HOW TO THINK LOGICALLY
Second Edition
GARY SEAY
Medgar Evers College, City University of New York
SUSANA NUCCETELLI
St. Cloud State University
PEARSON
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Library of Congress Cataloging-in-Publication Data Seay, Gary.
How to think logically / Gary Seay, Susana Nuccetelli.-2nd ed. p. cm.
Includes index. ISBN-13: 978-0-205-15498-2 ISBN-10: 0-205-15498-0 1. Logic-Textbooks. I. Nuccetelli, Susana. II. Title. BC108.S34 2012 160-dc22
2011014099
14 16
PEARSON ISBN 10: 0-205-15498-0 ISBN 13: 978-0-205-15498-2
Preface xi
About the Authors xiv
Part I The Building Blocks of Reasoning 1
brief contents .-.�?
CHAPTER 1 What Is Logical Thinking? And Why Should We Care? 3
CHAPTER 2 Thinking Logically and Speaking One’s Mind 24
CHAPTER 3 The Virtues of Belief 49
Part II Reason and Argument 71
CHAPTER 4 Tips for Argument Analysis 73
CHAPTER 5 Evaluating Deductive Arguments 94
CHAPTER 6 Analyzing Inductive Arguments 122
Part Ill Informal Fallacies 145
CHAPTER 7 Some Ways an Argument Can Fail 147
CHAPTER 8 Avoiding Ungrounded Assumptions 166
CHAPTER 9 From Unclear Language to Unclear Reasoning 187
CHAPTER 10 Avoiding Irrelevant Premises 209
Part IV More on Deductive Reasoning 227
CHAPTER 11 Compound Propositions 229
CHAPTER 12 Checking the Validity of Propositional Arguments 261
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CHAPTER 13 Categorical Propositions and Immediate Inferences 293
CHAPTER 14 Categorical Syllogisms 330
Solutions to Selected Exercises 365
Glossary /Index 386
Index 396
detailed contents
Preface xi
About the Authors xiv
PART I The Building Blocks of Reasoning 1
CHAPTER 1 What Is Logical Thinking? And Why Should We Care? 3
1.1 The Study of Reasoning 4 Inference or Argument 4 • 1.2 Logic and Reasoning 5
Dimensions of the Subject 5 Formal Logic 5 Informal Logic 6 Exercises 7 •
1.3 What Arguments Are 8 Argument Analysis 9 • 1.4 Reconstructing Arguments 10
Identifying Premises and Conclusion 10 Premise and Conclusion Indicators 11
Arguments with No Premise or Conclusion Indicators 13 Exercises 14
1.5 Arguments and Non-arguments 16 Explanations 16 Conditionals 17
Fictional Discourse 18 Exercises 19 Writing Project 21 Chapter Summary 21
• Key Words 23
CHAPTER 2 Thinking Logically and Speaking One’s Mind 24
2.1 Rational Acceptability 25 Logical Connectedness 25 Evidential Support 26 Truth and
Evidence 27 2.2 Beyond Rational Acceptability 28 Linguistic Merit 28 Rhetorical
Power 28 Rhetoric vs. Logical Thinking 29 Exercises 29 2.3 From Mind to Language 32 Propositions 32 Uses of Language 33 Types of Sentence 35
2.4 Indirect Use and Figurative Language 36 Indirect Use 37 Figurative
Meaning 37 Exercises 38 • 2.5 Definition: An Antidote to Unclear Language 42 Reconstructing Definitions 42 Reportive Definitions 43 Testing Reportive
Definitions 43 Ostensive and Contextual Definitions 45 Exercises 45 ■ Writing Project 47 Chapter Summary 47 Key Words 48
CHAPTER 3 The Virtues of Belief 49
3.1 Belief, Disbelief, and Non belief 50 Exercises 52 • 3.2 Beliefs’ Virtues and
Vices 53 3.3 Accuracy and Truth 54 Accuracy and Inaccuracy 54 Truth and
Falsity 54 • 3.4 Reasonableness 56 Two Kinds of Reasonableness 56
3.5 Consistency 58 Defining ‘Consistency’ and ‘Inconsistency’ 58 Logically Possible
Propositions 59 Logically Impossible Propositions 59 Consistency and Possible
Worlds 60 Consistency in Logical Thinking 61 ■ 3.6 Conservatism and
Revisability 61 Conservatism without Dogmatism 61 Revisability without Extreme
Relativism 62 3.7 Rationality vs. Irrationality 63 Exercises 65 Writing
Project 69 • Chapter Summary 69 Key Words 70
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PART 11 Reason and Argument 71
CHAPTER 4 Tips for Argument Analysis 73
4.1 A Principled Way of Reconstructing Arguments 74 Faithfulness 74 Charity 74
When Faithfulness and Charity Conflict 74 4.2 Missing Premises 76 • 4.3 Extended Arguments 77 Exercises 78 4.4 Types of Reason 81 Deductive vs. Inductive
Reasons 81 Exercises 83 4.5 Norm and Argument 85 What Is a Normative
Argument? 85 Missing Normative Premises 87 Exercises 88 Writing Project 92 Chapter Summary 93 Key Words 93
CHAPTER 5 Evaluating Deductive Arguments 94
5.1 Validity 95 Valid Arguments and Argument Form 97 ‘Validity’ as a Technical
Word 98 Exercises 99 Propositional Argument Forms 102 Categorical Argument
Forms 104 The Cash Value ofValidity 107 Exercises 108 ■ 5.2 Soundness 114 The Cash Value of Soundness 116 5.3 Cogency 116 The Cash Value of Cogency 117
Exercises 118 • Writing Project 119 • Chapter Summary 120 • Key Words 121
CHAPTER 6 Analyzing Inductive Arguments 122
6.1 Reconstructing Inductive Arguments 123 • 6.2 Some Types of Inductive Argument 125 Enumerative Induction 125 Statistical Syllogism 128 Causal Argument 130
Analogy 133 Exercises 135 • 6.3 Evaluating Inductive Arguments 137 Inductive
Reliability 137 Inductive Strength 138 Exercises 140 ■ Writing Project 143 Chapter Summary 143 Key Words 144
PART Ill Informal Fallacies 145
CHAPTER 7 Some Ways an Argument Can Fail 147
7,1 What Is a Fallacy? 148 • 7.2 Classification of Informal Fallacies 149 7.3 When Inductive Arguments Go Wrong 150 Hasty Generalization 150
Weak Analogy 152 False Cause 153 Appeal to Ignorance 156 Appeal to Unqualified
Authority 158 Exercises 160 Writing Project 164 • Chapter Summary 164 Key Words 165
CHAPTER 8 Avoiding Ungrounded Assumptions 166
8.1 Fallacies of Presumption 167 • 8.2 Begging the Question 167 Circular
Reasoning 169 Benign Circularity 170 The Burden of Proof 172 • 8.3 Begging the Question Against 173 Exercises 174 8.4 Complex Question 178
8.5 False Alternatives 179 • 8.6 Accident 181 Exercises 182 • Writing Project 185 • Chapter Summary 185 • Key Words 186
CHAPTER 9 From Unclear Language to Unclear Reasoning 187
9.1 Unclear Language and Argument Failure 188 • 9.2 Semantic Unclarity 189 9.3 Vagueness 191 The Heap Paradox 192 The Slippery-Slope Fallacy 194
9.4 Ambiguity 195 Equivocation 196 Amphiboly 197 ■ 9.5 Confused Predication 199
Composition 200 Division 201 Exercises 203 ■ Writing Project 207
Chapter Summary 207 ■ Key Words 208
CHAPTER 10 Avoiding Irrelevant Premises 209
10.1 Fallacies of Relevance 210 10.2 Appeal to Pity 210 10.3 Appeal to
Force 211 ■ 10.4 Appeal to Emotion 213 The Bandwagon Appeal 214 Appeal to
Vanity 214 10.5 Ad Hominem 215 The Abusive Ad Hominem 216 Tu Quoque 216
Nonfallacious Ad Hominem 217 10.6 Beside the Point 218 10.7 Straw Man 219
10.8 Is the Appeal to Emotion Always Fallacious? 221 Exercises 222 ■ Writing
Project 226 ■ Chapter Summary 226 ■ Key Words 226
PART IV More on Deductive Reasoning 227
CHAPTER 11 Compound Propositions 229
11.1 Argument as a Relation between Propositions 230 11.2 Simple and
Compound Propositions 231 Negation 232 Conjunction 234 Disjunction 236 Material
Conditional 237 Material Biconditional 240 Exercises 241 ■ 11.3 Propositional Formulas
for Compound Propositions 244 Punctuation Signs 244 Well-Formed
Formulas 244 Symbolizing Compound Propositions 245 Exercises 247 11.4 Defining
Connectives with Truth Tables 251 ■ 11.5 Truth Tables for Compound
Propositions 254 11.6 Logically Necessary and Logically Contingent
Propositions 256 ■ Contingencies 256 Contradictions 256 Tautologies 256 Exercises 257
Writing Project 259 Chapter Summary 259 Key Words 260
CHAPTER 12 Checking the Validity of Propositional Arguments 261
12.1 Checking Validity with Truth Tables 262 Exercises 266 12.2 Some Standard
Valid Argument Forms 268 Modus Ponens 268 Modus Tollens 269
Contraposition 269 Hypothetical Syllogism 270 Disjunctive Syllogism 271 More Complex
Instances ofValid Forms 271 Exercises 273 12.3 Some Standard Invalid Argument
Forms 276 Affirming the Consequent 278 Denying the Antecedent 279 Affirming a
Disjunct 280 Exercises 281 ■ 12.4 A Simplified Approach to Proofs of Validity 284
The Basic Rules 285 What Is a Proof of Validity? 285 How to Construct a Proof of
Validity 286 Proofs vs. Truth Tables 287 Exercises 287 Writing Project 291
Chapter Summary 291 Key Words 292
CHAPTER 13 Categorical Propositions and Immediate Inferences 293
13.1 What Is a Categorical Proposition? 294 Categorical Propositions 294 Standard
Form 296 Non-Standard Categorical Propositions 298 Exercises 299 13.2 Venn Diagrams
for Categorical Propositions 301 Exercises 305 13.3 The Square of Opposition 308
The Traditional Square of Opposition 308 Existential Import 312 The Modern Square of
Opposition 314 Exercises 315 13.4 Other Immediate Inferences 319 Conversion 319
Obversion 320 Contraposition 322 Exercises 325 ■ Writing Project 328
■ Chapter Summary 328 • Key Words 329
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CHAPTER 14 Categorical Syllogisms 330
14.1 What Is a Categorical Syllogism? 331 The Terms of a Syllogism 331 The Premises of a
Syllogism 332 Recognizing Syllogisms 333 14.2 Syllogistic Argument Forms 335
Figure 335 Mood 336 Determining a Syllogism’s Form 337 Exercises 339 14.3 Testing for
Validity with Venn Diagrams 342 How to Diagram a Standard Syllogism 342
Exercises 351 ■ 14.4 Distribution of Terms 354 14.5 Rules of Validity and
Syllogistic Fallacies 356 Rules ofValidity vs. Venn Diagrams 359 Exercises 360 ■
Writing Project 363 ■ Chapter Summary 363 ■ Key Words 364
Solutions to Selected Exercises 365
Glossary /Index 386
Index 396
preface
This is a book intended for introductory courses in logic and critical thinking, but its scope is broadly focused to include some issues in philosophy as well as treatments of induction, informal fallacies, and both propositional and traditional syllogistic logic. Its aim throughout, however, is to broach these topics in a way that will be accessible to beginners in college-level work. How to Think Logically is a user-friendly text designed for students who have never encountered philosophy before, and for whom a systematic approach to analytical thinking may be an unfamiliar exercise. The writing style is simple and direct, with jargon kept to a min imum. Symbolism is also kept simple. Scattered through the text are special-emphasis boxes in which important points are summarized to help students focus on crucial distinctions and fundamental ideas. The book’s fourteen chapters unfold in a way that undergraduates will find understandable and easy to follow. Even so, the book maintains a punctilious regard for the principles of logic. At no point does it compromise rigor.
How to Think Logically is a guide to the analysis, reconstruction, and evaluation of argu ments. It is designed to help students learn to distinguish good reasoning from bad. The book is divided into four parts. The first is devoted to argument recognition and the building blocks of argument. Chapter 1 introduces argument analysis, focusing on argument recognition and the difference between formal and informal approaches to inference. Chapter 2 offers a closer look at the language from which arguments are constructed and examines such topics as logical strength, linguistic merit, rhetorical power, types of sentences, uses of language, and definition. Chapter 3 considers epistemic aspects of the statements that are the components of an inference. It explains the assumption that when speakers are sincere and competent, what they state is what they believe, so that the epistemic virtues and vices of belief may also affect statements. Part II is devoted to the analysis of deductive and inductive arguments, distinguishing under each of these two general classifications several different types of argument that students should be able to recognize. It also includes discussions of the principles of charity and faithfulness, extended arguments, enthymemes, and normative arguments of four different kinds. In Part III, students are shown how some very basic confusions in thinking may lead to defective reasoning, and they learn to spot twenty of the most common informal fallacies. Part N, which comprises Chapters 11
through 14, offers a feature many instructors will want: a detailed treatment of some common elementary procedures for determining validity in propositional logic-including a simplified approach to proofs-and traditional syllogistic logic. Here students will be able to go well beyond the intuitive procedures learned in Chapter 5.
Each of the book’s four parts is a self-contained unit. The topics are presented in a way that permits instructors to teach the chapters in different sequences and combinations, according to the needs of their courses. For example, an instructor in a critical thinking course could simply assign Chapters 1 through 10. But in a course geared more to deductive
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logic, Chapters 1, 4, 5, and 6 and then 11 through 14 might serve best. Other instructors might want to do some of both critical thinking and deductive logic, for which the best strategy might be to assign Chapter 1 and then either 4 through 12, or 4 through 10 plus 13 and 14.
How to Think Logically, in this new second-edition format, includes a number of improvements, thanks to the helpful suggestions of anonymous reviewers selected by Pearson and of philosophers we know who are using the book:
■ Chapter 1 has been reworked to present a better introduction to argument, the central topic of the book. The treatment of non-arguments now includes entries for explanations, conditionals, and fictional discourse. A more concise treatment of definition now follows discussions of figurative meaning and indirect use of language in Chapter 2. Also added to this chapter is an expanded treatment of sentence types, including speech acts, in connection with the discussion of uses of language, providing a more nuanced and timely treatment of this topic. The discussions of contradiction and consistency in Chapter 3 have been rewritten for greater clarity.
The section on evaluative reasoning in Chapter 4 has been expanded into a much improved discussion of moral, legal, prudential, and aesthetic norms and arguments. Many new examples, of varying degrees of difficulty, have been incorporated in the book’s account of informal fallacies. First-edition examples have been brought up to date. Exercise sections in all chapters have been greatly expanded. Many new exercises have been added, so that students can now get more practice in applying what they’re learning. As a result, instructors will now have a larger selection of exercises from which to choose
in assigning homework or in engaging students in class discussions. ■ The program of the book has been simplified so that it does much better, and more
economically, what instructors need it to do: namely, serve as a text for teaching students how to develop critical-reasoning skills. The ‘Philosopher’s Corner’ features of the first edition have been taken out, following the consensus of reviewers, who said that they almost never had time in a fifteen-week semester to use them if they were teaching the logic, too. In this new edition, references to philosophical theories have been minimized and woven into topics of informal logic. In this way, the overall length of the book has been kept about the same as in the first edition, and the price of the
book has been kept low.
But many features of the earlier edition have been retained here. There are abundant
pedagogical aids in the book, including not only more exercises, but also study questions and lists of key words. At the end of each chapter are a chapter summary and a writing project. And in the back of the book is a detailed glossary of important terms.
We wish to thank our editor at Pearson Education, Nancy Roberts, and Kate Fernandes, the
project manager for this book. Special thanks are due also to Pearson editor-in-chief Dickson Musslewhite, who provided judicious guidance at crucial points in bringing out this new edition. We are also grateful for the criticisms of the philosophers selected as anonymous reviewers by Pearson. Their sometimes barbed but always trenchant observations about the first edition have helped us to make this a much better textbook.
Support for Instructors and Students
MySearchLab.com is an online tool that offers a wealth of resources to help student learning
and comprehension, including practice quizzes, primary source readings and more. Please
contact your Pearson representative for more information or visit www.MySearchLab.com
Instructor’s Manual with Tests (0-205-15534-0) for each chapter in the text, this valuable
resource provides a detailed outline, list of objectives, and discussion questions. In addition,
test questions in multiple-choice, true/false, fill-in-the-blank, and short answer formats are
available for each chapter; the answers are page referenced to the text. For easy access, this
manual is available at www.pearsonhighered.com/irc.
PowerPoint Presentation Slides for How to Think Logically (0-205-15538-3): These
PowerPoint Slides help instructors convey logic principles in a clear and engaging way. For
easy access, they are available at www.pearsonhighered.com/irc. w
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about the authors
GARY SEAY has taught formal and informal logic since 1979 at the City University of New York, where he is presently professor of phi
losophy at Medgar Evers College. His articles on moral philosophy and bioethics have appeared in The American Philosophical Q.uarter!Y, The Journal of Value Inquiry, The Journal of Medicine and Philosophy, and The Cambridge Q_uarter!Y of Healthcare Ethics, among other journals. With Susana Nuccetelli, he is editor of Themes from G. E. Moore: New Essays in Epistemology and Ethics (Oxford University Press, 2007), Philosophy of Language: The Central Topics (Rowman and Littlefield, 2007), and Latin American Philosophy: An Introduction with
Readings (Prentice Hall, 2004).
SUSANA NUCCETELLI is professor of philosophy at St. Cloud
State University in Minnesota. Her essays in epistemology and
philosophy of language have appeared in Anarysis, The American Philosophical Q!iarter!Y, Metaphilosophy, The Philosophical Forum, Inquiry, and The Southern Journal of Philosophy, among other
journals. She is editor of New Essays in Semantic Externalism and Self-Knowledge (MIT Press, 2003) and author of Latin American Thought: Philosophical Problems and Arguments (Westview Press,
2002). She is co-editor of The Blackwell Companion to Latin American Philosophy (Blackwell, 2009) and, with Gary Seay, Ethical Naturalism: Current Debates (Cambridge University Press, forthcoming, 2011).
xiv
The Building Blocks of Reasoning
Pa rt
What Is Logical Thinking? And Why Should We Care?
CHAPTER
After reading this chapter, you’ll be able to answer questions about
logical thinking, such as
What is its subject matter?
■ How does its approach to reasoning differ from those of neuroscience and psychology?
■ Which are the main dimensions of logical thinking?
■ How does logical thinking differ from formal logic?
■ What is an argument? And how is it distinguished from a non-argument?
■ What are the steps in argument analysis?
3
1.1 The Study of Reasoning
Logical thinking, or informal logic, is a branch of philosophy devoted to the study of reason
ing. Although it shares this interest with other philosophical and scientific disciplines, it differs from them in a number of ways. Compare, for example, cognitive psychology and neuro science. These also study reasoning but are chiefly concerned with the mental and physiolog ical processes underlying it. By contrast, logical thinking focuses on the outcomes of such processes: namely, certain logical relations among beliefs and their building blocks that obtain when reasoning is at work. It also focuses on logical relations among statements, which, when speakers are sincere and competent, express the logical relations among their beliefs.
Inference or Argument
As far as logical thinking is concerned, reasoning consists in logical relations. Prominent
among them is a relation whereby one or more beliefs are taken to offer support for another. Known as inference or argument, this relation obtains whenever a thinker entertains one or more beliefs as being reasons in support of another belief. Inferences could be strong, weak, or
failed. Here is an example of a strong inference:
1 All whales are mammals, and Moby Dick is a whale; therefore, Moby Dick is a mammal.
(1) is a strong inference because, if the beliefs offered as reasons (‘All whales are mammals,’ and
‘Moby Dick is a whale’) are true, then the belief they are supposed to support (‘Moby Dick is a mammal’) must also be true. But compare
2 No oranges from Florida are small; therefore, no oranges from the United States
are small.
In (2) the logical relation of inference between the beliefs is weak, since the reason offered (‘No
oranges from Florida are small’) could be true and the belief it’s offered to support (‘No oranges from the United States are small’) false. But by no means does (2) illustrate the worst-case scenario. In some attempted inferences, a belief or beliefs offered to support another belief
might fail to do so. Consider
3 No oranges are apples; therefore, all elms are trees.
Since in (3) ‘therefore’ occurs between the two beliefs, it is clear that ‘No oranges are apples’ is offered as a reason for ‘All elms are trees.’ Yet it is not. Although these two beliefs
both happen to be true, they do not stand in the relation of inference. Here is another such
case of failed inference, this time involving false beliefs:
4 All lawyers are thin; therefore, the current pope is Chinese.
Since in (4) the component beliefs have little to do with each other, neither of them actually supports the other. As in (3), the inference fails.
Success and failure in inference are logical thinking’s central topic. Let’s now look more
closely at how it approaches this subject.
1.2 Logic and Reasoning
Dimensions of the Subject
Inference is the most fundamental relation between beliefs or thoughts when reasoning is at
work. Logical thinking studies this and other logical relations, with an eye toward
1. Describing patterns of reasoning. 2. Evaluating good- and bad-making features of reasoning. 3. Sanctioning rules for maximizing reasoning’s good-making features.
Each of these tasks may be thought of as a dimension of logical thinking. The first describes
logical relations, which initially requires identifying common patterns of inference. The
second distinguishes good and bad traits in those relations. And the third sanctions rules for
adequate reasoning. Rules are norms that can help us maximize the good (and minimize the
bad) traits of our reasoning. The picture that emerges is as in Box 1.
Understanding these dimensions is crucial to the study of reasoning. Since the third
dimension especially bears on how well we perform at reasoning, it has practical worth or cash
value. Its cash value consists in the prescriptions it issues for materially improving our reason
ing. But this dimension depends on the other two, because useful prescriptions for adequate
reasoning require accurate descriptions of the common logical relations established by
reasoning (such as inference). And they require adequate criteria to distinguish good and bad
features in those relations.
Formal Logic
What we’re calling ‘logical thinking’ is often known as informal logic. This discipline shares
with another branch of philosophy.formal logic, its interest in inference and other logical
relations. Informal and formal logic differ, however, in their scope and methods. Formal logic
is also known as symbolic logic. It develops its own formal languages for the purpose of
BOX 1 ■ THREE MAIN TASKS OF LOGICAL THINKING
DESCRIPTIVE
DIMENSION
Studies the logical relations among
beliefs typical of reasoning
DIMENSIONS OF
LOGICAL THINKING
EVALUATIVE NORMATIVE
DIMENSION DIMENSION
Identifies good and bad Gives rules for achieving good
traits in reasoning and avoiding bad reasoning
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deducing theorems from formulas accepted as axioms (in ways somewhat like mathematical proofs). Any such system consists of basic symbolic expressions, the initial vocabulary of the formal language, and rules for operations with them. The rules prescribe how to form correct
expressions and how to determine which formulas are the logical consequence of other formulas. In formal logic, then, inference is a relation among formulas: one that holds when
ever a formula follows from one or more formulas. Formal logic uses a symbolic notation, which may be quite complex. And its formulas need not be translated into a natural language, which is the language of a speech community, such as English, Arabic, or Japanese. As far as formal logic is concerned, inference is a relation among formulas. It need be neither a relation
among beliefs nor one among statements. Furthermore, it need not be identified with inferences people actually make in ordinary reasoning.
Informal Logic
In contrast to formal logic, logical thinking is completely focused on the study of logical
relations as they occur when ordinary reasoning is at work. Its three dimensions can be shown relevant to reasoning in a variety of common contexts, as when we deliberate about issues
such as those in Box 2.
The study of the inferences we make in these and other issues is approached by logical thinking in its three dimensions: once it describes the logical relations underlying particular
inferences, it evaluates them and determines whether they conform to rules of good reason
ing. Since doing this requires no formal languages, logical thinking is sometimes known as ‘informal logic.’ Although this discipline may introduce special symbols, it need not do so: it
can be conducted entirely in a natural language. Furthermore, in contrast to formal logic, what
we’re here calling ‘logical thinking’ approaches the study of inference as a relation among beliefs-or among statements, the linguistic expressions of beliefs.
Why, then, should we care about logical thinking? First, we want to avoid false beliefs and have as many true beliefs as possible, all related in a way that makes logical sense, and logical thinking is instrumental in achieving this goal. Second, for the intellectually curious, learning
BOX 2 ■ SOME PRACTICAL USES OF LOGICAL THINKING
A criminal trial:
A domestic question:
A scientific puzzle:
A philosophical issue:
An ethical problem:
A political decision:
A financial decision:
A health matter:
Is the defendant guilty?What shall we make of the alibi?
What’s the best school for our kids? Should they go to a private school, or a public school?
How to choose between equal!), supported,yet opposite, scientific theories?
Are mind and body the same thing, or different?
Is euthanasia moral!}, right?What about abortion?
Whom should I vote for in the general election?
Shall I follow my broker’s advice and invest in this new fund?
Given my medical records, is exercise good for me? Do I need more health insurance?
about the logical relations that take place in reasoning is an activity worthwhile for its own
sake. Moreover, it can help us in practical situations where competent reasoning is required,
which are exceedingly common. They arise whenever we wish to do well in intellectual
tasks such as those listed in Box 2. Each of us has faced them at some point-for example,
in attempting to convince someone of a view, in writing on a controversial topic, or simply in
deciding between two seemingly well-supported yet incompatible claims. To succeed in
meeting these ordinary challenges requires the ability to think logically. In the next section,
we’ll have a closer look at this important competence.
Exercises
1. How does logical thinking differ from scientific disciplines that study reasoning?
2. What is informal logic? And how does it differ from formal logic?
3. What is the main topic of logical thinking?
4. List one feature that logical thinking and formal logic have in common and one about which they
differ.
5. What is an inference?
6. Could an inference fail completely? If so, how? If not, why not?
7. What are the different dimensions of logical thinking?
8. Which dimension of logical thinking is relevant to determining reasoning’s good- and bad-making
traits?
9. Which is the dimension of logical thinking that has “cash value”? And what does this mean?
10. What is a natural language? Give three examples of a natural language.
II. YOUR OWN THINKING LAB
1 . Construct two inferences.
2. Construct a strong inference (one in which, if the supporting beliefs are true, the supported belief
must be true).
3. Construct a weak inference (one in which the supporting beliefs could be true and the belief they’re
intended to support false).
4. Construct a blatantly failed inference.
5. Describe a scenario for which logical thinking could help a thinker in everyday life.
6. Describe a scenario for which logical thinking could help with your own studies in college.
7. Suppose someone says, “Thinking logically has no practical worth!” How would you respond?
8. ‘Cats are carnivorous animals. No carnivorous animals are vegetarians; therefore, no cat is a vegetarian’
is a strong inference. Why?
9. Consider ‘All geckos are nocturnal. Therefore, there will be peace in the Middle East next year.’
What’s the matter with this inference?
10. Consider ‘Politicians are all crooks. Therefore, it never snows in the Sahara.’ What’s the matter with
this inference?
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1.3 What Arguments Are
In this book, we call ‘inference’ the relation whereby one or more beliefs are taken to support
another belief, and ‘argument’ the relation whereby one or more statements are offered in
support of another statement. When speakers are sincere and competent, they believe what
they assert, and their statements express their beliefs. Thus ‘inference’ and ‘argument’ may be
taken to apply to the same relation. Just as beliefs are the fundamental parts, or building
blocks, of inference, so statements are the building blocks from which arguments are con
structed. A statement is like a belief, in that it has a truth value, which is a way of saying that it
is either true (‘No apples are oranges’) or false (‘The Pope is Chinese’).
But not all relations between statements constitute arguments. Suppose someone says:
5 Philadelphia is a large city, and Chicago is larger still, but New York is the largest
of all.
Although (s) is made up of three simple statements grouped together, it does not amount to an
argument, for there is no attempt at presenting a supported claim; that is, the statements are
not arranged so that one of them makes a claim for which the others are offered as reasons.
Rather, they are just three conjoined statements. By contrast,
6 I think, therefore I am.
7 All lawyers are attorneys. Jack McCoy is a lawyer. Thus Jack McCoy is an attorney.
8 No chiropractors are surgeons. Only surgeons can legally perform a coronary bypass.
Hence, no chiropractors can legally perform a coronary bypass.
9 A Chevrolet Impala is faster than a bicycle. A Maserati is faster than a Chevrolet
Impala. A Japanese bullet train is faster than a Maserati. It follows that a Japanese
bullet train is faster than a bicycle.
In each of these examples, a claim is made and at least one other statement is offered in
support of that claim. This is the basic feature that all arguments share: every argument must
BOX 3 ■ THE BUILDING BLOCKS OF ARGUMENT
• Statements are the building blocks of argument
• They have truth values, because they express beliefs, and beliefs also have truth values • Each statement is either true or false
• Only sentences that can be used to express beliefs can be used to make statements
• Sentences of the following types cannot be used to make statements
•1. Expressive sentences (e.g., “What a lovely day!”) •2. Imperative sentences (e.g., “Please close the door”) •3. Interrogative sentences (“What did you do last weekend?”) More on this in Chapter 2
consist of at least two statements, one that makes a claim of some sort, and one or more others that are offered in support of it. The statement that makes the claim is the conclusion, and that
offered to support it is the premise (or premises, if there are more than one).
Now, clearly we are introducing some special terminology here. For in everyday English, ‘argu
ment’ most often means ‘dispute,’ a hostile verbal exchange between two or more people. But that is
very different from the more technical use of ‘argument’ in logical thinking, where its meaning is
similar to that common in a court of law. In a trial, each attorney is expected to present an argument.
This amounts to making a claim (e.g., ‘My client is innocent’) and then giving some reasons to
support it (‘He was visiting his mother on the night of the crime’). In doing this, the attorney is not
having a dispute with someone in the courtroom; rather, she is making an assertion and offering
evidence that supposedly backs it up. This is very much like what we mean by ‘argument’ in logical
thinking. An argument is a group of statements that are intended to make a supported claim. By this
definition, then, an argument is not a verbal confrontation between two hostile parties.
Before we look more closely at argument, let’s consider Box 4, which summarizes what we already know about this relation among statements.
BOX 4 ■ SECTION SUMMARY
■ In logical thinking, the meaning of the term ‘argument’ is similar to that common in a court of law.
■ For a set of statements to be an argument, one of them must be presented as supported by the other or others.
■ An argument is a logical relation between two or more statements: a conclusion that makes a claim of some sort, and one or more premises that are the reasons offered to support that claim.
Argument Analysis
One essential competence that all logical thinkers must have is the ability to analyze
arguments, a technique summarized in Box 5. What, exactly, is required for this competence? It
involves knowing
1. How to recognize arguments, 2. How to identify the logical relation between their parts, and 3. How to evaluate arguments.
Recognizing an argument requires identifying the logical relations among the statements that
make it up, which is essential to the process of reconstructing an argument. Reconstruction
begins by paying close attention to the piece of spoken or written language that might contain
an argument. One must read a passage carefully or listen attentively in order to determine
whether or not a claim is being made, with reasons offered in support of it. If we have identified
a conclusion and at least one premise, we can then be confident that the passage does contain
an argument. The next step is to put the parts of the argument into an orderly arrangement, so
that the relation between premise/s and conclusion becomes plain.
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BOX 5 ■ THE STEPS IN ARGUMENT ANALYSIS
Argument or
Nonargument?
Nonargument: Argument:
STOP Proceed to
Analysis
Argument
Aecon8tructlon
Argument
Evaluation
Argument reconstruction is the first step in argument analysis, and argument evalua tion is the second. But before argument analysis can get started, we need to determine whether the passage under consideration contains an argument or not. If it does, then we proceed to argument reconstruction: we first make sure that we have identified premises and conclusion correctly. To do that, it’s helpful to rewrite these parts of the argument in logical order, placing the conclusion at the end. During argument evaluation, we assess whether the argument’s premises do actually succeed in supporting its conclusion, thereby giving good reasons for it. But before we can move ahead to the evaluation of arguments, we
must reconstruct them properly. There is, then, one important thing to which we must pay attention before we can go further, and that is the matter of how to distinguish correctly
between premises and conclusion.
1.4 Reconstructing Arguments
Identifying Premises and Conclusion
Let’s now reconstruct arguments (6) through (9) from the previous section of this chapter. For each argument, we rewrite its premise/s first and the conclusion last, listing each of these
statements with a number, which makes it easy to refer to them later if needed. If there are two or more premises, for our purposes here, the order does not matter. It is also customary to introduce, before the conclusion, either a horizontal line or the word ‘therefore’ to indicate that what comes next is the conclusion. In a reconstructed argument, then, we use the line to signal that a conclusion is being drawn; when you see it, you should think: ‘therefore.’ Thus re constructed, (6) through (9) are as follows:
6′ 1. I think.
2. I am.
7′ 1. All lawyers are attorneys. 2. Jack McCoy is a lawyer. 3. Jack McCoy is an attorney.
8′ 1. No chiropractors are surgeons. 2. Only surgeons can legally perform a coronary bypass. 3. No chiropractors can legally perform a coronary bypass.
9′ 1. A Chevrolet Impala is faster than a bicycle. 2. A Maserati is faster than a Chevrolet Impala. 3. A Japanese bullet train is faster than a Maserati. 4. A Japanese bullet train is faster than a bicycle.
Examples (6′), (7′), (8′), and (9′) all have at least one premise, but, as shown here, there may be more-in principle, there is no upper limit to how many premises an argument could have. In all these reconstructed arguments, the premise/s have been listed first and the conclusion last. But ‘premise’ does not mean ‘statement that comes first.’ Nor does ‘conclusion’ mean ‘state ment that comes last.’ Rather, a premise is a reason for an argument’s conclusion: its job is to support it. And the conclusion is the claim that is to be supported. Sometimes the conclusion of an unreconstructed argument does come last, but it does not have to: it can come at the beginning of the argument, or in the middle of it, surrounded by premises. The same holds for the premises of unreconstructed arguments: although they sometimes come at the beginning, they don’t have to. They can come after the conclusion; or there can be some premises at the beginning, then the conclusion, then more premises. What is essential to a premise is that it is a statement offered in support of some other statement (the conclusion). As we shall see later, sometimes the attempted support succeeds, and other times it fails. But let us now consider some more examples of arguments.
1 0 Aunt Theresa won’t vote in the Republican primary next week, because she is a Democrat, and Democrats can’t vote in a Republican primary election.
11 Simon’s cell phone will cause an incident at the Metropolitan Museum, since art museums don’t allow cell phone use in the galleries, and Simon’s is always ringing.
12 It gets lousy gas mileage, so I ought to sell the SUV as soon as possible! After all, it is just too expensive to maintain that vehicle, and besides, it pollutes the atmosphere worse than a regular car.
In each of these arguments, the conclusion is in underlined. As you can see, in both (10) and (n) it comes first, followed by two premises. But in (12), a premise comes first, followed by the conclusion, which is itself followed by two more premises.
Premise and Conclusion Indicators
We have seen that the premises of an argument are sentences offered in support of a certain claim or conclusion. But how can we tell, in any actual argument, which is which? As the examples considered so far demonstrate, when arguments are presented in natural language, the order of premises and conclusion can be scrambled in various ways. So how do we distinguish one from the other? Fortunately, certain words and phrases are often helpful
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in determining this. These are of two kinds: premise indicators and conclusion indicators.
Premise indicators include such expressions as
because since for
given that assuming that provided that
as whereas after all
for the reason that inasmuch as in that
follows from is a consequence of considering that
When we see one of these expressions, it very often means that a premise is coming next.
In other words, one of these (or another synonymous expression) may precede the statements
of an argument that are its premises. You can see this in some of the earlier example
arguments. Recall
10 Aunt Theresa won’t vote in the Republican primary next week, because she is a
Democrat, and Democrats can’t vote in a Republican primary election.
11 Simon’s cell phone will cause an incident at the Metropolitan Museum, since art
museums don’t allow cell phone use in the galleries, and Simon’s is always ringing .
In (10), ‘because’ is used as a premise indicator; in (11), the premise indicator is ‘since.’ In (12),
‘after all’ functions as an indicator of two of its premises:
12 It gets lousy gas mileage, so I ought to sell the SUV as soon as possible! After all, it is
just too expensive to maintain that vehicle, and besides, it pollutes the atmosphere
worse than a regular car.
We must, however, be careful here. This method is more like a rule of thumb and is not one
hundred percent dependable-not all occurrences of these words and phrases actually do
indicate that premises are coming next. But many do. How to recognize when they mean this,
and when they don’t, is a competence acquired with practice, and you’ll be getting some of
that when you do the exercises in this chapter.
Conclusion indicators also have different degrees of reliability. Here is a list of some
conclusion indicators:
therefore hence so entails that
suggests that accordingly supports that consequently
from this we can see that we may conclude that we may infer that it follows that
thus recommends that for this reason as a result
When we see a conclusion indicator, it often means that a conclusion is coming after it.
Arguments containing such indicators can be seen in some of the examples in this chapter. In
(6), ‘therefore’ functions as a conclusion indicator, as does ‘thus’ in (7):
6 I think, therefore I am.
7 All lawyers are attorneys.Jack McCoy is a lawyer. Thus Jack McCoy is an attorney.
In (8), the conclusion indicator is ‘hence’; in (9), it’s ‘it follows that’:
8 No chiropractors are surgeons. Only surgeons can legally perform a coronary bypass.
Hence, no chiropractors can legally perform a coronary bypass.
9 A Chevrolet Impala is faster than a bicycle. A Maserati is faster than a Chevrolet
Impala. A Japanese bullet train is faster than a Maserati. It follows that a Japanese
bullet train is faster than a bicycle.
Again, you will get more practice in recognizing conclusion indicators when you do the exercises in this chapter. But, as just noted, premise and conclusion indicators are reliable only
for the most part and not in all cases. What, then, are some cases where these expressions do not
function as indicators of premises or conclusions? Consider the following:
13 Since he first came to New York in 1979, Max has read El Diario every day.
14 Alice took out a health insurance policy on her own, because her employer did not
provide a health plan as a part of her employment contract.
In (13) ‘since’ is not functioning as a premise indicator. Although there are two statements
in this sentence, they do not amount to an argument, because neither statement attempts
to offer support for the other. Here, ‘since’ serves merely to introduce a temporal reference:
the sentence describes a sequence of actions beginning in the past and continuing for
some time. In (14) there are two statements, but it would be a mistake to think of their
relation as an argument. Rather, one statement offers an explanation of the other: the last
statement serves to account for the action described in the first, not to offer support for it.
Here is another case in which words that often are premise indicators have some other
function:
15 The best way to maintain the peace is to be prepared for war. As a means to peace,
disarmament will surely fail.
This is not an argument, because neither statement really attempts to offer support for the
other (in fact, they are both saying much the same thing). This should make us suspect that
‘for,’ in the first statement, and ‘as,’ in the second, are not serving here as premise indicators at
all. This suspicion would be correct-for although both words sometimes serve as premise
indicators, neither is doing so in (15).
Again, we must bear in mind that learning how to recognize when words of these
kinds are functioning as indicators comes with practice. As with learning to ride a bicycle,
one gets better at it by doing it. The more one works at trying to see the distinction and
to draw it correctly, the easier it becomes. You’ll get some practice at this later, in the
exercises.
Arguments with No Premise or Conclusion Indicators
A further problem, however, must be noted at this point: not all arguments have premise or conclusion indicators! Some have none at all. When this happens in an argument, there is
simply no other reliable way of identifying premises and conclusion than to ask yourself:
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What is the claim being made? (that will be the conclusion) and Which statements are offered
in support of the claim that is being made? (those are the premises). Consider this example:
16 Crocodiles aren’t really dangerous at all. I’ve seen them on television many times,
and they seem very peaceful. And I remember seeing Paul Hogan wrestle one in
the movie Crocodile Dundee.
This is plainly an argument-a rather bad one-yet it has no indicators of any kind. Even so,
we can easily see what its conclusion is: it’s the first statement. This is because the first statement
is the claim that the other three statements are supposed to support. That the support here seems
a bit dim-witted does not change the fact that the last three statements are functioning as
premises. It only means that the argument does not really succeed: it gives no good reason to
accept the conclusion. In (16), then, we don’t really need indicators to be able to recognize
premises and conclusion. When arguments do have some indicators of premises and/or the
conclusion, that is usually enough to tell you what’s what. For arguments that lack such
indicators altogether, asking the questions suggested above will be sufficient for this purpose.
Exercises
1 . What is an argument?
2. What are the parts of an argument?
3. How should the parts of an argument be arranged if one wants to make their logical role clear?
4. How many premises could an argument have?
5. What are premises for? What is their purpose with respect to a conclusion?
6. What sense of the word ‘argument’ is irrelevant to logical thinking?
7. What are the steps in argument analysis?
8. What is involved in reconstructing an argument?
9. Can premises with no indicators be identified? Explain.
1 O. What should you ask yourself to identify the conclusion of an argument?
IV. The following expressions usually are premise indicators, conclusion indicators,
or neither. Identify which is which. (For exercises marked with a star; answers can be
found in the back of the book.)
SAMPLE ANSWER: 1 . ‘since’ is a premise indicator
1. since
2. as a result *3. after all
4. if and only if
5. however *6.and
7. thus
*8.perhaps 9. because
*10. for *13. accordingly
11. it follows that 14. we may infer 12. given that 15. just in case
v. In the following arguments, put premises in parentheses and underline the
conclusion. Mark indicators of premises and conclusion, if any. Use angles'<>’
for premise indicators and square brackets ‘[ ]’ for conclusion indicators.
1. SAMPLE: <Since> (all the Dobermans I have known were dangerous) and (my neighbor’s new dog,
Franz, is a Doberman), [it follows that] Franz is dangerous.
2. Reverend Sharpton has no chance of being elected this time, because his campaign is not well
financed , and any politician who is not well financed has no real chance of being elected.
*3. Badgers are native to southern Wisconsin. After all, they are always spotted there.
4. Since all theoretical physicists have studied quadratic equations, no theoretical physicists are
dummies at math, for no one who has studied quadratic equations is a dummy at math.
5. Thousands of salamanders have been observed by naturalists and none has ever been found to be
warm-blooded. We may conclude that no salamanders are warm-blooded animals.
*6. In the past, every person who ever lived did eventually die. This suggests that all human beings are
mortal.
7. Since architects regularly study engineering, Frank Gehry did, for he is an architect.
8. Britney Spears’s new CD is her most innovative album so far. It’s got the best music of any new pop
music CD this year, and all the DJs are playing it on radio stations across the United States.
Accordingly, Britney Spears’s new CD is sure to win an award this year.
*9. Online education is a great option for working adults in general, regardless of their ethnic back
ground. For one thing, there is a large population of working adults who simply are not in a position
to attend a traditional university.
10. Any airline that can successfully pass some of the increases in costs on to its passengers will be able
to recover from higher fuel costs. South Airlink Airlines seems able to successfully pass some of the
increases in costs on to its passengers. As a result, South Airlink Airlines will remain in business.
11. Jackrabbits can be found in Texas. Jackrabbits are speedy rodents. Hence, some speedy rodents
can be found in Texas.
*12. There is evidence that galaxies are flying outward and apart from each other, so the cosmos will grow
darker and colder.
13. The Cubans are planning to boycott the conference, so the Venezuelans will boycott it, too.
14. Since Reverend Windfield will preach an extra-long sermon this Sunday, we may therefore expect
that some of his congregation will fall asleep.
*15. Captain Binnacle will not desert his sinking ship, for only a cowardly captain would desert a sinking
ship, and Captain Binnacle is no coward.
16. A well-known biologist recently admitted having fabricated data on stem-cell experiments. So his
claim that he has a cloned dog is probably false.
17. The French minister of culture has announced that France will not restrict American movies.
Assuming that film critics are right in questioning the overall quality of American movies, it follows that
French movie theaters will soon feature movies of questionable quality.
*18. The University of California at Berkeley is strong in math, for many instructors in its Math Department
have published breakthrough papers in the core areas of mathematics.
19. Her Spanish must be good now. She spent a year in Mexico living with a Mexican family, and she
took courses at the Autonomous University of Mexico.
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