With Good Reason: A Guide to Critical Thinking

With Good Reason: A Guide to Critical Thinking

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Copyright

James Hardy, Christopher Foster, and Gloria Zúñiga y Postigo

With Good Reason: A Guide to Critical Thinking

Editor in Chief, AVP: Steve Wainwright

Executive Editor: Anna Lustig

Development Editor: Rebecca Paynter

Assistant Editor: Jessica Sarra

Editorial Assistant: Lukas Schulze

Production Editor: Catherine Morris

Media Production: Amanda Nixon, LSF Editorial

Copy Editor: Lauri Scherer, LSF Editorial

Photo Researcher: Amanda Nixon, LSF Editorial

Cover Design: Bambang Suparman Ibrahim

Printing Services: Bordeaux

Production Services: Lachina

Permission Editor: D’Stair Permissions Agency

Cover Image: juuce/iStock and espiegle/iStock

ISBN-10: 1621785661

ISBN-13: 978-1-62178-566-8

Copyright © 2015 Bridgepoint Education, Inc.

All rights reserved.

GRANT OF PERMISSION TO PRINT: The copyright owner of this material hereby grants the holder of this publication the right to print these materials for personal use. The holder of this material may print the materials herein for personal use only. Any print, reprint, reproduction or distribution of these materials for commercial use without the express written consent of the copyright owner constitutes a violation of the U.S. Copyright Act, 17 U.S.C. §§ 101-810, as amended.

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About the Authors

James Hardy, Ashford University Dr. James Hardy is lead faculty of the Humanities & Science department at Ashford University. He obtained a PhD in philosophy from Indiana University, a master’s degree in philosophy from the University of Washington, and bachelor’s degrees in philosophy and psychology from Utah State University. He has taught philosophy at multiple universities since 1998 and has had the opportunity to teach across the general education spectrum, including courses in algebra, speech, English, and physics. Dr. Hardy’s favorite part of teaching is watching students get excited about learning, helping them achieve their dreams, and seeing their excitement as new worlds of knowledge open up to them.

Dr. Hardy loves spending time outdoors hiking, backpacking, and canoeing—especially when he can do so with family members. He has lived all over the United States and has always found beauty and natural wonders wherever he has lived. The only time he is happier than when he is in nature is when he is spending time with his family.

Christopher Foster, Ashford University Dr. Christopher Foster is lead faculty of the Humanities & Science department at Ashford University. He holds a PhD in philosophy with a specialization in logic and language and a master’s degree in philosophy from the University of Kansas (KU). His undergraduate work was completed at the University of California–Davis, where he earned bachelor’s degrees in mathematics and philosophy. Dr. Foster began his career as a graduate teaching assistant at KU and went on to teach at Brigham Young University and Utah Valley University. Dr. Foster has a passion for philosophy and believes that digging deeply into life’s ultimate questions is often the best way to improve students’ critical thinking and writing skills. He lives in Orem, Utah, with his wife, Cherie, and two daughters, Avery and Adia.

Gloria Zúñiga y Postigo, Ashford University Dr. Gloria Zúñiga y Postigo is lead faculty of the Humanities & Science department at Ashford University. She earned a PhD in philosophy from the University at Buffalo, specializing in ontology, ethics, and philosophy of economics. Her previous studies are in philosophy at the University of California–Berkeley and economics at California State University–East Bay. Dr. Zúñiga y Postigo’s present research interests include examinations of the affect in our experiences of moral, aesthetic, and economic phenomena; and value in the Brentano School, the Menger School, and the Göttingen Circle scholars. Teaching philosophy is one her greatest passions. She especially enjoys teaching informal logic, because it empowers students with a tool for distinguishing truth from the mere appearance of truth, thereby making it possible for them to achieve ful�illing lives with greater ef�icacy.

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Acknowledgments

The authors would like to acknowledge the people who made signi�icant contributions to the development of this text: Anna Lustig, executive editor; Rebecca Paynter, development editor; Jessica Sarra, assistant editor; Lukas Schulze, editorial assistant; Catherine Morris, production editor; Amanda Nixon, media production; and Lauri Scherer and LSF Editorial, copy editors. Additional thanks go to Justin Harrison and Marc Joseph for their work creating and accuracy checking the ancillary materials for this text.

The authors would also like to thank the following reviewers, as well as other anonymous reviewers, for their valuable feedback and insight:

Justin Harrison, Ashford University

Mark Hébert, Austin College

Marc Joseph, Mills College

Stephen Krogh, Ashford University

Renee Levant, Ashford University

Andrew Magrath, Kent State University

Zachary Martin, Florida State University

John McAteer, Ashford University

Bradley Thames, Ashford University

Finally, but not least importantly, the authors would like to acknowledge their respective spouses—Teresa Hardy, Cherie Farnes, and Jacob Arfwedson—for their loving understanding of the long hours that this project demanded, as well as all characters in popular culture (for example, Sherlock Holmes, Mr. Spock, and Dr. House) who have kept logic present in everyday conversations. The rewards of our work are enriched by the former and reassured by the latter.

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Preface

With Good Reason: A Guide to Critical Thinking examines the speci�ic ways we use language to reason about things. The study of logic improves our ability to think. It forces us to pay closer attention to the way language is used (and misused). It helps make us better at providing good reasons for our decisions. With Good Reason: A Guide to Critical Thinking seeks to help you examine and develop these abilities in order to improve them and to avoid being persuaded by the faulty reasoning of others.

Textbook Features With Good Reason: A Guide to Critical Thinking includes a number of features to help students understand key concepts and think critically:

Everyday Logic boxes give students the opportunity to see principles applied to a variety of real-world scenarios.

A Closer Look boxes give students the chance to explore more in-depth concepts and issues in critical thinking.

Figures illustrate a variety of concepts in easy-to-understand ways.

Practice Problems provide an opportunity for students to exercise the knowledge they have learned in each chapter.

Knowledge Checks test preconceptions about and comprehension of each chapter’s topics and lead to a personalized reading plan based on these results.

Moral of the Story boxes and Chapter Summaries review the key ideas and takeaways in each chapter.

Interactive Features in the e-book allow students to engage with the content on a more dynamic level. Animated scenarios in Logic in Action show students how logic might be used in real life. Consider This interactions invite students to think about various issues in more depth. Interactive exercises in Connecting the Dots give students further opportunities to practice what they have learned.

Key Terms list and de�ine important vocabulary discussed in the chapter, offering an opportunity for a �inal review of chapter concepts. In the e-book, students can click on the term to reveal the de�inition and quiz themselves in the process.

Accessible Anywhere. Anytime.

With Constellation, faculty and students have full access to eTextbooks at their �ingertips. The eTextbooks are instantly accessible on web, mobile, and tablet.

iPhone To download the Constellation iPhone or iPad app, go to the App Store on your device, search for “Constellation for Ashford University,” and download the free application. You may log in to the application with the same username and password used to access Constellation on the web.

NOTE: You will need iOS version 7.0 or higher.

Android Tablet and Phone To download the Constellation Android app, go to the Google Play Store on your Android Device, search for “Constellation for Ashford University,” and download the free application. You may log in to the Android application with the same username and password used to access Constellation on the web.

NOTE: You will need a tablet or phone running Android version 2.3 (Gingerbread) or higher.

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Learning Objectives

After reading this chapter, you should be able to:

1. Explain the importance of critical thinking and logic.

2. Describe the relationship between critical thinking and logic.

3. Explain why logical reasoning is a natural human attribute that we all have to develop as a skill.

4. Identify logic as a subject matter applicable to many other disciplines and everyday life.

5. Distinguish the various uses of the word argument that do not pertain to logic.

6. Articulate the importance of language in logical reasoning.

7. Describe the connection between logic and philosophy.

1An Introduction to Critical Thinking and Logic

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This book will introduce you to the tools and practices of critical thinking. Since the main tool for critical thinking is logical reasoning, the better part of this book will be devoted to discussing logic and how to use it effectively to become a critical thinker.

We will start by examining the practical importance of critical thinking and the virtues it requires us to nurture. Then we will explore what logic is and how the tools of logic can help us lead easier and happier lives. We will also brie�ly review a critical concept in logic—the argument—and discuss the importance of language in making good judgments. We will conclude with a snapshot of the historical roots of logic in philosophy.

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Critical thinking involves carefully assessing information and its sources.

1.1 What Is Critical Thinking?

What is critical thinking? What is a critical thinker? Why do you need a guide to think critically? These are good questions, but ones that are seldom asked. Sometimes people are afraid to ask questions because they think that doing so will make them seem ignorant to others. But admitting you do not know something is actually the only way to learn new things and better understand what others are trying to tell you.

There are differing views about what critical thinking is. For the most part, people take bits and pieces of these views and carry on with their often imprecise—and sometimes con�licting—assumptions of what critical thinking may be. However, one of the ideas we will discuss in this book is the fundamental importance of seeking truth. To this end, let us unpack the term critical thinking to better understand its meaning.

First, the word thinking can describe any number of cognitive activities, and there is certainly more than one way to think. We can think analytically, creatively, strategically, and so on (Sousa, 2011). When we think analytically, we take the whole that we are examining—this could be a term, a situation, a scienti�ic phenomenon—and attempt to identify its components. The next step is to examine each component individually and understand how it �its with the other components. For example, we are currently examining the meaning of each of the words in the term critical thinking so we can have a better understanding of what they mean together as a whole.

Analytical thinking is the kind of thinking mostly used in academia, science, and law (including crime scene investigation). In ordinary life, however, you engage in analytical thinking more often than you imagine. For example, think of a time when you felt puzzled by someone else’s comment. You might have tried to recall the original situation and then parsed out the language employed, the context, the mood of the speaker, and the subject of the comment. Identifying the different parts and looking at how each is related to the other, and how together they contribute to the whole, is an act of analytical thinking.

When we think creatively, we are not focused on relationships between parts and their wholes, as we are when we think analytically. Rather, we try to free our minds from any boundaries such as rules or conventions. Instead, our tools are imagination and innovation. Suppose you are cooking, and you do not have all the ingredients called for in your recipe. If you start thinking creatively, you will begin to look for things in your refrigerator and pantry that can substitute for the missing ingredients. But in order to do this, you must let go of the recipe’s expected outcome and conceive of a new direction.

When we think strategically, our focus is to �irst lay out a master plan of action and then break it down into smaller goals that are organized in such a way as to support our outcomes. For example, undertaking a job search involves strategic planning. You must identify due dates for applications, request letters of recommendations, prepare your résumé and cover letters, and so on. Thinking strategically likely extends to many activities in your life, whether you are going grocery shopping or planning a wedding.

What, then, does it mean to think critically? In this case the word critical has nothing to do with criticizing others in a negative way or being surly or cynical. Rather, it refers to the habit of carefully evaluating ideas and beliefs, both those we hear from others and those we formulate on our own, and only accepting those that meet certain standards. While critical thinking can be viewed from a number of different perspectives, we will de�ine critical thinking as the activity of careful assessment and self-assessment in the process of forming

judgments. This means that when we think critically, we become the vigilant guardians of the quality of our thinking.

Simply put, the “critical” in critical thinking refers to a healthy dose of suspicion. This means that critical thinkers do not simply accept what they read or hear from others—even if the information comes from loved ones or is accompanied by plausible-sounding statistics. Instead, critical thinkers check the sources of information. If none are given or the sources are weak or unreliable, they research the information for themselves. Perhaps most importantly, critical thinkers are guided by logical reasoning.

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Can you recall a time when you acted or made a decision while you were experiencing strong emotions? Relying on our emotions to make decisions undermines our ability to develop con�idence in our rational judgments. Moreover, emotional decisions cannot typically be justi�ied and often lead to regret.

Psychologist Barry Schwartz tells a story of how a simple error —and arguably a lack of critical thinking—led a family to fall into the child protective system.

How Lack of Wisdom Creates Problems

As a critical thinker, always ask yourself what is unclear, not understood, or unknown. This is the �irst step in critical thinking because you cannot make good judgments about things that you do not understand or know.

The Importance of Critical Thinking

Why should you care about critical thinking? What can it offer you? Suppose you must make an important decision—about your future career, the person with whom you might want to spend the rest of your life, your �inancial investments, or some other critical matter. What considerations might come to mind? Perhaps you would wonder whether you need to think about it at all or whether you should just, as the old saying goes, “follow your heart.” In doing so, you are already clarifying the nature of your decision: purely rational, purely emotional, or a combination of both.

In following this process you are already starting to think critically. First you started by asking questions. Once you examine the answers, you would then assess whether this information is suf�icient, and perhaps proceed to research further information from reliable sources. Note that in all of these steps, you are making distinctions: You would distinguish between relevant and irrelevant questions, and from the relevant questions, you would distinguish the clear and precise ones from the others. You also would distinguish the answers that are helpful from those that are not. And �inally, you would separate out the good sources for your research, leaving aside the weak and biased ones.

Making distinctions also determines the path that your examination will follow, and herein lies the connection between critical thinking and logic. If you decide you should examine the best reasons that support each of the possible options available, then this choice takes you in the direction of logic. One part of logical reasoning is the weighing of evidence. When making an important decision, you will need to identify which factors you consider favorable and which you consider unfavorable. You can then see which option has the strongest evidence in its favor (see Everyday Logic: Evidence, Beliefs, and Good Thinking for a discussion of the importance of evidence).

Consider the following scenario. You are 1 year away from graduating with a degree in business. However, you have a nagging feeling that you are not cut out for business. Based on your research, a business major is practical and can lead to many possibilities for well-paid employment. But you have discovered that you do not enjoy the application or the analysis of quantitative methods—something that seems to be central to most jobs in business. What should you do?

Many would seek advice from trusted people in their lives—people who know them well and thus theoretically might suggest the best option for them. But even those closest to us can offer con�licting advice. A practical parent may point out that it would be wasteful and possibly risky to switch to another major with only 1 more year to go. A re�lective friend may point out that the years spent studying business could be considered simply part of a journey of self-discovery, an investment of time that warded off years of unhappiness after graduation. In these types of situations, critical thinking and logical reasoning can help you sort out competing considerations and avoid making a haphazard decision.

We all �ind ourselves at a crossroads at various times in our lives, and whatever path we choose will determine the direction our lives will take. Some rely on their

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Critical Thinking Questions

1. This clip is from a TED Talk in which Barry Schwartz makes a passionate call for what he calls “practical wisdom” as an antidote to bureaucracy. Based on this clip, what do you think he means by “practical wisdom”? What is its relationship to critical thinking? How do you think one can develop practical wisdom?

2. According to Schwartz, rules often fail us: “Real- world problems are often ambiguous and ill-de�ined, and the context is always changing. . . . A wise person knows when and how to make the exception to every rule . . . a wise person knows how to improvise.” What are some rules that you tend to follow that you think you could break and actually create better outcomes at work, your home, and in your relationships?

emotions to help them make their decisions. Granted, it is dif�icult to deny the power of emotions. We recall more vividly those moments or things in our lives that have had the strongest emotional impact: a favorite toy, a �irst love, a painful loss. Many interpret gut feelings as revelations of what they need to do. It is thus easy to assume that emotions can lead us to truth. Indeed, emotions can reveal phenomena that may be otherwise inaccessible. Empathy, for example, permits us to share or recognize the emotions that others are experiencing (Stein, 1989).

The problem is that, on their own, emotions are not reliable sources of information. Emotions can lead you only toward what feels right or what feels wrong—but cannot guarantee that what feels right or wrong is indeed the right or wrong thing to do. For example, acting sel�ishly, stealing, and lying are all actions that can bring about good feelings because they satisfy our self-serving interests. By contrast, asking for forgiveness or forgiving someone can feel wrong because these actions can unleash feelings of embarrassment, humiliation, and vulnerability. Sometimes emotions can work against our best interests. For example, we are often fooled by false displays of goodwill and even affection, and we often fall for the emotional appeal of a politician’s rhetoric.

The best alternative is the route marked by logical reasoning, the principal tool for developing critical thinking. The purpose of this book is to help you learn this valuable tool. You may be wondering, “What’s in it for me?” For starters, you are bound to gain the peace of mind that comes from knowing that your decisions are not based solely on a whim or a feeling but have the support of the �irmer ground of reason. Despite the compelling nature of your own emotional barometer, you may always wonder whether you made the right

choice, and you may not �ind out until it is too late. Moreover, the emotional route for decision making will not help you develop con�idence in your own judgments in the face of uncertainty.

In contrast, armed with the skill of logical reasoning, you can lead a life that you choose and not a life that just happens to you. This power alone can make the difference between a happy and an unhappy life. Mastering critical thinking results in practical gains—such as the ability to defend your views without feeling intimidated or inadequate and to protect yourself from manipulation or deception. This is what’s in it for you, and this is only the beginning.

Everyday Logic: Evidence, Beliefs, and Good Thinking

It is wrong always, everywhere, and for anyone to believe anything on insuf�icient evidence.

—W. K. Clifford (1879, p. 186)

British philosopher and mathematician W. K. Clifford’s claim—that it is unethical to believe anything if you do not have suf�icient evidence for it—elicited a pronounced response from the philosophical community. Many argued

How Lack of Wisdom Creates Problems From Title: TEDTalks: Barry Schwartz—The Real Crisis? We S…

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that Clifford’s claim was too strong and that it is acceptable to believe things for which we lack the requisite evidence. Whether or not one absolutely agrees with Clifford, he raises a good point. Every day, millions of people make decisions based on insuf�icient evidence. They claim that things are true or false without putting in the time, effort, and research necessary to make those claims with justi�ication.

You have probably witnessed an argument in which people continue to make the same claims until they either begin to become upset or merely continue to restate their positions without adding anything new to the discussion. These situations often devolve and end with statements such as, “Well, I guess we will just agree to disagree” or “You are entitled to your opinion, and I am entitled to mine, and we will just have to leave it at that.” However, upon further re�lection we have to ask ourselves, “Are people really entitled to have any opinion they want?”

From the perspective of critical thinking, the answer is no. Although people are legally entitled to their beliefs and opinions, it would be intellectually irresponsible of them to feel entitled to an opinion that is unsupported by logical reasoning and evidence; people making this claim are con�lating freedom of speech with freedom of opinion. A simple example will illustrate this point. Suppose someone believes that the moon is composed of green cheese. Although he is legally entitled to his belief that the moon is made of green cheese, he is not rationally entitled to that belief, since there are many reasons to believe and much evidence to show that the moon is not composed of green cheese.

Good thinkers constantly question their beliefs and examine multiple sources of evidence to ensure their beliefs are true. Of course, people often hold beliefs that seem warranted but are later found not to be true, such as that the earth is �lat, that it is acceptable to paint baby cribs with lead paint, and so on. However, a good thinker is one who is willing to change his or her views when those views are proved to be false. There are certain criteria that must be met for us to claim that someone is entitled to a speci�ic opinion or position on an issue.

There are other examples where the distinction is not so clear. For instance, some people believe that women should be subservient to men. They hold this belief for many reasons, but the predominant one is because speci�ic religions claim this is the case. Does the fact that a religious text claims that women should serve men provide suf�icient evidence for one to believe this claim? Many people believe it does not. However, many who interpret their religious texts in this manner would claim that these texts do provide suf�icient evidence for such claims.

It is here that we see the danger and dif�iculty of providing hard-and-fast de�initions of what constitutes suf�icient evidence. If we believe that written words in books came directly from divine sources, then we would be prone to give those words the highest credibility in terms of the strength of their evidence. However, if we view written words as arguments presented by their authors, then we would analyze the text based on the evidence and reasoning presented. In the latter case we would �ind that these people are wrong and that they are merely making claims based on their cultural, male-dominated environments.

Of course, all people have the freedom to believe what they want. However, if we think of entitlement as justi�ication, then we cannot say that all people are entitled to their opinions and beliefs. As you read this book, think about what you believe and why. If you do not have reasons or supporting evidence for your beliefs and opinions, you should attempt to �ind it. Try not to get sucked into arguments without having evidence. Most important, as a good thinker, you should be willing and able to admit the strengths and weaknesses of various positions on issues, especially your own. At the same time, if in your search for evidence you �ind that the opposing position is the stronger one, you should be willing to change your position. It is also a sign of good thinking to suspend judgment when you suspect that the arguments of others are not supported by evidence or logical reasoning. Suspending judgment can protect you from error and making rash decisions that lead to negative outcomes.

Becoming a Critical Thinker

By now it should be clear that critical thinking is an important life skill, one that will have a decisive impact on our lives. It does not take luck or a genetic disposition to be a critical thinker. Anyone can master critical thinking skills. So how do

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you become a critical thinker? Earlier in the chapter, logical reasoning was described as the main tool for critical thinking. Thus, the most fundamental step in becoming a critical thinker is to recognize the importance of reason as the �ilter for your beliefs and actions. Once you have done this, you will be in the right frame of mind to start learning about logic and identify what tools of logic are at your disposal.

It is also important to note that becoming a critical thinker demands intellectual modesty. We can understand intellectual modesty as the willingness to put our egos in check because we see truth seeking as a far greater and more satisfying good than seeking to be right. Critical thinkers do not care about seeking approval by trying to show that they are right. They do not assume that disagreement re�lects a lack of intelligence or insight. Being intellectually modest means recognizing not only that we can make mistakes, but also that we have much to learn. If we are (a) aware that we are bound to make mistakes and that we will bene�it when we recognize them; (b) willing to break old habits and embrace change; and, perhaps most importantly, (c) genuinely willing to know what others think, then we can be truly free to experience life as richly and satisfactorily as a human being can.

Practice Problems 1.1

Click on the question to check your answer.

1. When people are engaged in critical thinking, what types of questions do they ask?

When people think critically, they examine things carefully. They question things that others say, especially when those things are not backed with evidence.

2. What does the word “critical” mean in critical thinking?

The word “critical” in critical thinking refers to assessing and evaluating the information that we view around us. Critical does not mean something negative. Instead, it is the act by which we analyze and evaluate information to determine the truth of the information.

3. What does it mean to weigh evidence and why is it important for a critical thinker to weigh evidence?

When people weigh evidence, they examine the truth or falsity of the evidence, the strength of the argument, and the credibility of the author. It is important to weigh evidence when thinking critically about the conclusion or beliefs the evidence is supposed to support. Without analyzing multiple sources and verifying the quality of the evidence, one can fall into the trap of believing something that is not true or making detrimental decisions that lead to negative outcomes.

4. What is a danger of following emotions without consulting reason?

While emotions themselves are not bad or misleading, emotions sometimes merely re�lect the feelings that we have towards things. Feelings can be distorted by past experiences. Sometimes good acts are accompanied by uncomfortable feelings while bad acts are accompanied by pleasure and good feelings. Utilizing reason to evaluate feelings can help determine whether the feelings are aligning with one’s concept of the best acts or decisions.

5. What positive outcomes result from thinking critically?

There are many positive outcomes to thinking critically. One of the most important is gaining the con�idence to present reasons for what you believe. Have you ever been in a situation where you knew that someone was trying to bully you and you just couldn’t quite get out the reasons you have for what you believe? Practicing critical thinking allows us to clearly present the reasons we have for our beliefs. As you will �ind out later in this book, critical thinking skills also help us to point out when others are using illogical techniques to try to bully people or convince others to believe what they believe.

6. Think of a time when you lacked intellectual modesty. What could you have done differently to display more intellectual modesty?

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Your answer will depend on your personal experience, but know that many people �ind it dif�icult to be intellectually modest when others disagree with them. They often respond in anger or lose control and attack the other person. Critical thinkers do not see disagreement as challenging their identity or humanity. Instead, they see disagreement as an opportunity to learn from others. Also, they work to recognize the strengths and weaknesses of their own positions as well as those of others. They readily admit these strengths and weaknesses and are able to separate their beliefs from their inherent identity.

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1.2 Three Misconceptions About Logic

If logic is so important to critical thinking, we must of course examine what logic is. This task is not as easy as it sounds, and before we tackle it we must �irst dismantle some common misconceptions about the subject.

Logic Is for Robots

The �irst misconception is that it is not normal for humans to display a command of logic. (In fact, some suggest that humans created, rather than discovered, these patterns of thought; see A Closer Look: Logic: A Human Invention?) Think of how popular culture and media often depict characters endowed with logical reasoning. In American slang they are the eggheads, the geeks, the nerds, the ones who can use their minds but have trouble relating to other people. Such people often lack compassion or social charisma, or they are emotionally unexpressive. They are only logical and lack the blend of attributes that people actually have.

Consider the logically endowed characters on the Star Trek series. Vulcans, for example, are beings who suppress all emotions in favor of logic because they believe that emotions are dangerous. What appear to be heartless decisions by the Vulcans no doubt make logic seem quite unsavory to some viewers. The android Data—from The Next Generation series in the Star Trek franchise—is another example. Data’s positronic brain is devoid of any emotional capacity and thus processes all information exclusively by means of a logical calculus. Logic is thus presented as a source of alienation, as Data yearns for the affective depth that his human colleagues experience, such as humor and love.

Such presentations of logic as the polar opposite of emotion are false dichotomies because all human beings are naturally endowed with both logical and emotional faculties—not just one or the other. In other words, we have a broader range of abilities than that for which we give ourselves credit. So if you think that you are mostly emotional, then you simply have yet to discover your logical side.

Nonetheless, some believe emotions are the fundamental mark of human beings. It is quite likely that emotion has played a signi�icant role in our survival as a species. Neuroscientists, for example, have discovered that our emotions have a faster pathway to the action centers of the brain than the methodical decision-making approach of our logical faculties (LeDoux, 1986, 1992). It pays, for example, to give no thought to running if we fear we are being hunted by a predator.

In most human civilizations today, however, dodging predators is not a main necessity. In fact, methodical reasoning is more advantageous in most of today’s situations. Thinking things through logically assists learning at all levels, produces better results in the job market (in seeking jobs, obtaining promotions, and procuring raises), and helps us make better choices. As noted in the previous section, we are more likely to be satis�ied and experience fewer regrets if we reason carefully about our most critical choices in life. Indeed, logical reasoning can prove to be a better strategy for attaining the individual quest for personal ful�illment than any available alternative such as random choice, emotional impulse, waiting and seeing, and so on.

Moral of the Story: Emotions Versus Logic

Embracing logical reasoning does not mean disregarding our emotions altogether. Instead, we should recognize that emotions and logic are both essential components of what it is to be human.

A Closer Look: Logic: A Human Invention?

One objection to the use of logic—often from what is known as a postmodern perspective—is that logic is a human invention and thus inferior to emotions or intuitions. In other words, what some call the “rules of logic” cannot be seen as

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Aristotle’s Organon is a compilation of six treatises in which Aristotle formulated principles that laid the foundation for the �ield of logic.

universally applicable because logic originated in the Western world; thus, logic is relative and only a matter of perspective.

For example, the invention of chairs seems indispensable to those of us who live where chairs have become part of our cultural background. But those from different cultural backgrounds or those who lived during different time periods may not use chairs at all, or may employ alternative seating devices, such as the traditional Japanese tatami mats. To broadly apply the concept of chair as an appropriate place to sit would be ethnocentric, or applying the standards of one’s own culture to all other cultures.

In response to the foregoing objection, the authors of this text argue that logic is not a human invention, nor a convention that spread in certain parts of the world. Rather, logic was discovered in people’s ordinary encounters with reality, as early as antiquity. Based on available historical records, the �irst study of the principles at work in good reasoning emerged in ancient Greece. Aristotle was the �irst to formulate principles of logic, and he did so in six treatises that ancient commentators grouped together under the title Organon, which means “instrument” (re�lecting the view that logic is the fundamental instrument for philosophy, which will be discussed later in the chapter).

Importantly, other civilizations have developed logic independently of the Greek tradition. For example, Dignaga was an important thinker in India who lived a few hundred years after Aristotle. Dignaga’s work begins with certain practices of debate within the Nyaya school of Hinduism and transitions to a more formal approach to reasoning. Although the result of Dignaga’s studies is not identical to Aristotle’s, there is enough similarity to strongly suggest that basic logical principles are not merely cultural artifacts.

In the Middle Ages, Aristotelian logic was brought to the West by Islamic philosophers and thus became part of the scholarship of Christian philosophers until the 14th or 15th century. The emergence of modern logic did not take place until the 19th and 20th centuries, during which new ways of analyzing propositions gave rise to new discoveries concerning the foundations of mathematics, as well as a new system of logical notation and a new system of logical principles that replaced the Aristotelian system.

Thus, the examination of good reasoning was fundamental in the development of human civilization. Logical reasoning has helped us to identify the laws that guide physical phenomena, which brought us to the state of technological advancement that we experience today. How else could we have erected pyramids and other marvels in the ancient world without having discovered a principle for checking the accuracy of the geometry employed to design them?

Logic Does Not Need to Be Learned

A second misconception is that logic does not need to be learned. After all, humankind’s unique distinction among other animals is the faculty of rationality and abstract thought. Although many nonhuman animals have very high levels of intelligence, to the best of our knowledge, abstract thought seems to be the mark of humankind’s particular brand of rationality. Today the applications of logical reasoning are all around us. We are able to experience air travel and marvel at rockets in space. We are also able to enjoy cars, skyscrapers, computers, cell phones, air-conditioning, home insulation, and even smart homes that allow users to regulate light, temperature, and other functions remotely via smartphones and other devices. Logical reasoning has afforded us an increasingly better picture of reality, and as a result, our lives have become more comfortable.

However, if logical reasoning is a natural human trait, then why should anyone have to learn it? We certainly experience emotions without any need to be trained, so why would the case be different with our rational capacities? Consider the difference between natural capacities that are nonvoluntary or automatic, on the one hand, and natural capacities that involve our will, on the other. Swallowing, digesting, and breathing are nonvoluntary natural capacities, as are emotions.

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We usually do not will ourselves to feel happy, angry, or excited. Rather, we usually just �ind ourselves feeling happy, angry, or excited.

Now contrast these with voluntary natural capacities such as walking, running, or sitting. We usually need to will these actions in order for them to take place. We do not just �ind ourselves running without intending to run, as is the case with swallowing, breathing, or feeling excited or angry. If logic were akin to breathing, the world would likely look like a different place.

Logic is practiced with intention and must be learned, just like we learn to walk, sit, and run. True, almost everyone learns to run to some degree as part of the normal process of growing up. Similarly, almost everyone learns a certain amount of logical reasoning as they move from infant to adult. However, to be a good runner, you need to learn and practice speci�ic skills. Similarly, although everyone has some ability in logic, becoming a good critical thinker requires learning and practicing a range of logical skills.

Moral of the Story: Logic as a Skill

Having a natural capacity for something does not amount to being good at it. Even as emotions seem to come so naturally, some people have to work at being less sensitive or more empathetic. The same is true for logical reasoning.

Logic Is Too Hard

The �inal misconception is that logic is too hard or dif�icult to learn. If you have survived all these years without studying logic, you might wonder why you should learn it now. It is true that learning logic can be challenging and that it takes time and effort before it feels like second nature. But consider that we face the same challenge whenever we learn anything new, whether it is baking, automotive repair, or astrophysics. These are all areas of human knowledge that have a speci�ic terminology and methodology, and you cannot expect to know how to bake a souf�lé, �ix a valve cap leak, or explain black holes without any investment in learning the subject matter.

Let us return to our running analogy. Just as we must intend to run in order to do it, we must intend to think methodically in order to do it. When we become adept at running, we do not have to put in as much effort or thought. A �it body can perform physical tasks more easily than an un�it one. The mind is no different. A mind accustomed to logical reasoning will �ind activities of the intellect easier than an un�it one. The best part is that if you wish to achieve logical �itness, all you need to do is learn and practice the necessary tools for it. The purpose of this book is to guide you toward this goal.

Without a doubt, learning logic will be challenging. But keep in mind that starting a logical �itness program is very much like starting a physical �itness program: There will be a little pain in the beginning. When out-of-shape muscles are exercised, they hurt. You might �ind that some lessons or concepts might give you a bit of trouble. When this happens, don’t give up! In a physical �itness program, we know that if we keep going, over time the pain goes away, the muscles get in shape, and movement becomes joyful. Likewise, as you keep working diligently on learning and developing your natural logical abilities, you will discover that you understand new things more easily, reading is less of a struggle for you, and logical reasoning is actually fun and rewarding. Eventually, you will begin to recognize logical connections (or the lack thereof) that you did not previously notice, make decisions that you are less likely to regret, and develop the con�idence to defend the positions you hold in a way that is less emotionally taxing.

Practice Problems 1.2

Click on the question to check your answer.

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1. What do you believe is most important in learning critical thinking and logical reasoning skills?

There could be multiple correct answers here. However, it is important to remember that regular practice and tenacity are important skills in learning to think well. You can grow your mind’s ability to think well. However, just like the muscles in your body, the only way to make them strong is to stress and exercise them. If you fail to exercise your mind it will stay the same throughout your life.

2. What is something that you do that does not contribute to exercising your mind? What is an alternative activity or hobby that would help develop your mind more fully?

Answers will vary here, but many people immediately think of television or some other media that does not contribute to their mind’s development. Consider this: You do not need to totally eliminate these activities but instead do them differently. True, you can choose to watch intellectually stimulating programs or read a classic of literature. Or, you might develop the habit of examining your favorite media with a critical mind. For example, you might watch your favorite sitcom through a feminist lens or read the latest 50 Shades of Something novel while thinking of issues of autonomy and ethics. The more you develop your mind, the greater the pleasure you will feel in engaging in higher forms of intellectual activity. It just takes practice and effort.

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In logic, an argument is the methodical presentation of one’s position on a topic, not a heated �ight with another person.

1.3 What Is Logic?

Having dispelled some common misconceptions, we can now occupy ourselves with a fundamental question for this book: What is logic? A �irst attempt to de�ine logic might be to say that it is the study of the methods and principles of good reasoning. This de�inition implies that there are certain principles at work in good reasoning and that certain methods have been developed to encourage it. It is important to clarify that these principles and methods are not a matter of opinion. They apply to someone in your hometown as much as to someone in the smallest village on the other side of the world. Furthermore, they are as suitable today as they were 200 or 2,000 years ago.

This de�inition is a good place to start, but it leaves open the questions of what we mean by “good reasoning” and what makes some reasoning good relative to others. Although it is admittedly dif�icult to cram answers to all possible questions into a pithy statement, de�initions should attempt to be more speci�ic. In this book, we shall employ the following de�inition: Logic is the study of arguments that serve as tools for arriving at warranted judgments. Notice that this de�inition states how logic can be of service to you now, in your daily routine, and in whatever occupation you hold. To understand how this is the case, let us unpack this de�inition a bit.

The Study of Arguments

This de�inition of logic does not explain that there are principles at work in good reasoning or that these principles are not necessarily informed by experience: The meaning of the word argument in logic does the job. Argument has a very technical meaning in logic, and for this reason, Chapter 2 is dedicated entirely to the de�inition of arguments—what they are, what they are not, what they consist of, and what makes them good. Later in this chapter, we will survey other meanings for the word argument outside of logic.

For now, let us refer to an argument as a methodical defense of a position. Suppose that Diana is against a proposed increase in the tax rate. She decides to write a letter to the editor to present her reasons why a tax increase would be detrimental to all. She researches the subject, including what economists have to say about tax increases and the position of the opposition. She then writes an informed defense of her position. By advancing a methodical defense of a position, Diana has prepared an argument.

A Tool for Arriving at Warranted Judgments

For our purposes, the word judgment refers simply to an informed evaluation. You examine the evidence with the goal of verifying that if it is not factual, it is at least probable or theoretically conceivable. When you make a judgment, you are determining whether you think something is true or false, good or bad, right or wrong, beautiful or ugly, real or fake, delicious or disgusting, fun or boring, and so on. It is by means of judgments that we furnish our world of beliefs. The richer our world of beliefs, the clearer we can be about what makes us happy. Judgments are thus very important, so we need to make sure they are sound.

What about the word warrant? Why are warranted judgments preferable to unwarranted ones? What is a warrant? If you are familiar with the criminal justice system or television crime dramas, you may know that a warrant is an authoritative document that permits the search and seizure of potential evidence or the arrest of a person believed to have committed a crime. Without a warrant, such search and seizure, as well as coercing an individual to submit to interrogation or imprisonment, is a violation of the protections and rights that individuals in free societies enjoy. The warrant certi�ies that the search or arrest of a person is justi�ied—that there is suf�icient reason or evidence to show that the search or arrest does not unduly violate the person’s rights. More generally, we say that an action is warranted if it is based on adequate reason or evidence.

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In his Summa Theologica, Thomas Aquinas advanced the idea that belief in the existence of God can be grounded in logical argument.

Accordingly, our judgments are warranted when there is adequate reason or evidence for making them. In contrast, when we speak of something being unwarranted, we mean that it lacks adequate reason or evidence. For example, unwarranted fears are fears we have without good reason. Children may have unwarranted fears of monsters under their beds. They are afraid of the monsters, but they do not have any real evidence that the monsters are there. Our judgments are unwarranted when, like a child’s belief in lurking monsters under the bed, there is little evidence that they are actually true.

In the criminal justice system, the move from suspicion to arrest must be warranted. Similarly, in logic, the move from grounds to judgment must be warranted (see A Closer Look: Warrants for the Belief in God for an example). We want our judgments to be more like a properly executed search warrant than a child’s fear of monsters. If we fail to consider the grounds for our judgments, then we are risking our lives by means of blind decisions; our judgments are no more likely to give us true beliefs than false ones. It is thus essential to master the tools for arriving at warranted judgments.

It is important to recognize the urgency for obtaining such mastery. It is not merely another nice thing to add to the bucket list—something we will get around to doing, right after we trek to the Himalayas. Rather, mastering the argument —the fundamental tool for arriving at warranted judgments—is as essential as learning to read and write. Knowledge of logic is a relatively tiny morsel of information compared to all that you know thus far, but it has the capacity to change your life for the better.

A Closer Look: Warrants for the Belief in God

Striving for warranted judgments might seem dif�icult when it comes to beliefs that we have accepted on faith. Note that not all that we accept on faith is necessarily related to God or religion. For example, we likely have faith that the sun will rise tomorrow, that our spouses are honest with us, and that the car we parked at the mall will still be there when we return from shopping. Many American children have faith that the tooth fairy will exchange money for baby teeth and that Santa Claus will bring toys come Christmas. Are we reasoning correctly by judging such beliefs as warranted? Whatever your answer in regard to these other issues, questions of religious belief are more likely to be held up as beyond the reach of logic. It is important to recognize this idea is far from being obviously true. Many deeply religious people have nonetheless found it advisable to offer arguments in support of their beliefs.

One such individual was Thomas Aquinas, a 13th-century Roman Catholic Dominican priest and philosopher. In his Summa Theologica (Aquinas, 1947), he advanced �ive logical arguments for God’s existence that do not depend on faith.

The 20th-century Oxford scholar and Christian apologist C. S. Lewis, perhaps best known for the popular children’s series The Chronicles of Narnia, did not embrace his Anglican religion until he was in his thirties. In his books Mere Christianity and

Miracles: A Preliminary Study, he employs reason to defend Christian beliefs and the logical possibility of miracles.

There are, of course, many more examples. The important point to draw from this is that all of our judgments of faith—from the faith in the sun rising tomorrow to the faith in the existence of God—should be warranted beliefs and not just beliefs that we readily accept without question. In other words, even faith should make sense in order to be able to communicate such beliefs to those who do not share those beliefs. Note that philosophers who have presented arguments in defense of their religious views have helped transform the nature of religious disagreement to one in which the differences are generally debated in an intellectually enlightening way.

We have not yet reached the point in which differences in religious views are no longer the cause of wars or killing. Nonetheless, the power of argument in the formation of our beliefs is that it supports social harmony despite diversity and disagreement in views, and we all gain from presenting our unique positions in debated issues.

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Formal Versus Informal Logic

Logic is a rich and complex �ield. Our focus here will be how logic contributes to the development and honing of critical thinking in everyday life. Primarily, the concepts we will discuss will re�lect principles of informal logic. The principal aim in informal logic is to examine the reasoning we employ in the ordinary and everyday claims we make.

In contrast, formal logic is far more abstract, often involving the use of symbols and mathematics to analyze arguments. Although this text will touch on a few formal concepts of logic in its discussions of deduction (see Chapter 3 and Chapter 4), the purpose in doing so is to develop methodology for good reasoning that is directly applicable to ordinary life.

Practice Problems 1.3

Click on the question to check your answer.

1. What is a belief you have for which you think you have suf�icient warrant? What about a belief for which you do not have warrant?

Answers will depend on your own beliefs, but remember that warranted beliefs are those for which we have adequate evidence. However, if one does not know how to evaluate evidence then one might believe to have warrant where one does not. For example, the best places to �ind the best information on subjects are peer-reviewed journal articles and academically published books. Many people use the news media or people they know as warrants for their beliefs. Critical thinkers take the extra step and examine the academic literature on the topics for which they are trying to formulate their beliefs.

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1.4 Arguments Outside of Logic

Although Chapter 2 will explore the term argument in more detail, it is important to clarify that the word is not exclusive to logic. Its meaning varies widely, and you may �ind that one of the descriptions in this section �its your own understanding of what is an argument. Knowing there is more than one meaning of this word, depending on context or application, will help you correctly understand what is meant in a given situation.

Arguments in Ordinary Language

Often, we apply the word argument to an exchange of diverging views, sometimes in a heated, angry, or hostile setting. Suppose you have a friend named Lola, and she tells you, “I had an argument with a colleague at work.” In an ordinary setting you might be correct in understanding Lola’s meaning of the term argument as equivalent to a verbal dispute. In logic, however, an argument does not refer to a �ight or an angry dispute. Moreover, in logic an argument does not involve an exchange between two people, and it does not necessarily have an emotional context.

Although in ordinary language an argument requires that at least two or more people be involved in an exchange, this is not the case in logic. A logical argument is typically advanced by only one person, either on his or her behalf or as the representative of a group. No exchange is required. Although an argument may be presented as an objection to another person’s point of view, there need not be an actual exchange of opposing ideas as a result.

Now, if two persons coordinate a presentation of their defenses of what can be identi�ied as opposing points of view, then we have a debate. A debate may contain several arguments but is not itself an argument. Accordingly, only debates are exchanges of diverging views.

Even if a logical argument is both well supported and heartfelt, its emotional context is not its driving force. Rather, any emotion that may be inevitably tied in with the defense of the argument’s principal claim is secondary to the reasons advanced. But let us add a little contextual reference to the matter of debates. If the arguments on each side of the debate are presented well, then the debate may lead to the discovery of perspectives that each party had not previously considered. As such, debates can be quite enlightening because every time our own perspective is broadened with ideas not previously considered and that are well supported and defended, it is very dif�icult for the experience to be negative. Instead, a good debate is an intellectually exhilarating experience, regardless of how attached one may be to the side one is defending.

Not even debates need to be carried out with an angry or hostile demeanor, or as a means to vent one’s frustration or other emotions toward the opposition. To surrender to one’s emotions in the midst of a debate can cause one to lose track of the opposition’s objections and, consequently, be able to muster only weak rebuttals.

Moral of the Story: De�ining the Word Argument

To avoid con�lating the two widely different uses of the word argument (that is, as a dispute in ordinary language and as a defense of a point of view in logic) is to use the word only in its classical sense. In its classical meaning, an argument does not refer to a vehicle to express emotions, complaints, insults, or provocations. For these and all other related meanings, there are a wide variety of terms that would do a better job, such as disagreement, quarrel, bicker, squabble, �ight, brawl, altercation, having words, insult match, word combat, and so on. The more precise we are in our selection of words, the more ef�icient our communications.

Rhetorical Arguments

Think about how politicians might try to persuade you to vote for them. They may appeal to your patriotism. They may suggest that if the other candidate wins, things will go badly. They may choose words and examples that help speci�ic

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audiences feel like the politician empathizes with their situation. All of these techniques can be effective, and all are part of what someone who studies rhetoric—the art of persuasion—might include under the term argument.

Rhetoric is a �ield that uses the word argument almost as much as logic does. You are likely to encounter this use in English, communication, composition, or argumentation classes. From the point of view of rhetoric, an argument is an attempt to persuade—to change someone’s opinion or behavior. Because the goal of a rhetorical argument is persuasion, good arguments are those that are persuasive. In fact, any time someone attempts to persuade you to do something, they can be seen as advancing an argument in this sense.

Think about how you might have persuaded a sibling to do something for you when you were young. You might have offered money, tried to manipulate with guilt-inducing tactics, appealed to his or her sense of pride or duty, or just attempted to reason with him or her. All of these things can be motivating, and all may be part of a rhetorical approach to arguments. However, while getting someone to do something out of greed, guilt, pride, or pity can indeed get you what you want, this does not mean you have succeeded in achieving a justi�ied defense of your position.

Some of the most impressive orators in history—Demosthenes, Cicero, Winston Churchill—were most likely born with a natural talent for rhetoric, yet they groomed their talent by becoming well educated and studying the speeches of previous great orators. Rhetoric depends not only on the mastery of a language and broad knowledge, but also on the �ine-tuning of the use of phrases, metaphors, pauses, crescendos, humor, and other devices. However, a talent for rhetoric can be easily employed by unscrupulous people to manipulate others. This characteristic is precisely what distinguishes rhetorical arguments from arguments in logic.

Whereas rhetorical arguments aim to persuade (often with the intent to manipulate), logical arguments aim to demonstrate. The distinction between persuading and demonstrating is crucial. Persuading requires only the appearance of a strong position, perhaps camou�laged by a strong dose of emotional appeal. But demonstrating requires presenting a position in a way that may be conceivable even by opponents of the position. To achieve this, the argument must be well informed, supported by facts, and free from �lawed reasoning. Of course, an argument can be persuasive (meaning, emotionally appealing) in addition to being logically strong. The important thing to remember is that the fundamental end of logical arguments is not to persuade but to employ good reasoning in order to demonstrate truths.

Moral of the Story: Persuasion Versus Demonstration

Purely persuasive arguments are undoubtedly easier to advance, which makes them the perfect tool for manipulation and deceit. However, only arguments that demonstrate with logic serve the end of pursuing truth; thus, they are the preferable ones to master.

Revisiting Arguments in Logic

Suppose you and your friend watch a political debate, and she tells you that she thought one of the candidates gave a good argument about taxes. You respond that you thought the candidate’s argument was not good. Have you disagreed with each other? You might think that you had, but you may just be speaking past each other, using the term argument in different senses. Your friend may mean that she found the argument persuasive, while you mean that the argument did not establish that the candidate’s position was true. It may turn out that you both agree on these points. Perhaps the candidate gave a rousing call to action regarding tax reform but did not spend much time spelling out the details of his position or how it would work to solve any problems. In this sort of case, the candidate may have given a good argument in the rhetorical sense but a bad argument in the logical sense.

To summarize:

In contrast to ordinary arguments, logical arguments do not involve an exchange of any kind. In contrast to ordinary arguments and rhetorical arguments, logical arguments are not driven by emotions. In logic, only the reasons provided in defense of the conclusion make up the force of the argument.

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In contrast to rhetorical arguments, logical arguments are not primarily attempts to persuade, because there is no attempt to appeal to emotions. Rather, logical arguments attempt only to demonstrate with reasons. Of course, good logical arguments may indeed be persuasive, but persuasion is not the primary goal.

The goal of an argument in logic is to demonstrate that a position is likely to be true.

So before you go on to have a quarrel with your friend, make sure you are both using the word in the same way. Only then can you examine which sense of argument is the most crucial to the problem raised. Should we vote for a candidate who can get us excited about important issues but does not tell us how he or she proposes to solve them? Or shall we vote for a candidate who may not get us very excited but who clearly outlines how he or she is planning to solve the nation’s problems?

In the rest of this book, you should read the word argument in the logical sense and no other. If the word is ever used in other ways, the meaning will be clearly indicated. Furthermore, outside of discussions of logic, you must clarify how the word is being used.

Practice Problems 1.4

Click on the question to check your answer.

1. How is the word “argument” de�ined in logic?

Many people think an argument is a heated verbal exchange between two or more people. However, in logic, the word “argument” has a specialized de�inition. An argument is a list of premises (the reasons) that support a conclusion. In fact, in logic and critical thinking, arguments should be presented outside of the anger that is usually thought of in the typical de�inition.

2. How would you explain the difference between logical argumentation and rhetorical argumentation?

Rhetorical arguments attempt to persuade people to believe something. Logical arguments attempt to convince others that the conclusions are the best positions on issues. While rhetorical arguments often appeal to strong emotions to persuade the audience, logical arguments rely on the presentation of evidence and proper reasoning to support the conclusion on the issue. The goal in a logical argument is not necessarily to persuade.

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Logic in Action: Argument at the Museum

NEXT

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Hume’s essay Of the Standard of Taste stated that taste depends on the re�inement of sensory properties, but recent neurobiological research suggests that taste may actually be dependent on language.

1.5 The Importance of Language in Logic

The foregoing distinction of the different uses and meanings of the word argument show the importance of employing language precisely. In addition to creating misunderstandings, misused words or the lack of knowledge of distinctions in meaning also prevent us from formulating clear positions about matters that pertain to our personal goals and happiness. Language affects how we think, what we experience, how we experience it, and the kind of lives we lead.

Language is our most ef�icient means of communicating what is in our minds. However, it is not the only means by which humans communicate. We also communicate via facial expressions, gestures, and emotions. However, these nonverbal cues often need clarifying words so we can clearly grasp what someone else is expressing or feeling, especially people we don’t know very well. If we see a stranger crying, for example, we might not be able to distinguish at �irst glance if the tears are from happiness or sadness. If we are visiting a foreign land and hear a man speaking in a loud voice and gesturing wildly, we might not know if he is quarrelling or just very enthusiastic unless we understand his language.

This suggests that words matter very much because they are the universal means for making ourselves clear to others. This may seem obvious, since we all use language to communicate and, generally speaking, seem to manage satisfactorily. What we do not often recognize, however, is the difference we could experience if we took full advantage of clear and precise language in its optimal form. One result could be that many will no longer ignore what we say. Another could be that as our vocabulary expands, we will no longer be limited to what we can express to others or in what we can grasp from our experiences.

Suppose, for example, that you are invited to a dinner that unbeknownst to you introduces you to a spice you have never tasted before. As you savor the food on your plate, you may taste something unfamiliar, but the new �lavor may be too faint for you, amidst the otherwise familiar �lavors of the dish you are consuming. In fact, you may be cognitively unaware of the character of this new �lavor because you are unable to identify it by name and, thus, as a new �lavor category in your experience.

According to philosopher David Hume (1757), many of us do not have a sensitive enough palate to actually recognize new or unfamiliar �lavors in familiar taste experiences. For those who do, it would seem that the test of a sensitive palate lies not with strong �lavors but with faint ones. However, recent neurobiological research suggests that our responses to taste are not entirely dependent on the re�inement of our sensory properties but, rather, on higher levels of linguistic processing (Grabenhorst, Rolls, & Bilderbeck, 2008). In other words, if you cannot describe it, it may be quite possible you are unable to taste it; our ability to skillfully use language thus improves our experience.

Logicians and philosophers in general take language very seriously because it is the best means for expressing our thoughts, to be understood by others, and to clarify ideas that are in need of clari�ication. Communicating in a language, however, is more complex than we recognize. As renowned philosopher John Searle observed, “Speaking a language is engaging in a rule-governed form of behavior” (Searle, 1969, p. 22). This means that whenever we talk or write, we are performing according to speci�ic rules. Pauses in speech are represented by punctuation marks such as commas or periods. If we do not pause, the meaning of the same string of words could change its meaning completely. The same principle applies in writing. But although we are more conscious of making such pauses in speech, sometimes we overlook their importance in writing. A clever saying on a T-shirt illustrates this point, and it reads as follows:

Let’s eat Grandma.

Let’s eat, Grandma.

Commas save lives.

Indeed, even what may seem like a meaningless little comma can dramatically change the meaning of a sentence. If we want to make sure others understand our written meaning, we need to be mindful of relevant punctuation, grammatical

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correctness, and proper spelling. If something is dif�icult to read because the grammar is faulty, punctuation is missing, or the words are misspelled, these obstacles will betray the writer’s meaning.

Moral of the Story: The Importance of Language in Logic

Clarity, precision, and correctness in language are not only important to the practical quest of communicating your ideas to others; they are fundamental to the practice of logical reasoning.

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christinagasner/iStock/Thinkstock

Children’s inquisitive nature personi�ies the act of being philosophical. Asking questions to clarify ideas or seek the truth is fundamental to engaging in philosophy.

Logic and the Pursuit of Truth

1.6 Logic and Philosophy

By this point, you may have noticed that logic and philosophy are often mentioned together. There is good reason for this. Logic is not only an area of philosophy but also its bread and butter. It is important to understand the connection between these two �ields because understanding the pursuit of philosophy will help clarify in your mind the value of logic in your life.

First, however, let us confront the elephant in the room. Some people have no idea what philosophers do. Others think that philosophers simply spend time thinking about things that have little practical use. The stereotypical image of a philosopher, for instance, is a bearded man asking himself: “If a tree falls in the forest and there is no one else to hear it, is there sound?” Your response to this may be: “Why should anyone care?” The fact is that many do, and not only bearded philosophers: Such a question is also critical to those who work at the boundaries of philosophy and science, as well as scientists who investigate the nature of sound, such as physicists, researchers in medicine and therapy, and those in the industry of sound technology.

Spatial views regarding sound, for example, have given rise to three theories: (a) sound is where there is a hearer, (b) sound is in the medium between the resonating sound and the hearer, and (c) sound is at the resonating object (Casati & Dokic, 2014). Accordingly, the tree in the forest question would have the following three corresponding answers: (a) no, if sound is where there is a hearer; (b) no, if sound is in the medium between the resonating sound and a hearer; and (c) yes, if sound is located in the resonating object such as a human ear. This seemingly impractical question, as it turns out, is not only quite interesting but also bears tangible results that lead to our better understanding of acoustics, hearing impairments, and sound technology. The best part is that the results affect us all. Many modern technologies arose from a “tree in the forest” examination.

The Goal of Philosophy

Now that the practical nature of philosophical inquiry has been demonstrated, we can move to a more fruitful examination of what exactly philosophy is. In one view, philosophy is the activity of clarifying ideas. It is an activity because philosophy is not fundamentally a body of knowledge (as is history or biology, for example) but rather an activity. The goal of philosophical activity is to clarify ideas in the quest for truth.

How does one clarify ideas? By asking questions—especially “why?,” “what does that mean?,” and “what do you mean?” Philosophers have observed that asking such questions may be a natural human inclination. Consider any 2-year-old. As he or she begins to command the use of language, the child’s quest seems to be an attempt to understand the world by identifying what things are called. This may be annoying to some adults, but if we understand this activity as philosophical, the child’s goal is clear: Names are associated with meanings, and this process of making distinctions and comparisons of similarity is essentially the philosophical mechanism for learning (Sokolowski, 1998).

Once we name things, we can distinguish things that are similar because names help us separate things that appear alike. To a 2-year-old, a toy car and a toy truck may appear similar—both are vehicles, for example, and have four tires—but their different names re�lect that there are also differences between them. So a 2-year-old will most likely go on to ask questions such as why a car is not the same as a truck until she grasps the fundamental differences between these two things. This is the truth-seeking nature of philosophy.

Philosophy and Logical Reasoning

Since children’s natural learning state is a philosophical attitude, by the time we start elementary school, we

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Like philosophy, logic seeks to discover the truth of our conceptions.

Critical Thinking Questions

1. It is stated that logic brings clarity to our conceptions of the world. Is it possible that through studying logic and applying it to your daily life, some of your long-standing beliefs might shift once you apply the principles of logic?

2. What is the distinction between logic and critical thinking? Are they fundamentally the same? Is logic just a systematic form of critical thinking?

already have a few years of philosophical thinking under our belt. Unfortunately, the philosophical attitude is not always sustained beyond this point. Over time, we stop clarifying ideas because we might get discouraged from asking or we just get tired or complacent. We then begin to accept everything that we are told or shown by those around us, including what we watch on television or learn through social media. Once we stop �iltering what we accept by means of questions, as we did when we were very small children, we become vulnerable to manipulation and deceit.

When we stop using questions to rationally discern among alternatives or to make judgments concerning disputed social problems, we begin to rely entirely on emotions or on past experience as the basis for our decisions and judgments. As discussed earlier in the chapter, although emotions are valid and worthwhile, they can also be unreliable or lead us to make rash decisions. This may be somewhat inconsequential if we are simply buying something on impulse at the mall. But if we make judgments based purely on fear or anger, then emotions have much more dire consequences, perhaps causing us to mistreat or discriminate against others.

Past experience can also be misleading. Consider Jay, a university student, who has done very well in his �irst four university courses. He has found the courses relatively easy and not very demanding, so he assumes that all university courses are easy. He is then surprised when he discovers that Introduction to Physics is a challenging course, when he should have rationally recognized that undertaking a university education is a challenging task. Asking himself questions about the

past courses—subject matter, professor, and so on—may help Jay adjust his expectations.

Let us review two important points that we have discussed so far. First, philosophy is an activity of clarifying ideas. Second, the goal of philosophy is to seek truth about all phenomena in our experience. Logic provides us with an effective method for undertaking the task of philosophy and discovering truths. This view has thus remained mainstream in Western philosophy. When we think philosophically with regard to our mundane practical purposes, logic offers us the tools to break the habit of relying on our emotions, feelings, or our past experiences exclusively for making our decisions. Arriving at this recognition alone in your own case will be part and parcel of your journey, with this book as your guide.

Practice Problems 1.6

Click on the question to check your answer.

1. Think of a time where your past experience led you to draw an improper conclusion about something. What could you have done to protect yourself?

Your answer will depend on your own experience, but know that many people draw conclusions about others based on too little evidence, and this leads them to believe things that are untrue. For example, a handful of terrorists can make people think that all people from a single country are terrorists. If someone

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who robs you is white, you might think that all white people are thieves. It is important to examine large, representative samples of things in order to draw proper inferences from the data.

2. Think of a time when you tried something new and it opened up a new perspective for you. What happened to your life after this event? Why do most people fear trying that which is unfamiliar?

Your answer will depend on your own experiences, but coffee is one excellent example of something that starts out rough and can lead to whole new worlds of experience. When young children try coffee, almost all of them �ind the taste bitter and revolting. When one starts to drink coffee, one might experience something similar. However, at some point when one becomes accustomed to the taste, one can fully appreciate the �lavors and even come to learn the difference between good coffee and bad coffee. The hope is that as you engage in critical thinking you will have a similar experience.

3. Is it important to know the truth, even when the truth is painful or leads to negative outcomes?

This is a dif�icult question. Most philosophers live by the creed that understanding the truth is necessary, even when it causes pain. You might have experienced this. For example, learning that one is an alcoholic is a dif�icult truth. Recognizing that children starve to death around the world every day is dif�icult to comprehend. This is a question that you must answer for yourself. If you undertake the journey toward critical thought you will probably have to confront some dif�icult truths and might even question your own most strongly held beliefs.

4. What is something you have learned in this chapter that can help you make wiser choices? How can you apply what you have learned to your immediate life circumstances?

One simple question you can always ask yourself when it comes to thinking and action is, “Will this decision make my life or the lives of those I care about better?” This question can guide your actions. We all make decisions and perform actions that contribute negatively to our lives. Many times we know that these decisions will lead to negative outcomes but we can’t help but make them. If we can learn to ask ourselves this question and honestly answer it, we can use this as a technique in all life circumstances.

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Summary and Resources

Chapter Summary We have covered a lot of ground in this chapter. First we introduced the ideas of critical thinking and logic as tools that help us identify warranted judgments. In other words, if we have a belief, then logic helps us �ind an argument that warrants either our acceptance or rejection of this belief. By means of arguments, logic thus helps us clarify when our judgments are warranted and our beliefs are likely true. Second, we have presented a preliminary understanding of the argument as a methodical defense of a position advanced in relation to a disputed issue. Arguments provide us with a structure that will help us discern fact from purely emotional appeal and identify sober judgment from wishful thinking. Third, we have de�ined philosophy as an activity of clarifying ideas. As such, it can be applied to ideas in every activity— for example, raising children, learning, tasks at work, cooking, making decisions—and to every discipline—for example, physics, mathematics, economics, biology, information systems, engineering, sociology, and so on.

Chapter 2 will introduce you to the argument, the principal tool of logic. Chapters 3 through 8 will teach you the applications of logical reasoning, and Chapter 9 will show you how the knowledge that you gained can be applied in your everyday life. Approach these chapters methodically: Do a �irst reading to get a general idea, then go back and focus on the details of each section of the chapters, always taking notes. Keep in mind that what you are learning is a method for thinking, so you cannot adopt it simply by reading. Practice what you are learning by doing the indicated exercises and activities.

The goal of this chapter has been to show you why logic is an indispensable tool in your life. (For some thoughts on how critical thinking and logic might apply to your life as a student, see Everyday Logic: Thinking Critically About Your Studies.) Over the course of this book, you will see how logical reasoning can help you make wiser choices. You will also �ind that the bene�its extend beyond yourself, since by developing the habit of good reasoning you will also become more enlightened parents, better spouses, wiser voters, and more productive community members. There is a fundamental humanity in logical reasoning that brings people together rather than alienating them from one another. To achieve the habit of logical reasoning, this book will lead you in a methodical process in which each chapter will provide you with an important element. Each component of this book is not only important but also necessary in learning the tools of logical reasoning.

Everyday Logic: Thinking Critically About Your Studies

You will likely �ind that there are multiple opportunities to apply and develop critical thinking skills in your life, but one of the most obvious opportunities at this juncture should be in your academic career. As you move forward in your studies, the decisions you make about participation and study habits will affect your ability to succeed, so it is important that you approach them thoughtfully, carefully, and even critically. The goal of this feature box is to provide some insight into how good thinkers approach their studies and to offer some concrete methods for developing your own vision of academic success.

How have you approached school and education throughout your life? From a theoretical standpoint, all students know that the goal of college is to leave with skills that will allow them to pursue certain careers or, at the very least, help them survive and pursue their conception of a good life. Recall how interested you were in the world around you as a child or perhaps how excited you became when you acquired a new skill or discovered a new interest. These feelings and experiences are the essence of learning. Unfortunately, many people’s experience in formal education is not one of wonder and enjoyment, but one of boredom and tedium. The experience of the young child who found wonder and joy in discovering new things is often crushed in formal educational experiences.

So what can we do? How can we learn to love learning again and improve our thinking and study skills to make the most of our education? First you must identify and address your weaknesses and bad habits. Do you aim only to pass a class, cramming for tests or doing the bare minimum on assignments, instead of steadily studying, reading, and taking notes for retention and understanding? Do you tune out when you think material is boring? Do you

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avoid asking questions because you are afraid of looking foolish or because it is easier to just accept ideas at face value? Do you allow certain activities to interfere with your studies?

It is impossible to change all of our bad habits instantaneously, but starting with just one or two can make a great difference. Here are some methods you can use to begin the journey toward becoming a better student and thinker:

Avoid trying to multitask while studying, and perhaps even consider “fasting” from any media that tend to distract you or occupy inordinate amounts of your time. Tell others to turn off the TV, Xbox, computer, and so forth when they see you zoning out while engaging in these activities. Keep a journal and record urges that you have to fall into bad habits as well as goals you have for your intellectual and academic future. Make note of your triumphs over those negative urges. Review the journal regularly and re�lect on how you are changing through what you are learning. Surround yourself with people who will push you to higher levels of thinking and social action. Read slowly and repeatedly. Having to read a text more than once does not mean you are a poor reader. The philosopher Friedrich Nietzsche said that to read well, a human must become a cow. What does that mean? It means we need to ruminate, to chew and chew until we can swallow the meal. The process continues until we swallow and the food stays down, becoming nourishment to our minds. Take notes and practice writing skills when you get some free time. Try to learn a new grammar or usage rule every week. For example, do you know exactly when you should use a semicolon? If not, look it up right now. It is a really simple rule. Teach what you are learning to others. One of the best ways to determine if you have knowledge of something is if you can explain it and teach it to someone else. Recognize that this will take years of practice and will probably be slow going at �irst. Remember that small positive changes will add up to a whole new way of thinking and approaching life over time.

Finally, always remember that we are privileged to have the opportunity to pursue education. There are billions of people that will never have the opportunity to go to school or to provide that opportunity to their loved ones. Reformatting our perspective from one of frustration to one of gratitude can do a lot to change the way we approach education and learning. As you move forward this week, think about the following questions and how you might make changes in your own life that will lead to positive intellectual change.

What is my view of education, and what experiences led me to that view? What are my greatest strengths as a student? What are my greatest weaknesses as a student? How do I waste my time, and what might I do to utilize that time more effectively? What is something I can do today that will help me become a better student and thinker? What am I learning, and how has what I have learned changed who I am?

Critical Thinking Questions 1. What does the word critical in critical thinking mean? How would you explain critical thinking to someone you

know? 2. Do you have reasons for your most strongly held beliefs? To what extent are they based on emotions? Are they

based in factual evidence and fair reasoning? Would other people �ind them convincing? 3. Are there beliefs that others hold that make you upset or angry? Why? How might you change your perspective in

order not to react negatively when you hear contradictory beliefs? 4. Is it important to use language clearly? Why or why not? What are some steps that one can take to use language

more clearly? 5. What is a logical argument? What role do you think logical argument could play in your life?

Web Resources

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http://www.criticalthinking.org (http://www.criticalthinking.org) The Foundation for Critical Thinking maintains an extensive website regarding critical thinking and related scholarship.

http://herebedragonsmovie.com (http://herebedragonsmovie.com) If you like to watch videos, Brian Dunning’s Here Be Dragons provides a nice introduction to some of critical thinking’s advantages and tools.

http://philosophy.hku.hk/think/critical/ct.php (http://philosophy.hku.hk/think/critical/ct.php) Hong Kong professors Joe Lau and Jonathan Chan sponsor open courseware on critical thinking at this website. This is a great place to look up speci�ic concepts and ideas within critical thinking.

http://plato.stanford.edu (http://plato.stanford.edu) The Stanford Encyclopedia of Philosophy is an excellent resource for any topics related to philosophy.

http://www.iep.utm.edu (http://www.iep.utm.edu) The Internet Encyclopedia of Philosophy is a peer-reviewed online academic resource of articles on philosophy.

Key Terms

critical thinking

formal logic

informal logic

logic

philosophy

rhetoric

assessment that employs logical reasoning as the principal basis for accepting beliefs or

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Learning Objectives

After reading this chapter, you should be able to:

1. Articulate a clear de�inition of logical argument.

2. Name premise and conclusion indicators.

3. Extract an argument in the standard form from a speech or essay with the aid of paraphrasing.

4. Diagram an argument.

5. Identify two kinds of arguments—deductive and inductive.

6. Distinguish an argument from an explanation.

2The Argument

Rolphot/iStock/Thinkstock

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Chapter 1 de�ined logic as the study of arguments that provides us with the tools for arriving at warranted judgments. The concept of argument is indeed central to this de�inition. In this chapter, then, our focus shall be entirely on de�ining arguments—what they are, how their component parts function, and how learning about arguments helps us lead better lives. Most especially, in this chapter we will introduce the standard argument form, which is the structure that helps us identify arguments and distinguish good ones from bad ones.

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2.1 Arguments in Logic

Chapter 1 provisionally de�ined argument as a methodical defense of a position. We referred to this as the commonsense understanding of the way the word argument is employed in logic. The commonsense de�inition is very useful in helping us recognize a unique form of expression in ordinary human communication. It is part of the human condition to differ in opinion with another person and, in response, to attempt to change that person’s opinion. We may attempt, for example, to provide good reasons for seeing a particular movie or to show that our preferred kind of music is the best. Or we may try to show others that smoking or heavy drinking is harmful. As you will see, these are all arguments in the commonsense understanding of the term.

In Chapter 1 we also distinguished the commonsense understanding of argument from the meaning of argument in ordinary use. Arguments in ordinary use require an exchange between at least two people. As clari�ied in Chapter 1, commonsense arguments do not necessarily involve a dialogue and therefore do not involve an exchange. In fact, one could develop a methodical defense of a position—that is, a commonsense argument—in solitude, simply to examine what it would require to advocate for a particular position. In contrast, arguments, as understood in ordinary use, are characterized by verbal disputes between two or more people and often contain emotional outbursts. Commonsense arguments are not characterized by emotional outbursts, since unbridled emotions present an enormous handicap for the development of a methodical defense of a position.

In logic an argument is a set of claims in which some, called the premises, serve as support for another claim, called the conclusion. The conclusion is the argument’s main claim. For the most part, this technical de�inition of argument is what we shall employ in the remainder of this book, though we may use the commonsense de�inition when talking about less technical examples. Table 2.1 should help clarify which meanings are acceptable within logic. Take a moment to review the table and �ix these de�initions in your mind.

Table 2.1: Comparing meanings for the term argument

Meaning in ordinary use Commonsense meaning Technical meaning in logic

A verbal quarrel or disagreement, often characterized by raised voices and �laring emotions.

The methodical and well-researched defense of a position or point of view advanced in relation to a disputed issue.

A set of claims in which some, called premises, serve as support for another claim, called the conclusion.

Arguments in the technical sense are a primary way in which we can defend a position. Accordingly, we can �ind the structure of logical arguments in commonsense arguments all around us: in letters to the editor, social media, speeches, advertisements, sales pitches, proposals submitted for grant funds or bank loans, job applications, requests for a raise, communications of values to children, marriage proposals, and so on. Arguments often provide the basis on which most of our decisions are made. We read or hear an argument, and if we are convinced by it, then we accept its conclusion. For example, consider the following argument:

“I’m just not a math person.” We hear this all the time from anyone who found high school math challenging. . . . In high school math at least, inborn talent is less important than hard work, preparation, and self-con�idence. This is what high school math teachers, college professors, and private tutors have observed as the pattern of those who become good in high school math. They point out that in any given class, students fall in a wide range of levels of math preparation. This is not due to genetic predisposition. What is rarely observed is that some children come from households in which parents introduce them to math early on and encourage them to practice it. These students will immediately obtain perfect scores while the rest do not. As a result, the students without previous preparation in math immediately assume that those with perfect scores have a natural math talent, without knowing about the preparation that these students had in their homes. In turn, the students who obtain perfect scores assume that they have a natural math talent given their scores relative to the rest of the class, so they are motivated to continue honing their math skills and, by doing this, they cement their top of the class standing. Thus, the belief that math ability cannot change becomes a self-ful�illing prophecy. (Kimball & Smith, 2013)

In this argument, the position defended by the authors is that the belief that math ability cannot change becomes a self- ful�illing prophecy. The authors support this claim with reasons that show good performance in math is not typically the

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result of a natural ability but of having a family support system for learning, a prior preparation in math from home, and continuous practice. It makes the case that it is hard work and preparation that lead to a person’s pro�iciency in math and other subjects, not genetic predisposition. This argument helps us recognize that we frequently accept oft-repeated information as fact without even questioning the basis. As you can see, an argument such as this can provide a solid basis for our everyday decisions, such as encouraging our children to work hard and practice in the subjects they �ind most dif�icult or deciding to obtain a university degree with con�idence later in life.

To understand the more technical de�inition of an argument as a set of premises that support a conclusion, consider the following presentation of the reasoning from the commonsense argument we have just examined.

Good performance in math is not due to genetics.

Good performance in math only requires preparation and continuous practice.

Students who do well initially assume they have natural talent and practice more.

Students who do less well initially assume they do not have natural talent and practice less.

Therefore, believing that one’s math ability cannot change becomes a self-ful�illing prophecy.

Presenting the reasoning this way can do a great deal to clarify the argument and allow us to examine its central claims and reasoning. This is why the �ield of logic adopts the more technical de�inition of argument for much of its work.

Regardless of what we think about math, an important contribution of this argument is that it makes the case that it is hard work and preparation that lead to our pro�iciency in math, and not the factor of genetic predisposition. Logic is much the same way. If you �ind some concepts dif�icult, don’t assume that you just lack talent and that you aren’t a “logic person.” With practice and persistence, anyone can be a logic person.

On your way to becoming a logic person, it is important to remember that not everything that presents a point of view is an argument (see Table 2.2 for examples of arguments and nonarguments). Consider that when one expresses a complaint, command, or explanation, one is indeed expressing a point of view. However, none of these amount to an argument.

Table 2.2: Is it an argument?

Argument Not an argument

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Argument Not an argument

Reprinted with permission from The Hill Times.

Why? This letter to the editor presents a defense of a position.

©Bettmann/Corbis

Why not? This news story just reports facts in a straightforward manner. It does not defend a speci�ic position.

Greg Gibson/Associated Press

Why? This is a photo of former president Bill Clinton making a speech, in which he defends his position that the facts are different than those reported by the media. Not all speeches contain arguments, only those that defend a position.

©MIKE SEGAR/Reuters/Corbis

Why not? This is a debate between two presidential candidates. Although each candidate may present various arguments, the debate as a whole is not an argument. It is not a defense of a position; it is an exchange between two people on various subjects.

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Image Source Pink/Image Source/Thinkstock

What factual claims can you make about this image?

Argument Not an argument

Emmanuel Dunand/AFP/Getty Images

Why? This ad makes a claim and offers a reason for why viewers should take notice.

©James Lawrence/Transtock/Corbis

Why not? This ad has no words, so it makes no speci�ic claim. Even if we try to interpret it to make a claim, no defense is offered.

To help us properly identify logical arguments, we need clear criteria for what a logical argument is. Let us start unpacking what is involved in arguments by addressing their smallest element: the claim.

Claims

A claim is an assertion that something is or is not the case. Claims take the form of declarative sentences. It is important to note that each premise or conclusion consists of one single claim. In other words, each premise or conclusion consists of one single declarative sentence.

Claims can be either true or false. This means that if what is asserted is actually the case, then the claim is true. If the claim does not correspond to what is actually the case, then the claim is false. For example, the claim “milk is in the refrigerator” predicates that the subject of the claim, milk, is in the refrigerator. If this claim corresponds to the facts (if the refrigerator contains milk), then this claim is true. If it does not correspond to the facts (if the refrigerator does not contain milk), then the claim is false.

Not all claims, however, can be easily checked for truth or falsity. For example, the truth of the claim “Jacob has the best wife in the world” cannot be settled easily, even if Jacob is the one asserting this claim (“I have the best wife in the world”). In order to understand what he could possibly mean by “best wife in the world,” we would have to propose the criteria for what makes a good wife in the �irst place, and as if this were not challenging enough, we would then have to establish a method or procedure to make comparisons among good wives. Of course, Jacob could merely mean “I like being married to my wife,” in which case he is not stating a claim about his wife being the best in the world but merely stating a feeling. It is not uncommon to hear people state things that sound like claims but are actually just expressions of preference or affection, and distinguishing between these is often challenging because we are not always clear in the way we employ language. Nonetheless, it is important to note that we often make claims from a particular point of view, and these claims are different from factual claims. Claims that advance a point of view, such

as the example of Jacob’s wife—and especially claims about morality and ethicality—are indeed more challenging to settle as true or false than factual claims, such as “The speed limit here is 55.”

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The important point is that both kinds of claims—the factual claim and the point-of-view claim—assert that something is or is not the case, af�irm or deny a particular predicate of a subject, and can be either true or false. The following sentences are examples of claims that meet these criteria.

There is a full moon tonight. Pecans are better than peanuts. All �lights to Paris are full. BMWs are expensive to maintain. Lola is my sister.

The following are not claims:

Is it raining? Why? Because questions are not, and cannot be, assertions that something is the case. Oh, to be in Paris in the springtime! Why? Because this expresses a sentiment but does not state that anything might be true or false. Buy a BMW! Why? Because a command is not an assertion that something is the case.

We often intend to advance claims in ways that do not present our claims clearly and properly—for example, by means of rhetorical questions, vague expressions of affection, and commands or metaphors that demand interpretation. But it is important to recognize that intention is not suf�icient when communicating with others. In order for our intended claims to be identi�ied as claims, they should meet the three criteria previously mentioned.

Claims are sometimes called propositions. We will use the terms claims and propositions interchangeably in this book. In this chapter we will stick to the word claim, but in subsequent chapters, we will move to the more formal terminology of propositions.

The Standard Argument Form

In informal logic the main method for identifying, constructing, or examining arguments is to extract what we hear or read as arguments and put this in what is known as the standard argument form. It consists of claims, some of which are called premises and one of which is called the conclusion. In the standard argument form, premises are listed �irst, each on a separate line, with the conclusion on the line after the last premise. There are various methods for displaying standard form. Some methods number the premises; others separate the conclusion with a line. We will generally use the following method, prefacing the conclusion with the word therefore:

Premise Premise Therefore, Conclusion

The number of premises can be as few as one and as many as needed. We must approach either extreme with caution given that, on the one hand, a single premise can offer only very limited support for the conclusion, and on the other hand, many premises risk error or confusion. However, there are certain kinds of arguments that, because of their formal structure, may contain only a limited number of premises.

In the standard argument form, each premise or conclusion should be only one sentence long, and premises and conclusions should be stated as clearly and brie�ly as possible. Accordingly, we must avoid premises or conclusions that have multiple sentences or single sentences with multiple claims. The following example shows what not to do:

I live in Boston, and I like clam chowder. My family also lives in Boston. They also like clam chowder. My friends live in Boston. They all like clam chowder, too. Therefore, everyone I know in Boston likes clam chowder.

If you want to make more than one claim about the same subject, then you can break your declarative sentences into several sentences that each contain only one claim. The clam chowder argument can then be rewritten as follows:

I live in Boston.

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I like clam chowder. My family lives in Boston. My family likes clam chowder. My friends live in Boston. My friends like clam chowder.

Therefore, everyone I know in Boston likes clam chowder.

The relationship between premises and the conclusion is that of inference—the process of drawing a claim (the conclusion) from the reasons offered in the premises. The act of reasoning from the premises serves as the glue connecting the premises with the conclusion.

Practice Problems 2.1

Determine whether the following sentences are claims (propositions) or nonclaims (nonpropositions). Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems2.1.pdf) to check your answers.

1. Moby Dick is a great novel. 2. Computers have made our lives easier. 3. If we go to the movies, we will need to drive the minivan. 4. Do you want to drive the minivan to the movies? 5. Drive the minivan. 6. Either I am a human or I am a dog. 7. Michael Jordan was a great football player. 8. Was it time for you to leave? 9. Private property is a right of every American. 10. Universalized health care is communism. 11. Don’t you dare vote for universalized health care. 12. Nietzsche collapsed in a square upon seeing a man beat a horse. 13. Hooray! 14. Those who reject equality seek tyranny. 15. How many feet are in a mile? 16. If you cannot understand the truth value of a claim, then it is not a claim. 17. Something is a claim if and only if it has a truth value. 18. Treat your boss with respect. 19. Men are much less likely to have osteoporosis than women are. 20. Why are women less likely to have heart attacks? 21. Do as we say. 22. I believe that you should do as your parents say. 23. Socrates is mortal. 24. Why did Freud hold such strange beliefs about parent–child relationships? 25. A democracy exists if and only if its citizens participate in autonomous elections. 26. Do your best. 27. The unexamined life is not worth living. 28. Ayn Rand believed that sel�ishness was a virtue. 29. Is sel�ishness a virtue? 30. What people love is not the object of desire, but desire itself. 31. Hey! 32. Those who cannot support themselves should not be supported by taxpayer dollars. 33. Particle and wave behavior are properties of light. 34. Why do we feed so many pounds of plants to animals each year? 35. Go and give your brother a kiss. 36. Because the mind conditions reality, it is impossible to know the thing as such.

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37. The library at the local university has more than 300,000 books. 38. Does the nature of reality consist of an ultimately creative impulse? 39. You are taking a quiz. 40. Are you taking a quiz?

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Punctuation, parentheses, and conclusion indicators all serve as signposts to assist us when deconstructing an argument. They provide important clues about where to �ind the conclusion as well as supporting claims.

2.2 Putting Arguments in the Standard Form

Presenting arguments in the standard argument form is crucial because it provides us with a dispassionate method that will allow us to �ind out whether the argument is good, regardless of how we feel about the subject matter. The �irst step is to identify the fundamental argument being presented.

At �irst it might seem a bit daunting to identify an argument, because arguments typically do not come neatly presented in the standard argument form. Instead, they may come in confusing and unclear language, much like this statement by Special Prosecutor Francis Schmitz of Wisconsin regarding Governor Scott Walker:

Governor Walker was not a target of the investigation. At no time has he been served with a subpoena. . . . While these documents outlined the prosecutor’s legal theory, they did not establish the existence of a crime; rather, they were arguments in support of further investigation to determine if criminal charges against any person or entity are warranted. (Crocker, 2014, para. 7 & 10)

This was a position presented in regard to the investigation of an alleged illegal campaign �inance coordination during the 2011–2012 recall elections (Stein, 2014). Does it claim a vindication of Walker? Or does it suggest that there may be suf�icient evidence to make Walker a central �igure in the investigation? How would you even begin to make heads or tails of such a confusing argument? Do not despair. The remainder of this section will show you exactly what to look for in order to make sense of the most complicated argument. With a little practice, you will be able to do this without much effort.

Find the Conclusion First

Although the conclusion is last in the standard form, the conclusion is the �irst thing to �ind because the conclusion is the main claim in an argument. The other claims—the premises—are present for the sole purpose of supporting the conclusion. Accordingly, if you are able to �ind the conclusion, then you should be able to �ind the premises.

The good news is that language is not only a means for expressing ideas; it also offers a road map for the ideas presented. Chapter 1 underscored the fundamental importance of clear, precise, and correct language in logical reasoning. When used properly, language also offers structures and directions for communicating meaning, thus facilitating our understanding of what others are saying. One punctuation mark—the question mark—tells us that we are confronting a question. A different punctuation mark—the parentheses—tells us that we are being given relevant information but only as an aside or afterthought to the main point; if removed, the parenthetical information would not alter the main point. In the case of arguments, some words serve as signposts identifying conclusions. Take the following example of an argument in the standard argument form:

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

The word therefore indicates that the sentence is a conclusion. In fact, the word therefore is the standard conclusion indicator we will use when constructing arguments in the standard argument form. However, there are other conclusion indicators that are used in ordinary arguments, including:

Consequently . . . So . . . Hence . . .

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Thus . . . Wherefore . . . As a result . . . It follows that . . . For these reasons . . . We may conclude that . . .

When a conclusion indicator is present, it can help identify the conclusion in an argument. Unfortunately, many arguments do not come with conclusion indicators. In such cases start by trying to identify the main point. If you can clearly identify a single main point, then that is likely to be the conclusion. But sometimes you will have to look at a passage closely to �ind the conclusion. Suppose you encounter the following argument:

Don’t you know that driving without a seat belt is dangerous? Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. Besides, in our state you can get �ined $100 if you are caught not wearing one. You ought to wear one even if you are driving a short distance.

Arguments are often longer and more complicated than this one, but let us work with this simple case before trying more complicated examples. You know that the �irst thing you need to do is to look for the conclusion. The problem is that the author of the argument does not use a conclusion indicator. Now what? Nothing to worry about. Just remember that the conclusion is the main claim, so the thing to look for is what the author may be trying to defend. Although the �irst sentence is stated as a question—remember, punctuation marks give us important clues—the author seems to intend to assert that driving without a seat belt is dangerous. In fact, the second sentence offers evidence in support of this claim. On the other hand, the third sentence seems to be important, yet it does not speak to driving without a seat belt being dangerous, only expensive. In the �inal sentence, we �ind a claim that is supported by all the others. Because of this, the �inal sentence presents the conclusion.

Now, it so happens that in this case, the conclusion is at the end of this short argument, but keep in mind that conclusions can be found in various places in essays, such as the beginning or sometimes in the middle. Now that you have identi�ied your �irst piece of the puzzle, we have this:

Premise 1: ? Premise 2: ? Premise 3: ? Therefore, you ought to wear a seat belt whenever you drive.

You might have noticed that the conclusion does not appear as it did in the essay. The original sentence is “You ought to wear one even if you are driving a short distance.” Why did we modify it? Once again, clarity is of the essence in logical reasoning. Conclusions should make the subject clear, so the pronoun one was replaced with the actual subject to which the author is referring: seat belt. In addition, the predicate “even if you are driving a short distance” was rewritten to re�lect the more inclusive point that the author seems to be making: that you should wear a seat belt whenever you drive.

This modi�ication of language, known as paraphrasing, is part of the construction of arguments in the standard argument form. The act of extracting an argument from a longer piece to its fundamental claims in the standard argument form necessarily involves paraphrasing the original language to the clearest and most precise form possible. This concept will be addressed in greater detail later in this section.

Find the Premises Next

After identifying the conclusion, the next thing to do is look for the reasons the author offers in defense of his or her position. These are the premises. As with conclusions, there are premise indicators that serve as signposts that reasons are being offered for the main claim or conclusion. Some examples of premise indicators are:

Since . . . For . . . Given that . . . Because . . . As . . .

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Much like a map will get you from point A to point B, putting an argument into the standard argument form will help you navigate from the conclusion to the premises and vice versa.

Owing to . . . Seeing that . . . May be inferred from . . .

To practice identifying premises, let us return to our seat belt example:

Don’t you know that driving without a seat belt is dangerous? Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. Besides, in our state you can get �ined $100 if you are caught not wearing one. You ought to wear one even if you are driving a short distance.

Notice again that this argument starts with a question: “Don’t you know that driving without a seat belt is dangerous?” The author is not really asking whether you know that driving without a seat belt is dangerous. Rather, the author seems to be asking a rhetorical question —a question that does not actually demand an answer—to assert that driving without a seat belt is dangerous. You should avoid asking rhetorical questions in the essays that you write, because the outcome can be highly uncertain. The success of a rhetorical question depends on the reader or listener �irst understanding the hidden meaning behind the rhetorical question and then correctly articulating the answer you have in mind. This does not always work.

For the sake of this example, however, let us do our best to try to get at the author’s intention. We could paraphrase the �irst premise to the following claim: Driving without a seat belt is dangerous. Does this paraphrased claim serve as a premise in support of the conclusion? In order to answer this, we need to put the conclusion in the form of a question. Again, premises are reasons offered in support of the conclusion, so if we have a well-constructed argument, then the premises should answer why the conclusion is the case. This is what

we would have:

Question: Why must you wear a seat belt whenever you drive?

Answer: Because driving without a seat belt is dangerous.

This works, so the paraphrased claim that we drew from the author’s rhetorical question is indeed a reason in defense of the conclusion. So now we have one more piece of the puzzle:

Premise 1: Driving without a seat belt is dangerous. Premise 2: ? Premise 3: ? Therefore, you ought to wear a seat belt whenever you drive.

Let us now move to the next sentence: “Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.” Is this a claim that can be a support for the conclusion? In other words, if we put the conclusion in the form of a question again as we did before, would this sentence be an adequate reason in response? Let us see.

Question: Why must you wear a seat belt whenever you drive?

Answer: Because statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.

The answer provides a reason in support of the conclusion, and thus, we have another premise. Now we have most of the puzzle completed, as follows:

Premise 1: Driving without a seat belt is dangerous.

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Premise 2: Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. Premise 3: ? Therefore, you ought to wear a seat belt whenever you drive.

We have one more sentence left in the argument, which reads: “Besides, in our state you can get �ined $100 if you are caught not wearing one.” Is this a premise? Well, it is uncertain, since the sentence is not presented in the form of a claim. So let us paraphrase it as a claim as follows: “Not wearing a seat belt can result in a $100 �ine.” This is now a claim, and the paraphrasing has not altered the meaning, so we can proceed to our question: Is this a premise for the argument that we are examining? Once again, let us put the conclusion into a question:

Question: Why must you wear a seat belt whenever you drive?

Answer: Because not wearing a seat belt can result in a $100 �ine.

This is a claim that can be a support for the conclusion, and thus, we have another premise. We can now see the argument presented more formally as follows:

Driving without a seat belt is dangerous. Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. Not wearing a seat belt can result in a $100 �ine. Therefore, you ought to wear a seat belt whenever you drive.

The Necessity of Paraphrasing

As we have discussed, extracting the fundamental claims from a written or a spoken argument often involves paraphrasing. Paraphrasing is not merely an option but rather a necessity in order to uncover the intended argument in the best way possible. Most other arguments presented to you (especially those in the media) will not consist of only premises and the conclusion in clearly identi�iable language. Furthermore, many arguments will be much longer and complicated than the seat belt argument example. Often, arguments are presented with many other sentences that do not serve the purposes of an argument, such as empty rhetorical devices, �iller sentences that aim to manipulate your emotions, and so on. So your task in extracting an argument from such sources is akin to that of a surgeon—removing all those linguistic tumors that obscure the argument in order to reveal the basic claims presented and their supporting evidence. In other words, you should expect to do paraphrasing as a necessary task when you attempt to draw an argument in the standard form from almost any source.

It is important to recognize that not everyone who advances an argument does so clearly or even coherently. This is precisely why the structure of the standard argument form is such a powerful tool to command. It offers you the machinery to distinguish arguments from what are not arguments. It also helps you unearth the elements of an argument that are buried under complicated prose and rhetoric. And it helps you evaluate the worthiness of the argument presented once it has been fully clari�ied. You should paraphrase all claims when presenting them in the standard argument form, whether the claims are implied in a long argumentative essay or speech or in shorter arguments that may be ambiguous or unclear. (To understand the added bene�its, see Everyday Logic: Modesty and Charity.)

Everyday Logic: Modesty and Charity

The goal of paraphrasing is to �ind the best presentation of the premises and conclusions intended. By presenting the argument offered in its best possible light, this will help you see not only how far off the argument is from an optimal defense, but also how good it is despite its bad presentation. Why should you be so charitable?

First we must keep in mind that ideas are important, even if the ideas are not ours. So we must always give our utmost due diligence to the examination of ideas. Sometimes even the roughest presentation of ideas can contain the most impressive pearls of insight. If we are not charitable to the ideas of others, then we might miss out on hidden wisdom.

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Second, modesty is a good intellectual habit to develop. It is very easy to fall into the trap of thinking that our thoughts are the best ones around. This is generally far from the truth. The most fruitful innovations of mankind have been quite unexpected, often as the result of someone paying attention to others’ ideas and coming up with a new way of putting them to use. This applies to all sorts of things, including everything from the ways in which cooking methods turned into regional cuisines, to scienti�ic discoveries, product innovations, and the emergence of the Internet.

That modesty has advantages is not a new idea. In the 1980s Peter Drucker wrote the book Innovation and Entrepreneurship, in which he recounts, among many other stories, the story of how Ray Kroc founded the burger chain McDonald’s®. As the well-known story goes, Kroc bought a hamburger stand from the McDonald brothers, along with their invention of a milkshake machine. Although Kroc never invented anything, his entrepreneurial genius was in seeing the potential of a hamburger, fries, and milkshake business that catered to mothers with little children and turning this vision into a billion-dollar standardized operation (Drucker, 1985/2007).

Even if you dislike McDonald’s, the point is that Kroc noticed the potential for something that many, including the McDonald brothers themselves, had overlooked. Gems are everywhere in the world of ideas, but we often have to dust them off, remove all the excess baggage, and extract what is good in them. Intellectual modesty allows us to do this; we don’t blind ourselves by assuming our own ideas are best. Once we seek to fully understand others’ ideas and allow them to challenge our own, we can do all sorts of good things: understand an idea more clearly, understand someone better, and understand ourselves (our values, what we �ind important, and so on) better as well.

Given that our human social world is characterized by diversity of ideas, modesty also marks the path of cooperation, harmony, and respect among human beings. This is one of the many small ways in which the application of logical reasoning can help us all have better lives and better relations with other people. If we could all use logical reasoning on a regular basis, perhaps we would not have as many wars and atrocities as we have today.

Thinking Analytically

Identifying an argument’s components as we have just done is an example of analytical thinking. When we analyze something, we examine its architectural structure—that is, the relation of the whole to its parts—to identify its parts and to see how the parts �it together as a whole.

Let us examine an excerpt from President Barack Obama’s (2014) speech on Ebola as a way of bringing the new skills from this section all together:

In West Africa, Ebola is now an epidemic of the likes that we have not seen before. It’s spiraling out of control. It is getting worse. It’s spreading faster and exponentially. Today, thousands of people in West Africa are infected. That number could rapidly grow to tens of thousands. And if the outbreak is not stopped now, we could be looking at hundreds of thousands of people infected, with profound political and economic and security implications for all of us. So this is an epidemic that is not just a threat to regional security—it’s a potential threat to global security if these countries break down, if their economies break down, if people panic. That has profound effects on all of us, even if we are not directly contracting the disease. (para. 8)

We have identi�ied “The West African Ebola epidemic is a potential threat to global security” as the conclusion. What are the premises? Read the passage a few times while asking yourself, “Why should I think the epidemic is a global threat?” Obama says that the epidemic is not like others, that it is growing faster and exponentially. He moves from there being thousands of people infected, to tens of thousands, to the possibility of hundreds of thousands. So far, everything is about how fast the epidemic is growing.

In the middle of the seventh sentence, the president switches from talking about the growth of the epidemic to claiming that it has profound economic and security implications. What is the basis for the claim that the growth will have these effects? Notice that it is not in the seventh sentence, at least not explicitly. However, the last part of the eighth sentence

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does address this. In that sentence, Obama suggests three conditions that might lead to a global security threat: “if these countries break down, if their economies break down, if people panic.” So the extreme growth of the epidemic may lead to the breakdown of economies or countries, or it may lead to widespread panic. If any of these things happen, there are “profound effects on all of us.” Therefore, the epidemic is a potential threat to global security. We can now list the premises, and indeed the entire argument, in standard form as follows:

The West African Ebola epidemic is growing extremely fast. If the growth isn’t stopped, the countries may break down. If the growth isn’t stopped, the economies may break down. If the growth isn’t stopped, people may panic. Any of these things would have profound effects on people outside of the region. Therefore, the West African Ebola epidemic is a potential threat to global security.

Notice that putting the argument in standard form may lose some of the �luidity of the original, but it more than makes up for it in increased clarity.

Practice Problems 2.2

Identify the premises and conclusions in the following arguments. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems2.2.pdf) to check your answers.

1. Every time I turn on the radio, all I hear is vulgar language about sex, violence, and drugs. Whether it’s rock and roll or rap, it’s all the same. The trend toward vulgarity has to change. If it doesn’t, younger children will begin speaking in these ways, and this will spoil their innocence.

2. Letting your kids play around on the Internet all day is like dropping them off in downtown Chicago to spend the day by themselves. They will �ind something that gets them into trouble.

3. Too many intravenous drug users continue to risk their lives by sharing dirty needles. This situation could be changed if we were to supply drug addicts with a way to get clean needles. This would lower the rate of AIDS in this high-risk population as well as allow for the opportunity to educate and attempt to aid those who are addicted to heroin and other intravenous drugs.

4. I know that Stephen has a lot of money. His parents drive a Mercedes. His dogs wear cashmere sweaters, and he paid cash for his Hummer.

5. Dogs are better than cats, since they always listen to what their masters say. They also are more fun and energetic.

6. All dogs are warm-blooded. All warm-blooded creatures are mammals. Hence, all dogs are mammals. 7. Chances are that I will not be able to get in to see Slipknot since it is an over-21 show, and Jeffrey, James,

and Sloan were all carded when they tried to get in to the club. 8. This is not the best of all possible worlds, because the best of all possible worlds would not contain

suffering, and this world contains much suffering. 9. Some apples are not bananas. Some bananas are things that are yellow. Therefore, some things that are

yellow are not apples. 10. Since all philosophers are seekers of truth, it follows that no evil human is a seeker after truth, since no

philosophers are evil humans. 11. All squares are triangles, and all triangles are rectangles. So all squares are rectangles. 12. Deciduous trees are trees that shed their leaves. Maple trees are deciduous trees. Thus, maple trees will

shed their leaves at some point during the growing season. 13. Joe must make a lot of money teaching philosophy, since most philosophy professors are rich. 14. Since all mammals are cold-blooded, and all cold-blooded creatures are aquatic, all mammals must be

aquatic. 15. If you drive too fast, you will get into an accident. If you get into an accident, your insurance premiums will

increase. Therefore, if you drive too fast, your insurance premiums will increase. 16. The economy continues to descend into chaos. The stock market still moves down after it makes progress

forward, and unemployment still hovers around 10%. It is going to be a while before things get better in

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the United States. 17. Football is the best sport. The athletes are amazing, and it is extremely complex. 18. We should go to see Avatar tonight. I hear that it has amazing special effects. 19. All doctors are people who are committed to enhancing the health of their patients. No people who

purposely harm others can consider themselves to be doctors. It follows that some people who harm others do not enhance the health of their patients.

20. Guns are necessary. Guns protect people. They give people con�idence that they can defend themselves. Guns also ensure that the government will not be able to take over its citizenry.

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2.3 Representing Arguments Graphically

In the preceding section, we discussed the component parts of an argument and how we can identify each when we encounter them in writing. Although the standard argument form is useful and will be used throughout this book, you may �ind it easier to display the structure of an argument by drawing the connections between the parts of an argument. We will start by learning some simple techniques for diagramming arguments. An argument diagram (also called an argument map) is just a drawing that shows how the various pieces of an argument are related to each other.

Representing Reasons That Support a Conclusion

The simplest argument consists of two claims, one of which supports the other—which means that one is the premise and the other is the conclusion. For example:

There is snow on the ground, so it must be cold outside.

To represent this argument, we put each claim in a box and draw an arrow to show which one supports the other. We can diagram this argument in the following way:

Notice that the claims are represented by simple, complete sentences. The premise is at the start of the arrow, and the conclusion is at the end. The arrow represents the process of inferring the conclusion from the premise. Seeing snow on the ground is indeed a reason for believing that it is cold.

But arguments can be more complex. First, consider that an argument may have more than one line of support. For example:

The important thing here is that the two lines of support are independent of each other. Knowing that it is February in Idaho is a reason for thinking that it is cold outside, even if you do not see snow. Similarly, seeing snow outside is a reason for thinking it is cold regardless of when or where you see it.

Second, it can also be the case that a single line of support contains multiple premises that work together. For example, although February in Idaho offers good grounds for thinking it is cold outside, this reason is strengthened if it also

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happens to be a particularly cold year. A year being particularly cold is not by itself much of a reason to think it is cold outside. Even a cold year will be warm in the summer. But a February day in a cold year is even more likely to be cold than a February day in a warm one. We represent this by starting the arrow at a group of premises (bottom):

Although arrows can sometimes start at a group of claims, they always end at a single claim. This is because every simple argument or inference has only one conclusion, no matter how many premises it may have.

Finally, arguments can form chains with some claims being used as a conclusion for one inference and a premise for another. For example, if your reason for thinking that there is snow on the ground is that your friend John just came in with snow on his boots, this can be indicated in a diagram as follows:

Notice that the claim “There is snow on the ground” is a conclusion for one inference and a premise for another. From these basic patterns we can build extremely complicated arguments.

Representing Counterarguments

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We will discuss one more re�inement, and then we will have all of the basic tools we need for constructing argument maps. Sometimes lines of reasoning count against a conclusion rather than support it. If we look out the window and notice that most of the students outside are not wearing coats, that might lead us to believe that it is not very cold even though it is February and we see snow. We will represent this sort of contrary argument by using a red arrow with a slash through it:

Just as with supporting lines of reasoning, opposing lines may have multiple premises or chains. From the point of view of logic, these lines of opposing reasoning are not really part of the argument. However, such reasoning is often included when presenting an argument, so it is useful to have a way to represent it. This is especially true when you are trying to understand an argument in order to write an essay about it. It is good practice to note what objections an author has already considered so that you do not just repeat them.

With that, you have all the basic tools you need to create argument diagrams. In principle, arguments of any complexity can be represented with diagrams of this sort. In practice, as arguments get more complex, there are many interpretational choices about how to represent them.

Diagramming Ef�iciently

One issue that arises when creating argument diagrams is that including each premise and conclusion can make diagrams large and cumbersome. A common practice is to number each statement in an argument and make the diagram with circled numbers representing each premise and conclusion. See Figure 2.1 for an illustration of the seat belt example from the previous section.

Figure 2.1: Diagramming the structure of an argument

This diagram shows the relationship between each of the sentences in the seat belt example. Here are the claims: 1. Don’t you know that driving without a seat belt is dangerous? 2. Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. 3. Besides, in our state you can get �ined $100 if you are caught not wearing one. 4. You ought to wear one even if you are driving a short distance. Notice how numbering the individual components of each argument and diagramming them will help you see the relationship among the pieces and how the pieces work together to support the conclusion.

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The seat belt example is not a complex argument, but the diagram in Figure 2.1 is able to show how the hidden assertion in the �irst question is supported by the second statement and how, together with the third assertion, the conclusion is supported. Sketching diagrams that show the relationship among the premises and their connections to the conclusion is very helpful in understanding complex arguments. Yet you must keep in mind that the diagramming is the second stage of the process, since you will have to �irst identify the elements of the argument.

Practice Problems 2.3

Consider This: Argument Maps

NEXT

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Draw an argument map of each of the following arguments, using the described method of numbering each statement and making a diagram with circled numbers representing each premise and conclusion. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems2.3.pdf) to check your answers.

1. (1) I know that Stephen has a lot of money. (2) His parents drive a Mercedes. (3) His dogs wear cashmere sweaters, and (4) he paid cash for his Hummer.

2. (1) Guns are necessary. (2) Guns protect people, because (3) they give people con�idence that they can defend themselves. (4) Guns also ensure that the government will not be able to take over its citizenry.

3. (1) If you drive too fast, you will get into an accident. (2) If you get into an accident, your insurance premiums will increase. Therefore, (3) if you drive too fast, your insurance premiums will increase.

4. Since (1) all philosophers are seekers of truth, it follows that (2) no evil human is a seeker after truth, since (3) no philosophers are evil humans.

5. (1) This cat can experience pain. So (2) it has the right to not suffer. (3) Since we shouldn’t cause suffering, (4) we should not harm the cat.

6. (1) If we change the construction of the conveyer belt, then the timing of the line will change. (2) Thus, if the timing of the line doesn’t change, then we didn’t change the construction of the conveyor belt. (3) In fact, the timing of the line hasn’t changed. (4) So that means we didn’t change the conveyer belt.

7. (1) The affordable health care act is becoming less popular. (2) Cultural sentiment is increasingly negative, and (3) the Senate and House are progressively moving toward opposition to it. (4) Just last week �ive Democratic senators joined their Republican counterparts to attempt to block certain aspects of the act.

8. (1) Everyone should have to study logic. (2) It is becoming more important to be able to adapt to changes and (3) to evaluate information in today’s workplace. (4) Logic enhances these abilities. (5) Plus, logic helps protect us against manipulators who try to pawn off their fallacious arguments as truth.

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2.4 Classifying Arguments

There are many ways of classifying arguments. In logic, the broadest division is between deductive and inductive arguments. Recall that Section 2.1 introduced the notion of inference, the process of drawing a judgment from the reasons offered in the premises. The distinction between deductive and inductive arguments is based on the strength of that inference. A conclusion can follow from the premises very tightly or very loosely, and there is a wide range in between. For deductive arguments, the expectation is that the conclusion will follow from the premises necessarily. For inductive arguments, the expectation is that the conclusion will follow from the premises probably but not necessarily. We shall explore these two kinds of arguments in greater depth in subsequent chapters. In this section our goal is to achieve a basic grasp of their respective de�initions and understand how the two types differ from one another. Finally, we will improve our understanding of the concept of an argument by comparing arguments to explanations, which are often mistaken for arguments.

Deductive Arguments

In logic the terms deductive and inductive are used in a technical sense that is somewhat different than the way the terms may be used in other contexts. For example, Sherlock Holmes, the protagonist in Sir Arthur Conan Doyle’s detective novels, often referred to his own style of reasoning as deductive. In fact, the popularity of Sherlock Holmes introduced deductive reasoning into ordinary speech and made it a commonplace term. Unfortunately, deductive reasoning is often misunderstood, and in the case of Sherlock Holmes, his clever style of reasoning is actually more inductive than deductive. For example, in The Adventure of the Cardboard Box, he says:

Let me run over the principal steps. We approached the case, you remember, with an absolutely blank mind, which is always an advantage. We had formed no theories. We were simply there to observe and to draw inferences from our observations. (Doyle, 1892/2008, para. 114)

The foregoing does not describe deductive reasoning as it is employed in logic. In fact, Sherlock Holmes mostly uses inductive rather than deductive reasoning. For now, the simplest way to present deductive arguments is to say that deductive reasoning is the sort of reasoning that we normally encounter in mathematical proofs. In a mathematical proof, as long as you do not make a mistake, you can count on the conclusion being true. If the conclusion is not true, you have either made an error in the proof or assumed something that was false. The same is true of deductive reasoning, because good deductive arguments are characterized by their truth-preserving nature—if the premises are true, then the conclusion is guaranteed to be true also. Consider the following deductive argument:

All married men are husbands. Jacob is a married man. Therefore, Jacob is a husband.

In this example, the conclusion necessarily follows from the given premises. In other words, if it is true that all married men are husbands and, moreover, that Jacob is a married man, then it must be necessarily true that Jacob is a husband.

But suppose that Jacob is a 3-year-old boy, so he is not a married man. Would the argument still be a good deductive argument and, thereby, truth preserving? The answer is yes, because deductive reasoning re�lects the relations between premises and the conclusion such that if it were to be the case that the premises were true, then it would be impossible for the conclusion to be false. If it so happens that Jacob is a 3-year-old boy, then the second premise would not be true, and thus, the necessity for the conclusion to be true is broken.

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However, this does not mean that all we need are true premises and a true conclusion. Good deductive arguments are not free form; rather, they use speci�ic patterns that must be followed strictly in the inferential operation. Although this might sound rigid, the greatest advantage of good deductive arguments is that their precise structure guides us into grasping a truth that we might not otherwise have recognized with the same certainty. The use of deductive reasoning is quite broad —in science, mathematics, and the examination of moral problems, to name a few examples. Subsequent chapters will demonstrate more about the powerful machinery of deductive arguments.

Inductive Arguments

In contrast to deductive arguments, good inductive arguments do not need to be truth preserving. Even those that have true premises do not guarantee the truth of their conclusion. At best, true premises in inductive arguments make the conclusion highly probable. The premises of good inductive arguments offer good grounds for accepting the conclusion, but they do not guarantee its truth. Consider the following example:

The produce at my corner store is stocked by local farmers every day. They have a bakery, too, and they re�ill their shelves with fresh-baked bread twice a day. I have been shopping at my corner store continuously for 5 years, and every day is the same. Therefore, my corner store will have fresh produce and baked goods every day of the week.

Let us suppose that all the premises are true. After 5 years of going to the corner store and getting to know its practices and the quality of its daily offerings, the conclusion would seem to be highly probable. But is it necessarily true? At some point the store may change hands, close, or experience something else that interrupts its normal operations. Such cases show that even though the reasoning is good, the conclusion is not guaranteed to be true just because the premises are true.

Another way to think of what is going on here is to address a likely familiar fact of the human condition: Past experience does not guarantee that the future will be the same. Think of that great car you loved that did not require any expensive maintenance—and then suddenly one day it started to break down bit by bit with age. Time changes the performance of things. Or think of the great quality of a clothing brand you counted on year after year that one day was no longer as good. Products also change with time as the leaders of the manufacturing company change or the standards become somewhat relaxed. Things change. Sometimes the changes are for the better, sometimes for the worse. But our observation of how things are now and have been in the past does not guarantee that things will remain the same in the future. Accordingly, even if the conclusion in our corner store example seems suf�iciently justi�ied for us to venture saying that it is true, the fact is that at some point it could change. At best, we can say that the premises give us good grounds to assert that it is probably true that the store will have good produce and baked goods this coming week.

Despite having a weaker connection between premises and conclusion, inductive arguments are more widely used than deductive arguments. In fact, you have likely been using inductive reasoning your entire life without knowing it. Think about the expectation you have that your car, house, or other object will be in the location you last left it. This expectation is based on good inductive reasoning. You have good reasons for expecting your car to be sitting in the parking space where you left it. We can represent your reasoning as follows:

I left my car in that spot. I have always found my car in the same parking spot I left it in. Therefore, my car will be in that spot when I return.

Of course, having good reason is not the same as having a guarantee, as anyone who has experienced having their vehicle stolen can attest. This is the difference between deductive and inductive arguments. Because inductive arguments only establish that their conclusions are probable, the conclusions can turn out to be false even when the premises are all true. The chance may be small, but there is always a chance. By contrast, a good deductive argument is airtight; it is absolutely impossible for the conclusion to be false when the premises are true. Of course, if one of the premises is false, then neither kind of argument can establish its conclusion. If you misremember which spot you parked in, then you are not likely to �ind your car immediately, even if it is right where you left it.

Arguments Versus Explanations

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Mastering logical reasoning requires not only understanding what arguments are, but also being able to distinguish arguments from their closest conceptual neighbors. Although it might be clear by now why news articles, debates, and commands are not considered arguments, we should take a closer look at explanations, because they are commonly mistaken for arguments and present a similar framework. Arguments provide a methodical defense of a position, presenting evidence by means of premises in support of a conclusion that is disputed. Explanations, in contrast, tell why or how something is the case.

Suppose that we have the following claim:

We have to travel by train instead of by plane.

If you disagree with this decision, then you might question this claim, thus presenting a request for evidence. Accordingly, an argument would be the appropriate response. We could then have the following:

The total cost for plane tickets is $2,000. The total cost for train tickets is $1,000. We have a budget of $1,200 for this trip. Therefore, we have to travel by train instead of by plane.

Now, suppose that you do not question the claim, but you still want to know why we have to travel by train. This is not a request for evidence for the conclusion. Rather, this is a request for the cause that leads to the conclusion. This is thus a request for an explanation, which may be as simple as this:

Because we do not have enough money for plane tickets.

The point of an argument is to establish its main claim as true. The point of an explanation is to say how or why its main claim is true. In arguments, the premises will likely be less controversial than the conclusion. It is dif�icult to convince someone that your conclusion is true if they are even less likely to agree with your premises. In explanations, the thing being explained is likely to be less controversial than the explanation given. There is little reason to explain why or how something is true if the listener does not already accept that it is true. Unlike arguments, then, explanations do not involve contested conclusions but, instead, accepted ones. Their point is to say why or how the primary claim is true, not to provide reasons for believing that it is true. This explanation might be fairly straightforward, but distinguishing between arguments and explanations in real life may seem a bit more blurry.

As an example, suppose you try to start your car one morning and it will not start. You recall that your son drove the car last night and know that he has a bad habit of leaving the lights on. You see the light switch is on. You now understand why the car will not start. In our scenario, you found out your car would not start and then looked around for the reason. After noticing that the light switch was on, you came up with the following explanation:

Your son left the lights on. Leaving the lights on will drain the battery. A drained battery will prevent the car from starting. That’s why your car won’t start.

It is an explanation because you already know that your car will not start; you just want to know why.

On the other hand, suppose that after your son got home last night, you noticed that he left the lights on. Rather than turn them off or tell him to do it, you decide to teach him a lesson by letting the battery go dead. In the morning you have the following conversation with your son:

You: I hope you don’t need to go anywhere with the car this morning.

Son: Why?

You: You left the car’s lights on last night.

Son: So?

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You: The lights will have completely drained the battery. The car won’t start with a dead battery, so it’s not going to start this morning.

In this case the thing you are most sure of is that your son left the lights on. You reason from that to the conclusion that the car will not start. In this scenario, knowing that the lights were left on is a reason for believing that the car will not start. You are trying to convince your son that the car will not start, and the fact that he left the lights on last night is the starting point for doing so. We can show the structure of your argument as follows:

Your son left the lights on. Leaving the lights one will drain the battery. A drained battery will prevent the car from starting. Therefore, your car won’t start.

Notice that the structure of this argument is the same as the structure of the explanation example. The only difference is whether you are trying to show that the car will not start or to understand why it will not start after already realizing that it will not. Finding the structure will help you understand the details of the argument or explanation, but it will not, by itself, help you determine which one you are dealing with. For that, you have to determine what the author is trying to accomplish and what the author sees as common ground with the reader. Understanding the structure of what is said can help you become clearer about what the author is doing, so it is a good thing to look for, but understanding the structure is not enough.

Determining whether a passage is an argument or an explanation is thus often a matter of interpreting the intention of the speaker or writer of the claim. A good �irst step is to identify the main point or central focus of the passage. What you are looking for is the sentence that will be either the conclusion to the argument or the claim being explained. If the author has not done so, paraphrase the main claim as a single, simple sentence. Try to avoid including words like because or therefore in your paraphrase. Ask yourself, if this is an argument, what is its conclusion? Once you have identi�ied the potential conclusion, try to determine whether the author is attempting to convince you that that sentence is true, or whether the author assumes you agree with the sentence and is trying to help you understand why or how the sentence is true. If the author is trying to convince you, then the author is advancing an argument. If the author is trying to help you get a deeper understanding, the author is providing an explanation.

It is important to be able to tell the difference between arguments and explanations both when listening to others and when crafting our own arguments and explanations. This is because arguments and explanations are trying to accomplish different goals; what makes an effective argument may not make an effective explanation.

Moral of the Story: Arguments Versus Explanations

If the main claim is accepted as true from the beginning, then the speaker or writer may be advancing an explanation, not an argument. If the point of a passage is to convince the reader that the main claim is true, then it is most likely an argument. Of course, you may question an explanation, thus requesting an argument that the explanation is correct.

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Summary and Resources

Chapter Summary This chapter introduced the standard argument form, which is the principal tool that we will employ in the ensuing chapters. We examined the elements of an argument in standard form, starting from the fundamental notion of claim to an argument’s proper parts—premises and conclusion—and the relationship between these, or what we call inference. Although the standard argument form is simple, the relationship between those claims we call premises and those we call conclusions is crucial to distinguishing between different kinds of arguments. Diagramming these relationships is merely one way we can analyze arguments more fully.

In this chapter we also brie�ly discussed two kinds of arguments—deductive and inductive. However, each one of these will be addressed individually in subsequent chapters as we employ them in more sophisticated applications. Additionally, we explored how to identify arguments in the sources we encounter, as well as how to extract what we �ind and paraphrase it so that it can be presented in the standard form. Finally, we discussed how to distinguish arguments from explanations and presented a simple method for making such a distinction.

As you continue to read this book, remember that logic is not learned by reading alone. Learning logic demands taking notes of structures and terminology, and it requires practice. Accordingly, practice the exercises provided in each chapter. Once you gain mastery of the standard argument form, you will be able to recognize good arguments from bad arguments, and you will be able to present good arguments in defense of your views. This is a powerful skill to have, and it is now in your hands.

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Critical Thinking Questions 1. Try to �ind a political commercial, and outline the argument that is presented in the commercial. Is it easy or

dif�icult to �ind premises and conclusions in the content of the commercial? Does the argument relate to politics or to something outside of politics? Are there components of the ad that you think attempt to manipulate the viewer? Why or why not?

2. How can you utilize what you have learned in this chapter about arguments in your own life? At work? At home? How does an understanding of being able to outline and structure arguments translate into your everyday activities?

3. Now that you understand the components of an argument, think back to a time that someone you know attempted to provide an argument but failed to do so in a convincing fashion. What were the mistakes that this person made in his or her reasoning? What were the structural or content errors that weakened the argument?

4. Suppose that your child refuses to go to bed. You want to convince your child that he or she needs to get to sleep. You feel the urge to say, “You have to go to bed because I said so.” However, you are now trying to use what you are learning in this course. What argument would you present to your child to try to convince him or her to go to sleep? Do you think that a strong argument would be effective in convincing your child? Why or why not?

5. Suppose you have a coworker who refuses to help you with a mandatory project. You want to convince him that he needs to help you. What premises would you use to support the conclusion that he ought to help you with the project? Assuming that he fails to �ind your argument convincing, what would you do next? Why?

Connecting the Dots Chapter 2

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Web Resources http://austhink.com/critical/pages/argument_mapping.html (http://austhink.com/critical/pages/argument_mapping.html) The group Austhink provides a number of resources on argument mapping, including tutorials on how to diagram arguments.

http://www.manyworldso�logic.com/index.html (http://www.manyworldso�logic.com/index.html) The Many Worlds of Logic website discusses many of the topics that will be covered in this book.

Key Terms

argument The methodical defense of a position advanced in relation to a disputed issue; a set of claims in which some, called premises, serve as support for another claim, called the conclusion.

claim A sentence that presents an assertion that something is the case. In logic, claims are often referred to as propositions in order to recognize that these may be true or false.

conclusion The main claim of an argument; the claim that is supported by the premises but does not itself support any other claims in the argument.

conclusion indicators The words that signal the appearance of a conclusion in an argument.

explanations Statements that tell why or how something is the case. Unlike arguments, explanations do not involve contested conclusions but, instead, accepted ones.

inference The process of drawing the necessary judgment or, at least, the judgment that would follow from the reasons offered in the premises.

premise indicators The words that signal the appearance of a premise in an argument.

premises Claims in an argument that serve as support for the conclusion.

standard argument form The structure of an argument that consists of premises and a conclusion. This structure displays each premise of an argument on a separate line, with the conclusion on a line following all the premises.

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p of claims in which some, called

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Learning Objectives

After reading this chapter, you should be able to:

1. De�ine basic key terms and concepts within deductive reasoning.

2. Use variables to represent an argument’s logical form.

3. Use the counterexample method to evaluate an argument’s validity.

4. Categorize different types of deductive arguments.

5. Analyze the various statements—and the relationships between them—in categorical arguments.

6. Evaluate categorical syllogisms using the rules of the syllogism and Venn diagrams.

7. Differentiate between sorites and enthymemes.

3Deductive Reasoning

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By now you should be familiar with how the �ield of logic views arguments: An argument is just a collection of sentences, one of which is the conclusion and the rest of which, the premises, provide support for the conclusion. You have also learned that not every collection of sentences is an argument. Stories, explanations, questions, and debates are not arguments, for example. The essential feature of an argument is that the premises support, prove, or give evidence for the conclusion. This relationship of support is what makes a collection of sentences an argument and is the special concern of logic. For the next four chapters, we will be taking a closer look at the ways in which premises might support a conclusion. This chapter discusses deductive reasoning, with a speci�ic focus on categorical logic.

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3.1 Basic Concepts in Deductive Reasoning

As noted in Chapter 2, at the broadest level there are two types of arguments: deductive and inductive. The difference between these types is largely a matter of the strength of the connection between premises and conclusion. Inductive arguments are de�ined and discussed in Chapter 5; this chapter focuses on deductive arguments. In this section we will learn about three central concepts: validity, soundness, and deduction.

Validity

Deductive arguments aim to achieve validity, which is an extremely strong connection between the premises and the conclusion. In logic, the word valid is only applied to arguments; therefore, when the concept of validity is discussed in this text, it is solely in reference to arguments, and not to claims, points, or positions. Those expressions may have other uses in other �ields, but in logic, validity is a strict notion that has to do with the strength of the connection between an argument’s premises and conclusion.

To reiterate, an argument is a collection of sentences, one of which (the conclusion) is supposed to follow from the others (the premises). A valid argument is one in which the truth of the premises absolutely guarantees the truth of the conclusion; in other words, it is an argument in which it is impossible for the premises to be true while the conclusion is false. Notice that the de�inition of valid does not say anything about whether the premises are actually true, just whether the conclusion could be false if the premises were true. As an example, here is a silly but valid argument:

Everything made of cheese is tasty. The moon is made of cheese. Therefore, the moon is tasty.

No one, we hope, actually thinks that the moon is made of cheese. You may or may not agree that everything made of cheese is tasty. But you can see that if everything made of cheese were tasty, and if the moon were made of cheese, then the moon would have to be tasty. The truth of that conclusion simply logically follows from the truth of the premises.

Here is another way to better understand the strictness of the concept of validity: You have probably seen some far- fetched movies or read some bizarre books at some point. Books and movies have magic, weird science �iction, hallucinations, and dream sequences—almost anything can happen. Imagine that you were writing a weird, bizarre novel, a novel as far removed from reality as possible. You certainly could write a novel in which the moon was made of cheese. You could write a novel in which everything made of cheese was tasty. But you could not write a novel in which both of these premises were true, but in which the moon turned out not to be tasty. If the moon were made of cheese but was not tasty, then there would be at least one thing that was made of cheese and was not tasty, making the �irst premise false.

Therefore, if we assume, even hypothetically, that the premises are true (even in strange hypothetical scenarios), it logically follows that the conclusion must be as well. Therefore, the argument is valid. So when thinking about whether an argument is valid, think about whether it would be possible to have a movie in which all the premises were true but the conclusion was false. If it is not possible, then the argument is valid.

Here is another, more realistic, example:

All whales are mammals. All mammals breathe air. Therefore, all whales breathe air.

Is it possible for the premises to be true and the conclusion false? Well, imagine that the conclusion is false. In that case there must be at least one whale that does not breathe air. Let us call that whale Fred. Is Fred a mammal? If he is, then there is at least one mammal that does not breathe air, so the second premise would be false. If he isn’t, then there is at least one whale that is not a mammal, so the �irst premise would be false. Again, we see that it is impossible for the conclusion to be false and still have all the premises be true. Therefore, the argument is valid.

Here is an example of an invalid argument:

All whales are mammals.

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Consider the following argument: “If it is raining, then the streets are wet. The streets are wet. Therefore, it is raining.” Is this a valid argument? Could there be another reason why the road is wet?

No whales live on land. Therefore, no mammals live on land.

In this case we can tell that the truth of the conclusion is not guaranteed by the premises because the premises are actually true and the conclusion is actually false. Because a valid argument means that it is impossible for the premises to be true and the conclusion false, we can be sure that an argument in which the premises are actually true and the conclusion is actually false must be invalid. Here is a trickier example of the same principle:

All whales are mammals. Some mammals live in the water. Therefore, some whales live in the water.

This one is trickier because both premises are true, and the conclusion is true as well, so many people may be tempted to call it valid. However, what is important is not whether the premises and conclusion are actually true but whether the premises guarantee that the conclusion is true. Think about making a movie: Could you make a movie that made this argument’s premises true and the conclusion false?

Suppose you make a movie that is set in a future in which whales move back onto land. It would be weird, but not any weirder than other ideas movies have presented. If seals still lived in the water in this movie, then both premises would be true, but the conclusion would be false, because all the whales would live on land.

Because we can create a scenario in which the premises are true and the conclusion is false, it follows that the argument is invalid. So even though the conclusion isn’t actually false, it’s enough that it is possible for it to be false in some situation that would make the premises true. This mere possibility means the argument is invalid.

Soundness

Once you understand what valid means in logic, it is very easy to understand the concept of soundness. A sound argument is just a valid argument in which all the premises are true. In de�ining validity, we saw two examples of valid arguments; one of them was sound and the other was not. Since both examples were valid, the one with true premises was the one that was sound.

We also saw two examples of invalid arguments. Both of those are unsound simply because they are invalid. Sound arguments have to be valid and have all true premises. Notice that since only arguments can be valid, only arguments can be sound. In logic, the concept of soundness is not applied to principles, observations, or anything else. The word sound in logic is only applied to arguments.

Here is an example of a sound argument, similar to one you may recall seeing in Chapter 2:

All men are mortal. Bill Gates is a man. Therefore, Bill Gates is mortal.

There is no question about the argument’s validity. Therefore, as long as these premises are true, it follows that the conclusion must be true as well. Since the premises are, in fact, true, we can reason the conclusion is too.

It is important to note that having a true conclusion is not part of the de�inition of soundness. If we were required to know that the conclusion was true before deciding whether the argument is sound, then we could never use a sound argument to discover the truth of the conclusion; we would already have to know that the conclusion was true before we could judge it to be sound. The magic of how deductive reasoning works is that we can judge whether the reasoning is

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Interpreting the intention of the person making an argument is a key step in

valid independent of whether we know that the premises or conclusion are actually true. If we also notice that the premises are all true, then we may infer, by the power of pure reasoning, the truth of the conclusion.

Therefore, knowledge of the truth of the premises and the ability to reason validly enable us to arrive at some new information: that the conclusion is true as well. This is the main way that logic can add to our bank of knowledge.

Although soundness is central in considering whether to accept an argument’s conclusion, we will not spend much time worrying about it in this book. This is because logic really deals with the connections between sentences rather than the truth of the sentences themselves. If someone presents you with an argument about biology, a logician can help you see whether the argument is valid—but you will need a biologist to tell you whether the premises are true. The truth of the premises themselves, therefore, is not usually a matter of logic. Because the premises can come from any �ield, there would be no way for logic alone to determine whether such premises are true or false. The role of logic—speci�ically, deductive reasoning—is to determine whether the reasoning used is valid.

Deduction

You have likely heard the term deduction used in other contexts: As Chapter 2 noted, the detective Sherlock Holmes (and others) uses deduction to refer to any process by which we infer a conclusion from pieces of evidence. In rhetoric classes and other places, you may hear deduction used to refer to the process of reasoning from general principles to a speci�ic conclusion. These are all acceptable uses of the term in their respective contexts, but they do not re�lect how the concept is de�ined in logic.

In logic, deduction is a technical term. Whatever other meanings the word may have in other contexts, in logic, it has only one meaning: A deductive argument is one that is presented as being valid. In other words, a deductive argument is one that is trying to be valid. If an argument is presented as though it is supposed to be valid, then we may infer it is deductive. If an argument is deductive, then the argument can be evaluated in part on whether it is, in fact, valid. A deductive argument that is not found to be valid has failed in its purpose of demonstrating its conclusion to be true.

In Chapters 5 and 6, we will look at arguments that are not trying to be valid. Those are inductive arguments. As noted in Chapter 2, inductive arguments simply attempt to establish their conclusion as probable—not as absolutely guaranteed. Thus, it is not important to assess whether inductive arguments are valid, since validity is not the goal. However, if a deductive argument is not valid, then it has failed in its goal; therefore, for deductive reasoning, validity is a primary concern.

Consider someone arguing as follows:

All donuts have added sugar. All donuts are bad for you. Therefore, everything with added sugar is bad for you.

Even though the argument is invalid—exactly why this is so will be clearer in the next section—it seems clear that the person thinks it is valid. She is not merely suggesting that maybe things with added sugar might be bad for you. Rather, she is presenting the reasoning as though the premises guarantee the truth of the conclusion. Therefore, it appears to be an attempt at deductive reasoning, even though this one happens to be invalid.

Because our de�inition of validity depends on understanding the author’s intention, this means that deciding whether something is a deductive argument requires a bit of interpretation—we have to �igure out what the person giving the argument is trying to do. As noted brie�ly in Chapter 2, we ought to seek to provide the most favorable possible interpretation of the author’s intended reasoning. Once we know that an argument is deductive, the next question in evaluating it is whether it is valid. If it is deductive but not valid, we really do not

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determining whether the argument is deductive.

need to consider anything further; the argument fails to demonstrate the truth of its conclusion in the intended sense.

Practice Problems 3.1

Examine the following arguments. Then determine whether they are deductive arguments or not. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems3.1.pdf) to check your answers.

1. Charles is hard to work with, since he always interrupts others. Therefore, I do not want to work with Charles in the development committee.

2. No physical object can travel faster than light. An electron is a physical object. So an electron cannot travel faster than light.

3. The study of philosophy makes your soul more slender, healthy, and beautiful. You should study philosophy.

4. We should go to the beach today. It’s sunny. The dolphins are out, and I have a bottle of �ine wine. 5. Triangle A is congruent to triangle B. Triangle A is an equilateral triangle. Therefore, triangle B is an

equilateral triangle. 6. The farmers in Poland have produced more than 500 bushels of wheat a year on average for the past 10

years. This year they will produce more than 500 bushels of wheat. 7. No dogs are �ish. Some guppies are �ish. Therefore, some guppies are not dogs. 8. Paying people to mow your lawn is not a good policy. When people mow their own lawns, they create self-

discipline. In addition, they are able to save a lot of money over time. 9. If Mount Roosevelt was completed in 1940, then it’s only 73 years old. Mount Roosevelt is not 73 years

old. Therefore, Mount Roosevelt was not completed in 1940. 10. You’re either with me, or you’re against me. You’re not with me. Therefore, you’re against me. 11. The worldwide use of oil is projected to increase by 33% over the next 5 years. However, reserves of oil

are dwindling at a rapid rate. That means that the price of oil will drastically increase over the next 5 years.

12. A nation is only as great as its people. The people are reliant on their leaders. Leaders create the laws in which all people can �lourish. If those laws are not created well, the people will suffer. This is why the people of the United States are currently suffering.

13. If we save up money for a house, then we will have a place to stay with our children. However, we haven’t saved up any money for a house. Therefore, we won’t have a place to stay with our children.

14. We have to focus all of our efforts on marketing because right now; we don’t have any idea of who our customers are.

15. Walking is great exercise. When people exercise they are happier and they feel better about themselves. I’m going to start walking 4 miles every day.

16. Because all libertarians believe in more individual freedom, all people who believe in individual freedom are libertarians.

17. Our dogs are extremely sick. I have to work every day this week, and our house is a mess. There’s no way I’m having my family over for Festivus.

18. Pigs are smarter than dogs. Animals that are easier to train are smarter than other animals. Pigs are easier to train than dogs.

19. Seventy percent of the students at this university come from upper class families. The school budget has taken a hit since the economic downturn. We need funding for the three new buildings on campus. I think it’s time for us to start a phone campaign to raise funds so that we don’t plunge into bankruptcy.

20. If she wanted me to buy her a drink, she would’ve looked over at me. But she never looked over at me. So that means that she doesn’t want me to buy her a drink.

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In addition to his well- known literary works, Lewis Carroll wrote several mathematical works, including three books on logic: Symbolic Logic Parts 1 and 2, and The Game of Logic, which was intended to introduce logic to children.

3.2 Evaluating Deductive Arguments

If validity is so critical in evaluating deductive arguments, how do we go about determining whether an argument is valid or invalid? In deductive reasoning, the key is to look at the pattern of an argument , which is called its logical form. As an example, see if you can tell whether the following argument is valid:

All quidnuncs are shunpikers. All shunpikers are �libbertigibbets. Therefore, all quidnuncs are �libbertigibbets.

You could likely tell that the argument is valid even though you do not know the meanings of the words. This is an important point. We can often tell whether an argument is valid even if we are not in a position to know whether any of its propositions are true or false. This is because deductive validity typically depends on certain patterns of argument. In fact, even nonsense arguments can be valid. Lewis Carroll (a pen name for C. L. Dodgson) was not only the author of Alice’s Adventures in Wonderland, but also a clever logician famous for both his use of nonsense words and his tricky logic puzzles.

We will look at some of Carroll’s puzzles in this chapter’s sections on categorical logic, but for now, let us look at an argument using nonsense words from his poem “Jabberwocky.” See if you can tell whether the following argument is valid:

All bandersnatches are slithy toves. All slithy toves are uf�ish. Therefore, all bandersnatches are uf�ish.

If you could tell the argument about quidnuncs was valid, you were probably able to tell that this argument is valid as well. Both arguments have the same pattern, or logical form.

Representing Logical Form

Logical form is generally represented by using variables or other symbols to highlight the pattern. In this case the logical form can be represented by substituting capital letters for certain parts of the propositions. Our argument then has the form:

All S are M. All M are P. Therefore, all S are P.

Any argument that follows this pattern, or form, is valid. Try it for yourself. Think of any three plural nouns; they do not have to be related to each other. For example, you could use submarines, candy bars, and mountains. When you have thought of three, substitute them for the letters in the pattern given. You can put them in any order you like, but the same word has to replace the same letter. So you will put one noun in for S in the �irst and third lines, one noun for both instances of M, and your last noun for both cases of P. If we use the suggested nouns, we would get:

All submarines are candy bars. All candy bars are mountains. Therefore, all submarines are mountains.

This argument may be close to nonsense, but it is logically valid. It would not be possible to make up a story in which the premises were true but the conclusion was false. For example, if one wizard turns all submarines into candy bars, and then a second wizard turns all candy bars into mountains, the story would not make any sense (nor would it be logical) if, in the end, all submarines were not mountains. Any story that makes the premises true would have to also make the conclusion true, so that the argument is valid.

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As mentioned, the form of an argument is what you get when you remove the speci�ic meaning of each of the nonlogical words in the argument and talk about them in terms of variables. Sometimes, however, one has to change the wording of a claim to make it �it the required form. For example, consider the premise “All men like dogs.” In this case the �irst category would be “men,” but the second category is not represented by a plural noun but by a predicate phrase, “like dogs.” In such cases we turn the expression “like dogs” into the noun phrase “people who like dogs.” In that case the form of the sentence is still “All A are B,” in which B is “people who like dogs.” As another example, the argument:

All whales are mammals. Some mammals live in the water. Therefore, at least some whales live in the water.

can be rewritten with plural nouns as:

All whales are mammals. Some mammals are things that live in the water. Therefore, at least some whales are things that live in the water.

and has the form:

All A are B. Some B are C. Therefore, at least some A are C.

The variables can represent anything (anything that �its grammatically, that is). When we substitute speci�ic expressions (of the appropriate grammatical category) for each of the variables, we get an instance of that form. So another instance of this form could be made by replacing A with Apples, B with Bananas, and C with Cantaloupes. This would give us

All Apples are Bananas. Some Bananas are Cantaloupes. Therefore, at least some Apples are Cantaloupes.

It does not matter at this stage whether the sentences are true or false or whether the reasoning is valid or invalid. All we are concerned with is the form or pattern of the argument.

We will see many different patterns as we study deductive logic. Different kinds of deductive arguments require different kinds of forms. The form we just used is based on categories; the letters represented groups of things, like dogs, whales, mammals, submarines, or candy bars. That is why in these cases we use plural nouns. Other patterns will require substituting entire sentences for letters. We will study forms of this type in Chapter 4. The patterns you need to know will be introduced as we study each kind of argument, so keep your eyes open for them.

Using the Counterexample Method

By de�inition, an argument form is valid if and only if all of its instances are valid. Therefore, if we can show that a logical form has even one invalid instance, then we may infer that the argument form is invalid. Such an instance is called a counterexample to the argument form’s validity; thus, the counterexample method for showing that an argument form is invalid involves creating an argument with the exact same form but in which the premises are true and the conclusion is false. (We will examine other methods in this chapter and in later chapters.) In other words, �inding a counterexample demonstrates the invalidity of the argument’s form.

Consider the invalid argument example from the prior section:

All donuts have added sugar. All donuts are bad for you. Therefore, everything with added sugar is bad for you.

By replacing predicate phrases with noun phrases, this argument has the form:

All A are B.

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Can you think of a counterexample that can prove this dog’s argument is invalid?

All A are C. Therefore, all B are C.

This is the same form as that of the following, clearly invalid argument:

All birds are animals. All birds have feathers. Therefore, all animals have feathers.

Because we can see that the premises of this argument are true and the conclusion is false, we know that the argument is invalid. Since we have identi�ied an invalid instance of the form, we know that the form is invalid. The invalid instance is a counterexample to the form. Because we have a counterexample, we have good reason to think that the argument about donuts is not valid.

One of our recent examples has the form:

All A are B. Some B are C. Therefore, at least some A are C.

Here is a counterexample that challenges this argument form’s validity:

All dogs are mammals. Some mammals are cats. Therefore, at least some dogs are cats.

By substituting dogs for A, mammals for B, and cats for C, we have found an example of the argument’s form that is clearly invalid because it moves from true premises to a false conclusion. Therefore, the argument form is invalid.

Here is another example of an argument:

All monkeys are primates. No monkeys are reptiles. Therefore, no primates are reptiles.

The conclusion is true in this example, so many may mistakenly think that the reasoning is valid. However, to better investigate the validity of the reasoning, it is best to focus on its form. The form of this argument is:

All A are B. No A are C. Therefore, no B are C.

To demonstrate that this form is invalid, it will suf�ice to demonstrate that there is an argument of this exact form that has all true premises and a false conclusion. Here is such a counterexample:

All men are human. No men are women. Therefore, no humans are women.

Clearly, there is something wrong with this argument. Though this is a different argument, the fact that it is clearly invalid, even though it has the exact same form as our original argument, means that the original argument’s form is also invalid.

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Consider This: The Counterexample Method

NEXT

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A mathematical proof is a valid deductive argument that attempts to prove the conclusion. Because mathematical proofs are deductively valid, mathematicians establish mathematical truth with complete certainty (as long as they agree on the premises).

3.3 Types of Deductive Arguments

Once you learn to look for arguments, you will see them everywhere. Deductive arguments play very important roles in daily reasoning. This section will discuss some of the most important types of deductive arguments.

Mathematical Arguments

Arguments about or involving mathematics generally use deductive reasoning. In fact, one way to think about deductive reasoning is that it is reasoning that tries to establish its conclusion with mathematical certainty. Let us consider some examples.

Suppose you are splitting the check for lunch with a friend. In calculating your portion, you reason as follows:

I had the chicken sandwich plate for $8.49. I had a root beer for $1.29. I had nothing else. $8.49 + $1.29 = $9.78. Therefore, my portion of the bill, excluding tip and tax, is $9.78.

Notice that if the premises are all true, then the conclusion must be true also. Of course, you might be mistaken about the prices, or you might have forgotten that you had a piece of pie for dessert. You might even have made a mistake in how you added up the prices. But these are all premises. So long as your premises are correct and the argument is valid, then the conclusion is certain to be true.

But wait, you might say—aren’t we often mistaken about things like this? After all, it is common for people to make mistakes when �iguring out a bill. Your friend might even disagree with one of your premises: For example, he might think the chicken sandwich plate was really $8.99. How can we say that the conclusion is established with mathematical certainty if we are willing to admit that we might be mistaken?

These are excellent questions, but they pertain to our certainty of the truth of the premises. The important feature of valid arguments is that the reasoning is so strong that the conclusion is just as certain to be true as the premises. It would be a very strange friend indeed who agreed with all of your premises and yet insisted that your portion of the bill was something other than $9.78. Still, no matter how good our reasoning, there is almost always some possibility that we are mistaken about our premises.

Arguments From De�initions

Another common type of deductive argument is argument from de�inition. This type of argument typically has two premises. One premise gives the de�inition of a word; the second premise says that something meets the de�inition. Here is an example:

Bachelor means “unmarried male.” John is an unmarried male. Therefore, John is a bachelor.

Notice that as with arguments involving math, we may disagree with the premises, but it is very hard to agree with the premises and disagree with the conclusion. When the argument is set out in standard form, it is typically relatively easy to see that the argument is valid.

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When crafting or evaluating a deductive argument via de�inition, special attention should be paid to the clarity of the de�inition.

On the other hand, it can be a little tricky to tell whether the argument is sound. Have we really gotten the de�inition right? We have to be very careful, as de�initions often sound right even though they are a little bit off. For example, the stated de�inition of bachelor is not quite right. At the very least, the de�inition should apply only to human males, and probably only adult ones. We do not normally call children or animals “bachelors.”

An interesting feature of de�initions is that they can be understood as going both ways. In other words, if bachelor means “unmarried male,” then we can reason either from the man being an unmarried male to his being a bachelor, as in the previous example, or from the man being a bachelor to his being an unmarried male, as in the following example.

Bachelor means “unmarried male.” John is a bachelor. Therefore, John is an unmarried male.

Arguments from de�inition can be very powerful, but they can also be misused. This typically happens when a word has two meanings or when the de�inition is not fully accurate. We will learn more about this when we study fallacies in Chapter 7, but here is an example to consider:

Murder is the taking of an innocent life. Abortion takes an innocent life. Therefore, abortion is murder.

This is an argument from de�inition, and it is valid—the premises guarantee the truth of the conclusion. However, are the premises true? Both premises could be disputed, but the �irst premise is probably not right as a de�inition. If the word murder really just meant “taking an innocent life,” then it would be impossible to commit murder by killing

someone who was not innocent. Furthermore, there is nothing in this de�inition about the victim being a human or the act being intentional. It is very tricky to get de�initions right, and we should be very careful about reaching conclusions based on oversimpli�ied de�initions. We will come back to this example from a different angle in the next section when we study syllogisms.

Categorical Arguments

Historically, some of the �irst arguments to receive a detailed treatment were categorical arguments, having been thoroughly explained by Aristotle himself (Smith, 2014). Categorical arguments are arguments whose premises and conclusions are statements about categories of things. Let us revisit an example from earlier in this chapter:

All whales are mammals. All mammals breathe air. Therefore, all whales breathe air.

In each of the statements of this argument, the membership of two categories is compared. The categories here are whales, mammals, and air breathers. As discussed in the previous section on evaluating deductive arguments, the validity of these arguments depends on the repetition of the category terms in certain patterns; it has nothing to do with the speci�ic categories being compared. You can test this by changing the category terms whales, mammals, and air breathers with any other category terms you like. Because this argument’s form is valid, any other argument with the same form will be valid. The branch of deductive reasoning that deals with categorical arguments is known as categorical logic. We will discuss it in the next two sections.

Propositional Arguments

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Propositional arguments are a type of reasoning that relates sentences to each other rather than relating categories to each other. Consider this example:

Either Jill is in her room, or she’s gone out to eat. Jill is not in her room. Therefore, she’s gone out to eat.

Notice that in this example the pattern is made by the sentences “Jill is in her room” and “she’s gone out to eat.” As with categorical arguments, the validity of propositional arguments can be determined by examining the form, independent of the speci�ic sentences used. The branch of deductive reasoning that deals with propositional arguments is known as propositional logic, which we will discuss in Chapter 4.

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3.4 Categorical Logic: Introducing Categorical Statements

The �ield of deductive logic is a rich and productive one; one could spend an entire lifetime studying it. (See A Closer Look: More Complicated Types of Deductive Reasoning.) Because the focus of this book is critical thinking and informal logic (rather than formal logic), we will only look closely at categorical and propositional logic, which focus on the basics of argument. If you enjoy this introductory exposure, you might consider looking for more books and courses in logic.

A Closer Look: More Complicated Types of Deductive Reasoning

As noted, deductive logic deals with a precise kind of reasoning in which logical validity is based on logical form. Within logical forms, we can use letters as variables to replace English words. Logicians also frequently replace other words that occur within arguments—such as all, some, or, and not—to create a kind of symbolic language. Formal logic represented in this type of symbolic language is called symbolic logic.

Because of this use of symbols, courses in symbolic logic end up looking like math classes. An introductory course in symbolic logic will typically begin with propositional logic and then move to something called predicate logic. Predicate logic combines everything from categorical and propositional logic but allows much more �lexibility in the use of some and all. This �lexibility allows it to represent much more complex and powerful statements.

Predicate logic forms the basis for even more advanced types of logic. Modal logic, for example, can be used to represent many deductive arguments about possibility and necessity that cannot be symbolized using predicate logic alone. Predicate logic can even help provide a foundation for mathematics. In particular, when predicate logic is combined with a mathematical �ield called set theory, it is possible to prove the fundamental truths of arithmetic. From there it is possible to demonstrate truths from many important �ields of mathematics, including calculus, without which we could not do physics, engineering, or many other fascinating and useful �ields. Even the computers that now form such an essential part of our lives are founded, ultimately, on deductive logic.

Categorical arguments have been studied extensively for more than 2,000 years, going back to Aristotle. Categorical logic is the logic of argument made up of categorical statements. It is a logic that is concerned with reasoning about certain relationships between categories of things. To learn more about how categorical logic works, it will be useful to begin by analyzing the nature of categorical statements, which make up the premises and conclusions of categorical arguments. A categorical statement talks about two categories or groups. Just to keep things simple, let us start by talking about dogs, cats, and animals.

One thing we can say about these groups is that all dogs are animals. Of course, all cats are animals, too. So we have the following true categorical statements:

All dogs are animals.

All cats are animals.

In categorical statements, the �irst group name is called the subject term; it is what the sentence is about. The second group name is called the predicate term. In the categorical sentences just mentioned, dogs and cats are both in the subject position, and animals is in the predicate position. Group terms can go in either position, but of course, the sentence might be false. For example, in the sentence “All animals are dogs” the term dogs is in the predicate position.

You may recall that we can represent the logical form of these types of sentences by replacing the category terms with single letters. Using this method, we can represent the form of these categorical statements in the following way:

All D are A.

All C are A.

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Another true statement we can make about these groups is “No dogs are cats.” Which term is in subject position, and which is in predicate position? If you said that dogs is the subject and cats is the predicate, you’re right! The logical form of “No dogs are cats” can be given as “No D are C.”

We now have two sentences in which the category dogs is the subject: “All dogs are animals” and “No dogs are cats.” Both of these statements tell us something about every dog. The �irst, which starts with all, tells us that each dog is an animal. The second, which begins with no, tells us that each dog is not a cat. We say that both of these types of sentences are universal because they tell us something about every member of the subject class.

Not all categorical statements are universal. Here are two statements about dogs that are not universal:

Some dogs are brown.

Some dogs are not tall.

Statements that talk about some of the things in a category are called particular statements. The distinction between a statement being universal or particular is a distinction of quantity.

Another distinction is that we can say that the things mentioned are in or not in the predicate category. If we say the things are in that category, our statement is af�irmative. If we say the things are not in that category, our statement is negative. The distinction between a statement being af�irmative or negative is a distinction of quality. For example, when we say “Some dogs are brown,” the thing mentioned (dogs) is in the predicate category (brown things), making this an af�irmative statement. When we say “Some dogs are not tall,” the thing mentioned (dogs) is not in the predicate category (tall things), and so this is a negative statement.

Taking both of these distinctions into account, there are four types of categorical statements: universal af�irmative, universal negative, particular af�irmative, and particular negative. Table 3.1 shows the form of each statement along with its quantity and quality.

Table 3.1: Types of categorical statements

Quantity Quality

All S is P Universal Af�irmative

No S is P Universal Negative

Some S is P Particular Af�irmative

Some S is not P Particular Negative

To abbreviate these categories of statement even further, logicians over the millennia have used letters to represent each type of statement. The abbreviations are as follows:

A: Universal af�irmative (All S is P)

E: Universal negative (No S is P)

I: Particular positive (Some S is P)

O: Particular negative (Some S is not P)

Accordingly, the statements are known as A propositions, E propositions, I propositions, and O propositions. Remember that the single capital letters in the statements themselves are just placeholders for category terms; we can �ill them in with any category terms we like. Figure 3.1 shows a traditional way to arrange the four types of statements by quantity and quality.

Figure 3.1: The square of opposition

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The square of opposition serves as a quick reference point when evaluating categorical statements. Note that A statements and O statements always contradict one another; when one is true, the other is false. The same is true of E statements and I statements.

Now we need to get just a bit clearer on what the four statements mean. Granted, the meaning of categorical statements seems clear: To say, for example, that “no dogs are reptiles” simply means that there are no things that are both dogs and reptiles. However, there are certain cases in which the way that logicians understand categorical statements may differ somewhat from how they are commonly understood in everyday language. In particular, there are two speci�ic issues that can cause confusion.

Clarifying Particular Statements

The �irst issue is with particular statements (I and O propositions). When we use the word some in everyday life, we typically mean more than one. For example, if someone says that she has some apples, we generally think that this means that she has more than one. However, in logic, we take the word some simply to mean at least one. Therefore, when we say that some S is P, we mean only that at least one S is P. For example, we can say “Some dogs live in the White House” even if only one does.

Clarifying Universal Statements

The second issue involves universal statements (A and E propositions). It is often called the “issue of existential presupposition”—the issue concerns whether a universal statement implies a particular statement. For example, does the fact that all dogs are animals imply that some dogs are animals? The question really becomes an issue only when we talk about things that do not really exist. For example, consider the claim that all the survivors of the Civil War live in New York. Given that there are no survivors of the Civil War anymore, is the statement true or not?

The Greek philosopher Aristotle, the inventor of categorical logic, would have said the statement is false. He thought that “All S is P” could only be true if there was at least one S (Parsons, 2014). Modern logicians, however, hold that that “All S is P” is true even when no S exists. The reasons for the modern view are somewhat beyond the scope of this text—see A Closer Look: Existential Import for a bit more of an explanation—but an example will help support the claim that universal statements are true when no member of the subject class exists.

Suppose we are driving somewhere and stop for snacks. We decide to split a bag of M&M’s. For some reason, one person in our group really wants the brown M&M’s, so you promise that he can have all of them. However, when we open the bag, it turns out that there are no brown candies in it. Since this friend did not get any brown M&M’s, did you break your promise? It seems clear that you did not. He did get all of the brown M&M’s that were in the bag; there just weren’t any. In order for you to have broken your promise, there would have to be a brown M&M that you did not let your friend have. Therefore, it is true that your friend got all the brown M&M’s, even though he did not get any.

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George Boole, for whom Boolean logic is named, challenged Aristotle’s assertion that the truth of A statements implies the truth of corresponding I statements. Boole suggested that some valid forms of syllogisms had to be excluded.

This is the way that modern logicians think about universal propositions when there are no members of the subject class. Any universal statement with an empty subject class is true, regardless of whether the statement is positive or negative. It is true that all the brown M&M’s were given to your friend and also true that no brown M&M’s were given to your friend.

A Closer Look: Existential Import

It is important to remember that particular statements in logic (I and O propositions) refer to things that actually exist. The statement “Some dogs are mammals” is essentially saying, “There is at least one dog that exists in the universe, and that dog is a mammal.” The way that logicians refer to this attribute of I and O statements is that they have “existential import.” This means that for them to be true, there must be something that actually exists that has the property mentioned in the statement.

The 19th-century mathematician George Boole, however, presented a problem. Boole agreed with Aristotle that the existential statements I and O had to refer to existing things to be true. Also, for Aristotle, all A statements that are true necessarily imply the truth of their corresponding I statements. The same goes with E and O statements.

Boole pointed out that some true A and E statements refer to things that do not actually exist. Consider the statement “All vampires are creatures that drink blood.” This is a true statement. That means that the corresponding I statement, “Some vampires are creatures that drink blood,” would also be true, according to Aristotle. However, Boole noted that there are no existing things that are vampires. If vampires do not exist, then the I statement, “Some vampires are creatures that drink blood,” is not true: The truth of this statement rests on the idea that there is an actually existing thing called a vampire, which, at this point, there is no evidence of.

Boole reasoned that Aristotle’s ideas did not work in cases where A and E statements refer to nonexisting classes of objects. For example, the E statement “No vampires are time machines” is a true statement. However, both classes in this statement refer to things that do not actually exist. Therefore, the statement “Some vampires are not time machines” is not true, because this statement could only be true if vampires and time machines actually existed.

Boole reasoned that Aristotle’s claim that true A and E statements led necessarily to true I and O statements was not universally true. Hence, Boole claimed that there needed to be a revision of the forms of categorical syllogisms that are considered valid. Because one cannot generally claim that an existential statement (I or O) is true based on the truth of the corresponding universal (A or E), there were some valid forms of syllogisms that had to be excluded under the Boolean (modern) perspective. These syllogisms were precisely those that reasoned from universal premises to a particular conclusion.

Of course, we all recognize that in everyday life we can logically infer that if all dogs are mammals, then it must be true that some dogs are mammals. That is, we know that there is at least one existing dog that is a mammal. However, because our logical rules of evaluation need to apply to all instances of syllogisms, and because there are other instances where universals do not lead of necessity to the truth of particulars, the rules of evaluation had to be reformed after Boole presented his analysis. It is important to avoid committing the existential fallacy, or assuming that a class has members and then drawing an inference about an actually existing member of the class.

Accounting for Conversational Implication

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These technical issues likely sound odd: We usually assume that some implies that there is more than one and that all implies that something exists. This is known as conversational implication (as opposed to logical implication). It is quite common in everyday life to make a conversational implication and take a statement to suggest that another statement is true as well, even though it does not logically imply that the other must be true. In logic, we focus on the literal meaning.

One of the common reasons that a statement is taken to conversationally imply another is that we are generally expected to make the most fully informative statement that we can in response to a question. For example, if someone asks what time it is and you say, “Sometime after 3,” your statement seems to imply that you do not know the exact time. If you knew it was 3:15 exactly, then you probably should have given this more speci�ic information in response to the question.

For example, we all know that all dogs are animals. Suppose, however, someone says, “Some dogs are animals.” That is an odd thing to say: We generally would not say that some dogs are animals unless we thought that some of them are not animals. However, that would be making a conversational implication, and we want to make logical implications. For the purposes of logic, we want to know whether the statement “some dogs are animals” is true or false. If we say it is false, then we seem to have stated it is not true that some dogs are animals; this, however, would seem to mean that there are no dogs that are animals. That cannot be right. Therefore, logicians take the statement “Some dogs are animals” simply to mean that there is at least one dog that is an animal, which is true. The statement “Some dogs are not animals” is not part of the meaning of the statement “Some dogs are animals.” In the language of logic, the statement that some S are not P is not part of the meaning of the statement that some S are P.

Of course, it would be odd to make the less informative statement that some dogs are animals, since we know that all dogs are animals. Because we tend to assume someone is making the most informative statement possible, the statement “Some dogs are animals” may conversationally imply that they are not all animals, even though that is not part of the literal meaning of the statement.

In short, a particular statement is true when there is at least one thing that makes it true, even if the universal statement would also be true. In fact, sometimes we emphasize that we are not talking about the whole category by using the words at least, as in, “At least some planets orbit stars.” Therefore, it appears to be nothing more than conversational implication, not literal meaning, that leads our statement “Some dogs are animals” to suggest that some also are not. When looking at categorical statements, be sure that you are thinking about the actual meaning of the sentence rather than what might be conversationally implied.

Practice Problems 3.2

Complete the following problems. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems3.2.pdf) to check your answers.

1. “All dinosaurs are things that are extinct.” Which of the following is the subject term in this statement? a. dinosaurs b. things that are extinct

2. “No Honda Civics are Lamborghinis.” Which of the following is the predicate term in this statement? a. Lamborghinis b. Honda Civics

3. “Some authors are people who write horror.” Which of the following is the predicate term in this statement?

a. authors b. people who write horror

4. “Some politicians are not people who can be trusted.” Which of the following is the subject term in this statement?

a. politicians b. people who can be trusted

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5. “All mammals are pieces of cheese.” Which of the following is the predicate term in this statement? a. pieces of cheese b. mammals

6. What is the quantity of the following statement? “All dinosaurs are things that are extinct.” a. universal b. particular c. af�irmative d. negative

7. What is the quality of the following statement? “No Honda Civics are Lamborghinis.” a. universal b. particular c. af�irmative d. negative

8. What is the quality of the following statement? “Some authors are people who write horror.” a. universal b. particular c. af�irmative d. negative

9. What is the quantity of the following statement? “Some politicians are not people who can be trusted.” a. universal b. particular c. af�irmative d. negative

10. What is the quality of the following statement? “All mammals are pieces of cheese.” a. universal b. particular c. af�irmative d. negative

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3.5 Categorical Logic: Venn Diagrams as Pictures of Meaning

Given that it is sometimes tricky to parse out the meaning and implications of categorical statements, a logician named John Venn devised a method that uses diagrams to clarify the literal meanings and logical implications of categorical claims. These diagrams are appropriately called Venn diagrams (Stapel, n.d.). Venn diagrams not only give a visual picture of the meanings of categorical statements, they also provide a method by which we can test the validity of many categorical arguments.

Drawing Venn Diagrams

Here is how the diagramming works: Imagine we get a bunch of people together and all go to a big �ield. We mark out a big circle with rope on the �ield and ask everyone with brown eyes to stand in the circle. Would you stand inside the circle or outside it? Where would you stand if we made another circle and asked everyone with brown hair to stand inside? If your eyes or hair are sort of brownish, just pick whether you think you should be inside or outside the circles. No standing on the rope allowed! Remember your answers to those two questions.

Here is an image of the brown-eye circle, labeled “E” for “eyes”; touch inside or outside the circle indicating where you would stand.

Here is a picture of the brown-hair circle, labeled “H” for “hair”; touch inside or outside the circle indicating where you would stand.

Notice that each circle divides the people into two groups: Those inside the circle have the feature we are interested in, and those outside the circle do not.

Where would you stand if we put both circles on the ground at the same time?

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As long as you do not have both brown eyes and brown hair, you should be able to �igure out where to stand. But where would you stand if you have brown eyes and brown hair? There is not any spot that is in both circles, so you would have to choose. In order to give brown-eyed, brown-haired people a place to stand, we have to overlap the circles.

Now there is a spot where people who have both brown hair and brown eyes can stand: where the two circles overlap. We noted earlier that each circle divides our bunch of people into two groups, those inside and those outside. With two circles, we now have four groups. Figure 3.2 shows what each of those groups are and where people from each group would stand.

Figure 3.2: Sample Venn diagram

With this background, we can now draw a picture for each categorical statement. When we know a region is empty, we will darken it to show there is nobody there. If we know for sure that someone is in a region, we will put an x in it to represent a person standing there. Figure 3.3 shows the pictures for each of the four kinds of statements.

Figure 3.3: Venn diagrams of categorical statements

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Each of the four categorical statements can be represented visually with a Venn diagram.

In drawing these pictures, we adopt the convention that the subject term is on the left and the predicate term is on the right. There is nothing special about this way of doing it, but diagrams are easier to understand if we draw them the same way as much as possible. The important thing to remember is that a Venn diagram is just a picture of the meaning of a statement. We will use this fact in our discussion of inferences and arguments.

Drawing Immediate Inferences

As mentioned, Venn diagrams help us determine what inferences are valid. The most basic of such inferences, and a good place to begin, is something called immediate inference. Immediate inferences are arguments from one categorical statement as premise to another as conclusion. In other words, we immediately infer one statement from another. Despite the fact that these inferences have only one premise, many of them are logically valid. This section will use Venn diagrams to help discern which immediate inferences are valid.

The basic method is to draw a diagram of the premises of the argument and determine if the diagram thereby shows the conclusion is true. If it does, then the argument is valid. In other words, if drawing a diagram of just the premises automatically creates a diagram of the conclusion, then the argument is valid. The diagram shows that any way of making the premises true would also make the conclusion true; it is impossible for the conclusion to be false when the premises are true. We will see how to use this method with each of the immediate inferences and later extend the method to more complicated arguments.

Conversion Conversion is just a matter of switching the positions of the subject and predicate terms. The resulting statement is called the converse of the original statement. Table 3.2 shows the converse of each type of statement.

Table 3.2: Conversion

Statement Converse

All S is P. All P is S.

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Statement Converse

No S is P. No P is S.

Some S is P. Some P is S.

Some S is not P. Some P is not S.

Forming the converse of a statement is easy; just switch the subject and predicate terms with each other. The question now is whether the immediate inference from a categorical statement to its converse is valid or not. It turns out that the argument from a statement to its converse is valid for some statement types, but not for others. In order to see which, we have to check that the converse is true whenever the original statement is true.

An easy way to do this is to draw a picture of the two statements and compare them. Let us start by looking at the universal negative statement, or E proposition, and its converse. If we form an argument from this statement to its converse, we get the following:

No S is P.

Therefore, no P is S.

Figure 3.4 shows the Venn diagrams for these statements.

As you can see, the same region is shaded in both pictures—the region that is inside both circles. It does not matter which order the circles are in, the picture is the same. This means that the two statements have the same meaning; we call such statements equivalent.

The Venn diagrams for these statements demonstrate that all of the information in the conclusion is present in the premise. We can therefore infer that the inference is valid. A shorter way to say it is that conversion is valid for universal negatives.

We see the same thing when we look at the particular af�irmative statement, or I proposition.

In the case of particular af�irmatives as well, we can see that all of the information in the conclusion is contained within the premises. Therefore, the immediate inference is valid. In fact, because the diagram for “Some S is P” is the same as the diagram for its converse, “Some P is S” (see Figure 3.5), it follows that these two statements are equivalent as well.

Figure 3.4: Universal negative statement and its converse

In this representation of “No S is P. Therefore, no P is S,” the areas shaded are the same, meaning the statements are equivalent.

Figure 3.5: Particular af�irmative statement and its converse

As with the E proposition, all of the information contained in the conclusion of the I proposition is also contained within the premises, making the inference valid.

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However, there will be a big difference when we draw pictures of the universal af�irmative (A proposition), the particular negative (O proposition), and their converses (see Figure 3.6 and Figure 3.7).

In these two cases we get different pictures, so the statements do not mean the same thing. In the original statements, the marked region is inside the S circle but not in the P circle. In the converse statements, the marked region is inside the P circle but not in the S circle. Because there is information in the conclusions of these arguments that is not present in the premises, we may infer that conversion is invalid in these two cases.

Figure 3.6: Universal af�irmative statement and its converse

Unlike Figures 3.4 and 3.5 where the diagrams were identical, we get two different diagrams for A propositions. This tells us that there is information contained in the conclusion that was not included in the premises, making the inference invalid.

Figure 3.7: Particular negative statement and its converse

As with A propositions, O propositions present information in the conclusion that was not present in the premises, rendering the inference invalid.

Let us consider another type of immediate inference.

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Contraposition Before we can address contraposition, it is necessary to introduce the idea of a complement class. Remember that for any category, we can divide things into those that are in the category and those that are out of the category. When we imagined rope circles on a �ield, we asked all the brown-haired people to step inside one of the circles. That gave us two groups: the brown-haired people inside the circle, and the non-brown-haired people outside the circle. These two groups are complements of each other. The complement of a group is everything that is not in the group. When we have a term that gives us a category, we can just add non- before the term to get a term for the complement group. The complement of term S is non-S, the complement of term animal is nonanimal, and so on. Let us see what complementing a term does to our Venn diagrams.

Recall the diagram for brown-eyed people. You were inside the circle if you have brown eyes, and outside the circle if you do not. (Remember, we did not let people stand on the rope; you had to be either in or out.) So now consider the diagram for non-brown-eyed people.

If you were inside the brown-eyed circle, you would be outside the non-brown-eyed circle. Similarly, if you were outside the brown-eyed circle, you would be inside the non-brown-eyed circle. The same would be true for complementing the brown-haired circle. Complementing just switches the inside and outside of the circle.

Do you remember the four regions from Figure 3.2? See if you can �ind the regions that would have the same people in the complemented picture. Where would someone with blue eyes and brown hair stand in each picture? Where would someone stand if he had red hair and green eyes? How about someone with brown hair and brown eyes?

In Figure 3.8, the regions are colored to indicate which ones would have the same people in them. Use the diagram to help check your answers from the previous paragraph. Notice that the regions in both circles and outside both circles trade places and that the region in the left circle only trades places with the region in the right circle.

Figure 3.8: Complement class

Now that we know what a complement is, we are ready to look at the immediate inference of contraposition. Contraposition combines conversion and complementing; to get the contrapositive of a statement, we �irst get the converse and then �ind the complement of both terms.

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Let us start by considering the universal af�irmative statement, “All S is P.” First we form its converse, “All P is S,” and then we complement both class terms to get the contrapositive, “All non-P is non-S.” That may sound like a mouthful, but you should see that there is a simple, straightforward process for getting the contrapositive of any statement. Table 3.3 shows the process for each of the four types of categorical statements.

Table 3.3: Contraposition

Original Converse Contrapositive

All S is P. All P is S. All non-P is non-S.

No S is P. No P is S. No non-P is non-S.

Some S is P. Some P is S. Some non-P is non-S.

Some S is not P. Some P is not S. Some non-P is not non-S.

Figure 3.9 shows the diagrams for the four statement types and their contrapositives, colored so that you can see which regions represent the same groups.

Figure 3.9: Contrapositive Venn diagrams

Using the converse and contrapositive diagrams, you can infer the original statement.

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As you can see, contraposition preserves meaning in universal af�irmative and particular negative statements. So from either of these types of statements, we can immediately infer their contrapositive, and from the contrapositive, we can infer the original statement. In other words, these statements are equivalent; therefore, in those two cases, the contrapositive is valid.

In the other cases, particular af�irmative and universal negative, we can see that there is information in the conclusion that is not present in diagram of the premise; these immediate inferences are invalid.

There are more immediate inferences that can be made, but our main focus in this chapter is on arguments with multiple premises, which tend to be more interesting, so we are going to move on to syllogisms.

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Practice Problems 3.3

Answer the following questions about conversion and contraposition. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems3.3.pdf) to check your answers.

1. What is the converse of the statement “No humperdinks are picklebacks”? a. No humperdinks are picklebacks. b. All picklebacks are humperdinks. c. Some humperdinks are picklebacks. d. No picklebacks are humperdinks.

2. What is the converse of the statement “Some mammals are not dolphins”? a. Some dolphins are mammals. b. Some dolphins are not mammals. c. All dolphins are mammals. d. No dolphins are mammals.

3. What is the contrapositive of the statement “All couches are pieces of furniture”? a. All non-couches are non-pieces of furniture. b. All pieces of furniture are non-couches. c. All non-pieces of furniture are couches. d. All non-pieces of furniture are non-couches.

4. What is the contrapositive of the statement “Some apples are not vegetables”? a. Some non-apples are not non-vegetables. b. Some non-vegetables are not non-apples. c. Some non-vegetables are non-apples. d. Some non-vegetables are apples.

5. What is the converse of the statement “Some men are bachelors”? a. Some bachelors are men. b. Some bachelors are non-men. c. All bachelors are men. d. No women are bachelors.

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Aristotle’s categorical syllogism uses two categorical premises to form a deductive argument.

3.6 Categorical Logic: Categorical Syllogisms

Whereas contraposition and conversion can be seen as arguments with only one premise, a syllogism is a deductive argument with two premises. The categorical syllogism, in which a conclusion is derived from two categorical premises, is perhaps the most famous—and certainly one of the oldest—forms of deductive argument. The categorical syllogism— which we will refer to here as just “syllogism”—presented by Aristotle in his Prior Analytics (350 BCE/1994), is a very speci�ic kind of deductive argument and was subsequently studied and developed extensively by logicians, mathematicians, and philosophers.

Terms

We will �irst discuss the syllogism’s basic outline, following Aristotle’s insistence that syllogisms are arguments that have two premises and a conclusion. Let us look again at our standard example:

All S are M. All M are P. Therefore, all S are P.

There are three total terms here: S, M, and P. The term that occurs in the predicate position in the conclusion (in this case, P) is the major term. The term that occurs in the subject position in the conclusion (in this case, S) is the minor term. The other term, the one that occurs in both premises but not the conclusion, is the middle term (in this case, M).

The premise that includes the major term is called the major premise. In this case it is the �irst premise. The premise that includes the minor term, the second one here, is called the minor premise. The conclusion will present the relationship between the predicate term of the major premise (P) and the subject term of the minor premise (S) (Smith, 2014).

There are 256 possible different forms of syllogisms, but only a small fraction of those are valid, which can be shown by testing syllogisms through the traditional rules of the syllogism or by using Venn diagrams, both of which we will look at later in this section.

Distribution

As Aristotle understood logical propositions, they referred to classes, or groups: sets of things. So a universal af�irmative (type A) proposition that states “All Clydesdales are horses” refers to the group of Clydesdales and says something about the relationship between all of the members of that group and the members of the group “horses.” However, nothing at all is said about those horses that might not be Clydesdales, so not all members of the group of horses are referred to. The idea of referring to members of such groups is the basic idea behind distribution: If all of the members of a group are referred to, the term that refers to that group is said to be distributed.

Using our example, then, we can see that the proposition “All Clydesdales are horses” refers to all the members of that group, so the term Clydesdales is said to be distributed. Universal af�irmatives like this one distribute the term that is in the �irst, or subject, position.

However, what if the proposition were a universal negative (type E) proposition, such as “No koala bears are carnivores”? Here all the members of the group “koala bears” (the subject term) are referred to, but all the members of the group “carnivores” (the predicate term) are also referred to. When we say that no koala bears are carnivores, we have said something about all koala bears (that they are not carnivores) and also something about all carnivores (that they are not koala bears). So in this universal negative proposition, both of its terms are distributed.

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To sum up distribution for the universal propositions, then: Universal af�irmative (A) propositions distribute only the �irst (subject) term, and universal negative (E) propositions distribute both the �irst (subject) term and the second (predicate) term.

The distribution pattern follows the same basic idea for particular propositions. A particular af�irmative (type I) proposition, such as “Some students are football players,” refers only to at least one member of the subject class (“students”) and only to at least one member of the predicate class (“football players”). Thus, remembering that some is interpreted as meaning “at least one,” the particular af�irmative proposition distributes neither term, for this proposition does not refer to all the members of either group.

Finally, a particular negative (type O) proposition, such as “Some Floridians are not surfers,” only refers to at least one Floridian—but says that at least one Floridian does not belong to the entire class of surfers or is excluded from the entire class of surfers. In this way, the particular negative proposition distributes only the term that refers to surfers, or the predicate term.

To sum up distribution for the particular propositions, then: particular af�irmative (I) propositions distribute neither the �irst (subject) nor the second (predicate) term, and particular negative (O) propositions distribute only the second (predicate) term. This is a lot of detail, to be sure, but it is summarized in Table 3.4.

Table 3.4: Distribution

Proposition Subject Predicate

A Distributed Not

E Distributed Distributed

I Not Not

O Not Distributed

Once you understand how distribution works, the rules for determining the validity of syllogisms are fairly straightforward. You just need to see that in any given syllogism, there are three terms: a subject term, a predicate term, and a middle term. But there are only two positions, or “slots,” a term can appear in, and distribution relates to those positions.

Rules for Validity

Once we know how to determine whether a term is distributed, it is relatively easy to learn the rules for determining whether a categorical syllogism is valid. The traditional rules of the syllogism are given in various ways, but here is one standard way:

Rule 1: The middle term must be distributed at least once.

Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise.

Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the syllogism has a negative conclusion, it must have a negative premise.

Rule 4: The syllogism cannot have two negative premises.

Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the syllogism has a particular conclusion, it must have a particular premise.

A syllogism that satis�ies all �ive of these rules will be valid; a syllogism that does not will be invalid. Perhaps the easiest way of seeing how the rules work is to go through a few examples. We can start with our standard syllogism with all universal af�irmatives:

All M are P. All S are M.

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The text describes �ive rules for determining a syllogism’s validity, but Aristotle’s fundamental rules were far more basic.

The Origins of Logic

Critical Thinking Questions

1. The law of noncontradiction and the excluded middle establish that a proposition cannot be both true and false and must be either true or false. Can you think of a proposition that violates either of these rules?

2. Aristotle’s syllogism form, or the standard argument form, allows us to condense arguments into their fundamental pieces for easier evaluation. Try putting an argument you have heard into the standard form.

Therefore, all S are P.

Rule 1 is satis�ied: The middle term is distributed by the �irst premise; a universal af�irmative (A) proposition distributes the term in the �irst (subject) position, which here is M. Rule 2 is satis�ied because the subject term that is distributed by the conclusion is also distributed by the second premise. In both the conclusion and the second premise, the universal af�irmative proposition distributes the term in the �irst position. Rule 3 is also satis�ied because there is not a negative premise without a negative conclusion, or a negative conclusion without a negative premise (all the propositions in this syllogism are af�irmative). Rule 4 is passed because both premises are af�irmative. Finally, Rule 5 is passed as well because there is a universal conclusion. Since this syllogism passes all �ive rules, it is valid.

These get easier with practice, so we can try another example:

Some M are not P. All M are S. Therefore, some S are not P.

Rule 1 is passed because the second premise distributes the middle term, M, since it is the subject in the universal af�irmative (A) proposition. Rule 2 is passed because the major term, P, that is distributed in the O conclusion is also distributed in the corresponding O premise (the �irst premise) that includes that term. Rule 3 is passed because there is a negative conclusion to go with the negative premise. Rule 4 is passed because there is only one negative premise. Rule 5 is passed because the �irst premise is a particular premise (O). Since this syllogism passes all �ive rules, it is valid; there is no way that all of its premises could be true and its conclusion false.

Both of these have been valid; however, out of the 256 possible syllogisms, most are invalid. Let us take a look

at one that violates one or more of the rules:

No P are M. Some S are not M. Therefore, all S are P.

Rule 1 is passed. The middle term is distributed in the �irst (major) premise. However, Rule 2 is violated. The subject term is distributed in the conclusion, but not in the corresponding second (minor) premise. It is not necessary to check the other rules; once we know that one of the rules is violated, we know that the argument is invalid. (However, for the curious, Rule 3 is violated as well, but Rules 4 and 5 are passed).

Venn Diagram Tests for Validity

Another value of Venn diagrams is that they provide a nice method for evaluating the validity of a syllogism. Because every valid syllogism has three categorical terms, the diagrams we use must have three circles:

Origins of Logic From Title: Logic: The Structure of Reason

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The idea in diagramming a syllogism is that we diagram each premise and then check to see if the conclusion has been automatically diagrammed. In other words, we determine whether the conclusion must be true, according to the diagram of the premises.

It is important to remember that we never draw a diagram of the conclusion. If the argument is valid, diagramming the premises will automatically provide a diagram of the conclusion. If the argument is invalid, diagramming the premises will not provide a diagram of the conclusions.

Diagramming Syllogisms With Universal Statements Particular statements are slightly more dif�icult in these diagrams, so we will start by looking at a syllogism with only universal statements. Consider the following syllogism:

All S is M. No M is P. Therefore, no S is P.

Remember, we are only going to diagram the two premises; we will not diagram the conclusion. The easiest way to diagram each premise is to temporarily ignore the circle that is not relevant to the premise. Looking just at the S and M circles, we diagram the �irst premise like this:

Here is what the diagram for the second premise looks like:

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Now we can take those two diagrams and superimpose them, so that we have one diagram of both premises:

Now we can check whether the argument is valid. To do this, we see if the conclusion is true according to our diagram. In this case our conclusion states that no S is P; is this statement true, according to our diagram? Look at just the S and P circles; you can see that the area between the S and P circles (outlined) is fully shaded. So we have a diagram of the conclusion. It does not matter if the S and P circles have some extra shading in them, so long as the diagram has all the shading needed for the truth of the conclusion.

Let us look at an invalid argument next.

All S is M. All P is M. Therefore, all S is P.

Again, we diagram each premise and look to see if we have a diagram of the conclusion. Here is what the diagram of the premises looks like:

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Now we check to see whether the conclusion must be true, according to the diagram. Our conclusion states that all S is P, meaning that no unshaded part of the S circle can be outside of the P circle. In this case you can see that we do not have a diagram of the conclusion. Since we have an unshaded part of S outside of P (outlined), the argument is invalid.

Let us do one more example with all universals.

All M are P. No M is S. Therefore, no S is P. Here is how to diagram the premises:

Is the conclusion true in this diagram? In order to know that the conclusion is true, we would need to know that there are no S that are P. However, we see in this diagram that there is room for some S to be P. Therefore, these premises do not guarantee the truth of this conclusion, so the argument is invalid.

Diagramming Syllogisms With Particular Statements Particular statements (I and O) are a bit trickier, but only a bit. The problem is that when you diagram a particular statement, you put an x in a region. If that region is further divided by a third circle, then the single x will end up in one of those subregions even though we do not know which one it should go in. As a result, we have to adopt a convention to indicate that the x may be in either of them. To do this, we will draw an x in each subregion and connect them with a line to show that we mean the individual might be in either subregion. To see how this works, let us consider the following syllogism.

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Some S is not M. All P are M. Therefore, some S is not P.

We start by diagramming the �irst premise:

Then we add the diagram for the second premise:

Notice that in diagramming the second premise, we shaded over one of the linked x’s. This leaves us with just one x. When we look at just the S and P circles, we can see that the remaining is inside the S circle but outside the P circle.

To see if the argument is valid, we have to determine whether the conclusion must be true according to this diagram. The truth of our conclusion depends on there being at least one S that is not P. Here we have just such an entity: The remaining x is in the S circle but not in the P circle, so the conclusion must be true. This shows that the conclusion validly follows from the premises.

Here is an example of an invalid syllogism.

Some S is M. Some M is P. Therefore, some S is P.

Here is the diagram with both premises represented:

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Now it seems we have x’s all over the place. Remember, our job now is just to see if the conclusion is already diagrammed when we diagram the premises. The diagram of the conclusion would have to have an x that was in the region between where the S and P circles overlap. We can see that there are two in that region, each linked to an x outside the region. The fact that they are linked to other x’s means that neither x has to be in the middle region; they might both be at the other end of the link. We can show this by carefully erasing one of each pair of linked x’s. In fact, we will erase one x from each linked pair, trying to do so in a way that makes the conclusion false. First we erase the right-hand x from the pair in the S circle. Here is what the diagram looks like now:

Now we erase the left-hand x from the remaining pair. Here is the �inal diagram:

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Notice that there are no x’s remaining in the overlapped region of S and P. This modi�ication of the diagram still makes both premises true, but it also makes the conclusion false. Because this combination is possible, that means that the argument must be invalid.

Here is a more common example of an invalid categorical syllogism:

All S are M. Some M are P. Therefore, some S are P.

This argument form looks valid, but it is not. One way to see that is to notice that Rule 1 is violated: The middle term does not distribute in either premise. That is why this argument form represents an example of the common deductive error in reasoning known as the “undistributed middle.”

A perhaps more intuitive way to see why it is invalid is to look at its Venn diagram. Here is how we diagram the premises:

The two x’s represent the fact that our particular premise states that some M are P and does not state whether or not they are in the S circle, so we represent both possibilities here. Now we simply need to check if the conclusion is necessarily true.

We can see that it is not, because although one x is in the right place, it is linked with another x in the wrong place. In other words, we do not know whether the x in “some M are P” is inside or outside the S boundary. Our conclusion requires that the x be inside the S boundary, but we do not know that for certain whether it is. Therefore, the argument is invalid. We could, for example, erase the linked x that is inside of the S circle, and we would have a diagram that makes both premises be true and the conclusion false.

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Because this diagram shows that it is possible to make the premises true and the conclusion false, it follows that the argument is invalid.

A �inal way to understand why this form is invalid is to use the counterexample method and consider that it has the same form as the following argument:

All dogs are mammals. Some mammals are cats. Therefore, some dogs are cats.

This argument has the same form and has all true premises and a false conclusion. This counterexample just veri�ies that our Venn diagram test got the right answer. If applied correctly, the Venn diagram test works every time. With this example, all three methods agree that our argument is invalid.

Moral of the Story: The Venn Diagram Test for Validity

Here, in summary, are the steps for doing the Venn diagram test for validity:

1. Draw the three circles, all overlapping. 2. Diagram the premises.

a. Shade in areas where nothing exists. b. Put an x for areas where something exists. c. If you are not sure what side of a line the x should be in, then put two linked x’s, one on each side.

3. Check to see if the conclusion is (must be) true in this diagram. a. If there are two linked x’s, and one of them makes the conclusion true and the other does not, then

the argument is invalid because the premises do not guarantee the truth of the conclusion. b. If the conclusion must be true in the diagram, then the argument is valid; otherwise it is not.

Practice Problems 3.4

Answer the following questions. Note that some questions may have more than one answer. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems3.4_corrected.pdf) to check your answers.

1. Which rules does the following syllogism pass?

All M are P. Some M are S. Therefore, some S are P.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. All the rules

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2. Which rules does the following syllogism fail?

No P are M. All S are M. Therefore, all S are P.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. All the rules

3. Which rules does the following syllogism fail?

Some M are P. Some S are not M. Therefore, some S are not P.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. All the rules

4. Which rules does the following syllogism fail?

No P are M. No M are S. Therefore, no S are P.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. All the rules

5. Which rules does the following syllogism fail?

All M are P. Some M are not S. Therefore, no S are P.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise.

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f. All the rules

6. Which rules does the following syllogism fail?

All humans are dogs. Some dogs are mammals. Therefore, no humans are mammals.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. None of the rules

7. Which rules does the following syllogism fail?

Some books are hardbacks. All hardbacks are published materials. Therefore, some books are published materials.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. None of the rules

8. Which rules does the following syllogism fail?

No politicians are liars. Some politicians are men. Therefore, some men are not liars.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. None of the rules

9. Which rules does the following syllogism fail?

Some Macs are computers. No PCs are Macs. Therefore, all PCs are computers.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises.

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e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the syllogism has a particular conclusion, it must have a particular premise.

f. None of the rules

10. Which rules does the following syllogism fail?

All media personalities are people who manipulate the masses. No professors are media personalities. Therefore, no professors are people who manipulate the masses.

a. Rule 1: The middle term must be distributed at least once. b. Rule 2: Any term distributed in the conclusion must be distributed in its corresponding premise. c. Rule 3: If the syllogism has a negative premise, it must have a negative conclusion, and if the

syllogism has a negative conclusion, it must have a negative premise. d. Rule 4: The syllogism cannot have two negative premises. e. Rule 5: If the syllogism has a particular premise, it must have a particular conclusion, and if the

syllogism has a particular conclusion, it must have a particular premise. f. None of the rules

11. Examine the following syllogisms. In the �irst pair, the terms that are distributed are marked in bold. Can you explain why? The second pair is left for you to determine which terms, if any, are distributed.

Some P are M. Some M are not S. Therefore, some S are not P.

No P are M. All M are S. Therefore, no S are P.

All M are P. All M are S. Therefore, all S are P.

Some P are not M. No S are M. Therefore, no S are P.

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3.7 Categorical Logic: Types of Categorical Arguments

Many examples of deductively valid arguments that we have considered can seem quite simple, even if the theory and rules behind them can be a bit daunting. You might even wonder how important it is to study deduction if even silly arguments about the moon being tasty are considered valid. Remember that this is just a brief introduction to deductive logic. Deductive arguments can get quite complex and dif�icult, even though they are built from smaller pieces such as those we have covered in this chapter. In the same way, a brick is a very simple thing, interesting in its form, but not much use all by itself. Yet someone who knows how to work with bricks can make a very complex and sturdy building from them.

Thus, it will be valuable to consider some of the more complex types of categorical arguments, sorites and enthymemes. Both of these types of arguments are often encountered in everyday life.

Sorites

A sorites is a speci�ic kind of argument that strings together several subarguments. The word sorites comes from the Greek word meaning a “pile” or a “heap”; thus, a sorites-style argument is a collection of arguments piled together. More speci�ically, a sorites is any categorical argument with more than two premises; the argument can then be turned into a string of categorical syllogisms. Here is one example, taken from Lewis Carroll’s book Symbolic Logic (1897/2009):

The only animals in this house are cats; Every animal is suitable for a pet, that loves to gaze at the moon; When I detest an animal, I avoid it; No animals are carnivorous, unless they prowl at night; No cat fails to kill mice; No animals ever take to me, except what are in this house; Kangaroos are not suitable for pets; None but carnivora kill mice; I detest animals that do not take to me; Animals, that prowl at night, always love to gaze at the moon. Therefore, I always avoid kangaroos. (p. 124)

Figuring out the logic in such complex sorites can be challenging and fun. However, it is easy to get lost in sorites arguments. It can be dif�icult to keep all the premises straight and to make sure the appropriate relationships are established between each premise in such a way that, ultimately, the conclusion follows.

Carroll’s sorites sounds ridiculous, but as discussed earlier in the chapter, many of us develop complex arguments in daily life that use the conclusion of an earlier argument as the premise of the next argument. Here is an example of a relatively short one:

All of my friends are going to the party. No one who goes to the party is boring. People that are not boring interest me. Therefore, all of my friends interest me.

Here is another example that we might reason through when thinking about biology:

All lizards are reptiles. No reptiles are mammals. Only mammals nurse their young. Therefore, no lizards nurse their young.

There are many examples like these. It is possible to break them into smaller syllogistic subarguments as follows:

All lizards are reptiles. No reptiles are mammals. Therefore, no lizards are mammals.

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No lizards are mammals. Only mammals nurse their young. Therefore, no lizards nurse their young.

Breaking arguments into components like this can help improve the clarity of the overall reasoning. If a sorites gets too long, we tend to lose track of what is going on. This is part of what can make some arguments hard to understand. When constructing your own arguments, therefore, you should beware of bunching premises together unnecessarily. Try to break a long argument into a series of smaller arguments instead, including subarguments, to improve clarity.

Enthymemes

While sorites are sets of arguments strung together into one larger argument, a related argument form is known as an enthymeme, a syllogistic argument that omits either a premise or a conclusion. There are also many nonsyllogistic arguments that leave out premises or conclusions; these are sometimes also called enthymemes as well, but here we will only consider enthymemes based on syllogisms.

A good question is why the arguments are missing premises. One reason that people may leave a premise out is that it is considered to be too obvious to mention. Here is an example:

All dolphins are mammals. Therefore, all dolphins are animals.

Here the suppressed premise is “All mammals are animals.” Such a statement probably does not need to be stated because it is common knowledge, and the reader knows how to �ill it in to get to the conclusion. Technically speaking, we are said to “suppress” the premise that does not need to be stated.

Sometimes people even leave out conclusions if they think that the inference involved is so clear that no one needs the conclusion stated explicitly. Arguments with unstated conclusions are considered enthymematic as well. Let us suppose a baseball fan complains, “You have to be rich to get tickets to game 7, and none of my friends is rich.” What is the implied conclusion? Here is the argument in standard form:

Everyone who can get tickets to game 7 is rich. None of my friends is rich. Therefore, ???

In this case we may validly infer that none of the fan’s friends can get tickets to game 7.

To be sure, you cannot always assume your audience has the required background knowledge, and you must attempt to evaluate whether a premise or conclusion does need to be stated explicitly. Thus, if you are talking about math to professional physicists, you do not need to spell out precisely what the hypotenuse of an angle is. However, if you are talking to third graders, that is certainly not a safe assumption. Determining the background knowledge of those with whom one is talking—and arguing—is more of an art than a science.

Validity in Complex Arguments

Recall that a valid argument is one whose premises guarantee the truth of the conclusion. Sorites are illustrations of how we can “stack” smaller valid arguments together to make larger valid arguments. Doing so can be as complicated as building a cathedral from bricks, but so long as each piece is valid, the structure as a whole will be valid.

How do we begin to examine a complex argument’s validity? Let us start by looking at another example of sorites from Lewis Carroll’s book Symbolic Logic (1897/2009):

Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised. Therefore, no babies can manage a crocodile. (p. 112)

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Is this argument valid? We can see that it is by breaking it into a pair of syllogisms. Start by considering the �irst and third premises. We will rewrite them slightly to show the All that Carroll has assumed. With those two premises, we can build the following valid syllogism:

All babies are illogical. All illogical persons are despised. Therefore, all babies are despised.

Using the tools from this chapter (the rules, Venn diagrams, or just by thinking it through carefully), we can check that the syllogism is valid. Now we can use the conclusion of our syllogism along with the remaining premise and conclusion from the original argument to construct another syllogism.

All babies are despised. No despised persons can manage a crocodile. Therefore, no babies can manage a crocodile.

Again, we can check that this syllogism is valid using the tools from this chapter. Since both of these arguments are valid, the string that combines them is valid as well. Therefore, the original argument (the one with three premises) is valid.

This process is somewhat like how we might approach adding a very long list of numbers. If you need to add a list of 100 numbers (suppose you are checking a grocery bill), you can do it by adding them together in groups of 10, and then adding the subtotals together. As long as you have done the addition correctly at each stage, your �inal answer will be the correct total. This is one reason validity is important. It allows us to have con�idence in complex arguments by examining the smaller arguments from which they are, or can be, built. If one of the smaller arguments was not valid, then we could not have complete con�idence in the larger argument.

But what about soundness? What use is the argument about babies managing crocodiles when we know that babies are not generally despised? Again, let us make a comparison to adding up your grocery bill. Arithmetic can tell you if your bill is added correctly, but it cannot tell you if the prices are correct or if the groceries are really worth the advertised price. Similarly, logic can tell you whether a conclusion validly follows from a set of premises, but it cannot generally tell you whether the premises are true, false, or even interesting. By themselves, random deductive arguments are as useful as sums of random numbers. They may be good practice for learning a skill, but they do not tell us much about the world unless we can somehow verify that their premises are, in fact, true. To learn about the world, we need to apply our reasoning skills to accurate facts (usually outside of arithmetic and logic) known to be true about the world.

This is why logicians are not as concerned with soundness as they are with validity, and why a mathematician is only concerned with whether you added correctly, and not with whether the prices were correctly recorded. Logic and mathematics give us skills to apply valid reasoning to the information around us. It is up to us, and to other �ields, to make sure the information that we use in the premises is correct.

Practice Problems 3.5

Answer the following questions. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems3.5.pdf) to check your answers.

1. This is the name that is given to an argument that has two premises and one conclusion. a. syllogism b. creative syllogism c. enthymeme d. sorites e. none of the above

2. The discovery of categorical logic is often attributed to this philosopher. a. Plato

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b. Boole c. Aristotle d. Kant e. Hume

3. Which of the following is a type of deductive argument? a. generalization b. categorical syllogism c. argument by analogy d. modus spartans e. none of the above

4. All categorical statements have which of the following? a. mood and placement b. �igure and form c. number and validity d. quantity and quality e. all of the above

5. The premise that contains the predicate term of the conclusion in a categorical syllogism is __________. a. the minor premise b. the major premise c. the necessary premise d. the conclusion e. none of the above

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Summary and Resources

Chapter Summary Validity is the central concept of deductive reasoning. An argument is valid when the truth of the premises absolutely guarantees the truth of the conclusion. For valid arguments, if the premises are true, then the conclusion must be true also. Valid arguments need not have true premises, but if they do, then they are sound arguments. Because they use valid reasoning and have true premises, sound arguments are guaranteed to have true conclusions.

Deductive arguments can include mathematical arguments, arguments from de�initions, categorical arguments, and propositional arguments. Categorical arguments allow us to reason about things based on their properties. Categorical arguments with two premises are called syllogisms. The validity of syllogisms can be evaluated either with a system of rules or by using Venn diagrams.

Syllogisms often leave one premise or the conclusion unstated. These are called enthymemes. Sometimes strings of syllogisms are combined into a larger argument called a sorites. If we have a string of valid arguments that are combined to make a larger argument, then we may infer that the long argument composed of these parts is valid as well.

The process of using subarguments to create longer ones allows us to make rather complex valid arguments out of simple parts. This is an important motivation for studying deductive logic. As with arithmetic, computer programming, and structural engineering, combining smaller steps in a careful way allows us to create complex structures that are fully reliable because they are built out of reliable parts.

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Critical Thinking Questions 1. How does the logical de�inition of validity differ from the way that the term valid is used in everyday speech? How

do you plan on differentiating the two as you continue studying logic? 2. In the chapter, you read a section about the importance of having evidence that supports your arguments. Is it

important to claim to believe things only when one has evidence, or are there some things that people can justi�iably believe without evidence? Why?

3. How would you describe what a deductive argument is to someone who does not know the technical terms that apply to arguments? What examples would you use to demonstrate deduction?

4. What is the point of being able to understand if a deductive argument is valid or sound? Why is it important to be able to determine these things? If you do not think it is important, how would you justify your claims that it is not important to be able to determine validity?

5. Has there ever been a time that you presented an argument in which you had little or no evidence to support your claims? What types of claims did you use in the place of premises? What types of techniques did you use to try to present an argument with no information to back up your conclusion(s)? What is a better method to use in the future?

Web Resources

Connecting the Dots Chapter 3

NEXT

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http://www.philosophyexperiments.com/validorinvalid/Default.aspx (http://www.philosophyexperiments.com/validorinvalid/Default.aspx) This game at the Philosophy Experiments website tests your ability to determine whether an argument is valid.

http://www.the�irstscience.org/syllogistic-machine (http://www.the�irstscience.org/syllogistic-machine) This professor’s blog includes an online syllogism solver that allows you to explore fallacies, �igures, terms, and modes of syllogisms. Click on “Notes on Syllogistic Logic” for more coverage of topics discussed in this chapter.

Key Terms

argument from de�inition An argument in which one premise is a de�inition.

categorical argument An argument entirely composed of categorical statements.

categorical logic The branch of deductive logic that is concerned with categorical arguments.

categorical statement A statement that relates one category or class to another. Speci�ically, if S and P are categories, the categorical statements relating them are: All S is P, No S is P, Some S is P, and Some S is not P.

complement class For a given class, the complement class consists of all things that are not in the given class. For example, if S is a class, its complement class is non-S.

contraposition The immediate inference obtained by switching the subject and predicate terms with each other and complementing them both.

conversion The immediate inference obtained by switching the subject and predicate terms with each other.

counterexample method The method of proving an argument form to be not valid by constructing an instance of it with true premises and a false conclusion.

deductive argument An argument that is presented as being valid—if the primary evaluative question about the argument is whether it is valid.

distribution Referring to members of groups. If all the members of a group are referred to, the term that refers to that group is said to be distributed.

enthymeme An argument in which one or more claims are left unstated.

immediate inferences Arguments from one categorical statement as premise to another as conclusion. In other words, we immediately infer one statement from another.

instance A term in logic that describes the sentence that results from replacing each variable within the form with speci�ic sentences.

logical form

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The pattern of an argument or claim.

predicate term The second term in a categorical proposition.

quality In logic, the distinction between a statement being af�irmative or negative.

quantity In logic, the distinction between a statement being universal or particular.

sorites A categorical argument with more than two premises.

sound Describes an argument that is valid and in which all of the premises are true.

subject term The �irst term in a categorical proposition.

syllogism A deductive argument with exactly two premises.

valid An argument in which the premises absolutely guarantee the conclusion, such that is impossible for the premises to be true while the conclusion is false.

Venn diagram A diagram constructed of overlapping circles, with shaded areas or x’s, which shows the relationships between the represented groups.

An argument in which one premise is a definition

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Learning Objectives

After reading this chapter, you should be able to:

1. Explain key words and concepts from propositional logic.

2. Describe the basic logical operators and how they function in a statement.

3. Symbolize complex statements using logical operators.

4. Generate truth tables to evaluate the validity of truth-functional arguments.

5. Evaluate common logical forms.

Chapter 3 discussed categorical logic and touched on how analyzing an argument’s logical form helps determine its validity. The usefulness of form in determining validity will become even clearer in this chapter’s discussion of what is known as propositional logic, another type of deductive logic. Whereas categorical logic analyzes arguments whose

4Propositional Logic

�lytosky11/iStock/Thinkstock

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validity is based on quantitative terms like all and some, propositional logic looks at arguments whose validity is based on the way they combine smaller sentences to make larger ones, using connectives like or, and, and not.

In this chapter, we will learn about the symbols and tools that help us analyze arguments and test for validity; we will also examine several common deductive argument forms. Whereas Chapter 3 introduced the idea of form—and thereby, formal logic—this chapter will more thoroughly consider the study of validity based on logical form. We shall see that by adding a couple more symbols to propositional logic, it is also possible to represent the types of statements represented in categorical logic, creating the robust and highly applicable discipline known today as predicate logic. (See A Closer Look: Translating Categorical Logic for more on predicate logic.)

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4.1 Basic Concepts in Propositional Logic

Propositional logic aims to make the concept of validity formal and precise. Remember from Chapter 3 that an argument is valid when the truth of its premises guarantees the truth of its conclusion. Propositional logic demonstrates exactly why certain types of premises guarantee the truth of certain types of conclusions. It does this by breaking down the forms of complex claims into their simple component parts. For example, consider the following argument:

Either the maid or the butler did it. The maid did not do it. Therefore, the butler did it.

This argument is valid, but not because of anything about the maid or butler. It is valid because of the way that the sentences combine words like or and not to make a logically valid form. Formal logic is not concerned about the content of arguments but with their form. Recall from Chapter 3, Section 3.2, that an argument’s form is the way it combines its component parts to make an overall pattern of reasoning. In this argument, the component parts are the small sentences “the butler did it” and “the maid did it.” If we give those parts the names P and Q, then our argument has the form:

P or Q. Not P. Therefore, Q.

Note that the expression “not P” means “P is not true.” In this case, since P is “the butler did it,” it follows that “not P” means “the butler did not do it.” An inspection of this form should reveal it is logically valid reasoning.

As the name suggests, propositional logic deals with arguments made up of propositions, just as categorical logic deals with arguments made up of categories (see Chapter 3). In philosophy, a proposition is the meaning of a claim about the world; it is what that claim asserts. We will refer to the subject of this chapter as “propositional logic” because that is the most common terminology in the �ield. However, it is sometimes called “sentence logic.” The principles are the same no matter which terminology we use, and in the rest of the chapter we will frequently talk about P and Q as representing sentences (or “statements”) as well.

The Value of Formal Logic

This process of making our reasoning more precise by focusing on an argument’s form has proved to be enormously useful. In fact, formal logic provides the theoretical underpinnings for computers. Computers operate on what are called “logic circuits,” and computer programs are based on propositional logic. Computers are able to understand our commands and always do exactly what they are programmed to do because they use formal logic. In A Closer Look: Alan Turing and How Formal Logic Won the War, you will see how the practical applications of logic changed the course of history.

Another value of formal logic is that it adds ef�iciency, precision, and clarity to our language. Being able to examine the structure of people’s statements allows us to clarify the meanings of complex sentences. In doing so, it creates an exact, structured way to assess reasoning and to discern between formally valid and invalid arguments.

A Closer Look: Alan Turing and How Formal Logic Won the War

The idea of a computing machine was conceived over the last few centuries by great thinkers such as Gottfried Leibniz, Blaise Pascal, and Charles Babbage. However, it was not until the �irst half of the 20th century that philosophers, logicians, mathematicians, and engineers were actually able to create “thinking machines” or “electronic brains” (Davis, 2000).

One pioneer of the computer age was British mathematician, philosopher, and logician Alan Turing. He came up with the concept of a Turing machine, an

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Science and Society/SuperStock

An Enigma cipher machine, which was widely used by the Nazi Party to encipher and decipher secret military messages during World War II.

Bill Long/Cartoonstock

Formal logic uses symbols and statement forms to clarify an argument’s reasoning.

electronic device that takes input in the form of zeroes and ones, manipulates it according to an algorithm, and creates a new output (BBC News, 1999).

Computers themselves were invented by creating electric circuits that do basic logical operations that you will learn about in this chapter. These electric circuits are called “logic gates” (see Figure 4.2 later in the chapter). By turning logic into circuits, basic “thinking” could be done with a series of fast electrical impulses.

Using logical brilliance, Turing was able to design early computers for use during World War II. The British used these early computers to crack the Nazis’ very complex Enigma code. The ability to know the German plans in advance gave the Allies a huge advantage. Prime Minister Winston Churchill even said to King George VI, “It was thanks to Ultra [one of the computers used] that we won the war” (as cited in Shaer, 2012).

Statement Forms

As we have discussed, propositional logic clari�ies formal reasoning by breaking down the forms of complex claims into the simple parts of which they are composed. It does this by using symbols to represent the smaller parts of complex sentences and showing how the larger sentence results from combining those parts in a certain way. By doing so, formal logic clari�ies the argument’s form, or the pattern of reasoning it uses.

Consider what this looks like in mathematics. If you have taken a course in algebra, you will remember statements such as the following:

x + y = y + x

This statement is true no matter what we put for x and for y. That is why we call x and y variables; they do not represent just one number but all numbers. No matter what speci�ic numbers we put in, we will still get a true statement, like the following:

5 + 3 = 3 + 5

7 + 2 = 2 + 7

1,235 + 943 = 943 + 1,235

By replacing the variables in the general equation with these speci�ic values, we get instances (as discussed in Chapter 3) of that general truth. In other words, 5 + 3 = 3 + 5 is an instance of the general statement x + y = y + x. One does not even need to use a calculator to know that the last statement of the three is true, for its truth is not based on the speci�ic numbers used but on the general form of the equation. Formal logic works in the exact same way.

Take the statement “If you have a dog, then you have a dog or you have a cat.” This statement is true, but its truth does not depend on anything about dogs or cats; its truth is based on its logical form—the way the sentence is structured. Here are

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Before moving on, watch this video to learn about how modern propositional logic came to be, thanks to the contributions of George Boole and Gottlob Frege.

two other statements with the same logical form: “If you are a miner, then you are a miner or you are a trapper” and “If you are a man, then you are a man or a woman.” These statements are all true not because of their content, but because of their shared logical form.

To help us see exactly what this form is, propositional logic uses variables to represent the different sentences within this form. Just as algebra uses letters like x and y to represent numbers, logicians use letters like P and Q to represent sentences. These letters are therefore called sentence variables.

The chief difference between propositional and categorical logic is that, in categorical logic (Chapter 3), variables (like M and S) are used to represent categories of things (like dogs and mammals), whereas variables in propositional logic (like P and Q) represent whole sentences (or propositions).

In our current example, propositional logic enables us to take the statement “If you have a dog, then you have a dog or you have a cat” and replace the simple sentences “You have a dog” and “You have a cat,” with the variables P and Q, respectively (see Figure 4.2). The result, “If P, then P or Q,” is known as the general statement form. Our speci�ic sentence, “If you have a dog, then you have a dog or you have a cat,” is an instance of this general form. Our other example statements—”If you are a miner, then you are a miner or you are a trapper” and “If you are a man, then you are a man or a woman”—are other instances of that same statement form, “If P, then P or Q.” We will talk about more speci�ic forms in the next section.

Figure 4.1: Finding the form

In this instance of the statement form, you can see that P and Q relate to the prepositions “you have a dog” and “you have a cat,” respectively.

At �irst glance, propositional logic can seem intimidating because it can be very mathematical in appearance, and some students have negative associations with math. We encourage you to take each section one step at a time and see the symbols as tools you can use to your advantage. Many students actually �ind that logic helps them because it presents symbols in a friendlier manner than in math, which can then help them warm up to the use of symbols in general.

The Origins of Modern Logic

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Critical Thinking Questions

1. How did Boole re�ine the manner in which logic could be applied? What did Frege do to build on Boole’s developments?

2. Why did logicians take words and turn them into variables and constants? What does this provide them as they examine propositions and arguments?

19th Century Modern Logic From Title: Logic: The Structure of Reason

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4.2 Logical Operators

In the prior section, we learned about what constitutes a statement form in propositional logic: a complex sentence structure with propositional variables like P and Q. In addition to the variables, however, there are other words that we used in representing forms, words like and and or. These terms, which connect the variables together, are called logical operators, also known as connectives or logical terms.

Logicians like to express formal precision by replacing English words with symbols that represent them. Therefore, in a statement form, logical operators are represented by symbols. The resulting symbolic statement forms are precise, brief, and clear. Expressing sentences in terms of such forms allows logic students more easily to determine the validity of arguments that include them. This section will analyze some of the most common symbols used for logical operators.

Conjunction

Those of you who have heard the Schoolhouse Rock! song “Conjunction Junction” (what’s your function?)—or recall past English grammar lessons—will recognize that a conjunction is a word used to connect, or conjoin, sentences or concepts. By that de�inition, it refers to words like and, but, and or. Logic, however, uses the word conjunction to refer only to and sentences. Accordingly, a conjunction is a compound statement in which the smaller component statements are joined by and.

For example, the conjunction of “roses are red” and “violets are blue” is the sentence “roses are red and violets are blue.” In logic, the symbol for and is an ampersand (&). Thus, the general form of a conjunction is P & Q. To get a speci�ic instance of a conjunction, all you have to do is replace the P and the Q with any speci�ic sentences. Here are some examples:

P Q P & Q

Joe is nice. Joe is tall. Joe is nice, and Joe is tall.

Mike is sad. Mike is lonely. Mike is sad, and Mike is lonely.

Winston is gone. Winston is not forgotten. Winston is gone and not forgotten.

Notice that the last sentence in the example does not repeat “Winston is” before “forgotten.” That is because people tend to abbreviate things. Thus, if we say “Jim and Mike are on the team,” this is actually an abbreviation for “Jim is on the team, and Mike is on the team.”

The use of the word and has an effect on the truth of the sentence. If we say that P & Q is true, it means that both P and Q are true. For example, suppose we say, “Joe is nice and Joe is tall.” This means that he is both nice and tall. If he is not tall, then the statement is false. If he is not nice, then the statement is false as well. He has to be both for the conjunction to be true. The truth of a complex statement thus depends on the truth of its parts. Whether a proposition is true or false is known as its truth value: The truth value of a true sentence is simply the word true, while the truth value of a false sentence is the word false.

To examine how the truth of a statement’s parts affects the truth of the whole statement, we can use a truth table. In a truth table, each variable (in this case, P and Q) has its own column, in which all possible truth values for those variables are listed. On the right side of the truth table is a column for the complex sentence(s) (in this case the conjunction P & Q) whose truth we want to test. This last column shows the truth value of the statement in question based on the assigned truth values listed for the variables on the left. In other words, each row of the truth table shows that if the letters (like P and Q) on the left have these assigned truth values, then the complex statements on the right will have these resulting truth values (in the complex column).

Here is the truth table for conjunction:

P Q P & Q

T (Joe is nice.) T (Joe is tall.) T (Joe is nice, and Joe is tall.)

T (Joe is nice.) F (Joe is not tall.) F (It is not true that Joe is nice and tall.)

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F (Joe is not nice.) T (Joe is tall.) F (It is not true that Joe is nice and tall.)

F (Joe is not nice.) F (Joe is not tall.) F (It is not true that Joe is nice and tall.)

What the �irst row means is that if the statements P and Q are both true, then the conjunction P & Q is true as well. The second row means that if P is true and Q is false, then P & Q is false (because P & Q means that both statements are true). The third row means that if P is false and Q is true, then P & Q is false. The �inal row means that if both statements are false, then P & Q is false as well.

A shorter method for representing this truth table, in which T stands for “true” and F stands for “false,” is as follows:

P Q P & Q

T T T

T F F

F T F

F F F

The P and Q columns represent all of the possible truth combinations, and the P & Q column represents the resulting truth value of the conjunction. Again, within each row, on the left we simply assume a set of truth values (for example, in the second row we assume that P is true and Q is false), then we determine what the truth value of P & Q should be to the right. Therefore, each row is like a formal “if–then” statement: If P is true and Q is false, then P & Q will be false.

Truth tables highlight why propositional logic is also called truth-functional logic. It is truth-functional because, as truth tables demonstrate, the truth of the complex statement (on the right) is a function of the truth values of its component statements (on the left).

Everyday Logic: The Meaning of But

Like the word and, the word but is also a conjunction. If we say, “Mike is rich, but he’s mean,” this seems to mean three things: (1) Mike is rich, (2) Mike is mean, and (3) these things are in contrast with each other. This third part, however, cannot be measured with simple truth values. Therefore, in terms of logic, we simply ignore such conversational elements (like point 3) and focus only on the truth conditions of the sentence. Therefore, strange as it may seem, in propositional logic the word but is taken to be a synonym for and.

Disjunction

Disjunction is just like conjunction except that it involves statements connected with an or (see Figure 4.2 for a helpful visualization of the difference). Thus, a statement like “You can either walk or ride the bus” is the disjunction of the statements “You can walk” and “you can ride the bus.” In other words, a disjunction is an or statement: P or Q. In logic the symbol for or is ∨. An or statement, therefore, has the form P ∨ Q.

Here are some examples:

P Q P ∨ Q

Mike is tall. Doug is rich. Mike is tall, or Doug is rich.

You can complain. You can change things. You can complain, or you can change things.

The maid did it. The butler did it. Either the maid or the butler did it.

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Notice that, as in the conjunction example, the last example abbreviates one of the clauses (in this case the �irst clause, “the maid did it”). It is common in natural (nonformal) languages to abbreviate sentences in such ways; the compound sentence actually has two complete component sentences, even if they are not stated completely. The nonabbreviated version would be “Either the maid did it, or the butler did it.”

The truth table for disjunction is as follows:

P Q P ∨ Q

T T T

T F T

F T T

F F F

Note that or statements are true whenever at least one of the component sentences (the “disjuncts”) is true. The only time an or statement is false is when P and Q are both false.

Figure 4.2: Simple logic circuits

These diagrams of simple logic circuits (recall the reference to these circuits in A Closer Look: Alan Turing and How Formal Logic Won the War) help us visualize how the rules for conjunctions (AND gate) and disjunctions (OR gate) work. With the AND gate, there is only one path that will turn on the light, but with the OR gate, there are two paths to illumination.

Everyday Logic: Inclusive Versus Exclusive Or

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The top line of the truth table for disjunctions may seem strange to some. Some think that the word or is intended to allow only one of the two sentences to be true. They therefore argue for an interpretation of disjunction called exclusive or. An exclusive or is just like the or in the truth table, except that it makes the top row (the one in which P and Q are both true) false.

One example given to justify this view is that of a waiter asking, “Do you want soup or salad?” If you want both, the answer should not be “yes.” Some therefore suggest that the English or should be understood in the exclusive sense.

However, this example can be misleading. The waiter is not asking “Is the statement ‘do you want soup or salad’ true?” The waiter is asking you to choose between the two options. When we ask for the truth value of a sentence of the form P or Q, on the other hand, we are asking whether the sentence is true. Consider it this way: If you wanted both soup and salad, the answer to the waiter’s question would not be “no,” but it would be if you were using an exclusive or.

When we see the connective or used in English, it is generally being used in the inclusive sense (so called because it includes cases in which both disjuncts are true). Suppose that your tax form states, “If you made more than $20,000, or you are self-employed, then �ill out form 201-Z.” Suppose that you made more than $20,000, and you are self-employed—would you �ill out that form? You should, because the standard or that we use in English and in logic is the inclusive version. Therefore, in logic we understand the word or in its inclusive sense, as seen in the truth table.

Negation

The simplest logical symbol we use on sentences simply negates a claim. Negation is the act of asserting that a claim is false. For every statement P, the negation of P states that P is false. It is symbolized ~P and pronounced “not P.” Here are some examples:

P ~P

Snow is white. Snow is not white.

I am happy. I am not happy.

Either John or Mike got the job. Neither John nor Mike got the job.

Since ~P states that P is not true, its truth value is the opposite of P’s truth value. In other words, if P is true, then ~P is false; if P is false then ~P is true. Here, then, is the truth table:

P ~P

T F

F T

Everyday Logic: The Word Not

Sometimes just putting the word not in front of the verb does not quite capture the meaning of negation. Take the statement “Jack and Jill went up the hill.” We could change it to “Jack and Jill did not go up the hill.” This, however, seems to mean that neither Jack nor Jill went up the hill, but the meaning of negation only requires that at least one did not go up the hill. The simplest way to correctly express the negation would be to write “It is not true that Jack and Jill went up the hill” or “It is not the case that Jack and Jill went up the hill.”

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Monkey Business/Thinkstock

People use conditionals frequently in real life. Think of all the times someone has said, “Get some rest if you are tired” or “You don’t have to do something if you don’t want to.”

Similar problems affect the negation of claims such as “John likes you.” If John does not know you, then this statement is not true. However, if we put the word not in front of the verb, we get “John does not like you.” This seems to imply that John dislikes you, which is not what the negation means (especially if he does not know you). Therefore, logicians will instead write something like, “It is not the case that John likes you.”

Conditional

A conditional is an “if–then” statement. An example is “If it is raining, then the street is wet.” The general form is “If P, then Q,” where P and Q represent any two claims. Within a conditional, P—the part that comes between if and then—is called the antecedent; Q—the part after then—is called the consequent. A conditional statement is symbolized P → Q and pronounced “if P, then Q.”

Here are some examples:

P Q P → Q

You are rich. You can buy a boat. If you are rich, then you can buy a boat.

You are not satis�ied. You can return the product. If you are not satis�ied, then you can return the product.

You need bread or milk. You should go to the market. If you need bread or milk, then you should go to the market.

Everyday Logic: Other Instances of Conditionals

Sometimes conditionals are expressed in other ways. For example, sometimes people leave out the then. They say things like, “If you are hungry, you should eat.” In many of these cases, we have to be clever in determining what P and Q are.

Sometimes people even put the consequent �irst: for example, “You should eat if you are hungry.” This statement means the same thing as “If you are hungry, then you should eat”; it is just ordered differently. In both cases the antecedent is what comes after the if in the English sentence (and prior to the → in the logical form). Thus, “If P then Q” is translated “P → Q,” and “P if Q” is translated “Q → P.”

Formulating the truth table for conditional statements is somewhat tricky. What does it take for a conditional statement to be true? This is actually a controversial issue within philosophy. It is actually easier to think of it as: What does it mean for a conditional statement to be false?

Suppose Mike promises, “If you give me $5, then I will wash your car.” What would it take for this statement to be false? Under what conditions, for example, could you accuse Mike of breaking his promise?

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It seems that the only way for Mike to break his promise is if you give him the $5, but he does not wash the car. If you give him the money and he washes the car, then he kept his word. If you did not give him the money, then his word was simply not tested (with no payment on your part, he is under no obligation). If you do not pay him, he may choose to wash the car anyway (as a gift), or he may not; neither would make him a liar. His promise is only broken in the case in which you give him the money but he does not wash it. Therefore, in general, we call conditional statements false only in the case in which the antecedent is true and the consequent is false (in this case, if you give him the money, but he still does not wash the car). This results in the following truth table:

P Q P → Q

T T T

T F F

F T T

F F T

Some people question the bottom two lines. Some feel that the truth value of those rows should depend on whether he would have washed the car if you had paid him. However, this sophisticated hypothetical is beyond the power of truth- functional logic. The truth table is as close as we can get to the meaning of “if . . . then . . .” with a simple truth table; in other words, it is best we can do with the tool at hand.

Finally, some feel that the third row should be false. That, however, would mean that Mike choosing to wash the car of a person who had no money to give him would mean that he broke his promise. That does not appear, however, to be a broken promise, only an act of generosity on his part. It therefore does not appear that his initial statement “If you give me $5, then I will wash your car” commits to washing the car only if you give him $5. This is instead a variation on the conditional theme known as “only if.”

Only If So what does it mean to say “P only if Q”? Let us take a look at another example: “You can get into Harvard only if you have a high GPA.” This means that a high GPA is a requirement for getting in. Note, however, that that is not the same as saying, “You can get into Harvard if you have a high GPA,” for there might be other requirements as well, like having high test scores, good letters of recommendation, and a good essay.

Thus, the statement “You can get into Harvard only if you have a high GPA” means:

You can get into Harvard → You have a high GPA

However, this does not mean the same thing as “You have a high GPA → You can get into Harvard.”

In general, “P only if Q” is translated P → Q. Notice that this is the same as the translation of “If P, then Q.” However, it is not the same as “P if Q,” which is translated Q → P. Here is a summary of the rules for these translations:

P only if Q is translated: P → Q

P if Q is translated: Q → P

Thus, “P if Q” and “P only if Q” are the converse of each other. Recall the discussion of conversion in Chapter 3; the converse is what you get when you switch the order of the elements within a conditional or categorical statement.

To say that P → Q is true is to assert that the truth of Q is necessary for the truth of P. In other words, Q must be true for P to be true. To say that P → Q is true is also to say that the truth of P is suf�icient for the truth of Q. In other words, knowing that P is true is enough information to conclude that Q is also true.

In our earlier example, we saw that having a high GPA is necessary but not suf�icient for getting into Harvard, because one must also have high test scores and good letters of recommendation. Further discussion of the concepts of necessary and suf�icient conditions will occur in Chapter 5.

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In some cases P is both a necessary and a suf�icient condition for Q. This is called a biconditional.

Biconditional A biconditional asserts an “if and only if” statement. It states that if P is true, then Q is true, and if Q is true, then P is true. For example, if I say, “I will go to the party if you will,” this means that if you go, then I will too (P → Q), but it does not rule out the possibility that I will go without you. To rule out that possibility, I could state “I will go to the party only if you will” (Q → P). If we want to assert both conditionals, I could say, “I will go to the party if and only if you will.” This is a biconditional.

The statement “P if and only if Q” literally means “P if Q and P only if Q.” Using the translation methods for if and only if, this is translated “(Q → P) & (P → Q).” Because the biconditional makes the arrow between P and Q go both ways, it is symbolized: P ↔ Q.

Here are some examples:

P Q P ↔ Q

You can go to the party. You are invited. You can go to the party if and only if you are invited.

You will get an A. You get above a 92%. You will get an A if and only if you get above a 92%.

You should propose. You are ready to marry her. You should propose if and only if you are ready to marry her.

There are other phrases that people sometimes use instead of “if and only if.” Some people say “just in case” or something else like it. Mathematicians and philosophers even use the abbreviation iff to stand for “if and only if.” Sometimes people even simply say “if” when they really mean “if and only if.” One must be clever to understand what people really mean when they speak in sloppy, everyday language. When it comes to precision, logic is perfect; English is fuzzy!

Here is how we do the truth table: For the biconditional P ↔ Q to be true, it must be the case that if P is true then Q is true and vice versa. Therefore, one cannot be true when the other one is false. In other words, they must both have the same truth value. That means the truth table looks as follows:

P Q P ↔ Q

T T T

T F F

F T F

F F T

The biconditional is true in exactly those cases in which P and Q have the same truth value.

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Practice Problems 4.1

Complete the following identi�ications. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems4.1.pdf) to check your answers.

1. “I am tired and hungry.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

2. “If we learn logic, then we will be able to evaluate arguments.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

Consider This: Reviewing the Symbols

NEXT

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3. “We can learn logic if and only if we commit ourselves to intense study.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

4. “We either attack now, or we will lose the war.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

5. “The tide will rise only if the moon’s gravitational pull acts on the ocean.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

6. “If I am sick or tired, then I will not go to the interpretive dance competition.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

7. “One can surf monster waves if and only if one has experience sur�ing smaller waves.” This statement is a __________.

a. conjunction b. disjunction c. conditional d. biconditional

8. “The economy is recovering, and people are starting to make more money.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

9. “If my computer crashes again, then I am going to buy a new one.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

10. “You can post responses on 2 days or choose to write a two-page paper.” This statement is a __________. a. conjunction b. disjunction c. conditional d. biconditional

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4.3 Symbolizing Complex Statements

We have learned the basic logical operators and their corresponding symbols and truth tables. However, these basic symbols also allow us analyze much more complicated statements. Within the statement form P → Q, what if either P or Q itself is a complex statement? For example:

P Q P → Q

You are hungry or thirsty. We should go to the diner. If you are hungry or thirsty, then we should go to the diner.

In this example, the antecedent, P, states, “You are hungry or thirsty,” which can be symbolized H ∨ T, using the letter H for “You are hungry” and T for “You are thirsty.” If we use the letter D for “We should go to the diner,” then the whole statement can be symbolized (H ∨ T) → D.

Notice the use of parentheses. Parentheses help specify the order of operations, just like in arithmetic. For example, how would you evaluate the quantity 3 + (2 × 5)? You would execute the mathematical operation within the parentheses �irst. In this case you would �irst multiply 2 and 5 and then add 3, getting 13. You would not add the 3 and the 2 �irst and then multiply by 5 to get 25. This is because you know to evaluate what is within the parentheses �irst.

It is the exact same way with logic. In the statement (H ∨ T) → D, because of the parentheses, we know that this statement is a conditional (not a disjunction). It is of the form P → Q, where P is replaced by H ∨ T and Q is replaced by D.

Here is another example:

N & S G (N & S) → G

He is nice and smart. You should get to know him. If he is nice and smart, then you should get to know him.

This example shows a complex way to make a sentence out of three component sentences. N is “He is nice,” S is “he is smart,” and G is “you should get to know him.” Here is another:

R (S & C) R → (S & C)

You want to be rich.

You should study hard and go to college.

If you want to be rich, then you should study hard and go to college.

If R is “You want to be rich,” S is “You should study hard,” and C is “You should go to college,” then the whole statement in this �inal example, symbolized R → (S & C), means “If you want to be rich, then you should study hard and go to college.”

Complex statements can be created in this manner for every form. Take the statement (~A & B) ∨ (C → ~D). This statement has the general form of a disjunction. It has the form P ∨ Q, where P is replaced with ~A & B, and Q is replaced with C → ~D.

Everyday Logic: Complex Statements in Ordinary Language

It is not always easy to determine how to translate complex, ordinary language statements into logic; one sometimes has to pick up on clues within the statement.

For instance, notice in general that neither P nor Q is translated ~(P ∨ Q). This is because P ∨ Q means that either one is true, so ~(P ∨ Q) means that neither one is true. It happens to be equivalent to saying ~P & ~Q (we will talk about logical equivalence later in this chapter).

Here are some more complex examples:

Statement Translation

If you don’t eat spinach, then you will neither be big nor strong. ~S → ~(B ∨ S)

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Statement Translation

Either he is strong and brave, or he is both reckless and foolish. (S & B) ∨ (R & F)

Come late and wear wrinkled clothes only if you don’t want the job. (L & W) → ~J

He is strong and brave, and if he doesn’t like you, he will let you know. (S & B) & (~L → K)

Truth Tables With Complex Statements

We have managed to symbolize complex statements by seeing how they are systematically constructed out of their parts. Here we use the same principle to create truth tables that allow us to �ind the truth values of complex statements based on the truth values of their parts. It will be helpful to start with a summary of the truth values of sentences constructed with the basic truth-functional operators:

P Q ~P P & Q P ∨ Q P → Q P ↔ Q

T T F T T T T

T F F F T F F

F T T F T T F

F F T F F T T

The truth values of more complex statements can be discovered by applying these basic formulas one at a time. Take a complex statement like (A ∨ B) → (A & B). Do not be intimidated by its seemingly complex form; simply take it one operator at a time. First, notice the main form of the statement: It is a conditional (we know this because the other operators are within parentheses). It therefore has the form P → Q, where P is “A ∨ B” and Q is “A & B.”

The antecedent of the conditional is A ∨ B; the consequent is A & B. The way to �ind the truth values of such statements is to start inside the parentheses and �ind those truth values �irst, and then work our way out to the main operator—in this case →.

Here is the truth table for these components:

A B A ∨ B A & B

T T T T

T F T F

F T T F

F F F F

Now we take the truth tables for these components to create the truth table for the overall conditional:

A B A ∨ A & B (A ∨ B) → (A & B)

T T T T T

T F T F F

F T T F F

F F F F T

In this way the truth values of very complex statements can be determined from the values of their parts. We may refer to these columns (in this case A ∨ B and A & B) as helper columns, because they are there just to assist us in determining the truth values for the more complex statement of which they are a part.

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Here is another one: (A & ~B) → ~(A ∨ B). This one is also a conditional, where the antecedent is A & ~B and the consequent is ~(A ∨ B). We do these components �irst because they are inside parentheses. However, to �ind the truth table for A & ~B, we will have to �ill out the truth table for ~B �irst (as a helper column).

A B ~B A & ~B

T T F F

T F T T

F T F F

F F T F

We found ~B by simply negating B. We then found A & ~B by applying the truth table for conjunctions to the column for A and the column for ~B.

Now we can �ill out the truth table for A ∨ B and then use that to �ind the values of ~(A ∨ B):

A B A ∨ B ~(A ∨ B)

T T T F

T F T F

F T T F

F F F T

Finally, we can now put A & ~B and ~(A ∨ B) together with the conditional to get our truth table:

A B A & ~B ~(A ∨ B) (A & ~B) → ~(A ∨ B)

T T F F T

T F T F F

F T F F T

F F F T T

Although complicated, it is not hard when one realizes that one has to apply only a series of simple steps in order to get the end result.

Here is another one: (A → ~B) ∨ ~(A & B). First we will do the truth table for the left part of the disjunction (called the left disjunct), A → ~B:

A B ~B A → ~B

T T F F

T F T T

F T F T

F F T T

Of course, the last column is based on combining the �irst column, A, with the third column, ~B, using the conditional. Now we can work on the right disjunct, ~(A & B):

A B A & B ~(A & B)

T T T F

T F F T

F T F T

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F F F T

The �inal truth table, then, is:

A B A→~B ~(A & B) (A→~B) ∨ ~(A & B)

T T F F F

T F T T T

F T T T T

F F T T T

You may have noticed that three formulas in the truth table have the exact same values on every row. That means that the formulas are logically equivalent. In propositional logic, two formulas are logically equivalent if they have the same truth values on every row of the truth table. Logically equivalent formulas are therefore true in the exact same circumstances. Logicians consider this important because two formulas that are logically equivalent, in the logical sense, mean the same thing, even though they may look quite different. The conditions for their truth and falsity are identical.

The fact that the truth value of a complex statement follows from the truth values of its component parts is why these operators are called truth-functional. The operators, &, ∨, ~, →, and ↔, are truth-functions, meaning that the truth of the whole sentence is a function of the truth of the parts.

Because the validity of argument forms within propositional logic is based on the behavior of the truth-functional operators, another name for propositional logic is truth-functional logic.

Truth Tables With Three Letters

In each of the prior complex statement examples, there were only two letters (variables like P and Q or constants like A and B) in the top left of the truth table. Each truth table had only four rows because there are only four possible combinations of truth values for two variables (both are true, only the �irst is true, only the second is true, and both are false).

It is also possible to do a truth table for sentences that contain three or more variables (or constants). Recall one of the earlier examples: “Come late and wear wrinkled clothes only if you don’t want the job,” which we represented as (L & W) → ~J. Now that there are three letters, how many possible combinations of truth values are there for these letters?

The answer is that a truth table with three variables (or constants) will have eight lines. The general rule is that whenever you add another letter to a truth table, you double the number of possible combinations of truth values. For each earlier combination, there are now two: one in which the new letter is true and one in which it is false. Therefore, to make a truth table with three letters, imagine the truth table for two letters and imagine each row splitting in two, as follows:

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The resulting truth table rows would look like this:

P Q R

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

The goal is to have a row for every possible truth value combination. Generally, to �ill in the rows of any truth table, start with the last letter and simply alternate T, F, T, F, and so on, as in the R column. Then move one letter to the left and do twice as many Ts followed by twice as many Fs (two of each): T, T, F, F, and so on, as in the Q column. Then move another letter to the left and do twice as many of each again (four each), in this case T, T, T, T, F, F, F, F, as in the P column. If there are more letters, then we would repeat the process, adding twice as many Ts for each added letter to the left.

With three letters, there are eight rows; with four letters, there are sixteen rows, and so on. This chapter does not address statements with more than three letters, so another way to ensure you have enough rows is to memorize this pattern.

The column with the forms is �illed out the same way as when there were two letters. The fact that they now have three letters makes little difference, because we work on only one operator, and therefore at most two columns of letters, at a time. Let us start with the example of P → (Q & R). We begin by solving inside the parentheses by determining the truth values for Q & R, then we create the conditional between P and that result. The table looks like this:

P Q R Q & R P → (Q & R)

T T T T T

T T F F F

T F T F F

T F F F F

F T T T T

F T F F T

F F T F T

F F F F T

The rules for determining the truth values of Q & R and then of P → (Q & R) are exactly the same as the rules for & and → that we used in the two-letter truth tables earlier; now we just use them for more rows. It is a formal process that generates truth values by the same strict algorithms as in the two-letter tables.

Practice Problems 4.2

Symbolize the following complex statements using the symbols that you have learned in this chapter. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems4.2.pdf) to check your answers.

1. One should be neither a borrower nor a lender.

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2. Atomic bombs are dangerous and destructive. 3. If we go to the store, then I need to buy apples and lettuce. 4. Either Microsoft enhances its product and Dell’s sales decrease, or Gateway will start making computers

again. 5. If Hondas have better gas mileage than Range Rovers and you are looking for something that is easy to

park, I recommend that you buy the Honda. 6. Global warming will decrease if and only if emissions decrease in China and other major polluters around

the world. 7. One cannot be both happy and successful in our society, but one can be happy or successful. 8. I will pass this course if and only if I study hard and practice regularly, if I have the time and energy to do

so. 9. God can only exist if evil does not exist, if it is true that God is both all-powerful and all-good. 10. The con�lict in Israel will end only if the Palestinians feel that they can live outside the supervision of the

Israelis and the two sides stop attacking one another.

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4.4 Using Truth Tables to Test for Validity

Truth tables serve many valuable purposes. One is to help us better understand how the logical operators work. Another is to help us understand how truth is determined within formally structured sentences. One of the most valuable things truth tables offer is the ability to test argument forms for validity. As mentioned at the beginning of this chapter, one of the main purposes of formal logic is to make the concept of validity precise. Truth tables help us do just that.

As mentioned in previous chapters, an argument is valid if and only if the truth of its premises guarantees the truth of its conclusion. This is equivalent to saying that there is no way that the premises can be true and the conclusion false.

Truth tables enable us to determine precisely if there is any way for all of the premises to be true and the conclusion false (and therefore whether the argument is valid): We simply create a truth table for the premises and conclusion and see if there is any row on which all of the premises are true and the conclusion is false. If there is, then the argument is invalid, because that row shows that it is possible for the premises to be true and the conclusion false. If there is no such line, then the argument is valid:

Since the rows of a truth table cover all possibilities, if there is no row on which all of the premises are true and the conclusion is false, then it is impossible, so the argument is valid.

Let us start with a simple example—note that the symbol means “therefore”:

P ∨ Q ~Q ∴ P

This argument form is valid; if there are only two options, P and Q, and one of them is false, then it follows that the other one must be true. However, how can we formally demonstrate its validity? One way is to create a truth table to �ind out if there is any possible way to make all of the premises true and the conclusion false.

Here is how to set up the truth table, with a column for each premise (P1 and P2) and the conclusion (C):

P1 P2 C

P Q P ∨ Q ~Q P

T T

T F

F T

F F

We then �ill in the columns, with the correct truth values:

P1 P2 C

P Q P ∨ Q ~Q P

T T T F T

T F T T T

F T T F F

F F F T F

We then check if there are any rows in which all of the premises are true and the conclusion is false. A brief scan shows that there are no such lines. The �irst two rows have true conclusions, and the remaining two rows each have at least one false premise. Since the rows of a truth table represent all possible combinations of truth values, this truth table therefore demonstrates that there is no possible way to make all of the premises true and the conclusion false. It follows, therefore, that the argument is logically valid.

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To summarize, the steps for using the truth table method to determine an argument’s validity are as follows:

1. Set up the truth table by creating rows for each possible combination of truth values for the basic letters and a column for each premise and the conclusion.

2. Fill out the truth table by �illing out the truth values in each column according to the rules for the relevant operator (~, &, ∨, →, ↔).

3. Use the table to evaluate the argument’s validity. If there is even one row on which all of the premises are true and the conclusion is false, then the argument is invalid; if there is no such row, then the argument is valid.

This truth table method works for all arguments in propositional logic: Any valid propositional logic argument will have a truth table that shows it is valid, and every invalid propositional logic argument will have a truth table that shows it is invalid. Therefore, this is a perfect test for validity: It works every time (as long as we use it accurately).

Examples With Arguments With Two Letters

Let us do another example with only two letters. This argument will be slightly more complex but will still involve only two letters, A and B.

Example 1

A → B ~(A & B) ∴ ~(B ∨ A)

To test this symbolized argument for validity, we �irst set up the truth table by creating rows with all of the possible truth values for the basic letters on the left and then create a column for each premise (P1 and P2) and conclusion (C), as follows:

P1 P2 C

A B A → B ~(A & B) ~(B ∨ A)

T T

T F

F T

F F

Second, we �ill out the truth table using the rules created by the basic truth tables for each operator. Remember to use helper columns where necessary as steps toward �illing in the columns of complex formulas. Here is the truth table with only the helper columns �illed in:

P1 P2 C

A B A → B A & B ~(A & B) B ∨ A ~(B ∨ A)

T T T T

T F F T

F T F T

F F F F

Here is the truth table with the rest of the columns �illed in:

P1 P2 C

A B A → B A & B ~(A & B) B ∨ A ~(B ∨ A)

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T T T T F T F

T F F F T T F

F T T F T T F

F F T F T F T

Finally, to evaluate the argument’s validity, all we have to do is check to see if there are any lines in which all of the premises are true and the conclusion is false. Again, if there is such a line, since we know it is possible for all of the premises to be true and the conclusion false, the argument is invalid. If there is no such line, then the argument is valid.

It does not matter what other rows may exist in the table. There may be rows in which all of the premises are true and the conclusion is also true; there also may be rows with one or more false premises. Neither of those types of rows determine the argument’s validity; our only concern is whether there is any possible row on which all of the premises are true and the conclusion false. Is there such a line in our truth table? (Remember: Ignore the helper columns and just focus on the premises and conclusion.)

The answer is yes, all of the premises are true and the conclusion is false in the third row. This row supplies a proof that this argument’s form is invalid. Here is the line:

P1 P2 C

A B A → B ~(A & B) ~(B ∨ A)

F T T T F

Again, it does not matter what is on the other row. As long as there is (at least) one row in which all of the premises are true and the conclusion false, the argument is invalid.

Example 2

A → (B & ~A) A ∨ ~B ∴ ~(A ∨ B)

First we set up the truth table:

P1 P2 C

A B ~A B &~A A → (B & ~A) ~B

A ∨ ~B

A ∨ B

~(A ∨ B)

T T

T F

F T

F F

Next we �ill in the values, �illing in the helper columns �irst:

P1 P2 C

A B ~A B &~A A → (B & ~A) ~B

A ∨ ~B

A ∨ B

~(A ∨ B)

T T F F F T

T F F F T T

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F T T T F T

F F T F T F

Now that the helper columns are done, we can �ill in the rest of the table’s values:

P1 P2 C

A B ~A B &~A A → (B & ~A) ~B

A ∨ ~B

A ∨ B

~(A ∨ B)

T T F F F F T T F

T F F F F T T T F

F T T T T F F T F

F F T F T T T F T

Finally, we evaluate the table for validity. Here we see that there are no lines in which all of the premises are true and the conclusion is false. Therefore, there is no possible way to make all of the premises true and the conclusion false, so the argument is valid.

The earlier examples each had two premises. The following example has three premises. The steps of the truth table test are identical.

Example 3

~(M ∨ B) M → ~B B ∨ ~M ∴ ~M & B)

First we set up the truth table. This table already has the helper columns �illed in.

P1 P2 P3 C

M B M >∨B ~(M ∨ B) ~B

M → ~B ~M

B ∨ ~M

~M & B

T T T F F

T F T T F

F T T F T

F F F T T

Now we �ill in the rest of the columns, using the helper columns to determine the truth values of our premises and conclusion on each row:

P1 P2 P3 C

M B M ∨B ~(M ∨ B) ~B

M → ~B ~M

B ∨ ~M

~M & B

T T T F F F F T F

T F T F T T F F F

F T T F F T T T T

F F F T T T T T F

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Now we look for a line in which all of the premises are true and the conclusion false. The �inal row is just such a line. This demonstrates conclusively that the argument is invalid.

Examples With Arguments With Three Letters

The last example had three premises, but only two letters. These next examples will have three letters. As explained earlier in the chapter, the presence of the extra letter doubles the number of rows in the truth table.

Example 1

A → (B ∨ C) ~(C & B) ∴ ~(A & B)

First we set up the truth table. Note, as mentioned earlier, now there are eight possible combinations on the left.

P1 P2 C

A B C B ∨ C

A → (B ∨ C)

C & B

~(C & B)

A & B

~(A & B)

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Then we �ill the table out. Here it is with just the helper columns:

P1 P2 C

A B C B ∨ C

A → (B ∨ C)

C & B

~(C & B)

A & B

~(A & B)

T T T T T T

T T F T F T

T F T T F F

T F F F F F

F T T T T F

F T F T F F

F F T T F F

F F F F F F

Here is the full truth table:

P1 P2 C

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A B C B ∨C A → (B ∨

C) C & B

~ (C & B)

A & B

~(A & B)

T T T T T T F T F

T T F T T F T T F

T F T T T F T F T

T F F F F F T F T

F T T T T T F F T

F T F T T F T F T

F F T T T F T F T

F F F F T F T F T

Finally, we evaluate; that is, we look for a line in which all of the premises are true and the conclusion false. This is the case with the second line. Once you �ind such a line, you do not need to look any further. The existence of even one line in which all of the premises are true and the conclusion is false is enough to declare the argument invalid.

Let us do another one with three letters:

Example 2

A → ~B B ∨ C ∴ A → C

We begin by setting up the table:

P1 P2 C

A B C ~B A → ~B B ∨ C A → C

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Now we can �ill in the rows, beginning with the helper columns:

P1 P2 C

A B C ~B A → ~B B ∨ C A → C

T T T F F T T

T T F F F T F

T F T T T T T

T F F T T F F

F T T F T T T

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F T F F T T T

F F T T T T T

F F F T T F T

Here, when we look for a line in which all of the premises are true and the conclusion false, we do not �ind one. There is no such line; therefore the argument is valid.

Practice Problems 4.3

Answer these questions about truth tables. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems4.3_corrected.pdf) to check your answers.

1. A truth table with two variables has how many lines? a. 1 b. 2 c. 4 d. 8

2. A truth table with three variables has how many lines? a. 1 b. 2 c. 4 d. 8

3. In order to prove that an argument is invalid using a truth table, one must __________. a. �ind a line in which all premises and the conclusion are false b. �ind a line in which the premises are true and the conclusion is false c. �ind a line in which the premises are false and the conclusion is true d. �ind a line in which the premises and the conclusion are true

4. This is how one can tell if an argument is valid using a truth table: a. There is a line in which the premises and the conclusion are true. b. There is no line in which the premises are false. c. There is no line in which the premises are true and the conclusion is false. d. All of the above e. None of the above

5. When two statements have the same truth values in all circumstances, they are said to be __________. a. logically contradictory b. logically equivalent c. logically cogent d. logically valid

6. An if–then statement is called a __________. a. conjunction b. disjunction c. conditional d. biconditional

7. An if and only if statement is called a __________. a. conjunction b. disjunction c. conditional

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d. biconditional

8. An and statement is called a __________. a. conjunction b. disjunction c. conditional d. biconditional

Utilize truth tables to determine the validity of the following arguments.

9. J → K J ∴ K

10. H → G G ∴ H

11. K→ K ∴ K

12. ~(H & Y) Y ∨~H ∴ ~H

13. W → Q ~W ∴ ~Q

14. A → B B → C ∴ A → C

15. ~(P ↔ U) ∴ ~(P → U)

16. ~S ∨ H ~S ∴ ~H

17. ~K → ~L J → ~K ∴ J → ~L

18. Y & P P ∴ ~Y

19. A → ~G V → ~G ∴ A → V

20. B & K & I ∴ K

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Mark Wragg/iStock/Thinkstock

Rather than base decisions on chance, people use the information around them to make deductive and inductive inferences with varying degrees of strength and validity. Logicians use proofs to show the validity of inferences.

4.5 Some Famous Propositional Argument Forms

Using the truth table test for validity, we have seen that we can determine the validity or invalidity of all propositional argument forms. However, there are some basic argument forms that are so common that it is worthwhile simply to memorize them and whether or not they are valid. We will begin with �ive very famous valid argument forms and then cover two of the most famous invalid argument forms.

Common Valid Forms

It is helpful to know some of the most commonly used valid argument forms. Those presented in this section are used so regularly that, once you learn them, you may notice people using them all the time. They are also used in what are known as deductive proofs (see A Closer Look: Deductive Proofs).

A Closer Look: Deductive Proofs

A big part of formal logic is constructing proofs. Proofs in logic are a lot like proofs in mathematics. We start with certain premises and then use certain rules—called rules of inference—in a step-by-step way to arrive at the conclusion. By using only valid rules of inference and applying them carefully, we make certain that every step of the proof is valid. Therefore, if there is a logical proof of the conclusion from the premises, then we can be certain that the argument itself is valid.

The rules of inference used in deductive proofs are actually just simple valid argument forms. In fact, the valid argument forms covered here—including modus ponens, hypothetical syllogisms, and disjunctive syllogisms—are examples of argument forms that are used as inference rules in logical proofs. Using these and other formal rules, it is possible to give a logical proof for every valid argument in propositional logic (Kennedy, 2012).

Logicians, mathematicians, philosophers, and computer scientists use logical proofs to show that the validity of certain inferences is absolutely certain and founded on the most basic principles. Many of the inferences we make in daily life are of limited certainty; however, the validity of inferences that have been logically proved is considered to be the most certain and uncontroversial of all knowledge because it is derivable from pure logic.

Covering how to do deductive proofs is beyond the scope of this book, but readers are invited to peruse a book or take a course on formal logic to learn more about how deductive proofs work.

Modus Ponens Perhaps the most famous propositional argument form of all is known as modus ponens—Latin for “the way of putting.” (You may recognize this form from the earlier section on the truth table method.) Modus ponens has the following form:

P → Q P ∴ Q

You can see that the argument is valid just from the meaning of the conditional. The �irst premise states, “If P is true, then Q is true.” It would logically follow that if P is true, as the second premise states, then Q must be true. Here are some examples:

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Ruth Black/iStock/Thinkstock

Evaluate this argument form for validity: If the cake is made with sugar, then the

If you want to get an A, you have to study. You want to get an A. Therefore, you have to study.

If it is raining, then the street is wet. It is raining. Therefore, the street is wet.

If it is wrong, then you shouldn’t do it. It is wrong. Therefore, you shouldn’t do it.

A truth table will verify its validity.

P1 P2 C

P Q P → Q P Q

T T T T T

T F F T F

F T T F T

F F T F F

There is no line in which all of the premises are true and the conclusion false, verifying the validity of this important logical form.

Modus Tollens A closely related form has a closely related name. Modus tollens—Latin for “the way of taking”—has the following form:

P → Q ~Q ∴ ~P

A truth table can be used to verify the validity of this form as well. However, we can also see its validity by simply thinking it through. Suppose it is true that “If P, then Q.” Then, if P were true, it would follow that Q would be true as well. But, according to the second premise, Q is not true. It follows, therefore, that P must not be true; otherwise, Q would have been true. Here are some examples of arguments that �it this logical form:

In order to get an A, I must study. I will not study. Therefore, I will not get an A.

If it rained, then the street would be wet. The street is not wet. Therefore, it must not have rained.

If the ball hit the window, then I would hear glass shattering. I did not hear glass shattering. Therefore, the ball must not have hit the window.

For practice, construct a truth table to demonstrate the validity of this form.

Disjunctive Syllogism A disjunctive syllogism is a valid argument form in which one premise states that you have two options, and another premise allows you to rule one of them out. From such

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cake is sweet. The cake is not sweet. Therefore, the cake is not made with sugar.

premises, it follows that the other option must be true. Here are two versions of it formally (both are valid):

P ∨ Q ~P ∴ Q

P ∨ Q ~Q ∴ P

In other words, if you have “P or Q” and not Q, then you may infer P. Here is another example: “Either the butler or the maid did it. It could not have been the butler. Therefore, it must have been the maid.” This argument form is quite handy in real life. It is frequently useful to consider alternatives and to rule one out so that the options are narrowed down to one.

Hypothetical Syllogism One of the goals of a logically valid argument is for the premises to link together so that the conclusion follows smoothly, with each premise providing a link in the chain. Hypothetical syllogism provides a nice demonstration of just such premise linking. Hypothetical syllogism takes the following form:

P → Q Q → R ∴ P → R

For example, “If you lose your job, then you will have no income. If you have no income, then you will starve. Therefore, if you lose your job, then you will starve!”

Double Negation Negating a sentence (putting a ~ in front of it) makes it say the opposite of what it originally said. However, if we negate it again, we end up with a sentence that means the same thing as our original sentence; this is called double negation.

Imagine that our friend Johnny was in a race, and you ask me, “Did he win?” and I respond, “He did not fail to win.” Did he win? It would appear so. Though some languages allow double negations to count as negative statements, in logic a double negation is logically equivalent to the original statement. Both of these forms, therefore, are valid:

P ∴ ~~P

~~P ∴ P

A truth table will verify that each of these forms is valid; both P and ~~P have the same truth values on every row of the truth table.

Common Invalid Forms

Both modus ponens and modus tollens are logically valid forms, but not all famous logical forms are valid. The last two forms we will discuss—denying the antecedent and af�irming the consequent—are famous invalid forms that are the evil twins of the previous two.

Denying the Antecedent Take a look at the following argument:

If you give lots of money to charity, then you are nice. You do not give lots of money to charity. Therefore, you must not be nice.

This might initially seem like a valid argument. However, it is actually invalid in its form. To see that this argument is logically invalid, take a look at the following argument with the same form:

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If my cat is a dog, then it is a mammal. My cat is not a dog. Therefore, my cat is not a mammal.

This second example is clearly invalid since the premises are true and the conclusion is false. Therefore, there must be something wrong with the form. Here is the form of the argument:

P → Q ~P ∴ ~Q

Because this argument form’s second premise rejects the antecedent, P, of the conditional in the �irst premise, this argument form is referred to as denying the antecedent. We can conclusively demonstrate that the form is invalid using the truth table method.

Here is the truth table:

P1 P2 C

P Q P → Q ~P ~Q

T T T F F

T F F F T

F T T T F

F F T T T

We see on the third line that it is possible to make both premises true and the conclusion false, so this argument form is de�initely invalid. Despite its invalidity, we see this form all the time in real life. Here some examples:

If you are religious, then you believe in living morally. Jim is not religious, so he must not believe in living morally.

Plenty of people who are not religious still believe in living morally. Here is another one:

If you are training to be an athlete, then you should stay in shape. You are not training to be an athlete. Thus, you should not stay in shape.

There are plenty of other good reasons to stay in shape.

If you are Republican, then you support small government. Jack is not Republican, so he must not support small government.

Libertarians, for example, are not Republicans, yet they support small government. These examples abound; we can generate them on any topic.

Because this argument form is so common and yet so clearly invalid, denying the antecedent is a famous fallacy of formal logic.

Af�irming the Consequent Another famous formal logical fallacy also begins with a conditional. However, the other two lines are slightly different. Here is the form:

P → Q Q ∴ P

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Because the second premise states the consequent of the conditional, this form is called af�irming the consequent. Here is an example:

If you get mono, you will be very tired. You are very tired. Therefore, you have mono.

The invalidity of this argument can be seen in the following argument of the same form:

If my cat is a dog, then it is a mammal. My cat is a mammal. Therefore, my cat is a dog.

Clearly, this argument is invalid because it has true premises and a false conclusion. Therefore, this must be an invalid form. A truth table will further demonstrate this fact:

P1 P2 C

P Q P → Q Q P

T T T T T

T F F F T

F T T T F

F F T F F

The third row again demonstrates the possibility of true premises and a false conclusion, so the argument form is invalid. Here are some examples of how this argument form shows up in real life:

In order to get an A, I have to study. I am going to study. Therefore, I will get an A.

There might be other requirements to get an A, like showing up for the test.

If it rained, then the street would be wet. The street is wet. Therefore, it must have rained.

Sprinklers may have done the job instead.

If he committed the murder, then he would have had to have motive and opportunity. He had motive and opportunity. Therefore, he committed the murder.

This argument gives some evidence for the conclusion, but it does not give proof. It is possible that someone else also had motive and opportunity.

The reader may have noticed that in some instances of af�irming the consequent, the premises do give us some reason to accept the conclusion. This is because of the similarity of this form to the inductive form known as inference to the best explanation, which is covered in more detail in Chapter 6. In such inferences we create an “if–then” statement that expresses something that would be the case if a certain assumption were true. These things then act as symptoms of the truth of the assumption. When those symptoms are observed, we have some evidence that the assumption is true. Here are some examples:

If you have measles, then you would present the following symptoms. . . . You have all of those symptoms. Therefore, it looks like you have measles.

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If he is a faithful Catholic, then he would go to Mass. I saw him at Mass last Sunday. Therefore, he is probably a faithful Catholic.

All of these seem to supply decent evidence for the conclusion; however, the argument form is not logically valid. It is logically possible that another medical condition could have the same symptoms or that a person could go to Mass out of curiosity. To determine the (inductive) inferential strength of an argument of that form, we need to think about how likely Q is under different assumptions.

A Closer Look: Translating Categorical Logic

The chapter about categorical logic seems to cover a completely different type of reasoning than this chapter on propositional logic. However, logical advancements made just over a century ago by a man named Gottlob Frege showed that the two types of logic can be combined in what has come to be known as quanti�icational logic (also known as predicate logic) (Frege, 1879).

In addition to truth-functional logic, quanti�icational logic allows us to talk about quantities by including logical terms for all and some. The addition of these terms dramatically increases the power of our logical language and allows us to represent all of categorical logic and much more. Here is a brief overview of how the basic sentences of categorical logic can be represented within quanti�icational logic.

The statement “All dogs are mammals” can be understood to mean “If you are a dog, then you are a mammal.” The word you in this sentence applies to any individual. In other words, the sentence states, “For all individuals, if that individual is a dog, then it is a mammal.” In general, statements of the form “All S is M” can be represented as “For all things, if that thing is S, then it is M.”

The statement “Some dogs are brown” means that there exist dogs that are brown. In other words, there exist things that are both dogs and brown. Therefore, statements of the form “Some S is M” can be represented as “There exists a thing that is both S and M” (propositions of the form “Some S are not M” can be represented by simply adding a negation in front of the M).

Statements like “No dogs are reptiles” can be understood to mean that all dogs are not reptiles. In general, statements of the form “No S are M” can be represented as “For all things, if that thing is an S, then it is not M.”

Quanti�icational logic allows us to additionally represent the meanings of statements that go well beyond the AEIO propositions of categorical logic. For example, complex statements like “All dogs that are not brown are taller than some cats” can also be represented with the power of quanti�icational logic though they are well beyond the capacity of categorical logic. The additional power of quanti�icational logic enables us to represent the meaning of vast stretches of the English language as well as statements used in formal disciplines like mathematics. More instruction in this interesting area can be found in a course on formal logic.

Practice Problems 4.4

Each of the following arguments is a deductive form. Identify the valid form under which the example falls. If the example is not a valid form, select “not a valid form.” Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems4.4.pdf) to check your answers.

1. If we do not decrease poverty in society, then our society will not be an equal one. We are not going to decrease poverty in society. Therefore, our society will not be an equal one.

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a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

2. If we do not decrease poverty in society, then our society will not be an equal one. Our society will be an equal one. Therefore, we will decrease poverty in society.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

3. If the moon is full, then it is a good time for night �ishing. If it’s a good time for night �ishing, then we should go out tonight. Therefore, if the moon is full, then we should go out tonight.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

4. Either the Bulls or the Knicks will lose tonight. The Bulls are not going to lose. Therefore, the Knicks will lose.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

5. If the battery is dead, then the car won’t start. The car won’t start. Therefore, the battery is dead. a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

6. If I take this new job, then we will have to move to Alaska. I am not going to take the new job. Therefore, we will not have to move to Alaska.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

7. If human perception conditions reality, then humans cannot know things in themselves. If humans cannot know things in themselves, then they cannot know the truth. Therefore, if human perceptions conditions reality, then humans cannot know the truth.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

8. We either adopt the plan or we will be in danger of losing our jobs. We are not going to adopt the plan. Therefore, we will be in danger of losing our jobs.

a. modus ponens

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b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

9. If media outlets are owned by corporations with advertising interests, then it will be dif�icult for them to be objective. Media outlets are owned by corporations with advertising interests. Therefore, it will be dif�icult for them to be objective.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

10. If you eat too much aspartame, you will get a headache. You do not have a headache. Therefore, you did not eat too much aspartame.

a. modus ponens b. modus tollens c. disjunctive syllogism d. hypothetical syllogism e. not a valid form

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Summary and Resources

Chapter Summary Propositional logic shows how the truth values of complex statements can be systematically derived from the truth values of their parts. Words like and, or, not, and if . . . then . . . each have truth tables that demonstrate the algorithms for determining these truth values. Once we have found the logical form of an argument, we can determine whether it is logically valid by using the truth table method. This method involves creating a truth table that represents all possible truth values of the component parts and the resulting values for the premises and conclusion of the argument. If there is even one row of the truth table in which all of the premises are true and the conclusion is false, then the argument is invalid; if there is no such row, then it is valid.

Knowledge of propositional logic has proved very valuable to humankind: It allows us to formally demonstrate the validity of different types of reasoning; it helps us precisely understand the meaning of certain types of terms in our language; it enables us to determine the truth conditions of formally complex statements; and it forms the basis for computing.

Critical Thinking Questions

Connecting The Dots Chapter 4

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1. Symbolizing arguments makes them easier to visualize and examine in the realm of propositional logic. Do you �ind that the symbols make things easier to visualize or more confusing? If logicians use these methods to make things easier, then what does that mean if you think that using these symbols is confusing?

2. In your own words, what is the difference between categorical logic and propositional logic? How do they relate to one another? How do they differ?

3. How does understanding how to symbolize statements and complete truth tables relate to your everyday life? What is the practical importance of understanding how to use these methods to determine validity?

4. If you were at work or with your friends and someone presented an argument, do you think you could evaluate it using the methods you have learned thus far in this book? Is it important to evaluate arguments, or is this just something academics do in their spare time? Why do you believe this is (or is not) the case?

5. How would you now explain the concept of validity to someone with whom you interact on a daily basis who might not have an understanding of logic? How would you explain how validity differs from truth?

Web Resources http://www.manyworldso�logic.com/exercises/quizTruthFunctional.html (http://www.manyworldso�logic.com/exercises/quizTruthFunctional.html) Test your understanding of propositional, or truth-functional, logic by taking the quizzes available at philosophy professor Paul Herrick’s Many Worlds of Logic website.

https://www.youtube.com/watch?v=moHkk_89UZE (https://www.youtube.com/watch?v=moHkk_89UZE) Watch a video that walks you through how to construct a truth table.

https://www.youtube.com/watch?feature=player_embedded&v=83xPkTqoulE (https://www.youtube.com/watch? feature=player_embedded&v=83xPkTqoulE) Watch Ashford University professor Justin Harrison explain how to construct a conjunction truth table.

Key Terms

af�irming the consequent

antecedent

biconditional

conditional

conjunction

connectives

consequent

converse

denying the antecedent

disjunction

disjunctive syllogism

double negation

hypothetical syllogism

logically equivalent

modus ponens

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modus tollens

negation

operators

proposition

propositional logic

sentence variables

statement form

truth table

truth value

is a conditional and the other of which is the consequent of that conditional It has the

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Learning Objectives

After reading this chapter, you should be able to:

1. De�ine key terms and concepts in inductive logic, including strength and cogency.

2. Differentiate between strong inductive arguments and weak inductive arguments.

3. Identify general methods for strengthening inductive arguments.

4. Identify statistical syllogisms and describe how they can be strong or weak.

5. Evaluate the strength of inductive generalizations.

6. Differentiate between causal and correlational relationships and describe various types of causes.

7. Use Mill’s methods to evaluate causal arguments.

8. Recognize arguments from authority and evaluate their quality.

5Inductive Reasoning

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9. Identify key features of arguments from analogy and use them to evaluate the strength of such arguments.

When talking about logic, people often think about formal deductive reasoning. However, most of the arguments we encounter in life are not deductive at all. They do not intend to establish the truth of the conclusion beyond any possible doubt; they simply try to provide good evidence for the truth of their conclusions. Arguments that intend to reason in this way are called inductive arguments. Inductive arguments are not any worse than deductive ones. Often the best evidence available is not �inal or conclusive but can still be very good.

For example, to infer that the sun will rise tomorrow because it has every day in the past is inductive reasoning. The inference, however, is very strongly supported. Not all inductive arguments are as strong as that one. This chapter will explore different types of inductive arguments and some principles we can use to determine whether they are strong or weak. The chapter will also discuss some speci�ic methods that we can use to try to make good inferences about causation. The goal of this chapter is to enable you to identify inductive arguments, evaluate their strength, and create strong inductive arguments about important issues.

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Weather forecasters use inductive reasoning when giving their predictions. They have tools at their disposal that provide support for their arguments, but some arguments are weaker than others.

5.1 Basic Concepts in Inductive Reasoning

Inductive is a technical term in logic: It has a precise de�inition, and that de�inition may be different from the de�inition used in other �ields or in everyday conversation. An inductive argument is one in which the premises provide support for the conclusions but fall short of establishing complete certainty. If you stop to think about arguments you have encountered recently, you will probably �ind that most of them are inductive. We are seldom in a position to prove something absolutely, even when we have very good reasons for believing it.

Take, for example, the following argument:

The odds of a given lottery ticket being the winning ticket are extremely low. You just bought a lottery ticket. Therefore, your lottery ticket is probably not the winning ticket.

If the odds of each ticket winning are 1 in millions, then this argument gives very good evidence for the truth of its conclusion. However, the argument is not deductively valid. Even if its premises are true, its conclusion is still not absolutely certain. This means that there is still a remote possibility that you bought the winning ticket.

Chapter 3 discussed how an argument is valid if our premises guarantee the truth of the conclusion. In the case of the lottery, even our best evidence cannot be used to make a valid argument for the conclusion. The given reasons do not guarantee that you will not win; they just make it very likely that you will not win.

This argument, however, helps us establish the likelihood of its conclusion. If it were not for this type of reasoning, we might spend all our money on lottery tickets. We would also not be able to know whether we should do such things as drive our car because we would not be able to reason about the likelihood of getting into a crash on the way to the store. Therefore, this and other types of inductive reasoning are essential in daily life. Consequently, it is important that we learn how to evaluate their strength.

Inductive Strength

Some inductive arguments can be better or worse than others, depending on how well their premises increase the likelihood of the truth of their conclusion. Some arguments make their conclusions only a little more likely; other arguments make their conclusions a lot more likely. Arguments that greatly increase the likelihood of their conclusions are called strong arguments; those that do not substantially increase the likelihood are called weak arguments.

Here is an example of an argument that could be considered very strong:

A random fan from the crowd is going to race (in a 100 meter dash) against Usain Bolt. Usain Bolt is the fastest sprinter of all time. Therefore, the fan is going to lose.

It is certainly possible that the fan could win—say, for example, if Usain Bolt breaks an ankle—but it seems highly unlikely. This next argument, however, could be considered weak:

I just scratched off two lottery tickets and won $2 each time. Therefore, I will win $2 on the next ticket, too.

The previous lottery tickets would have no bearing on the likelihood of winning on the next one. Now this next argument’s strength might be somewhere in between:

The Bears have beaten the Lions the last four times they have played. The Bears have a much better record than the Lions this season.

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Context plays an important role in inductive arguments. What makes an argument strong in one context might not be strong enough in another. Would you be more likely to play the lottery if your chances of winning were supported at 99%?

Fuse/Thinkstock

The strength of an inductive argument can change when new premises are added. When evaluating or presenting an inductive argument, gather as many details as possible to have a more complete understanding of the strength of the argument.

Therefore, the Bears will beat the Lions again tomorrow.

This sounds like good evidence, but upsets happen all the time in sports, so its strength is only moderate.

Considering the Context It is important to realize that inductive strength and weakness are relative terms. As such, they are like the terms tall and short. A person who is short in one context may be tall in another. At 6’0”, professional basketball player Allen Iverson was considered short in the National Basketball Association. But outside of basketball, someone of his height might be considered tall. Similarly, an argument that is strong in one context may be considered weak in another. You would probably be reasonably happy if you could reliably predict sports (or lottery) results at an accuracy rate of 70%, but researchers in the social sciences typically aim for certainty upward of 90%. In high-energy physics, the goal is a result that is supported at the level of 5 sigma—a probability of more than 99.99997%!

The same is true when it comes to legal arguments. A case tried in a civil court needs to be shown to be true with a preponderance of evidence, which is much less stringent than in a criminal case, in which the defendant must be proved guilty beyond reasonable doubt. Therefore, whether the argument is strong or weak is a matter of context.

Moreover, some subjects have the sort of evidence that allows for extremely strong arguments, whereas others do not. A psychologist trying to predict human behavior is unlikely to have the same strength of argument as an astronomer trying to predict the path of a comet. These are important things to keep in mind when it comes to evaluating inductive strength.

Strengthening Inductive Arguments Regardless of the subject matter of an argument, we generally want to create the strongest arguments we can. In general, there are two ways of strengthening inductive arguments. We can either claim more in the premises or claim less in the conclusion.

Claiming more in the premises is straightforward in theory, though it can be dif�icult in practice. The idea is simply to increase the amount of evidence for the conclusion. Suppose you are trying to convince a friend that she will enjoy a particular movie. You have shown her that she has liked other movies by the same director and that the movie is of the general kind that she likes. How could you strengthen your argument? You might show her that her favorite actors are cast in the lead roles, or you might appeal to the reviews of critics with which she often agrees. By adding these additional pieces of evidence, you have increased the strength of your argument that your friend will enjoy the movie.

However, if your friend looks at all the evidence and still is not sure, you might take the approach of weakening your conclusion. You might say something like, “Please go with me; you may not actually like the movie, but at least you can be pretty sure you won’t hate it.” The very same evidence you presented earlier—about the director, the genre, the actors, and so on—actually makes a stronger argument for your new, less ambitious claim: that your friend won’t hate the movie.

It might help to have another example of how each of the two approaches can help strengthen an inductive argument. Take the following argument:

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Every crow I have ever seen has been black. Therefore, all crows are black.

This seems to provide decent evidence, provided that you have seen a lot of crows. Here is one way to make the argument stronger:

Studies by ornithologists have examined thousands of crows in every continent in which they live, and they have all been black. Therefore, all crows are black.

This argument is much stronger because there is much more evidence for the truth of the conclusion within the premise. Another way to strengthen the argument—if you do not have access to lots of ornithological studies—would simply be to weaken the stated conclusion:

Every crow I have ever seen has been black. Therefore, most crows are probably black.

This argument makes a weaker claim in the conclusion, but the argument is actually much stronger than the original because the premises make this (weaker) conclusion much more likely to be true than the original (stronger) conclusion.

By the same token, an inductive argument can also be made weaker either by subtracting evidence from the premises or by making a stronger claim in the conclusion. (For another way to weaken or strengthen inductive arguments, see A Closer Look: Using Premises to Affect Inductive Strength.)

A Closer Look: Using Premises to Affect Inductive Strength

Suppose we have a valid deductive argument. That means that, if its premises are all true, then its conclusion must be true as well. Suppose we add a new premise. Is there any way that the argument could become invalid? The answer is no, because if the premises of the new argument are all true, then so are all the premises of the old argument. Therefore, the conclusion still must be true.

This is a principle with a fancy name; it is called monotonicity: Adding a new premise can never make a deductive argument go from valid to invalid. However, this principle does not hold for inductive strength: It is possible to weaken an inductive argument by adding new premises.

The following argument, for example, might be strong:

99% of birds can �ly. Jonah is a bird. Therefore, Jonah can �ly.

This argument may be strong as it is, but what happens if we add a new premise, “Jonah is an ostrich”? The addition of this new premise just made the argument’s strength plummet. We now have a fairly weak argument! To use our new big word, this means that inductive reasoning is nonmonotonic. The addition of new premises can either enhance or diminish an argument’s inductive strength.

An interesting “game” is to see if you can continue to add premises that continue to �lip the inductive argument’s degree of strength back and forth. For example, we could make the argument strong again by adding “Jonah is living in the museum of amazing �lying ostriches.” Then we could weaken it again with “Jonah is now retired.” It could be strengthened again with “Jonah is still sometimes seen �lying to the roof of the museum,” but it could be weakened again with “He was seen �lying by the neighbor child who has been known to lie.” The game demonstrates the sensitivity of inductive arguments to new information.

Thus, when using inductive reasoning, we should always be open to learning more details that could further serve to strengthen or weaken the case for the truth of the conclusion. Inductive strength is a never-ending process of

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gathering and evaluating new and relevant information. For scientists and logicians, that is partly what makes induction so exciting!

Inductive Cogency

Notice that, like deductive validity, inductive strength has to do with the strength of the connection between the premises and the conclusion, not with the truth of the premises. Therefore, an inductive argument can be strong even with false premises. Here is an example of an inductively strong argument:

Every lizard ever discovered is purple. Therefore, most lizards are probably purple.

Of course, as with deductive reasoning, for an argument to give good evidence for the truth of the conclusion, we also want the premises to actually be true. An inductive argument is called cogent if it is strong and all of its premises are true. Whereas inductive strength is the counterpart of deductive validity, cogency is the inductive counterpart of deductive soundness.

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5.2 Statistical Arguments: Statistical Syllogisms

The remainder of this chapter will go over some examples of the different types of inductive arguments: statistical arguments, causal arguments, arguments from authority, and arguments from analogy. You will likely �ind that you have already encountered many of these various types in your daily life. Statistical arguments, for example, should be quite familiar. From politics, to sports, to science and health, many of the arguments we encounter are based on statistics, drawing conclusions from percentages and other data.

In early 2013 American actress Angelina Jolie elected to have a preventive double mastectomy. This surgery is painful and costly, and the removal of both breasts is deeply disturbing for many women. We might have expected Jolie to avoid the surgery until it was absolutely necessary. Instead, she had the surgery before there was any evidence of the cancer that normally prompts a mastectomy. Why did she do this?

Jolie explained some of her reasoning in an opinion piece in the New York Times.

I carry a “faulty” gene, BRCA1, which sharply increases my risk of developing breast cancer and ovarian cancer.

My doctors estimated that I had an 87 percent risk of breast cancer and a 50 percent risk of ovarian cancer, although the risk is different in the case of each woman. (Jolie, 2013, para. 2–3)

As you can see, Jolie’s decision was based on probabilities and statistics. If these types of reasoning can have such profound effects in our lives, it is essential that we have a good grasp on how they work and how they might fail. In this section, we will be looking at the basic structure of some simple statistical arguments and some of the things to pay attention to as we use these arguments in our lives.

One of the main types of statistical arguments we will discuss is the statistical syllogism. Let us start with a basic example. If you are not a cat fancier, you may not know that almost all calico cats are female—to be more precise, about 99.97% of calico cats are female (Becker, 2013). Suppose you are introduced to a calico cat named Puzzle. If you had to guess, would you say that Puzzle is female or male? How con�ident are you in your guess?

Since you do not have any other information except that 99.97% of calico cats are female and Puzzle is a calico cat, it should seem far more likely to you that Puzzle is female. This is a statistical syllogism: You are using a general statistic about calico cats to make an argument for a speci�ic case. In its simplest form, the argument would look like this:

99.97% of calico cats are female. Puzzle is a calico cat. Therefore, Puzzle is female.

Clearly, this argument is not deductively valid, but inductively it seems quite strong. Given that male calico cats are extremely rare, you can be reasonably con�ident that Puzzle is female. In this case we can actually put a number to how con�ident you can be: 99.97% con�ident.

Of course, you might be mistaken. After all, male calico cats do exist; this is what makes the argument inductive rather than deductive. However, statistical syllogisms like this one can establish a high degree of certainty about the truth of the conclusion.

Form

If we consider the calico cat example, we can see that the general form for a statistical syllogism looks like this:

X% of S are P. i is an S. Therefore, i is (probably) a P.

There are also statistical syllogisms that conclude that the individual i does not have the property P. Take the following example:

Only 1% of college males are on the football team.

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Mike is a college male. Therefore, Mike is probably not on the football team.

This type of statistical syllogism has the following form:

X% of S are P. i is an S. Therefore, i is (probably) not a P.

In this case, for the argument to be strong, we want X to be a low percentage.

Note that statistical syllogisms are similar to two kinds of categorical syllogisms presented in Chapter 3 (see Table 5.1). We see from the table that statistical syllogisms become valid categorical syllogisms when the percentage, X, becomes 100% or 0%.

Table 5.1: Statistical syllogism versus categorical syllogism

Statistical syllogism Similar valid categorical syllogism

Example 99.97% of calico cats are female. Puzzle is calico. Therefore, Puzzle is female.

All calico cats are female. Puzzle is calico. Therefore, Puzzle is female.

Form X% of S are P. i is an S. Therefore, i is (probably) P.

All M are P. S is M. Therefore, S is P.

Example 1% of college males are on the football team. Mike is a college male. Therefore, Mike is not on the football team.

No college males are on the football team. Mike is a college male. Therefore, Mike is not on the football team.

Form X% of S are P. i is an S. Therefore, i is P.

X% of S are P. i is an S. Therefore, i is not P.

When identifying a statistical syllogism, it is important to keep the speci�ic form in mind, since there are other kinds of statistical arguments that are not statistical syllogisms. Consider the following example:

85% of community college students are younger than 40. John is teaching a community college course. Therefore, about 85% of the students in John’s class are under 40.

This argument is not a statistical syllogism because it does not �it the form. If we make i “John” then the conclusion states that John, the teacher, is probably under 40, but that is not the conclusion of the original argument. If we make i “the students in John’s class,” then we get the conclusion that it is 85% likely that the students in John’s class are under 40. Does this mean that all of them or that some of them are? Either way, it does not seem to be the same as the original conclusion, since that conclusion has to do with the percentage of students under 40 in his class. Though this argument has the same “feel” as a statistical syllogism, it is not one because it does not have the same form as a statistical syllogism.

Weak Statistical Syllogisms

There are at least two ways in which a statistical syllogism might not be strong. One way is if the percentage is not high enough (or low enough in the second type). If an argument simply includes the premise that most of S are P, that means only that more than half of S are P. A probability of only 51% does not make for a strong inductive argument.

Another way that statistical syllogisms can be weak is if the individual in question is more (or less) likely to have the relevant characteristic P than the average S. For example, take the reasoning:

99% of birds do not talk.

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My pet parrot is a bird. Therefore, my pet parrot cannot talk.

The premises of this argument may well be true, and the percentage is high, but the argument may be weak. Do you see why? The reason is that a pet parrot has a much higher likelihood of being able to talk than the average bird. We have to be very careful when coming to �inal conclusions about inductive reasoning until we consider all of the relevant information.

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To ensure a sample is representative, participants should be randomly selected

5.3 Statistical Arguments: Inductive Generalizations

In the example about Puzzle, the calico cat, the �irst premise said that 99.97% of calico cats are female. How did someone come up with that �igure? Clearly, she or he did not go out and look at every calico cat. Instead, he or she likely looked at a bunch of calicos, �igured out what percentage of those cats were female, and then reasoned that the percentage of females would have been the same if they had looked at all calico cats. In this sort of reasoning, the group of calico cats that were actually examined is called the sample, and all the calico cats taken as a group are called the population. An inductive generalization is an argument in which we reason from data about a sample population to a claim about a large population that includes the sample. Its general form looks like this:

X% of observed Fs are Gs. Therefore, X% of all Fs are Gs.

In the case of the calico cats, the argument looks like this:

99.97% of calico cats in the sample were female. Therefore, 99.97% of all calico cats are female.

Whether the argument is strong or weak depends crucially on whether the sample population is representative of the whole population. We say that a sample is representative of a population when the sample and the population both have the same distribution of the trait we are interested in—when the sample “looks like” the population for our purposes. In the case of the cats, the strength of the argument depends on whether our sample group of calico cats had about the same proportion of females as the entire population of all calico cats.

There is a lot of math and research design—which you might learn about if you take a course in applied statistics or in quantitative research design—that goes into determining the likelihood that a sample is representative. However, even with the best math and design, all we can infer is that a sample is extremely likely to be representative; we can never be absolutely certain it is without checking the entire population. However, if we are careful enough, our arguments can still be very strong, even if they do not produce absolute certainty. This section will examine how researchers try to ensure the sample population is representative of the whole population and how researchers assess how con�ident they can be in their results.

Representativeness

The main way that researchers try to ensure that the sample population is representative of the whole population is to make sure that the sample population is random and suf�iciently large. Researchers also consider a measure called the margin of error to determine how similar the sample population is to the whole population.

Randomness Suppose you want to know how many marshmallow treats are in a box of your favorite breakfast cereal. You do not have time to count the whole box, so you pour out one cup. You can count the number of marshmallows in your cup and then reason that the box should have the same proportion of marshmallows as the cup. You found 15 marshmallows in the cup, and the box holds eight cups of cereal, so you �igure that there should be about 120 marshmallows in the box. Your argument looks something like this:

A one-cup sample of cereal contains 15 marshmallows. The box holds eight cups of cereal. Therefore, the box contains 120 marshmallows.

What entitles you to claim that the sample is representative? Is there any way that the sample may not represent the percentage of marshmallows in the whole box? One potential problem is that marshmallows tend to be lighter than the cereal pieces. As a result,

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from the larger population. Careful consideration is required to ensure selections truly represent the larger population.

One must be careful when making inductive generalizations based on statistical data. Consider the examples in this video. Raw numbers can sound more alarming than percentages. Likewise, rate statistics can be misleading.

Making Inferences From Statistics

Critical Thinking Questions

1. The characteristics of the sample is an important consideration when drawing inferences from statistics. Before reading on, what qualities do you think an ideal sample possesses?

2. How can one ensure that one is making proper inferences from evidence?

they tend to rise to the top of the box as the cereal pieces settle toward the bottom of the box over time. If you just scoop out a cup of cereal from the top, then, your sample may not be representative of the whole box and may have too many marshmallows.

One way to solve this problem might be to shake the box. Vigorously shaking the box would probably distribute the marshmallows fairly evenly. After a good shake, a particular piece of marshmallow or cereal might equally end up anywhere in the box, so the ones that make it into your sample will be largely random. In this case the argument may be fairly strong.

In a random sample, every member of the population has an equal chance of being included. Understanding how randomness works to ensure representativeness is a bit tricky, but another example should help clear it up.

Almost all students at my high school have laptops. Therefore, almost all high school students in the United States have laptops.

This reasoning might seem pretty strong, especially if you go to a large high school. However, is there a way that the sample population (the students at the high school) may not be truly random? Perhaps if the high school is in a relatively wealthy area, then the students will be more likely to have laptops than random American high schoolers. If the sample population is not truly random but has a greater or lesser tendency to have the relevant characteristic than a random member of the whole population, this is known as a biased sample. Biased samples will be discussed further in Chapter 7, but note that they often help reinforce people’s biased viewpoints (see Everyday Logic: Why You Might Be Wrong).

The principle of randomness applies to other types of statistical arguments as well. Consider the argument about John’s community college class. The argument, again, goes as follows:

85% of community college students are younger than 40. John is teaching a community college course. Therefore, about 85% of the students in John’s class are under 40.

Since 85% of community college students are younger than 40, we would expect a suf�iciently large random sample of community college students to have about the same percentage. There are several ways, however, that John’s class may not be a random sample. Before going on to the next paragraph, stop and see how many ways you can think of on your own.

So how is John’s class not a random sample? Notice �irst that the argument references a course at a single community college. The average student age likely varies from college to college, depending on the average age of the nearby population. Even within this one community college, John’s class is not random. What time is John’s class? Night classes tend to attract a higher percentage of older students than daytime classes. Some subjects also attract different age groups. Finally, we should think about John himself. His age and reputation may affect the kind of students who enroll in his classes.

In all these ways, and maybe others, John’s class is not a random sample: There is not an equal chance that

Making Inferences From Statistics From Title: Evidence in Argument: Critical Thinking

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Con�irmation bias, or the tendency to seek out support for our beliefs, can be seen in the friends we choose, books we read, and news sources we select.

3. What is the danger of expressing things using rates? What example is given that demonstrates this danger?

every community college student might be included. As a result, we do not really have good reason to think that John’s class will be representative of the general population of community college students. So we have little reason to expect it to be representative of the larger population. As a result, we cannot use his class to reliably predict what the population will look like, nor can we use the population to reliably predict what John’s class will look like.

Everyday Logic: Why You Might Be Wrong

People are often very con�ident about their views, even when it comes to very controversial issues that may have just as many people on the other side. There are probably several reasons for this, but one of them is due to the use of biased sampling. Consider whether you think your views about the world are shared by many people or by only a few. It is not uncommon for people to think that their views are more widespread than they actually are. Why is that?

Think about how you form your opinion about how much of the nation or world agrees with your view. You probably spend time talking with your friends about these views and notice how many of your friends agree or disagree with you. You may watch television shows or read news articles that agree or disagree with you. If most of the sources you interact with agree with your view, you might conclude that most people agree with you.

However, this would be a mistake. Most of us tend to interact more with people and information sources with which we agree, rather than those with which we disagree. Our circle of friends tends to be concentrated near us both geographically and ideologically. We share similar concerns, interests, and views; that is part of what makes us friends. As with choosing friends, we also tend to select information sources that con�irm our beliefs. This is a well-known psychological tendency known as con�irmation bias (this will be discussed further in Chapter 8).

We seem to reason as follows:

A large percentage of my friends and news sources agree with my view. Therefore, a large percentage of all people and sources agree with my view.

We have seen that this reasoning is based on a biased sample. If you take your friends and information sources as a sample, they are not likely to be representative of the larger population of the nation or world. This is because rather than being a random sample, they have been selected, in part, because they hold views similar to yours. A good critical thinker takes sampling bias into account when thinking about controversial issues.

Sample Size Even a perfectly random sample may not be representative, due to bad luck. If you �lip a coin 10 times, for example, there is a decent chance that it will come up heads 8 of the 10 times. However, the more times you �lip the coin, the more likely it is that the percentage of heads will approach 50%.

The smaller the sample, the more likely it is to be nonrepresentative. This variable is known as the sample size. Suppose a teacher wants to know the average height of students in his school. He randomly picks one student and measures her height. You should see that this is not a big enough sample. By measuring only one student, there is a decent chance that the teacher may have randomly picked someone extremely tall or extremely short. Generalizing on an overly small sample would be making a hasty generalization, an error in reasoning that will be discussed in greater detail in Chapter 7. If the

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teacher chooses a sample of two students, it is less likely that they will both be tall or both be short. The more students the teacher chooses for his sample, the less likely it is that the average height of the sample will be much different than the average height of all students. Assuming that the selection process is unbiased, therefore, the larger the sample population is, the more likely it is that the sample will be representative of the whole population (see A Closer Look: How Large Must a Sample Be?).

A Closer Look: How Large Must a Sample Be?

In general, the larger a sample is, the more likely it is to be representative of the population from which it is drawn. However, even relatively small samples can lead to powerful conclusions if they have been carefully drawn to be random and to be representative of the population. As of this writing, the population of the United States is in the neighborhood of 317 million, yet Gallup, one of the most respected polling organizations in the country, often publishes results based on a sample of fewer than 3,000 people. Indeed, its typical sample size is around 1,000 (Gallup, 2010). That is a sample size of less than 1 in every 300,000 people!

Gallup can do this because it goes to great lengths to make sure that its samples are randomly drawn in a way that matches the makeup of the country’s population. If you want to know about people’s political views, you have to be very careful because these views can vary based on a person’s locale, income, race or ethnicity, gender, age, religion, and a host of other factors.

There is no single, simple rule for how large a sample should be. When samples are small or incautiously collected, you should be suspicious of the claims made on their basis. Professional research will generally provide clear descriptions of the samples used and a justi�ication of why they are adequate to support their conclusions. That is not a guarantee that the results are correct, but they are bound to be much more reliable than conclusions reached on the basis of small and poorly collected samples.

For example, sometimes politicians tour a state with the stated aim of �inding out what the people think. However, given that people who attend political rallies are usually those with similar opinions as the speaker, it is unlikely that the set of people sampled will be both large enough and random enough to provide a solid basis for a reliable conclusion. If politicians really want to �ind out what people think, there are better ways of doing so.

Margin of Error It is always possible that a sample will be wildly different than the population. But equally important is the fact that it is quite likely that any sample will be slightly different than the population. Statisticians know how to calculate just how big this difference is likely to be. You will see this reported in some studies or polls as the margin of error. The margin of error can be used to determine the range of values that are likely for the population.

For example, suppose that a poll �inds that 52% of a sample prefers Ms. Frazier in an election. When you read about the result of this poll, you will probably read that 52% of people prefer Ms. Frazier with a margin of error of ±3% (plus or minus 3%). This means that although the real number probably is not 52%, it is very likely to be somewhere between 49% (3% lower than 52%) and 55% (3% higher than 52%). Since the real percentage may be as low as 49%, Ms. Frazier should not start picking out curtains for her of�ice just yet: She may actually be losing!

Con�idence Level

We want large, random samples because we want to be con�ident that our sample is representative of the population. The more con�ident we are that are sample is representative, the more con�ident we can be in conclusions we draw from it. Nonetheless, even a small, poorly drawn sample can yield informative results if we are cautious about our reasoning.

If you notice that many of your friends and acquaintances are out of work, you may conclude that unemployment levels are up. Clearly, you have some evidence for your conclusion, but is it enough? The answer to this question depends on

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how strong you take your argument to be. Remember that inductive arguments vary from extremely weak to extremely strong. The strength of an argument is essentially the level of con�idence we should have in the conclusion based on the reasons presented. Consider the following ways you might state your con�idence that unemployment levels were up, based on noting unemployment among your friends and acquaintances.

a. “I’m certain that unemployment is up.” b. “I’m reasonably sure that unemployment is up.” c. “It’s more likely than not that unemployment is up.” d. “Unemployment might be up.”

Clearly, A is too strong. Your acquaintances just are not likely to represent the population enough for you to be certain that unemployment is up. On the other hand, D is weak enough that it really does not need much evidence to support it. B and C will depend on how wide and varied your circle of acquaintances is and on how much unemployment you see among them. If you know a lot of people and your acquaintances are quite varied in terms of profession, income, age, race, gender, and so on, then you can have more con�idence in your conclusion than if you had only a small circle of acquaintances and they tended to all be like each other in these ways. B also depends on just what you mean by “reasonably sure.” Does that mean 60% sure? 75%? 85%?

Most reputable studies will include a “con�idence level” that indicates how con�ident one can be that their conclusions are supported by the reasons they give. The degree of con�idence can vary quite a bit, so it is worth paying attention to. In most social sciences, researchers aim to reach a 95% or 99% con�idence level. A con�idence level of 95% means that if we did the same study 100 times, then in 95 of those tests the results would fall within the margin of error. As noted earlier, the �ield of physics requires a con�idence level of about 99.99997%, much higher than is typically required or attained in the social sciences. On the other end, sometimes a con�idence level of just over 50% is enough if you are only interested in knowing whether something is more likely than not.

Applying This Knowledge

Now that we have learned something about statistical arguments, what can we say about Angelina Jolie’s argument, presented at the beginning of the prior section? First, notice that it has the form of a statistical syllogism. We can put it this way, written as if from her perspective:

87% of women with certain genetic and other factors develop breast cancer. I am a woman with those genetic and other factors. Therefore, I have an 87% risk of getting breast cancer.

We can see that the argument �its the form correctly. While not deductive, the argument is inductively strong. Unless we have reason to believe that she is more or less likely than the average person with those factors to develop breast cancer, if these premises are true then they give strong evidence for the truth of the conclusion. However, what about the �irst premise? Should we believe it?

In evaluating the �irst premise, we need to consider the evidence for it. Were the samples of women studied suf�iciently random and large that we can be con�ident they were representative of the population of all women? With what level of con�idence are the results established? If the samples were small or not randomized, then we may have less con�idence in them. Jolie’s doctors said that Jolie had an 87% chance of developing breast cancer, but there’s a big difference between being 60% con�ident that she has this level of risk and being 99% certain that she does. To know how con�ident we should be, we would need to look at the background studies that establish that 87% of women with those factors develop breast cancer. Anyone making such an important decision would be well advised to look at these issues in the research before acting.

Practice Problems 5.1

Which of the following attributes might negatively in�luence the data drawn from the following samples? Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.1.pdf) to

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check your answers.

1. A teacher surveys the gifted students in the district about the curriculum that should be adopted at the high school.

a. sample size b. representativeness of the sample c. a and b d. There is no negative in�luence in this case.

2. A researcher for Apple analyzes a large group of tribal people in the Amazon to determine which new apps she should create in 2014.

a. sample size b. representativeness of the sample c. a and b d. There is no negative in�luence in this case.

3. A researcher on a college campus interviews 10 students after a yoga class about their drug use habits and determines that 80% of the student population probably smokes marijuana.

a. sample size b. representativeness of the sample c. a and b d. There is no negative in�luence in this case.

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Suf�icient conditions are present in classroom grading systems. If you need a total of 850 points to receive an A, the suf�icient condition to receive an A is earning 850 points.

5.4 Causal Relationships: The Meaning of Cause

It is dif�icult to say exactly what we mean when we say that one thing causes another. Think about turning on the lights in your room. What is the cause of the lights turning on? Is it the �lipping of the switch? The electricity in the wires? The fact that the bulb is not broken? Your initial desire for the lights to be on? There are many things we could identify as a plausible cause of the lights turning on. However, for practical purposes, we generally look for the set of conditions without which the event in question would not have occurred and with which it will occur. In other words, logicians aim to be more speci�ic about causal relationships by discussing them in terms of suf�icient and necessary conditions. Recall that we used these terms in Chapter 4 when discussing propositional logic. Here we will discuss how these terms can help us understand causal relationships.

Suf�icient Conditions

According to British philosopher David Hume, the notion of cause is based on nothing more than a “constant conjunction” that holds between events—the two events always occur together (Morris & Brown, 2014). We notice that events of kind A are always followed by events of kind B, and we say “A causes B.” Thus, to claim a causal relationship between events of type A and B might be to say: Whenever A occurs, B will occur.

Logicians have a fancy phrase for this relationship: We say that A is a suf�icient condition for B. A factor is a suf�icient condition for the occurrence of an event if whenever the factor occurs, the event also occurs: Whenever A occurs, B occurs as well. Or in other words:

If A occurs, then B occurs.

For example, having a billion dollars is a suf�icient condition for being rich; being hospitalized is a suf�icient condition for being excused from jury duty; having a ticket is a suf�icient condition for being able to be admitted to the concert.

Often several factors are jointly required to create suf�icient conditions. For example, each state has a set of jointly suf�icient conditions for being able to vote, including being over 18, being registered to vote, and not having been convicted of a felony, among other possible quali�ications.

Here is an example of how to think about suf�icient conditions when thinking about real-life causation.

We know room lights do not go on just because you �lip the switch. The points of the switch must come into contact with a power source, electricity must be present, a working lightbulb has to be properly secured in the socket, the socket has to be properly connected, and so forth. If any one of the conditions is not satis�ied, the light will not come on. Strictly speaking, then, the whole set of conditions constitutes the suf�icient condition for the event.

We often choose one factor from a set of factors and call it the cause of an event. The one we call the cause is the one with which we are most concerned for some reason or other; often it is the one that represents a change from the normal state of things. A working car is the normal state of affairs; a hole in the radiator tube is the change to that state of affairs that results in the overheated engine. Similarly, the electricity and lightbulb are part of the normal state of things; what changed most recently to make the light turn on was the �lipping of the switch.

Necessary Conditions

A factor is a necessary condition for an event if the event would not occur in the absence of the factor. Without the necessary condition, the effect will not occur. A is a necessary condition for B if the following statement is always true:

If A is not present, then neither is B.

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Although water is a necessary condition for life, it is not a suf�icient condition for life because humans also need oxygen and food.

This statement happens to be equivalent to the statement that if B is present, then A is present. Thus, a handy way to understand the difference between necessary and suf�icient conditions is as follows:

“A is suf�icient for B” means that if A occurs, then B occurs.

“A is necessary for B” means that if B occurs, then A occurs.

Let us take a look at a real example. Poliomyelitis, or polio, is a disease caused by a speci�ic virus. In only a small minority of those with poliovirus does the virus infect the central nervous system and lead to the terrible condition known as paralytic polio. In the large majority of cases, however, the virus goes undetected and does not result in paralysis. Thus, infection with poliovirus is not a suf�icient condition for getting paralytic polio. However, because one must have the virus to have that condition, being infected with poliovirus is a necessary condition for getting paralytic polio (Mayo Clinic, 2014).

On the other hand, being squashed by a steamroller is a suf�icient condition for death, but it is not a necessary condition. Whenever someone has been squashed by a steamroller, that person is quite dead. However, it is not the case that anyone who is dead has been run over by a steamroller.

If our purpose in looking for causes is to be able to produce an effect, it is reasonable to look for suf�icient conditions for that effect. If we

can manipulate circumstances so that the suf�icient condition is present, the effect will also be present. If we are looking for causes in order to prevent an effect, it is reasonable to look for necessary conditions for that effect. If we prevent a necessary condition from materializing, we can prevent the effect.

The eradication of yellow fever is a striking example. Research showed that being bitten by a certain type of mosquito was a necessary condition for contracting yellow fever (though it was not a suf�icient condition, for some people who were bitten by these mosquitoes did not contract yellow fever). Consequently, a campaign to destroy that particular species of mosquito through the widespread use of insecticides virtually eliminated yellow fever in many parts of the world (World Health Organization, 2014).

Necessary and Suf�icient Conditions

The most restrictive interpretation of a causal relationship consists of construing “cause” as a condition both necessary and suf�icient for the occurrence of an event. If factor A is necessary and suf�icient for the occurrence of event B, then whenever A occurs, B occurs, and whenever A does not occur, B does not occur. In other words:

If A, then B, and if not-A, then not-B.

For example, to produce diamonds, certain very speci�ic conditions must exist. Diamonds are produced if and only if carbon is subjected to immense pressure and heat for a certain period of time. Diamonds do not occur through any other process. If all of the conditions exist, then diamonds will result; diamonds exist only when all of those conditions have been met. Therefore, carbon subjected to the right combination of pressure, heat, and time constitutes both a necessary and suf�icient condition for diamond production.

This construction of cause is so restrictive that very few actual relationships in ordinary experience can satisfy it. However, some scientists think that this is the kind of invariant relationship that scienti�ic laws must express. For instance, according to Newton’s law of gravitation, objects attract each other with a force proportional to the inverse of the square of their distance. Therefore, if we know the force of attraction between two bodies, we can calculate the distance between them (assuming we know their masses). Conversely, if we know the distance between them, we can calculate the force of attraction. Thus, having a certain degree of attraction between two bodies constitutes both a necessary and suf�icient condition for the distance between them. It happens frequently in math and science that the

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values assigned to one factor determine the values assigned to another, and this relationship can be understood in terms of necessary and suf�icient conditions.

Other Types of Causes

The terms necessary condition and suf�icient condition give us concrete and technical ways to describe types of causes. However, in everyday life, the factor we mention as the cause of an event is rarely one we consider suf�icient or even necessary. We frequently select one factor from a set and say it is the cause of the event. Our aims and interests, as well as our knowledge, affect that choice. Thus, practical, moral, or legal considerations may in�luence our selection. There are three principal considerations that may lead us to choose a single factor as “the cause,” although this is not an exhaustive listing.

Trigger cause. The trigger cause, or the factor that initiates an event, is often designated the cause of the event. Usually, this is the factor that occurs last and completes a causal chain—the set of suf�icient conditions—producing the effect. Flipping the switch triggers the lights. All the other factors may be present and as such constitute the standing conditions that allow the event to be triggered. The trigger factor is sometimes referred to as the proximate cause since it is the factor nearest the �inal event (or effect).

Unusual factor. Let us suppose that someone turns on a light and an explosion follows. Turning on the light caused an explosion because the room was full of methane gas. Now being in a room is fairly normal, turning on lights is fairly normal, having oxygen in a room is fairly normal, and having an unsealed light switch is fairly normal. The only condition outside the norm is the presence of a large quantity of explosive gas. Therefore, the presence of methane is referred to as the cause of the explosion. What is unusual, what is outside the norm, is the cause. If we are concerned with �ixing moral or legal responsibility for an effect, we are likely to focus on the person who left the gas on, not the person who turned on the lights.

Controllable factor. Sometimes we call attention to a controllable factor instrumental in producing the event and point out that since the factor could have been controlled, so could the event. Thus, although smoking is neither a suf�icient nor a necessary condition for lung cancer, it is a controllable factor. Therefore, over and above uncontrollable factors like heredity and chance, we are likely to single out smoking as the cause. Similarly, drunk driving is neither a suf�icient nor a necessary condition for getting into a car accident, but it is a controllable factor, so we are likely to point to it as a cause.

Correlational Relationships

In both the case of smoking and drunk driving, neither were necessary nor suf�icient conditions for the subsequent event in question (lung cancer and car accidents). Instead, we would say that both are highly correlated with the respective events. Two things can be said to be correlated, or in correlation, when they occur together frequently. In other words, A is correlated with B, so B is more likely to occur if A occurs, and vice versa. For example, having gray hair is correlated with age. The older someone is, the more likely he or she is to have gray hair, and vice versa. Of course, not all people with gray hair are old, and not all old people have gray hair, so age is neither a necessary nor a suf�icient condition for gray hair. However, the two are highly correlated because they have a strong tendency to go together.

Two things that vary in the same direction are said to be directly correlated or to vary directly; the higher one’s age, the more gray hair. Things that are correlated may also vary in opposite directions; these are said to vary inversely. For example, there is an inverse correlation between the size of a car and its fuel economy. In general, the bigger a car is, the lower its fuel economy is. If you want a car that gets high miles per gallon, you should focus on cars that are smaller. There are other factors to consider too, of course. A small sports car may get lower fuel economy than a larger car with less power. Correlation does not mean that the relationship is perfect, only that variables tend to vary in a certain way.

You may have heard the phrase “correlation does not imply causation,” or something similar. Just because two things happen together, it does

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Variables, such as buffalo and White men, can be correlated in two ways—directly and inversely. Which type of correlation is being discussed in this cartoon?

not necessarily follow that one causes the other. For example, there is a well-known correlation between shoe size and reading ability in elementary children. Children with larger feet have a strong tendency to read better than children with smaller feet. Of course, no one supposes that a child’s shoe size has a direct effect on his or her reading ability, or vice versa. Instead, both of these things are related to a child’s age. Older children tend to have bigger feet than younger children; they also tend to read better. Sometimes the connection between correlated things is simple, as in the case of shoe size and reading, and sometimes it is more complicated.

Whenever you read that two things have been shown to be linked, you should pay attention to the possibility that the correlation is spurious or possibly has another explanation. Consider, for example, a study showing a strong correlation between the amount of fat in a country’s diet and the amount of certain types of cancer in that country (such as K. K. Carroll’s 1975 study, as cited in Paulos, 1997). Such a correlation may lead you to think that eating fat causes cancer, but this could potentially be a mistake. Instead, we should consider whether there might be some other connection between the two.

It turns out that countries with high fat consumption also have high sugar consumption—perhaps sugar is the culprit. Also, countries with high fat and sugar consumption tend to be wealthier; fat and sugar are expensive compared to grain. Perhaps the correlation is the result of some other aspect of a wealthier lifestyle, such as lower rates of physical exercise. (Note that wealth is a particularly common confounding factor, or a factor that correlates with the dependent and independent variables being studied, as it bestows a wide range of advantages and dif�iculties on those who have it.) Perhaps it is a combination of factors, and perhaps it is the fat after all; however, we cannot simply conclude with certainty from a correlation that one causes the other, not without further research.

Sometimes correlation between two things is simply random. If you search through enough data, you may �ind two factors that are strongly correlated but that have nothing at all to do with each other. For example, consider Figure 5.1. At �irst glance, you might think the two factors must be closely connected. But then you notice that one of them is the divorce rate in Maine and the other is the per capita consumption of margarine in the United States. Could it be that by eating less margarine you could help save the marriages of people in Maine?

Figure 5.1: Are these two factors correlated?

Although it may seem like two factors are correlated, we sometimes have to look harder to understand the relationship.

Source: www.tylervigen.com (http://www.tylervigen.com) .

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On the other hand, although correlation does not imply causation, it does point to it. That is, when we see a strong correlation, there is at least some reason to suspect a causal connection of some sort between the two correlates. It may be that one of the correlates causes the other, a third thing causes them both, there is some more complicated causal relation between them, or there is no connection at all.

However, the possibility that the correlation is merely accidental becomes increasingly unlikely if the sample size is large and the correlation is strong. In such cases we may have to be very thoughtful in seeking and testing possible explanations of the correlation. The next section discusses ways that we might �ind and narrow down potential factors involved in a causal relationship.

Consider This: Causal Reasoning and Superstition

NEXT

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5.5 Causal Arguments: Mill’s Methods

Reasoning about causes is extremely important. If we can correctly identify what causes a particular effect, then we have a much better chance of controlling or preventing the effect. Consider the search for a cure for a disease. If we do not understand what causes a particular disease, then our chances of being able to cure it are small. If we can identify the cause of the disease, we can be much more precise in searching for a way to prevent the disease. On the other hand, if we think we know the cause when we do not, then we are likely to look in the wrong direction for a cure.

A causal argument—an argument about causes and effects—is almost always an inductive argument. This is because, although we can gather evidence about these relationships, we are almost never in a position to prove them absolutely.

The following four experimental methods were formally stated in the 19th century by John Stuart Mill in his book A System of Logic and so are often referred to as Mill’s methods. Mill’s methods express the most basic underlying logic of many current methods for investigating causality. They provide a great introduction to some of the basic concepts involved—but know that modern methods are much more rigorous.

Used with caution, Mill’s methods can provide a guide for exploring causal connections, especially when one is looking at speci�ic cases against the background of established theory. It is important to remember that although they can be useful, Mill’s methods are only the beginning of the study of causation. By themselves, they are probably most useful as methods for identifying potential subjects for further study using more robust methods that are beyond the scope of this book.

Method of Agreement

In 1976 an unknown illness affected numerous people in Philadelphia. Although it took some time to fully identify the cause of the disease, a bacterium now called Legionella pneumophila, the �irst step in the investigation was to �ind common features of those who became ill. Researchers were quick to note that sufferers had all attended an American Legion convention at the Bellevue-Stratford Hotel. As you can guess, the focus of the investigation quickly narrowed to conditions at the hotel. Of course, the convention and the hotel were not the actual cause of getting sick, but neither was it mere coincidence that all of the ill had attended the convention. By �inding the common elements shared by those who became ill, investigators were able to quickly narrow their search for the cause. Ultimately, the bacterium was located in a fountain in the hotel.

The method of agreement involves comparing situations in which the same kind of event occurs. If the presence of a certain factor is the only respect in which the situations are the same (that is, they agree), then this factor may be related to the cause of the event. We can represent this with something like Table 5.2. The table indicates whether each of four factors was present in a speci�ic case (A, B, or C) and, in the last column, whether the effect manifested itself (in the earlier case of what is now known as Legionnaires’ disease, the effect we would be interested in is whether infection occurred).

Table 5.2: Example of method of agreement

Case Factor 1 Factor 2 Factor 3 Factor 4 Effect

A No Yes Yes No Yes

B No No Yes Yes Yes

C Yes Yes Yes Yes Yes

The three cases all resulted in the same effect but differed in which factors were present—with the exception of Factor 3, which was present in all three cases. We may then suspect that Factor 3 may be causally related to the effect. Our notion of cause here is that of suf�icient condition. The common factor is suf�icient to account for the effect.

In general, the method of agreement works best when we have a large group of cases that is as varied as possible. A large group is much more likely to vary across many different factors than a small group. Unfortunately, the world almost never presents us with two situations wholly unlike except for one factor. We may have three or more situations that are greatly similar. For example, all of the af�licted in the 1976 outbreak were members of the American Legion, all were adults, all were men, all lived in Pennsylvania. Here is where we have to use common sense and what we already know. It is unlikely

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that merely being a member of an organization is the cause of a disease. We expect diseases to be caused by environmental factors: bacteria, viruses, contaminants, and so on. As a result, we can focus our search on those similarities that seem most likely to be relevant to the cause. Of course, we may be wrong; that is a hallmark of inductive reasoning generally, but by being as careful and as reasonable as we can, we can often make great progress.

Method of Difference

The method of difference involves comparing a situation in which an event occurs with similar situations in which it does not. If the presence of a certain factor is the only difference between the two kinds of situations, it is likely to be causally related to the effect.

Suppose your mother comes to visit you and makes your favorite cake. Unfortunately, it just does not turn out. You know she made it in the same way she always does. What could the problem be? Start by looking at differences between how she made the cake at your house and how she makes it at hers. Ultimately, the only difference you can �ind is that your mom lives in Tampa and you live in Denver. Since that is the only difference, that difference is likely to be causally related to the effect. In fact, Denver is both much higher and much drier than Tampa. Both of these factors make a difference in baking cakes.

Let us suppose we are interested in two cases, A and B, in which A has the effect we are interested in (the cake not turning out right) and B does not. This is outlined in Table 5.3. If we can �ind only one factor that is different between the two cases—in this case, Factor 1—then that factor is likely to be causally related to the effect. This does not tell us whether the factor directly causes the effect, but it does suggest a causal link. Further investigation might reveal just exactly what the connection is.

Table 5.3: Example of method of difference

Case Factor 1 Factor 2 Factor 3 Factor 4 Effect

A Yes No No Yes Yes

B No No No Yes No

In this example, Factor 1 is the one factor that is different between the two cases. Perhaps the presence of Factor 1 is related to why Case A had the effect but Case B did not. Here we are seeing Factor 1 as a necessary condition for the effect.

The method of difference is employed frequently in clinical trials of experimental drugs. Researchers carefully choose or construct two situations that resemble each other in as many respects as possible. If a drug is employed in one but not the other, then they can ascribe to the drug any change in one situation not matched by a change in the other. Note that the two sets must be as similar as possible, since variation could introduce other possible causal links. The group in which change is expected is often referred to as the experimental group, and the group in which change is not expected is often referred to as the control group.

The method of difference may seem obvious and its results reliable. Yet even in a relatively simple experimental setup like this one, we may easily �ind grounds for doubting that the causal claim has been adequately established.

One important factor is that the two cases, A and B, have to be as similar as possible in all other respects for the method of difference to be used effectively. If your 8-year-old son made the cake without supervision, there are likely to be a whole host of differences that could explain the failure. The same principle applies to scienti�ic studies. One thing that can subtly skew experimental results is experimental bias. For example, if the experimenters know which people are receiving the experimental drug, they might unintentionally treat them differently.

To prevent such possibilities, so-called blind experiments are often used. Those conducting the experiment are kept in ignorance about which subjects are in the control group and which are in the experimental group so that they do not even unintentionally treat the subjects differently. Experimenters therefore, do not know whether they are injecting distilled water or the actual drug. In this way the possibility of a systematic error is minimized.

We also have to keep in mind that our inquiry is guided by background beliefs that may be incorrect. No two cases will ever be completely the same except for a single factor. Your mother made the cake on a different day than she did at home,

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she used a different spoon, different people were present in the house, and so on. We naturally focus on similarities and differences that we expect to be relevant. However, we should always realize that reality may disagree with our expectations.

Causal inquiry is usually not a matter of conducting a single experiment. Often we cannot even control for all relevant factors at the same time, and once an experiment is concluded, doubts about other factors may arise. A series of experiments in which different factors are kept constant while others are varied one by one is always preferable.

Joint Method of Agreement and Difference

The joint method of agreement and difference is, as the name suggests, a combination of the methods of agreement and difference. It is the most powerful of Mill’s methods. The basic idea is to have two groups of cases: One group shows the effect, and the other does not. The method of agreement is used within each group, by seeing what they have in common, and the method of difference is used between the two groups, by looking for the differences between the two. Table 5.4 shows how such a chart would look, if we were comparing three different cases (1, 2, and 3) among two groups (A and B).

Table 5.4: Example of joint method of agreement and difference

Case/group Factor 1 Factor 2 Factor 3 Factor 4 Effect

1/A Yes No No Yes Yes

2/A No No Yes Yes Yes

3/A No Yes No Yes Yes

1/B No Yes Yes No No

2/B Yes Yes No No No

3/B Yes No Yes No No

As you can see, within each group the cases agree only on Factor 4 and the effect. But when you compare the two groups, the only consistent differences between them are in Factor 4 and the effect. This result suggests the possibility that Factor 4 may be causally related to the effect in question. In this method, we are using the notion of a necessary and suf�icient condition. The effect happens whenever Factor 4 is present and never when it is absent.

The joint method is the basis for modern randomized controlled experiments. Suppose you want to see if a new medicine is effective. You begin by recruiting a large group of volunteers. You then randomly assign them to either receive the medicine or a placebo. The random assignment ensures that each group is as varied as possible and that you are not unknowingly deciding whether to give someone the medicine based on some common factor. If it turns out that everyone who gets the medicine improves and everyone who gets the placebo stays the same or gets worse, then you can infer that the medicine is probably effective.

In fact, advanced statistics allow us to make inferences from such studies even when there is not perfect agreement on the presence or absence of the effect. So, in reading studies, you may note that the discussion talks about the percentage of each group that shows or does not show the effect. Yet we may still make good inferences about causation by using the method of concomitant variation.

Method of Concomitant Variation

The method of concomitant variation is simply the method of looking for correlation between two things. As we noted in our discussion of correlation, this cannot be used to conclude conclusively that one thing causes the other, but it is suggestive that there is perhaps some causal connection between the two. Stronger evidence can be found by further scienti�ic study.

You may have noticed that, in discussing causes, we are trying to explain a phenomenon. We observe something that is interesting or important to us, and we seek to know why it happened. Therefore, the study of Mill’s methods, as well as

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correlation and concomitant variation, can be seen as part of a broader type of reasoning known as inference to the best explanation, the effort to �ind the best or most accurate explanation of our observations. Because this type of reasoning is sometimes classi�ied as a separate type of reasoning (sometimes called abductive reasoning), it will be covered in Chapter 6.

In summary, Mill’s methods provide a framework for exploring causal relationships. It is important to remember that although they can be useful, they are only the beginning of this important �ield. By themselves, they are probably most useful as methods for identifying potential subjects for further study using more robust methods that are beyond the scope of this book.

Practice Problems 5.2

Identify which of Mill’s methods discussed in the chapter relates to the following examples. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.2.pdf) to check your answers.

1. After going to dinner, all the members of a family came down with vomiting. They all had different entrées but shared a salad as an appetizer. The mother of the family determines that it must have been the salad that caused the sickness.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

2. A couple goes to dinner and shares an appetizer, entrée, and dessert. Only one of the two gets sick. She drank a glass of wine, and her husband drank a beer. She believes that the wine was the cause of her sickness.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

3. In a speci�ic city, the number of people going to emergency rooms for asthma attacks increases as the level of pollution increases in the summer. When the winter comes and pollution goes down, the number of people with asthma attacks decreases.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

4. In the past 15 years there has never been a safety accident in the warehouse. Each day for the past 15 years Lorena has been conducting the morning safety inspections. However, today Lorena missed work, and there was an accident.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

5. Since we have hired Earl, productivity in the of�ice has decreased by 20%. a. method of agreement b. method of difference c. joint method d. method of concomitant variation

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6. In the past, lead was put into many paints. It was found that the number of infant fatalities increased in relation to the amount of exposure these infants had to lead-based paints that were used on their cribs.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

7. It appears that the likelihood of catching the Zombie virus increases the more one is around people who have already been turned into zombies.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

8. In order to determine how a disease was spread in humans, researchers placed two groups of people into two rooms. Both rooms were exactly alike. However, in one room they placed someone who was infected with the disease. The researchers found that those who were in the room with the infected person got sick, whereas those who were not with an infected person remained well.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

9. In a certain IQ test, students in a speci�ic group performed at a much higher level than those of the other groups. After analyzing the group, the researchers found that the high-performing students all smoked marijuana before the exam.

a. method of agreement b. method of difference c. joint method d. method of concomitant variation

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badahos/iStock/Thinkstock

The ability to think critically about an authority’s argument will allow you to determine reliable sources from unreliable ones, which can be quite helpful when writing research papers, reading news articles, or taking advice from someone.

5.6 Arguments From Authority

An argument from authority, also known as an appeal to authority, is an inductive argument in which one infers that a claim is true because someone said so. The general reasoning looks like this:

Person A said that X is true. Person A is an authority on the subject. Therefore, X is true.

Whether this type of reasoning is strong depends on the issue discussed and the authority cited. If it is the kind of issue that can be settled by an argument from authority and if the person is actually an authority on the subject, then it can actually be a strong inductive argument.

Some people think that arguments from authority in general are fallacious. However, that is not generally the case. To see why, try to imagine life without any appeals to authority. You could not believe anyone’s statements, no matter how credible. You could not believe books; you could not believe published journals, and so on. How would you do in college if you did not listen to your textbooks, teachers, or any other sources of information?

Even in science class, you would have to do every experiment on your own because you could not believe published reports. In math, you could not trust the book or teacher, so you would have to prove every theorem by yourself. History class would be a complete waste of time because, unless you had a time machine, there would be no way to verify any claims about what happened in the past without appeal to historical records, newspapers, journals, and so forth. You would also have a hard time following medical advice, so you might end up with serious health problems. Finally, why would you go to school or work if you could not trust the claim that you were going to get a degree or a paycheck after all of your efforts?

Therefore, in order to learn from others and to succeed in life, it is essential that we listen to appropriate authorities. However, since many sources are unreliable, misleading, or even downright deceptive, it is essential that we learn to distinguish reliable sources of authority from unreliable ones. Chapter 7 will discuss how to distinguish between legitimate and fallacious appeals to authority.

Here are some examples of legitimate arguments from authority:

“The theory of relativity is true. I know because my physics professor and my physics textbook teach that it is true.”

“Pine trees are not deciduous; it says so right here in this tree book.”

“The Giants won the pennant! I read it on ESPN.com.”

“Mike hates radishes. He told me so yesterday.”

All of these inferences seem pretty strong. For examples of arguments to authority that are not as strong, or even downright fallacious, visit Chapter 7.

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5.7 Arguments From Analogy

An argument from analogy is an inductive argument that draws conclusions based on the use of analogy. An analogy is a comparison of two items. For example, many object to de�icit spending (when the country spends more money than it takes in) based on the reasoning that debt is bad for household budgets. The person’s argument depends on an analogy that compares the national budget to a household budget. The two items being compared may be referred to as analogs (or analogues, depending on where you live) but are referred to technically as cases. Of the two analogs, one should be well known, with a body of knowledge behind it, and so is referred to as the familiar case; the second analog, about which much less is known, is called the unfamiliar case.

The basic structure of an argument from analogy is as follows:

B is similar to A. A has feature F. Therefore, B probably also has feature F.

Here, A is the familiar case and B is the unfamiliar case. We made an inference about thing B based on its similarity to the more familiar A.

Analogical reasoning proceeds from this premise: Since the analogs are similar either in many ways or in some very important ways, they are likely to be similar in other ways as well. If there are many similarities, or if the similarities are signi�icant, then the analogy can be strong. If the analogs are different in many ways, or if the differences are important, then it is a weak analogy. Conclusions arrived at through strong analogies are fairly reliable; conclusions reached through weak analogies are less reliable and often fallacious (the fallacy is called false analogy). Therefore, when confronted with an analogy (“A is like B”), the �irst question to be asked is this: Are the two analogs very similar in ways that are relevant to the current discussion, or are they different in relevant ways?

Analogies occur in both arguments and explanations. As we saw in Chapter 2, arguments and explanations are not the same thing. The key difference is whether the analogy is being used to give evidence that a certain claim is true—an argument—or to give a better understanding of how or why a claim is true—an explanation. In explanations, the analogy aims to provide deeper understanding of the issue. In arguments, the analogy aims to provide reasons for believing a conclusion. The next section provides some tips for evaluating the strength of such arguments.

Evaluating Arguments From Analogy

Again, the strength of the argument depends on just how much A is like B, and the degree to which the similarities between A and B are relevant to F. Let us consider an example. Suppose that you are in the market for a new car, and your primary concern is that the car be reliable. You have the opportunity to buy a Nissan. One of your friends owns a Nissan. Since you want to buy a reliable car, you ask a friend how reliable her car is. In this case you are depending on an analogy between your friend’s car and the car you are looking to buy. Suppose your friend says that her car is reliable. You can now make the following argument:

The car I’m looking at is like my friend’s car. My friend’s car is reliable. Therefore, the car I’m looking at will be reliable.

How strong is this argument? That depends on how similar the two cases are. If the only thing the cars have in common is the brand, then the argument is fairly weak. On the other hand, if the cars are the same model and year, with all the same options and a similar driving history, then the argument is stronger. We can list the similarities in a chart (see Table 5.5). Initially, the analogy is based only on the make of the car. We will call the car you are looking at A and your friend’s car B.

Table 5.5: Comparing cars by make

Car Make Reliable?

B Nissan Yes

A Nissan ?

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The make of a car is relevant to its reliability, but the argument is weak because that is the only similarity we know about. To strengthen the argument, we can note further relevant similarities. For example, if you �ind out that your friend’s car is the same model and year, then the argument is strengthened (see Table 5.6).

Table 5.6: Comparing cars by make, model, and year

Car Make Model Year Reliable?

B Nissan Sentra 2000 Yes

A Nissan Sentra 2000 ?

The more relevant similarities there are between the two cars, the stronger the argument. However, the word relevant is critical here. Finding out that the two cars have the same engine and similar driving histories is relevant and will strengthen the argument. Finding out that both cars are the same color and have license plates beginning with the same letter will not strengthen the argument. Thus, arguments from analogy typically require that we already have some idea of which features are relevant to the feature we are interested in. If you really had no idea at all what made some cars reliable and others not reliable, then you would have no way to evaluate the strength of an argument from analogy about reliability.

Another way we can strengthen an argument from analogy is by increasing the number of analogs. If you have two more friends who also own a car of the same make, model, and year, and if those cars are reliable, then you can be more con�ident that your new car will be reliable. Table 5.7 shows what the chart would look like. The more analogs you have that match the car you are looking at, the more con�idence you can have that the car you’re looking at will be reliable.

Table 5.7: Comparing multiple analogs

Car Make Model Year Reliable?

B Nissan Sentra 2000 Yes

C Nissan Sentra 2000 Yes

D Nissan Sentra 2000 Yes

A Nissan Sentra 2000 ?

In general, then, analogical arguments are stronger when they have more analogous cases with more relevant similarities. They are weaker when there are signi�icant differences between the familiar cases and the unfamiliar case. If you discover a signi�icant difference between the car you are looking at and the analogs, that reduces the strength of the argument. If, for example, you �ind that all your friends’ cars have manual transmission, whereas the one you are looking at has an automatic transmission, this counts against the strength of the analogy and hence against the strength of the argument.

Another way that an argument from analogy can be weakened is if there are cases that are similar but do not have the feature in question. Suppose you �ind a fourth friend who has the same model and year of car but whose car has been unreliable. As a result, you should have less con�idence that the car you are looking at is reliable.

Here are a couple more examples, with questions about how to gauge the strength.

“Except for size, chickens and turkeys are very similar birds. Therefore, if a food is good for chickens, it is probably good for turkeys.”

Relevant questions include how similar chickens and turkeys are, whether there are signi�icant differences, and whether the difference in size is enough to allow turkeys to eat things that would be too big for chickens.

“Seattle’s climate is similar, in many ways to the United Kingdom’s. Therefore, this plant is likely to grow well in Seattle, because it grows well in the United Kingdom.”

Just how similar is the climate between the two places? Is the total about of rain about the same? How about the total amount of sun? Are the low and high temperatures comparable? Are there soil differences that would matter?

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“I am sure that my favorite team will win the bowl game next week; they have won every game so far this season.”

This example might seem strong at �irst, but it hides a very relevant difference: In a bowl game, college football teams are usually matched up with an opponent of approximately equal strength. It is therefore likely that the team being played will be much better than the other teams played so far this season. This difference weakens the analogy in a relevant way, so the argument is much weaker than it may at �irst appear. It is essential when studying the strength of analogical arguments to be thorough in our search for relevant similarities and differences.

Analogies in Moral Reasoning

Analogical reasoning is often used in moral reasoning and moral arguments. Examples of analogical reasoning are found in ethical or legal debates over contentious or controversial issues such as abortion, gun control, and medical practices of all sorts (including vaccinations and transplants). Legal arguments are often based on �inding precedents—analogous cases that have already been decided. Recent arguments presented in the debate over gun control have drawn conclusions based on analogies that compare the United States with other countries, including Switzerland and Japan. Whether these and similar arguments are strong enough to establish their conclusions depends on just how similar the cases are and the degree and number of dissimilarities and contrary cases. Being aware of similar cases that have already occurred or that are occurring in other areas can vastly improve one’s wisdom about how best to address the topic at hand.

The importance of analogies in moral reasoning is sometimes captured in the principle of equal treatment—that if two things are analogous in all morally relevant respects, then what is right (or wrong) to do in one case will be right (or wrong) to do in the other case as well. For example, if it is right for a teacher to fail a student for missing the �inal exam, then another student who does the same thing should also be failed. Whether the teacher happens to like one student more than the other should not make a difference, because that is not a morally relevant difference when it comes to grading.

The reasoning could look as follows:

Things that are similar in all morally relevant respects should be treated the same. Student A was failed for missing the �inal exam. Student B also missed the �inal exam. Therefore, student B should be failed as well.

It follows from the principle of equal treatment that if two things should be treated differently, then there must be a morally relevant difference between them to justify this different treatment. An example of the application of this principle might be in the interrogation of prisoners of war. If one country wants to subject prisoners of war to certain kinds of harsh treatments but objects to its own prisoners being treated the same way by other countries, then there need to be relevant differences between the situations that justify the different treatment. Otherwise, the country is open to the charge of moral inconsistency.

This principle, or something like it, comes up in many other types of moral debates, such as about abortion and animal ethics. Animal rights advocates, for example, say that if we object to people harming cats and dogs, then we are morally inconsistent to accept to the same treatment of cows, pigs, and chickens. One then has to address the question of whether there are differences in the beings or in their use for food that justify the differences in moral consideration we give to each.

Other Uses of Analogies

Analogies are the basis for parables, allegories, and forms of writing that try to give a moral. The phrase “The moral of the story is . . .” may be featured at the end of such stories, or the author may simply imply that there is a lesson to be learned from the story. Aesop’s Fables are one well-known example of analogy used in writing. Consider the fable of the ant and the grasshopper, which compares the

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Jupiterimages/BananaStock/Thinkstock

Retailers such as bookstores commonly use arguments from analogy when they suggest purchases based on their similarity to other items.

hardworking, industrious ant with the footloose and fancy-free grasshopper. The ant gathers and stores food all summer to prepare for winter; the grasshopper �iddles around and plays all summer, giving no thought for tomorrow. When winter comes, the ant lives warm and comfortable while the grasshopper starves, freezes, and dies. The fable argues that we should be like the ant if we want to survive harsh times. The ant and grasshopper are analogs for industrious people and lazy people. How strong is the argument? Clearly, ants and grasshoppers are quite different from people. Are the differences relevant to the conclusion? What are the relevant similarities? These are the questions that must be addressed to get an idea of whether the argument is strong or weak.

Practice Problems 5.3

Determine whether the following arguments are inductive or deductive. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.3.pdf) to check your answers.

1. All voters are residents of California. But some residents of California are Republican. Therefore, some voters are Republican.

a. deductive b. inductive

2. All doctors are people who are committed to enhancing the health of their patients. No people who purposely harm others can consider themselves to be doctors. Therefore, some people who harm others do not enhance the health of their patients.

a. deductive b. inductive

3. Guns are necessary. Guns protect people. They give people con�idence that they can defend themselves. Guns also ensure that the government will not be able to take over its citizenry.

a. deductive b. inductive

4. Every time I turn on the radio, all I hear is vulgar language about sex, violence, and drugs. Whether it’s rock and roll or rap, it’s all the same. The trend toward vulgarity has to change. If it doesn’t, younger children will begin speaking in these ways and this will spoil their innocence.

a. deductive b. inductive

5. Letting your kids play around on the Internet all day is like dropping them off in downtown Chicago to spend the day by themselves. They will �ind something that gets them into trouble.

a. deductive b. inductive

6. Many people today claim that men and women are basically the same. Although I believe that men and women are equally capable of completing the same tasks physically as well as mentally, to say that they are intrinsically the same detracts from the differences between men and women that are displayed every

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day in their social interactions, the way they use their resources, and the way in which they �ind themselves in the world.

a. deductive b. inductive

7. Too many intravenous drug users continue to risk their lives by sharing dirty needles. This situation could be changed if we were to supply drug addicts with a way to get clean needles. This would lower the rate of AIDS in this high-risk population as well as allow for the opportunity to educate and attempt to aid those who are addicted to heroin and other intravenous drugs.

a. deductive b. inductive

8. I know that Stephen has a lot of money. His parents drive a Mercedes. His dogs wear cashmere sweaters, and he paid cash for his Hummer.

a. deductive b. inductive

9. Dogs are better than cats, since they always listen to what their masters say. They also are more fun and energetic.

a. deductive b. inductive

10. All dogs are warm-blooded. All warm-blooded creatures are mammals. Hence, all dogs are mammals. a. deductive b. inductive

11. Chances are that I will not be able to get in to see Slipknot since it is an over 21 show, and Jeffrey, James, and Sloan were all carded when they tried to get in to the club.

a. deductive b. inductive

12. This is not the best of all possible worlds, because the best of all possible worlds would not contain suffering, and this world contains much suffering.

a. deductive b. inductive

13. Some apples are not bananas. Some bananas are things that are yellow. Therefore, some things that are yellow are not apples.

a. deductive b. inductive

14. Since all philosophers are seekers of truth, it follows that no evil human is a seeker after truth, since no philosophers are evil humans.

a. deductive b. inductive

15. All squares are triangles, and all triangles are rectangles. Therefore, all squares are rectangles. a. deductive b. inductive

16. Deciduous trees are trees that shed their leaves. Maple trees are deciduous trees. Therefore, maple trees will shed their leaves at some point during the growing season.

a. deductive b. inductive

17. Joe must make a lot of money teaching philosophy, since most philosophy professors are rich. a. deductive b. inductive

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18. Since all mammals are cold-blooded, and all cold-blooded creatures are aquatic, all mammals must be aquatic.

a. deductive b. inductive

19. I felt �ine until I missed lunch. I must be feeling tired because I don’t have anything in my stomach. a. deductive b. inductive

20. If you drive too fast, you will get into an accident. If you get into an accident, your insurance premiums will increase. Therefore, if you drive too fast, your insurance premiums will increase.

a. deductive b. inductive

21. The economy continues to descend into chaos. The stock market still moves down after it makes progress forward, and unemployment still hovers around 10%. It is going to be a while before things get better in the United States.

a. deductive b. inductive

22. Football is the best sport. The athletes are amazing, and it is extremely complex. a. deductive b. inductive

23. We should go to see Avatar tonight. I hear that it has amazing special effects. a. deductive b. inductive

24. Pigs are smarter than dogs. It’s easier to train them. a. deductive b. inductive

25. Seventy percent of the students at this university come from upper-class families. The school budget has taken a hit since the economic downturn. We need funding for the three new buildings on campus. I think it’s time for us to start a phone campaign to raise funds so that we don’t plunge into bankruptcy.

a. deductive b. inductive

26. Justin was working at IBM. The last person we got from IBM was a horrible worker. I don’t think that it’s a good idea for us to go with Justin for this job.

a. deductive b. inductive

27. If she wanted me to buy her a drink, she would’ve looked over at me. But she never looked over at me. So that means that she doesn’t want me to buy her a drink.

a. deductive b. inductive

28. Almost all the people I know who are translators have their translator’s license from the ATA. Carla is a translator. Therefore, she must have a license from the ATA.

a. deductive b. inductive

29. The economy will not recover anytime soon. Big businesses are struggling to keep their pro�its high. This is due to the fact that consumers no longer have enough money to purchase things that are luxuries. Most of them buy only those things that they need and don’t have much left over. Those same businesses have been �iring employees left and right. If America’s largest businesses are losing employees, then there won’t

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be any jobs for the people who are already unemployed. That means that these people will not have money to pump back into the system, and the circle will continue to descend into recession.

a. deductive b. inductive

Determine which of the following forms of inductive reasoning are taking place.

30. The purpose of ancient towers that were discovered in Italy are unknown. However, similar towers were discovered in Albania, and historical accounts in that country indicate that the towers were used to store grain. Therefore, the towers in Italy were probably used for the same purpose.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

31. After the current presidential administration passes a bill that increases the amount of time people can be on unemployment, the unemployment rate in the country increases. Economists studying the bill claim that there is a direct relation between the bill and the unemployment rate.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

32. When studying a group of electricians, it was found that 60% of them did not have knowledge of the new safety laws governing working on power lines. Therefore, 60% of the electricians in the United States probably do not have knowledge of the new laws.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

33. In the state of California, studies found that violent criminals who were released on parole had a 68% chance of committing another violent crime. Therefore, a majority of violent criminals in society are likely to commit more violent crimes if they are released from prison.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

34. Psilocybin mushrooms cause hallucinations in humans who ingest them. A new species of mushroom shares similar visual characteristics to many forms of psilocybin mushrooms. Therefore, it is likely that this form of mushroom has compounds that have neurological effects.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

35. A recent survey at work indicates that 60% of the employees believe that they do not make enough money for the work that they do. It is likely that a majority of the people that work for this company are unhappy in their jobs.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

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36. A family is committed to buying Hondas because every Honda they have owned has had few problems and been very reliable. They believe that all Hondas must be reliable.

a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument

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Summary and Resources

Chapter Summary The key feature of inductive arguments is that the support they provide for a conclusion is always less than perfect. Even if all the premises of an inductive argument are true, there is at least some possibility that the conclusion may be false. Of course, when an inductive argument is very strong, the evidence for the conclusion may still be overwhelming. Even our best scienti�ic theories are supported by inductive arguments.

This chapter has looked at four broad types of inductive arguments: statistical arguments, causal arguments, arguments from authority, and arguments from analogy. We have seen that each type can be quite strong, very weak, or anywhere in between. The key to success in evaluating their strength is to be able to (a) identify the type of argument being used, (b) know the criteria by which to evaluate its strength, and (c) notice the strengths and weaknesses of the speci�ic argument in question within the context that it is given. If we can perform all of these tasks well, then we should be good evaluators of inductive reasoning.

Critical Thinking Questions

Connecting the Dots Chapter 5

NEXT

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1. What are some ways that you can now protect yourself from making hasty generalizations through inductive reasoning?

2. Can you think of an example that relates to each one of Mill’s methods of determining causation? What are they, and how did you determine that it �it with Mill’s methods?

3. Think of a time where you reasoned improperly about correlation and causation. Have you seen anyone in the news or in your place of employment fall into improper analysis of causation? What did they do, and what errors did they make?

4. Learning how to evaluate arguments is a great way to empower the mind. What are three forms of empowerment that result when people understand how to identify and evaluate arguments?

5. Why do you believe that superstitions are so prevalent in many societies? What forms of illogical reasoning lead to belief in superstitions? Are there any superstitions that you believe are true? What evidence do you have that supports your claims?

6. Think of an example of a strong inductive argument, then think of a premise that you can add that signi�icantly weakens the argument. Now think of a new premise that you can add that strengthens it again. Now �ind one that makes it weaker, and so on. Repeat this process several times to notice how the strength of inductive arguments can change with new premises.

Web Resources http://austhink.com/critical/pages/stats_prob.html (http://austhink.com/critical/pages/stats_prob.html) This website offers a number of resources and essays designed to help you learn more about statistics and probability.

http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+calculator (http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+calculator) The Australian government hosts a sample size calculator that allows users to approximate how large a sample they need.

http://www.gutenberg.org/ebooks/27942 (http://www.gutenberg.org/ebooks/27942) Read John Stuart Mill’s A System of Logic, which is where Mill �irst introduces his methods for identifying causality.

Key Terms

appeal to authority See argument from authority.

argument from analogy Reasoning in which we draw a conclusion about something based on characteristics of other similar things.

argument from authority An argument in which we infer that something is true because someone (a purported authority) said that it was true.

causal argument An argument about causes and effects.

cogent An inductive argument that is strong and has all true premises.

con�idence level In an inductive generalization, the likelihood that a random sample from a population will have results that fall within the estimated margin of error.

correlation An association between two factors that occur together frequently or that vary in relation to each other.

inductive arguments Arguments in which the premises increase the likelihood of the conclusion being true but do not guarantee that it is.

inductive generalization

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An argument in which one draws a conclusion about a whole population based on results from a sample population.

joint method of agreement and difference A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs and absent in all cases in which it does not.

margin of error A range of values above and below the estimated value in which it is predicted that the actual result will fall.

method of agreement A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs.

method of concomitant variation A way of selecting causal candidates by looking for a factor that is highly correlated with the effect in question.

method of difference A way of selecting causal candidates by looking for a factor that is present when effect occurs and absent when it does not.

necessary condition A condition for an event without which the event will not occur; A is a necessary condition of B if A occurs whenever B does.

population In an inductive generalization, the whole group about which the generalization is made; it is the group discussed in the conclusion.

proximate cause See trigger cause.

random sample A group selected from within the whole population using a selection method such that every member of the population has an equal chance of being included.

sample A smaller group selected from among the population.

sample size The number of individuals within the sample.

statistical arguments Arguments involving statistics, either in the premises or in the conclusion.

statistical syllogism An argument of the form X% of S are P; i is an S; Therefore, i is (probably) a P.

strong arguments Inductive arguments in which the premises greatly increase the likelihood that the conclusion is true.

suf�icient condition A condition for an event that guarantees that the event will occur; A is a suf�icient condition of B if B occurs whenever A does.

trigger cause The factor that completes the cause chain resulting in the effect. Also known as proximate cause.

weak arguments Inductive arguments in which the premises only minimally increase the likelihood that the conclusion is true.

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g about something based on characteristics of

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Learning Objectives

After reading this chapter, you should be able to:

1. Compare and contrast the advantages of deduction and induction.

2. Explain why one might choose an inductive argument over a deductive argument.

3. Analyze an argument for its deductive and inductive components.

4. Explain the use of induction within the hypothetico–deductive method.

5. Compare and contrast falsi�ication and con�irmation within scienti�ic inquiry.

6. Describe the combined use of induction and deduction within scienti�ic reasoning.

7. Explain the role of inference to the best explanation in science and in daily life.

6Deduction and Induction: Putting It AllTogether

Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock

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Now that you have learned something about deduction and induction, you may be wondering why we need both. This chapter is devoted to answering that question. We will start by learning a bit more about the differences between deductive and inductive reasoning and how the two types of reasoning can work together. After that, we will move on to explore how scienti�ic reasoning applies to both types of reasoning to achieve spectacular results. Arguments with both inductive and deductive elements are very common. Recognizing the advantages and disadvantages of each type can help you build better arguments. We will also investigate another very useful type of inference, known as inference to the best explanation, and explore its advantages.

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Fuse/Thinkstock

New information can have an impact on both deductive and inductive arguments. It can render deductive arguments unsound and can strengthen or weaken inductive arguments, such as arguments for buying one car over another.

6.1 Contrasting Deduction and Induction

Remember that in logic, the difference between induction and deduction lies in the connection between the premises and conclusion. Deductive arguments aim for an absolute connection, one in which it is impossible that the premises could all be true and the conclusion false. Arguments that achieve this aim are called valid. Inductive arguments aim for a probable connection, one in which, if all the premises are true, the conclusion is more likely to be true than it would be otherwise. Arguments that achieve this aim are called strong. (For a discussion on common misconceptions about the meanings of induction and deduction, see A Closer Look: Doesn’t Induction Mean Going From Speci�ic to General?). Recall from Chapter 5 that inductive strength is the counterpart of deductive validity, and cogency is the inductive counterpart of deductive soundness. One of the purposes of this chapter is to properly understand the differences and connections between these two major types of reasoning.

There is another important difference between deductive and inductive reasoning. As discussed in Chapter 5, if you add another premise to an inductive argument, the argument may become either stronger or weaker. For example, suppose you are thinking of buying a new cell phone. After looking at all your options, you decide that one model suits your needs better than the others. New information about the phone may make you either more convinced or less convinced that it is the right one for you—it depends on what the new information is. With deductive reasoning, by contrast, adding premises to a valid argument can never render it invalid. New information may show that a deductive argument is unsound or that one of its premises is not true after all, but it cannot undermine a valid connection between the premises and the conclusion. For example, consider the following argument:

All whales are mammals. Shamu is a whale. Therefore, Shamu is a mammal.

This argument is valid, and there is nothing at all we could learn about Shamu that would change this. We might learn that we were mistaken about whales being mammals or about Shamu being a whale, but that would lead us to conclude that the argument is unsound, not invalid. Compare this to an inductive argument about Shamu.

Whales typically live in the ocean. Shamu is a whale. Therefore, Shamu lives in the ocean.

Now suppose you learn that Shamu has been trained to do tricks in front of audiences at an amusement park. This seems to make it less likely that Shamu lives in the ocean. The addition of this new information has made this strong inductive argument weaker. It is, however, possible to make it stronger again with the addition of more information. For example, we could learn that Shamu was part of a captive release program.

An interesting exercise for exploring this concept is to see if you can keep adding premises to make an inductive argument stronger, then weaker, then stronger again. For example, see if you can think of a series of premises that make you change your mind back and forth about the quality of the cell phone discussed earlier.

Determining whether an argument is deductive or inductive is an important step both in evaluating arguments that you encounter and in developing your own arguments. If an argument is deductive, there are really only two questions to ask: Is it valid? And, are the premises true? If you determine that the argument is valid, then only the truth of the premises remains in question. If it is valid and all of the premises are true, then we know that the argument is sound and that therefore the conclusion must be true as well.

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Use this video to review deductive and inductive arguments.

On the other hand, because inductive arguments can go from strong to weak with the addition of more information, there are more questions to consider regarding the connection between the premises and conclusion. In addition to considering the truth of the premises and the strength of the connection between the premises and conclusion, you must also consider whether relevant information has been left out of the premises. If so, the argument may become either stronger or weaker when the relevant information is included.

Later in this chapter we will see that many arguments combine both inductive and deductive elements. Learning to carefully distinguish between these elements will help you know what questions to ask when evaluating the argument.

A Closer Look: Doesn’t Induction Mean Going From Speci�ic to General?

A common misunderstanding of the meanings of induction and deduction is that deduction goes from the general to the speci�ic, whereas induction goes from the speci�ic to the general. This de�inition is used by some �ields, but not by logic or philosophy. It is true that some deductive arguments go from general premises to speci�ic conclusions, and that some inductive arguments go from the speci�ic premises to general conclusions. However, neither statement is true in general.

First, although some deductive arguments go from general to speci�ic, there are many deductive arguments that do not go from general to speci�ic. Some deductive arguments, for example, go from general to general, like the following:

All S are M. All M are P. Therefore, all S are P.

Propositional logic is deductive, but its arguments do not go from general to speci�ic. Instead, arguments are based on the use of connectives (and, or, not, and if . . . then). For example, modus ponens (discussed in Chapter 4) does not go from the general to the speci�ic, but it is deductively valid. When it comes to inductive arguments, some— for example, inductive generalizations—go from speci�ic to general; others do not. Statistical syllogisms, for example, go from general to speci�ic, yet they are inductive.

This common misunderstanding about the de�initions of induction and deduction is not surprising given the different goals of the �ields in which the terms are used. However, the de�initions used by logicians are especially suited for the classi�ication and evaluation of different types of reasoning.

For example, if we de�ined terms the old way, then the category of deductive reasoning would include arguments from analogy, statistical syllogisms, and some categorical syllogisms. Inductive reasoning, on the other hand, would include only inductive generalizations. In addition, there would be other types of inference that would �it into neither category, like many categorical syllogisms, inferences to the best explanation, appeals to authority, and the whole �ield of propositional logic.

The use of the old de�initions, therefore, would not clear up or simplify the categories of logic at all but would make them more confusing. The current distinction, based on whether the premises are intended to guarantee the truth of the conclusion, does a much better job of simplifying logic’s categories, and it does so based on a very important and relevant distinction.

Deductive and Inductive Arguments

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Critical Thinking Questions

1. What does it mean when we say that validity is independent of the truth of the premises and conclusions in an argument?

2. What are the differences between deductive and inductive arguments? What is the relationship between truth and the structure of a deductive versus an inductive argument?

Practice Problems 6.1

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.1.pdf) to check your answers.

1. A deductive argument that establishes an absolute connection between the premises and conclusion is called a __________.

a. strong argument b. weak argument c. invalid argument d. valid argument

2. An inductive argument whose premises give a lot of support for the truth of its conclusion is said to be __________.

a. strong b. weak c. valid d. invalid

3. Inductive arguments always reason from the speci�ic to the general. a. true b. false

Deductive and Inductive Arguments From Title: Logic: The Structure of Reason

(https://fod.infobase.com/PortalPlaylists.aspx?wID=100753&xtid=32714)

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4. Deductive arguments always reason from the general to the speci�ic. a. true b. false

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Alistair Scott/iStock/Thinkstock

Despite knowing that a helium-�illed balloon will rise when we let go of it, we still hold our belief in gravity due to strong inductive reasoning and our reliance on observation.

6.2 Choosing Between Induction and Deduction

You might wonder why one would choose to use inductive reasoning over deductive reasoning. After all, why would you want to show that a conclusion was only probably true rather than guaranteed to be true? There are several reasons, which will be discussed in this section. First, there may not be an available deductive argument based on agreeable premises. Second, inductive arguments can be more robust than deductive arguments. Third, inductive arguments can be more persuasive than deductive arguments.

Availability

Sometimes the best evidence available does not lend itself to a deductive argument. Let us consider a readily accepted fact: Gravity is a force that pulls everything toward the earth. How would you provide an argument for that claim? You would probably pick something up, let go of it, and note that it falls toward the earth. For added effect, you might pick up several things and show that each of them falls. Put in premise–conclusion form, your argument looks something like the following:

My coffee cup fell when I let go of it. My wallet fell when I let go of it. This rock fell when I let go of it. Therefore, everything will fall when I let go of it.

When we put the argument that way, it should be clear that it is inductive. Even if we grant that the premises are true, it is not guaranteed that everything will fall when you let go of it. Perhaps gravity does not affect very small things or very large things. We could do more experiments, but we cannot check every single thing to make sure that it is affected by gravity. Our belief in gravity is the result of extremely strong inductive reasoning. We therefore have great reasons to believe in gravity, even if our reasoning is not deductive.

All subjects that rely on observation use inductive reasoning: It is at least theoretically possible that future observations may be totally different than past ones. Therefore, our inferences based on observation are at best probable. It turns out that there are very few subjects in which we can proceed entirely by deductive reasoning. These tend to be very abstract and formal subjects, such as mathematics. Although other �ields also use deductive reasoning, they do so in combination with inductive reasoning. The result is that most �ields rely heavily on inductive reasoning.

Robustness

Inductive arguments have some other advantages over deductive arguments. Deductive arguments can be extremely persuasive, but they are also fragile in a certain sense. When something goes wrong in a deductive argument, if a premise is found to be false or if it is found to be invalid, there is typically not much of an argument left. In contrast, inductive arguments tend to be more robust. The robustness of an inductive argument means that it is less fragile; if there is a problem with a premise, the argument may become weaker, but it can still be quite persuasive. Deductive arguments, by contrast, tend to be completely unconvincing once they are shown not to be sound. Let us work through a couple of examples to see what this means in practice.

Consider the following deductive argument:

All dogs are mammals. Some dogs are brown. Therefore, some mammals are brown.

As it stands, the argument is sound. However, if we change a premise so that it is no longer sound, then we end up with an argument that is nearly worthless. For example, if you change the �irst premise to “Most dogs are mammals,” you end up

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with an invalid argument. Validity is an all-or-nothing affair; there is no such thing as “sort of valid” or “more valid.” The argument would simply be invalid and therefore unsound; it would not accomplish its purpose of demonstrating that the conclusion must be true. Similarly, if you were to change the second premise to something false, like “Some dogs are purple,” then the argument would be unsound and therefore would supply no reason to accept the conclusion.

In contrast, inductive arguments may retain much of their strength even when there are problems with them. An inductive argument may list several reasons in support of a conclusion. If one of those reasons is found to be false, the other reasons continue to support the conclusion, though to a lesser degree. If an argument based on statistics shows that a particular conclusion is extremely likely to be true, the result of a problem with the argument may be that the conclusion should be accepted as only fairly likely. The argument may still give good reasons to accept the conclusion.

Fields that rely heavily on statistical arguments often have some threshold that is typically required in order for results to be publishable. In the social sciences, this is typically 90% or 95%. However, studies that do not quite meet the threshold can still be instructive and provide evidence for their conclusions. If we discover a �law that reduces our con�idence in an argument, in many cases the argument may still be strong enough to meet a threshold.

As an example, consider a tweet made by President Barack Obama regarding climate change.

Twitter/Public Domain

Although the tweet does not spell out the argument fully, it seems to have the following structure:

A study concluded that 97% of scientists agree that climate change is real, man-made, and dangerous. Therefore, 97% of scientists really do agree that climate change is real, man-made, and dangerous. Therefore, climate change is real, man-made, and dangerous.

Given the politically charged nature of the discussion of climate change, it is not surprising that the president’s argument and the study it referred to received considerable criticism. (You can read the study at http://iopscience.iop.org/1748– 9326/8/2/024024/pdf/1748 –9326_8_2_024024.pdf (http://iopscience.iop.org/1748-9326/8/2/024024/pdf/1748- 9326_8_2_024024.pdf) .) Looking at the effect some of those criticisms have on the argument is a good way to see how inductive arguments can be more robust than deductive ones.

One criticism of Obama’s claim is that the study he referenced did not say anything about whether climate change was dangerous, only about whether it was real and man-made. How does this affect the argument? Strictly speaking, it makes the �irst premise false. But notice that even so, the argument can still give good evidence that climate change is real and man-made. Since climate change, by its nature, has a strong potential to be dangerous, the argument is weakened but still may give strong evidence for its conclusion.

A deeper criticism notes that the study did not �ind out what all scientists thought; it just looked at those scientists who expressed an opinion in their published work or in response to a voluntary survey. This is a signi�icant criticism, for it may expose a bias in the sampling method (as discussed in Chapters 5, 7, and 8). Even granting the criticism, the argument can retain some strength. The fact that 97% of scientists who expressed an opinion on the issue said that climate change is real and man-made is still some reason to think that it is real and man-made. Of course, some scientists may have chosen not to voice an opposing opinion for reasons that have nothing to do with their beliefs about climate change; they may have simply wanted to keep their views private, for example. Taking all of this into account, we get the following argument:

A study found that 97% of scientists who stated their opinion said that climate change is real and man-made.

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Therefore, 97% of scientists agree that climate change is real and man-made. Climate change, if real, is dangerous. Therefore, climate change is real, man-made, and dangerous.

This is not nearly as strong as the original argument, but it has not collapsed entirely in the way a purely deductive argument would. There is, of course, much more that could be said about this argument, both in terms of criticizing the study and in terms of responding to those criticisms and bringing in other considerations. The point here is merely to highlight the difference between deductive and inductive arguments, not to settle issues in climate science or public policy.

Persuasiveness

A �inal point in favor of inductive reasoning is that it can often be more persuasive than deductive reasoning. The persuasiveness of an argument is based on how likely it is to convince someone of the truth of its conclusion. Consider the following classic argument:

All Greeks are mortal. Socrates was a Greek. Therefore, Socrates was mortal.

Is this a good argument? From the standpoint of logic, it is a perfect argument: It is deductively valid, and its premises are true, so it is sound (therefore, its conclusion must be true). However, can you persuade anyone with this argument?

Imagine someone wondering whether Socrates was mortal. Could you use this argument to convince him or her that Socrates was mortal? Probably not. The argument is so simple and so obviously valid that anyone who accepts the premises likely already accepts the conclusion. So if someone is wondering about the conclusion, it is unlikely that he or she will be persuaded by these premises. He or she may, for example, remember that some legendary Greeks, such as Hercules, were granted immortality and wonder whether Socrates was one of these. The deductive approach, therefore, is unlikely to win anyone over to the conclusion here. On the other hand, consider a very similar inductive argument.

Of all the real and mythical Greeks, only a few were considered to be immortal. Socrates was a Greek. Therefore, it is extremely unlikely that Socrates was immortal.

Again, the reasoning is very simple. However, in this case, we can imagine someone who had been wondering about Socrates’s mortality being at least somewhat persuaded that he was mortal. More will likely need to be said to fully persuade her or him, but this simple argument may have at least some persuasive power where its deductive version likely does not.

Of course, deductive arguments can be persuasive, but they generally need to be more complicated or subtle in order to be so. Persuasion requires that a person change his or her mind to some degree. In a deductive argument, when the connection between premises and conclusion is too obvious, the argument is unlikely to persuade because the truth of the premises will be no more obvious than the truth of the conclusion. Therefore, even if the argument is valid, someone who questions the truth of the conclusion will often be unlikely to accept the truth of the premises, so she or he may be unpersuaded by the argument. Suppose, for example, that we wanted to convince someone that the sun will rise tomorrow morning. The deductive argument may look like this:

The sun will always rise in the morning. Therefore, the sun will rise tomorrow morning.

One problem with this argument, as with the Socrates argument, is that its premise seems to assume the truth of the conclusion (and therefore commits the fallacy of begging the question, as discussed in Chapter 7), making the argument unpersuasive. Additionally, however, the premise might not even be true. What if, billions of years from now, the earth is swallowed up into the sun after it expands to become a red giant? At that time, the whole concept of morning may be out the window. If this is true then the �irst premise may be technically false. That means that the argument is unsound and therefore fairly worthless deductively.

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The inductive version, however, does not lose much strength at all after we learn of this troubling information:

The sun has risen in the morning every day for millions of years. Therefore, the sun will rise again tomorrow morning.

This argument remains extremely strong (and persuasive) regardless of what will happen billions of years in the future.

Practice Problems 6.2

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.2.pdf) to check your answers.

1. Which form of reasoning is taking place in this example?

The sun has risen every day of my life. The sun rose today. Therefore, the sun will rise tomorrow.

a. inductive b. deductive

2. Inductive arguments __________. a. can retain strength even with false premises b. collapse when a premise is shown to be false c. are equivalent to deductive arguments d. strive to be valid

3. Deductive arguments are often __________. a. less persuasive than inductive arguments b. more persuasive than inductive arguments c. weaker than inductive arguments d. less valid than inductive arguments

4. Inductive arguments are sometimes used because __________. a. the available evidence does not allow for a deductive argument b. they are more likely to be sound than deductive ones c. they are always strong d. they never have false premises

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Fran/Cartoonstock

Sometimes a simple deductive argument needs to be combined with a persuasive inductive argument to convince others to accept it.

6.3 Combining Induction and Deduction

You may have noticed that most of the examples we have explored have been fairly short and simple. Real-life arguments tend to be much longer and more complicated. They also tend to mix inductive and deductive elements. To see how this might work, let us revisit an example from the previous section.

All Greeks are mortal. Socrates was Greek. Therefore, Socrates was mortal.

As we noted, this simple argument is valid but unlikely to convince anyone. So suppose now that someone questioned the premises, asking what reasons there are for thinking that all Greeks are mortal or that Socrates was Greek. How might we respond?

We might begin by noting that, although we cannot check each and every Greek to be sure he or she is mortal, there are no documented cases of any Greek, or any other human, living more than 200 years. In contrast, every case that we can document is a case in which the person dies at some point. So, although we cannot absolutely prove that all Greeks are mortal, we have good reason to believe it. We might put our argument in standard form as follows:

We know the mortality of a huge number of Greeks. In each of these cases, the Greek is mortal. Therefore, all Greeks are mortal.

This is an inductive argument. Even though it is theoretically possible that the conclusion might still be false, the premises provide a strong reason to accept the conclusion. We can now combine the two arguments into a single, larger argument:

We know the mortality of a huge number of Greeks. In each of these cases, the Greek is mortal. Therefore, all Greeks are mortal. Socrates was Greek. Therefore, Socrates was mortal.

This argument has two parts. The �irst argument, leading to the subconclusion that all Greeks are mortal, is inductive. The second argument (whose conclusion is “Socrates was mortal”) is deductive. What about the overall reasoning presented for the conclusion that Socrates was mortal (combining both arguments); is it inductive or deductive?

The crucial issue is whether the premises guarantee the truth of the conclusion. Because the basic premise used to arrive at the conclusion is that all of the Greeks whose mortality we know are mortal, the overall reasoning is inductive. This is how it generally works. As noted earlier, when an argument has both inductive and deductive components, the overall argument is generally inductive. There are occasional exceptions to this general rule, so in particular cases, you still have to check whether the premises guarantee the conclusion. But, almost always, the longer argument will be inductive.

A similar thing happens when we combine inductive arguments of different strength. In general, an argument is only as strong as its weakest part. You can think of each inference in an argument as being like a link in a chain. A chain is only as strong as its weakest link.

Practice Problem 6.3

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1. When an argument contains both inductive and deductive elements, the entire argument is considered deductive.

a. true b. false

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6.4 Reasoning About Science: The Hypothetico–Deductive Method

Science is one of the most successful endeavors of the modern world, and arguments play a central role in it. Science uses both deductive and inductive reasoning extensively. Scienti�ic reasoning is a broad �ield in itself—and this chapter will only touch on the basics—but discussing scienti�ic reasoning will provide good examples of how to apply what we have learned about inductive and deductive arguments.

At some point, you may have learned or heard of the scienti�ic method, which often refers to how scientists systematically form, test, and modify hypotheses. It turns out that there is not a single method that is universally used by all scientists.

In a sense, science is the ultimate critical thinking experiment. Scientists use a wide variety of reasoning techniques and are constantly examining those techniques to make sure that the conclusions drawn are justi�ied by the premises—that is exactly what a good critical thinker should do in any subject. The next two sections will explore two such methods—the hypothetico–deductive method and inferences to the best explanation—and discover ways that they can improve our understanding of the types of reasoning used in much of science.

The hypothetico–deductive method consists of four steps:

1. Formulate a hypothesis. 2. Deduce a consequence from the hypothesis. 3. Test whether the consequence occurs. 4. Reject the hypothesis if the consequence does not occur.

Although these four steps are not suf�icient to explain all scienti�ic reasoning, they still remain a core part of much discussion of how science works. You may recognize them as part of the scienti�ic method that you likely learned about in school. Let us take a look at each step in turn.

Step 1: Formulate a Hypothesis

A hypothesis is a conjecture about how some part of the world works. Although the phrase “educated guess” is often used, it can give the impression that a hypothesis is simply guessed without much effort. In reality, scienti�ic hypotheses are formulated on the basis of a background of quite a bit of knowledge and experience; a good scienti�ic hypothesis often comes after years of prior investigation, thought, and research about the issue at hand.

You may have heard the expression “necessity is the mother of invention.” Often, hypotheses are formulated in response to a problem that needs to be solved. Suppose you are unsatis�ied with the performance of your car and would like better fuel economy. Rather than buy a new car, you try to �igure out how to improve the one you have. You guess that you might be able to improve your car’s fuel economy by using a higher grade of gas. Your guess is not just random; it is based on what you already know or believe about how cars work. Your hypothesis is that higher grade gas will improve your fuel economy.

Of course, science is not really concerned with your car all by itself. Science is concerned with general principles. A scientist would reword your hypothesis in terms of a general rule, something like, “Increasing fuel octane increases fuel economy in automobiles.” The hypothetico–deductive method can work with either kind of hypothesis, but the general hypothesis is more interesting scienti�ically.

Step 2: Deduce a Consequence From the Hypothesis

Your hypothesis from step 1 should have predictive value: Things should be different in some noticeable way, depending on whether the hypothesis is true or false. Our hypothesis is that increasing fuel octane improves fuel economy. If this general fact is true, then it is true for your car. So from our general hypothesis we can deduce the consequence that your car will get more miles per gallon if it is running on higher octane fuel.

It is often but not always the case that the prediction is a more speci�ic case of the hypothesis. In such cases it is possible to infer the prediction deductively from the general hypothesis. The argument may go as follows:

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Hypothesis: All things of type A have characteristic B.

Consequence (the prediction): Therefore, this speci�ic thing of type A will have characteristic B.

Since the argument is deductively valid, there is a strong connection between the hypothesis and the prediction. However, not all predictions can be deductively inferred. In such cases we can get close to the hypothetico–deductive method by using a strong inductive inference instead. For example, suppose the argument went as follows:

Hypothesis: 95% of things of type A have characteristic B.

Consequence: Therefore, a speci�ic thing of type A will probably have characteristic B.

In such cases the connection between the hypothesis and the prediction is less strong. The stronger the connection that can be established, the better for the reliability of the test. Essentially, you are making an argument for the conditional statement “If H, then C,” where H is your hypothesis and C is a consequence of the hypothesis. The more solid the connection is between H and C, the stronger the overall argument will be.

In this speci�ic case, “If H, then C” translates to “If increasing fuel octane increases fuel economy in all cars, then using higher octane fuel in your car will increase its fuel economy.” The truth of this conditional is deductively certain.

We can now test the truth of the hypothesis by testing the truth of the consequence.

Step 3: Test Whether the Consequence Occurs

Your prediction (the consequence) is that your car will get better fuel economy if you use a higher grade of fuel. How will you test this? You may think this is obvious: Just put better gas in the car and record your fuel economy for a period before and after changing the type of gas you use. However, there are many other factors to consider. How long should the period of time be? Fuel economy varies depending on the kind of driving you do and many other factors. You need to choose a length of time for which you can be reasonably con�ident the driving conditions are similar on average. You also need to account for the fact that the �irst tank of better gas you put in will be mixed with some of the lower grade gas that is still in your tank. The more you can address these and other issues, the more certain you can be that your conclusion is correct.

In this step, you are constructing an inductive argument from the outcome of your test as to whether your car actually did get better fuel economy. The arguments in this step are inductive because there is always some possibility that you have not adequately addressed all of the relevant issues. If you do notice better fuel economy, it is always possible that the increase in economy is due to some factor other than the one you are tracking. The possibility may be very small, but it is enough to make this kind of argument inductive rather than deductive.

Step 4: Reject the Hypothesis If the Consequence Does Not Occur

We now compare the results to the prediction and �ind out if the prediction came true. If your test �inds that your car’s fuel economy does not improve when you use higher octane fuel, then you know your prediction was wrong.

Does this mean that your hypothesis, H, was wrong? That depends on the strength of the connection between H and C. If the inference from H to C is deductively certain, then we know for sure that, if H is true, then C must be true also. Therefore, if C is false, it follows logically that H must be false as well.

In our speci�ic case, if your car does not get better fuel economy by switching to higher octane fuel, then we know for sure that it is not true that all cars get better fuel economy by doing so. However, if the inference from H to C is inductive, then the connection between H and C is less than totally certain. So if we �ind that C is false, we are not absolutely sure that the hypothesis, H, is false.

For example, suppose that the hypothesis is that cars that use higher octane fuel will have a higher tendency to get better fuel mileage. In that case if your car does not get higher gas mileage, then you still cannot infer for certain that the hypothesis is false. To test that hypothesis adequately, you would have to do a large study with many cars. Such a study would be much more complicated, but it could provide very strong evidence that the hypothesis is false.

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At best, the fuel economy hypothesis will be a strong inductive argument because there is a chance that something other than higher octane gas is improving fuel economy. The more you can address relevant issues that may impact your test results, the stronger your conclusions will be.

It is important to note that although the falsity of the prediction can demonstrate that the hypothesis is false, the truth of the prediction does not prove that the hypothesis is true. If you �ind that your car does get better fuel economy when you switch gas, you cannot conclude that your hypothesis is true.

Why? There may be other factors at play for which you have not adequately accounted. Suppose that at the same time you switch fuel grade, you also get a tune-up and new tires and start driving a completely different route to work. Any one of these things might be the cause of the improved gas mileage; you cannot conclude that it is due to the change in fuel (for this reason, when conducting experiments it is best to change only one variable at a time and carefully control the rest). In other words, in the hypothetico– deductive method, failed tests can show that a hypothesis is wrong, but tests that succeed do not show that the hypothesis was correct.

This logic is known as falsi�ication; it can be demonstrated clearly by looking at the structure of the argument. When a test yields a negative result, the hypothetico–deductive method sets up the following argument:

If H, then C. Not C. Therefore, not H.

You may recognize this argument form as modus tollens, or denying the consequent, which was discussed in the chapter on propositional logic (Chapter 4). This argument form is a valid, deductive form. Therefore, if both of these premises are true, then we can be certain that the conclusion is true as well; namely, that our hypothesis, H, is not true. In the speci�ic case at hand, if your test shows that higher octane fuel does not increase your mileage, then we can be sure that it is not true that it improves mileage in all vehicles (though it may improve it in some).

Contrast this with the argument form that results when your fuel economy yields a positive result:

If H, then C. C. Therefore, H.

This argument is not valid. In fact, you may recognize this argument form as the invalid deductive form called af�irming the consequent (see Chapter 4). It is possible that the two premises are true, but the conclusion false. Perhaps, for example, the improvement in fuel economy was caused by a change in tires or different driving conditions instead. So the hypothetico –deductive method can be used only to reject a hypothesis, not to con�irm it. This fact has led many to see the primary role of science to be the falsi�ication of hypotheses. Philosopher Karl Popper is a central source for this view (see A Closer Look: Karl Popper and Falsi�ication in Science).

A Closer Look: Karl Popper and Falsi�ication in Science

Karl Popper, one of the most in�luential philosophers of science to emerge from the early 20th century, is perhaps best known for rejecting the idea that scienti�ic theories could be proved by simply �inding con�irming evidence—the prevailing philosophy at the time. Instead, Popper emphasized that claims must be testable and falsi�iable in order to be considered scienti�ic.

A claim is testable if we can devise a way of seeing if it is true or not. We can test, for instance, that pure water will freeze at 0°C at sea level; we cannot currently test the

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Karl Popper, a 20th- century philosopher of science, put forth the idea that unfalsi�iable claims are unscienti�ic.

Learn more about Karl Popper’s criterion of falsi�iability in this video.

Karl Popper and Falsi�ication

Critical Thinking Questions

1. Karl Popper argues that only hypotheses that can be tested and falsi�ied are scienti�ic. Do you agree?

2. In addition to being unscienti�ic, Popper states that unfalsi�iable claims tell us nothing and do not allow us to learn from our mistakes. Can you make an argument against Popper’s?

claim that the oceans in another galaxy taste like root beer. We have no realistic way to determine the truth or falsity of the second claim.

A claim is said to be falsi�iable if we know how one could show it to be false. For instance, “there are no wild kangaroos in Georgia” is a falsi�iable claim; if one went to Georgia and found some wild kangaroos, then it would have been shown to be false. But what if someone claimed that there are ghosts in Georgia but that they are imperceptible (unseeable, unfeelable, unhearable, etc.)? Could one ever show that this claim is false? Since such a claim could not conceivably be shown to be false, it is said to be unfalsi�iable. While being unfalsi�iable might sound like a good thing, according to Popper it is not, because it means that the claim is unscienti�ic.

Following Popper, most scientists today operate with the assumption that any scienti�ic hypothesis must be testable and must be the kind of claim that one could possibly show to be false. So if a claim turns out not to be conceivably falsi�iable, the claim is not really scienti�ic—and some philosophers have gone so far as to regard such claims as meaningless (Thornton, 2014).

As an example, suppose a friend claims that “everything works out for the best.” Then suppose that you have the worst month of your life, and you go back to your friend and say that the claim is false: Not everything is for the best. Your friend might then reply that in fact it was for the best because you learned from the experience. Such a statement may make you feel better, but it runs afoul of Popper’s rule. Can you imagine any circumstance that your friend would not claim is for the best? Since your friend would probably say that it was for the best no matter what happens, your friend’s claim is unfalsi�iable and therefore unscienti�ic.

In logic, claims that are interpreted so that they come out true no matter what happens are called self-sealing propositions. They are understood as being internally protected against any objections. People who state such claims may feel that they are saying something deeply meaningful, but according to Popper’s rule, since the claim could never be falsi�ied no matter what, it does not really tell us anything at all.

Other examples of self-sealing propositions occur within philosophy itself. There is a philosophical theory known as psychological egoism, for example, which teaches that everything everyone does is completely sel�ish. Most people respond to this claim by coming up with examples of unsel�ish acts: giving to the needy, spending time helping others, and even dying to save someone’s life. The psychological egoist predictably responds to all such examples by stating that people who do such things really just do them in order to feel better about themselves. It appears that the word sel�ish is being interpreted so that everything everyone does will automatically be considered

sel�ish by de�inition. It is therefore a self-sealing claim (Rachels, 1999). According to Popper’s method, since this

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claim will always come out true no matter what, it is unfalsi�iable and unscienti�ic. Such claims are always true but are actually empty because they tell us nothing about the world. They can even be said to be “too true to be good.”

Popper’s explorations of scienti�ic hypotheses and what it means to con�irm or discon�irm such hypotheses have been very in�luential among both scientists and philosophers of scientists. Scientists do their best to avoid making claims that are not falsi�iable.

If the hypothetico-deductive method cannot be used to con�irm a hypothesis, how can this test give evidence for the truth of the claim? By failing to falsify the claim. Though the hypothetico–deductive method does not ever speci�ically prove the hypothesis true, if researchers try their hardest to refute a claim but it keeps passing the test (not being refuted), then there can grow a substantial amount of inductive evidence for the truth of the claim. If you repeatedly test many cars and control for other variables, and if every time cars are �illed with higher octane gas their fuel economy increases, you may have strong inductive evidence that the hypothesis might be true (in which case you may make an inference to the best explanation, which will be discussed in Section 6.5).

Experiments that would have the highest chance of refuting the claim if it were false thus provide the strongest inductive evidence that it may be true. For example, suppose we want to test the claim that all swans are white. If we only look for swans at places in which they are known to be white, then we are not providing a strong test for the claim. The best thing to do (short of observing every swan in the whole world) is to try as hard as we can to refute the claim, to �ind a swan that is not white. If our best methods of looking for nonwhite swans still fail to refute the claim, then there is a growing likelihood that perhaps all swans are indeed white.

Similarly, if we want to test to see if a certain type of medicine cures a certain type of disease, we test the product by giving the medicine to a wide variety of patients with the disease, including those with the least likelihood of being cured by the medicine. Only by trying as hard as we can to refute the claim can we get the strongest evidence about whether all instances of the disease are treatable with the medicine in question.

Notice that the hypothetico–deductive method involves a combination of inductive and deductive reasoning. Step 1 typically involves inductive reasoning as we formulate a hypothesis against the background of our current beliefs and knowledge. Step 2 typically provides a deductive argument for the premise “If H, then C.” Step 3 provides an inductive argument for whether C is or is not true. Finally, if the prediction is falsi�ied, then the conclusion—that H is false—is derived by a deductive inference (using the deductively valid modus tollens form). If, on the other hand, the best attempts to prove C to be false fail to do so, then there is growing evidence that H might be true.

Therefore, our overall argument has both inductive and deductive elements. It is valuable to know that, although the methodology of science involves research and experimentation that goes well beyond the scope of pure logic, we can use logic to understand and clarify the basic principles of scienti�ic reasoning.

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Practice Problems 6.4

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1. A hypothesis is __________. a. something that is a mere guess b. something that is often arrived at after a lot of research c. an unnecessary component of the scienti�ic method d. something that is already solved

2. In a scienti�ic experiment, __________. a. the truth of the prediction guarantees that the hypothesis was correct b. the truth of the prediction negates the possibility of the hypothesis being correct c. the truth of the prediction can have different levels of probability in relation to the hypothesis

being correct d. the truth of the prediction is of little importance

Consider This: Scientific Reasoning and Objectivity

NEXT

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3. The argument form that is set up when a test yields negative results is __________. a. disjunctive syllogism b. modus ponens c. hypothetical syllogism d. modus tollens

4. A claim is testable if __________. a. we know how one could show it to be false b. we know how one could show it to be true c. we cannot determine a way to prove it false d. we can determine a way to see if it is true or false

5. Which of the following claims is not falsi�iable? a. The moon is made of cheese. b. There is an invisible alien in my garage. c. Octane ratings in gasoline in�luence fuel economy. d. The Willis Tower is the tallest building in the world.

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Sherlock Holmes often used abductive reasoning, not deductive reasoning, to solve his mysteries.

6.5 Inference to the Best Explanation

You may feel that if you were very careful about testing your fuel economy, you would be entitled to conclude that the change in fuel grade really did have an effect. Unfortunately, as we have seen, the hypothetico–deductive method does not support this inference. The best you can say is that changing fuel might have an effect; that you have not been able to show that it does not have an effect. The method does, however, lend inductive support to whichever hypothesis withstands the falsi�ication test better than any other. One way of articulating this type of support is with an inference pattern known as inference to the best explanation.

As the name suggests, inference to the best explanation draws a conclusion based on what would best explain one’s observations. It is an extremely important form of inference that we use every day of our lives. This type of inference is often called abductive reasoning, a term pioneered by American logician Charles Sanders Peirce (Douven, 2011).

Suppose that you are in your backyard gazing at the stars. Suddenly, you see some �lashing lights hovering above you in the sky. You do not hear any sound, so it does not appear that the lights are coming from a helicopter. What do you think it is? What happens next is abductive reasoning: Your brain searches among all kinds of possibilities to attempt to come up with the most likely explanation.

One possibility is that it is an alien spacecraft coming to get you (one could joke that this is why it is called abductive reasoning). Another possibility is that it is some kind of military vessel or a weather balloon. A more extreme hypothesis is that you are actually dreaming the whole thing.

Notice that what you are inclined to believe depends on your existing beliefs. If you already think that alien spaceships come to Earth all the time, then you may arrive at that conclusion with a high degree of certainty (you may even shout, “Take me with you!”). However, if you are somewhat skeptical of those kinds of theories, then you will try hard to �ind any other explanation. Therefore, the strength of a particular inference to the best explanation can be measured only in relation to the rest of the things that we already believe.

This type of inference does not occur only in unusual circumstances like the one described. In fact, we make inferences to the best explanation all the time. Returning to our fuel economy example from the previous section, suppose that you test a higher octane fuel and notice that your car gets better gas mileage. It is possible that the mileage change is due to the change in fuel. However, as noted there, it is possible that there is another explanation. Perhaps you are not driving in stop-and-go traf�ic as much. Perhaps you are driving with less weight in the car. The careful use of inference to the best explanation can help us to discern what is the most likely among many possibilities (for more examples, see A Closer Look: Is Abductive Reasoning Everywhere?).

If you look at the range of possible explanations and �ind one of them is more likely than any of the others, inference to the best explanation allows you to conclude that this explanation is likely to be the correct one. If you are driving the same way, to the same places, and with the same weight in your car as before, it seems fairly likely that it was the change in fuel that caused the improvement in fuel economy (if you have studied Mill’s methods in Chapter 5, you should recognize this as the method of difference). Inference to the best explanation is the engine that powers many inductive techniques.

The great �ictional detective Sherlock Holmes, for example, is fond of claiming that he uses deductive reasoning. Chapter 2 suggested that Holmes instead uses inductive reasoning. However, since Holmes comes up with the most reasonable explanation of observed phenomena, like blood on a coat, for example, he is actually doing abductive reasoning. There is some dispute about whether inference to the best explanation is inductive or whether it is an entirely different kind of argument that is neither inductive nor deductive. For our purposes, it is treated as inductive.

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A Closer Look: Is Abductive Reasoning Everywhere?

Some see inference to the best explanation as the most common type of inductive inference. A few of the inferences we have discussed in this book, for example, can potentially be cast as examples of inferences to the best explanation.

For example, appeals to authority (discussed in Chapter 5) can be seen as implicitly using inference to the best explanation (Harman, 1965). If you accept something as true because someone said it was, then you can be described as seeing the truth of the claim as the best explanation for why he or she said it. If we have good reason to think that the person was deluded or lying, then we are less certain of this conclusion because there are other likely explanations of why the person said it.

Furthermore, it is possible to see what we do when we interpret people’s words as a kind of inference to the best explanation of what they probably mean (Hobbs, 2004). If your neighbor says, “You are so funny,” for instance, we might use the context and tone to decide what he means by “funny” and why he is saying it (and whether he is being sarcastic). His comment can be seen as either rude or �lattering, depending on what explanation we give for why he said it and what he meant.

Even the classic inductive inference pattern of inductive generalization can possibly be seen as implicitly involving a kind of inference to the best explanation: The best explanation of why our sample population showed that 90% of students have laptops is probably that 90% of all students have laptops. If there is good evidence that our sample was biased, then there would be a good competing explanation of our data.

Finally, much of scienti�ic inference may be seen as trying to provide the best explanation for our observations (McMullin, 1992). Many hypotheses are attempts to explain observed phenomena. Testing them in such cases could then be seen as being done in the service of seeking the best explanation of why certain things are the way they are.

Take a look at the following examples of everyday inferences and see if they seem to involve arriving at the conclusion because it seems to offer the most likely explanation of the truth of the premise:

“John is smiling; he must be happy.” “My phone says that Julie is calling, so it is probably Julie.” “I see a brown Labrador across the street; my neighbor’s dog must have gotten out.” “This movie has great reviews; it must be good.” “The sky is getting brighter; it must be morning.” “I see shoes that look like mine by the door; I apparently left my shoes there.” “She still hasn’t called back yet; she probably doesn’t like me.” “It smells good; someone is cooking a nice dinner.” “My congressperson voted against this bill I support; she must have been afraid of offending her wealthy donors.” “The test showed that the isotopes in the rock surrounding newly excavated bones had decayed X amount; therefore, the animals from which the bones came must have been here about 150 million years ago.”

These examples, and many others, suggest to some that inference to the explanation may be the most common form of reasoning that we use (Douven, 2011). Do you agree? Whether you agree with these expanded views on the role of inference or not, it clearly makes an enormous contribution to how we understand the world around us.

Form

Inferences to the best explanation generally involve the following pattern of reasoning:

X has been observed to be true.

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Y would provide an explanation of why X is true. No other explanation for X is as likely as Y. Therefore, Y is probably true.

One strange thing about inferences to the best explanation is that they are often expressed in the form of a common fallacy, as follows:

If P is the case, then Q would also be true. Q is true. Therefore, P is probably true.

This pattern is the logical form of a deductive fallacy known as af�irming the consequent (discussed in Chapter 4). Therefore, we sometimes have to use the principle of charity to determine whether the person is attempting to provide an inference to the best explanation or making a simple deductive error. The principle of charity will be discussed in detail in Chapter 9; however, for our purposes here, you can think of it as giving your opponent and his or her argument the bene�it of the doubt.

For example, the ancient Greek philosopher Aristotle reasoned as follows: “The world must be spherical, for the night sky looks different in the northern and southern regions, and that would be the case if the earth were spherical” (as cited in Wolf, 2004). His argument appears to have this structure:

If the earth is spherical, then the night sky would look different in the northern and southern regions. The night sky does look different in the northern and southern regions. Therefore, the earth is spherical.

It is not likely that Aristotle, the founding father of formal logic, would have made a mistake as silly as to af�irm the consequent. It is far more likely that he was using inference to the best explanation. It is logically possible that there are other explanations for southern stars moving higher in the sky as one moves south, but it seems far more likely that it is due to the shape of the earth. Aristotle was just practicing strong abductive reasoning thousands of years before Columbus sailed the ocean blue (even Columbus would have had to use this type of reasoning, for he would have had to infer why he did not sail off the edge).

In more recent times, astronomers are still using inference to the best explanation to learn about the heavens. Let us consider the case of discovering planets outside our solar system, known as “exoplanets.” There are many methods employed to discover planets orbiting other stars. One of them, the radial velocity method, uses small changes in the frequency of light a star emits. A star with a large planet orbiting it will wobble a little bit as the planet pulls on the star. That wobble will result in a pattern of changes in the frequency of light coming from the star. When astronomers see this pattern, they conclude that there is a planet orbiting the star. We can more fully explicate this reasoning in the following way:

That star’s light changes in a speci�ic pattern. Something must explain the changes. A large planet orbiting the star would explain the changes. No other explanation is as likely as the explanation provided by the large planet. Therefore, that star probably has a large planet orbiting it.

The basic idea is that if there must be an explanation, and one of the available explanations is better than all the others, then that explanation is the one that is most likely to be true. The key issue here is that the explanation inferred in the conclusion has to be the best explanation available. If another explanation is as good—or better—then the inference is not nearly as strong.

Virtue of Simplicity

Another way to think about inferences to the best explanation is that they choose the simplest explanation from among otherwise equal explanations. In other words, if two theories make the same prediction, the one that gives the simplest explanation is usually the best one. This standard for comparing scienti�ic theories is known as Occam’s razor, because it was originally posited by William of Ockham in the 14th century (Gibbs & Hiroshi, 1997).

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©Warner Bros./Courtesy Everett Collection

In The Matrix, we learn that our world is simulated by machines, and although we can see X, hear X, and feel X, X does not exist.

A great example of this principle is Galileo’s demonstration that the sun, not the earth, is at the center of the solar system. Galileo’s theory provided the simplest explanation of observations about the planets. His heliocentric model, for example, provides a simpler explanation for the phases of Venus and why some of the planets appear to move backward (retrograde motion) than does the geocentric model. Geocentric astronomers tried to explain both of these with the idea that the planets sometimes make little loops (called epicycles) within their orbits (Gronwall, 2006). While it is certainly conceivable that they do make little loops, it seems to make the theory unnecessarily complex, because it requires a type of motion with no independent explanation of why it occurs, whereas Galileo’s theory does not require such extra assumptions.

Therefore, putting the sun at the center allows one to explain observed phenomena in the most simple manner possible, without making ad hoc assumptions (like epicycles) that today seem absurd. Galileo’s theory was ultimately correct, and he demonstrated it with strong inductive (more speci�ically, abductive) reasoning. (For another example of Occam’s razor at work, see A Closer Look: Abductive Reasoning and the Matrix.)

A Closer Look: Abductive Reasoning and the Matrix

One of the great questions from the history of philosophy is, “How do we know that the world exists outside of us as we perceive it?” We see a tree and we infer that it exists, but do we actually know for sure that it exists? The argument seems to go as follows:

I see a tree. Therefore, a tree exists.

This inference, however, is invalid; it is possible for the premise to be true and the conclusion false. For example, we could be dreaming. Perhaps we think that the testimony of our other senses will make the argument valid:

I see a tree, I hear a tree, I feel a tree, and I smell a tree. Therefore, a tree exists.

However, this argument is still invalid; it is possible that we could be dreaming all of those things as well. Some people state that senses like smell do not exist within dreams, but how do we know that is true? Perhaps we only dreamed that someone said that! In any case, even that would not rescue our argument, for there is an even stronger way to make the premise true and the conclusion false: What if your brain is actually in a vat somewhere attached to a computer, and a scientist is directly controlling all of your perceptions? (Or think of the 1999 movie The Matrix, in which humans are living in a simulated reality created by machines.)

One individual who struggled with these types of questions (though there were no computers back then) was a French philosopher named René Descartes. He sought a deductive proof that the world outside of us is real, despite these types of disturbing possibilities (Descartes, 1641/1993). He eventually came up with one of philosophy’s most famous arguments, “I think, therefore, I am” (or, more precisely, “I am thinking, therefore, I exist”), and from there attempted to prove that the world must exist outside of him.

Many philosophers feel that Descartes did a great job of raising dif�icult questions, but most feel that he failed in his attempt to �ind deductive proof of the world outside of our minds. Other philosophers, including David Hume, despaired of the possibility of a proof that we know that there is a world outside of us and became skeptics: They decided that absolute knowledge of a world outside of us is impossible (Hume, 1902).

However, perhaps the problem is not the failure of the particular arguments but the type of reasoning employed. Perhaps the solution is not deductive at all but rather abductive. It is not that it is logically impossible that tables and chairs and trees (and even other people) do not really exist; it is just that their actual existence provides the best explanation of our experiences. Consider these competing explanations of our experiences:

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We are dreaming this whole thing. We are hallucinating all of this. Our brains are in a vat being controlled by a scientist. Light waves are bouncing off the molecules on the surface of the tree and entering our eyeballs, where they are turned into electrical impulses that travel along neurons into our brains, somehow causing us to have the perception of a tree.

It may seem at �irst glance that the �inal option is the most complex and so should be rejected. However, let us take a closer look. The �irst two options do not offer much of an explanation for the details of our experience. They do not tell us why we are seeing a tree rather than something else or nothing at all. The third option seems to assume that there is a real world somewhere from which these experiences are generated (that is, the lab with the scientist in it). The full explanation of how things work in that world presumably must involve some complex laws of physics as well. There is no obvious reason to think that such an account would require fewer assumptions than an account of the world as we see it. Hence, all things considered, if our goal is to create a full explanation of reality, the �inal option seems to give the best account of why we are seeing the tree. It explains our observations without needless extra assumptions.

Therefore, if knowledge is assumed only to be deductive, then perhaps we do not know (with absolute deductive certainty) that there is a world outside of us. However, when we consider abductive knowledge, our evidence for the existence of the world as we see it may be rather strong.

How to Assess an Explanation

There are many factors that in�luence the strength of an inference to the best explanation. However, when testing inferences to the best explanation for strength, these questions are good to keep in mind:

Does it agree well with the rest of human knowledge? Suggesting that your roommate’s car is gone because it �loated away, for example, is not a very credible story because it would violate the laws of physics. Does it provide the simplest explanation of the observed phenomena? According to Occam’s razor, we want to explain why things happen without unnecessary complexity. Does it explain all relevant observations? We cannot simply ignore contradicting data because it contradicts our theory; we have to be able to explain why we see what we see. Is it noncircular? Some explanations merely lead us in a circle. Stating that it is raining because water is falling from the sky, for example, does not give us any new information about what causes the water to fall. Is it testable? Suggesting that invisible elves stole the car does not allow for empirical con�irmation. An explanation is stronger if its elements are potentially observable. Does it help us explain other phenomena as well? The best scienti�ic theories do not just explain one thing but allow us to understand a whole range of related phenomena. This principle is called fecundity. Galileo’s explanation of the orbits of the planets is an example of a fecund theory because it explains several things all at once.

An explanation that has all of these virtues is likely to be better than one that does not.

A Limitation

One limitation of inference to the best explanation is that it depends on our coming up with the correct explanation as one of the candidates. If we do not think of the correct explanation when trying to imagine possible explanation, then inference to the best explanation can steer us wrong. This can happen with any inductive argument, of course; inductive arguments always carry some possibility that the conclusion may be false even if the premises are true. However, this limitation is a particular danger with inference to the best explanation because it relies on our being able to imagine the true explanation.

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This is one reason that it is essential to always keep an open mind when using this technique. Further information may introduce new explanations or change which explanation is best. Being open to further information is important for all inductive inferences, but especially so for those involving inference to the best explanation.

Practice Problems 6.5

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.5.pdf) to check your answers.

1. This philosopher coined the term abductive reasoning. a. Karl Popper b. Charles Sanders Peirce c. Aristotle d. G. W. F. Hegel

2. Sherlock Holmes is often said to be engaging in this form of reasoning, even though from a logical perspective he wasn’t.

a. deductive b. inductive c. abductive d. productive

3. In a speci�ic city that happens to be a popular tourist destination, the number of residents going to the emergency rooms for asthma attacks increases in the summer. When the winter comes and tourism decreases, the number of asthma attacks goes down. What is the most probable inference to be drawn in this situation?

a. The locals are allergic to tourists. b. Summer is the time that most people generally have asthma attacks. c. The increased tourism leads to higher levels of air pollution due to traf�ic. d. The tourists pollute the ocean with trash that then causes the locals to get sick.

4. A couple goes to dinner and shares an appetizer, entrée, and dessert. Only one of the two gets sick. She drank a glass of wine, and her husband drank a beer. What is the most probable inference to be drawn in this situation?

a. The wine was the cause of the sickness. b. The beer protected the man from the sickness. c. The appetizer affected the woman but not the man. d. The wine was rotten.

5. You are watching a magic performance, and there is a woman who appears to be �loating in space. The magician passes a ring over her to give the impression that she is �loating. What explanation �its best with Occam’s razor?

a. The woman is actually �loating off the ground. b. The magician is a great magician. c. There is some sort of unseen physical object holding the woman.

6. You get a stomachache after eating out at a restaurant. What explanation �its best with Occam’s razor? a. You contracted Ebola and are in the beginning phases of symptoms. b. Someone poisoned the food that you ate. c. Something was wrong with the food you ate.

7. In order to determine how a disease was spread in humans, researchers placed two groups of people into two rooms. Both rooms were exactly alike, and no people touched each other while in the rooms. However, researchers placed someone who was infected with the disease in one room. They found that those who

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were in the room with the infected person got sick, whereas those who were not with an infected person remained well. What explanation �its best with Occam’s razor?

a. The disease is spread through direct physical contact. b. The disease is spread by airborne transmission. c. The people in the �irst room were already sick as well.

8. There is a dent in your car door when you come out of the grocery store. What explanation �its best with Occam’s razor?

a. Some other patron of the store hit your car with their car. b. A child kicked your door when walking into the store. c. Bad things tend to happen only to you in these types of situations.

9. A student submits a paper that has an 80% matching rate when submitted to Turnitin. There are multiple sites that align exactly with the content of the paper. What explanation �its best with Occam’s razor?

a. The student didn’t know it was wrong to copy things word for word without citing. b. The student knowingly took material that he did not write and used it as his own. c. Someone else copied the student’s work.

10. You are a man, and you jokingly take a pregnancy test. The test comes up positive. What explanation �its best with Occam’s razor?

a. You are pregnant. b. The test is correct. c. The test is defective.

11. A bomb goes off in a supermarket in London. A terrorist group takes credit for the bombing. What explanation �its best with Occam’s razor?

a. The British government is trying to cover up the bombing by blaming a terrorist group. b. The terrorist group is the cause of the bombing. c. The U.S. government actually bombed the market to get the British to help them �ight terrorist

groups.

12. You have friends and extended family over for Thanksgiving dinner. There are kids running through the house. You check the turkey and �ind that it is overcooked because the temperature on the oven is too high. What explanation �its best with Occam’s razor?

a. The oven increased the temperature on its own. b. Someone turned up the heat to sabotage your turkey. c. You bumped the knob when you were putting something into the oven.

13. Researchers recently mapped the genome of a human skeleton that was 45,000 years old. They found long fragments of Neanderthal DNA integrated into this human genome. What explanation �its best with Occam’s razor?

a. Humans and Neanderthals interbred at some point prior to the life of this human. b. The scientists used a faulty method in establishing the genetic sequence. c. This was actually a Neanderthal skeleton.

14. There is a recent downturn in employment and the economy. A politically far-leaning radio host claims that the downturn in the economy is the direct result of the president’s actions. What explanation �its best with Occam’s razor?

a. The downturn in employment is due to many factors, and more research is in order. b. The downturn in employment is due to the president’s actions. c. The downturn in employment is really no one’s fault.

15. In order for an explanation to be adequate, one should remember that __________. a. it should agree with other human knowledge b. it should include the highest level of complexity c. it should assume the thing it is trying to prove d. there are outlying situations that contradict the explanation

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16. The fecundity of an explanation refers to its __________. a. breadth of explanatory power b. inability to provide an understanding of a phenomenon c. lack of connection to what is being examined d. ability to bear children

17. Why might one choose to use an inductive argument rather than a deductive argument? a. One possible explanation must be the correct one. b. The argument relates to something that is probabilistic rather than absolute. c. An inductive argument makes the argument valid. d. One should always use inductive arguments when possible.

18. This is the method by which one can make a valid argument invalid. a. adding false supporting premises b. demonstrating that the argument is valid c. adding true supporting premises d. valid arguments cannot be made invalid

19. This form of inductive argument moves from the general to the speci�ic. a. generalizations b. statistical syllogisms c. hypothetical syllogism d. modus tollens

Questions 20–24 relate to the following passage:

If I had gone to the theater, then I would have seen the new �ilm about aliens. I didn’t go to the theater though, so I didn’t see the movie. I think that �ilms about aliens and supernatural events are able to teach people a lot about what the future might hold in the realm of technology. Things like cell phones and space travel were only dreams in old movies, and now they actually exist. Science �iction can also demonstrate new futures in which people are more accepting of those that are different from them. The different species of characters in these �ilms all working together and interacting with one another in harmony displays the unity of different people without explicitly making race or ethnicity an issue, thereby bringing people into these forms of thought without turning those away who do not want to explicitly confront these issues.

20. How many arguments are in this passage? a. 0 b. 1 c. 2 d. 3

21. How many deductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3

22. How many inductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3

23. Which of the following are conclusions in the passage? Select all that apply. a. If I had gone to the theater, then I would have seen the new �ilm about aliens. b. I didn’t go to the theater.

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c. Films about aliens and supernatural events are able to teach people a lot about what the future might hold in the realm of technology.

d. The different species of characters in these �ilms all working together and interacting with one another in harmony displays the unity of different people without explicitly making race or ethnicity an issue.

24. Which change to the deductive argument would make it valid? Select all that apply. a. Changing the �irst sentence to “If I would have gone to the theater, I would not have seen the new

�ilm about aliens.” b. Changing the second sentence to “I didn’t see the new �ilm about aliens.” c. Changing the conclusion to “Alien movies are at the theater.” d. Changing the second sentence to “I didn’t see the movie, so I didn’t go to the theater.”

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Summary and Resources

Chapter Summary Although induction and deduction are treated differently in the �ield of logic, they are frequently combined in arguments. Arguments with both deductive and inductive components are generally considered to be inductive as a whole, but the important thing is to recognize when deduction and induction are being used within the argument. Arguments that combine inductive and deductive elements can take advantage of the strengths of each. They can retain the robustness and persuasiveness of inductive arguments while using the stronger connections of deductive arguments where these are available.

Science is one discipline in which we can see inductive and deductive arguments play out in this fashion. The hypothetico–deductive method is one of the central logical tools of science. It uses a deductive form to draw a conclusion from inductively supported premises. The hypothetico–deductive method excels at discon�irming or falsifying hypotheses but cannot be used to con�irm hypotheses directly.

Inference to the best explanation, however, does provide evidence supporting the truth of a hypothesis if it provides the best explanation of our observations and withstands our best attempts at refutation. A key limitation of this method is that it depends on our being able to come up with the correct explanation as a possibility in the �irst place. Nevertheless, it is a powerful form of inference that is used all the time, not only in science but in our daily lives.

Connecting the Dots Chapter 6

NEXT

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Critical Thinking Questions 1. You have probably encountered numerous conspiracy theories on the Internet and in popular media. One such

theory is that 9/11 was actually plotted and orchestrated by the U.S. government. What is the relationship between conspiracy theories and inference to the best possible explanation? In this example, do you think that this is a better explanation than the most popular one? Why or why not?

2. What are some methods you can use to determine whether or not information represents the best possible explanation of events? How can you evaluate sources of information to determine whether or not they should be trusted?

3. Descartes claimed that it might be the case that humans are totally deceived about all aspects of their existence. He went so far as to claim that God could be evil and could be making it so that human perception is completely wrong about everything. However, he also claimed that there is one thing that cannot be doubted: So long as he is thinking, it is impossible for him to doubt that it is he who is thinking. Hence, so long as he thinks, he exists. Do you think that this argument establishes the inherent existence of the thinking being? Why or why not?

4. Have you ever been persuaded by an argument that ended up leading you to a false conclusion? If so, what happened, and what could you have done differently to prevent yourself from believing a false conclusion?

5. How can you incorporate elements of the hypothetico–deductive method into your own problem solving? Are there methods here that can be used to analyze situations in your personal and professional life? What can we learn about the search for truth from the methods that scientists use to enhance knowledge?

Web Resources https://www.youtube.com/watch?v=RauTW8F-PMM (https://www.youtube.com/watch?v=RauTW8F-PMM) Watch Ashford professor Justin Harrison lecture on the difference between inductive and deductive arguments.

https://www.youtube.com/watch?v=VXW5mLE5Y2g (https://www.youtube.com/watch?v=VXW5mLE5Y2g) Shmoop offers an animated video on the difference between induction and deduction.

http://www.ac4d.com/2012/06/03/abductive-reasoning-in-airport-security-and-pro�iling (http://www.ac4d.com/2012/06/03/abductive-reasoning-in-airport-security-and-pro�iling) >Design expert Jon Kolko applies abductive reasoning to airport security in this blog post.

Key Terms

abductive reasoning See inference to the best explanation.

falsi�iable Describes a claim that is conceivably possible to prove false. That does not mean that it is false; only that prior to testing, it is possible that it could have been.

falsi�ication The effort to disprove a claim (typically by �inding a counterexample to it).

hypothesis A conjecture about how some part of the world works.

hypothetico–deductive method The method of creating a hypothesis and then attempting to falsify it through experimentation.

inference to the best explanation The process of inferring something to be true because it is the most likely explanation of some observations. Also known as abductive reasoning.

Occam’s razor The principle that, when seeking an explanation for some phenomena, the simpler the explanation the better.

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self-sealing propositions Claims that cannot be proved false because they are interpreted in a way that protects them against any possible counterexample.

to prove false. That does not mean that it is false; only that prior to testing it is possible

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Learning Objectives

After reading this chapter, you should be able to:

1. Describe the various fallacies of support, their origins, and circumstances in which speci�ic arguments may not be fallacious.

2. Describe the various fallacies of relevance, their origins, and circumstances in which speci�ic arguments may not be fallacious.

3. Describe the various fallacies of clarity, their origins, and circumstances in which speci�ic arguments may not be fallacious.

We can conceive of logic as providing us with the best tools for seeking truth. If our goal is to seek truth, then we must be clear that the task is not limited to the formation of true beliefs based on a solid logical foundation, for the task also

7Informal Fallacies

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involves learning to avoid forming false beliefs. Therefore, just as it is important to learn to employ good reasoning, it is also important to learn to avoid bad reasoning.

Toward this end, this chapter will focus on fallacies. Fallacies are errors in reasoning; more speci�ically, they are common patterns of reasoning with a high likelihood of leading to false conclusions. Logical fallacies often seem like good reasoning because they resemble perfectly legitimate argument forms. For example, the following is a perfectly valid argument:

If you live in Paris, then you live in France. You live in Paris. Therefore, you live in France.

Assuming that both of the premises are true, it logically follows that the conclusion must be true. The following argument is very similar:

If you live in Paris, then you live in France. You live in France. Therefore, you live in Paris.

This second argument, however, is invalid; there are plenty of other places to live in France. This is a common formal fallacy known as af�irming the consequent. Chapter 4 discussed how this fallacy was based on an incorrect logical form. This chapter will focus on informal fallacies, fallacies whose errors are not so much a matter of form but of content. The rest of this chapter will cover some of the most common and important fallacies, with de�initions and examples. Learning about fallacies can be a lot of fun, but be warned: Once you begin noticing fallacies, you may start to see them everywhere.

Before we start, it is worth noting a few things. First, there are many, many fallacies. This chapter will consider only a sampling of some of the most well-known fallacies. Second, there is a lot of overlap between fallacies. Reasonable people can interpret the same errors as different fallacies. Focus on trying to understand both interpretations rather than on insisting that only one can be right. Third, different philosophers often have different terminology for the same fallacies and make different distinctions among them. Therefore, you may �ind that others use different terminology for the fallacies that we will learn about in this chapter. Not to worry—it is the ideas here that are most important: Our goal is to learn to identify and avoid mistakes in reasoning, regardless of speci�ic terminology.

Finally, there are many ways to divide the fallacies into categories. This chapter will refer to fallacies of support, fallacies of clarity, and fallacies of relevance. Avoiding fallacies may be dif�icult at �irst, but ultimately, as we learn to reason more fairly and carefully, we will �ind that avoiding fallacious reasoning helps us develop habits of mental fairness, trustworthiness, and openness, enhancing our ability to discern truth from error.

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Ingram Publishing/Thinkstock

With fallacious reasoning, the premises only appear to support the conclusion. When you look closely at a fallacious argument, you can see how the premises fail to offer support.

7.1 Fallacies of Support

When reasoning, it is essential to reach conclusions based on adequate evidence; otherwise, our views are unsubstantiated. The better the evidence, the more credible our claims are, and the more likely they are to be true. Fallacies can lead us to accept conclusions that are not adequately supported and may be false. Let us learn some of the most common ways this can happen.

Begging the Question

One of the most common fallacies is called begging the question, also known as petitio principii. This fallacy occurs when someone gives reasoning that assumes a major point at issue; it assumes a particular answer to the question with which we are concerned. In other words, the premises of the argument claim something that someone probably would not agree with if he or she did not already accept the conclusion. Take a look at the following argument:

Abortion is wrong because a fetus has a right to live.

There is nothing wrong with this argument as an expression of a person’s belief. The question is whether it will persuade anyone who does not already agree with the conclusion. The premise of this argument assumes the major point at issue. If fetuses have a right to live, then it would follow almost automatically that abortion is wrong. However, those who do not accept the conclusion probably do not accept this premise (perhaps they do not feel that the developing embryo is developed enough to have human rights yet). It is therefore unlikely that they will be persuaded by the argument. To improve the argument, it would be necessary to give good reasons why a fetus has a right to life, reasons that would be persuasive to people on the other side of the argument.

For more clarity about this problem, take a look at these similar arguments:

Capital punishment is wrong because all humans have a right to live.

Eating meat is wrong because animals have a right to live.

These arguments are nearly identical, yet they reach different conclusions about what types of killing are wrong because of different assumptions about who has the right to live. Each, however, is just as unlikely to persuade people with a different view. In order to be persuasive, it is best to give an argument that does not rest on controversial views that are merely assumed to be true. It is not always easy to create non-question-begging arguments, but such is the challenge for those who would like to have a strong chance of persuading those with differing views.

Here are examples on both sides of a different question:

Joe: I know that God exists because it says so in the Bible.

Doug: God doesn’t exist because nothing supernatural is real.

Do you think that either argument will persuade someone on the other side? Someone who does not believe in God probably does not accept the Bible to be completely true, so this reasoning will not make the person change his or her mind. The other argument does the same thing by simply ruling out the possibility that anything could exist other than physical matter. Someone who believes in God will probably not accept this premise.

Both arguments, on the other hand, will probably sound very good to someone who shares the speaker’s point of view, but they will not sound persuasive at all to those who do not. Committing the fallacy of begging the question can be compared to “preaching to the choir” because the only people who will accept the premise are those who already agree with the conclusion.

Circular Reasoning

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Concept by Christopher Foster | Illustration by Steve Zmina

Some inductive arguments make generalizations about certain groups, but in

An extreme form of begging the question is called circular reasoning. In circular reasoning, a premise is identical, or virtually identical, to the conclusion.

Here is an example:

Mike: Capital punishment is wrong.

Sally: Why is it wrong?

Mike: Because it is!

Mike’s reasoning here seems to be, “Capital punishment is wrong. Therefore, capital punishment is wrong.” The premise and conclusion are the same. The reasoning is technically logically valid because there is no way for the premise to be true and the conclusion false—since they are the same—but this argument will never persuade anyone, because no one will accept the premise without already agreeing with the conclusion.

As mentioned, circular reasoning can be considered an extreme form of begging the question. For another example, suppose the conversation between Joe and Doug went a little further. Suppose each questioned the other about how they knew that the premise was true:

Joe: I know that the Bible is true because it says so right here in the Bible, in 2 Timothy 3:16.

Doug: I know that there is nothing supernatural because everything has a purely natural explanation.

Here both seem to reason in a circular manner: Joe says that the Bible is true because it says so, which assumes that it is true. On the other side, to say that everything has a purely natural explanation is the same thing as to say that there is nothing supernatural, so the premise is synonymous with the conclusion. If either party hopes to persuade the other to accept his position, then he should offer premises that the other is likely to �ind persuasive, not simply another version of the conclusion.

Moral of the Story: Begging the Question and Circular Reasoning

To demonstrate the truth of a conclusion, it is not enough to simply assume that it is true; we should give evidence that has a reasonable chance of being persuasive to people on the other side of the argument. The way to avoid begging the question and circular reasoning is to think for a minute about whether someone with a different point of view is likely to accept the premises you offer. If not, strive to modify your argument so that it has premises that are more likely to be accepted by parties on the other side of the debate.

Hasty Generalizations and Biased Samples

Chapter 5 demonstrated that we can reason from a premise about a sample population to a conclusion about a larger population that includes the sample. Here is a simple example:

Every crow I have ever seen has been black.

Therefore, all crows are black.

This is known as making an inductive generalization; you are making a generalization about all crows based on the crows you have seen. However, if you have seen only a small number of crows, then this inductive argument is weak because the sample of crows was not large enough. A hasty generalization is an inductive generalization in

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a hasty generalization, the sample size is inadequate.

Social psychologist Mahzarin Banaji explains that prejudice is something that is learned, rather than something with which we are born. In other words, we are prone to making hasty generalizations simply because we make observations about the world around us. The good news, according to Banaji, is that we can change our thinking.

The Acquisition of Biases

Critical Thinking Questions

1. What are some ways that the human mind works that naturally lead it to make false generalizations?

2. What are the positive and negative aspects of the manner in which the human mind functions?

3. How does perception relate to prejudice? How can humans work to overcome the natural functions of their minds?

which the sample size is too small. The person has generalized too quickly, without adequate support.

Notice that stereotypes are often based on hasty generalizations. For example, sometimes people see a person of a different demographic driving poorly and, based on only one example, draw a conclusion about the whole demographic. As Chapter 8 will discuss, such generalizations can act as obstacles to critical thinking and have led to many erroneous and hurtful views (see also http://www.sciencedaily.com/releases/2010/08/100810122210.htm (http://www.sciencedaily.com/releases/2010/08/100810122210.htm) for a discussion of the long-term effects of stereotyping).

Not all inductive generalizations are bad, however. A common form of inductive generalization is a poll. When someone takes a poll, he or she samples a group to draw a conclusion about a larger group. Here would be an example:

We sampled 1,000 people, and 70% said they will vote for candidate A. Therefore, candidate A will win.

Here, the sample size is relatively large, so it may supply strong evidence for the conclusion. Recall Chapter 5’s discussion of assessing the strength of statistical arguments that use samples. That chapter discussed how an inductive generalization could be affected if a sample population is not truly random. For example, what if all of the people polled were in the same county? The results of the poll might then be skewed toward one candidate or other based on who lives in that county. If, in a generalization, the sample population is not truly representative of the whole population, then the argument uses a biased sample (recall the Chapter 5 discussion of Gallup’s polling techniques and see this chapter’s A Closer Look: Biased Samples in History for a historical example of how even well-intentioned polling can go wrong).

Slanted polling questions represent just one method of creating deliberately biased samples; another method is called cherry picking. Cherry picking involves a deliberate selection of data to support only one side of an issue. If there is evidence on both sides of a controversial question and you focus only on evidence supporting one side, then you are manipulating the data by ignoring the evidence that does not support the conclusion you desire.

For example, suppose an infomercial gives many examples of people who used a certain product and had amazing results and therefore suggests that you will probably get great results, too. Even if those people are telling the truth, it is very possible that many more people did not have good results. The advertisers will, of course, only put the people in the commercial that had the best results. This can be seen as cherry picking, because the viewer of the commercial does not get to see all of the people who felt that the product was a waste of money.

A Closer Look: Biased Samples in History

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In 1936 the largest poll ever taken (10 million questionnaires) showed that Alf Landon would soundly defeat Franklin D. Roosevelt in the presidential election. The results were quite the opposite, however. What went wrong? The answer, it turns out, was that the names and addresses that were used to send out the questionnaires were taken from lists of automobile owners, phone subscribers, and country club memberships (DeTurk, n.d.). Therefore, the polls tended to be sent to wealthier people, who were more likely to vote for Landon.

Typically, �inding a representative sample means selecting a sample randomly from within the whole population. However, as this example shows, it is sometimes dif�icult to make certain that there is no source of bias within one’s sampling method. In fact, it is really dif�icult to get inductive generalizations just right. We must have a suf�iciently large sample, and it must be truly representative of the whole population. We should be careful to look at a large sample of data that accurately represents the population in general. There is a complex science of polling and analyzing the data to predict things like election results. A more in-depth discussion of this topic can be found in Chapter 5.

Appeal to Ignorance and Shifting the Burden of Proof

Sometimes we lack adequate evidence that a claim is true or false; in such situations it would seem wise to be cautious and search for further evidence. Sometimes, however, people take the lack of proof on one side to constitute a proof of the other side. This type of reasoning is known as the appeal to ignorance; it consists of arguing either that a claim is true because it has not been proved to be false or that a claim is false because it has not been proved to be true.

Here is a common example on both sides of another issue:

UFO investigator: “You can’t prove that space aliens haven’t visited Earth, so they probably have.”

Skeptic: “We haven’t yet veri�ied the existence of space aliens, so they must not exist.”

Both the believer and the skeptic in these examples mistakenly take a failure to prove one side to constitute a demonstration of the truth of the other side. It is sometimes said that the absence of evidence is not evidence of absence. However, there are some exceptions in which such inferences are justi�ied. Take a look at the following example:

John: There are no elephants in this room.

Cindy: How do you know?

John: Because I do not see any.

In this case the argument may be legitimate. If there were an elephant in the room, one would probably notice. Another example might be in a medical test in which the presence of an antibody would trigger a certain reaction in the lab. The absence of that reaction is then taken to demonstrate that the antibody is not present. For such reasoning to work, we need to have good reason to believe that if the antibody were present, then the reaction would be observed.

However, for that type of reasoning to work in the case of space aliens, the believer would have to demonstrate that if there were none, then we would be able to prove that. Likewise, the skeptic’s argument would require that if there were space aliens, then we would have been able to verify it. Such a statement is likely to be true for the case of an elephant, but it is not likely to be the case for space aliens, so the appeal to ignorance in those examples is fallacious.

The appeal to ignorance fallacy is closely related to the fallacy of shifting the burden of proof, in which those who have the responsibility of demonstrating the truth of their claims (the so-called burden of proof) simply point out the failure of the other side to prove the opposing position. People who do this have not met the burden of proof but have merely acted as though the other side has the burden instead. Here are two examples of an appeal to ignorance that seem to shift the burden of proof:

Power company: “This new style of nuclear power plant has not been proved to be unsafe; therefore, its construction should be approved.” (It would seem that, when it comes to high degrees of risk, the burden of

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Concept by Christopher Foster | Illustration by Steve Zmina

If the guitar player were stating his position on the best guitar to purchase, we might be inclined to follow his advice, as he would be a legitimate authority. However, in this case he is an inadequate authority.

proof would be on the power plant’s side to show that the proposed plants are safe.)

Prosecuting attorney: “The defense has failed to demonstrate that their client was not at the scene of the crime. Therefore, we must put this criminal in jail.” (This prosecutor seems to assume that it is the duty of the defense to demonstrate the innocence of its client, when it is actually the prosecution’s responsibility to show that the accused is guilty beyond reasonable doubt.)

It is not always easy to determine who has the burden of proof. However, here are some reasonable questions to ask when it comes to making such a determination:

Which side is trying to change the status quo? One person trying to get another person to change views will usually have the burden of proof; otherwise, the other person will not be persuaded to change. Which side’s position involves greater risk? A company that designs parachutes or power plants, for example, would be expected to demonstrate the safety of the design. Is there a rule that determines the burden of proof in this context? For example, the American legal system requires that, in criminal cases, the prosecution prove its case “beyond reasonable doubt.” Debates often put the burden of proof on the af�irmative position.

Generally speaking, we should arrive at conclusions based on good evidence for that conclusion, not based on an absence of evidence to the contrary. An exception to this rule is the case of negative tests: cases in which if the claim P is true, then result Q would very likely be observed. In these cases, if the result Q is not observed, then we may infer that P is unlikely to be true. In general, when one side has the burden of proof, it should be met; simply shifting the burden to the other side is a sneaky and fallacious move.

Appeal to Inadequate Authority

An appeal to authority is the reasoning that a claim is true because an authority �igure said so. Some people are inclined to think that all appeals to authority are fallacious; however, that is not the case. Appeals to authority can be quite legitimate if the person cited actually is an authority on the matter. However, if the person cited is not in fact an authority on the subject at hand, then it is an appeal to inadequate authority.

To see why appeals to authority in general are necessary, try to imagine how you would do in college if you did not listen to your teachers, textbooks, or any other sources of information. In order to learn, it is essential that we listen to appropriate authorities. However, many sources are unreliable, misleading, or even downright deceptive. It is therefore necessary to learn to distinguish reliable sources of authority from unreliable sources. How do we know which is which? Here are some good questions to ask when considering whether to trust a given source or authority:

Is this the kind of topic that can be settled by an appeal to authority? Is there much agreement among authorities about this issue? Is this person or source an actual authority on the subject matter in question? Can this authority be trusted to be honest in this context? Am I understanding or interpreting this authority correctly?

If the answer to all of these is “yes,” then it may be a legitimate appeal to authority; if the answer to any of them is “no,” then it may be fallacious. Here are some examples of how appeals to authority can fail at each of these questions:

Is this the kind of topic that can be settled by an appeal to authority?

Student: “Capitalism is wrong; Karl Marx said so.” (The morality of capitalism may not be an issue that authority alone can resolve. We should look at reasons on both sides to determine where the best arguments are.)

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Is there much agreement among authorities about this issue?

Student: “Abortion is wrong. My philosophy teacher said so.” (Philosophers do carefully consider arguments about abortion, but there is no consensus among them about this topic; there are good philosophers on both sides of the issue. Furthermore, this might not be the type of question that can be settled by an appeal to authority. One should listen to the best arguments on each side of such issues rather than simply trying to appeal to an authority.)

Is this person or source an actual authority on the subject matter in question?

Voter: “Global warming is real. My congressperson said so.” (A politician may not be an actual authority on the matter, since politicians often choose positions based on likely voting behavior and who donates to their campaigns. A climatologist is more likely to be a more reliable and informed source in this �ield.)

Can this authority be trusted to be honest in this context?

Juror: “I know that the accused is innocent because he said he didn’t do it.” (A person or entity who has a stake in a matter is called an interested party. A defendant is de�initely an interested party. It would be better to have a witness who is a neutral party.)

Am I understanding or interpreting this authority correctly?

Christian: “War is always wrong because the Bible states, ‘Thou shalt not kill.’” (This one is a matter of interpretation. What does this scripture really mean? In this sort of case, the interpretation of the source is the most important issue.)

Finally, here is an example of a legitimate appeal to authority:

“Martin Van Buren was a Democrat; it says so in the encyclopedia.” (It is hard to think of why an encyclopedia— other than possibly an openly editable resource such as Wikipedia—would lie or be wrong about an easily veri�iable fact.)

It may still be hard to be certain about many issues even after listening to authorities. In such cases the best approach is to listen to and carefully evaluate the reasoning of many experts in the �ield, to determine to what degree there is consensus, and to listen to the best arguments for each position. If we do so, we are less prone to being misled by our own biases and the biases of interested parties.

False Dilemma

An argument presents a false dilemma, sometimes called a false dichotomy, when it makes it sound as though there were only two options when in fact there are more than just those two options. People are often prone to thinking of things in black-and-white terms, but this type of thinking can oversimplify complex matters. Here are two simple examples:

Wife to husband: “Now that we’ve agreed to get a dog, should it be a poodle or a Chihuahua?” (Perhaps the husband would rather get a Great Dane.)

Online survey: “Are you a Republican or a Democrat?” (This ignores many other options like Libertarian, Green, Independent, and so on. If you are in one of those other parties, how should you answer?)

Such examples actually appear to be manipulative, which is why this can be such a problematic fallacy. Take a look at the following examples:

Partygoer: “What is it going to be? Are you going to go drink with us, or are you going to be a loser?” (This seems to imply that there are no other options, like not drinking and still being cool.)

Activist: “You can either come to our protest or you can continue to support the abuse we are protesting.” (This assumes that if you are not protesting, you do not support the cause and in fact support the other side. Perhaps you believe there are better ways to change the system.)

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We must take care to avoid committing the false cause fallacy when looking at evidence. Sometimes, there is an alternative explanation or interpretation, and our inference may have no causal basis.

Analyzing the Evidence

Critical Thinking Questions

1. What are some questions that we can ask to help us examine evidence?

2. How can a critical thinker analyze evidence to determine its truth or falsity?

Though the fallacy is called a dilemma, implying two options, the same thing can happen with more than two options— for example, if someone implies that there are only �ive options when there are in fact other options as well.

False Cause

The assumption that because two things are related, one of them is the cause of the other is called the fallacy of false cause. It is traditionally called post hoc ergo propter hoc (often simply post hoc), which is Latin for “it came after it therefore it was caused by it.” Clearly, not everything that happens after something else was caused by it. Take this example:

John is playing the basketball shooting game of H- O-R-S-E and tries a very dif�icult shot. Right before the shot someone coughs, and the ball goes in. The next time John is going to shoot, he asks that person to cough. (John seems to be assuming that the cough played some causal role in the ball going in. That seems unlikely.)

Here is a slightly more subtle example:

John is taller than Sally, and John won the election, so it must have been because he was taller. (In this case, he was taller �irst and then won the election, so the speaker assumes that is the reason. It is conceivable that his height was a factor, but that does not follow merely because he won; we would need more evidence to infer that was the reason.)

Large-scale correlations might be more complex, but they can commit the same fallacy. Suppose that two things, A and B, correlate highly with each other, as in this example:

The number of police cars in a city correlates highly with the amount of crime in a city. Therefore, police cars cause crime.

It does not necessarily follow that A, the number of police cars, causes B, crime. Another possibility is that B causes A; the amount of crime causes the higher number of police cars. Another option is that a third thing is causing both A and B; in this case the city’s population might be causing both. It is also possible that in some cases the correlation has no causal basis.

Practice Problems 7.1

Identify the fallacy in each statement or exchange. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems7.1.pdf) to check your answers.

1. Politician: “We either decide to keep the handgun laws in the city limits and maintain peace, or we revoke the laws and let the city become a modern day Wild West.”

Analyzing the Evidence From Title: Evidence in Argument: Critical Thinking

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a. begging the question b. circular reasoning c. hasty generalization d. false dilemma e. no fallacy

2. PTA Parent: “Should school kids say the Pledge of Allegiance before class? Certainly, why shouldn’t they?” a. appeal to ignorance b. appeal to inadequate authority c. false dilemma d. shifting the burden of proof e. no fallacy

3. “Both times I went to the movies at Northpark Mall the people watching the movies were extremely disruptive. That movie theater is horrible.”

a. false cause b. hasty generalization c. begging the question d. circular reasoning e. no fallacy

4. “After I had been in a coma for 10 days following my accident, the swelling in my brain went down right after the priest put holy water on my forehead. The water healed me.”

a. begging the question b. hasty generalization c. cherry picking d. false cause e. no fallacy

5. Tom: “Early humans had a simple form of music played on instruments made from animal bones and skins.” Boris: “How do you know that?” Tom: “Well, no one has proved that they didn’t.”

a. biased sample b. appeal to inadequate authority c. appeal to ignorance d. false dilemma e. no fallacy

6. “My father always only bought Ford cars. He said they were the best cars ever. So I only buy Fords.” a. circular reasoning b. biased sample c. false cause d. appeal to inadequate authority e. no fallacy

7. “Ice cream is bad because it’s unhealthy.” a. hasty generalization b. false cause c. begging the question d. false dilemma e. no fallacy

8. “Michael Jordan wears Hanes, so they must be the best.” a. biased sample b. begging the question

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c. appeal to inadequate authority d. shifting the burden of proof e. no fallacy

9. Father: “Republicans only care about making more money and paying lower taxes. That is what they really care about.” Son: “Why is that?” Father: “Because they want to keep more of their money and not have to support others through payment.”

a. circular reasoning b. appeal to pity c. false cause d. appeal to ridicule e. no fallacy

10. Student: “A recent study found that people who have braces and other work to straighten their teeth are more con�ident and better looking, according to members of the American Association of Dental Health.”

a. ad hominem b. biased sample c. burden of proof d. false dilemma e. no fallacy

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7.2 Fallacies of Relevance

We have seen examples in which the premises are unfounded or do not provide adequate support for the conclusion. In extreme cases the premises are barely even relevant to the truth of the conclusion, yet somehow people draw those inferences anyway. This section will take a look at some examples of common inferences based on premises that are barely relevant to the truth of the conclusion.

Red Herring and Non Sequitur

A red herring fallacy is a deliberate attempt to distract the listener from the question at hand. It has been suggested that the phrase’s origins stem from the practice of testing hunting dogs’ skills by dragging a rotting �ish across their path, thus attempting to divert the dogs from the track of the animal they are supposed to �ind. The best dogs could remain on the correct path despite the temptation to follow the stronger scent of the dead �ish (deLaplante, 2009). When it comes to reasoning, someone who uses a red herring is attempting to steer the listener away from the path that leads to the truth of the conclusion.

Here are two examples:

Political campaigner: “This candidate is far better than the others. The �lag tie he is wearing represents the greatest country on Earth. Let me tell you about the great country he represents. . . .” (The campaigner seems to be trying to get the voter to associate love for America with that particular candidate, but presumably all of the candidates love their country. In this case patriotism is the red herring; the real issue we should be addressing is which candidate’s policies would be better for the country.)

Debater in an argument about animal rights: “How can you say that animals have rights? There are humans suffering all around the world. For example, there are human beings starving in Africa; don’t you care about them?” (There may indeed be terrible issues with human suffering, but the existence of human suffering does not address the question of whether animals have rights as well. This line of thinking appears to distract from the question at hand).

An extreme case in which someone argues in an irrelevant manner is called a non sequitur, meaning that the conclusion does not follow from the premises.

Football player: “I didn’t come to practice because I was worried about the game this week; that other team is too good!” (Logically, the talent of the other team would seem to give the player all the more reason to go to practice.)

One student to another: “I wouldn’t take that class. I took it and had a terrible time. Don’t you remember: That semester, my dog died, and I had a car accident. It was terrible.” (These events are irrelevant to the quality of the class, so this inference is unwarranted.)

Whereas a red herring seems to take the conversation to a new topic in an effort to distract people from the real question, a non sequitur may stay on topic but simply make a terrible inference—one in which the conclusion is entirely unjusti�ied by the premises given.

Appeal to Emotion

The appeal to emotion is a fallacy in which someone argues for a point based on emotion rather than on reason. As noted in Chapter 1, people make decisions based on emotion all the time, yet emotion is unreliable as a guide. Many philosophers throughout history thought that emotion was a major distraction from living a life guided by reason. The ancient Greek philosopher Plato, for example, compared emotion and other desires to a beast that tries to lead mankind in several different directions at once (Plato, 360 BCE). The solution to this problem, Plato reasons, is to allow reason, not emotion, to be in charge of our thinking and decision making. Consider the following examples of overreliance on emotion:

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Dave Carpenter/Cartoonstock

With an appeal to pity, it is important to recognize when the appeal is fallacious versus genuine. Telling possible consumers you will cry if they do not purchase your product is most likely a fallacious appeal to pity.

Impulsive husband: “Honey, let’s buy this luxury car. Think of how awesome it would be to drive it around. Plus, it would really impress my ex-coworkers.” (This might feel like the fun choice at the time, but what about when they cannot afford it in a few years?)

Columnist: “Capital punishment should be legal. If someone broke into your house and killed your family, wouldn’t you want him dead?” (You perhaps would want him dead, but that alone does not settle the issue. There are many other issues worth considering, including the issue of innocent people accidentally getting on death row, racism in the system, and so on.)

This is not to say that emotion is never relevant to a decision. The fun of driving a car is one factor (among many) in one’s choice of a car, and the emotions of the victim’s family are one consideration (out of many) in whether capital punishment should be allowed. However, we must not allow that emotion to override rational consideration of the best evidence for and against a decision.

One speci�ic type of appeal to emotion tries to get someone to change his or her position only because of the sad state of an individual affected. This is known as the appeal to pity.

Student: “Professor, you need to change my grade; otherwise, I will lose my scholarship.” (The professor might feel bad, but to base grades on that would be unjust to other students.)

Salesman: “You should buy this car from me because if I don’t get this commission, I will lose my job!” (Whether or not this car is a good purchase is not settled by which salesperson needs the commission most. This salesman appears to play on the buyer’s sense of guilt.)

As with other types of appeal to emotion, there are cases in which a decision based on pity is not fallacious. For example, a speaker may speak truthfully about terrible conditions of children in the aftermath of a natural disaster or about the plight of homeless animals. This may cause listeners to pity the children or animals, but if this is pity for those who are actually suffering, then it may provide a legitimate motive to help. The fallacious use of the appeal to pity occurs when the pity is not (or should not be) relevant to the decision at hand or is used manipulatively.

Another speci�ic type of appeal to emotion is the appeal to fear. The appeal to fear is a fallacy that tries to get someone to agree to something out of fear when it is contrary to a rational assessment of the evidence.

Mom: “You shouldn’t swim in the ocean; there could be sharks.” (The odds of being bitten by a shark are much smaller than the odds of being struck by lightning [International Wildlife Museum, n.d.]. However, the fear of sharks tends to produce a strong aversion.)

Dad: “Don’t go to that country; there is a lot of crime there.” (Here you should ask: How high is the crime rate? Where am I going within that country? Is it much more dangerous than my own country? How important is it to go there? Can I act so that I am

safe there?)

Political ad: “If we elect that candidate, then the economy will collapse.” (Generally, all candidates claim that their policies will be better for the economy. This statement seems to use fear in order to change votes.)

This is not to say that fear cannot be rational. If, in fact, many dangerous sharks have been seen recently in a given area, then it might be wise to go somewhere else. However, a fallacy is committed if the fears are exaggerated—as they often are—or if one allows the emotion of fear to make the decision rather than a careful assessment of the evidence.

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The appeal to fear has been used throughout history. Many wars, for example, have been promoted by playing on people’s fears of an outside group or of the imagined consequences of nonaction.

Politician: “We have to go to war with that country; otherwise its in�luence will destroy our civilization.” (There may or may not be good rational arguments for the war, but getting citizens to support it out of exaggerated fears is to commit the appeal to fear fallacy.)

Sometimes, a person using the appeal to fear personally threatens the listener if she or he does not agree. This fallacy is known as the appeal to force. The threat can be direct:

Boss: “If you don’t agree with me, then you are �ired.”

Or the threat can be implied:

Mob boss: “I’d sure like to see you come around to our way of seeing things. It was a real shame what happened to the last guy who disagreed with us.”

Either way, the listener is being coerced into believing something rather than rationally persuaded that it is true. A statement of consequences, however, may not constitute an appeal to force fallacy, as in the following example:

Boss: “If you don’t �inish that report by Friday, then you will be �ired.” (This example may be harsh, but it might not be fallacious because the boss is not asking you to accept something as true just to avoid consequences, even if it is contrary to evidence. This boss just gives you the information that you need to get this thing done in time in order to keep your job.)

It may be less clear if the consequences are imposed by a large or nebulous group:

Campaign manager: “If you don’t come around to the party line on this issue, then you will not make it through the primary.” (This gives the candidate a strong incentive to accept his or her party’s position on the issue; however, is the manager threatening force or just stating the facts? It could that the implied force comes from the voters themselves.)

It is sometimes hard to maintain integrity in life when there are so many forces giving us all kinds of incentives to conform to popular or lucrative positions. Understanding this fallacy can be an important step in recognizing when those in�luences are being applied.

When it comes to appeals to emotions in general, it is good to be aware of our emotions, but we should not allow them to be in charge of our decision making. We should carefully and rationally consider the evidence in order to make the best decisions. We should also not let those competing forces distract us from trusting only the best and most rational assessment of the evidence.

Appeal to Popular Opinion

The appeal to popular opinion fallacy, also known as the appeal to popularity fallacy, bandwagon fallacy, or mob appeal fallacy, occurs when one accepts a point of view because that is what most people think. The reasoning pattern looks like this:

“Almost everyone thinks that X is true. Therefore, X must be true.”

The error in this reasoning seems obvious: Just because many people believe something does not make it true. After all, many people used to believe that the sun moved around the earth, that women should not vote, and that slavery was morally acceptable. While these are all examples of past erroneous beliefs, the appeal to popular opinion fallacy remains more common than we often realize. People tend to default to the dominant views of their

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Concept by Christopher Foster | Illustration by Steve Zmina

The appeal to popular opinion fallacy can be harmless, like when you see a movie because all your friends said it was great, but other times it can have negative consequences, such as bullying or discriminating against others.

respective cultures, and it takes guts to voice a different opinion from what is normally accepted. Because people with uncommon views are often scorned and because people strongly want to �it in to their culture, our beliefs tend not to be as autonomous as one might imagine.

The philosopher Immanuel Kant discussed the great struggle to learn to think for ourselves. He de�ined enlightenment as the ability to use one’s own understanding without oversight from others (Kant, 1784). However, extricating ourselves from bandwagon thinking is harder than one might think. Consider these examples of popular opinions that might seem appealing:

Patriot: “America is the best country in the world; everyone here knows it.” (To evaluate this claim objectively, we would need a de�inition of best and relevant data about all of the countries in the world.)

Animal eater: “It would be wrong to kill a dog to eat it, but killing a pig for food is �ine. Why? Because that’s what everyone does.” (Can one logically justify this distinction? It seems simply to be based on a majority opinion in one’s culture.)

Business manager: “This business practice is the right way to do it; it is what everyone is doing.” (This type of thinking can sti�le innovation or even justify violations of ethics.)

General formula: “Doing thing of type X is perfectly �ine; it is common and legal.” (You could �ill in all kinds of things for X that people ethically seem to take for granted without thinking about it. Have you ever questioned the ethics of what is “normal”?)

It is also interesting to note that the “truths” of one culture are often different from the “truths” of another. This may not be because truth is relative but because people in each culture are committing the bandwagon fallacy rather than thinking independently. Do you think that we hold many false beliefs today just because a majority of people also believe them? It is possible that much of the so-called common sense of today could someday come to be seen as once popular myths.

It is often wise to listen to the wisdom of others, including majority opinions. However, just because the majority of people think and act a certain way does not mean that it is right or that it is the only way to do things; we should learn to think independently and rationally when deciding what things are right and true and best.

Appeal to Tradition

Closely related to the appeal to popular opinion is the appeal to tradition, which involves believing in something or doing something simply because that is what people have always believed and done. One can see that this reasoning is fallacious because people have believed and done false and terrible things for millennia. It is not always easy, however, to undo these thought patterns. For example, people tried to justify slavery for centuries based partly on the reasoning that it had always been done and was therefore “right” and “natural.” Some traditions may not be quite as harmful. Religious traditions, for example, are often considered to be valuable to people’s identity and collective sense of meaning. In seeking to avoid the fallacy, therefore, it is not always easy to distinguish which things from history are worth keeping. Here is an example:

“This country got where it is today because generations of stay-at-home mothers taught their children the importance of love, hard work, and respect for their elders. Women should stay at home with their kids.” (Is this a tradition that is worth keeping or is it a form of social discrimination?)

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The fallacy would be to assume that something is acceptable simply because it is a tradition. We should be open to rational evaluation of whether a tradition is acceptable or whether it is time to change. For example, in response to proposals of social change, some will argue:

“If people start changing aspect X of society, then our nation will be ruined.” (People have used such reasoning against virtually every form of positive social change.)

You may be realizing that sometimes whether a piece of reasoning is fallacious can be a controversial question. Sometimes traditions are good; however, we should not assume that something is right just because it is a tradition. There would need to be more evidence that the change would be bad than evidence that it would be good. As with appeals to popularity, it is important to reason carefully and independently about what is best, despite the biases of our culture.

Ad Hominem and Poisoning the Well

Ad hominem is Latin for “to the person.” One commits the ad hominem fallacy when one rejects or dismisses a person’s reasoning because of who is saying it. Here are some examples:

“Who cares what Natalie Portman says about science? She’s just an actress.” (Despite being an actress, Natalie Portman has relevant background.)

“Global warming is not real; climate change activists drive cars and live in houses with big carbon footprints.” (Whether the advocates are good personal exemplars is independent of whether the problem is real or whether their arguments are sound.)

“I refuse to listen to the arguments about the merits of home birth from a man.” (A man may not personally know the ordeal of childbirth, but that does not mean that a man cannot effectively reason about the issue.)

It is not always a fallacy to point out who is making a claim. A person’s credentials are often relevant to that person’s credibility as an authority, as we discussed earlier with the appeal to authority. However, a person’s personal traits do not refute that person’s reasoning. The difference, then, is whether one rejects or ignores that person’s views or reasoning due to those traits. To simply assume that someone’s opinion has no merit based on who said it is to commit the fallacy; to question whether or not we should trust someone as an authority may not be.

This next example commits the ad hominem fallacy:

“I wouldn’t listen to his views about crime in America; he is an ex-convict.” (This statement is fallacious because it ignores the person’s reasoning. Ex-convicts sometimes know a lot about problems that lead to crime.)

This example, however, may not commit the fallacy:

“I wouldn’t trust his claims about lung cancer; he works for the tobacco industry.” (This simply calls into question the credibility of the person due to a source of bias.)

One speci�ic type of ad hominem reasons that someone’s claim is not to be listened to if he or she does not live up to the truth of that claim. It is called the tu quoque (Latin for “you too”). Here is an example:

“Don’t listen to his claims that smoking is bad; he smokes!” (Even if the person is a hypocrite, that does not mean his claims are false.)

Another type of fallacy commits the ad hominem in advance. It is called poisoning the well: when someone attempts to discredit a person’s credibility ahead of time, so that all those who are listening will automatically reject whatever the person says.

“The next speaker is going to tell you all kinds of things about giving money to his charity, but keep in mind that he is just out to line his pockets with your money.” (This may unfairly color everyone’s perceptions of what the speaker says.)

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To ignore arguments because of their source is often lazy reasoning. A logical thinker neither rejects nor blindly accepts whatever someone says, but carefully evaluates the quality of the reasoning used on both sides. We should evaluate the truth or falsity of people’s claims on the merits of the claims themselves and based on the quality of the reasoning for them.

Practice Problems 7.2

Identify the fallacy in each statement or exchange. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems7.2.pdf) to check your answers.

1. Jeff: “I think that it is sacrilegious to tell children that a bunny drops off eggs on Easter morning. This totally detracts from the true meaning of Easter.” Steve: “C’mon man! Everybody puts out eggs for their kids on Easter.”

a. false cause b. begging the question c. red herring d. appeal to popular opinion e. no fallacy

2. Radio announcer: “I’ll tell you what: I am appalled that this new bill about the economy is even being looked at by Congress! The bureaucrats in Washington want us all to just sit around and forget about the fact that every day we are getting closer to losing this great nation. I think you’ll agree with me that we don’t want our nation to collapse because a bunch of sissies are worried about people who don’t care about our country anyway!”

a. red herring b. appeal to tradition c. begging the question d. false cause e. no fallacy

3. Spouse: “I know that you get angry a lot. I’m sure that soon you will hit me or something. And what are we going to do when we have kids? You will probably beat them until they run out of the house, and I will be left childless and abused!

a. slippery slope b. begging the question c. red herring d. appeal to emotion e. no fallacy

4. Sloan: “Dude, you play way too many video games.” John: “Whatever, bro! When Eternal Death Slayer III came out, you were waiting in line outside the store for 4 hours to be the �irst to get it.”

a. ad hominem b. appeal to popularity c. false dilemma d. false cause e. no fallacy

5. TV preacher: “Just a $50 gift per month is all it takes to live a life of economic health and prosperity. God will reward your generous donation with 10 times more blessings in your own life if you donate to our ministry. Call now to start enjoying more happiness every day.”

a. appeal to emotion

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b. false dilemma c. appeal to force d. red herring e. no fallacy

6. TV preacher: “You know, in the Old Testament, God told people to give 10% of whatever they had as an offering to him. In fact, in one story, God kills 100,000 Israelites because they fail to honor his demands. This teaching remains true to this day. Now let’s pass around the offering plates.”

a. ad hominem b. hasty generalization c. appeal to ignorance d. appeal to fear e. no fallacy

7. “July is the month during which more ice cream is sold than any other time of the year. July is also the month with the highest crime rate. Therefore, to curb crime, we should ban sales of ice cream during July.”

a. slippery slope b. ad hominem c. false cause d. false dilemma e. no fallacy

8. “Did you see the men land on the moon? Then how can you be so sure that it happened?” a. appeal to ignorance b. hasty generalization c. appeal to inadequate authority d. appeal to force e. no fallacy

9. “Which are you going to do—help your mother or be a lazy bum?” a. false dilemma b. begging the question c. red herring d. shifting the burden of proof e. no fallacy

10. “The last two summers saw record heat; therefore, global warming will soon kill us all.” a. hasty generalization b. appeal to fear c. false dilemma d. false cause e. no fallacy

11. “Why do I think that abortion should be illegal? That doesn’t matter. What matters is, why do you think it should be legal?”

a. shifting the burden of proof b. hasty generalization c. appeal to popular opinion d. appeal to force e. no fallacy

12. “If Brad Pitt’s children go to that elementary school, it must be the best school in Los Angeles.” a. appeal to fear b. begging the question c. appeal to inadequate authority d. appeal to tradition e. no fallacy

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13. Father to son: “Now that we have �inished the Thanksgiving meal, it’s time to go watch football.” Son: “Why should we watch football?” Father: “Because my father and my grandfather before him used to watch football.”

a. appeal to fear b. false cause c. accident d. appeal to tradition e. no fallacy

14. “I wouldn’t listen to Bob. After all, he’s just a mechanic.” a. slippery slope b. ad hominem c. false cause d. false dilemma e. no fallacy

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Thomas Bros./Cartoonstock

Is having to do chores an intolerable consequence that stems from learning to walk, or is this a slippery slope fallacy?

7.3 Fallacies of Clarity

Another category of fallacies consists of arguments that depend on an unclear use of words; they are called fallacies of clarity. Problems with clarity often result from words in our language that are vague (imprecise in meaning, with so- called gray areas) or ambiguous (having more than one meaning). Fallacies of clarity can also result from misunderstanding or misrepresenting others’ arguments.

The Slippery Slope

The slippery slope fallacy occurs when someone reasons, without adequate justi�ication, that doing one thing will inevitably lead to a whole chain of other things, ultimately resulting in intolerable consequences; therefore, the person reasons, we should not do that �irst thing.

It is perfectly appropriate to object to a policy that will truly have bad consequences. A slippery slope fallacy, however, merely assumes that a chain of events will follow, leading to a terrible outcome, when such a chain is far from inevitable. Such assumptions cause people to reject the policy out of fear rather than out of actual rational justi�ication.

Here is an example:

Student: “Why can’t I keep my hamster in my dorm room?”

Administrator: “Because if we let you keep your hamster, then other students will want to bring their snakes, and others will bring their dogs, and others will bring their horses, and it will become a zoo around here!” (There may be good reasons not to

allow hamsters in dorm rooms—allergies, droppings, and so on—but the idea that it will inevitably lead to allowing all kinds of other large, uncaged animals seems to be unjusti�ied.)

As with many fallacies, however, there are times when similar reasoning may actually be good reasoning. For example, an alcoholic may reason as follows:

“I can’t have a beer because if I do, then it will lead to more beers, which will lead to whiskey, which will lead to me getting in all kinds of trouble.”

For an alcoholic, this may be perfectly good reasoning. Based on past experience, one may know that one action leads inevitably to another. One way to test if an argument commits a slippery slope fallacy, as opposed to merely raising legitimate questions about the dif�iculty of drawing a line, is to ask whether it would be possible to draw a line that would stop the slippery slope from continuing. What do you think about the following examples?

“We can’t legalize marijuana because if we do, then we will have to legalize cocaine and then heroine and then crack, and everyone will be a druggie before you know it!”

“If you try to ban pornography, then you will have to make the distinction between pornography and art, and that will open the door to all kinds of censorship.”

Some examples may present genuine questions as to where to draw a line; others may represent slippery slope fallacies. The question is whether those consequences are likely to follow from the initial change.

As some examples show, the dif�iculty of drawing precise lines is sometimes relevant to important political questions. For example, in the abortion debate, there is a very important question about at what point a developing embryo becomes a human being with rights. Some say that it should be at conception; some say at birth. The Supreme Court, in its famous Roe v. Wade decision (1973), chose the point of viability—the point at which a fetus could survive outside the womb; the decision remains controversial today.

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True, it is dif�icult to decide exactly where the line should be drawn, but the failure to draw one at all can lead to slippery slope problems. To reason that we should not make any distinctions because it is hard to draw the line is like reasoning that there should be no speed limit because it is dif�icult to decide exactly when fast driving becomes unsafe. The trick is to �ind good reasons why a line should be drawn in one place rather than another.

Another example is in the same-sex marriage debate. Some feel that if same-sex marriage were to be universally legalized, then all kinds of other types of objectionable marriage will become legal as well. Therefore, they argue, we must not legalize it. This would appear to commit the slippery slope fallacy, because there are ways that gay marriage laws could be written without leading to other objectionable types of marriages becoming legal.

Moral of the Story: The Slippery Slope

It can be dif�icult to draw sharp boundaries and create clear de�initions, but we must not allow this dif�iculty to prevent us from making the best and most useful distinctions we can. Policy decisions, for example, should be judged with careful reasoning, making the best distinctions we can, not by the mere application of slippery slope reasoning.

Equivocations

Equivocation is a fallacy based on ambiguity. An ambiguous term is a word that means two different things. For example, fast can mean “going without food,” or it can mean “rapid.” Some ambiguities are used for humor, like in the joke, “How many therapists does it take to change a lightbulb? Just one, but the lightbulb has to really want to change!” This, of course, is a pun on two meanings of change. However, when ambiguity is used in reasoning, it often creates an equivocation, in which an ambiguous word is used with one meaning at one point in an argument and another meaning in another place in the argument in a misleading way. Take the following argument:

Mark plays tennis.

Mark is poor.

Therefore, Mark is a poor tennis player.

If the conclusion meant that Mark is poor and a tennis player then this would be a logically valid argument. However, the conclusion actually seems to mean that he is bad at playing tennis, which does not follow from the fact that he is poor. This argument seems to switch the meaning of the word poor in between the premises and the conclusion. As another example, consider the following exchange:

Person A: “I broke my leg; I need a doctor!”

Person B: “I am a doctor.”

Person A: “Can you help me with my leg?”

Person B: “I have a PhD in sociology; what do I know about medicine?”

Can you identify the equivocation? Person B seemed to reason as follows:

I have a PhD in sociology.

Therefore, I am a doctor.

Although this reasoning is right in some sense, it does not follow that person B is the type of doctor that person A needs. The word doctor is being used ambiguously.

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Here is another example:

Of�icer: Have you been drinking at all tonight?

Driver: Yes.

Of�icer: Then you are under arrest.

Driver: But I only had a soda!

Clearly, the of�icer came to a false conclusion because he and the driver meant different things by drinking. See A Closer Look: Philosophical Equivocations for more examples.

It is very important when reasoning (or critiquing reasoning) that we are consistent and clear about our meanings when we use words. A subtle switch in meanings within an argument can be highly misleading and can mean that arguments that initially appear to be valid may actually be invalid once we correctly understand the terms involved.

A Closer Look: Philosophical Equivocations

In real life, equivocations are not always so obvious. The philosopher John Stuart Mill, for example, attempted to demonstrate his moral theory, known as utilitarianism, by arguing that, if the only thing that people desire is pleasure, then pleasure is the only thing that is desirable (Mill, 1879). Many philosophers think that Mill is equivocating between two different meanings of desirable. One interpretation means “able to be desired,” which he uses in the premise. The other interpretation is “thing that is good or should be desired,” which he uses in the conclusion. His argument would therefore be invalid, based on a subtle shift in meaning.

Another historical example is one of the most famous philosophical arguments of all time. The philosopher Saint Anselm long ago presented an argument for the existence of God based on the idea that the word God means the greatest conceivable thing and that a thing must exist to be greatest (Anselm, n.d.). His argument may be simpli�ied as follows:

God means the greatest conceivable thing. A thing that exists is greater than one that does not. We can conceive of God existing. Therefore, God must exist.

Though this is still an in�luential argument for the existence of God, some think it commits a subtle equivocation in its application of the word great. The question is whether it is talking about the greatness of the concept or the greatness of the thing. The �irst premise seems to take it be about the greatness of the concept. The second premise, however, seems to depend on talking about the thing itself (actual existence does not change the greatness of the concept). If this analysis is right, then the word greatest has different meanings in the �irst two premises, and the argument may commit an equivocation. In that case the argument that appears to be valid may in fact be subtly invalid.

The Straw Man

Have you ever heard your views misrepresented? Most of us have. Whether it is our religion, our political views, or our recreational preferences, we have probably heard someone make our opinions sound worse than they are. If so, then you know that can be a very frustrating experience.

The straw man fallacy is an attack on a person’s position based on a (deliberate or otherwise) misrepresentation of his or her actual views. The

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Concept by Christopher Foster | Illustration by Steve Zmina

Misrepresenting the views of the other side through a straw man fallacy can be frustrating and will fail to advance the issue.

straw man fallacy is so named because it is like beating up a scarecrow (a straw man) rather than defeating a real person (or the real argument). The straw man fallacy can be pernicious; it is hard for any debate to progress if the differing sides are not even fairly represented. We can hope to refute or improve on a view only once we have understood and represented it correctly.

If you have listened to people arguing about politics, there is a good chance that you have heard statements like the following:

Democrat: “Republicans don’t care about poor people.”

Republican: “Democrats want the government to control everything.”

These characterizations do not accurately represent the aims of either side. One way to tell whether this is a fair representation is to determine whether someone with that view would agree with the characterization of their view. People may sometimes think that if they make the other side sound dumb, their own views will sound smart and convincing by comparison. However, this approach is likely to back�ire. If our audience is wise enough to know that the other party’s position is more sophisticated than was expressed, then it actually sounds unfair, or even dishonest, to misrepresent their views.

It is much harder to refute a statement that re�lects the complexity of someone’s actual views. Can you imagine if politically partisan people spoke in a fairer manner?

Democrat: “Republicans believe that an unrestrained free market incentivizes innovation and ef�iciency, thereby improving the economy.”

Republican: “Democrats believe that in a country with as much wealth as ours, it would be immoral to allow the poorest among us to go without life’s basic needs, including food, shelter, and health care.”

That would be a much more honest world; it would also be more intellectually responsible, but it would not be as easy to make other people sound dumb. Here are more—possibly familiar—examples of straw man fallacies, used by those on opposing sides of a given issue:

Environmentalist: “Corporations and politicians want to destroy the earth. Therefore, we should pass this law to stop them.” (Perhaps the corporations and politicians believe that corporate practices are not as destructive as some imply or that the progress of industry is necessary for the country’s growth.)

Developer: “Environmentalists don’t believe in growth and want to destroy the economy. Therefore, you should not oppose this power plant.” (Perhaps environmentalists believe that the economy can thrive while shifting to more eco-friendly sources.)

Young Earth creationist: “Evolutionists think that monkeys turned into people! Monkeys don’t turn into people, so their theory should be rejected.” (Proponents of evolution would state that there was a common ancestor millions of years ago. Genetic changes occurred very gradually between thousands and thousands of generations, leading to eventual species differences.)

Atheist: “Christians don’t believe in science. They think that Adam and Eve rode around on dinosaurs! Therefore, you should not take their views seriously.” (Many Christians �ind their religion to be compatible with science or have nonliteral interpretations of biblical creation.)

Closely related to the straw man fallacy is the appeal to ridicule, in which one simply seeks to make fun of another person’s view rather than actually refute it. Here is an example:

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“Vegans are idiots who live only on salad. Hooray for bacon!” (Actually, vegans are frequently intelligent people who object to the con�inement of animals for food.)

“People with those political opinions are Nazis!” (Comparisons to Nazis in politics are generally clichéd, exaggerated, and disrespectful to the actual victims of the Holocaust. See Chapter 8 for a discussion of the fallacy reductio ad Hitlerum.)

In an academic or any other context, it is essential that we learn not to commit the straw man fallacy. If you are arguing against a point of view, it is necessary �irst to demonstrate that you have accurately understood it. Only then have you demonstrated that you are quali�ied to discuss its truthfulness. Furthermore, the attempt to ridicule other’s views is rationally counterproductive; it does not advance the discussion and seeks only to mock other people. (See Everyday Logic: Love and Logic for how you can avoid the straw man fallacy and the appeal to ridicule.)

When we seek to defend our own views, the intellectually responsible thing to do is to understand opposing viewpoints as fully as possible and to represent them fairly before we give the reasons for our own disagreement. The same applies in philosophy and other academic topics. If someone want to ponti�icate about a topic without having understood what has already been done in that �ield, then that person simply sounds naive. To be intellectually responsible, we have to make sure to correctly understand what has been done in the �ield before we begin to formulate our own contribution to the �ield.

Everyday Logic: Love and Logic

When it comes to real-life disagreements, people can become very upset—even aggressive. This is an understandable reaction, particularly if the disagreement concerns positions we think are wrong or perspectives that challenge our worldview. However, this kind of emotional reaction can lead to judgments about what the other side may believe—judgments that are not based on a full and sophisticated understanding of what is actually believed and why. This pattern can be the genesis of much of the hostility we see surrounding controversial topics. It can also lead to common fallacies such as the straw man and appeal to ridicule, which are two of the most pernicious and hurtful fallacies of them all.

Logic can help provide a remedy to these types of problems. Logic in its fullest sense is not just about creating arguments to prove our positions right—and certainly not just about proving others wrong. It is about learning to discover truth while avoiding error, which is a goal all participants can share. Therefore, there need not be any losers in this quest.

If we stop short of a full appreciation of others’ perspectives, then we are blocked from a full understanding of the topic at hand. One of the most important marks of a sophisticated thinker is the appreciation of the best reasoning on all sides of each issue.

We must therefore resist the common temptation to think of people with opposing positions as “stupid” or “evil.” Those kinds of judgments are generally unfair and unkind. Instead we should seek to expand our own points of view and remove any animosity. Here are some places to begin:

We can read what smart people have written to represent their own views about the topic, including reading top scholarly articles explaining different points of view. We can really listen with intelligence, openness, and empathy to people who feel certain ways about the topic without seeking to refute or minimize them. We can seek to put ourselves “in their shoes” with sensitivity and compassion. We can speak in ways that re�lect civility and mutual understanding.

It will take time and openness, but eventually it is possible to appreciate more fully a much wider variety of perspectives on life’s questions.

Furthermore, once we learn to fairly represent opposing points of view, we may not �ind those views to be as crazy as we once thought. Even the groups that we initially think of as the strangest actually have good reasons for their

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beliefs. We may or may not come to agree, but only in learning to appreciate why these groups have such beliefs can we truly say that we understand their views. The process and effort to do so can make us more civil, more mature, more sophisticated, more intelligent, and more kind.

Fallacy of Accident

The fallacy of accident consists of applying a general rule to cases in which it is not properly applied. Often, a general rule is true in most cases, but people who commit this fallacy talk as though it were always true and apply it to cases that could easily be considered to be exceptions.

Some may �ind the name of this fallacy confusing. It is called the fallacy of accident because someone committing this fallacy confuses the “essential” meaning of a statement with its nonessential, or “accidental,” meaning. It is sometimes alternately called dicto simpliciter, meaning “unquali�ied generalization” (Fallacy Files, n.d.). Here are some examples:

“Of course ostriches must be able to �ly. They are birds, and birds �ly.” (There clearly are exceptions to that general rule, and ostriches are among them.)

“If you skip class, then you should get detention. Therefore, because you skipped class in order to save someone from a burning building, you should get detention.” (This may be an extreme case, but it shows how a misapplication of a general rule can go astray.)

“Jean Valjean should go to prison because he broke the law.” (This example, from the novel Les Miserables, involves a man serving many years in prison for stealing bread to feed his starving family. In this case the law against stealing perhaps should not be applied as harshly when there are such extenuating circumstances.)

The last example raises the issue of sentencing. One area in which the fallacy of accident can occur in real life is with extreme sentencing for some crimes. In such cases, though an action may meet the technical de�inition of a type of crime under the law, it may be far from the type of case that legislators had in mind when the sentencing guidelines were created. This is one reason that some argue for the elimination of mandatory minimum sentencing.

Another example in which the fallacy of accident can occur is in the debate surrounding euthanasia, the practice of intentionally ending a person’s life to relieve her or him of long-term suffering from a terminal illness. Here is an argument against it:

It is wrong to intentionally kill an innocent human being.

Committing euthanasia is intentionally killing an innocent human being.

Therefore, euthanasia is wrong.

The moral premise here is generally true; however, when we think of the rule “It is wrong to intentionally kill an innocent human being,” what one may have in mind is a person willfully killing a person without justi�ication. In the case of euthanasia, we have a person willingly terminating his or her own life with a strong type of justi�ication. Whatever one’s feelings about euthanasia, the issue is not settled by simply applying the general rule that it is wrong to kill a human being. To use that rule seems to oversimplify the issue in a way that misses the subtleties of this speci�ic case. An argument that properly addresses the issue will appeal to a moral principle that makes sense when applied to the speci�ic issues that pertain to the case of euthanasia itself.

It is dif�icult to make general rules that do not have exceptions. Therefore, when speci�ic troubling cases come up, we should not simply assume the rule is perfect but rather consider the merits of each case in light of the overall purpose for which we have the rule.

Fallacies of Composition and Division

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Two closely related fallacies come from confusing the whole with its parts. The fallacy of composition occurs when one reasons that a whole group must have a certain property because its parts do. Here is an example:

Because the citizens of that country are rich; it follows that the country is rich. (This may not be the case at all; what if the government has outspent its revenue?)

You should be able to see why this one reaches an incorrect conclusion:

“If I stand up at a baseball game then I will be able to see better. Therefore, if everyone stands up at the baseball game, then everyone will be able to see better.”

This statement seems to make the same mistake as the baseball example:

If the government would just give everyone more money, then everyone would be wealthier. (Actually, giving away money to all would probably reduce the value of the nation’s currency.)

A similar fallacy, known as the fallacy of division, does the opposite. Namely, it makes conclusions about members of a population because of characteristics of the whole. Examples might include the following:

That country is wealthy; therefore, its citizens must be wealthy. (This one may not follow at all; the citizens could be much poorer than the country as a whole.)

That team is the best; the players on the team must be the best in the league. (Although the ability of the team has a lot to do with the skills of the players, there are also reasons, including coaching and teamwork, why a team might outperform the average talent of its roster.)

These types of fallacies can lead to stereotyping as well, in which people arrive at erroneous conclusions about a group because of (often fallacious) generalizations about its members. Conversely, people often make assumptions about individuals because of (often fallacious) views about the whole group. We should be careful when reasoning about populations, lest we commit such harmful fallacies.

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Practice Problems 7.3

Identify the fallacy in each statement or exchange. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems7.3.pdf) to check your answers.

1. “Jim says that it is bad to invest in bonds right now. What does he know; he’s just a janitor!” a. appeal to force b. ad hominem c. appeal to popular opinion d. equivocation e. no fallacy

2. Student #1: “Animals are on the earth for humans to eat.” Student #2: “How do you know that?” Student #1: “Because they provide nourishment for us.”

a. biased sample

Logic in Action: Fallacies in the Coffeehouse

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b. inadequate authority c. equivocation d. begging the question e. no fallacy

3. Politician: “The best way to create equity in society is to tax the rich more and redistribute wealth to those who have less.” Moderator: “And how do you plan on implementing these tax changes in Congress?” Politician: “If we don’t �igure out how to do this, then more and more children will feel the pain of hunger at night.”

a. appeal to tradition b. poisoning the well c. red herring d. false dilemma e. no fallacy

4. “If we legalize gay marriage, the whole world will decay morally.” a. appeal to emotion b. appeal to ignorance c. slippery slope d. false cause e. no fallacy

5. “You know communism was going to fail! After all, Karl Marx was an alcoholic!” a. slippery slope b. ad hominem c. false cause d. false dilemma e. no fallacy

6. “You think that Stanford is better only because you went there.” a. appeal to popularity b. appeal to ignorance c. hasty generalization d. ad hominem e. no fallacy

7. “Look at this picture of an aborted fetus. How can you support abortion?!!” a. false cause b. appeal to emotion c. appeal to popular opinion d. appeal to force e. no fallacy

8. “Everyone likes Friends, so it must be a good show.” a. non sequitur b. ad hominem c. appeal to popular opinion d. appeal to inadequate authority e. no fallacy

9. “I strongly oppose the opposition’s view that we shouldn’t care about our children’s education.” a. straw man b. begging the question c. red herring d. appeal to tradition

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e. no fallacy

10. “You have the right to make money, so making money is right.” a. appeal to emotion b. appeal to ignorance c. slippery slope d. equivocation e. no fallacy

11. “Houses in the United States with storm cellars are more often hit by tornadoes, so you shouldn’t get a storm cellar.”

a. false cause b. equivocation c. appeal to ignorance d. appeal to ridicule e. no fallacy

12. “I am opposed to abortion because Jim is pro-choice, and he’s an idiot!” a. ad hominem b. poisoning the well c. shifting the burden of proof d. false dilemma e. no fallacy

13. “If I give this homeless person a dollar then I’ll have to give the next guy a dollar and so forth. . . . I’ll end up broke!”

a. ad hominem b. slippery slope c. shifting the burden of proof d. false dilemma e. no fallacy

14. “You oppose her policies only because you lost the election to her.” a. appeal to popular opinion b. appeal to ignorance c. hasty generalization d. ad hominem e. no fallacy

15. “I am pro-choice because I don’t think that women should have no rights in our society.” a. appeal to force b. ad hominem c. straw man d. appeal to ridicule e. no fallacy

16. “We should have prescription drug care. Would you want your grandma to suffer?” a. appeal to emotion b. hasty generalization c. red herring d. appeal to popular opinion e. no fallacy

17. “There is no solid scienti�ic evidence for the existence of spirits, so they don’t exist.” a. appeal to inadequate authority b. appeal to force c. biased sample

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d. appeal to ignorance e. no fallacy

18. “Most Americans support this policy, so it must be right.” a. appeal to popularity b. slippery slope c. shifting the burden of proof d. false dilemma e. no fallacy

19. “I don’t think that we should bomb innocent people in order to steal their oil.” a. false cause b. hasty generalization c. straw man d. appeal to popular opinion e. no fallacy

20. “Timothy was 10 minutes late to the meeting this morning. I can tell he’s going to be a horrible employee.” a. shifting the burden of proof b. hasty generalization c. appeal to pity d. appeal to force e. no fallacy

21. “If I cheat on a curved test, I’ll get a better grade, so if we all cheat on the test, we will all get better grades.” a. slippery slope b. ad hominem c. post hoc d. fallacy of composition e. no fallacy

22. “I promised myself I would never lie again. That is why I have to tell this drunk angry man that the child who just escaped his basement is hiding behind the bush in my yard.”

a. burden of proof b. fallacy of accident c. red herring d. appeal to tradition e. no fallacy

23. Doctor: “It is ethically acceptable to test newly developed medications on homeless people who need money.” Nurse: “But doesn’t that exploit these people based on their need?” Doctor: “Prove to me that it is not acceptable.”

a. appeal to force b. appeal to inadequate authority c. straw man d. shifting the burden of proof e. no fallacy

24. “What? You believe that peace is actually possible in the Middle East? Ha! That’s the craziest thing I have ever heard.”

a. appeal to ridicule b. appeal to tradition c. poisoning the well d. appeal to popular opinion e. no fallacy

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25. “It’s not acceptable to harm another person. Since jail harms the freedoms of a person, we should release serial killers and rapists.”

a. begging the question b. false cause c. equivocation d. fallacy of accident e. no fallacy

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Summary and Resources

Chapter Summary There are many fallacies beyond those covered in this chapter. However, learning this sample of important and common logical fallacies will help sharpen one’s critical thinking skills so that one is less likely to become the victim (knowingly or otherwise) of logical tricks. However, when learning about fallacies it is also important to stay positive and to use the knowledge for good: to promote high-quality reasoning delivered in a sincere and respectful manner (for some ideas on how to stay positive, see Everyday Logic: Staying Positive in the Face of Fallacies).

It is a mark of a mature thinker to consider multiple points of view and come to conclusions only after thorough consideration of the best evidence and best reasoning available. We should never fall for these types of traps (often set by a lack of effort in carefully thinking through the evidence). Learning the fallacies helps one think critically and avoid erroneous reasoning—and can help us avoid falling for fallacies in the future.

Everyday Logic: Staying Positive in the Face of Fallacies

Learning about the fallacies should come with a warning: Once you learn to identify the fallacies, you may start to notice them everywhere. People commit them on TV, in newspapers, in books, and in face-to-face conversations all the time. Noticing the prevalence of these fallacies can be fascinating and eye-opening; however, it can also be dangerous. One of the risks of noticing fallacies is cynicism, in which one becomes overly skeptical of anything and everything. Becoming discouraged about the power of reason can even lead some to misology, the hatred of logic itself. Socrates himself warned about misology, stating that “no greater misfortune could happen to anyone than that of developing a dislike for argument” (Plato, 1961, p. 71). Some people hear so many fallacies that they begin to wonder if reason itself is ever to be trusted.

We need not come to that conclusion. One of the main reasons that we learn about fallacies is to learn not to commit them and to reason sincerely, honestly, and carefully. The chief purpose of the Moral of the Story feature boxes in this chapter is to focus on the positive message that we can learn from each fallacy, rather than just focusing on people’s mistakes. By reasoning with great care, we can constantly improve our abilities to develop trustworthy patterns of reasoning that can lead to the discovery of all kinds of truths of which we may never have previously been aware. In so doing, we can be more honest, intelligent, civil, and deep.

A second danger in noticing fallacies is becoming what Kevin deLaplante (2014), philosopher of science and founder of the Critical Thinking Academy, calls a “fallacy bully.” Some people learn about fallacies and then become exceptionally eager to point them out. However, pointing out someone’s fallacies is a bit like pointing out his or her grammatical mistakes; it can be considered annoying or rude.

American writer Max Shulman’s short story “Love Is a Fallacy,” in which the main character’s attempt to educate his love interest about fallacies back�ires, is one humorous illustration of a fallacy bully in action. (Numerous dramatic adaptations of Shulman’s story are available on YouTube, including one produced by George Argento, which takes place on a college campus: https://www.youtube.com/watch?v=7_81fz6kUJI (https://www.youtube.com/watch?v=7_81fz6kUJI) .) One ought to be quite judicious about when it is appropriate to point out other people’s fallacies.

Another problem is that fallacy bullies often overreach. It is important to remember that almost all of the argument forms de�ined in this chapter have legitimate uses. As noted, appeals to authority, slippery slope reasoning, and even ad hominem arguments can have legitimate applications as well as fallacious ones. Knowing when, whether, and to what degree a certain argument may fail to adequately demonstrate the truth of its conclusion requires a kind of wisdom over and above recognizing the general form of the argument.

We should make sure to have that kind of wisdom and even kindness in our hearts as we seek to understand and critique people’s reasoning. The result will be that we can share reasoning in ways that are positive, respectful, civil, and productive. Remember, logic is not a competition; our goal should not be to defeat others in debate. If our

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goal is not so much to be right but to �ind truth, then we can see others, even those with whom we may disagree, as being on the same team.

Critical Thinking Questions 1. Think of a time that someone used an ad hominem argument against you or you used an ad hominem argument

against someone else. What was the topic you were discussing, and what would have been a better way to present the argument or disagree?

2. Now that you have studied the fallacies, think about how these fallacies are used in the media and advertisements. What are some examples of the use of fallacies in these areas, and how do they function to in�luence people?

3. Understanding the informal fallacies is a great way to protect oneself against manipulation. How do you plan on honing your skills in fallacy identi�ication as you move forward in your career and social life?

4. Often it is easier to use fallacies than it is to present well-reasoned positions to support your ideas and claims. Is there ever a time in which it is acceptable to use fallacious reasoning to get people to do what you want? Why is this ethically permissible?

Connecting the Dots Chapter 7

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Web Resources https://owl.english.purdue.edu/owl/resource/659/03 (https://owl.english.purdue.edu/owl/resource/659/03) Purdue’s Online Writing Lab (OWL) provides a list of fallacies, with slightly different terminology than ours (which is common), but it gives nice and clear de�initions of fallacies with examples.

http://www.nizkor.org/features/fallacies (http://www.nizkor.org/features/fallacies) The Nizkor Project, which is dedicated to education about the Holocaust, also provides a thorough list of fallacies with de�initions, examples, and explanations.

http://www.csun.edu/~dgw61315/fallacies.html (http://www.csun.edu/~dgw61315/fallacies.html) California State University Northridge’s debate team explains a number of fallacies and includes their Latin names.

Key Terms

ad hominem The fallacy of rejecting or dismissing a person’s reasoning on the basis of some irrelevant fact about him or her.

appeal to emotion A fallacy in which someone argues for a point based on emotion rather than on reason.

appeal to fear One speci�ic type of appeal to emotion that tries to get someone to agree with something out of fear rather than a rational assessment of the evidence.

appeal to force One speci�ic type of appeal to emotion that tries to get people to accept a conclusion by threatening them with negative consequences speci�ically for not accepting the conclusion.

appeal to ignorance The argument either that a claim must be false because it has not been demonstrated to be true or that a claim must be true because it has not been proved to be false.

appeal to inadequate authority A fallacy that reasons that something is true because someone said so, even though that person is, for one reason or another, not a reliable source on that topic.

appeal to pity One speci�ic type of appeal to emotion that tries to get someone to change his or her position only because of the unfortunate situation of an individual affected.

appeal to popular opinion A fallacy in which one—knowingly or not—accepts a point of view because that is what most other people think; also known as appeal to popularity, bandwagon fallacy, or mob appeal.

appeal to ridicule A fallacy that seeks to make fun of another person’s view rather than actually refute it.

appeal to tradition A fallacy that argues for a conclusion based on the claim that it is what people have always done or believed.

begging the question A fallacy in which one gives an argument that assumes a major point at issue; also known as petitio principii.

biased sample A sample that is not representative of the whole population, perhaps due to some tendency within the method of sampling to favor some results over others.

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cherry picking An inductive generalization that emphasizes evidence for a claim while ignoring the evidence against the claim, or vice versa.

circular reasoning A fallacy in which the premise is the same as, or is synonymous with, the conclusion.

equivocation A fallacy that switches the meaning of a key term so that the argument seems valid when it actually is not.

fallacies Common patterns of reasoning that have a high likelihood of leading to false conclusions.

fallacy of accident A fallacy that applies a general rule in cases in which the rule is not properly applied.

fallacy of composition A fallacy that infers that a whole group has a certain property because each member of it does.

fallacy of division A fallacy that infers that the members of a group must have a certain property because the whole group does.

false cause A fallacy that assumes something was caused by another thing just because it came after it; also known as post hoc ergo propter hoc.

false dilemma A fallacy that makes it sound as though there are only a certain number of options when in fact there are more than just those options; also known as false dichotomy.

hasty generalization An inductive generalization in which the sample size is too small to adequately support the conclusion.

non sequitur A fallacy in which the premises have little bearing on the truth of the conclusion.

poisoning the well A fallacy in which someone attempts to discredit someone’s credibility ahead of time, so that all those who listen to that person will automatically reject whatever he or she says.

red herring A fallacy in which a deliberate distraction is used in an attempt to veer the listener away from the real question at hand.

shifting the burden of proof A fallacy in which the reasoner has the burden to demonstrate the truth of his or her own side, but instead of meeting that burden simply points out the failure of the other side to prove its own position.

slippery slope A fallacy that argues that we should not do something because if we do, then it will lead to a series of events that will end in a terrible conclusion, when this chain of events is not likely at all.

straw man A fallacy in which one attempts to refute a very weak or inaccurate version of the other side’s position.

tu quoque A version of the ad hominem fallacy that argues that someone’s claim is not to be listened to if he or she does not live up to the truth of that claim.

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y j g g person’s reasoning on the basis of some

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Learning Objectives

After reading this chapter, you should be able to:

1. Identify common sources of bias in reasoning.

2. Explain common rhetorical devices that may interfere with good reasoning.

3. Describe the importance of evaluating mediated information.

4. Identify and demonstrate techniques for evaluating sources.

Critical thinking requires constant attention to ways in which our opinions might be swayed by reasons that do not correspond to the truth of a claim. This chapter will look at some common traps that endanger critical thinking. We will start by looking at tendencies within ourselves that can lead us astray: biases and stereotyping. Then we will examine ways in which information can be made to appear more plausible than it really is. Finally, we will focus on evaluating a

8Persuasion and Rhetoric

James Steidle/SuperStock

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source of information. Even when we are able to overcome our own biases and the effects of deceptive and manipulative tactics, it is important to recognize whether an information source is reliable and trustworthy before accepting its authority.

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Martha Campbell/Cartoonstock

Some stereotypes, like doctors having poor penmanship, are relatively harmless and frequently joked about. Think of the stereotypes like this one that you encounter each day.

8.1 Obstacles to Critical Thinking: The Self

In order to improve our ability to think critically and logically, we must �irst be aware that we ourselves are already highly prone to thinking uncritically and irrationally. Some of the reasons for this come from outside of us. Part of thinking well is the ability to focus on the actual claim being made and the reasons being put forth to support that claim. However, this is often dif�icult because so many other things might be going on, such as watching a TV commercial, listening to a political candidate, or talking with a friend, coworker, or boss. However, sometimes our tendency to be uncritical comes from our own beliefs—which we often accept without question—as well as inherent biases, or prejudices. For example, we might be affected by the status or other features of the person advancing the argument: Perhaps a claim made by your boss will be regarded as true, whereas the same claim made by a coworker might be subject to more critical scrutiny. Our positive biases lure us into favoring the views of certain people, whereas our negative biases often cause us to reject the views of others. Unfortunately, these responses are often automatic and unconscious but nevertheless leave us vulnerable to manipulation and deceit. Some people have been known to win arguments simply because they speak more loudly or assert their position with more force than their opponents. It is thus important to learn to recognize any such biases. This section will examine what are known as stereotypes and cognitive biases.

Stereotypes

A stereotype is a judgment about a person or thing based solely on the person or thing being a member of a group or of a certain type. Everybody stereotypes at times. Think about a time when you may have been judged—or in which you may have judged someone else— based only on gender, race, class, religion, language (including accent), clothes, height, weight, hair color, or some other attribute. Generalizations based on a person’s attributes often become the basis of stereotypes. Examples include the stereotypes that men are more violent than women, blonds are not smart, tall people are more popular, or fat people are lazy. (See A Closer Look: A Common Stereotype for another example.) Note that stereotypes can be positive or negative, harmless or harmful. Some stereotypes form the basis for jokes; others are used to justify oppression, abuse, or mistreatment. Even if a stereotype is not used explicitly to harm others, it is better to avoid drawing conclusions in this way, particularly if the evidence that supports such characterizations is partial, incomplete, or in some other way inadequate.

If you are thinking to yourself that you are already sensitive to the negative effects of stereotyping and thus guard your speech and actions carefully, you may want to think again. The fact is that we all accept certain stereotypes without even noticing. Our culture, upbringing, past experiences, and a myriad of other in�luences shape certain biases in our belief systems; these become so entrenched that we do not stop to question them. It is quite shocking to realize that we can be prone to prejudice. After all, most of us do not use stereotypes consciously—for example, we do not always think such things as “that person is of ethnicity X, so she must really like Y.” This is why stereotyping is both common and dif�icult to guard against. One of the advantages of logical reasoning is that it helps us develop the habits of thinking before acting and of questioning beliefs before accepting them. Is the conclusion I am drawing about this person justi�ied? Is there good evidence? How speci�ic is my characterization of this person? Is that characterization fair? Would I approve of someone drawing conclusions about me on the same amount of evidence? These are questions we should ask ourselves whenever we make a judgment about someone.

It can be even more dif�icult to avoid using stereotypes when some of these generalizations turn out to be accurate or have some

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As an experiment described in this video demonstrates, preexisting beliefs can distort logical reasoning. People are much more skeptical about information they do not want to believe than information they do. A challenge, however logical, only entrenches people in their own position.

How Preexisting Beliefs Distort Logical Reasoning

Critical Thinking Questions

1. Why do you believe that people cling more tightly to their beliefs when those beliefs are challenged?

2. Why are people more skeptical of information when they do not want to believe that the information is true? How does a critical thinker analyze information in relation to what he or she desires to be true?

support. For instance, it is rare to �ind an overweight marathon runner, a tall jockey, or a short basketball player. Thus, one might hear that a person is a professional jockey and reasonably conclude that this person is very short; after all, the conditions of the job tend to rule out tall individuals. But, of course, it is not impossible that there may well be a jockey who is 5’10” (Richard Hughes), or a 430-pound marathon runner (Kelly Gneiting), or a 5’3” NBA player (Muggsy Bogues). Stereotypes allow us to make quick judgments on little evidence, which can be important when our safety is involved and we have no way of getting information quickly. Although there may well be situations in which we have to make some generalizations, we need to be prepared to abandon such generalizations if good evidence to the contrary emerges.

Regardless, although stereotypes may be useful in some circumstances, in most cases they lead to hasty generalizations or harmful and misguided judgments. The reason for this is that stereotypes are founded on limited information. Accordingly, stereotypes are frequently based on extremely weak inductive arguments or on fallacies such as hasty generalization.

A Closer Look: A Common Stereotype

One damaging yet common stereotype is that women are not good (or not as good as men, at least) at mathematics. This stereotype can become a self-ful�illing prophecy: If young girls hear this stereotype often enough, they may begin to think that it is true and, in response, take fewer and less dif�icult math classes. This results in fewer women in math-related careers, which in turn fuels the stereotype further. Similarly, if a teacher is convinced that such a stereotype is true, he or she may be less likely to encourage female students to take more math courses, again leading to underrepresentation in the �ield. This stereotype may have prevented many women from being as successful at mathematics as they might have been otherwise.

This trend is not exclusive to mathematics. Numerous studies show that women are underrepresented in science and engineering as well, with fewer women receiving doctorates in those �ields. Furthermore, there are disparities in the science and engineering �ields between men and women in their pay, applying for grants, the size of the grants applied for, success in receiving funding, and being named in patents. The consistency of these results in both the United States and Europe and the number of studies that have come to the same conclusions suggest that

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there may be systematic bias at play, leading to fewer women being attracted to science and engineering careers and lower rewards for those who do enter those careers. For more details on these results, see http://genderedinnovations.stanford.edu/institutions /disparities.html (http://genderedinnovations.stanford.edu/institutions/disparities.html) .

Additional Discussion

http://womenshistory.about.com/od/sciencemath1/tp/aatpmathwomen.htm (http://womenshistory.about.com/od/sciencemath1/tp/aatpmathwomen.htm) For a brief list and discussion of accomplished women mathematicians, peruse this About .com article by women’s history expert Jone Johnson Lewis.

http://www.agnesscott.edu/lriddle/women/alpha.htm (http://www.agnesscott.edu/lriddle/women/alpha.htm) Women’s liberal arts college Agnes Scott offers an alphabetical list and discussion of accomplished women mathematicians.

Cognitive Biases

Errors in critical thinking can also stem from certain misperceptions of reality—what psychologists, economists, and others call cognitive biases, thus distinguishing them from the more harmful kind of prejudicial and bigoted judgments to which stereotypes can lead. A cognitive bias is a psychological tendency to �ilter information through our own subjective beliefs, preferences, or aversions, a tendency that may lead us to accept poor reasoning. Biases are related to the fallacies we discussed in Chapter 7. But whereas a fallacy is an error in an argument, a bias is a general tendency that people have. Biases may lead us to commit fallacies, but they also color our perception of evidence in broader ways. By understanding our tendencies to accept poor reasoning, we can try to compensate for our biases.

Let us begin by considering a simple example that shows one kind of cognitive bias that can prevent us from drawing a correct conclusion. Imagine you have �lipped a fair coin 10 times, and each time it has come up heads. The odds of 10 consecutive heads occurring are 1 in 1,024—not very good. What do you think the odds are of the 11th coin �lip in this sequence being heads again? Does it seem to you that after 10 heads in a row, the odds are much better that the 11th coin toss will turn up tails?

Reasoning that past random events (the �irst 10 coin tosses, in our example) will affect a future random event (the 11th coin toss) is known as the gambler’s fallacy. We are prone to accepting the gambler’s fallacy because we have a cognitive bias. We expect the odds to work out over the long run, so we think that events that lead to them working out are more likely than events that do not. We expect that over time the number of heads and tails will be approximately equal. This expectation is the bias that frequently leads to the gambler’s fallacy. So, many people reason that since 10 tosses have come up heads, the odds of it happening an 11th time are very small. But, of course, the odds of any individual coin toss coming up heads are 1 in 2.

Many people have lost quite a lot of money by committing the gambler’s fallacy—by overlooking this cognitive bias in their reasoning—and many people have, naturally, pro�ited from others making this mistake. Often the mistake is to think that an unusually long string of unlikely outcomes is more likely to be followed by similar outcomes—that lucky outcomes come in groups or “lucky streaks.” If you are gambling, whether with dice, coins, or a roulette wheel, the odds are the same for any individual play. To convince yourself that a roulette wheel is “hot” or that someone is on a “streak” is to succumb to this cognitive bias and can lead not just to mistakes in reasoning but also the loss of a lot of money.

Biased thinking leads to some of the same errors as stereotypical thinking—including arriving at the wrong conclusion by misinterpreting the assumptions that lead to the support for that conclusion. Unlike stereotypical thinking, however, biased thinking often involves common, broad tendencies that are dif�icult to avoid, even when we are aware of them. (See A Closer Look: Economic Choice: Rational Expectations Versus Cognitive Bias for an example.) Researchers have identi�ied many cognitive biases, and more are identi�ied every year. It would be impossible to compile a comprehensive list of all the ways in which our perceptions and judgments may be biased. From the standpoint of critical thinking, it is

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more important to be aware that we always face bias; hence, we should have a healthy dose of skepticism when considering even our own points of view. By examining a handful of biases—con�irmation bias, probability neglect, selection bias, status quo bias, and the bandwagon effect—we can be more aware of the biases we all are prone to and begin to work on compensating for them in our thinking.

A Closer Look: Economic Choice: Rational Expectations Versus Cognitive Bias

Psychologist and Nobel laureate Daniel Kahneman has dedicated his research to examining how people arrive at decisions under conditions of uncertainty. Mainstream economists generally believe that people can set aside their biases and correctly estimate the probabilities of various outcomes. This is known as rational expectations theory: People are able to use reason to make correct predictions.

Kahneman, however, discovered that this is not true. His classic article “Judgments of and by Representativeness,” written with his longtime research partner Amos Tversky and republished in the 1982 book Judgments Under Uncertainty, describes a number of cognitive biases that show a systematic departure from rational behavior. The �indings by Kahneman and Tversky are supported by data gathered from surveys that contained questions such as the following:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice and participated in antinuclear demonstrations. Which two of the following �ive alternatives are more probable?

1. Linda is a bank teller. 2. Linda wears glasses. 3. Linda enjoys skiing. 4. Linda is a bank teller and active in the feminist movement. 5. Linda runs a local bookstore.

How would you answer this question? How do you think most survey respondents answered this question? Rank these �ive claims in order of probability and then turn to the end of the chapter for the answer to the problem.

Kahneman found that most respondents ranked these incorrectly. If people are not able to make correct predictions about probability, then one of the assumptions of rational expectations theory is wrong. This in turn can lead to an inaccurate economic predictions. For example, the price we are willing to pay for a product is partially based on how long we think the product is likely to last. We are willing to pay more for a product that we think will last longer than for one we think will not last as long. If we cannot accurately estimate probabilities, then our purchasing decisions may be less rational than economic theory supposes they are.

Probability Neglect Probability neglect is, in a certain way, the reverse of gambler’s fallacy. With probability neglect, people simply ignore the actual statistical probabilities of an event and treat each event as equally likely. Thus, someone might argue that wearing a seat belt is not a good idea, because someone was once trapped in a burning car by a seat belt. Such a person might go on to say that since a seat belt can save your life or result in your death, there is no reason to wear one. This person is ignoring the fact that the probability of a seat belt saving one’s life is much higher than the probability of the seat belt causing one’s death.

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Although the probability of one’s home being destroyed by a natural disaster is relatively low, many people choose to ignore the statistical probability and pay monthly insurance premiums to protect themselves.

In the seat belt case, the probability of an unlikely event is overemphasized. But in many cases it is also possible to underestimate the odds of an unlikely event occurring. We may think such an event is miraculous, when in fact a simpler explanation is available. When there are many opportunities for an unlikely event to occur, the odds can actually be in favor of it occurring sometimes. The lottery provides a good illustration here. The odds of winning a lottery are extremely small, about 1 in 175 million for Powerball (Missouri Lottery, 2014). Accordingly, we often advise our loved ones to avoid being lured by the potential of a big win in light of such odds. Yet it is precisely this extremely small chance, combined with the huge number of tickets sold, that there is a decent chance that somebody will win. So it is no miracle when someone wins.

Or suppose that you happen to be thinking about a friend and feel a sudden concern for her welfare. Later you learn that just as you were worrying about your friend, she was going through a terrible time. Does this demonstrate a psychic connection between you and your friend? What are the chances that your worry was not connected to your friend’s distress? If we consider how many times people worry about friends and how many times people go through dif�iculties, then we can more easily see that the chances are high that we will think about friends while they are having dif�iculties. In other words, we overlook the high probability that our thinking about our loved ones will coincide with their experiencing problems. It would actually be more surprising if it never happened. No psychic connection is needed to explain this.

Moral of the Story: Gambler’s Fallacy and Probability Neglect

When your reasoning depends on how likely something is, be extra careful. It is very easy to hugely overestimate or underestimate how likely something is.

Con�irmation Bias People tend to look for information that con�irms what they already believe—or alternatively, dismiss or discount information that con�licts with what they already believe. As noted in Chapter 5, this is called con�irmation bias. For example, consider the case of a journalist who personally opposes the death penalty and, in writing an article about the effectiveness of the death penalty, interviews more people who oppose it than who favor it. Another example, which is also discussed in Chapter 5, is our own tendency to turn to friends—people likely to share our worldview—to validate our values and opinions.

The easy access to information on the Internet has made con�irmation bias both worse and yet easier to overcome. On the downside, it has become increasingly easy to �ind news sources with which we agree. No matter where you stand on an issue, it is easy to �ind a news outlet that agrees with you or a forum of like-minded people. Since we all tend to feel more comfortable around like-minded people, we tend to overemphasize the importance and quality of information we get from such places.

On the upside, it has also become easier to �ind information sources that disagree with our views. Overcoming con�irmation bias requires looking at both sides of an issue fairly and equally. That does not mean looking at the different sides as having equal justi�ication. Rather, it means making sure that you know the arguments on both sides of an issue and that you apply the same level of logical analysis to each. If we take the time and energy to explore sources that disagree with our position, we will better understand what issues are at stake and what the limitations of our own position may be. Even if we do not change our mind, we will at least know where to strengthen our argument and be equipped to anticipate contrary arguments. In this way our viewpoint becomes the result of solid reasoning rather than just something we believe because we do not know the arguments against it. The philosopher John Stuart Mill (1869/2011) had this to say:

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He who knows only his own side of the case, knows little of that. His reasons may be good, and no one may have been able to refute them. But if he is equally unable to refute the reasons on the opposite side; if he does not so much as know what they are, he has no ground for preferring either opinion. (p. 67)

Overcoming con�irmation bias may require actually being a little harsher—or so it might seem—on your own side of an issue than on the opposing side. Since we all have a natural tendency to accept arguments with whose conclusion we agree and reject those with whose conclusions we disagree, a truly fair analysis may seem like we are being harder on our own side than the other. Conversely, we need to be extra careful not to misrepresent the arguments with which we disagree. (This would be committing the straw man fallacy discussed in Chapter 7.) As you learn more about logic and critical thinking and practice the techniques and principles you are learning, you will be in a better position to be sure that you are treating both sides equally.

Moral of the Story: Con�irmation Bias

Always remember that you are more likely to accept arguments with conclusions you already believe and that you are likely to overestimate just how common your own beliefs are. Take time to study both sides of an issue before coming to a conclusion, and try to be a little extra critical of arguments on your own side.

Selection Bias Selection bias is introduced by not having a representative sampling of the group being studied. If the group is not chosen correctly, the results may be skewed by the sample being biased. For instance, if one surveyed women’s attitudes toward work and questioned only women in well-paid managerial jobs, many other women—who might not be as satis�ied with their salaries or work conditions—would not be represented.

Earlier in the section, we discussed how con�irmation bias is evident when we justify our views by relying only on people or sources with similar views. This is also an example of selection bias. As noted in Chapter 5, it is unlikely that your circle of friends is re�lective of the broader population; their opinions would not represent the opinions of all, or even most. If many people around you accept your opinions, you may even think that your opinions do not need much support and that they are more widespread than they actually are. Just as with con�irmation bias, overcoming selection bias would mean ensuring you considered the opinions of a range of people, including those who disagree with you.

Although con�irmation bias can be seen as a form of selection bias, selection bias is broader. For example, Londa Schiebinger (2003) discusses the fact that women have been underrepresented in medical research and considers some possible ways of improving the situation. Because this underrepresentation affects the representativeness of samples we see and is not simply a preference for samples with which we agree, it is a case of selection bias rather than con�irmation bias. We all prefer to do things in the easiest way possible. In general it is easier to reason from whatever samples are handiest rather than go to the extra effort to ensure that our samples are representative or that our evidence comes from the broadest scope of sources possible. When we simply gather our sample from whatever is convenient, we are falling prey to selection bias.

Status Quo Bias Status quo bias is the tendency to prefer that things remain as they are or have been recently rather than changing them. It may be exhibited when an individual argues that something is �ine just as it is, based on the observation that it has always been a certain way without observable problems. For example, some have argued that saying the Pledge of Allegiance should remain a school tradition, since reciting it has not caused problems in the past. Although the Pledge of Allegiance remains a controversial and undecided issue in some circles, one can see how status quo bias can be problematic when it is

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The status quo bias can be seen in the way some people vote. They may only vote for candidates from one party, despite quali�ications, because of their preference for things to remain the same.

used to rationalize the oppression of others. For example, in 1900, a (male) voter in the United States might have said, “Women never voted before, and we did just �ine”—would it follow, then, that women should not be allowed to vote?

As you may have guessed, the status quo bias is closely connected the appeal to tradition fallacy. Someone who commits that fallacy may do so because of a bias toward the status quo. But this bias also affects how we view the world more broadly. We have a strong tendency to simply accept the way things are without questioning them, simply because that way is familiar to us. Our days are �illed with routine and ordinary practices that we continue not because we have compared them to other ways of doing things, but simply because that is how we have been doing them. One need not make an argument in order to exhibit a status quo bias. A status quo bias is often increased by selection and con�irmation biases. We think that a policy has not created problems in the past because we have not heard of any problems. Even if we do hear of a problem, our tendency will often be to dismiss it as unimportant. Biases often work together to create a greater effect than they would individually.

The Bandwagon Effect The bandwagon effect (also referred to as “herd mentality” or “groupthink”) is our tendency to go along with what we see others doing and believing. This is commonly seen with investment trends and real estate “bubbles”—often with disastrous results. A video on YouTube may become widely seen just because a lot of people have seen it; others reason that it must be good if it has been seen by so many people. This is not a logical argument, any more than a book’s status alone as a best seller signi�ies anything about its quality; it simply has sold a lot of copies. Yet when a belief is widely held, we have a strong tendency to think that it must have something going for it. However, when we stop to think about it, we can see that this is not always the case. Few of us would think that the fact that many people were in favor of slavery is any indication at all that slavery is a good thing. Nonetheless, we often take beliefs to be obvious simply because they are widespread.

At the same time, it is important to point out that the bandwagon effect is not always problematic. For example, if people �lock to restaurant A while restaurant B remains largely empty, then it is reasonable to think that restaurant B is not attractive to most people. We can then choose to �ind out why for ourselves or choose to try the most favored restaurant �irst. Likewise, we often rely on Internet reviews of vendors, products, physicians, hairstylists, and even churches in order to get an idea of people’s opinions. This does not mean that what most people like will be the same as what we will like, but it gives us a starting point of information. If we receive bad news from a physician, then it is reasonable to seek more opinions. If two out of three doctors recommend a particular treatment, then it would be foolish to completely ignore the majority opinion, although we would likely need to take additional factors into account in deciding the course of treatment. Problems arise when we give too much importance to popular or majority opinion rather than researching the issue ourselves.

An interesting recent case that illustrates both the prevalence and signi�icant effects of biases is the change in public opinion regarding same-sex marriage. From 1996 to 2014 public opinion shifted from only 27% of people approving of same sex marriage to 55% approval (Gallup, 2014). This is a large and rapid shift in opinion on a topic that touches on a central part of many people’s lives. The shift is especially notable because it does not seem to be the result of newly discovered evidence. A more likely explanation is that biases played a signi�icant role in the shift. Perhaps people in 1996 suffered heavily from a status quo bias, which would have led them to reject marriages that were not like what they were used to. Perhaps many people in 2014 suffered from the bandwagon effect, accepting same-sex marriages largely because they perceived people around them as being more accepting of them. Perhaps selection biases led people in 1996 to undervalue how the inability to marry affected same-sex couples and their children. As same-sex couples became more vocal and visible in society, this information would be more readily available to people, thus leading to a change in opinion. We do not know just why there has been such a shift in public opinion on this issue, but it seems likely that

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biases played a signi�icant role. (See Everyday Logic: Cognitive Biases in Our Own Lives for some thoughts on how to address pervasive cognitive biases.)

Everyday Logic: Cognitive Biases in Our Own Lives

If you were raised in the United States, it is likely that you believe it is one of the greatest countries on earth, perhaps even the greatest country. It is also likely that you are opposed to communism and think that it is evil and oppressive. Yet not all people who hold these beliefs have done the research necessary to support them. Think about the kind of arguments and research it would take to convince you of the opposite of what you now believe in these cases. If your belief is not based on that same kind and amount of evidence, then it is likely due, at least in part, to some form of bias.

We cannot eliminate every source of bias in every one of our beliefs. Neither can we take the time and energy necessary to fully and dispassionately justify every one of our beliefs. Whether it is worth doing so in a particular case depends on what is at stake. Believing that your country is the greatest has some positive bene�its: It makes your life more pleasant, builds community spirit, and gives you optimism for the future. In this sense it is not really a bad thing to believe, even if you cannot fully support it. The problem arises when such a belief becomes the basis for arguments about other issues. Suppose someone suggests a policy change and uses data from other countries to support it. If your response is that your country, the greatest country on earth, does not do things that way— and if that belief is based largely on bias, rather than evidence—then that bias may have a real and negative effect.

As mentioned, there are many more of these cognitive biases that have been the focus of a great deal of research by psychologists, political scientists, economists, and others who study the phenomenon of decision making. Here again, logic can play an important role in eliminating or at least decreasing the effects of cognitive biases by helping us to examine the claims, the arguments, and whether the support for the claims is provided in a solid, objective way. Logic is an extremely helpful tool to help us step back, take a deep breath, and see if the claims we have made—and the reasoning we have provided to support those claims—are justi�iable or are instead subject to the kinds of mistakes introduced by stereotypes and cognitive bias.

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We encounter a variety of claims each day. Our ability to critically examine these claims, many of which encourage us to purchase products, allows us to make decisions based on merit, not irrelevant claims.

8.2 Obstacles to Critical Thinking: Rhetorical Devices

Today we are bombarded by information, but 100 years ago, unless one lived in a big city, information was available from just a few sources: books and magazines and a local newspaper or two. With the development of cable TV, satellite radio, and of course, the Internet, there is very little dif�iculty �inding information on virtually any topic; indeed, some might say that there is so much information that we have trouble �inding the information we need and knowing that the information we do �ind is credible. Much of this information is accompanied by advertising; one may sign in to a social media website one day, click on an advertisement for a product, and discover that everywhere one goes on the Internet there are ads for similar products, as well as messages about such products showing up in one’s e-mail. All of these communications are designed to persuade us of something. A research article attempts to persuade us to accept its conclusion. An advertisement attempts to persuade us to buy a product. In both cases we are being asked to accept certain claims and to base our beliefs and behavior on those claims. We should exercise caution in deciding whether to do so.

The fundamental point to keep in mind here is that when we encounter a claim and wish to evaluate it, it is important to focus on the evidence, the reasons, and the argument that support this claim. As this section will discuss, however, there are a variety of ways to state the claim that may make it seem either more or less reasonable than it may be. These are all techniques that seek to prevent us from focusing on what we should be emphasizing—whether there are good reasons to accept or reject a claim. Instead, they encourage us to react emotionally or irrationally, often based on pleasant (or unpleasant) memories and associations, rather than evaluate the claim on its own merits. If someone can convince you to buy laundry soap simply because of the way it is described, then there is no need to worry about the actual quality of the laundry soap. In the same way, if someone wants to convince you to vote a certain way or adopt a particular viewpoint simply because of the way the candidate or viewpoint is described, there is no need to focus on the actual merits of the case. Hence, we need to be conscious of these methods, especially since they do not occur just in commercial and political contexts. When we have a conversation—and particularly a disagreement—with someone, how that other person employs language may also appeal to things that prevent us from focusing on reasons, evidence, and the actual argument. We also need to be aware of our own tendency to employ these techniques so that our own attempts at persuasion can remain focused on the merits of the case rather than on getting someone to accept our position on irrelevant grounds.

As discussed in Chapter 1, rhetoric is the study and art of effective persuasion. Although rhetoric typically includes some focus on logic as a persuasive technique, many effective

persuasive techniques have little to do with logic and critical thinking. Rhetoric employs techniques known as rhetorical devices, and this section lists some of the best known and most popular. It is important to note that rhetorical devices are not necessarily contrary to logic—rhetoric is the art of persuasion, not of irrationality or duplicity—but many of these techniques are used to get us to focus on something other than the quality of the reasons and arguments offered. There are many others, and new ones are always being developed; in marketing, for example, once discerning consumers become aware of one such technique, it may become ineffective. As long as we are aware that how language is used can have an enormous impact on how effective a message is, we will be better prepared when that language is used in an illegitimate way, persuading us to do or believe something when we should not be persuaded.

Weasel Words

Weasel words, or weaselers, are terms used to qualify a claim to make it easier to accept and more dif�icult to reject by introducing some degree of probability or “watering down” the claim without really changing its signi�icance. If someone were to say, “All philosophers are brilliant,” that would be fairly easy to disprove; you need only �ind a single philosopher who is not brilliant to do so. But if someone were to say, “Most philosophers are brilliant,” or “A lot of philosophers are brilliant,” or “Philosophers generally seem to be brilliant,” the claim is not as easy to disprove.

Weasel words such as probably, most, seems, in a sense, up to, and many others have this same effect—they make a claim sound better than it may actually be and make it more dif�icult to show that the claim is false. If a particular over-the- counter pain reliever promises to relieve pain for “up to 12 hours,” that claim is actually true even if it only works for 20

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minutes; “up to 12 hours” includes that 20 minutes. But the force of the claim tends to suggest that the relief will be for all 12 hours, until one looks more closely at what precisely is being claimed. It should not be surprising that such terms are frequently encountered in advertising. After all, would you be more likely to buy a toothpaste that “may prevent cavities” or one that “may or may not prevent cavities,” even though the two claims are really the same? Weasel words, used effectively, can make a person (or a company) sound as if an important claim is being put forth. However, on closer inspection, we may �ind that the claim is weak because of the use of a weaseler.

On the other hand, you should not dismiss a claim simply because it contains words that could be used as weaselers. There are legitimate uses of such terms. Chapter 9 will discuss the use of quali�iers (sometimes known as guarding terms) that are legitimately used to make claims more accurate. Quali�iers like sometimes, usually, and possibly weaken claims so that they are more likely to be true. We generally call such terms “weasel words” only when they are being used in ways that are sneaky or deceptive.

Scienti�ic studies often employ what may appear as weasel words when describing their results, yet they frequently use them in a legitimate way. For example, a medical report may note that a certain substance may cause cancer in some populations. However, such a report is likely just being cautious (though accurate). When determining whether a claim uses weaselers in a manipulative sense, it is important to examine the claim and its justi�ication to determine whether the guarding terms are being used in a way that is legitimate or deceptive.

Euphemisms and Dysphemisms

Euphemisms and dysphemisms are both common ways of providing “spin” to information—that is, presenting the information in either a positive or negative light, respectively.

A euphemism is a term that makes something sound more positive than it might be otherwise. We are all familiar with some of these, and many are standard expressions. We might say that a person has passed on, passed away, or gone to a better place, rather than just say the person died. The actual facts in the situation do not change, of course, but it may be easier to hear of a loved one’s death if a euphemism is used.

For someone getting bad news, euphemisms make perfect sense in order to deliver that news in as painless a way as possible. In other settings, however, a euphemism may be used not to be sensitive but to avoid describing a harsh reality. Politicians are particularly adept at employing euphemisms. Would a potential voter prefer to hear about higher taxes or about “revenue enhancement”? Either one may cost the taxpayer $500 over the next year, but politicians are well aware of the fact that voters do not like to hear about taxes going up. A euphemism can help take the sting out of that message. If you want someone to accept what you are saying, euphemisms can be very helpful by putting your message in a more positive context. It is also worth noting that some terms that might have once been considered euphemisms were eventually adopted as both more sensitive and more accurate terms. For example, terms such as differently abled and disabled may have started out as euphemisms but are now considered simply appropriate descriptions of those with physical or mental disabilities.

Dysphemisms are the opposite of euphemisms; these are descriptions used to put something in a more negative light. Often such words are used to shock, offend, drive home a point, or get someone’s attention. We can see how the use of a dysphemism might be used to help support a certain agenda. Imagine a politician discussing two groups of insurgents in different foreign countries. Both groups use violence, kidnapping, bank robbery, and other similar means to make their political points. But one group is friendly to the politician’s own views, so the politician refers to the group’s members as “freedom �ighters.” The members of the other group, whom the politician abhors, are described as “terrorists.” These two groups are doing the same kinds of things, but the use of a euphemism (“freedom �ighter”) makes one group look much different than the use of a dysphemism (“terrorist”). One might also consider some of the dysphemisms that are used to refer to lawyers. Who would you trust more, an “attorney at law” or an “ambulance chaser”?

Table 8.1 provides more examples of euphemisms and dysphemisms.

Table 8.1: Euphemisms versus dysphemisms

Euphemism Neutral word Dysphemism

Lady of the night Prostitute Hooker

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Can you identify the proof surrogate in this advertisement for cold medicine?

Euphemism Neutral word Dysphemism

Voluptuous Overweight Fat

Pre-owned car Used car Clunker

Estate tax Inheritance tax Death tax

Collectible Old Junk

Salvage depot Wrecked and loose parts merchant Junkyard

Moral of the Story: Euphemisms and Dysphemisms

Pay attention to how things are worded. A careful choice of wording can lead you to accept or reject a position when there really is not enough evidence to justify doing so.

Proof Surrogates

A proof surrogate is used to provide some degree of authority to a claim without actually offering any genuine support. Frequently, one will hear “studies show” that something is the case, even in everyday conversation. Without the actual studies, we are not really told any additional information, but the claim sounds stronger. Thus, if someone says, “People in Slovakia live longer because they eat a lot of yogurt,” you may or may not accept that claim at face value. You may, after all, not really know the life expectancy of those in Slovakia or their rate of yogurt consumption. But if, instead, someone were to say, “Studies show that people in Slovakia live longer because they eat a lot of yogurt,” somehow that claim sounds more authoritative. Of course, without providing the actual studies, the second claim is no different from the �irst, but this is a surprisingly powerful and effective technique. Even if it is true that there are studies backing the claim, without access to the studies, we really are in no position to assess the level of support they provide. We do not know whether the studies were well done, whether they are unduly biased, or whether their conclusions have been interpreted properly.

The trick in this case is not so much what is being claimed; rather, it is in not believing a claim simply because it is preceded by “experts agree,” “studies show,” or “most people say.” To challenge this kind of statement is straightforward. If one is suspicious, one can always ask, “What studies?” or “Which experts?” A person who asserts something based on such a proof surrogate and who cannot actually provide any support beyond an empty rhetorical reference to “experts” and “studies” will generally be quickly exposed as not having much information to back up his or her claim. When you hear a claim that sounds odd or unlikely to be true based on what you already know, you should be careful to follow up on any potential proof surrogates. Many hoaxes use proof surrogates to lend an air of credibility to their claims. As hoaxes become more sophisticated, it is always a good idea to check on claims that seem unlikely, outrageous, or otherwise suspicious.

Moral of the Story: Proof Surrogates

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Be prepared to provide sources whenever you advance an appeal to experts, studies, or popular opinion. If a claim seems odd or unlikely, check the sources; do not assume that what has been claimed is actually true or that the proof surrogates correspond to actual sources.

Hyperbole

Hyperbole is really just another term for exaggeration. Consider these typical uses of hyperbole: A student e-mails her teacher to say she is “deathly ill” when she may actually just have a bad cold. A teenager accuses his parents of being dictators when he is asked to clean his room. A grandfather tells stories of his youth that involve walking 15 miles to school every morning in 3 feet of snow. A teacher says, “If I have to grade one more paper, it’s going to kill me.” Such hyperboles often do not do any harm. After all, if someone tells you that Bill Gates has “more money than God,” it is unlikely that you take that to mean much more than Bill Gates having a great deal of money.

But in some contexts, particularly political contexts, hyperbole can be used to make a point sound more plausible than it might be otherwise, and to immediately accept such a claim can be risky. As always, one should look at the reasons, evidence, and argument in evaluating such a claim. For instance, someone arguing against gun control might insist that those who favor it “want to take away all of our guns.” This would be using hyperbole if those who advocate gun control do not want to do so. Similarly, someone claiming that those who advocate using coal for electricity “don’t care if children can breathe” is using hyperbole. Most advocates of coal-�ired electricity do, in fact, care if children can breathe. Even if you are not fooled into actually believing such claims, the use of hyperbole indeed fuels our feelings of outrage (see A Closer Look: Hyperbole and Godwin’s Law for a classic example). Since political speech is aimed at getting us to do something (for example, vote), this outrage may be enough to achieve those aims, even if we realize there is some hyperbole going on. As you may have guessed, hyperbole is often used in the straw man fallacy (see Chapter 7).

Hyperbole can sometimes be dif�icult to identify. After all, if one claims that Pablo Picasso is the greatest painter of the 20th century or that Michael Jordan is the greatest basketball player of all time, are those examples of hyperbole or defensible claims? In any case one cannot simply assert such propositions without being prepared to defend them with evidence and argument.

A Closer Look: Hyperbole and Godwin’s Law

In 1990 Michael Godwin, after observing many conversations on the Internet devolve into name-calling, looked a bit more closely at the speci�ics of how this occurred. He came up with the idea that “as an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one” (Godwin, 1994, para. 8). In other words, the longer a debate continues, the more likely a comparison will be made between one’s opponent and Hitler or the Nazis. This became known as “Godwin’s Law” and is a good example of hyperbole. Internet disagreements are certainly common enough, but it is unjusti�ied to compare an opponent to Hitler merely because you disagree.

When one compares someone to Hitler, it is often a case of the informal fallacy reductio ad Hitlerum, in which the mere fact that someone is in some way comparable to Hitler is used as a reason for thinking he is wrong or his claim is mistaken. In some circles it is taken as a rule that the �irst person to compare an opponent to Hitler (or the Nazis) loses the Internet debate (or in other versions, that the debate is effectively over). It is rare to see a comparison to Hitler that furthers a discussion; getting to that stage indicates that one really has nothing productive to add. Note that many of these conversations can quickly devolve into the use of fallacious slippery slope claims, since characterizing people, actions, or measures in such an exaggerated manner can easily result in more illogical comparisons.

Additional Discussion

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Visions of America/SuperStock

During Bill Clinton’s campaign for the presidency in 1992, the Bush campaign’s political director used a paralipsis when speaking about the future president. See if you can identify the paralipsis in the following quote: “The larger issue is that [Bill Clinton] is evasive and slick. We’ve never said to the press that he’s a philandering, pot- smoking draft dodger.”

http://www.wired.com/wired/archive/2.10/godwin.if_pr.html (http://www.wired.com/wired/archive/2.10/godwin.if_pr.html) Read Michael Godwin’s original account at Wired.com.

http://www.jewcy.com/arts-and-culture/i_seem_be_verb_18_years_godwins_law (http://www.jewcy.com/arts- and-culture/i_seem_be_verb_18_years_godwins_law) Read Michael Godwin’s re�lections 18 years later.

http://www.smbc-comics.com/index.php?db=comics&id=1335#comic (http://www.smbc- comics.com/index.php?db=comics&id=1335#comic) The comic Saturday Morning Breakfast Cereal illustrates a humorous example of reductio ad Hitlerum.

Innuendo and Paralipsis

Often a point can be made—particularly about one’s opponent in a debate or confrontation—without directly stating it. It can be implied by what is actually said, which is generally known as innuendo. Or it can be emphasized by noting how something is not said, which is a common-enough strategy but referred to with an uncommon word, paralipsis.

In �ilms, books, TV shows, and elsewhere, there are often salacious or off-color jokes made using innuendo. In Alfred Hitchcock’s �ilm To Catch a Thief, the lead couple goes on a picnic, and the woman (played by Grace Kelly) reaches into the picnic basket and asks the man (played by Cary Grant), “Do you want a leg or a breast?” This was relatively shocking in 1955, but since then it has become an acceptable sexual innuendo in popular culture.

Innuendos can also be used to make points that are less risqué. For instance, if a teacher tells a student that her paper is extremely well typed, that might be an innuendo suggesting that the paper is not particularly good. After all, if the best compliment a teacher can offer is about the appearance of the paper, that might imply that the content of the paper is mediocre. One roommate might observe about another that he seems to be “extremely up-to-date” on TV shows; that might, again, be an innuendo suggesting that he is watching too much TV and could be spending his time more productively. For that matter, a simple gesture, such as looking at your watch (or looking at your wrist even if there is no watch there) can suggest, without saying anything, that time is being wasted or that a person is late. These are all pretty familiar. We simply need to be aware of situations in which a claim is implied by innuendo. If such a claim is being suggested and we wish to challenge it, then we need to look beyond the implications and instead at what explicit support exists.

Paralipsis is a technique that one can use to emphasize something by indicating that it will not be mentioned. This is frequently seen in political campaigns, in which a candidate might say, “I would never discuss my opponent’s frequent indiscretions and scandals.” By saying this, of course, the audience hears about both the indiscretions and the scandals, but the politician can respond that he or she never mentioned them. Frequently, this technique is introduced by such

phrases as, “It goes without saying,” “I need not mention,” or “I need not remind you,” after which what goes without saying is said, what does not need mentioning is mentioned, and one is immediately reminded of precisely that of which one does not need to be reminded. In this way some characteristic or feature of one’s opponent—often negative—is introduced without having to state it directly.

One of the most famous uses of innuendo and paralipsis in literature is Mark Antony’s speech in Shakespeare’s Julius Caesar, in which Antony eulogizes his assassinated friend and ruler. Antony is allowed to make his speech after promising

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Marcus Brutus, one of the conspirators against Caesar, that he will not speak ill of the conspirators in his speech. Antony’s speech thus begins by appearing to justify the actions of Brutus and the other conspirators. In the course of his speech, however, Antony uses various rhetorical techniques to paint Caesar in such a positive light that he succeeds in convincing his Roman audience to feel rage against the conspirators and to support him, rather than Brutus, as Caesar’s successor.

While reading this speech, see if you can �ind some of the rhetorical techniques we have examined here; in particular, Antony’s use of innuendo and paralipsis. Why do you think these techniques might be effective on Antony’s audience?

Friends, Romans, countrymen, lend me your ears; I come to bury Caesar, not to praise him. The evil that men do lives after them; The good is oft interred with their bones; So let it be with Caesar. The noble Brutus Hath told you Caesar was ambitious: If it were so, it was a grievous fault, And grievously hath Caesar answer’d it. Here, under leave of Brutus and the rest— For Brutus is an honourable man; So are they all, all honourable men— Come I to speak in Caesar’s funeral. He was my friend, faithful and just to me: But Brutus says he was ambitious; And Brutus is an honourable man. He hath brought many captives home to Rome Whose ransoms did the general coffers �ill: Did this in Caesar seem ambitious? When that the poor have cried, Caesar hath wept: Ambition should be made of sterner stuff: Yet Brutus says he was ambitious; And Brutus is an honourable man. You all did see that on the Lupercal I thrice presented him a kingly crown, Which he did thrice refuse: was this ambition? Yet Brutus says he was ambitious; And, sure, he is an honourable man. I speak not to disprove what Brutus spoke, But here I am to speak what I do know. You all did love him once, not without cause: What cause withholds you then, to mourn for him? O judgment! thou art �led to brutish beasts, And men have lost their reason. Bear with me; My heart is in the cof�in there with Caesar, And I must pause till it come back to me. (Shakespeare, 1599, 3.2.1617–1651)

Moral of the Story: Innuendo and Paralipsis

Implying something rather than stating it clearly can soften the presentation of a claim. However, it can also be used to make a claim seem more plausible than it really is. Try to set out the claims clearly before accepting them.

Practice Problems 8.1

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What rhetorical device is used in each of the following? Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems8.1.pdf) to check your answers.

1. “You should buy this product. Studies have shown that it works!” a. euphemism b. proof surrogate c. hyperbole d. innuendo e. none of the above

2. “At least this brand of pizza won’t cause you to get food poisoning.” a. innuendo b. euphemism c. weaseler d. proof surrogate e. none of the above

3. “This product is unlikely to cause you to get cancer.” a. hyperbole b. weaseler c. dysphemism d. euphemism e. none of the above

4. A pundit says of a political candidate: “I’m not going to suggest that he’s a felon.” a. euphemism b. hyperbole c. paralipsis d. proof surrogate e. none of the above

5. Which of the following rhetorical terms describes misleading by pretended omission? a. paralipsis b. euphemism c. innuendo d. hyperbole e. none of the above

6. Which of the following is a dysphemism? a. “He is a windbag.” b. “He is a brilliant speaker.” c. “He sure can talk.” d. “He expresses his opinions often.” e. none of the above

7. Which of the following is a weaseler? a. “Trust me; bungee jumping is safe.” b. “People don’t usually die while bungee jumping, so it should be OK.” c. “Bungee jumping is terri�ic.” d. “Don’t listen to anyone who says you shouldn’t bungee jump.” e. none of the above

8. Which of the following is a proof surrogate? a. “Mark is too nice to be the one who stole the cookie.” b. “Trust me; Mark would not have stolen the cookie.”

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c. “Shut up about Mark stealing the cookie!” d. “If Mark stole the cookie then he is evil.” e. none of the above

9. Which of the following is a hyperbole? a. “Studies show that this product is the best.” b. “This product is the greatest thing ever.” c. “Trust me; this is a great product.” d. “This product is usually effective.” e. none of the above

10. Name all of the rhetorical devices in the following passage.

“John is the nicest guy in the Western Hemisphere. Some have said that he is the most generous person they’ve ever met. Furthermore, trust me; his policies are just what this country needs. All kinds of studies show that his approach is better for the economy. I am not going to even talk about the problems that his opponent ‘may or may not’ have had with the law. Now, let me introduce a big celebrity who just announced that he endorses John!”

Before moving forward, consider (or discuss) the following scenarios:

1. Whenever Marcus hears news anchors talking about people on welfare in the United States, he imagines those people being ethnic minorities. Marcus is a White man. When he goes to work and hears people talking about people on welfare, his views are reinforced, since most of the people that Marcus works with and interacts with share his vision of the world. What is wrong with Marcus’s thinking and the thinking of those who have similar ideas? Explain why his thinking is illogical.

2. Stephanie dropped out of college because her parents were tragically killed in a car accident. However, when she hears about others dropping out of high school, she immediately thinks that they are lazy and what she calls “a waste of space.” What is illogical about the way that Stephanie interprets the lives of other people who drop out of institutions of education? How might Stephanie think in a more logical, fair- minded manner?

3. When Justin comes home from work, he expects his wife to have the house clean, dinner on the table, and their three kids under control. He constantly makes reference to how he “brings home the bacon” and regularly minimizes the contributions that his wife makes to their family. He often uses his control of the family’s �inancial resources to threaten his wife when she attempts to ask for help with the children. What is wrong with Justin’s thinking? What is a just distribution of labor in a family? What ideas about the roles of men and women might in�luence your own response to this question?

4. When Tiffany comes home from work, she expects her wife to have the house clean, dinner on the table, and their three kids under control. She constantly makes reference to how she “brings home the bacon” and regularly minimizes the contributions that her wife makes to their family. She often uses her control of the family’s �inancial resources to threaten her wife when she attempts to ask for help with the children. What is wrong with Tiffany’s thinking? What is a just distribution of labor in a family? What are some feelings that you have as you read an example in which the family consists of two mothers? Do those feelings or thoughts emerge from irrational foundations?

5. Jim and Mike have an argument over dinner about vegetarianism. Mike, a vegan, calls Jim a “murderer” with no sense of compassion. Jim gets angry and says that vegans are all “idiots” who have never heard of the food chain. How might you go about helping them better communicate with each other? Do you think that there are good points to be made on each side? Could you articulate the reasoning or point of view that each of them might have? Is one of them simply lacking information, or do they just see it from different points of view?

Also, see if you can create or �ind two examples of each of the following rhetorical devices. If these devices were being used to in�luence you, what was the person trying to get you to believe, and how did using these techniques either work or fail in your situation?

6. weasel word 7. euphemism 8. dysphemism

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9. proof surrogate 10. hyperbole 11. innuendo

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8.3 The Media and Mediated Information

As should be evident by now, rhetorical devices and other persuasive techniques can be found almost anywhere. However, it is perhaps easiest to see persuasion in action in what is known broadly and collectively as “the media”—the sources of mass communication that include television, newspapers, radio, and the Internet.

If we consider how the media functions, we can see the origins of the word media itself (the singular is medium). There is, of course, ourselves: the viewers, the readers, or the listeners. There is also the world that we want to understand. To a certain extent, a person can learn a great deal by observation—looking, listening, and so forth—to discover how that world is and how it functions. But a great deal of information is not available to us this way; we rely on the media to provide it. Thus, the media are intermediaries between ourselves and our world; the media mediate between us and the world we seek to understand.

With that role comes the risk that the information provided is distorted. Any media source has to make decisions about how to present information. After all, if we want to hear about what took place in a 3-hour meeting, we probably do not want to watch, read, or listen to 3 hours of content. Rather, we want the relevant information summarized accurately, in perhaps just a few sentences or a short video. Thus, media sources have to make numerous decisions about what to emphasize, what to omit, how to frame the information, what the relevant background is, how others might interpret it, and so on. These decisions can be dif�icult to make, and good writers and editors recognize that with each decision, one risks distorting the information. While there may not be a perfectly unbiased media source, some work extremely hard to present an objective perspective. Others, on the other hand, seem intent on using bias and spin to increase their viewership. As should be clear from our earlier discussion, this phenomenon is not limited to the media alone: Any source, whether it be a politician or your next-door neighbor, is mediating the information you receive.

The last section focused primarily on how language can be used to persuade a listener or an opponent of some claim— not based on the actual evidence or in terms of an argument, but on how that claim is stated. However, it is not just language that can be used and misused in this fashion. Images, or the combination of images and words, can also be manipulated to send a message, and we should be just as aware of this possibility as we are of rhetorical techniques.

Manipulating Images

Even before computer software made altering photos relatively easy, dictators were known to try to alter the historical record by changing photographs. One classic example involved the so-called Gang of Four in the People’s Republic of China in 1976. These four in�luential Chinese Communist Party of�icials, having fallen out of favor with the political leadership in China, were simply removed from a widely circulated picture of the 1976 memorial service for party founder Mao Zedong. (To see a copy of this photo, visit Scienti�ic American’s slideshow on photo tampering: http://www.scienti�icamerican.com/slideshow/photo-tampering -throughout-history/#2 (http://www.scienti�icamerican.com/slideshow/photo-tampering-throughout-history/#2) .)

This sort of photo manipulation might seem quite bold and blatant, but photo manipulation can also be more subtle. With the development of technology, it can be dif�icult to discern that there have been changes to an image and to determine what those changes may be. Most of us are familiar with the controversy surrounding airbrushed models and messages about body image they convey. But these same techniques can be used to color our perceptions of other things as well. During O. J. Simpson’s controversial murder trial in 1995, Simpson’s picture was presented on the cover of Time magazine and the cover of Newsweek magazine. The two magazines ran the same picture, but the darker cast of the Time cover seemed, in the view of many critics, to make Simpson look scarier and more menacing. (See the two covers side by side and read about what happened when that Time cover hit the newsstands at http://blogcritics.org/ojs-last-run-a-tale- of (http://blogcritics.org/ojs-last-run-a-tale-of) .)

Although it can be dif�icult to be aware of these kinds of alterations, the point is a general one: When information— whether words or images—looks suspicious, or an image might be considered to be just a bit too “convenient” to support a claim, one should investigate further. Are there other sources for the same picture? Are there ways of discovering that the image has been altered or even faked? As usual, the best we can do is be aware of the possibility, and when in doubt, see if we can critically examine the image (or information) to determine if it is genuine or not.

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Various photographers, as well as a museum curator and an advertising creative director, offer thoughts on and criticisms of advertising techniques.

Thinking About Advertising

Critical Thinking Questions

1. What are some techniques that advertisers use to promote their products?

2. What techniques did the artists interviewed in this clip use to get the audience thinking about the effects of advertising?

3. Think of some of today’s most in�luential advertisements or brands. Is there any way to prevent oneself from being in�luenced by advertising? Is it important to insulate oneself from advertising?

Moral of the Story: Manipulating Images

A picture may be worth a thousand words, but those words can still be lies. When in doubt, verify that the picture has not been altered or faked.

Advertising

Most of us are not surprised that advertising presents information in a way that tries to persuade the consumer to purchase a good, or a service; that is, after all, the purpose of advertising. However, being aware of advertisers’ goals helps us maintain a critical perspective. Indeed, there are slogans to remind us to regard advertising with a bit of skepticism: caveat emptor (“let the buyer beware”), “if it is too good to be true, it probably is,” and “always read the �ine print.”

We have already seen some of the techniques that advertisers use to convince viewers to buy a product, such as proof surrogates and weaselers: Recall the commercial about toothpaste that “may prevent cavities.” The Chapter 7 discussion about fallacies outlines many of the other ways others try to convince us (illegitimately) of something. In this section, we will look at a few more speci�ic examples how marketers pair images with rhetorical devices and fallacies to override our critical thinking skills.

One advertising technique is to pair positive images with the product, which can cause viewers to associate the product with positive feelings. Generally, most of us are not conscious of this—which is what marketing professions desire (see A Closer Look: Does Advertising Work?). If you have a positive response to a product because of what you associate with it, presumably you are more likely to buy it. For example, perhaps a certain beer is consumed by the world’s most interesting man; should we be drinking this beer too if we want to be more interesting ourselves? Of course, most marketing campaigns are considerably more subtle. Indeed, as viewers become more aware of advertising techniques, advertisers develop better techniques.

A Closer Look: Does Advertising Work?

Many people claim that advertising does not affect them. The obvious question is why marketers spend $70 billion dollars a year on television ads alone if they are so ineffective. Perhaps the marketers know something that those

Advertising From Title: Persuasion, Propaganda, and Photography

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Christopher Polk/Getty Images Entertainment/Getty Images

This Got Milk? advertisement says, “15% of adult height is added as a teen—see how milk’s nutrients can help.” Are the advertisers making a claim?

who deny the in�luence of advertising do not.

As market research analyst Nigel Hollis (2011) has observed:

Contrary to many people’s beliefs, advertising does in�luence them. But advertising’s in�luence is subtle. Strident calls to action are easily discounted and rejected because they are obvious. But engaging and memorable ads slip ideas past our defenses and seed memories that in�luence our behavior. You may not think advertising in�luences you. But marketers do. (para. 13)

Perhaps the best illustration of our myopic tendencies is a memorable experiment conducted by Daniel Simons and Chris Chabris. If you are unfamiliar with the study, you may want to watch the video (http://www.theinvisiblegorilla.com/videos.html (http://www.theinvisiblegorilla.com/videos.html) ) before the next paragraph spoils it for you.

In Simons and Chabris’s experiment, subjects were asked to watch a video of people in black T-shirts and white T- shirts passing a basketball. They were asked to count the number of passes between team members, and afterward were asked if anything out of the ordinary took place. While most participants were able to accurately count the passes made, most failed to notice that a person in a gorilla suit walked through the video—they were too busy counting passes.

Likewise, most of us are not devoting our full attention to advertising when we are watching TV or �lipping through a magazine. We are thus more likely to remain unconscious of the persuasive techniques being used to in�luence our opinions and buying habits. As University of Calgary psychology professor Julie Sedivy (2011) wrote:

In the scienti�ic work on persuasion, there’s a well-known result that, while not quite as funny as the Simons and Chabris study, is very similar to the invisible gorilla effect: it’s the �inding that people are often apt to ignore the difference between strong and weak arguments in forming attitudes or choosing how to behave. (para. 7)

Many commercials attempt to present weak arguments by means of images intended to offer the support that premises would otherwise provide.

Suppose that you saw a Coke commercial with the polar bears. Maybe you liked the polar bears, and these images remained in your memory. You suddenly realize that you are thirsty. And then you �ind yourself leaving the store with a six-pack of Coke. Indeed, some commercials do not offer any clear claims at all.

Consider the Got Milk? advertising campaign, often mentioned as one of the most effective campaigns in recent history (Bowman, 2012). Is there a claim in the pictured ad? If so, is the claim persuasive? Why or why not? If there is not a claim here, is this ad still effective? What message do you think the ad seeks to convey? How does professional basketball player Chris Bosh help convey that message? Does the ad make you less likely or more likely to buy milk?

If a marketer can leave you with an unconscious association between something pleasant and a particular product, you may be more likely to buy that product,

regardless of whether there is a claim or a suggested argument involved.

The ad in Figure 8.1 may simply appear amusing; after all, it would be rare to see physicians now endorse a particular brand of cigarette. But, you might notice a few rhetorical devices in use: First, the claim “more doctors smoke Camels” works as a weaseler. Few doctors may smoke; this ad simply claims that of those who do, one speci�ic brand is mentioned most often. We have very little ability to evaluate this ad. Second, the phrase “according to a recent nationwide survey” introduces a proof surrogate. This may be true, but it is a dif�icult to evaluate this cited survey, since no further information or documentation about the survey is provided. Finally, an authority �igure and thus theoretically credible

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source—a physician—is associated with this brand, further enforcing the ad viewer’s favorable impression of Camel cigarettes.

Figure 8.1: Proof surrogate example

Can you think of any modern-day advertisements that appeal to authority or use a proof surrogate like this vintage ad for Camel cigarettes?

Source: Apic/Hulton Archive/Getty Images

These associations are not meant to be taken literally or examined critically. Marketers do not expect viewers to drop everything and run to the store to buy their touted brand of cigarettes, much less interview doctors or demand access to a cited survey or study. Associations are meant to be stored in one’s brain in an unconscious way, so that those who have these associations will have a more positive view of the product. Maybe, just maybe, someone who sees a cigarette ad— especially one who sees it repeatedly but not in a conscious, critical way—will buy that brand of cigarettes in the future.

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As another example, consider the orange juice ad in Figure 8.2. In this ad, we have a mother and her two daughters, happily embracing and clearly enjoying being with each other. Few mothers, or parents, would have anything but a positive response to that image. Presumably, it is a natural demonstration of a mother’s love. Evidently, the only other thing that is natural in the picture is orange juice. Of course, there is no claim being made here, such as “Mothers, if you give your daughters more orange juice, you will receive more hugs.” You would be rightly dubious of such a claim. Rather, the ad merely links orange juice with one very positive thing, even though there is little logical or evidence-based connection. That makes it just a bit more likely that when a person who has seen this ad needs orange juice, this particular brand of orange juice will be purchased—all because of the emotional appeal of one image.

Figure 8.2: Positive associations example

Advertisers are hoping the positive emotion you feel when you see this image will lead you to purchase their brand of orange juice.

Source: Tropicana Products, Inc./PR Newswire/Associated Press

Other Types of Mediated Information

What other kind of information should we consider with at least a slightly critical perspective? As mentioned earlier, all information that is provided to us through the media is, as the name indicates, mediated. Almost all this information will be condensed and packaged in a way that it can be consumed, and thus, we have to be on guard that the information has not been distorted to the extent that it can be misleading or even false. So, it is not just toothpaste and beer commercials that we must thoughtfully evaluate, but also political speeches, reports on sporting events, and celebrity news—any information that is transmitted to us through others. Of course, if the local hockey game is reported with simply the score, that may not be terribly controversial, and we are unlikely to cast much doubt on that report. But, what about a politician’s speech or reports on an environmental disaster or economic data? How that material is presented can help determine what we think about it.

For instance, consider a standard sort of economic report, the federal government’s monthly report on jobs. The government reports that 200,000 new jobs were created and that the unemployment rate dropped to 7.5%. That seems to be relatively uncontroversial; we have a number reported, and that’s that. But it might be presented in different ways that can affect how this report is interpreted. Compare these two reports providing the same data:

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The government announced today that only 200,000 new jobs were created in the last month, barely keeping up with the numbers of those entering the workforce; the unemployment rate dropped only slightly, to 7.5%. Analysts indicate that this is more evidence of a sluggish economy.

The government announced today that at least 200,000 new jobs were created in the last month, a dramatic increase over recent months and outpacing the number of those entering the workforce. The unemployment rate continues to drop and reached 7.5%. Analysts indicate that this shows the economy is picking up steam.

Both reports state the same basic facts. But the way these facts are presented changes whether the numbers indicate a positive or negative result: “only” versus “at least,” the analysts selected to comment, “barely keeping up” versus “a dramatic increase.” This example indicates the way language can help frame even a speci�ic, “objective” number in two different ways, with different interpretations or “spin.” If this can be done with such a speci�ic number, it becomes clear how more complex or nuanced information can be presented, with similar results. A senator who puts forth a bill, a president who announces a new military strategy, or a governor who proposes a tax plan are all presenting information that has to be interpreted. The more complex that information, the greater the possibility that distortions will be introduced by how that information is presented.

We can thus see that critical evaluation of the information we are given is an activity and takes some energy. If we simply passively take in that information without evaluating it, we may end up understanding it incorrectly or inadequately or even be asked to believe two contradictory things. (If one report states that undocumented immigration is increasing, while another report at the same time claims that undocumented immigration is decreasing, these cannot both be true.) We may not want to work quite that hard when we hear a meteorologist tell us what tomorrow’s weather is going to be like; we may already have certain suspicions about how accurate such forecasts are anyway. But if you hear of public policy or a political platform that affects you directly, or indirectly, you may want to spend that extra energy listening (or reading) carefully, critically, and with at least a bit of skepticism. The following are some suggestions of questions to ask when critically evaluating information:

What is being stated? That is, what facts are involved? Is the information accurately stated, with the relevant context provided? Does the language used slant or bias the way the information is presented? What is omitted? Are any implications that are stated reasonable implications to draw from the information provided?

Practice Problems 8.2

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems8.2.pdf) to check your answers.

1. Which of the following is a common form of media manipulation? a. Using slant in the way a story is portrayed b. Manipulating images to make something appear better or worse than it is c. Omitting relevant information d. all of the above e. none of the above

2. According to studies about the in�luence of advertising, which of the following is true? a. Advertising does in�luence you, whether you admit it or not, in ways that you may not even be

aware of. b. Advertising affects only those who are less intelligent. c. Advertising does not work as much as they thought; people are too smart for that. d. Advertising is not very effective because it doesn’t use sound logic. e. none of the above

3. Which do you think is the most effective way to have a productive conversation about a controversial issue with someone with whom you strongly disagree?

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a. Seek to �ind out and point out where the other person is wrong. b. Seek to understand the other person’s point of view, focusing on their reasoning and carefully

sharing your reasoning. c. Compare the other person to Hitler (using Godwin’s law). d. Use deductive reasoning to show how right your position is. e. none of the above

4. Which of the following is not one of the ways to mislead while quoting someone? a. Take the statement out of context b. Change some of the wording of the statement c. Omit some crucial words from the statement d. Share a statement from someone with the opposite point of view as well e. none of the above

Before moving forward, consider (or discuss) the following scenarios:

1. Suppose a media outlet has a vested interest in the outcome of a particular issue. For example, media outlets will often not run negative stories about companies that regularly advertise their products on the media show. What are some other ways that media groups could go about biasing their coverage to in�luence public opinion? List at least three ways. List at least four reasons why you think that the media engage in manipulative practices. What do they have to gain from these things?

2. A news outlet airs a segment about a speech recently given by a famous candidate at a political rally. The candidate was booed quite loudly, as one could hear on the many private videos taken. However, the news outlet that covered it showed the candidate speaking with lots of cheering in the background. Apparently, the news outlet had changed the audio! Why do you suppose that a media outlet might do this? Do you think that media outlets (some or all) have people pulling the strings to affect public opinion in a partisan way? How can we escape from being biased by our media sources?

Also, see if you can create an example of each of the following types of media manipulation.

3. Someone’s statement is taken out of context. 4. Someone uses biased or slanted language to describe the issue. 5. Someone emphasizes certain things to make a person look bad. 6. Someone omits information to make a person look better (or worse). 7. Someone uses hyperbole, euphemism, or dysphemism to mislead his or her audience. 8. Someone uses untrustworthy sources to support his or her statement. 9. Someone uses “spin.”

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8.4 Evaluating the Source: Who to Believe

It is not only important to evaluate how information is presented, but who is presenting it. This points to an important implication behind all of our discussions about arguments and persuasive techniques: that many people or organizations have an agenda or some purpose when they are sending a message. Of course, a person’s intent might be fairly innocuous, but it also might not be. Knowing some background information about a source, particularly any biases the source may have, will in�luence how believable you should think the source is.

Evaluating the source is always an important part of evaluating information, but it becomes an even more critical task when you want to use this source to support one of your own arguments. This section highlights three factors that you might consider: the source’s reputation and authorship, accuracy and currency, and purpose and potential bias.

Reputation and Authorship

Think about something surprising you read on the Internet. Should you believe it? Should you pass on the information? You’re probably aware that not everything you read is true or should be taken seriously. Considering a source’s reputation and authorship can help you assess its reliability.

A source’s reliability comes from having procedures in place that ensure that the information it produces is accurate. Over time, this leads to its having a strong history of accuracy. Sources that have a strong reputation for being reliable are more likely to carry weight with the intended audience for your argument. On the other hand, citing sources that are known for being inaccurate or heavily biased will weaken your argument.

Longevity also plays a role in a source’s reputation. Sources that have a long history will have developed a reputation as either reliable or unreliable. Of course things can change, but a source that has a long history of providing relatively accurate information should be seen as more trustworthy than a source with a very short history, or one with a long history of providing inaccurate information. If a source often provides poor information, that will become known over time. This does not mean that the source will go out of business; some sources make their money precisely because they are sensationalist. You have probably seen some of these sources with incredible headlines as you went through the checkout line at a grocery store. Nonetheless, sources that have been around a long time, and which depend on being credible in order to survive, are generally likely to have reliable information. For example, mainstream newspapers that have been around for 50 or 100 years are likely to be relatively reliable in reporting information. If they were not generally reliable, they probably would not still be in business.

Another point to consider is whether a source has methods in place to ensure the accuracy of the information it presents. For example, most academic journals employ a process of peer review. Before a paper is published, it is reviewed by other experts in the �ield to ensure that the information presented is credible. The review is generally anonymous, so the reviewers do not know who wrote what they are reviewing, and the author does not know who the reviewers are. This anonymity encourages reviewers to be honest and objective in their reviews. Peer review is one of the strongest methods for ensuring that information is of high quality. The use of peer review allows even new academic journals to be credible. However, peer review is very time consuming, so it is not widely used outside of academic journals. Instead, editorial review may be used when a publication seeks to be not only accurate but timely. In editorial review, one or more editors review information before it is published. The editor makes sure that the information is believable and may ask the author for clari�ication or further research if needed. Editorial review can be quicker than peer review, but it does have limitations. First, editors are expensive, and better editors are more expensive. Small organizations are unlikely to have adequate editorial staff to fully ensure the accuracy of what they publish. Second, editorial review is subject to the biases of the editor doing the review. Finally, reviewing for information quality is only one of the jobs of an editor. Just because a source has an editor does not mean that the editor is solely focused on information quality rather than other issues.

The best sources have solid review methods and longevity in their favor. For example Cambridge University Press was begun in 1534 and employs careful editing and review processes. It is unlikely that a manuscript would be published by a long-standing university or commercial press that contained either an enormous number of factual errors or promoted an especially bizarre viewpoint. Of course, this does not mean that such sources are infallible: Mistakes can still be made, and misleading or inaccurate information published. However, these sources are unwilling to risk their reputations and thus will subject themselves and their materials to fact-checking, peer review, and other methods of scrutiny. Any mistakes that are made are much more likely to receive a great deal of attention in the media, which, in turn, helps to alert

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Marty Bucella/Cartoonstock

The Internet has increased our access to information, but unless we are diligent in determining the reliability of information sources, we can easily be misinformed.

us to the mistake. Indeed, credibility may be the most valuable commodity a publisher possesses: It may be the most dif�icult to obtain and the easiest to damage or lose.

When we talk about a source’s authorship, we are discussing who produced the information in question. This is particularly important in the age of the Internet (see A Closer Look: Using Wikipedia). A media source presents information that is originally produced by individuals or another organization. For example, a newspaper may present a story that is written by a speci�ic reporter or one that is carried by a wire service such as Associated Press or United Press International. Knowing who authored the story can help us assess how credible it is. If the source is authored by an organization, then we should consider the reputation of the organization. If the author is an individual or group of individuals, then we should consider whether they are trustworthy on the subject they are writing about. Being trustworthy on a subject amounts to knowing about the subject and being likely to be relatively unbiased about the subject. The next section will deal with bias. For now, let us consider the issue of the author’s knowledge.

What reason is there to think that an author knows the subject they write or talk about? If the author has credentials and experience in the subject matter, this is a good sign. Someone with a PhD in biology and years of experience working in the �ield is generally a good source for information about biology. However, this same person may not be credible on the issue of tax policy. As another example, let us say you �ind a book or article about the history of the American Civil War, and

the author is an air conditioner repair man. The author’s profession alone does not necessarily mean that you cannot trust the information, but it does suggest that you should look further to �ind reasons to do so. It is possible for someone to have extensive expertise in an area which is primarily a hobby for them. But if he or she is an expert, then you should be able to �ind evidence of that expertise. For example, if an author is widely cited by people who do have credentials, this may indicate that he or she is considered an expert. This is another good time to look at the reputation of the publisher. If the work is published by a reputable publisher, this is far better than if it is simply posted on the author’s own blog. It can be dif�icult to assess an author’s level of expertise, but it is essential to do so before simply accepting what he or she has to say.

Authorship does not necessarily have to refer to a person: Publications and websites can also have credentials. For example, many journals are associated with universities. A journal that is not so associated is not necessarily unreliable, but those that are need to uphold not only their own reputation but also the reputation of the af�iliated university. That the university allows the af�iliation can be seen as an endorsement, and the journal bene�its somewhat from the university’s own credibility. When it comes to websites, you should be aware of what domain hosts the web page. Internet sources will have a suf�ix indicating the top-level domain; for instance, .edu indicates an academic source, whereas .gov indicates a governmental source. These domains will tend to be more reliable than other domains, though there is still the potential for an individual publishing unveri�ied information on a personal page within the domain. Websites in .com, .net, and .org will require you to look closely at the credibility of the source, since anyone can purchase a website within these domains.

A Closer Look: Using Wikipedia

Questions about authorship become all the more important when we consider that many of us begin our research on the Internet. Anyone can publish whatever he or she pleases on the Internet. The online encyclopedia Wikipedia is a case in point: Most articles in Wikipedia can be edited by anyone, whether that person is an expert or not. Because the content is largely uncontrolled, many schools and professionals regard it as a wholly unreliable source. Others recommend using it but with caution, while still others do not object to its use in order to begin one’s research, but would strongly object to using it as an authoritative source itself. Typically, universities do not

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When evaluating a source for credibility, one must consider the source’s potential motive and bias.

Credibility, Motive, and Bias

consider Wikipedia an acceptable source because university papers must indicate the original sources and Wikipedia is not an original source. If you do use Wikipedia or a similar website in your research on a topic, it is up to you to follow up on the referenced sources and verify that they exist and agree with the article. Knowing the source of a claim is not enough to guarantee that the claim is true or false, but it is a good �irst step.

Before relying too heavily on Wikipedia as authoritative, you may want to look at some of the longstanding hoaxes that have been discovered there (http://en.wikipedia.org/wiki /Wikipedia:List_of_hoaxes_on_Wikipedia (http://en.wikipedia.org/wiki/Wikipedia:List_of_hoaxes_on_Wikipedia) ).

Accuracy and Currency

One of the advantages of the Internet is the free �low of information. However, with no controls in place, the most absurd rumors can be circulated, and before some may even realize they have been misled, a particular rumor may have been accepted by many as the truth. A popular saying states that a lie gets halfway around the world before the truth has a chance to get its pants on. Though this is true both online and off, it has never been truer than in the age of the Internet. Thus, it is critical that you examine whether the source is accurate and up-to-date, or current, before you accept it as truth or a worthwhile argument.

The value of accuracy is fairly self-explanatory. However, determining whether information is accurate can be trickier. Here are some tips: First, consider whether or not the information provided can be veri�ied in print sources. If a substantial claim is put forth, one should be able to �ind various sources that con�irm that claim. Second, investigate whether the source provides further references or a bibliography. Are these sources themselves credible? If a source cannot back up claims with references, this can be a warning that some of the material is conjectural, or even made up. Third, read carefully for misspellings, obvious errors, or embarrassing production values. Numerous minor errors often indicate that the source has not been vetted by others.

Though accuracy is paramount in evaluating a source, the currency of even accurate information can determine whether a source should be used. Information that is out-of-date is simply less useful and may lead to inaccuracy. Information that was the best available 30 years ago may have been discredited or substantially changed with the discovery of new information. Check the publication date of any source that has one. Look to see that the source references recent research and events. For instance, if an article about the American Civil Rights Movement does not include any information after 1966, this is an indication that its information is at least out-of-date; if it is a recent article, it may be an indication that the author has not stayed current on the issues involved. Note that what is considered out-of-date in one discipline may be considered current in another discipline. An algebra book from the 1950s is much more likely to be adequately up-to-date than a global communications book from the same era.

Interested Parties

We return to a point made at the start of this section: that many people and organizations have a purpose when sending a message. Thus, we must evaluate sources for any potential bias. An interested party is one that has a stake in the outcome of certain decisions, such as those made by legislatures and courts, and include anyone who has anything to gain from our believing something to be true. Often an interested party has an economic stake in how an issue is perceived in the media and thus, indirectly, by the public. Interested parties can be large, such as political entities and organizations. Interested parties can also be individual players, such as a sales associate who is paid on commission and thus is unlikely to be objective about the product he is selling. Or consider a

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Critical Thinking Questions

1. Think of a news article you have recently read. Using the criteria of motive put forth in the video, evaluate the credibility of the source. What do you believe their motive is?

2. The goal of advertisements is to get you to purchase their product. That’s their motive. Does this make them biased? Do you believe there can be unbiased advertisements?

political leader who supports a bill that will bring money to her home state and who knows that such a bill is likely to gain her votes when she comes up for reelection. She is an interested party because she stands to gain if the bill passes.

Nonetheless, having a personal interest in an outcome is not necessarily a problem. The important thing to keep in mind is the legitimacy of the argument presented by interested parties. When evaluating an argument, you must �ind out whether the source is an interested party. If so, does the individual or the group represented have a particular stake in the issue? You might hesitate to take “The Association of Cotton Growers” as an objective, disinterested source on whether the government should provide tax subsidies to cotton farmers. Or, if you are reading about climate change, you might consider whether the information is provided by a petroleum company or a solar energy company. If a source quotes an expert on whether a particular weapon should be developed by the military, it might make a difference if the expert works, has worked, or will work for the company that makes the weapon or a competitor of that company.

It is often dif�icult to determine whether a source is undermined by being an interested party. But if economic, political, or any other power-related connections can be established, or are suspected, then this demands heightened scrutiny when critically examining the arguments and information provided by such a source.

No source is perfectly reliable; all sources, thus, deserve some degree of critical scrutiny. Naturally, those sources that have, over many years, developed a reputation for journalistic integrity may need much less scrutiny than a website that appears to have been constructed in the last few weeks. As in all evaluation of information, one should always try to identify the facts involved and determine if the claims being made are plausible and if the reasoning that supports those claims is persuasive.

Moral of the Story: Interested Parties

If someone stands to gain from having their argument or claim accepted, that person is an interested party, and you should be alert for possible bias in what he or she says.

Credibility, Motive, and Bias From Title: Credibility: Critical Thinking

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Practice Problems 8.3

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems8.3.pdf) to check your answers.

1. A county has plans to renovate the highway. The local paper writes an article about the decision about which contractor gets the bid. The reporter interviews four sources. Which of the following sources is least likely to have an improper interest in the outcome of the decision?

a. a contractor who has a bid in to rebuild the highway b. a county commissioner concerned about public image and reelection c. a property developer who intends to develop land near the proposed renovation d. a third-party engineer hired to analyze each bid to determine the feasibility of meeting the

deadlines and staying within the stated costs e. none of the above

2. Which source seems the least credible? a. an article in a major newspaper b. a university website

Logic in Action: Persuasion at the Dealership

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c. a peer-reviewed journal article d. an article on a political blog e. none of the above

3. Which of the following is not a good reason to distrust a source? a. The source has a vested interest in the outcome. b. The source is peer reviewed (rather than reviewed by neutral superiors). c. The source only represents one political viewpoint. d. The source itself cites no sources of its information. e. none of the above

4. Which of the following is not one of the ways listed to check the reliability of a political source? a. whether the source has relevant credentials b. whether the source’s views align with one’s own c. what organization the source represents d. whether the source’s claims can be veri�ied in other reliable sources e. none of the above

5. Which of the following is the best way to make yourself more objective about your information about a controversial issue?

a. Trust your friends and family; they have your best interests at heart. b. Trust the news sources you are used to; you already know that they are good. c. Find many high-quality sources on all sides of the issue. d. Just think about the topic; your own opinions are just as valid as anyone else’s. e. all of the above

Before moving forward, consider (or discuss) the following scenarios:

1. Suppose you had to write a neutral article about a very controversial issue about which you had very strong opinions. How would you go about making sure that your article was fair and neutral? What kinds of sources would you use? How would you go about trying to understand the views that you hate?

2. If you were being paid to do PR for a company do you think that you would be able to be fully honest about the negative aspects of the company (assuming it had them)? What if there was strong pressure from your employer? What would you do in such a situation? Where would you draw the line at which you would quit?

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Summary and Resources

Chapter Summary Many of the arguments we encounter are not necessarily good arguments in the sense of being deductively sound or inductively strong, yet they can come across as very persuasive. Advertisers have always been quite effective in developing techniques to convince people to buy something, techniques that have not been ignored by politicians (who, in trying to get themselves elected, are often trying to convince the public to vote for them in a way not much different than selling toothpaste). The careful consumer—whether of products, politicians, or news—will be aware of these techniques and use the various tools available to evaluate information critically, particularly by focusing on the claims made, the reasons supporting those claims, and the arguments that connect those reasons with the conclusions they seek to establish.

Logic is, in a basic sense, the study of those tools that can help us improve our ability to evaluate these arguments so we can effectively accept those arguments that should be accepted, reject those arguments that should be rejected, and improve those arguments that can be and need to be improved. In addition, the tools of logic will help us develop the ability to distinguish among these three kinds of arguments (those that should be accepted, those that should be rejected, and those that can be improved).

Connecting the Dots Chapter 8

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Critical Thinking Questions 1. There are many political organizations in this country with views that most of us would consider “crazy.” Yet

people with those views look around and see the world con�irming their own beliefs. How is it possible that they could see the same world we see and yet use it to justify their very different views? How do you suppose they choose their media sources? What can we do to ensure that our thinking is not narrow or biased?

2. Read about Godwin’s Law in this chapter. Recount a time that you were involved in an Internet conversation or a verbal face-to-face conversation with someone and it devolved into this form of argument. Why did the conversation move into the realm of comparisons to Nazis or other horrendous people? Why are we so quick to make claims that others fall into these categories when their opinions differ from our own? What is a more ethical and fair way of handling conversations when they start to move down this track?

3. Think about a time that you were manipulated by the news media. What was the story that was presented, and how did it in�luence you? What were the errors in the story or the ways that the media used to manipulate the audience in this situation?

4. What do you think is the most important thing to do when you are trying to verify information that you gather from external sources? Which techniques do you use? Which techniques do you need to work on?

5. Do you think that Wikipedia is a good source of information? Why or why not? Think of a time that you used Wikipedia to make claims that were not veri�ied using other sources. What should you have done in that situation? What will you do in the future when these situations arise?

6. What are the strongest motives that tend to lead people to become interested parties? 7. Is there such a thing as true “objectivity”? Why or why not?

Web Resources http://www.psychologytoday.com/articles/199805/where-bias-begins-the-truth-about -stereotypes (http://www.psychologytoday.com/articles/199805/where-bias-begins-the-truth-about-stereotypes) This Psychology Today article suggests that stereotyping is not limited to the bigoted.

https://implicit.harvard.edu/implicit/takeatest.html (https://implicit.harvard.edu/implicit/takeatest.html) This test developed by the nonpro�it Project Implicit reveals that many people have cognitive biases they were unaware of.

http://www.scienti�icamerican.com/article/what-hand-you-favor-shapes-moral-space (http://www.scienti�icamerican.com/article/what-hand-you-favor-shapes-moral-space) This Scienti�ic American article suggests that bias exists for whether something is presented from the side of one’s dominant hand.

http://www.psych.cornell.edu/sec/pubPeople/tdg1/Gilo.Vallone.Tversky.pdf (http://www.psych.cornell.edu/sec/pubPeople/tdg1/Gilo.Vallone.Tversky.pdf) This article dispels the belief on the part of basketball fans and players alike that there is a positive correlation between the outcomes of successive shots (that is, believing the chance of hitting a shot is greater following a hit than a miss).

http://news.cnet.com/2100–1038_3–5997332.html (http://news.cnet.com/2100-1038_3-5997332.html) This article describes a study comparing Wikipedia’s errors with those in the Encyclopedia Britannica.

http://en.wikipedia.org/wiki/Reliability_of_Wikipedia (http://en.wikipedia.org/wiki/Reliability_of_Wikipedia) To be fair, Wikipedia also has an entry on its own reliability.

Key Terms

bandwagon effect The tendency to think that something is desirable or true merely because many people desire it or believe it.

cognitive bias A psychological tendency to �ilter information through one’s own subjective beliefs, preferences, or aversions, which may lead one to accept poor reasoning.

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con�irmation bias The tendency to select information that con�irms one’s beliefs while discounting information that would discon�irm those beliefs.

dysphemism A term that makes something sound more negative than it otherwise would.

euphemism A term that makes something sound more positive than it otherwise would.

hyperbole An exaggeration.

innuendo A statement or phrase that implies something without actually saying it.

interested party One that has a stake in the outcome of certain decisions.

paralipsis A technique for emphasizing a point by saying that it will not be mentioned.

probability neglect Ignoring the actual statistical probabilities of an event and treating each outcome as equally likely.

proof surrogate An assertion that evidence is available without actually providing the evidence; for example, “studies show.”

rhetorical devices Techniques that make an argument seem more persuasive without increasing its logical strength.

selection bias Bias resulting from a nonrepresentative sample.

status quo bias A tendency to believe that the way things are is �ine.

stereotype A judgment about a person or thing based solely on the person or thing being a member of a group or of a certain type.

weasel words Words used to make a claim technically true by introducing probability or otherwise watering it down, without really changing the import of the claim. Also known as weaselers.

weaselers See weasel words.

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y g desirable or true merely because many

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Learning Objectives

After reading this chapter, you should be able to:

1. Use the standard argument form to construct an argumentative essay.

2. Describe how to strengthen an argumentative essay.

3. Identify elements of the Toulmin model of argumentation and compare and contrast them with the elements employed in the standard argument form.

4. Apply the principles of accuracy and charity when confronting disagreement.

5. Identify and employ quali�iers, hypotheticals, and counterexamples.

6. Identify the differences in meaning between logical terminology and everyday uses of the same terms.

7. Explain the various applications of logic in other �ields.

9Logic in Real Life

Szepy/iStock/Thinkstock

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In this chapter we will step back and take a broader view of our subject. So far we have been focused on the nuts and bolts of arguments. We have learned about the elements that constitute them, different kinds of inference, and the many ways that arguments can go wrong. However, the real importance in learning the tools needed to construct arguments lies in our ability to apply them to arguments we encounter in real life. Logic and critical thinking are powerful tools for improving our reasoning, but to apply them successfully requires practice and attention. In this chapter we shall start by going over the necessary steps for constructing your own arguments. Next we will examine how to examine other arguments critically, as well as how to confront disagreement. Finally, we will look at some ways in which arguments and logic are used in various professions for very practical ends.

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Whether or not you realize it, everyday reports of your work to peers or higher-ups may require you to formulate an argument. Starting from the standard argument form, you can write an essay that helps you defend things such as a larger allocation of funds for your department.

9.1 The Argumentative Essay

In addition to serving as the framework for identifying claims, evaluating arguments, and defending your positions methodically, the standard argument form has another very practical use as the framework for writing argumentative essays. Simply put, an argumentative essay is a genre of writing that presents a logical and methodical defense of a thesis based on supporting research. It includes the recognition of the opposing position to the thesis and the presentation of a successful rebuttal. The argumentative essay format is introduced in some university courses (for example, it is the standard writing style in philosophy), but the format has broad applications when it comes to building arguments generally.

Arguments are the fundamental tool in several occupations. They are the frame for legal briefs, law review articles, opinions by Supreme Court justices, as well as public policy analyses and predictions by economists. They are the machinery employed for methodical commentaries by reporters and political pundits presented in the news media. Politicians may use arguments when they make a pitch for our votes.

However, the use of the argumentative essay is not restricted to these occupations alone. Many of us are called on to present arguments in this way, even if not explicitly. Your boss may ask you to present an argument, although she is not likely to put it that way. She is more likely to ask you to “encourage everyone” to do something (for example, get a �lu shot, come to work on time, or not access social media while working), rather than to “present an argument” that will persuade others. However, the request is still essentially a request to develop an argument. If you needed to request a raise, this, too, would essentially require an argumentative essay, whether in spoken or written form. Outside of the workplace, argumentative essays might take shape in conversations with a friend or loved one, letters to the editor, job applications, project proposals, bank loan dossiers, and even in love letters and marriage proposals. A convincing, structured argument comes in handy for many occasions.

It is important to note that argumentative writing is different from persuasive writing. An argumentative essay about the importance of getting a �lu vaccine would not only examine the reasons for doing so, but would likely weigh the pros and cons, examining why getting a vaccine is a good idea. On the other hand, a persuasive essay on the same topic would explicitly focus on trying to get the reader to get a

vaccine. Persuasive writing includes elements that are intended to motivate and persuade an audience in ways that may go beyond the boundaries of logic, such as passion or emotion. For example, an argumentative essay can convince us that a habit is bad, but it often is not enough to motivate us to change the habit. Persuasive writing tries to bridge the gap between recognizing that we should do something and actually doing it. Arguments are still central to persuasive writing; you cannot get someone to change a habit they do not think they should change. You can think of persuasive writing as argumentative writing with extra elements added.

In order to turn an argument into an argumentative essay, we will �irst need to examine both the structure of the standard argument form and the framework of an argumentative essay.

As shown in Table 9.1, the argumentative essay inverts the standard argument form so the writer can inform the reader of the objective at the outset of the essay. Note that we call the main claim the “conclusion” in the standard argument form, but in an argumentative essay it is called the “thesis.”

Table 9.1: Standard argument form versus argumentative essay framework

Standard argument form Form applied to argumentative essay

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When developing a thesis, you must be precise in your wording and clear about the exact nature of your argument. Precision and clarity will allow you to focus on premises that truly support your position.

Standard argument form Form applied to argumentative essay

Premise Premise Conclusion

Thesis (the equivalent of the conclusion in standard argument form) Premise Premise

With this initial structure in place, the argumentative essay needs a few additional elements. First, it needs a starting section that introduces the problem for which the thesis is a response. Second, each premise needs to be elaborated on and supported. Third and �inally, the essay must address objections in order to show that the argument can withstand scrutiny. The basic structure of an argumentative essay is determined by the introduction of the problem, the thesis, and the premises supporting the thesis. We will examine these three elements in the rest of this section and the remaining elements (clari�ication and support, objections, rebuttals, and closings) will be discussed in the next section.

The Problem

The problem section of an argumentative essay is its introductory section. The main objectives of the problem section are to present the speci�ic subject matter and the problem that motivates the thesis defended in the paper. Introducing the subject matter allows the reader to understand the context for the paper. The focus of the section should be the presentation of one clearly de�ined problem within this subject matter. Therefore, the bulk of this section must provide a clear picture of the particular position, event, or state of affairs that you, as the author, �ind problematic. If your subject matter is global warming, for example, and you want to support efforts to control it, then addressing global warming as a whole would be too broad. It would be better, for example, to identify whether you want to take a position with regard to what individuals can do, what businesses can do, or what whole governments can do to control global warming. Another way to narrow the problem would be to address a particular source of global warming that you �ind most problematic (for example, car emissions, speci�ic commercial pollution such as waste dumping from factory farms, or deforestation). Narrower problems are likely to be more clearly de�ined, and your research is therefore more likely to strongly support your position. Additionally, the more speci�ic you are regarding the problem you are addressing, the easier it will be for you to formulate your thesis.

The Thesis

The problem section of the argumentative essay should end in the formulation of the thesis. The thesis is the claim being defended in the argumentative essay and is equivalent to the conclusion in the standard argument form.

Precision is of the utmost importance in the thesis because even very similar theses will require different premises. Being clear about exactly what you are defending will help you keep your argument streamlined and focused on demonstrating your thesis. Consider, for example, these three similar theses:

Getting a �lu shot will help you not get the �lu. You should get a �lu shot. Get a �lu shot.

In a sense, each of these theses is aimed at the same result. But even though they are very similar, they require different premises. Let us take a closer look at each.

“Getting a �lu shot will help you to not get the �lu” is the narrowest candidate for a thesis of the three. If this is your thesis, all you need to do is appeal to studies regarding the effectiveness of �lu shots. For this thesis, you do not need to talk about the �lu shot’s cost, potential side effects, or even availability. Your claim is just that �lu shots reduce the chance of getting the �lu. You do not need to, and should not, address any issues that go beyond that. The reason for this is twofold. First, writing should always be focused.

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This is essential for clarity and to avoid confusing the reader about what is being addressed. In the case of argumentative essays, the thesis sets the parameters for what will be discussed in the body of the essay. Second, the premises offer reasons for the thesis. If we start adding reasons that are not directly relevant to the thesis, then the essay will lack clarity and will fail to convince the reader.

“You should get a �lu shot” is a broader candidate for a thesis. The fact that �lu shots reduce the chance of getting the �lu is part of what you will want to argue, but it is not enough. To show that your reader should get a �lu shot, you need to consider the pros and cons of doing so and show that the pros substantially outweigh the cons. Here it is critical to address the issues of side effects, cost, availability, and any other factors that directly bear on whether getting a �lu shot is a good idea. You may even want to bring up the idea that by reducing the overall prevalence of the �lu, �lu shots protect more people than just the person getting the shot.

“Get a �lu shot” crosses the line from an argumentative thesis to a persuasive one. A successful essay with this thesis will motivate the reader to get a �lu shot, rather than simply demonstrating the bene�its of doing so. Thus, the thesis must not only address why getting the shot is a good idea, but also try to tackle issues that keep people from getting the shots— issues such as fear, lack of time, misinformation, or just apathy. Notice that “get a �lu shot” is not a claim, so it cannot function as the conclusion of an argument. In a persuasive essay your thesis is not the same as the conclusion of your argument; the argument you develop is just part of how you develop your thesis. If you �ind yourself tempted to use a thesis that calls for action in an argumentative essay, try to reformulate the thesis as one that could be the conclusion of an argument in the standard form. You can then construct an argumentative essay for this new thesis and then add motivational elements to it.

As you can see, forming your thesis clearly is a key part of writing a successful essay. The argument you build in your essay must be tightly aimed at supporting its conclusion.

The Premises

Just like in the standard argument form, in argumentative essays the premises are the reasons that support the thesis. You should start developing your premises by listing a few of your main reasons for your conclusion. The best way to do this is to put your thesis in the form of a question. For our �lu shot thesis, that question could be: Why should your reader get a �lu shot?

Suppose that you come up with three reasons: It will help prevent your reader from getting the �lu, it will help keep others from getting the �lu, and �lu shots are cheap. We can now assemble the argument by putting these three reasons as premises in the inverted standard argument form, along with the thesis:

Thesis: You should get a �lu shot.

Premise 1: Getting a �lu shot will help keep you from getting the �lu.

Premise 2: Getting a �lu shot will also help protect others from the �lu.

Premise 3: Flu shots are cheap.

In sketching the basic premises of your argument, you have automatically developed the basic structure or skeleton of your argumentative essay. This is better than starting with one vague idea and then letting your thoughts �low freely and aimlessly.

The premises of your argument now indicate major sections of your essay. Accordingly, they should appear as the leading sentences for their respective sections. If your essay is short, each premise will be the topic sentence for a paragraph. If your essay is long, each premise will function as a thesis statement for its section.

When you are writing an essay longer than just a few paragraphs, you can repeat the process, asking what reasons there are for accepting each of the premises. Once you give the reasons why a premise is true, you will have the makings of a new argument for the premise in question. That is, you create an argument whose conclusion is one of the premises of your original argument. Such arguments are called subarguments or secondary arguments. The conclusion of a secondary argument, being a premise of the original argument, is called a subconclusion or secondary thesis. A

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secondary thesis is not the main thesis of your paper, but it is the thesis of a secondary argument supporting a premise of your main argument. With the inclusion of secondary arguments, a fuller defense of your thesis about �lu shots might look like this:

You should get a �lu shot. (Main thesis)

Getting a �lu shot will help keep you from getting the �lu. (Premise/secondary thesis)

Flu vaccines create an immune response that develops antibodies against the �lu. People with the right antibodies are less likely to suffer from a disease. Studies show that people who have had the �lu shot are less likely to get the �lu.

Getting a �lu shot also helps protect others from getting the �lu. (Premise/secondary thesis)

Flu is transmitted from person to person. The fewer infected people someone is exposed to, the lower his or her chance of getting infected.

Flu shots are cheap. (Premise/secondary thesis)

Flu shots normally cost about $10. Some places offer free �lu shots. Medicine for the �lu is more expensive than the shot.

This complex argumentative essay structure now provides a skeleton for a much longer essay. There is more to do, of course, but by starting with a structure for your argumentative essay, you ensure that your essay is well organized and focused on its thesis.

Practice Problems 9.1

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems9.1.pdf) to check your answers.

1. Which of the following is a difference between the standard argument form and that of the argumentative essay?

a. In argumentative essay form the conclusion is presented last, whereas standard argument form does not present a conclusion.

b. Standard argument form includes premises, whereas argumentative essay form does not. c. In standard argument form the conclusion is at the end of the argument, whereas in essay form the

conclusion is presented at the beginning. d. The conclusion in standard argument form is generally stronger than the conclusion in

argumentative essay form.

2. You are writing a paper about the effectiveness of for-pro�it education. You claim in your paper that “for- pro�it education provides an equally rigorous academic experience as that of nonpro�it education.” This statement would be which part of the argumentative essay?

a. thesis b. support c. secondary argument d. standard form argument e. problem

3. You are writing a paper in which you claim minor drug offenses should not result in prison sentences but in jail time and rehabilitation. In the paper, you make the claim that “an article in contemporary criminology demonstrates that placing petty criminals into prison for small crimes leads those people to

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become hardened criminals due to the conditions in those prisons.” This statement would be which part of the argumentative essay?

a. thesis b. support c. secondary argument d. standard form argument e. problem

4. You are creating an argument that people in af�luent countries have a duty to aid those who are starving or dying from treatable illness in other countries. Which of the following best represents the problem that is being addressed here?

a. Helping others is important, especially when some have more than others. b. Those who do not help others are morally inept. c. The problem is whether or not people live in the United States or a place where people are poor. d. The problem is whether or not people must help others when they have more resources.

5. You are creating an argument about whether or not pornography is healthy or harmful for people to view. Which of the following would be the best thesis for a formal paper (though you might not agree with it)?

a. Pornography is evil and will lead to the degradation of society. b. People who watch pornography are pedophiles. c. Pornography is enjoyable for those who view it. d. Pornography is harmful because it distorts images of female sexuality. e. Pornography is harmful because people’s children can view it.

6. Which is a secondary thesis that relates to the primary thesis that “citizens need to become less reliant on oil”?

a. Installing large-scale solar farms can help fuel the energy needs of large cities. b. Finding more oil reserves will provide energy for the future. c. Farming techniques continue to improve. d. Planting trees can contribute to more oxygen production.

7. Which is a primary thesis that relates to the secondary thesis that “there must be more exploration of oil reserves in the oceans”?

a. Finding more oil reserves in mountainous regions will provide energy for future generations. b. The Indian Ocean is largely unexplored. c. In order to maintain current energy usage, there need to be funds invested in �inding new reserves

of oil. d. Using electric and hybrid vehicles will allow society to move away from using oil as an energy

source.

8. Which is a secondary thesis that relates to the primary thesis that “it should be illegal for cell phone companies to track the locations of their users without consent”?

a. The government should not be allowed to monitor its citizens. b. There are new technological capabilities of large-scale Internet and phone providers. c. There are many providers, and one should shop around to �ind the right provider. d. The information gathered from tracking consumers could fall into the wrong hands.

9. Which is a primary thesis that relates to the secondary thesis that “human traf�icking turns the human into a piece of property”?

a. Turning a person into a piece of property negates their personhood. b. Human traf�icking between Mexico and the United States is morally wrong. c. Property rights exist in most countries. d. Usually women are the victims of human traf�icking.

10. Which is a secondary thesis that relates to the primary thesis that “sex education in public schools should take a more prominent role in adolescent education”?

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a. With the increased availability of sexually explicit materials and media that provide avenues for sexual activity, it is important that kids understand more about sexual activity.

b. Teaching children about forms of safer sex will encourage them to engage in such activities. c. Funding for the arts, music, and other forms of study is being lost, and legislators need to increase

the availability of funds for these activities. d. There are some areas of public education that need to be revisited and enhanced for the current

generation of high school students.

11. Which is a primary thesis that relates to the secondary thesis that “women should be allowed to engage in combat in war environments”?

a. The rights of women need to extend beyond what have been the traditionally de�ined roles. b. Many women are capable of �ighting in war. c. Many women desire to serve their countries by participating in active military engagement. d. Not to allow women to take part in battle effectively means that one is cutting out strong soldiers

from over 50% of the population.

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As you review your argument, you should evaluate the clarity of your premises. Can they be easily misunderstood? Are the de�initions of terms that are used widely accepted? Further elaboration in support of your premises may be required.

9.2 Strengthening the Argumentative Essay

With the basic outline of your argumentative essay in place, you can now turn to strengthening your argument using support and addressing objections to your argument.

Clari�ication and Support

If you have followed the process outlined thus far, you should have an introductory paragraph with a thesis and a series of topic sentences for the paragraphs of the body of your essay. The next step is to write the paragraph that goes with the topic sentence. You may need to explain what the premise means, and you will de�initely need to provide some reason for thinking it is true. When you wrote your argument in standard form, you knew what you meant by each claim. However, your meaning may not be as obvious to your reader as it is to you. It is your job, therefore, to clarify your premise, spelling out its meaning and implications. As you read each premise, try to think of ways that it might be misunderstood. Imagine someone objecting to it: What grounds could they have for doing so? What grounds can you offer for accepting it? These are things you will want to address in the paragraph.

Consider the third premise from our argument about �lu vaccines: “Flu shots are cheap.” That seems simple enough, right? But what do we mean by “cheap”? Sometimes cheap means inexpensive, but sometimes it means poorly made. We mean inexpensive, but it is not clear how inexpensive something has to be to be counted as cheap. If you think that there is a possibility that your reader may not understand precisely what you mean, use a sentence or two to elaborate. For example, you might say, “Although �lu vaccines are carefully constructed, they are not expensive” in order to let your reader know what you mean by “cheap.”

You can also clarify the premise by the way in which you provide support. As you develop your reasons for accepting each premise, your reader gains a clearer idea of what you take the premise to mean. Often, support appears in the form of a study or some type of empirical data. However, when offering empirical data as support in your essay, it is important to remember that even empirical data must be interpreted and supported, especially if they are likely to be unfamiliar to the reader or are only correlational. As we learned in Chapter 5, correlations do not offer proof for causal claims. In the case of empirical data, care must be taken to draw only from reliable

sources. (See Chapter 8 for a discussion on how to identify a reliable source.) Of course, you already know that you need to seek reliable sources at all times, but unjusti�ied or not, statistically signi�icant empirical data can easily be made to falsely appear as scienti�ically sound, so be especially cautious.

A common mistake is to think that studies and empirical data are the only accepted forms of support for a premise. While these are important types of support, there are many others. For example, commonly held beliefs can be used as support if you have good reason to think that your reader will accept them as true. Because the goal is to show your reader that your premise is true or plausible, if you can use a belief that your reader already holds, then you are off to a good start. You must be careful here, however. A belief that seems obviously true to you may seem obviously false to your reader. If you are not completely sure that your reader will agree, it is best to also cite a reliable source in support of the belief.

Many times the support you offer will appeal to theories or even broad views about the world. For example, abortion debates often center on the question of whether abortions amount to murder—the unjusti�ied killing of an innocent person. Although it is easy to show that abortions involve killing and that the fetus who is killed is innocent, it is much more dif�icult to show that the killing is unjusti�ied or that the fetus is a full person in the legal and moral senses of the term. One cannot just do a scienti�ic study on these matters, because the claims are not scienti�ic in nature. To provide support for the premise that abortions involve unjusti�ied killing, you will need to appeal to some theory or view on what makes some killings justi�ied while others are not. The best thing to do is to research what has been already advanced in the relevant area of knowledge. As we have seen, moral problems demand an examination of ethical theories. The same

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Often there is more to the truth than what we can see, what we know, or what is familiar to us. It is thus important to consider the views of others, especially if these present objections to ours, because we always have something new to learn. If such objections do not destroy our argument, then we can proceed with a well-researched rebuttal.

applies to research in other subjects. If we want to support a premise pertaining to the global warming debate, then we should use information from the research surrounding climate change.

De�initions can also provide support for and clari�ication of the premises of your argument. Claims such as “everyone deserves to die with dignity” or “abortion is a woman’s right” depend on just what is meant by the terms dignity and right, respectively. Some terms may not have an accepted de�inition even if we know what they mean. Most people, for example, �ind the word music dif�icult to de�ine, despite the fact that it is a word we all understand and may, in fact, use every day. Therefore, providing a clear de�inition of music might be an important step in supporting a premise about music.

Keep in mind that just being familiar with a term is not identical with being able to de�ine it. Neither is a dictionary the best source for more technical de�initions in an argument. Dictionaries report on common usage but do not necessarily describe how terms might be used in speci�ic �ields or debates. Even when a term is not being used in a technical sense, a dictionary is less likely to settle a dispute involving the term. Imagine two people arguing about whether a certain piece of graf�iti is art. In order to support their claims, they will need to de�ine what each means by the term art. However, just looking it up in a dictionary is unlikely to settle the dispute. Instead, they would be better off consulting a relevant technical encyclopedia—such as the Stanford Encyclopedia of Philosophy, which de�ines abstract terms such as reality, justice, morality, music, and so on—or refereed articles in scholarly journals that present developed de�initions.

This is not an exhaustive account of the forms that support may take. Anything that can be a good reason for accepting a claim can be used to support the claim. The kind of support you choose will be determined by the claim you are supporting and by what you know of your reader. For each premise, ask yourself what good reason you can offer your reader for agreeing with the premise. Do you need to provide empirical data, address your reader’s beliefs, include background theories, offer de�initions, or something else? As you might guess, this often involves forming a sort of mini argument in support of the topic sentence. Applying what we have learned about arguments can help you choose strong support for your claims.

The Objection

The objection is the most damaging criticism that can be advanced against your own thesis. In longer argumentative essays, it might be necessary to address more than one objection. But in any argumentative essay, you will need to propose at least one objection. Why is this necessary, given that it sounds contradictory to your purpose? Actually, being able to present a damaging objection and a successful rebuttal is a powerful way to demonstrate the unassailability of your thesis.

Presenting an objection shows your reader that you are aware of both sides of the issue, and this adds credibility to your presentation. For this reason, it is important to select a strong objection and to present it in a way that takes the objection seriously. If you present a weak objection, or if you present an objection in a way that seems not to take it seriously, then you give the impression that your own conclusion is not based on an even evaluation of all the relevant factors. You also may end up committing the straw man fallacy. (See Chapter 7 for a review of the straw man fallacy.) In order to avoid this impression, you must become very familiar with your topic by means of your research on the subject. This includes not only literature that supports your view, but also literature that challenges it.

Moral of the Story: The Objection

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Always present at least one strong objection to your thesis. Doing so shows that you are knowledgeable about your subject and care more for �inding the truth about it than merely promoting your own view.

The Rebuttal

The rebuttal is the section in your essay in which you respond to the objection(s) presented. To fail to address the contrary claim (that is, the objection) amounts to committing the red herring fallacy. (See Chapter 7 for a review of the red herring fallacy.) Your goal should be to advance a strong rebuttal, and it must attempt to overcome the objection. You cannot be timid in rebutting an objection that could destroy your argument. In addition, you have to provide support for your rebuttal.

However, suppose you �ind that, try as you might, you are not capable of coming up with a defensible rebuttal. Should this happen, you might have to start anew. The �irst step will be to rethink your thesis and your position in the argument in general. After additional thorough research on the subject, you will be in an even better position to reexamine your position because you will be better informed than when you �irst started. Do not be afraid, though. True beliefs will stand scrutiny. Yet as a critical thinker, you may �ind that one or more of your beliefs are not defensible. Or you may �ind that the opposition is too daunting to match. There is no shame in this. We are all mistaken about one thing or another at some point in our lives. Acknowledging when an objection cannot be overcome is indeed an expression of an examined life and, as Socrates stated, only an examined life is worth living.

If you �ind yourself in a situation in which you cannot overcome an objection, one response is to accept defeat and change your argument in response to the good objection. In this case you then repeat the process of considering objections to the new version of your argument until you have a version that can withstand its strongest objections. This revised argument then serves as the basis for rewriting your essay. Another possibility is to hold to your reasoning while acknowledging the strength of the objection. In this case you can acknowledge good objections within your essay while making a case for your own interpretation of the evidence for your conclusion. This kind of intellectual humility can actually demonstrate that your goal is not just to be right, but to �ind the truth. Either way, you win in terms of wisdom and not losing sight of the fundamental importance of seeking truth.

Closing Your Essay

Once you have demonstrated your thesis, how should you close your essay? It is a common mistake by many writers to assume that the closing of any essay, argumentative or otherwise, is a summation of what was presented in the essay from beginning to end. The strategy of closing an essay with such a summation is not only a little boring for the reader; it also misses the point of the argumentative essay. In an argumentative essay once the thesis has been demonstrated by means of premises and support, the job is done. There is no need to repeat how the thesis was demonstrated.

Consider the following example:

In conclusion, I have mentioned the following facts about my life. Ten years ago, I would have never believed that I would be living in the United States and communicating in English on a daily basis. I could not have imagined that I would be in university, much less doing scholarly research and writing in English. But here I am, writing this paper for my �irst class. As I have also mentioned, I am declaring an English major, and time will tell how far my studies will take me.

The ending, no doubt, has a charming sentiment. It is not, however, a proper ending for an argumentative essay or perhaps for most essays. Some exceptions might include a university lecture, in which it would be important to repeat the points covered or otherwise review instructional material. Notice, however, that if we replace the word conclusion in the quote with the word summary, the meaning does not change. This reveals that the word conclusion is employed to mean summary in this case. Beware of confusing the word conclusion in this context with the word conclusion as employed in a logical argument. Here the word conclusion refers to the closing of the essay. In the standard argument form, the word conclusion is the equivalent of the thesis in the argumentative essay. The thing to keep in mind is that argumentative essays do not need summaries to close.

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Argumentative essays do not need lengthy closings, either. A handful of sentences that present your re�lections of what the essay has attempted to accomplish will do the job. You can explain, for example, how the thesis would make a change in the problem that you laid out in the introduction, propose the direction in which the thesis could be taken, or consider the additional research or work that would be necessary to come closer to solving the problem. Above all, never add new information that may throw additional light on the problem or the thesis that you are defending, for this will weaken a good argument by begging the question. (See Chapter 7 for a review of the begging-the-question fallacy.) You must state all that you have to say in defense of your thesis in the body of your essay. The ending should attempt only to cast a positive light on your contribution in very broad strokes.

Practice Problems 9.2

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems9.2.pdf) to check your answers.

1. If you are writing a paper about the legality of immigration and you are arguing that immigration laws should be relaxed in this country such that illegal immigrants should not be deported, the portion of the paper where you cite a well-known economist who outlines the costs in health care and aid of increased immigration would be which part of the argumentative essay?

a. thesis b. support c. premises d. objection e. rebuttal

2. You are writing a paper in which you claim minor drug offenses should not result in prison sentences but in jail time and rehabilitation. You further explain the claim by stating, “Surveys of criminals with minor drug charges indicated that 70% of them had to commit even greater crimes in prison to maintain their safety.” This statement would be which part of the argumentative essay?

a. thesis b. premise c. support d. rebuttal e. problem

3. Which would be the best support for the claim that “police of�icers in St. Louis systematically target African Americans when policing the city”?

a. a peer-reviewed journal article that indicates that false arrests of African Americans are 80% higher than for Latinos and Whites in the city

b. a story on the news with interviews of two African Americans who live in St. Louis c. a Twitter feed that shows police pepper-spraying a crowd of protestors d. a newspaper article that outlines a case in which an of�icer pulled over an African American woman

and assaulted her

4. The portion of the essay in which the writer attempts to refute the counterargument is called the __________. a. thesis b. support c. objection d. rebuttal e. problem

5. When ending an argumentative essay, it is best to __________. a. restate exactly what you have said earlier in the paper in a shorter format b. explain a �inal problem that relates to the thesis that you created c. add additional information that relates to the problem

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d. make short comments about how your solution could lead to further research

6. What is the best support for the premise that “cover crop farming enhances productivity of plants”? a. a conversation you had with a farmer who uses cover crop methods of farming b. a news report from the local news channel on farmers in the region using cover crop techniques c. a chapter in an academically published book that claims that productivity of cotton plants on a

cover crop farm was 18% higher than one that did not use this method d. an article in a peer-reviewed journal article that claims that cover crop farms do not statistically

produce signi�icantly larger crops than noncover crop farms

7. When presenting the rebuttal in an argumentative paper, it is important to do which of the following? a. Make your opponent’s argument look ridiculous. b. Make negative comments about the opposing view. c. Attack the opponent’s strongest argument. d. Turn the attention off the counterargument and toward something else.

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9.3 Practical Arguments: Building Arguments for Everyday Use

The standard argument form is not the only framework we can use to build arguments. Stephen Toulmin (1958/2003), a philosopher and author of The Uses of Argument, developed a model of argumentation that he considered more practical: Rather than attempt to present premises that lead to an absolute, uncontested conclusion—a dif�icult, perhaps impossible challenge—an argument should simply seek to show the strengths and limitations of a point of view to get closer to the truth. Although the Toulmin model has not attracted much attention within philosophy or logic, it is widely used in �ields focused on rhetoric. If you have not seen this model already, it is likely that you will come across it in an English or communications course. Because the model is so prevalent in other �ields, we will take a bit of time to examine how it relates to the approach taken in this text.

In our analysis thus far, arguments have been described as consisting of premises, conclusions, and inferences. Toulmin’s analysis uses different basic parts. For Toulmin, the core of an argument consists of a claim, data, and a warrant. (The Toulmin model actually has three additional minor parts, but for our purposes, it is enough to understand the basic framework so we can compare it with the standard form and the argumentative essay framework.) As with other terms we have explored in this text, be aware that within the Toulmin model claim, data, and warrant have speci�ic meanings that may be different than their meanings in other contexts.

The Claim

The claim in the Toulmin model of argumentation has the same role as the conclusion in the standard argument form or the thesis in the argumentative essay. It is the proposition that is being argued for, the main point of the argument.

The Data

In the Toulmin model the term data refers to the basic support for the claim. Arguments very often appeal to certain evidence, facts, or statistics in support of their claims. If you want to argue that gun laws should be made more (or less) strict, you are likely to cite studies that draw a relationship between gun laws and crime rates. If you are prosecuting (or defending) someone accused of a crime, you will appeal to circumstances of the crime scene or facts about the defendant. For the most part, evidence, facts, and statistics are the starting point of an argument. They are themselves reasonably uncontroversial; the dispute typically involves what follows from them.

The Warrant

The warrant is the reasoning that links the data to the claim in the Toulmin model. The warrant is needed because there is always a gap between the evidence and the conclusion. Suppose that you have a study that shows that some countries with higher rates of gun ownership have lower gun-related crime rates than the United States. By itself, this study does not automatically show that stricter gun laws would be ineffective at reducing violent crime in the United States. After all, the United States may differ from the countries in the study in many ways. So you need some principle that links your basic evidence to your conclusion. In this case you might assert that a law’s effect is likely to be similar even when countries differ. Thus, you could argue, the study can be taken to imply that stricter gun laws are unlikely to reduce gun crimes in the United States. The point of the warrant is to support the inference from the data to the claim, not the claim itself. Notice in Figure 9.1 that the arrow from the warrant points to the arrow between the claim and the data, and not to the claim itself.

You should also note that warrants in the Toulmin model are sometimes left unstated. Warrants are often assumed background knowledge and need to be made explicit only when challenged or when there is reason to believe that the audience may not be familiar with them. If you already accept or know that a law will have a similar effect in a different country, then that warrant would not need to be stated. If your audience does not accept your warrant, though, you may need to provide further backing, as Toulmin called it, to support your claim. Data, on the other hand, are given explicitly when presenting an argument.

Figure 9.1: The Toulmin model

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In the Toulmin model, warrants provide support for the connection from the data to the claim. The warrant does not directly support the claim.

Comparing the Models

How, then, does the Toulmin model compare to the standard argument form and the argumentative essay? (See Table 9.2.) We have already noted that Toulmin’s claim is what we have been calling a conclusion in the standard argument form and the thesis in the argumentative essay. Thus, his data will similarly be equivalent to premises. However, it is more dif�icult to say how Toulmin’s warrant translates to our argumentative essay model. Most of the time, it will be a premise, but occasionally, it will be better classi�ied as an inference.

Remember that the warrant is often unstated in Toulmin’s model. When the warrant is explicitly stated, logic would treat it as a premise. Logic does not make a general distinction between types of premises, as Toulmin does between data and warrants. When the warrant is not stated but reasonably could be stated, then it is still a premise, just an unstated one. For example, consider the argument “John studies logic; he must be very intelligent.” In the Toulmin model the claim is that John is very intelligent, and the data is that John studies logic. The warrant is not stated but seems to be something like “Only intelligent people study logic.” From the standpoint of logic, “Only intelligent people study logic” is just another premise. It is very common for real-life arguments to have unstated premises.

On the other hand, suppose a friend claims that all logicians are boring. You disagree and argue, “Lewis Carroll was a logician and he wasn’t boring. So not all logicians are boring.” Here your data is that Lewis Carroll was a logician who was not boring. Your claim is that not all logicians are boring. What is your warrant? If you try to state it, you will end up with something like “Whenever there is at least one thing that is a non-boring logician, then not all logicians are boring.” Or perhaps you will end up with the more general “Whenever something is both A and not B, then not all A are B.” In either case you do not really have a premise, you just have a statement that the inference from the premises to the conclusion is logically acceptable. For complicated reasons, we cannot fully reduce these types of rules to premises. So in the rare case that the data by themselves actually fully imply the claim, then the warrant is not a premise but just a rule of logic.

Table 9.2: Comparing the models

Toulmin model Standard argument form Argumentative essay

Claim Conclusion Thesis

Data Premises Topic sentences

Warrant Premise or inference Topic sentence or support

Obviously, in a classroom situation, you should use the model of argument that your teacher prefers. Outside the classroom, you are free to use the one that you �ind most helpful. We have focused primarily on the premise–conclusion model in this text since it is the model overwhelmingly used in logic and philosophy, but there is merit in other models, too. (The “Web Resources” section at the end of this chapter links to more information about the Toulmin model, as well as others.) The Toulmin model does a good job of capturing something like our everyday notion of evidence for a claim. However, differentiating between data and warrant can sometimes obscure the very similar role that each can play in

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supporting a conclusion. Sometimes it works better just to list the premises that lead to a conclusion without making further distinctions.

Moral of the Story: Comparing Models of Argumentation

The study of argumentation is very broad with many different approaches. Learn what you can of each approach as you encounter it and use it to improve your own arguments.

Practice Problems 9.3

Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems9.3.pdf) to check your answers.

1. In the Toulmin model of argumentation, the warrant is __________. a. the evidence that one can use to support a claim b. the data points that support the thesis c. the thesis for which one is trying to argue d. the portion that supports the relationship between data and claim

2. If one presents data that indicates that same-sex marriage contributes $50 million to the economies of states in which it is legal, which of the following would be the most accurate corresponding claim that would be supported?

a. Marriage between same-sex partners should be legal. b. Marriage between same-sex partners should be illegal. c. Marriage is a sacred union between two people. d. Same-sex marriage has positive economic impact on communities.

3. If one were arguing for military action against a dictatorship and provided evidence that this regime had killed 40,000 of its own citizens because they dissented to the ruling party, what would be the warrant operating under this connection of data and claim?

a. We should take action against countries that control large amounts of oil. b. Governments that kill their own citizens in this manner are acting in a manner that must be

stopped. c. We have the right to stop this country from killing its own citizens. d. The people of that country should continue to stand up against the regime and attempt to

overthrow it.

4. If you make the claim that national public campaigns on obesity should be used in the United States based on evidence from Germany that its national public campaigns resulted in an 8% decline in obesity, what would be the warrant between the claim and the data?

a. Germany and the United States have the same public campaigns. b. Germany and the United State ought to have the same public campaigns. c. Germany and the United States both have high levels of obesity. d. Germany and the United States are similar enough that similar results will occur.

5. If I present data that indicates that Ebola is spreading rapidly and has a 70% death rate, and my warrant is that deadly diseases should be top priority in world health action, what would be the most accurate claim being defended?

a. Ebola is a deadly disease that kills many people it infects. b. Deadly diseases should be top priority in world health action.

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c. The World Health Organization needs to immediately respond to the Ebola outbreak. d. Other diseases like AIDS require immediate attention.

6. If I claim that Seinfeld was the greatest television show ever, and then I present data that indicates that it has sold the highest number of DVD copies of any other show ever produced, what would be the warrant operating under this connection?

a. Television shows that have no plot are the best shows. b. Greatness in a television show can be linked to pro�itability. c. Seinfeld had excellent characters and actors. d. Greatness in a television show can be measured by the level of performance.

7. If my claim is that genetically modi�ied plants should be restricted until more research about their safety has taken place, and my warrant is that academically published articles are examples of the highest form of support, which of the following would be the most applicable data?

a. an academically published book that argues that genetically modi�ied plants have the potential to eradicate world hunger

b. a newspaper article that explains the plight of farmers who cannot save seeds due to genetically modi�ied soybean plants

c. an academically published article that provides evidence that genetically modi�ied tomatoes have been linked to infertility in women in a speci�ic region of the United States

d. an academically published article that provides evidence that there was no higher incidence of diseases like cancer in people who ate genetically modi�ied plants over time versus those who did not

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Chris Wildt/Cartoonstock

By employing the principles of accuracy and charity, and by effectively criticizing arguments, there can be constructive disagreement that avoids heated emotions and verbal aggression.

9.4 Confronting Disagreement

Mastering the skills of identifying and constructing arguments is not easy, but at this stage you should feel fairly con�ident in your command of such skills. The big test now is how you will react when someone disagrees with your argument or when you disagree with someone else’s argument. Although advancing an argument does not require an interaction, as mentioned in Chapter 2, disagreements are bound to occur. Many of us likely prefer to avoid disagreements. Indeed, many people are terri�ied of debating a point because they fear offending others or worry that a debate will only bring out the worst in everyone, quickly escalating into an emotional display of verbal aggression and “I’ll show you!” attitudes on both parts. Few truly gain from or enjoy such an exchange. This is why most people avoid addressing touchy subjects during holiday dinners: No one wants a delicious meal to end with unpleasantness. However, few gain from allowing contested issues to go unchallenged, either, whether you are simply stewing in resentment over your uncle’s unenlightened remark about a group of people or whether society fails to question a wrongheaded direction in public policy. Not knowing how to disagree in a calm, productive manner can be quite problematic. We should recognize, however, that some do like the tension of the battle and �ind the raising of voices and the test of quick retorts very exciting. Even so, all they gain is the con�irmation that they can win by being the loudest, most articulate, or most aggressive. Unfortunately, this is an illusion, since quieting the opposition does not amount to having convinced them.

The solution to this common problem is threefold. The �irst part involves clearly articulating premises, examining the coherence of the argument, and identifying the support for each claim. This part is the

most technically dif�icult but is already within your reach, thanks to the standard argument form. As we have discussed throughout this book, being able to draw an argument buried underneath �iller sentences, rhetorical devices, and such allows us to grasp the meaning and coherence of what is being communicated. In this section, we will closely examine another factor in identifying arguments: the correct interpretation of an argument. We will call this the principle of accuracy.

The second part is not technically dif�icult, because it is an attitude or state of mind. In ordinary idiomatic language, it is referred to as giving a person the bene�it of the doubt, letting someone have his or her say, or putting suspicion aside. In other words, we should judge others and their ideas fairly, even if we may be less than inclined to do so. Philosophers call this attitude the principle of charity.

Finally, the third part involved in handling disagreement is developing good habits of criticism. Evaluating an argument effectively requires understanding the types of objections that might be raised and how to raise them effectively. This understanding can be equally helpful in recognizing criticisms that our own arguments may receive and criticizing opposing arguments effectively.

Applying the Principle of Accuracy

The principle of accuracy requires that you interpret the argument as close to how the author or speaker presents it as possible. Being accurate in your interpretation is not as easy as it may sound.

As we examined in Chapter 2, arguments are typically not presented in standard form, with premises and conclusion precisely stated. Instead, they may be drawn out over several pages or chapters or occasionally even distributed across different portions of an author’s work. In these sorts of cases, accurately interpreting an argument can require careful review of the work in which it occurs. Accurate interpretation may require familiarity with the author’s other works and

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amanaimagesRF/Thinkstock

Applying the principle of charity means to set aside our con�idence in our expertise and to be open to entertaining the positions presented by others by doing a fair reading of the argument provided.

the works of other authors with similar views. Knowing an author’s broader views can give us a better idea of what he or she means in a speci�ic case. Some academics spend their entire careers trying to clearly and accurately understand the work of important authors who were themselves trying to be as clear as possible.

At the other end of the spectrum, arguments can be presented in ways that give us very little to go on. A letter to the editor is short and self-contained but is often not stated clearly enough for us to really be certain about the details of the argument. If you are lucky enough to hear an argument presented verbally, you may be able to ask for clari�ication, but if the argument is written, then you are out of luck and have to go through the effort of attempting to �igure out what the author meant to say in its best light.

As discussed in Chapter 2, it is often not only tempting but also necessary to reword or paraphrase a claim. The principle of accuracy requires that you exercise a lot of care in doing this. Sometimes one can unintentionally change the meaning of a claim in subtle ways that affect its plausibility and what can be inferred from it.

In short, the principle of accuracy requires that you interpret any argument as closely as possible to the actual statement of the argument while paying attention to features of context. One test for assessing whether you have correctly presented another person’s argument is whether that person is likely to agree with your wording. This often involves making sure that you have interpreted the person favorably.

Applying the Principle of Charity

The principle of charity is likewise easy to understand but harder to apply. In being charitable philosophically, we seek to give our opponent (and his or her corresponding argument) our utmost care and attention, always seeking to understand the position presented in its strongest and most defensible light before subjecting the argument to scrutiny.

We tend to see the good in arguments that include conclusions we agree with and the bad in arguments that include conclusions we disagree with. When someone on our side of an issue presents an argument, we are prone to read their argument favorably, taking the most charitable interpretation as a matter of course. Think of how you respond when considering your choice for a candidate in an election. Do you tend to interpret more favorably the words of candidates who are members of your own political party, those who support positions that bene�it you personally, or even those whom you might �ind most visually appealing? Do you see positions different from yours as silly or unfounded, perhaps even immoral? If so, you may need to be more charitable in your interpretations. Remember that many intelligent, sincere, and thoughtful people hold positions that are very different from yours. If you see such positions as not having any basis, then it is likely you are being uncharitable. These tendencies are the manifestation of our biases (see Chapter 8), and ignoring them may lead to the entrenchment of our biases into dogmatic positions or fallacious positions. For example, if you criticize an argument based on an uncharitable interpretation, this can be considered a case of the straw man fallacy (see Chapter 7).

Our tendency to be overly critical of arguments for positions we disagree with is deep-rooted, and it requires a lot of effort and psychological strength to overcome. But the mechanics are simple: Suspend your own beliefs and seek a sympathetic understanding of the new idea or ideas. The principle of charity can become a habit if we approach it methodically, as follows:

1. Approach new or opposing ideas under the assumption that they could be true, even though our initial reaction may be to disagree.

2. Make it a goal to understand the opponent’s argument, instead of nitpicking and looking for contradictions or weaknesses.

3. Consider the strongest argument for the opposition instead of the weakest argument for it.

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Given how dif�icult it can be to charitably interpret arguments, you might wonder whether it is worth the effort. However, there are good reasons for being charitable.

First and foremost, it is important to remember that the goal of logic is not to win disputes but, rather, to arrive at the truth. We have reason to believe that the conclusions of stronger arguments are more likely to be true than the conclusions of weaker arguments. If we wish to know the truth of an issue, we should examine the best arguments that we can �ind on both sides. If we do this and notice that one side’s arguments are stronger than the other’s, then we have good reason for adopting that side of the issue. On the other hand, if we do not look at the strongest argument available, then we will have little reason to be con�ident in our �inal decision. Being uncharitable in interpreting others may help you score points in a dispute, but there is no reason to think that it will lead you to the truth of the matter. (For more discussion of this important point, see Chapter 7.)

Second, by making a habit of applying the principle of charity, you develop the skills and character that will help you make good decisions. As people come to recognize you as someone who is fair and charitable in discussions, you will �ind that they are more willing to share their views with you. In turn, your own views will be the product of a balanced look at all sides, rather than being largely controlled by your own biases.

Balancing the Principles of Accuracy and Charity

Consider This: Suspending Judgment

NEXT

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When it is dif�icult to balance the principles of accuracy and charity, try to be more charitable in your interpretation, especially in more informal settings and discussions.

DimaSobko/iStock/Thinkstock

The process of criticizing an argument is similar to a chess game. Both require an analysis of the strengths and weakness of your opponent’s position and a determination of whether the premise, or

If arguers always presented the strongest arguments available and did so in a clear and organized fashion, there would be little problem applying the principles of accuracy and charity. Unfortunately, we all sometimes present arguments that are not as strong as they could or should be. In these cases the two principles work can against each other—that is, the most charitable interpretation may not be the most accurate.

In general, the principle of charity should be given more weight than that of accuracy. This is especially true when the arguments are presented in less formal settings. By giving people the bene�it of the doubt and treating their views as charitably as possible, you will earn a reputation as someone who is more interested in productive discussions than in scoring points. You will have a lot more discussions this way, and both you and the other people involved are likely to learn a lot more. In informal settings, it is best to assume that people are making a stronger argument, rather than trying to hold them to precisely what they say.

The situation is somewhat different when interpreting arguments in academic writing such as journal articles. Journal articles are written carefully and revised many times. The authors are committing themselves to what they say and should understand the implications of it. Nonetheless, it is still good to be charitable when possible, but following the author’s exact presentation is more important than it is in less formal settings. In cases in which you are primarily examining an argument made by a single author in a published article and in which you are trying to judge how well the argument works, accuracy is paramount. Still, be as charitable as the circumstances allow.

Practicing Effective Criticism

The principles of charity and accuracy govern the interpretation of arguments—they help you decide what the argument actually is. But once you have �igured out what the argument is, you will want to evaluate it. In general, evaluating the strengths and weaknesses of arguments or other works is known as criticism. In everyday language, criticism is often assumed to be negative—to criticize something is to say what is wrong with it. In the case of argumentation, however, criticism means to provide a more general analysis and evaluation of both the strengths and weaknesses of an argument. This section will focus on what constitutes good criticism and how you can criticize in a productive manner. Understanding how to properly critique an argument will also help you make your own arguments more effective.

When criticizing arguments, it is important to note both the strengths and weaknesses of an argument. Very few arguments are so bad that they have nothing at all to recommend them. Likewise, very few arguments are so perfect that they cannot be improved. Focusing only on an argument’s weaknesses or only on its strengths can make you seem biased. By noting both, you will not only be seen as less biased, you will also gain a better appreciation of the true state of the argument.

As we have seen, logical arguments are composed of premises and conclusions and the relation of inference between these. If an argument fails to establish its conclusion, then the problem might lie with one of the premises or with the inference drawn. So objections to arguments are mostly objections to premises or to inferences. A handy way of remembering this comes by way of the philosophical lore that all objections reduce to either “Oh yeah?” or “So what?” (Sturgeon, 1986).

Oh Yeah? Criticizing Premises

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chess piece, is central to your opponent’s argument or strategy.

The “Oh yeah?” objection is made against a premise. A response of “Oh yeah?” means that the responder disagrees with what has been said, so it is an objection that a premise is either false or insuf�iciently supported.

Of course, if you are going to object to a premise, you really need to do more than just say, “Oh yeah?” At the very least, you should be prepared to say why you disagree with the premise. Whoever presented the argument has put the premise forward as true, and if all you can do is simply gainsay the person, then the discussion is not going to progress much. You need to support your objection with reasons for doubting the premise. The following is a list of questions that will help you not only methodically criticize arguments but also appreciate why your arguments receive negative criticism.

1. Is it central to the argument? The �irst thing to consider in questioning a premise is whether it is central to the argument. In other words, you should ask, “What would happen to the argument if the premise were wrong?” As noted in Chapter 5, inductive arguments can often remain fairly strong even if some of their premises turn out to be incorrect. Sometimes a premise is incorrect, but in a way that does not really make a difference. For example, consider someone who advises you to be careful of boiling water, claiming that it boils at 200°F and 200°F water can cause severe burns. Technically, the person’s premises are false: Water boils at 212°F, not at 200°F. This difference does not really impact the person’s argument, however. The arguer could easily correct the premise and reach the same conclusion. As a result, this is not a good place to focus an objection. Yes, it is worth mentioning that the premise is incorrect, but as problems go, this one is not very big. The amount of effort you should put into an objection should correlate to the signi�icance of the problem. Before putting a lot of emphasis on a particular objection, make sure that it will really impact the strength of the argument.

2. Is it believable? Another issue to consider is whether a premise is suf�iciently believable. In the context in which the premise is given, is it likely to be accepted by its intended audience? If not, then the premise might deserve higher levels of scrutiny. In such cases we might check to make sure we have understood it correctly and check if the author has provided further evidence for the strong claim in question. This can be a bit tricky, since it depends on several contextual issues. A premise may be acceptable to one audience but not to another. However, realize that it is just not possible to fully justify every premise in an argument. Premises are the starting points for arguments; they are statements that are presented as suf�iciently believable to base an argument on. Trying to justify every premise would introduce even more premises that would then have to be justi�ied, and so on. If you are going to challenge a premise, you should typically have speci�ic reasons for doing so. Merely challenging every premise is not productive. If you identify a speci�ic premise that is central to the argument yet insuf�iciently supported, you should make a mental note and move forward. If you are able to converse with the proponent of the argument, then you can ask for further justi�ication of the premise. If the proponent is not available to question—perhaps because the argument occurs in an article, book, or televised speech—then you should formulate some reasons for thinking the premise is weak. In essence, the burden is on you, the objector, to say why the premise is not suf�iciently believable, and not on the proponent of the argument to present premises that you �ind believable or suf�iciently supported. Never escalate your beliefs into accusations of lying or fraud. If you believe that the premise is false, the most productive next step is to come up with reasons why the premise is not suf�iciently plausible for the context of the argument.

3. Are there any quali�iers? A quali�ier is a word or phrase that affects the strength of a claim that a premise makes. Consider the difference between the statements “Humans are the cause of the current climate change” and “It is at least possible that humans are the cause of the current climate change.” While addressing the same point, these two statements have very different levels of believability. The quali�ier phrase “it is at least possible” makes the second statement more acceptable than the �irst. Whatever your view on the causes of climate change, you should see the second statement as having more going for it than the former, because the second statement only makes a claim about what is possible. Accordingly, it claims much less than the �irst one. If the �irst claim is true, the second one is also, but the second claim could be true even if the �irst turned out to be false. In focusing an objection on a premise, you need to be sure that your objection takes into account the quali�iers. If the premise is the second claim—”It is at least possible that humans are the cause of the current climate

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change”—then it would make little sense to object that it has not been fully proved that humans are the cause. Quali�iers can affect the strength of premises in many ways. The lesson here is that you need to be very clear about exactly what is being claimed before objecting to it. Sometimes premises take the form of hypotheticals—that is, sentences stating assumed situations merely for the sake of argument. Suppose that someone is arguing that the United States should aggressively pursue investment in alternative energy. Such a person might present the following argument as part of a larger argument: “Suppose climate change really is caused by humans. If so, then investing in alternative energy would help reduce or slow climate change.” If you happen to think climate change is not caused by humans, you might be tempted to object to the �irst premise here. That would be a mistake, since the premise is framed as a hypothetical. The author of the argument is only making a point about what would follow if the claim were true. It must be clear that in this context the author of the argument is not claiming that the �irst premise is true. The line of reasoning might continue as follows: “On the other hand, suppose that humans are not changing the climate. The increase in carbon in the atmosphere still shows that our energy production can only continue so long as we have carbon to burn on the ground. We would be well advised to �ind other alternatives.” Here, one might be tempted to object that humans are part of the cause of climate change. Again, this would be a mistake. The claim that humans are not changing the climate is also used here only as a hypothetical.

So What? Criticizing Inferences Even an argument with unobjectionable premises can fail to establish its conclusion. The problem in such cases lies with the inferences. Objecting to an inference is like saying, “So what if your premises are true? Your conclusion doesn’t follow from them!” Of course, “So what!” is neither the best feedback to receive nor the best response to offer to an opponent. A better method of showing that an argument is invalid is to offer a counterexample. Recall from Chapter 3 that a counterexample is a strategy that aims to show that even if the premises of an argument are true, the conclusion may very well be false. Counterexamples do not have to be real cases, they just have to be possible cases; they have to show that it is possible for the premises to be true while the conclusion is false—that the premises do not absolutely guarantee the conclusion.

Beware, however, that counterexamples work best for deductive arguments and do not work as decisively when the argument is inductive. This is because true premises in inductive arguments at best show that the conclusion is probably true, but this is not guaranteed as it is with deductive arguments. Thus, showing that it is merely possible that the premises of an inductive argument are true while its conclusion is false does not undermine the inference. The best that can be done in the case of inductive arguments is to show that the conclusion is not suf�iciently probable given the premises. There is no single best way to do this. Because each inductive argument has a different strength and may be based on a different kind of reasoning, objections must be crafted carefully based on the speci�ics of the argument. There are, fortunately, some broad guidelines to be offered about how to proceed.

First, be clear about just how strong the argument is supposed to be. Remember the contrast between claiming that “Humans are the cause of the current climate change” versus “It is at least possible that humans are the cause of the current climate change.” Many objections fail because they assume the argument is intended to be stronger than it is. Any objection to an inductive inference basically claims that the premises do not make the conclusion as likely as the arguer proposes. If the arguer is misinterpreted on this point, the objection will miss its mark.

Next, try to identify the style of reasoning used in the inductive argument. Chapter 5 presents several different forms of inductive reasoning. If the argument uses one of those forms, make sure that the argument follows the pattern shown. Look for any way in which the argument deviates from the pattern; these are points for possible objections.

Finally, consider whether the argument contains reasoning that is fallacious. A number of fallacies are discussed in Chapter 7. Remember that just pointing out a fallacy does not show that the conclusion of the argument is false. It can only show that the conclusion is not suf�iciently supported by that speci�ic argument.

Practice Problems 9.4

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Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems9.4.pdf) to check your answers.

Determine whether the following situations involve the principle of charity or accuracy.

1. Even though you agree that abortion should be illegal, you confront your cousin when he says that women who have had abortions are murderers. You claim that they might have other reasons or circumstances in their lives that have contributed to their decisions.

2. You are engaging in a debate about just war with a friend. Your friend claims that one of the premises of just war theory is that “a nation can act against another nation in whatever manner available so long as the other nation acted aggressively �irst.” You correct your friend and claim that just war theory really only says that a nation cannot act in any manner available but only in a manner that is proportional to the injury suffered from the other side.

3. Your friend is upset because he received a �ine from a record company that was suing people who downloaded music for free. He claims that “record companies just care about making money, and they are willing to go after regular people who aren’t hurting anyone.” You claim that record companies employ many people whose jobs would be in danger if their music were given away for free, and you suggest that perhaps record companies are simply trying to protect their employees.

4. You are arguing with a friend about the existence of God. Your friend proposes an argument for God’s existence that has been improved in a recent philosophical publication. Rather than attack the old argument, you strengthen your friend’s position by explaining the new development in relation to the argument.

5. You are arguing with a coworker about animal rights, animal suffering, and whether humans should harvest animals and eat them. You have taken the position that eating animals is acceptable. In supporting her position, your coworker claims that more than 2 billion animals are slaughtered for consumption in the Western world each year. You correct her and say that actually, more than 3 billion animals are slaughtered per year.

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Dorling Kindersley/Thinkstock

As in the example of evolution, objections that claim an inductive argument is not suf�iciently strong require that you thoroughly examine the initial argument, objection, and wording, so that you can draw a conclusion about the strength of the criticism.

9.5 Case Study: Interpretation and Criticism in Practice

Since most scienti�ic arguments are inductive, it can be instructive to look at how some common objections to scienti�ic theories fail from logic’s point of view. Consider, for example, an argument against the theory of evolution based on the idea that there are gaps in the fossil record. A simple version of the objection is given by John Morris (2011), president of the Institute for Creation Research: “The fossil record gives no clue that any basic type of animal has ever changed into another basic type of animal, for no undisputed chain of in-between forms has ever been discovered” (para. 3).

Examining the Initial Argument

Setting aside the question of whether Morris’s claim about the fossil record is correct, how does it fare as an objection to evolution in terms of logic? The �irst thing to note is that, like most scienti�ic claims, the theory of evolution is based on inductive reasoning. Although scientists do claim that evolution is true, they do not afford it the same status as mathematical theorems. It is fairly easy to see that it is at least theoretically possible that all the evidence could be as it is and yet evolution be false. Since the reasoning is inductive, the question is whether Morris’s objection shows that evolution is not suf�iciently likely, given the evidence for it.

A question that arises immediately is, how much evidence is required to overcome Morris’s objection? There is no precise answer to this question, since the arguments for evolution are typically not of the sort to establish a de�inite numerical likelihood. We cannot give a precise calculation of just how likely evolution is, given the evidence for it. Instead, we rely on quali�iers such as very likely and overwhelmingly likely and on comparisons to the likelihood of other scienti�ic theories. This is not at all unusual. Precise numerical statements of probability are typically available only in arguments based on statistics.

The argument for evolution based on the fossil record is not that sort of argument. Instead, we can view the argument as an inference to the best explanation (discussed in Chapter 6). We see differences and similarities among living animals and fossils. The similarities are close enough that we can group animals into families and arrange fossils chronologically to show change within a group. A good account of such an arrangement in the case of horses is available at the website for the Florida Museum of Natural History at http://www.�lmnh.u�l.edu /natsci/vertpaleo/�hc/Stratmap1.htm (http://www.�lmnh.u�l.edu/natsci/vertpaleo/�hc/Stratmap1.htm) and associated pages. The fact that the fossils can be neatly arranged in this way seems to cry out for an explanation. Evolution is the best explanation we have for this fact, so we conclude that evolution is likely to be correct. Just how likely it is to be correct depends on just how much better an explanation it is than the alternatives and just how much we see the fossil record as requiring an explanation.

Examining the Objection

Morris claims that there is “no undisputed chain of in-between forms” from one kind of animal to another. It is not clear whether he would take the extinct genus Eohippus to be the same basic type of animal as a modern horse. For the sake of argument and analysis, let us suppose that he takes them to be different types of animals and also grant that the fossil sequence shown in the Florida Museum of Natural History’s graphic has gaps. What effect would this have on the argument for evolution?

Morris’s objection is aimed at the degree to which the facts require an explanation and not at whether evolution is the best explanation of the facts. However, whether or not the fossil record contains gaps, it is still remarkable that animals that do not come from one another should show such a plausible set of transformations. We would not normally expect unrelated animals to be able to be arranged in such a way. So even with gaps, the fossil record needs an explanation. Pointing out gaps does not change that. Nor does pointing out gaps show that another theory better �its the evidence than does evolution. Even if we grant Morris’s main point, evolution remains the best available explanation of a rather remarkable fact. Of course, if the number of intermediate fossils were greatly decreased, then other explanations might be more successful in explaining the record. A complete, gapless record

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of transitional fossils would provide even more support for evolution because it would make it more dif�icult for any competing explanations to be correct. However, the fossil record supporting horse evolution has enough in it to provide a strong argument for evolution even if there are some gaps. So, as an objection to an inference to the best explanation, Morris’s claim is really not very good.

Examining the Wording

Morris says that the fossil record “gives no clue” that one basic type of animal has changed into another. So, as he states it, he takes his objection to not simply weaken the argument for evolution but to undermine it entirely. Morris is overstating his case here. It really does not take a lot of imagination to see the record as providing at least some support for evolution. Morris’s contention that an incomplete fossil record is no support at all for evolution is clearly a drastic overstatement. Why would Morris make such an obviously false claim?

One possibility is that he really believes the claim. But if he does, then one quick response may be to say that it is puzzling why he does not address the obvious counters to it. But a more charitable interpretation is that Morris may have addressed damaging counterexamples in other writings. The principle of accuracy demands that we seek to interpret an author’s position as completely as possible, based on all available information. In addition, the principle of accuracy demands that we attempt to grasp the intent of the author. On the other hand, it may be possible that Morris is engaging in hyperbole in this piece for rhetorical effect. People may overstate claims to draw attention to their point. We are more apt to pay attention to strong claims than weak ones. Think about the number of advertisements you have seen that claim that a product is the best of its kind, rather than merely as good as others. Are you more likely to buy detergent that claims “nothing cleans better” or one that claims it “cleans about as well” as other leading brands? By overstating his claim, Morris makes it stand out, which makes it seem interesting. Of course, he also makes the claim false as stated.

The interpretive issue here is whether we should hold him to this part of his claim or simply note it and go on to more important issues in his argument. Which way we decide to go will depend on how much he makes of the claim in the rest of his writing. If he really continues to drive home the point that evolution has absolutely no support from the fossil record, then the principle of accuracy suggests that it is appropriate to hold him to the claim. On the other hand, if it does not seem to be central to his position, then the principle of charity suggests that we give him the bene�it of the doubt and assume his statement is just a rhetorical �lourish.

The primary premise of Morris’s objection is that “no undisputed chain of in-between forms has ever been discovered.” Notice the use of undisputed in the premise. Morris carefully does not claim that no chain has been found, only that no undisputed chain has been found. This is a classic weasel word (see Chapter 8). Since Morris himself is likely to dispute any proposed chain, he can safely assert his premise.

In a similar vein, no undisputed video exists of humans walking on the moon. Of course, there is video of humans walking on the moon; it is just that a few people dispute it. So how seriously should we take Morris’s use of the undisputed quali�ier in his premise? If we take it at face value, then his premise is undoubtedly true, but so weak that it cannot really support his conclusion. If we ignore the quali�ier, then his premise gives better support to his conclusion, but his premise is likely to be false. Many chains of transitional fossils have been found; the example of horse evolution is one such chain. Morris may claim that this chain has gaps, but we have already seen that the mere existence of gaps does not seriously undermine the argument for evolution. The gaps would have to be much wider and more numerous than those we see in the horse lineage to present a real problem. Whether something counts as a gap in the fossil record is not quite settled. Whenever one fossil is different than another, there is room to place an intermediate fossil between them. There could be no such thing as a perfectly gapless record. The question is not whether there are gaps, but whether the gaps are large and frequent enough to undermine the evidence for evolution.

Drawing a Conclusion

Morris’s objection does not present a serious threat to evolution. His presentation contains weasel words and overstatements that should make us suspicious. His position with the Institute for Creation Research presents a possible indication of bias. These are reasons to be concerned with his objection from the outset. More importantly, even if we grant his objection, it turns out not to have much force against the speci�ic kind of argument that the fossil record provides for evolution. The gaps Morris alludes to would have to be far greater and more common than they are to

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seriously undermine the evidence for evolution. However, even at this stage, we should be careful. We have rejected Morris’s objection, but that is not by itself a reason to accept evolution. The theory of evolution should be judged on the merits of the evidence for it, not on the fact that it is possible to give a bad argument against it.

Similarly, we should acknowledge that our analysis here is just a beginning. We have only looked at the argument implied by one sentence of Morris’s writing—we have just touched the surface. If you were responding to Morris’s argument in an essay, you would need to go on and consider the rest of what he has to say and how the things you have learned about logic relate to it.

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Seth Wening/Associated Press

Watson, IBM’s supercomputer, is an arti�icially intelligent machine that runs off a logic-based program.

The Chinese Room Argument

9.6 Other Applications of Logic

As an introductory book in informal logic, we have only touched on the fundamental concepts of the �ield of logic, and even then we have only scratched the surface of those. We have not yet addressed, for instance, all the specializations and applications in logic. The following survey should give you a general idea of some of these specializations and how widespread the use of logic is in society.

Symbolic Logic

If you like deductive arguments and enjoyed the chapter on propositional logic, then you might consider looking into symbolic logic. Symbolic logic is very abstract; it is the area of investigations in which logic meets math. Symbolic logic is concerned solely with the form of arguments. In fact, arguments are generally represented with symbols and variables much like an equation in algebra. A beginning course typically starts with propositional logic.

Computer Science

As noted in Chapter 4, Alan Turing proposed a class of devices that became known as Turing machines and were intended to measure the extent of what can be computed (Barker-Plummer, 2012). Turing’s work contributed to the development of what is now known as computer science. His name has entered popular culture recently with the 2014 �ilm The Imitation Game, which takes a look at Turing’s role in breaking the Nazi Enigma code. Logic is at the center of Turing’s accomplishments, and it has since continued to play a prominent role in computer science. The design of computer circuits, for example, is based on propositional logic. Predicate logic is used in various computing languages. Many logic speci�ication languages use some form of predicate logic and set theory (logic’s mathematical cousin). Knowledge representation has formalisms based on logic. Probabilistic logic is increasingly becoming the foundation for machine learning systems. A growing �ield in computer science is veri�ication technology, which aims at verifying whether a program actually does what it is supposed to do; this �ield employs proof theory, model theory, and decision procedures.

Arti�icial Intelligence

Arti�icial intelligence (AI) is a �ield in computer science whose focus is to develop programs that allow computers to function in ways that display what we can very broadly call intelligence. Today we have impressive supercomputers, such as IBM’s Watson, that can beat humans at games such as Jeopardy! Nonetheless, even advanced supercomputers do not have the capacity to process information as the human brain does. In light of this, one of the most recent and controversial projects in AI is the attempt to formalize commonsense reasoning (Thomason, 2013). Yet the view that we can recreate human intelligence, cognition, and self-awareness (strong AI) is a matter of debate. In 1980 John Searle published a very famous article titled “Minds, Brains, and Programs,” in which he introduced the Chinese room argument. This argument claims that computers are incapable of reaching the level of human intelligence primarily because human minds are a result of biological processes. Although computers can become very sophisticated and fast at following syntactic rules, they do not understand the meaning of the information that they are processing. Searle’s views are, of course, disputed by those participants in the strong AI movement. But defenders of strong AI believe that it is only a matter of time before we design a computer able to perform at the level and complexity of the human brain.

Engineering

The logic used in some engineering �ields is often known as fuzzy logic. Fuzzy logic owes its name to the focus of its examination: phenomena about which our knowledge is approximate,

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Philosopher John Searle goes through his Chinese room argument to prove that no matter how powerful computers are, they aren’t minds.

Critical Thinking Questions

1. Searle argues that our understanding of the information we have is the key distinction between a human mind and one that is arti�icially created. Do you agree?

2. Searle outlines the Chinese room argument as a formal, three-step argument. Is it valid?

3. While a computer can outperform a human mind by performing numerous simulations rapidly, it doesn’t actually think. Can you think of a situation in which using a computer to “think” would be better or worse than having a human perform the same task?

uncertain, vague, or partially true, instead of exact and precise. Some examples of such phenomena that display such fuzzy data are the weather, the effect of age in faces, business cycles, currency valuation, and any other phenomena that challenge pattern recognition due to its unpredictability. Engineers thus need to characterize and quantify uncertainty arising from such unpredictability due to vagueness, imprecision, and lack of knowledge. As a result, the development of a set of methods to address such a state of affairs emerged. In engineering, some of the most interesting practical applications are in robotics, biomedical engineering, target tracking, and pattern recognition (including facial recognition), to name a few.

Politics (Speech Writing)

In our most cynical days, we may question whether logic and politics can mix. However, arguments are the vehicle by which we often receive the most information from political candidates and even presidents (through their State of the Union addresses) regarding matters that will affect us directly. So we need to pay close attention. Arguments in political speeches tend to be of a rhetorical nature because the focus is typically persuasive. Some of the most successful and informative political speeches, however, use logical arguments. Politicians, speechwriters, aides, and political analysts and researchers who are skilled at logical argumentation will be the most successful at their tasks. As voters, we all have an advantage by also being knowledgeable of the logical argument structure because we will be able to distinguish good reasoning from mere persuasion and emotional appeal.

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Summary and Resources

Chapter Summary Can logic be applied to practical purposes in our everyday lives? This is the question that we examined in this chapter. First we learned how to apply the standard argument form in the construction of an argumentative essay. We then brie�ly noted the Toulmin model as an example of how arguments are seen differently in other �ields. We also looked at applications of the principles of accuracy and charity that show how to productively and harmoniously confront disagreement. Finally, we concluded with a discussion of how logic is used in various other areas and professions.

Now take a moment to think back on the journey you started at the beginning of the book. Indeed, you now have the basic tools of logic that will empower you as a critical thinker throughout your life. But notice that there is a very meaningful way in which logic can transform you as a person, too. When we think about the many areas to which logic can be applied, we can say that it can change our lives by giving us the power to choose what we accept and what we do not accept based on the best available reasoning. This is the kind of power that will help us discover truth. You now have the basic tools to make this possible for yourself.

Critical Thinking Questions

Connecting the Dots Chapter 9

NEXT

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1. What are some improper techniques of argumentation that you have employed in the past? Now that you have read this chapter, how might you have corrected your approach?

2. How does applying the standard argument form to writing argumentative essays help you in your studies, work, or any other practical application?

3. Consider your strongest belief in either the political or religious realms. List the reasons you have for such a belief. Create the strongest argument you can against your own position.

4. What informal fallacies do you �ind most prevalent in the way others present criticism? What is the best way to handle a situation in which someone else uses a fallacy? How can one maintain the principle of charity and/or accuracy in these situations?

5. Which applications of logic in real life have surprised you the most? Explain why. Now that you have learned about the practical applications of logic, what has changed the most about your understanding of logic?

6. After having read this chapter, what would you say is the end goal of engaging in argumentative dialogue?

Web Resources https://archive.org/stream/mindpsycho04edinuoft#page/278/mode (https://archive.org/stream/mindpsycho04edinuoft#page/278/mode) Read the original Lewis Carroll essay in Mind titled “What the Tortoise Said to Achilles.”

https://www.youtube.com/watch?v=oPB0JOpvg_E (https://www.youtube.com/watch?v=oPB0JOpvg_E) >Watch a 90-second review of the principle of charity.

https://www.youtube.com/watch?v=lI-M7O_bRNg (https://www.youtube.com/watch?v=lI-M7O_bRNg) Watch a video on the participation of the supercomputer Watson in the game show Jeopardy!

http://www.criticalthinkeracademy.com (http://www.criticalthinkeracademy.com) The Critical Thinker Academy teaches many valuable concepts about logic, including how best to identify arguments in daily life.

http://austhink.com/critical (http://austhink.com/critical) For a number of other resources, visit Austhink’s Critical Thinking on the Web.

http://www.iep.utm.edu (http://www.iep.utm.edu) The Internet Encyclopedia of Philosophy is a peer-reviewed academic resource for scholarly information on philosophers and key topics in philosophy.

Key Terms

argumentative essay An essay that presents an argument. The basic structure for such an essay is the standard argument form.

hypotheticals Sentences stating an assumed situation merely for the sake of argument.

principle of accuracy A principle that requires one to interpret the argument under examination as closely as possible to the author’s intent.

principle of charity A principle that requires one to interpret others’ reasoning in as favorable a manner as possible.

quali�ier A word or phrase that affects the strength of a claim by weakening it thereby and making it more likely to be true.

secondary argument An argument whose conclusion is one of the premises of the original argument. Also called subargument.

secondary thesis

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The conclusion of a secondary argument; it is one of the premises of the original argument. Also called subconclusion.

Toulmin model A model for practical argumentation advanced by Stephen Toulmin that stems from the view that the arguments we read or hear in everyday life do not follow the standard argument form. According to this model, the core of an argument consists of a claim, data, and a warrant.y p g

structure for such an essay is the standard

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Glossary

abductive reasoning See inference to the best explanation.

ad hominem The fallacy of rejecting or dismissing a person’s reasoning on the basis of some irrelevant fact about him or her.

af�irming the consequent An argument with two premises, one of which is a conditional and the other of which is the consequent of that conditional. It has the form P → Q, Q, therefore P. It is invalid.

antecedent The part of a conditional statement that occurs after the if; it is the P in P → Q.

appeal to authority See argument from authority.

appeal to emotion A fallacy in which someone argues for a point based on emotion rather than on reason.

appeal to fear One speci�ic type of appeal to emotion that tries to get someone to agree with something out of fear rather than a rational assessment of the evidence.

appeal to force One speci�ic type of appeal to emotion that tries to get people to accept a conclusion by threatening them with negative consequences speci�ically for not accepting the conclusion.

appeal to ignorance The argument either that a claim must be false because it has not been demonstrated to be true or that a claim must be true because it has not been proved to be false.

appeal to inadequate authority A fallacy that reasons that something is true because someone said so, even though that person is, for one reason or another, not a reliable source on that topic.

appeal to pity One speci�ic type of appeal to emotion that tries to get someone to change his or her position only because of the unfortunate situation of an individual affected.

appeal to popular opinion A fallacy in which one—knowingly or not—accepts a point of view because that is what most other people think; also known as appeal to popularity, bandwagon fallacy, or mob appeal.

appeal to ridicule A fallacy that seeks to make fun of another person’s view rather than actually refute it.

appeal to tradition A fallacy that argues for a conclusion based on the claim that it is what people have always done or believed.

argument The methodical defense of a position advanced in relation to a disputed issue; a set of claims in which some, called premises, serve as support for another claim, called the conclusion.

argument from analogy Reasoning in which we draw a conclusion about something based on characteristics of other similar things.

argument from authority An argument in which we infer that something is true because someone (a purported authority) said that it was true.

argument from de�inition An argument in which one premise is a de�inition.

argumentative essay An essay that presents an argument. The basic structure for such an essay is the standard argument form.

bandwagon effect The tendency to think that something is desirable or true merely because many people desire it or believe it.

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begging the question A fallacy in which one gives an argument that assumes a major point at issue; also known as petitio principii.

biased sample A sample that is not representative of the whole population, perhaps due to some tendency within the method of sampling to favor some results over others.

biconditional A statement of the form P ↔ Q (P if and only if Q).

categorical argument An argument entirely composed of categorical statements.

categorical logic The branch of deductive logic that is concerned with categorical arguments.

categorical statement A statement that relates one category or class to another. Speci�ically, if S and P are categories, the categorical statements relating them are: All S is P, No S is P, Some S is P, and Some S is not P.

causal argument An argument about causes and effects.

cherry picking An inductive generalization that emphasizes evidence for a claim while ignoring the evidence against the claim, or vice versa.

circular reasoning A fallacy in which the premise is the same as, or is synonymous with, the conclusion.

claim A sentence that presents an assertion that something is the case. In logic, claims are often referred to as propositions in order to recognize that these may be true or false.

cogent An inductive argument that is strong and has all true premises.

cognitive bias A psychological tendency to �ilter information through one’s own subjective beliefs, preferences, or aversions, which may lead one to accept poor reasoning.

complement class For a given class, the complement class consists of all things that are not in the given class. For example, if S is a class, its complement class is non-S.

conclusion The main claim of an argument; the claim that is supported by the premises but does not itself support any other claims in the argument.

conclusion indicators The words that signal the appearance of a conclusion in an argument.

conditional An “if–then” statement. It is symbolized P → Q.

con�idence level In an inductive generalization, the likelihood that a random sample from a population will have results that fall within the estimated margin of error.

con�irmation bias The tendency to select information that con�irms one’s beliefs while discounting information that would discon�irm those beliefs.

conjunction A statement in which two sentences are joined with an and. It is symbolized P & Q. Also, an inference rule that allows us to infer P & Q from premises P and Q.

connectives See operators.

consequent The part of a conditional statement that occurs after the then; it is the Q in P → Q.

contraposition The immediate inference obtained by switching the subject and predicate terms with each other and complementing them both.

converse The result of switching the order of the terms within a conditional or categorical statement. The converse of P → Q is Q → P. The converse of “All S are M” is “All M are S.”

conversion The immediate inference obtained by switching the subject and predicate terms with each other.

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correlation An association between two factors that occur together frequently or that vary in relation to each other.

counterexample method The method of proving an argument form to be not valid by constructing an instance of it with true premises and a false conclusion.

critical thinking The activity of careful assessment and self-assessment that employs logical reasoning as the principal basis for accepting beliefs or making judgments.

deductive argument An argument that is presented as being valid—if the primary evaluative question about the argument is whether it is valid.

denying the antecedent An argument with two premises, one of which is a conditional and the other of which is the negation of the antecedent of that conditional. It has the form P → Q, ~P, therefore ~Q. It is invalid.

disjunction A sentence in which two smaller sentences are joined with an or. It is symbolized P ∨ Q.

disjunctive syllogism An inference rule that allows us to infer one disjunct from the negation of the other disjunct. If you have “P or Q” and you have not P, then you may infer Q. If you have “P or Q” and not Q, then you may infer P.

distribution Referring to members of groups. If all the members of a group are referred to, the term that refers to that group is said to be distributed.

double negation The result of negating a sentence that has already been negated (one that already has a ~ in front of it). The resulting sentence means the same thing as the original, non-negated sentence.

dysphemism A term that makes something sound more negative than it otherwise would.

enthymeme An argument in which one or more claims are left unstated.

equivocation A fallacy that switches the meaning of a key term so that the argument seems valid when it actually is not.

euphemism A term that makes something sound more positive than it otherwise would.

explanations Statements that tell why or how something is the case. Unlike arguments, explanations do not involve contested conclusions but, instead, accepted ones.

fallacies Common patterns of reasoning that have a high likelihood of leading to false conclusions.

fallacy of accident A fallacy that applies a general rule in cases in which the rule is not properly applied.

fallacy of composition A fallacy that infers that a whole group has a certain property because each member of it does.

fallacy of division A fallacy that infers that the members of a group must have a certain property because the whole group does.

false cause A fallacy that assumes something was caused by another thing just because it came after it; also known as post hoc ergo propter hoc.

false dilemma A fallacy that makes it sound as though there are only a certain number of options when in fact there are more than just those options; also known as false dichotomy.

falsi�iable Describes a claim that is conceivably possible to prove false. That does not mean that it is false; only that prior to testing, it is possible that it could have been.

falsi�ication The effort to disprove a claim (typically by �inding a counterexample to it).

formal logic The abstract study of arguments, often using symbolic notation for analysis.

hasty generalization An inductive generalization in which the sample size is too small to adequately support the conclusion.

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hyperbole An exaggeration.

hypothesis A conjecture about how some part of the world works.

hypothetical syllogism An inference rule that allows us to infer P → R from P → Q and Q → R.

hypotheticals Sentences stating an assumed situation merely for the sake of argument.

hypothetico–deductive method The method of creating a hypothesis and then attempting to falsify it through experimentation.

immediate inferences Arguments from one categorical statement as premise to another as conclusion. In other words, we immediately infer one statement from another.

inductive arguments Arguments in which the premises increase the likelihood of the conclusion being true but do not guarantee that it is.

inductive generalization An argument in which one draws a conclusion about a whole population based on results from a sample population.

inference The process of drawing the necessary judgment or, at least, the judgment that would follow from the reasons offered in the premises.

inference to the best explanation The process of inferring something to be true because it is the most likely explanation of some observations. Also known as abductive reasoning.

informal logic The study and description of reasoning in everyday life.

innuendo A statement or phrase that implies something without actually saying it.

instance A term in logic that describes the sentence that results from replacing each variable within the form with speci�ic sentences.

interested party One that has a stake in the outcome of certain decisions.

joint method of agreement and difference A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs and absent in all cases in which it does not.

logic The study of arguments as tools for arriving at warranted judgments.

logical form The pattern of an argument or claim.

logically equivalent Two statements are logically equivalent if they have the same values on every row of a truth table. That means they are true in the exact same circumstances.

margin of error A range of values above and below the estimated value in which it is predicted that the actual result will fall.

method of agreement A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs.

method of concomitant variation A way of selecting causal candidates by looking for a factor that is highly correlated with the effect in question.

method of difference A way of selecting causal candidates by looking for a factor that is present when effect occurs and absent when it does not.

modus ponens An argument that af�irms the antecedent of its conditional premise. It has the form P → Q, P, therefore Q.

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modus tollens An argument that denies the consequent of its conditional premise. It has the form P → Q, ~Q, therefore ~P.

necessary condition A condition for an event without which the event will not occur; A is a necessary condition of B if A occurs whenever B does.

negation A statement that asserts that another statement, P, is false. It is symbolized ~P and pronounced “not P.”

non sequitur A fallacy in which the premises have little bearing on the truth of the conclusion.

Occam’s razor The principle that, when seeking an explanation for some phenomena, the simpler the explanation the better.

operators Words (like and, or, not, and if . . . then . . . ) used to make complex statements whose truth values are functions of the truth values of their parts. Also known as connectives when they are used to link two sentences.

paralipsis A technique for emphasizing a point by saying that it will not be mentioned.

philosophy The activity of clarifying ideas with the goal of seeking truth.

poisoning the well A fallacy in which someone attempts to discredit someone’s credibility ahead of time, so that all those who listen to that person will automatically reject whatever he or she says.

population In an inductive generalization, the whole group about which the generalization is made; it is the group discussed in the conclusion.

predicate term The second term in a categorical proposition.

premise indicators The words that signal the appearance of a premise in an argument.

premises Claims in an argument that serve as support for the conclusion.

principle of accuracy A principle that requires one to interpret the argument under examination as closely as possible to the author’s intent.

principle of charity A principle that requires one to interpret others’ reasoning in as favorable a manner as possible.

probability neglect Ignoring the actual statistical probabilities of an event and treating each outcome as equally likely.

proof surrogate An assertion that evidence is available without actually providing the evidence; for example, “studies show.”

proposition The meaning expressed by a claim that asserts something is true or false.

propositional logic A way of clarifying reasoning by breaking down the forms of complex claims into the simple propositions of which they are composed, connected with truth-functional operators. Also known as sentence logic, sentential logic, statement logic, and truth-functional logic.

proximate cause See trigger cause.

quali�ier A word or phrase that affects the strength of a claim by weakening it thereby and making it more likely to be true.

quality In logic, the distinction between a statement being af�irmative or negative.

quantity In logic, the distinction between a statement being universal or particular.

random sample A group selected from within the whole population using a selection method such that every member of the population has an equal chance of being included.

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red herring A fallacy in which a deliberate distraction is used in an attempt to veer the listener away from the real question at hand.

rhetoric The art of persuasion.

rhetorical devices Techniques that make an argument seem more persuasive without increasing its logical strength.

sample A smaller group selected from among the population.

sample size The number of individuals within the sample.

secondary argument An argument whose conclusion is one of the premises of the original argument. Also called subargument.

secondary thesis The conclusion of a secondary argument; it is one of the premises of the original argument. Also called subconclusion.

selection bias Bias resulting from a nonrepresentative sample.

self-sealing propositions Claims that cannot be proved false because they are interpreted in a way that protects them against any possible counterexample.

sentence variables Letters like P and Q that are used in forms to represent any sentence at all, just as a variable in algebra represents any number.

shifting the burden of proof A fallacy in which the reasoner has the burden to demonstrate the truth of his or her own side, but instead of meeting that burden simply points out the failure of the other side to prove its own position.

slippery slope A fallacy that argues that we should not do something because if we do, then it will lead to a series of events that will end in a terrible conclusion, when this chain of events is not likely at all.

sorites A categorical argument with more than two premises.

sound Describes an argument that is valid and in which all of the premises are true.

standard argument form The structure of an argument that consists of premises and a conclusion. This structure displays each premise of an argument on a separate line, with the conclusion on a line following all the premises.

statement form The result of replacing the component statements in a sentence with statement variables (like P and Q), connected with logical operators.

statistical arguments Arguments involving statistics, either in the premises or in the conclusion.

statistical syllogism An argument of the form X% of S are P; i is an S; Therefore, i is (probably) a P.

status quo bias A tendency to believe that the way things are is �ine.

stereotype A judgment about a person or thing based solely on the person or thing being a member of a group or of a certain type.

straw man A fallacy in which one attempts to refute a very weak or inaccurate version of the other side’s position.

strong arguments Inductive arguments in which the premises greatly increase the likelihood that the conclusion is true.

subject term The �irst term in a categorical proposition.

suf�icient condition A condition for an event that guarantees that the event will occur; A is a suf�icient condition of B if B occurs whenever A does.

syllogism A deductive argument with exactly two premises.

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Toulmin model A model for practical argumentation advanced by Stephen Toulmin that stems from the view that the arguments we read or hear in everyday life do not follow the standard argument form.

trigger cause The factor that completes the cause chain resulting in the effect. Also known as proximate cause.

truth table A table in which columns to the right show the truth values of complex sentences based on each combination of truth values of their component sentences on the left.

truth value An indicator of whether a statement is true on a given row of a truth table. A statement’s truth value is true (abbreviated T) if the statement is true; it is false (abbreviated F) if the statement is false.

tu quoque A version of the ad hominem fallacy that argues that someone’s claim is not to be listened to if he or she does not live up to the truth of that claim.

valid An argument in which the premises absolutely guarantee the conclusion, such that is impossible for the premises to be true while the conclusion is false.

Venn diagram A diagram constructed of overlapping circles, with shaded areas or x’s, which shows the relationships between the represented groups.

weak arguments Inductive arguments in which the premises only minimally increase the likelihood that the conclusion is true.

weasel words Words used to make a claim technically true by introducing probability or otherwise watering it down, without really changing the import of the claim. Also known as weaselers.

weaselers See weasel words.

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