, LOGIC
A CONCISE
INTRODUCTION
TO
Thirteenth Edition
PATRICK J. HURLEY
University of San Diego
LORI WATSON
University of San Diego
Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States
,A Concise Introduction to Logic, © 2018, 2015, 2012 Cengage Learning
13th Edition
ALL RIGHTS RESERVED. No part of this work covered by the copyright
Patrick J. Hurley, Lori Watson
herein may be reproduced or distributed in any form or by any means,
Product Director: Paul Banks except as permitted by U.S. copyright law, without the prior written
permission of the copyright owner.
Product Manager: Joseph Potvin
Senior Content Developer: Florence Kilgo For product information and technology assistance, contact us at
Product Assistant: Staci Eckenroth Cengage Learning Customer & Sales Support, 1-800-354-9706
Marketing Manager: Sean Ketchem For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions
Senior Content Project Manager: Further permissions questions can be emailed to
Margaret Park Bridges
Senior Art Director: Marissa Falco
Manufacturing Planner: Julio Esperas Library of Congress Control Number: 2016941673
IP Analyst: Alex Ricciardi
Student Edition:
IP Project Manager: Nick Barrows ISBN: 978-1-305-95809-8
Production Service: Greg Hubit Bookworks Loose-leaf Edition:
Copy Editor: Marne Evans ISBN: 978-1-305-95976-7
Proofreader: Debra Nichols
Compositor: MPS Limited Cengage Learning
Text and Cover Designer: Deborah Dutton 20 Channel Center Street
Boston, MA 02210
Cover Images: iStockphoto.com/pavlen;
USA
Route55/Shutterstock.com
Cengage Learning is a leading provider of customized learning solutions
with employees residing in nearly 40 different countries and sales in more
than 125 countries around the world. Find your local representative at
www.cengage.com
Cengage Learning products are represented in Canada by
Nelson Education, Ltd.
To learn more about Cengage Learning Solutions, visit
www.cengage.com
Purchase any of our products at your local college store or at our preferred
online store www.cengagebrain.com
Unless otherwise noted, all content is © Cengage Learning 2018.
Printed in the United States of America
Print Number: 01 Print Year: 2016
, This is an electronic version of the print textbook. Due to electronic rights restrictions,
some third party content may be suppressed. Editorial review has deemed that any suppressed
content does not materially affect the overall learning experience. The publisher reserves the right
to remove content from this title at any time if subsequent rights restrictions require it. For
valuable information on pricing, previous editions, changes to current editions, and alternate
formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for
materials in your areas of interest.
Important Notice: Media content referenced within the product description or the product
text may not be available in the eBook version.
, To Linda
It is wrong always, everywhere, and for anyone,
to believe anything upon insufficient evidence.
–W. K. Clifford
Nothing can be more important than the art of
formal reasoning according to true logic .
–Gottfried Wilhelm Leibniz
,Brief Contents
PA RT I INFORMAL LOGIC
1 Basic Concepts 1
2 Language: Meaning and Definition 81
3 Informal Fallacies 125
PA RT II FORMAL LOGIC
4 Categorical Propositions 206
5 Categorical Syllogisms 274
6 Propositional Logic 327
7 Natural Deduction in Propositional Logic 403
8 Predicate Logic 470
PA RT I1I INDUCTIVE LOGIC
9 Analogy and Legal and Moral Reasoning 540
10 Causality and Mill’s Methods 560
11 Probability 585
12 Statistical Reasoning 604
13 Hypothetical/Scientific Reasoning 627
14 Science and Superstition 646
Answers to Selected Exercises 676
Glossary/Index 720
iv
,Contents
Preface xi
Why Study Logic? xxii
PA RT I INFORMAL LOGIC
1 Basic Concepts 1
1.1 Arguments, Premises, and Conclusions 1
Exercise 1.1 7
1.2 Recognizing Arguments 14
Exercise 1.2 25
1.3 Deduction and Induction 33
Exercise 1.3 40
1.4 Validity, Truth, Soundness, Strength, Cogency 45
Exercise 1.4 55
1.5 Argument Forms: Proving Invalidity 59
Exercise 1.5 65
1.6 Extended Arguments 67
Exercise 1.6 72
2 Language: Meaning and Definition 81
2.1 Varieties of Meaning 81
Exercise 2.1 86
2.2 The Intension and Extension of Terms 92
Exercise 2.2 96
2.3 Definitions and Their Purposes 97
Exercise 2.3 104
v
, 2.4 Definitional Techniques 106
Exercise 2.4 113
2.5 Criteria for Lexical Definitions 117
Exercise 2.5 121
3 Informal Fallacies 125
3.1 Fallacies in General 125
Exercise 3.1 127
3.2 Fallacies of Relevance 128
Exercise 3.2 142
3.3 Fallacies of Weak Induction 147
Exercise 3.3 159
3.4 Fallacies of Presumption, Ambiguity,
and Illicit Transference 165
Exercise 3.4 179
3.5 Fallacies in Ordinary Language 187
Exercise 3.5 193
PA RT I I FORMAL LOGIC
4 Categorical Propositions 206
4.1 The Components of Categorical Propositions 206
Exercise 4.1 209
4.2 Quality, Quantity, and Distribution 210
Exercise 4.2 214
4.3 Venn Diagrams and the Modern Square of Opposition 215
Exercise 4.3 228
4.4 Conversion, Obversion, and Contraposition 229
Exercise 4.4 237
4.5 The Traditional Square of Opposition 240
Exercise 4.5 246
4.6 Venn Diagrams and the Traditional Standpoint 252
Exercise 4.6 258
vi CONTENTS
,4.7 Translating Ordinary Language
Statements into Categorical Form 260
Exercise 4.7 267
5 Categorical Syllogisms 274
5.1 Standard Form, Mood, and Figure 274
Exercise 5.1 279
5.2 Venn Diagrams 282
Exercise 5.2 293
5.3 Rules and Fallacies 296
Exercise 5.3 302
5.4 Reducing the Number of Terms 305
Exercise 5.4 307
5.5 Ordinary Language Arguments 308
Exercise 5.5 311
5.6 Enthymemes 312
Exercise 5.6 314
5.7 Sorites 318
Exercise 5.7 321
6 Propositional Logic 327
6.1 Symbols and Translation 327
Exercise 6.1 337
6.2 Truth Functions 341
Exercise 6.2 351
6.3 Truth Tables for Propositions 354
Exercise 6.3 361
6.4 Truth Tables for Arguments 364
Exercise 6.4 367
6.5 Indirect Truth Tables 371
Exercise 6.5 379
6.6 Argument Forms and Fallacies 381
Exercise 6.6 393
CONTENTS vii
, 7 Natural Deduction in Propositional Logic 403
7.1 Rules of Implication I 403
Exercise 7.1 411
7.2 Rules of Implication II 416
Exercise 7.2 422
7.3 Rules of Replacement I 426
Exercise 7.3 433
7.4 Rules of Replacement II 440
Exercise 7.4 445
7.5 Conditional Proof 453
Exercise 7.5 457
7.6 Indirect Proof 460
Exercise 7.6 463
7.7 Proving Logical Truths 466
Exercise 7.7 467
8 Predicate Logic 470
8.1 Symbols and Translation 470
Exercise 8.1 477
8.2 Using the Rules of Inference 480
Exercise 8.2 489
8.3 Quantifier Negation Rule 493
Exercise 8.3 496
8.4 Conditional and Indirect Proof 498
Exercise 8.4 502
8.5 Proving Invalidity 505
Exercise 8.5 510
8.6 Relational Predicates and Overlapping Quantifiers 512
Exercise 8.6 520
8.7 Identity 523
Exercise 8.7 532
viii CONTENTS
A CONCISE
INTRODUCTION
TO
Thirteenth Edition
PATRICK J. HURLEY
University of San Diego
LORI WATSON
University of San Diego
Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States
,A Concise Introduction to Logic, © 2018, 2015, 2012 Cengage Learning
13th Edition
ALL RIGHTS RESERVED. No part of this work covered by the copyright
Patrick J. Hurley, Lori Watson
herein may be reproduced or distributed in any form or by any means,
Product Director: Paul Banks except as permitted by U.S. copyright law, without the prior written
permission of the copyright owner.
Product Manager: Joseph Potvin
Senior Content Developer: Florence Kilgo For product information and technology assistance, contact us at
Product Assistant: Staci Eckenroth Cengage Learning Customer & Sales Support, 1-800-354-9706
Marketing Manager: Sean Ketchem For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions
Senior Content Project Manager: Further permissions questions can be emailed to
Margaret Park Bridges
Senior Art Director: Marissa Falco
Manufacturing Planner: Julio Esperas Library of Congress Control Number: 2016941673
IP Analyst: Alex Ricciardi
Student Edition:
IP Project Manager: Nick Barrows ISBN: 978-1-305-95809-8
Production Service: Greg Hubit Bookworks Loose-leaf Edition:
Copy Editor: Marne Evans ISBN: 978-1-305-95976-7
Proofreader: Debra Nichols
Compositor: MPS Limited Cengage Learning
Text and Cover Designer: Deborah Dutton 20 Channel Center Street
Boston, MA 02210
Cover Images: iStockphoto.com/pavlen;
USA
Route55/Shutterstock.com
Cengage Learning is a leading provider of customized learning solutions
with employees residing in nearly 40 different countries and sales in more
than 125 countries around the world. Find your local representative at
www.cengage.com
Cengage Learning products are represented in Canada by
Nelson Education, Ltd.
To learn more about Cengage Learning Solutions, visit
www.cengage.com
Purchase any of our products at your local college store or at our preferred
online store www.cengagebrain.com
Unless otherwise noted, all content is © Cengage Learning 2018.
Printed in the United States of America
Print Number: 01 Print Year: 2016
, This is an electronic version of the print textbook. Due to electronic rights restrictions,
some third party content may be suppressed. Editorial review has deemed that any suppressed
content does not materially affect the overall learning experience. The publisher reserves the right
to remove content from this title at any time if subsequent rights restrictions require it. For
valuable information on pricing, previous editions, changes to current editions, and alternate
formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for
materials in your areas of interest.
Important Notice: Media content referenced within the product description or the product
text may not be available in the eBook version.
, To Linda
It is wrong always, everywhere, and for anyone,
to believe anything upon insufficient evidence.
–W. K. Clifford
Nothing can be more important than the art of
formal reasoning according to true logic .
–Gottfried Wilhelm Leibniz
,Brief Contents
PA RT I INFORMAL LOGIC
1 Basic Concepts 1
2 Language: Meaning and Definition 81
3 Informal Fallacies 125
PA RT II FORMAL LOGIC
4 Categorical Propositions 206
5 Categorical Syllogisms 274
6 Propositional Logic 327
7 Natural Deduction in Propositional Logic 403
8 Predicate Logic 470
PA RT I1I INDUCTIVE LOGIC
9 Analogy and Legal and Moral Reasoning 540
10 Causality and Mill’s Methods 560
11 Probability 585
12 Statistical Reasoning 604
13 Hypothetical/Scientific Reasoning 627
14 Science and Superstition 646
Answers to Selected Exercises 676
Glossary/Index 720
iv
,Contents
Preface xi
Why Study Logic? xxii
PA RT I INFORMAL LOGIC
1 Basic Concepts 1
1.1 Arguments, Premises, and Conclusions 1
Exercise 1.1 7
1.2 Recognizing Arguments 14
Exercise 1.2 25
1.3 Deduction and Induction 33
Exercise 1.3 40
1.4 Validity, Truth, Soundness, Strength, Cogency 45
Exercise 1.4 55
1.5 Argument Forms: Proving Invalidity 59
Exercise 1.5 65
1.6 Extended Arguments 67
Exercise 1.6 72
2 Language: Meaning and Definition 81
2.1 Varieties of Meaning 81
Exercise 2.1 86
2.2 The Intension and Extension of Terms 92
Exercise 2.2 96
2.3 Definitions and Their Purposes 97
Exercise 2.3 104
v
, 2.4 Definitional Techniques 106
Exercise 2.4 113
2.5 Criteria for Lexical Definitions 117
Exercise 2.5 121
3 Informal Fallacies 125
3.1 Fallacies in General 125
Exercise 3.1 127
3.2 Fallacies of Relevance 128
Exercise 3.2 142
3.3 Fallacies of Weak Induction 147
Exercise 3.3 159
3.4 Fallacies of Presumption, Ambiguity,
and Illicit Transference 165
Exercise 3.4 179
3.5 Fallacies in Ordinary Language 187
Exercise 3.5 193
PA RT I I FORMAL LOGIC
4 Categorical Propositions 206
4.1 The Components of Categorical Propositions 206
Exercise 4.1 209
4.2 Quality, Quantity, and Distribution 210
Exercise 4.2 214
4.3 Venn Diagrams and the Modern Square of Opposition 215
Exercise 4.3 228
4.4 Conversion, Obversion, and Contraposition 229
Exercise 4.4 237
4.5 The Traditional Square of Opposition 240
Exercise 4.5 246
4.6 Venn Diagrams and the Traditional Standpoint 252
Exercise 4.6 258
vi CONTENTS
,4.7 Translating Ordinary Language
Statements into Categorical Form 260
Exercise 4.7 267
5 Categorical Syllogisms 274
5.1 Standard Form, Mood, and Figure 274
Exercise 5.1 279
5.2 Venn Diagrams 282
Exercise 5.2 293
5.3 Rules and Fallacies 296
Exercise 5.3 302
5.4 Reducing the Number of Terms 305
Exercise 5.4 307
5.5 Ordinary Language Arguments 308
Exercise 5.5 311
5.6 Enthymemes 312
Exercise 5.6 314
5.7 Sorites 318
Exercise 5.7 321
6 Propositional Logic 327
6.1 Symbols and Translation 327
Exercise 6.1 337
6.2 Truth Functions 341
Exercise 6.2 351
6.3 Truth Tables for Propositions 354
Exercise 6.3 361
6.4 Truth Tables for Arguments 364
Exercise 6.4 367
6.5 Indirect Truth Tables 371
Exercise 6.5 379
6.6 Argument Forms and Fallacies 381
Exercise 6.6 393
CONTENTS vii
, 7 Natural Deduction in Propositional Logic 403
7.1 Rules of Implication I 403
Exercise 7.1 411
7.2 Rules of Implication II 416
Exercise 7.2 422
7.3 Rules of Replacement I 426
Exercise 7.3 433
7.4 Rules of Replacement II 440
Exercise 7.4 445
7.5 Conditional Proof 453
Exercise 7.5 457
7.6 Indirect Proof 460
Exercise 7.6 463
7.7 Proving Logical Truths 466
Exercise 7.7 467
8 Predicate Logic 470
8.1 Symbols and Translation 470
Exercise 8.1 477
8.2 Using the Rules of Inference 480
Exercise 8.2 489
8.3 Quantifier Negation Rule 493
Exercise 8.3 496
8.4 Conditional and Indirect Proof 498
Exercise 8.4 502
8.5 Proving Invalidity 505
Exercise 8.5 510
8.6 Relational Predicates and Overlapping Quantifiers 512
Exercise 8.6 520
8.7 Identity 523
Exercise 8.7 532
viii CONTENTS
