includes index.ISBN 0-13-238034-X

1. Logic—Textbooks. I. Cohen, Carl, 1931- II. Title. BC108.C685 2007160—dc22 2006009190

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Preface ixAcknowledgments xi

CHAPTER 1 Basic Logical Concepts 1

1.1 What Logic Is 11.2 Propositions and Sentences 11.3 Arguments, Premises, and Conclusions 31.4 Arguments and Explanations 71.5 Recognizing Arguments 12

A. Premise- and Conclusion-Indicators 12B. Arguments in Context 16C. Premises Not in Declarative Form 16D. Unstated Propositions 18

1.6 Deduction and Validity 241.7 Validity and Truth 251.8 Induction and Probability 291.9 Analyzing Arguments 31

A. Paraphrasing 31B. Diagramming Arguments 32C. Interwoven Arguments 34

1.10 Complex Argumentative Passages 36Essentials of Chapter 1 43

CHAPTER 2 Informal Fallacies 46

2.1 What Is a Fallacy? 462.2 Fallacies of Relevance 48

R1. Argument from Ignorance (argumentum ad ignoratiam) 48R2. Appeal to Illegitimate Authority (argumentum ad verecundiam) 51R3. Argument Against the Person (Personal Attack, argumentum ad hominem) 54R4. Appeal to Emotion (Mob Appeal, argumentum ad populum) 57R5. Appeal to Pity (argumentum ad misericordiam) 58R6. Appeal to Force (argumentum ad baculum) 59R7. Irrelevant Conclusion (ignoratio elenchi; non sequitur) 60

2.3 Fallacies of Presumption 67P1. Complex Question 67

C O N T E N T S

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P2. False Cause (post hoc, ergo propter hoc; non causa pro causa) 68P3. Begging the Question (petitio principii) 70P4. Accident 71P5. Converse Accident (Hasty Generalization) 73P6. Suppressed Evidence 74P7. False Dichotomy 75

2.4 Fallacies of Ambiguity 79A1. Equivocation 79A2. Amphiboly 80A3. Accent 82A4. Composition 83A5. Division 85

Essentials of Chapter 2 97

CHAPTER 3 Categorical Propositions 100

3.1 Categorical Logic 1003.2 Categorical Propositions and Classes 1013.3 Symbolism and Venn Diagrams for Categorical Propositions 1063.4 Distribution 1103.5 Existential Import 1133.6 The Aristotelian Square of Opposition and Immediate Inferences 115

A. Contradictories 116B. Contraries 116C. Subcontraries 117D. Subalternation 118

3.7 The Boolean Square of Opposition 1223.8 Logical Equivalence and Immediate Inferences 123

A. Conversion 123B. Obversion 125C. Contraposition 128

Essentials of Chapter 3 133

CHAPTER 4 Categorical Syllogisms 136

4.1 Standard Form Categorical Syllogisms 136A. Major, Minor, and Middle Terms 136B. Mood 137C. Figure 138

4.2 The Nature of Syllogistic Arguments 1414.3 Venn Diagram Technique for Testing Syllogisms 1434.4 Syllogistic Rules and Syllogistic Fallacies 152Essentials of Chapter 4 161

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CHAPTER 5 Arguments in Ordinary Language 164

5.1 Syllogistic Arguments in Ordinary Language 1645.2 Reducing the Number of Terms in a Syllogistic

Argument 1655.3 Translating Categorical Propositions into Standard Form 168

A. Singular Propositions 169B. Categorical Propositions with Adjectives or Adjectival Phrases as

Predicates 171C. Categorical Propositions with Verbs Other Than the Standard Form

Copula To Be 172D. Categorical Propositions in Nonstandard Order 173E. Categorical Propositions with Nonstandard Quantifiers 174F. Exclusive Propositions 175G. Propositions Without Quantifiers 177H.Propositions Not in Standard Form that Have Logically Equivalent Standard

Form Alternatives 177I. Exceptive Propositions 178J. More Complex Quantifiers 179

5.4 Uniform Translation 1825.5 Enthymemes 184Essentials of Chapter 5 190

CHAPTER 6 Symbolic Logic 191

6.1 The Symbolic Language of Modern Logic 1916.2 Symbolese 101: The Language of Propositional Logic 192

A. Negation 193B. Conjunction 194C. Disjunction 195D. Material Implication (Material Conditionality) 196E. Biconditionals (Material Equivalence) 197F. Grouping Indicators 197

6.3 Truth Tables as Tools for Analyzing Compound Propositions 2086.4 Tautologous, Contradictory, and Contingent Statement Forms 2156.5 Truth Tables as a Test for the Validity of Arguments 221

A. Some Common Valid Argument Forms 225B. Some Common Invalid Argument Forms 227C. More Complex Arguments 228

6.6 Incomplete and Reverse Truth Tables 233A. Incomplete Truth Tables 233B. Reverse Truth Tables 235

6.7 Arguments, Conditionals, and Tautologies 241Essentials of Chapter 6 241

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CHAPTER 7 The Method of Deduction 244

7.1 Natural Deduction Versus Truth Tables 2447.2 Formal Proofs of Validity 2457.3 The Rule of Replacement (1) 2577.4 The Rule of Replacement (2) 2657.5 Conditional Proof 2807.6 Indirect Proof 285Essentials of Chapter 7 293

CHAPTER 8 Quantification Theory 295

8.1 When Propositional Logic Is Not Enough 2958.2 Symbolese 102: The Language of Quantificational Logic 296

A. Singular Propositions, Subjects, and Predicates 296B. Universal and Particular Propositions 298C. And Sometimes the Statements Are More Complex 300

8.3 Proving Validity 3068.4 Conditional and Indirect Proof 3168.5 Proving Invalidity 321Essentials of Chapter 8 329

CHAPTER 9 Induction 330

9.1 Introduction to Induction 3309.2 Arguments by Analogy 3349.3 Appraising Arguments by Analogy 3399.4 Explanations and Hypotheses 3479.5 Arguments to the Best Explanation 354Essentials of Chapter 9 367

Appendix: Truth Trees 371A.1 Propositional Logic 371A.2 Quantificational Logic 377Essentials of the Appendix 382

Solutions to the Odd-Numbered Problems 383

Glossary/Index 439

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In a republican nation, whose citizens are to be led by reason and persuasion and notby force, the art of reasoning becomes of the first importance.

—THOMAS JEFFERSON

Since the publication of the first edition in 1953, Irving M. Copi’s Introductionto Logic has served thousands of instructors and students in both teaching andstudying the fundamentals of classical and modern logic. The first edition ofEssentials of Logic was written in response to numerous instructors’ requestsfor a concise introductory logic text for use in their courses. The second edi-tion was revised in light of many instructors’ suggestions. While retaining therigor for which Copi has been known for over half a century, it was revisedwith an eye to clearer explanations, somewhat wider coverage, and anincreased number of aids for students. We believe the revisions in this editionwill make the distinctions clearer to students while retaining the logical rigorone expects from Copi.

FEATURES OF THE SECOND EDITION

Section reduction and coverage. The number of sections in the second editionhas been reduced from 62 to 52, but the coverage of topics has been expanded.The discussion of informal fallacies (Chapter 2) has been revised to show moreclearly how informal fallacies are related to acceptable arguments. Thisreflects recent scholarship on informal fallacies. In Chapter 4, the distinctionbetween logically equivalent statement forms and immediate inference hasbeen clarified. Chapter 5 includes a systematic discussion of how to find themissing premise in an enthymematic categorical syllogism. Chapter 6 includesa new section on incomplete and reverse or “one-row” truth tables. Chapter 7includes new sections on conditional and indirect proofs for propositionallogic. Chapter 8 includes a new section on conditional and indirect proofsfor quantificational logic. The chapter on induction (Chapter 9) nowincludes discussions of evaluating hypotheses and argument to the best expla-nation. There is a new appendix on using truth trees in propositional andquantificational logic.

P R E F A C E

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Exercise sets. The exercise sets include over 1,200 exercises, nearly half ofwhich are new to this edition of Essentials of Logic. Further, the book nowincludes solutions to all the odd-numbered exercises.

Increased use of charts, tables, and hints to students. A significant numberof side-bars called “Essential Hints” have been added. These give hints,suggestions, and encouragement to students. In Chapter 5, there is a chart ofnonstandard quantifiers for categorical logic. In Chapter 6, there is an exten-sive dictionary (translation guide) for propositional logic. In Chapter 7 and 8,there are expanded rules of thumb (strategies) for constructing proofs. In Chapter 8, there is an extensive dictionary (translation guide) for quantifi-cational logic.

Instructor supplements. Accompanying Essentials of Logic for instructors is aninstructor’s manual with sample test questions and solutions to all the even-numbered exercises. The test questions are also available in a com-puterized test manager program to aid in the preparation of tests for students.

Student supplement. There is also a revision of Prentice Hall’s groundbreak-ing logic tutorial, eLogic This tutorial includes over 500 of the exercises inEssentials of Logic for students to work electronically. Together with the exer-cises from the text, eLogic includes the tools students need to solve logic prob-lems. Students can work problems—including diagramming arguments, cre-ating Venn diagrams, constructing truth tables, and building proofs—andreceive constant feedback to guide them through solutions. Students can sub-mit their work via email or hardcopy to their instructors, together with a LogBook showing how well they did. The following walkthrough provides an ini-tial introduction to what awaits students in their use of eLogic!

After students enter their own username and email address, they will decidewhich exercises they need to work by locating the appropriate chapter andentering the appropriate section where the exercises reside.

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Numerous navigation links are always available on the main screen, includinghelp and access to the Log Book, where students can see which exercisesthey’ve worked on and how well they’ve done!

NOTE that students can always refresh their understanding on how to useeLogic through the help link!

Students select exercises by chapter section, and have ready at their commandall necessary toolkits to solve logic problems—including diagramming argu-ments, Venn diagrams, truth tables, proof checkers, and a symbolic notationeditor. Additionally, rules and a glossary are available for student reference.

ACKNOWLEDGMENTS

The revisions in this edition of Essentials of Logic benefited greatly by com-ments from Norman R. Schultz (Metro State College), Robert Kimball(University of Louisville), Andrew Aberdein (Florida Institute of Technology),A.T. Anchustegui (Boise State University), Keith W. Krasemann (College of Du Page), and Harlan Miller (Virginia Polytechnic and State University).Working with Mical Moser and Carla Worner at Prentice Hall and EmilyAutumn at GGS Book Services has been delightful. I also want to thank myfamily for their love and tolerance.

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