Reflections on Reasoning [First Edition] 1138164682, 9781138164680

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REFLECTIONS on REASONING

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REFLECTIONS on REASONING

R a y m o n d S. N i c k e r s o n

Bolt Beranek & Newman Inc. Cambridge, Massachusetts

Psychology Press Taylor & Francis Group New York London

Copyright © 1986 by Lawrence Erlbaum Associates, Inc. A l l rights reserved. No part of this book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without the prior written permission of the publisher. First published by Lawrence Erlbaum Associates, Inc., Publishers 365 Broadway Hillsdale, New Jersey 07642 This edition published 2012 by Psychology Press Psychology Press Taylor & Francis Group 711 Third Avenue New York, N Y 10017

Psychology Press Taylor & Francis Group 27 Church Road Hove, East Sussex BN3 2FA

Library of Congress Cataloging-in-Publication Data Nickerson, Raymond S. Reflections on reasoning. Bibliography: p. Includes index. 1. Reasoning. 2. Logic. I. Title. BC177.N53 1986 160 85-27441 ISBN 0-89859-762-5 ISBN 0-89859-763-3 (pbk.)

To Daniel, Nathan, Betsy and Sheri

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Contents

PREFACE xi FOREWORD by P. N. Johnson-Laird

xiii

1. INTRODUCTION 1 1.1 What is Reasoning? 1 1.2 Organization of the Book 3 2. REASONING IN PERSPECTIVE 4 2.1 Reasoning and Language 4 2.2 Reasoning and Logic 6 2.3 Reasoning and Inventiveness 7 2.4 Reasoning and Knowledge 10 2.5 Reasoning and Truth 12 2.6 Reasoning Versus Rationalizing 13 2.7 Limitations and Impediments to Effective Reasoning 14 3. BELIEFS 19 3.1 Beliefs Versus Opinions 20 3.2 Properties of Beliefs 22 3.3 On Deciding What to Believe 25 3.4 Belief as a Matter of Degree 26 3.5 Conservativism 27 3.6 Suspended Judgment 28 3.7 The Reasonable Use of Incomplete Information 29 3.8 Relevance 30 3.9 The Myth of Objectivity 31 3.10 Consequences of False Beliefs 32 3.11 Appreciating Opposing Beliefs 33 3.12 Summary 34 vii

viii

CONTENTS

4. ASSERTIONS 4.1 Understanding Assertions 36 4.2 Types of Assertions 36 4.3 Quantifiers 37 4.4 Form Versus Meaning 39 4.5 Using Representations 40 4.6 On Deciding Whether Different Assertions Mean the Same Thing 47 4.7 Rewriting Assertions 50 4.8 Assertions About Cause and Effect 53 4.9 Indirect Assertions 54 4.10 Dealing with the Imprecision of Language 55 4.11 Implication and Contradiction 57 4.12 Evaluating Assertions 59 4.13 Consistency, Corroboration, and Proof 61 4.14 The Principle of Falsifiability 64 4.15 Counterexamples 66 4.16 Summary 66 5. ARGUMENTS 5.1 What is an Argument? 68 5.2 Inductive Versus Deductive Inference 70 5.3 Types of Arguments 72 5.4 Recognizing Arguments 75 5.5 Analyzing Arguments 77 5.6 Forms of Logical Arguments 80 5.7 Analyzing Incomplete Logical Arguments 84 5.8 Evaluating Logical Arguments 88 5.9 Using Diagrams to Help Judge the Validity of Logical Arguments 90 5.10 Evaluating Plausible Arguments 93 5.11 Weighing Evidence Versus Building a Case 96 5.12 Disputes 97 5.13 Indirect and Devious Arguments 98 5.14 Constructing Arguments 99 5.15 Summary 100 6. STRATAGEMS 6.1 The Art of Indirect Persuasion 103 6.2 Misrepresentations 104 6.3 The Deceptive Use of Truth 105 6.4 Overstatement of an Opposing Position 106

35

68

102

CONTENTS

6.5 Authoritative Manner 106 6.6 Sloganism 107 6.7 Leading Questions 107 6.8 Quoting Out of Context 108 6.9 Put-downs 108 6.10 Dilution by Generalization 109 6.11 Avoiding the Issue 109 6.12 Summary 110 7. SOME COMMON REASONING FALLACIES 7.1 Partiality in the Uses of Evidence 111 7.2 Biased Information Gathering 112 7.3 Uses of Irrelevant Reasons 113 7.4 Argumentum ad hominem 114 7.5 Appeal to Authority 114 7.6 Appeal to Inappropriate Authority 115 7.7 Credit or Discredit by Association 115 7.8 Appeal to Numbers 116 7.9 Appeal to Tradition 118 7.10 Uncritical Acceptance of Simple Explanations 119 7.11 Hasty Closure 120 7.12 Inappropriate Persistence 120 7.13 Inappropriate Dichotomizing 121 7.14 Drawing Contrary Conclusions From Inconclusive Arguments 122 7.15 Confusing Naming With Explaining 122 7.16 Confusing Temporal Succession With Causation 123 7.17 Confusing Shared Characteristics With Distinguishing Characteristics 124 7.18 Confusing Truth With Validity 124 7.19 "Proof by Analogy 125 7.20 Overgener alization 126 7.21 Stereotyping 127 7.22 Summary 128 8. CONCLUSION 8.1 Some Rules 130 8.2 Summary 132 APPENDIX A: ANSWER KEY

ix

111

129 133

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Preface

This book is an adaptation of a report entitled Notes about Reasoning, prepared under a project on The Training of Higher Cognitive Learning and Thinking Skills that was sponsored by the National Institute of Education. My purpose in producing the notes was to help me clarify my own thinking about reasoning and how the ability to reason effectively might be enhanced in the classroom. I did not intend to write a textbook on reasoning or a scholarly review of research on reasoning processes, and this book is not presented as either now. It still has the character of a collection of thoughts; it is being published with the hope that some of the ideas and suggestions in it may stimulate some others, especially teachers and students, to reflect more than they otherwise might have upon what it means to reason effectively. One does not, of course, become an effective reasoner by reading a book on reasoning or by taking a course in reasoning. Learning to reason well is surely a lifelong process—or at least a lifelong challenge. If this book is useful in helping some readers to see the value of an enduring commitment to that challenge, it will have served its purpose. I wish to thank the NIE Project Officers, Patricia Butler and Joseph Psotka, for their support and encouragement. I am grateful also to John Swets, Richard Herrnstein, David Perkins and Carol Chomsky for helpful comments on an early draft of the manuscript, to Anne Kerwin and Patricia Carroll for typing the manuscript and to Brenda Starr and Frank DiPace for making electronic delivery of it to the printer possible by working around the differences between the sending and receiving systems. Special thanks to my wife, Doris, for her constant help of countless types, and most especially for bringing into the world the four beautiful people to whom this book is dedicated. xi

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Foreword

Logic and reasoning are topics of perennial fascination. Without the ability to make deductions, human beings would have no science,no mathematics, no laws, and indeed few applicable principles of any sort. It is therefore hardly surprising that authors from many different disciplines have contributed to the literature on reasoning. Logicians, for example, are concerned with establishing the criteria for valid arguments. Since there has been more progress in logic in the last hundred years than in all the centuries since Aristotle, there is now a vast literature of logical treatises, as well as elementary introductions to the subject. Psychologists have studied the processes of thought by which adults and children reason, and many of their studies have been inspired by a knowledge—sometimes an inadequate knowledge—of formal logic. They have contributed a steadyflowof papers on the psychology of reasoning, and a somewhat more erratic supply of textbooks. Anthropologists and economists have examined that splendid logical notion, "rational man," debated whether or not it is a fiction or a fact, and sought the social and cultural reasons for alleged departures from rationality. Educators have worked to enhance the ratiocinative powers of students, sometimes by attempting to teach them to think and sometimes by more indirect methods. They and their colleagues in other disciplines have written books on how to detect fallacious arguments, how to reason logically, how to improve the ability to solve problems. Most recently, students of artificial intelligence have sought to implement computer programs capable of deductive thought. There are even one or two books on that recondite topic. Reflections on Reasoning falls into none of these three categories, but is unique; it consists of the author's reflections and advice on many of the xiii

xiv

FOREWORD

aforementioned topics. It is by turns practical and theoretical, thoughtprovoking and pedagogical. It expounds the basic foundations of logical reasoning; it examines the fundamental nature of argument; it contains a compendium of useful principles for improving thought. Yet, it remains accessible and informal throughout, and it is informed by an active acquaintance with the psychological literature. Who should read Reflections on Reasoning? Certainly, it should be studied with care by anyone involved in teaching people to think. But it deserves a wider readership: students in the many disciplines concerned with reasoning could read this book with profit, as could anyone interested in learning to reason more effectively. Raymond Nickerson takes nothing for granted. His book imparts rather than requires expertise. It is a concentrated dose of wisdom on logic and reasoning. P.N Johnson-Laird Medical Research Council Applied Psychology Unit Cambridge, England

1

Introduction

This book is about reasoning. It is not a textbook in the conventional sense. Nor does it provide a prescription for how to reason effectively. It is a collection of thoughts regarding various aspects of reasoning and what it means to reason well. The intent is to raise questions about reasoning; to invite the reader to reflect on the nature of reasoning; and to suggest that reasoning has many facets, none of which can safely be ignored by anyone who would reason effectively. Underlying the book is the assumption that while skill at reasoning is not likely to be acquired quickly and effortlessly, one can improve one's reasoning ability if one is sufficiently motivated to do so. Nothing is assumed with respect to the reader except interest in the subject of reasoning and a tolerance for ideas that are still in the process of being formed. Reasoning is viewed here as a matter of both attitude and knowledge: one is unlikely to reason well about any subject unless one is deeply desirous of doing so, and one has some knowledge of the subject about which the reasoning is to be done. Neither a closed mind nor an empty one is likely to produce much that would qualify as effective reasoning. On the other hand, an open and reflective mind, coupled with a little knowledge and an eagerness to acquire more, will reason as a matter of course. 1.1.

W H A T IS R E A S O N I N G ?

Reasoning, as the term is used here, encompasses many of the processes we use to form and evaluate beliefs—beliefs about the world, about people, about the truth or falsity of claims we encounter or make. It involves the 1

2 1. INTRODUCTION production and evaluation of arguments, the making of inferences and the drawing of conclusions, the generation and testing of hypotheses. It requires both deduction and induction, both analysis and synthesis, and both criticality and creativity. Reasoning also has to do with the careful and critical use of language. Indeed, reasoning and language usage are so tightly intertwined that it is often difficult to tell whether a particular problem should be considered a problem of reasoning or one of language usage—and perhaps, at least for practical purposes, it does not matter which way it is perceived. There is no easy prescription that will guarantee effective reasoning. To be sure, there are rules of logic, a knowledge of which should decrease the probability of certain types of identifiable reasoning errors; but there is much to reasoning that cannot be codified as a set of rules. Judgment plays an indispensable role, as do attitudes. We must make judgments of the relevance of arguments to issues, for example, as well as judgments of the plausibility of assertions and of the credibility of information sources. With respect to attitudes, effective reasoning requires an openness to evidence—a willingness to examine it objectively and to be influenced by it—and a commitment to truth, even in light of an awareness that the truth may sometimes be difficult or impossible to ascertain. Reasoning is, in short, not easily defined in a satisfactory way. We can talk about it and consider various aspects of what the word seems to connote in common usage; but we are likely tofindit difficult to come up with a crisp definition that will do justice to the richness of the concept and, at the same time, be precise enough to serve as a criterion for determining in all cases that X is an instance of reasoning, while Y is not. In this book, the discussion of reasoning is structured around three key concepts, belief, assertion, and argument. Belief is understood to be an intuitively meaningful notion: it is confidence that a particular thing is true, as evidenced by a willingness to act as though it were. The concept of an assertion does double duty: on the one hand, it can be an expression of a belief; on the other, it can be a component of an argument. An argument is a set of assertions that is used to support a belief. Deciding the order in which to discuss these topics poses a problem because no matter what order we choose, there will be times when some aspect of one of the topics would be easier to understand if the other topics have already been discussed. Moreover, no order is clearly more defensible than all the others, so our choice must be arbitrary to some degree. We might start with arguments, on the grounds that that is really what reasoning is all about; or with assertions, because they are the stuff of which arguments are made, as well as the vehicles for expressing beliefs; or with beliefs, because everyone understands intuitively what they are. Here, the topics are considered in the following order: first, beliefs;

3 second, assertions; third, arguments. Although the topics are discussed individually, it should be borne in mind that they are of special interest because of the ways in which they relate to each other. Assertions are of interest because they are both the components of arguments and the means by which we can represent beliefs. Arguments are of interest because they are used to form, sustain, or modify beliefs. We might say that beliefs are of interest in their own right, inasmuch as our beliefs, to a large extent, define what we are and determine what we do. However, we focus here on such issues as the defensibility of beliefs and the plausibility of the arguments used to support them. 1.2.

1.2.

ORGANIZATION OF THE BOOK

O R G A N I Z A T I O N OF THE B O O K

Beyond this introductory chapter, the book is organized as follows: Chapter 2 discusses, in a discursive way, the relationship between reasoning and the closely associated concepts of language, logic, inventiveness, knowledge, and truth. It ends with a contrast between reasoning and rationalizing and a consideration of three types of factors that can impede reasoning. Chapters 3,4, and 5 discuss beliefs, assertions, and arguments, respectively. Chapter 6 considers various stratagems that people use to persuade or to win disputes, and Chapter 7 describes several ways in which our reasoning is known often to go astray. Chapter 8 presents a few suggestions for attempting to improve our own reasoning capability. Think

about

it

Consider the following questions: • What does the term reasoning mean to you? • What are some of the aspects of effective reasoning? • What are some major impediments to effective reasoning? • How might we characterize the differences between good and poor reasoners? • Why is reasoning important in everyday life?

2

Reasoning in Perspective

2.1.

REASONING AND LANGUAGE

The relationship between reasoning and language is a complicated one. Sometimes it is not clear how to distinguish between reasoning deficiencies and problems arising from careless or inept use of language. If in reading a sentence we understand what the sentence says explicitly, but fail to understand what it implies, is that a failure of language comprehension or of reasoning? If I claim to believe both of two contradictory statements, is it more reasonable to assume that I must misunderstand at least one of the statements or that I am being illogical? A particularly bothersome aspect of language that has implications for reasoning is the problem of ambiguity and the inherent lack of definitional precision in the way we use words. The problem shows up in more than one guise. It occurs, for example, when two parties to a discussion use the same word but attach different meanings to it. It also happens when the same word is used in two premises in an argument, but with different meanings in the two cases. A humorous but convincing example of the latter is the familiar demonstration that a ham sandwich is better than eternal happiness: Nothing is better than eternal happiness. A ham sandwich is better than nothing. Therefore, a ham sandwich is better than eternal happiness. The problem here, of course, is in the ambiguity of the premises. Rewording the argument so that the fallacy becomes clear may not be as easy as you think. Superficially the argument appears to be perfectly sound. 4

5 It is identical in form, is it not, to the following argument, which we accept without difficulty: Tom is taller than Carl. Pete is taller than Tom. Therefore, Pete is taller than Carl. The problem with the first argument is that its premises are ambiguous because the term nothing is used to mean different things in different contexts. In particular, there are two ways to interpret the first premise: la. Having nothing at all is better than having eternal happiness. lb. There is nothing that is better than eternal happiness; or, equivalently, the set of things that are better than eternal happiness has no members. There are also two ways to interpret the second premise: 2a. Having a ham sandwich is better than having nothing at all. 2b. A ham sandwich is not better than anything. If the two premises were interpreted as la and 2a, then the argument would be sound, which is to say, the conclusion would indeed follow. However, it seems unlikely that anyone would interpret thefirstsentence as la. Most people reading the argument would probably interpret the two premises as lb and 2a, respectively. Given those interpretations, the argument does not have a logical structure, because the premises do not have a common term. Here is another example that illustrates how the imprecise use of language can be confusing. All of us are familiar with many sayings, which are sometimes called maxims, proverbs, adages, or aphorisms. Have you ever noticed that it is often easy to find pairs of sayings that seem to have opposite meanings? The fact that we can find such pairs is a little strange because these sayings usually are thought of as summarizing widely acknowledged truths. Consider the following: A stitch in time saves nine. Haste makes waste. Many hands make light work. Too many cooks spoil the broth. You cannot teach an old dog new tricks. One is never too old to learn. The point is that what appear to be contradictory statements when they are juxtaposed can also appear to express self-evident truths when they are seen in isolation or in certain specific contexts. Each of the sayings just 2.1.

REASONING AND LANGUAGE

6 2. REASONING IN PERSPECTIVE noted, while apparently contradicting the one with which it is paired, can certainly be viewed as true in some sense. That is, each applies sometimes and in certain circumstances, but not at other times or in other situations. The problem is that when such sayings are used to make points, the conditions under which they are assumed to apply are usually not specified. While we cannot hope to do more here than simply recognize the complex relationship between language usage and reasoning, it is certainly fair to say that careful language usage should greatly facilitate reasoning, and that, conversely, it probably is not possible to reason effectively unless we use language carefully. The importance of language and of the need for care in using it will be illustrated several times in this book. Special attention will be given to the subject, however, in the discussion of assertions in Chapter 4. Think

about

it

• Find as many examples as you can of contradictory sayings. Then try to rephrase or qualify them so that they preserve the original meaning but are no longer contradictory. • List a few words, particularly nouns and verbs, that could have different meanings in different contexts for different people, and consequently could contribute to misunderstanding or the appearance of faulty reasoning, if not used carefully. 2.2.

R E A S O N I N G A N D LOGIC

The question of whether reasoning follows the rules of logic is an old one and has been debated many times. Do the rules of logic reflect the way people naturally think? Do they represent only how skilled thinkers think? Or are they prescriptions for how we should think? That issue will not be discussed at length here. Unquestionably, an explicit understanding of some of the basic principles of logic is very useful; anyone who has such an understanding is likely to be able to reason more effectively than someone who does not. It is useful, for example, to understand the modus ponens and modus tollens forms of the conditional, or hypothetical, syllogism. (They are discussed in Chapter 5.) However, it is not necessary that we be familiar with the terminology of formal logic—that is, with such terms as modus ponens and modus tollens—in order to be able to reason effectively. It is essential, though, that we understand at least some of the basic principles of inference, such as those illustrated by the ponens and tollens modes of argument. Moreover, familiarity with some of the terms of logic can undoubtedly be helpful in reasoning, and a knowledge of rules of formal logic is a great asset indeed.

7 It is important to recognize that logic represents only one aspect of reasoning, and that a complete understanding of the rules of formal logic in and of itself will not assure effective reasoning. Logic deals with the validity, or form, of deductive arguments. It provides methods and rules for restating given information so as to make what is implicit explicit. It has little to do with the determination of truth or falsity. It does not provide techniques for going beyond the information given, except that it makes explicit what has been given only by implication. Effective reasoning requires the ability to think up arguments as well as to assess their validity. It requires the ability to generate hypotheses as well as to test them, to determine the degree of relevance certain information has to an issue, and to give appropriate weight to that information in attempting to decide the issue. It also requires the ability to judge the plausibility of assertions, the ability to bring evidence to bear on one's system of beliefs, and the willingness to modify those beliefs in accordance with that evidence as appropriate. In short, reasoning ability involves the ability to detect logical fallacies in formal arguments, but much more than that, it requires a lot of what we might consider aspects of inventiveness. Any view of reasoning that overlooks the less formal and more creative aspects of the process is an overly narrow view and is an inadequate foundation for programs to enhance reasoning. The following section expands on the point. 2.3.

Think

about

REASONING AND INVENTIVENESS

it

• The following words are often encountered in discussions of logic: imply, infer, deduce, conclude. Think about what these words mean to you. Then look up the meanings in a dictionary. Note that some of these words have more than one meaning. In particular, their meaning(s) in the context of logic may be different from, and perhaps somewhat more precise than, their meanings as they are used in day-to-day language. 2.3.

REASONING A N D INVENTIVENESS

The role of inventiveness or creativity in reasoning is far more important than is generally acknowledged. Often we think of reasoning as a process of working with information that is given. That may mean evaluating the logical validity of an argument, explicating information that is given only implicitly, piecing together isolated bits of information so as to clarify the justification of an inference, and so on. Indeed, the kinds of reasoning problems that we encounter in books about reasoning or in tests of reasoning ability typically provide all the information we need to solve the problem (although some of that information may be given in an obscure form); and

8

2.

REASONING IN PERSPECTIVE

each problem has one correct solution. In contrast, the reasoning demanded of us by the problems of everyday life often requires that much of the information used in the reasoning process come from our own heads. Moreover, for many of the problems we deal with every day, there is no single correct solution, or if there is, there is no sure way to tell whether or not we have found it. Much of reasoning involves debating with ourselves. That involves thinking up arguments and then evaluating them. In the evaluation process, we also think up arguments and especially counterarguments. Reasoning also involves identifying our options and thinking through the consequences of selecting any particular one of them. Benjamin Franklin proposed a procedure for making rational choices that is probably familiar to many people. The procedure involves listing the pros and cons of each of the available options and then making a selection based on the composite of positive and negative considerations associated with the various possibilities. The procedure is conceptually simple and straightforward; however, applying it raises some interesting questions about how to combine the positive and negative weights of the various pros and cons. Should we give equal weight to each factor and simply opt for the alternative with the greatest number of pros over cons? Should we attach different weights to the various factors and then decide on the basis of the sums of the weightings? Should we recognize that factors sometimes interact in complex ways, such that the importance of factor A is somehow contingent on the status of factor B? Such questions are interesting from both theoretical and practical points of view. However, a prior problem is how to identify the pros and cons in the first place. If, when we make up the list, we fail to include specific factors that are highly relevant to the choice, then regardless of the particular rule of decision used, the choice is likely to be less than ideal. How do we insure that we have a sufficiently complete list of pros and cons? How do we know we have not overlooked something of critical importance? Those problematic questions illustrate one way in which inventiveness or creativity is involved in the reasoning process. Compiling a list of factors that are relevant to a decision is a creative act in a very real sense, for in doing it we must go beyond the given, and even beyond what is implicit in the given. We must search our own knowledge for the relevant information and be able to determine for any particular item whether it is relevant to the choice. Furthermore, much of the information we produce will be uncertain to some degree. It will be in the form of surmises, hypotheses, conjectures, expectations, and weakly held opinions. With that in mind, we must exercise considerable judgment regarding how much weight should be given to the various items of information we find in our heads. The importance of creativity in reasoning is also apparent from a

9 consideration of the way in which science advances knowledge. Training in science puts heavy emphasis on methods for testing hypotheses. Typically, such methods involve the performing of carefully controlled experiments. One begins with a hypothesis—a statement of a relationship, a principle, a dependency—that is acknowledged to be tentative and in need of testing. One deduces from the hypothesis some effect that should be observed under specified conditions. One then produces the conditions in the laboratory and checks to see if the effect is observed. If it is, the hypothesis is said to be supported or corroborated. If the predicted effect is not observed, the hypothesis (assuming the experiment was carefully done) is considered disconfirmed or proven false. In subsequent chapters, we will consider in greater detail what it means to test a hypothesis; for now, it suffices to recognize that hypothesis testing is a key component of the scientific method for finding out about the world. Great emphasis is placed on hypothesis testing in science because the commitment to the subjection of hypotheses to empirical testing is what assures the integrity, consistency, and continuity of the scientific enterprise. If untested or untestable hypotheses were readily incorporated into scientific theory, science would quickly lose its contact with reality and would be of little practical use. It is the commitment to the rigorous testing of hypotheses that keeps science honest, as it were. Indeed, the insistence that hypotheses be tested before they can be promoted to the status of established principles or laws is what distinguishes scientific from nonscientific attempts to explain various aspects of the world. Any "theory" that is based on hypotheses that are inherently untestable is by definition nonscientific. That is not to say that it has no value from any perspective, but only to note that it fails to satisfy the fundamental requirement for being scientific. While a commitment to hypothesis testing is a fundamental tenet of science, hypothesis testing is only half of the picture. Before a hypothesis can be tested, there must be a hypothesis to test. The process of generating hypotheses is as essential to science as is that of testing hypotheses. In fact, the scientific approach can be summarized quite accurately by saying that it involves the generation and testing of hypotheses. Moreover, the process is cyclic: Hypotheses are generated and tested, and on the basis of the results, old hypotheses are modified or new ones generated, and then tested in turn. Hypothesis generation receives less emphasis in the formal training of scientists than does hypothesis testing, for an understandable reason. A great deal is known about how to test hypotheses effectively, and many methods have been developed to facilitate that process; in contrast, relatively little is known about the process by which hypotheses are generated. It is a creative process, and our lack of understanding of it reflects a lack of understanding of creative processes and reasoning in general. 2.3.

REASONING AND INVENTIVENESS

10 Think

2.

REASONING IN PERSPECTIVE

about

it

• Consider the difference between hypothesis testing and hypothesis generation. Why is it that while both of them are important in intellectually demanding tasks, we might argue that hypothesis generation demands more creative thinking than does hypothesis testing? • Outline a scenario in which a criminal investigator goes about trying to solve a crime, and in particular the roles that both hypothesis generation and hypothesis testing play in the process. • What do the roles that hypothesis generation and hypothesis testing play in the diagnosis of a disease? • Summarize for yourself the roles that hypothesis generation and hypothesis testing play in the development and refinement of scientific theories. 2.4.

REASONING AND KNOWLEDGE

Whatever else may be involved in reasoning, knowing a lot is certainly an asset, as is being able to get at what one knows when that knowledge is needed. Logical arguments are evaluated in terms of their logical validity and the plausibility of the premises from which conclusions are drawn. In order to evaluate arguments effectively, therefore, we must know something about rules of inference; but equally important is the ability to assess the plausibility of the premises from which the inferences are made. Such premises usually are considered to be statements of fact about the world, and in order to judge their plausibility, we must have some knowledge of those aspects of the world to which they pertain. Consider the following argument: All birds can fly. Emus cannot fly. Therefore emus are not birds. The conclusion of the argument is false, but it cannot be rejected on logical grounds, inasmuch as the logic of the argument is sound. What is wrong, of course, is that the claim that all birds canflyis not true. Recognizing that fact requires knowledge not about logic, but about birds. Similarly, in constructing logical arguments, we must be careful to structure them according to the rules of logic; however, if we want the conclusions not only to follow from the premises but to be empirically true, we must make sure that the premises on which they are based are themselves true. In composing an argument, we must draw upon our knowledge of the world; and to the extent that that knowledge is limited or inaccurate, the

11 argument is likely to be flawed. In general, the more we know about those aspects of the world to which an argument pertains, the more we are likely to structure arguments that are not only logically sound, but compelling. As we have already noted, often when attempting to make a decision or to come to a conclusion on some issue, we find ourselves engaged in an internal debate. We produce from our own store of knowledge arguments and counterarguments for the various decision alternatives or possible resolutions. Consider, for example, the following dialogue an imaginary man might have with himself in the process of trying tofigureout why his car will not start one morning: Perhaps it's out of gas. But the gas gauge registers one-quarter full. Of course, that could be broken. I don't believe that's the problem though, because I don't think I have driven far enough to use up a whole tank of gas since the last time I filled up. Of course, I could be losing gas from a leak. But I don't think so. Another possibility is that the carburetor is flooded. But if that were the case, I would smell gas, and I don't. Maybe there is dirt in the gas line. But if that were so, I would have noticed some evidence of a problem when I last drove the car. Maybe the fuel pump is not working, but it seems unlikely that that would break while the car is sitting in the driveway rather than when it is running. I've heard of people putting paper between the points of the distributor as a practical joke. My younger brother is the only one I know who would do that, and he's away. It rained hard and was very windy last night; maybe the spark plug wires got wet and are shorting out the ignition system [and so on]. While the preceding dialogue is imaginary, it is not unlike one that might actually occur, and it illustrates how heavily dependent on specific knowledge a reasoning process can be. The reasoner in this case is producing from his own store of information arguments and counterarguments for the various hypotheses he is considering about why his car will not start. To the extent that this illustration is representative of the type of reasoning process we often use when attempting to make a decision or to come to a conclusion on some issue, it is clear that knowledge plays an indispensable role; and presumably, the more knowledge we have that is relevant to the issue at hand, the better able we are to make the decision or to resolve the issue in a satisfactory way. Suppose our imaginary reasoner had no knowledge about such things as carburetors, gas lines, fuel pumps, distributors, and so on. His dialogue with himself would have been quite different, and the reasoning process we've imagined could not have occurred. 2.4.

REASONING AND KNOWLEDGE

12

2.

REASONING IN PERSPECTIVE

Of course, much of what applies to dialogues with ourselves applies to dialogues with others as well. There are important differences in the two cases, however, one of which is the fact that a two-person dialogue is drawing on two knowledge bases rather than only one. Moreover, typically the two knowledge bases are not identical, and that has some significance for the course that such a dialogue may take. In particular, when two people are debating opposite sides of an issue, it is, perhaps unfortunately, but indisputably, a fact that the person who has the greatest store of relevant knowledge has a distinct advantage in the debate, irrespective of the merits of the case. Think

about

it

• Consider the claim that while faclity with logic is important, it is not enough to ensure that one will draw true conclusions. Do you think this is a defensible claim? 2.5

REASONING AND

TRUTH

Any acceptable definition of reasonableness must acknowledge that there can be reasonable positions on a given issue that are mutually contradictory. People who are considered by many of their peers to be reasonable people often do take, and are able to defend quite convincingly, diametrically opposing positions on controversial matters. In keeping with that view is the position that reasonableness, or reasoning, does not always and invariably lead to truth. That is not to suggest that there is no relationship between reasoning and truth, or that a good reasoner is as likely as a poor one to hold false beliefs. The assumption made here is that the beliefs of effective reasoners are likely, in general, to be closer to the truth than those of ineffective reasoners, but that is quite different from assuming that careful reasoning can never lead to beliefs that may, in fact, be false. Another point about the relationship between reasoning and truth, which has already been made but bears repeating, is that effective reasoning presupposes a certain attitude toward the truth. In particular, it presupposes a questioning attitude, an openness to both arguments and facts, and a willingness to modify one's beliefs in the light of evidence that they should be modified. In other words, it presupposes a commitment to the truth insofar as the truth can be ascertained. One aspect of that commitment is the realization that certainty is seldom, if ever, within our grasp, which means that even strongly held beliefs deserve reexamining from time to time. Moreover, there may be no correct or true answer for many of the questions about which we desire, or are obliged, to reason, or if there is one, it may be beyond ourfindingout. That is not to say that reasoning serves no purpose in such cases, but simply to suggest that some issues must be decided on the

2.6

REASONING VERSUS RATIONALIZING

13

basis of preferences, tastes, or weakly held opinions regarding what the truth might be. The reasonable person will surely reason about such issues, but having reasoned, will recognize the tenuous nature of the basis of any conclusions drawn or decisions reached. Closely related to our concept of truth is the distinction that is often made between fact and belief. According to that distinction, a fact can be demonstrated to be true, whereas a belief cannot. We willfindit convenient in Chapter 4 to refer to statements of fact and to contrast them with assumptions and hypotheses, but we will not make a sharp distinction between a fact and a belief. Assertions can vary over a wide range of credibility, from those that evoke a very high degree of confidence to those that we can be reasonably sure are false. Rather than distinguishing fact from belief, the approach taken here is to speak of beliefs for which there are differing degrees of evidence or in which we have varying amounts of confidence. What is typically referred to as a fact is viewed as a belief that is supported by a great deal of evidence, and hence justifies a very high degree of confidence. The advantage in using the terms in this way is that it recognizes that factuality is not an either-or issue and that the evidence for the truth or falsity of an assertion can vary along a continuum from very weak to very compelling. It also acknowledges the fallibility of even our strongest beliefs. In some cases, what have been considered facts at one time, or by one culture or group, have been shown at another time or by other people not to be facts at all. Using the term beliefs to represent even that "knowledge" of the world about which we are most certain acknowledges that that certainty can never be absolute. When we speak of a fact, therefore, we will mean by that a belief the evidence for which is sufficiently strong to justify a very high level of confidence that the belief is true. A distinction must be made here, however, between belief and opinion. The term opinion is reserved for matters of taste and preference. Thus, the assertion that the earth revolves around the sun is considered a belief, as is the assertion that water is composed of hydrogen and oxygen. In contrast, the assertion that chess is more fun than checkers is considered an opinion, as is the assertion that listening to symphonic music is an enjoyable way to spend an evening. Beliefs, in other words, have to do with assertions that can be assumed to be either true or false, even if we do not know for certain what their truth value is; whereas opinions are reflections of personal values and preferences, and are therefore not subject to the same objective criteria of truth or falsity as are beliefs. We will return to this distinction in Chapter 3. 2.6

R E A S O N I N G V E R S U S RATIONALIZING

Sometimes we convince ourselves that we are reasoning when we really are not. That happens, for example, when we try to justify a decision we have

14

2.

REASONING IN PERSPECTIVE

made or wish to make, and in doing so, attend to evidence that favors the decision, but ignore the evidence that shows it to be a poor one. The proper term for this case is not reasoning but rationalizing. Another example of rationalizing is the selective gathering of information in order to support a conclusion that we have already drawn. Selectivity is the key word here. Again the idea is that we focus on information that supports the conclusion, but ignore or discount that which tends to weaken it. We can knowingly attempt to rationalize by deliberately using information or evidence in a biased way. However, rationalization need not be, and perhaps typically is not, deliberate. It seems very likely that most of us are capable of believing that we are being completely fair and objective in our uses of evidence, when in fact we may be strongly influenced by our preferences and desires. We may, for example, unwittingly give greater credence to a source of information when that source produces the kind of information we desire than when it produces the kind we prefer not to have, and we may apply other inconsistent standards to the interpretation of evidence without realizing that we are doing so. It is particularly easy after having made some choice that is significant in our lives to fall into the trap of convincing ourselves of the reasonableness of that choice. It is also easy to forget, with the passage of time, what the real determinants of the choice were and to substitute for them "reasons" that make the choice seem like a good one, and perhaps a better one than it actually was. Certainly one aspect of being a reasonable person is recognizing our own limitations and weaknesses. The tendency to rationalize is probably best assumed to be a universal one and therefore to be found in all of us. While recognizing that fact does not solve the problem of rationalization, it should perhaps mitigate it somewhat. Think

about

it

• Do you consider the distinction between reasoning and rationalizing a useful one? • Can you think of occasions in your own life when you thought you were reasoning but, in retrospect, were probably rationalizing? • Do you think it might be easier to recognize rationalization when it is being done by someone else than when it is being done by one's self. If so, why? 2.7

LIMITATIONS A N D I M P E D I M E N T S TO EFFECTIVE REASONING

We have remarkable pieces of machinery in our heads. They are really quite wonderful and mysterious—awesome is not an inappropriate word. We

2.7

LIMITATIONS AND IMPEDIMENTS TO EFFECTIVE REASONING

15

have only the vaguest idea how they do some of the things they do. However, they are by no means perfect. In particular, the evidence is abundantly clear that we often do not reason as effectively as we might. We do not know all the causes of faulty reasoning. However, we can identify certain factors that undoubtedly lessen our effectiveness as reasoners. Natural Limitations

While the capabilities of the human brain are truly remarkable, it also has some limitations, and some of those limitations have implications for the way we reason. One such limitation is that of memory and the accessibility of the knowledge that we have stored there. It is very difficult, perhaps impossible, to be sure that an individual model of the world is internally consistent—that each of one's beliefs is compatible with all the others— because we cannot recall at any given instance all that we know, or even all that we know that is relevant to a particular topic. Another limitation that has implications for our ability to reason is the fact that we are unable to think of many things at once. In dealing with any very complex problem, it is necessary for us to break it into small manageable parts, and work on those parts in sequence. We may be aware, for example, of a large number of factors that should be considered in judging how much credence to give to some claim, but we cannot consider all of them at the same time. We cannot, as it were, take in the whole picture in one glance. So, we are obliged to consider the factors individually and then somehow to combine the results of the somewhat fractionated thought process into a cohesive whole. The point is not that we are able to do this, but that we have no choice. How this limits our reasoning ability is not clear; that it does is certain. K n o w l e d g e Impediments

Sometimes a distinction is made between knowledge and reasoning ability. Knowledge is information that we have stored away in our heads; reasoning ability includes the ability to analyze, evaluate, and construct arguments. The distinction is a useful one, but it should not be drawn too sharply. While it may be possible to acquire some knowledge without demonstrating very great reasoning ability, it is probably not possible to reason very effectively in the absence of a substantial knowledge base. There are at least three types of knowledge that seem to be important, if not essential, to effective reasoning: topical knowledge, procedural knowledge, and self-knowledge. Topical

Knowledge

Topical knowledge refers to knowledge about a particular domain \ factual knowledge, declarative knowledge, and domain-specific knowledge have similar connotations. Topical knowledge refers to the kind of knowledge we must bring to bear in order to decide whether to accept any particular

16

2.

REASONING IN PERSPECTIVE

assertion as true, it is the kind of knowledge we must tap in order to generate a list of pros and cons relating to some decision alternative, to construct an argument in defense of some position, or to determine whether to believe some claim. It is the kind of knowledge we need in order to be able to think of counterexamples to claims we might wish to challenge. Although topical knowledge may be of limited value in the absence of reasoning ability, there can be little question about the claim that given adequate reasoning skill, the more we know about a particular topic, the better able we are to reason effectively about it. Procedural Knowledge

Knowledge of the rules of logic does not by itself guarantee effective reasoning, because, as we have noted, reasoning is, among other things, a creative process, on the other hand, ignorance of the rules of logic is very likely to ensure reasoning difficulties. In addition to the rules of logic, there is a great deal of procedural knowledge that can facilitate reasoning in a variety of ways. Knowledge of how to use diagrams, truth tables, and other ways of representing class or logical relationships can be helpful, as can knowledge of how to use a decision tree, a payoff matrix, a cost-benefit analysis, and many other reasoning tools. A skillful carpenter can do better work with a few simple tools than a poor carpenter can do with a complete set; however, even the best of carpenters will find it difficult to do finish work if all he has to work with is a hammer and saw. The analogy is a fairly apt one. A person with good reasoning ability can perhaps do better at many reasoning problems than can a poor reasoner who happens to know about a lot of procedures. However, even a good reasoner will find it difficult, if not impossible, to solve certain types of problems without the intellectual tools, the procedural knowledge, that those problems demand. Many procedures have been developed that can help us reason more effectively. Knowledge of those procedures and how to use them can facilitate our reasoning immensely. Self-Knowledge

We are in a much better position to exploit our own strengths and to compensate for our own weaknesses if we know what those strengths and weaknesses are. Thus, self-knowledge, and in particular, knowledge of our own capabilities and limitations as reasoners, is an important aspect of reasoning. It may be helpful to think of self-knowledge as being of two types. First, there is the knowledge of reasoning-related capabilities and limitations of human beings in general. While we are still a long way from a very thorough understanding of the human mind and how it works, much is known regarding things we do well and things we do poorly that has relevance for

2.7

LIMITATIONS AND IMPEDIMENTS TO EFFECTIVE REASONING

17

the way we should approach reasoning problems and for the selection of the kinds of tools and aids we should use. We also know that certain types of reasoning errors are commonly made by large numbers of people. That knowledge, too, can be helpful in making us better reasoners: presumably, if we know that a certain type of reasoning error is prevalent, we can be on our guard against making that type of error. The second type of self-knowledge to have is knowledge of our personal strengths and weaknesses as they pertain to reasoning. If, for example, we have a tendency to jump to conclusions without adequately considering all the available evidence, if we have a particularly good or particularly poor memory for details, or if we have sufficiently strong views on certain topics so as to preclude dealing impartially with arguments pertaining to those topics, it is well to be aware of such facts. Attitudinal Impediments

Another class of impediments to effective reasoning might be considered attitudinal or motivational. For example, ineffective reasoning sometimes is undoubtedly due to simple carelessness or lack of interest in having a reasoned position on a particular issue. Although most of us probably would not wish to be considered unreasonable or unreasoning people, not all issues are of great interest to us, and we may, in some cases, be willing to hold beliefs that have not been carefully thought out. Reasoning through issues, particularly complex ones, can be difficult work; sometimes we are not willing to make the effort that is required to gather relevant information, understand the pertinent factors, and come to a reasoned position. Moreover, in a culture that puts a premium on decisiveness, we may feel pressure to take sides in controversial matters, even when we are ill-prepared to do so. We may feel obliged to vote at elections and on referenda, for example, even if we have been unwilling to take the time to educate ourselves about the candidates or choices involved. Thus, people with good reasoning ability may find themselves behaving in an unreasoning way. It also seems that we tend to want—perhaps need—explanations, and often the easiest way to get an explanation is to accept one ready-made. Sometimes we adopt an offered explanation uncritically for no better reason than an unwillingness to invest the time and effort required to produce an explanation that fits the facts. Attitudinal impediments to reasoning also arise sometimes from vested interests. A strong desire for a particular outcome or a preference for one of several possible conclusions that an investigation might produce can interfere with a fair and impartial weighing of evidence. In fact, the problem of vested interest might be the most serious impediment to reasoning that there is. The most subtle manifestation of vested interest may be seen in our frequent failure to distinguish between impartially weighing evidence and

18

2.

REASONING IN PERSPECTIVE

building a case. There is a very great difference between weighing evidence objectively, with the goal of coming to an unbiased conclusion on some matter, and using evidence to support a conclusion that we have already drawn. Unfortunately, the difference seems to be more easily recognized by a disinterested witness to a dispute than by a participant. We seem to be amazingly adept at convincing ourselves that we are being unbiased and objective, even—perhaps especially—when we are being most parochial in our behavior. The unwillingness, or inability, to be objective when engaged in disputes can be seen at all levels of disputation, from individuals discussing local politics, to disputes between special interest groups (e.g., labor and management) regarding issues of mutual interest, to government leaders arguing matters of international relations. Typically, in such confrontations, both parties claim to be rational and objective. It seems reasonable to assume, at least in many cases, that the claim is a sincere one. Biases are seldom perceived as such by the people who hold them, which is what makes the problem of bias such an insidious one. How might the problem be attacked? How might people be convinced to accept the idea that it does not matter who is right and who is wrong (assuming it is not an oversimplification to think in those terms), but that the importance lies in arriving at a reasoned conclusion and in being willing to modify that conclusion in the light of further relevant evidence or information? Those are not easy questions to answer. We allfindit difficult to give due weight to ideas that we dislike, to admit that our reasoning may have been fallacious or incomplete, to modify positions that we have taken, especially in public. We are highly motivated to demonstrate that those views are correct and can be substantiated with evidence and arguments. At the same time that we pay homage to the idea that we are committed to the truth independently of what the truth might be, we are also strongly biased to defend our own views. Think about it

• Why is it that the development of a carefully reasoned position on an issue, particularly a complex issue, requires an investment of time and effort? • How may lack of interest in an issue contribute to the uncritical acceptance of a position with respect to that issue? • Consider the idea that great interest in an issue—and in particular vested interest in the outcome of an investigation or a decision process—can have the effect of making our reasoning on an issue less objective than it should be. • Consider your own strengths and weaknesses as a reasoner. Try to identify your greatest asset as a reasoner and your greatest liability or limitation.

3

Beliefs

Our understanding of the world is represented in our beliefs and our behavior is determined by them. Beliefs are the "stuff of reasoning: they are what reasoning produces and the basis on which reasoning is done. It is by means of reasoning that we modify old beliefs in the light of new information. A primary goal of reasoning is to arrive at beliefs that are as consistent as possible with the evidence available to us about reality. The concept of belief is central to the view of reasoning that is presented here. As already noted, belief is assumed to be an intuitively meaningful concept. I expect most people to understand what I mean, for example, when I say that one of my beliefs is that the earth revolved about the sun, and that another is that skill in reasoning is an asset in life. Each of us believes certain things to be true and certain other things to be false. Sometimes we are not sure whether we believe a particular thing to be true or false. Sometimes we can give good reasons for believing something to be true or false, and sometimes we cannot. However, whether or not we can give good reasons for what we believe, our beliefs play key roles in our lives because they determine, to a large degree, how we act. Not only do we all have many beliefs, but also we are continually being given opportunities to acquire new ones. Everyday we encounter claims from many sources (the newspaper, radio, television, books, friends, employers, employees, teachers, students, classmates) about various aspects of the world. We must decide which of those claims to accept as true and which of them to dismiss as false. This is a very demanding task, but one that we cannot avoid. As a consequence of all our experiences over all the years of our lives, each of us acquires a system of beliefs about ourselves, about our 19

20 3. BELIEFS acquaintances, about work, about education, about language, and about the world in general that is really quite complex. Some of those beliefs are old, strong, and unchanging. For example, the belief that if one jumps as high as one can, one will not keep going up, but will quickly return to the ground is such a belief for most of us. In contrast, some of our beliefs have been acquired very recently and may be weakly held and readily subject to change. The belief that there is an extraordinarily large region in the universe that contains no stars is such a belief for me. I acquired it only weeks ago from reading an article in a scientific publication; I have little basis to judge its plausibility other than the claim of the author who wrote the article; and I am prepared to change the belief readily if I come across evidence disconfirming the claim. Given the central role that beliefs play in our lives, effective reasoning requires both an awareness that our beliefs are indeed beliefs and a desire to make those beliefs consistent with whatever relevant evidence is available. That means a willingness to examine our beliefs, even those that are old and well established, to try to understand what they are and the basis on which they are held, and to modify them when the evidence indicates that they should be modified. It also means a recognition that some beliefs are held more strongly than others. Finally, effective reasoning demands a continuing effort to make the strength of any belief commensurate with the weight of evidence in its favor. In the following sections, several aspects of beliefs and their importance to reasoning are discussed. 3.1

BELIEFS V E R S U S OPINIONS

The terms belief and opinion are often used as synonyms. As was suggested earlier, however, it is important to make a distinction between the concepts. When the term belief is used here, it should be understood to mean a belief about objective reality. Thus, the statement The sun is very much larger than the moon represents a belief that probably all of us hold and, indeed, one that we hold on very good evidence. Compare that with the statement Chocolate ice cream tastes better than vanilla. That too might be considered a belief that at least some of us hold; however, it is rather different from the first example, because even those of us who believe that chocolate ice cream tastes better than vanilla would probably be willing to admit that it is a matter of personal preference and not something on which we would expect agreement by anyone who examined the facts.

3.1

BELIEFS VERSUS OPINIONS

21

Therefore, it seems more appropriate to refer to the ice cream statement as an opinion than as a belief. We might say that a belief is something that, at least in principle, can be shown to be either true or false. It does not make sense to say that an opinion is true or false, because people differ greatly in their preferences and tastes. So what would be true, or right, for one person might be false, or wrong, for another. Here, an effort will be made to use beliefs to represent our ideas about what is objectively true, and opinions to represent such subjective matters as preferences and tastes. However, more important than terminology is our recognition of the two different concepts. Most of our attention will be devoted to the first, or what we are referring to as beliefs, inasmuch as they are more important in the context of a discussion of reasoning. However, to clarify for yourself the distinction between beliefs and opinions as those terms are used here, you may find it helpful to do the exercise in Table 1, which involves sorting assertions into the two categories. For most cases in Table 1, you will probably find it quite easy to decide whether the statement should be thought of as representing a belief or an opinion. It is not always so easy, however, to make that judgment. Consider, for example, the following assertion: Tom has a better personality than Dick. Is that a belief or an opinion? You might argue that it is a belief, because in principle it might be possible to determine which of two personalities is the better. On the other hand, what constitutes better in this case is probably a matter of debate. So you might consider it more appropriate to think of the assertion as representing an opinion. Consider the following assertion: The TV program "All in the Family" was a very humorous program. Table 1 Distinguishing Opinions from Beliefs

7. Baseball is more fun to play than basketball. 2. Rock 'n' roll music is not at all enjoyable to listen to. 3. There are more termites than people in the world. 4. It is better not to play a musical instrument at all than to play one poorly. 5. The core of the Earth is molten iron. 6. Being a doctor is more satisfying than being a lawyer. 7. Milk is more nutritious than coffee. 8. Mathematics is a boring subject. 9. Hydrogen is the most abundant element in the universe. 10. Sugar is a primary cause of tooth decay. The correct answers (from my point of view) are given in the answer key at the back of the book.

22 3. BELIEFS Again, you might be willing to think of this as a belief on the assumption that it is possible in principle to determine how humorous something is. On the other hand, inasmuch as what is considered humorous by one person may not be considered humorous by another, you might argue that it makes more sense to think of that statement as an opinion. Certainly if one persons says, "I think 'All in theFamily'was humorous," and another person says "I do not think it was humorous," you cannot say that either of them is wrong. Thus, we see that sometimes it may not be entirely clear whether a particular assertion represents a belief or an opinion. However, that does not diminish the importance of the distinction. Many, if not most, of the category distinctions that we find useful become fuzzy at their boundaries. The distinction between children and adults is certainly a useful one, but the line dividing members of one category from those of the other cannot be very sharply drawn. The distinction between mammals and nonmammals also serves a useful function, in spite of the fact that there are certain species (e.g., the duckbill or platypus) that are not easily classified in those terms. Likewise, the distinction between beliefs and opinions can serve a useful purpose, even though there may be instances that are difficult to classify unambiguously as either the one or the other. Think

about

it

• Why is the distinction between beliefs and opinions an important one? • How might a failure to make that distinction contribute to unnecessary disputes? • The area of ethics is one in which the dividing line between beliefs and opinions is often quite fuzzy. Consider how one can resolve disputes regarding questions of morality or ethical right and wrong. Might it be that sometimes such disputes are not resolvable? • Consider the following statements: "It is my belief that, on the average, people in industrialized countries have more material possessions than did their predecessors of a hundred years ago." "It is my opinion that on the average, people in industrialized countries are not happier today than were their predecessors of a hundred years ago." Is the use of "belief and "opinion" here consistent with the foregoing discussion? 3.2

PROPERTIES OF BELIEFS

Any belief may be characterized in terms of a variety of properties. Here are a few possibilities:

3.2

PROPERTIES OF BELIEFS

23

• Explicitness: The extent to which a belief is articulate. A belief may be more or less well formulated. To lack a belief is quite different from holding a false one. Our information-seeking behavior may be different before we have arrived at a well-formulated belief than after. In the former case, we may be motivated to arrive at a clear and true belief. Once a belief has been formulated, however, our information-seeking strategy may shift to collecting data to corroborate an already established belief-to increase our confidence in that belief by acquiring more evidence in its favor. • Veridicality: The degree to which a belief reflects reality. Probably most of us want, or at least believe we want, our beliefs to correspond as closely as possible to reality. A primary motivation for science is to develop beliefs—theories—that are accurate representations of at least certain aspects of reality. Although one might argue that we can never know for certain how close we have come to realizing that objective in any particular case, inasmuch as the question of the extent to which a belief reflects reality is itself a matter of belief, we will avoid that problem here and accept the idea that for most purposes the rules of evidence commonly applied in science suffice to distinguish among beliefs with respect to veridicality. • Logical validity: The degree to which a belief is at least consistent with, and preferably derivable from the information we have at our disposal. Note that logical validity is not the same as veridicality. If the information we have available on a specific topic is very limited, we may hold a belief about that topic that is logically valid vis-a-vis that information, even though in the light of more complete information, it would be considered nonveridical. Many generally held beliefs that were logically valid in the past are now known to be nonveridical; many of the beliefs we now hold are logically valid in terms of currentday knowledge but may well prove to be nonveridical when more has been learned about the world. • Strength: The degree of confidence the holder of a belief has in that belief. One crude, but compelling, measure of our confidence in a belief is your willingness to act as is the belief were true. Our insistence that we are confident that a bridge is safe may be suspect if we are unwilling to step onto that bridge. • Relatedness: The degree to which one belief has implications for others within an individual's belief system or conceptual model of reality. One can make a case that everything is related to everything else but that the relationship is more direct and obvious in some instances than in others. However that may be, for practical purposes, the relationship between two beliefs is sometimes sufficiently remote that the truth or falsity of one seems to have no implications for the tenability

24

3.

•

• • •

•

•

BELIEFS

of the other. In other cases, the relationship is sufficiently strong that a change in the tenability of one belief has immediate consequences for the tenability of the other. Relatedness is a difficult property to objectify, but it is an important one nonetheless. Consistency: The degree to which a belief—as one element in a system of beliefs—is logically consistent with other elements of that system. This is more properly a characteristic of a set of beliefs. A particular belief may be consistent with some elements of the set and inconsistent with others. It is not to be assumed, of course, that identification of logical incompatibilities in a set of beliefs is inevitably sufficient to effect a modification. Age: How long a belief has been held. Public commitment: The extent to which a belief has been made public. Evidence suggests that beliefs are more difficult to change after a public commitment has been made to them than before. Value: The extent to which the holding of a particular belief is important to the individual who holds it. It may be very important to the individual to have a well-formulated belief about a particular aspect of reality and quite unimportant to have any belief with respect to another. A change in, or demonstration of the implausibility of, one belief might have serious implications for a person's philosophy, value system, or behavior, whereas in the case of another belief, a necessitated change might be inconsequential. Malleability: The degree to which a belief is modifiable by relevant information. This property is not to be confused with confidence. Malleability has to do not with the degree to which one is convinced of the veridicality of a belief, but rather with the ease with which it may be modified by evidence. There tend to be strong links between this property of beliefs and others, such as value, commitment, and age. The amount of evidence that may be required to effect a very radical modification of a belief is unlikely to be independent of the degree of public commitment, the critical nature of the belief with respect to a valued set of beliefs, and the consequences of a change. Plausibility: The credibility or compellingness of a belief. This is the property of beliefs that will be emphasized here. Inasmuch as plausibility is more or less synonymous with believability, the property may sound redundant — any belief must be believable, or it would not be believed. But our interest is not in the fact that beliefs are believable, or plausible, but in the question of what makes them so. Two questions might be asked in this regard: 1. What determines how plausible any given claim will be? 2. What should determine how plausible it will be? The first is a question of psychology: What makes us the way we are? The second is of interest for pedagogical purposes; if we could say

3.3

ON DECIDING WHAT TO BELIEVE

25

what should determine plausibility, we might be able to give some useful instruction in how to form reasonable beliefs. Think

about

it

• Can you add to the above list some other properties that characterize beliefs? 3.3

O N DECIDING W H A T TO BELIEVE

A significant reasoning problem that each of us faces daily is that of deciding what we should and should not believe. You read on the front page of the newspaper that Poland has declared martial law. How do you know whether the claim is true? Should you believe it or not? You hear a candidate for public office claim that most major corporations are insensitive to environmental problems and oppose any kind of government action that is aimed at conserving natural resources or protecting the environment from pollution. Should you believe that claim or not? You have been saving money to buy a radio, and now have enough but do not know which type to get. In a magazine, you find an ad for Brand X radios. The ad claims that Brand A" makes the best radio available for your price range. It claims that last year Brand X sold more radios than the two leading competitors combined. Should you be persuaded by the ad to buy Brand X? From every quarter, each of us is being told more or less continuously that certain things are so. Newspapers, magazines, books, radio, and TV bombard us with assertions that purport to represent the facts. Often information is given to us for the purpose of influencing our behavior in some specific way. Advertisers make claims about products in the hope of influencing us to buy those products; politicians tell us about the dire consequences of voting for their opponents and the benefits of voting for themselves, in the hope of influencing our voting behavior; parents and teachers give us information and advice in the hope of influencing our personal or academic behavior. Most of us are probably naturally skeptical of claims that we recognize as being intended to influence our behavior, especially if the behavior that is being encouraged would have beneficial consequences for those making the claims. We are probably less likely to be skeptical of the "factual" reporting of news in the various news media, on the assumption that the only

26

3.

BELIEFS

motivation for that reporting is to provide us with accurate information about what is going on in the world. However, we must recognize that the media are businesses and can survive only so long as they have listeners, viewers, and readers; and the market is highly competitive. Consequently, there are pressures both to present the news that people want to know about and to present it in the way that they want to receive it. In other words, news is a commodity that must be sold, and the seller who has the most attractive package from the buyer's point of view is most likely to survive and prosper. Accuracy, of course, or at least the appearance of it, is undoubtedly one of the factors that helps sell news, but it is certainly not the only one. All of that being true, deciding what to believe is a very complex problem, and one that is constantly with us. It is quite clear that we cannot reasonably believe all the claims we hear or read, because many of them are mutually contradictory. But how do we decide whether to believe a particular claim or not? Less simplistically, how do we decide how much credence (where the extremes are complete belief and complete disbelief) to give to any particular claim? We will return to that complex question in subsequent chapters in discussing assertions and arguments. Suffice it to say at this point that the problem of determining whether—or the degree to which—we should believe this, that, or the other thing is as fundamental as any problem that life presents, and it is central to what reasoning is all about. Think

about

it

• Suppose one were not all critical with respect to what one hears or reads, and accepted everything without question. What would be the effect on one's belief system? 3.4

BELIEF A S A M A T T E R OF D E G R E E

When we say that a person either believes something or does not, we oversimplify things quite a bit. A more accurate conceptualization of beliefs would recognize that they vary in degree. We all believe some things more strongly than others and also disbelieve some things more strongly than others. To say the same thing another way: our degree of confidence in the truth of an assertion may vary from very high to very low. We recognize that fact when we describe our beliefs in such terms as "I am positive," "I am quite sure," "I am not sure, but I think," "I guess," and so on. It is important to recognize this aspect of our beliefs about the world, and indeed it is reasonable that we should hold different beliefs with different degrees of confidence. In general, the amount of confidence we have in a

3.5

CONSERVATIVISM

27

Table 2 Assorted Assertions

After each statement put a Tor F indicating whether you think it is true or false, and a number from 1 to 5 indicating how confident you are of your answer, letting the numbers represent roughly the following degrees of confidence: 5, certain; 4, very sure but not certain; 3, moderately sure; 2, not at all sure, but better than a guess; 1, pure guess. The correct true-false answers are given in the answer key at the back of the book. 1. The sun is larger than the moon. 2. The population of Spain is larger than the population of Italy. 3. Bananas are a good source of protein. 4. Caracas is the capital of Venezuela. 5. Turtles lay eggs. 6. The Suez Canal is in Asia. 7. Many cities are located near rivers. 8. If the following statement is true, then "this man" is me: Brothers and sisters have I none, but this man's father is my father's son. 9. All species of birds can fly. 10. Peru is larger in land area than Brazil. 11. The longest river in the world is the Amazon. 12. The earth is the fourth closest planet to the sun in the solar system. 13. The largest bird with an ability toflyis the albatross. 14. Wombats are marsupials. 15. Infants have more bones than adults. 16. Mt. Everest in Asia is the tallest mountain in the world. 17. Water boils at a higher temperature on a mountain top than at sea level. 18. There is more nitrogen than oxygen in the earth's atmosphere. 19. The scientist who is remembered as having first described the law of gravitation is Isaac Newton. 20. The liver is the largest gland in the body. 21. Viruses are larger than bacteria. 22. Chess is one of the oldest games known. 23. The printing press was invented by a man named Switzer. 24. Franklin Pierce was the 21st president of the United States. 25. The flag of Sweden is yellow and blue.

belief should depend on the amount of evidence we have that the belief is true. Also, if we are reasonable people, we should be willing to modify the degree of confidence we have in a belief as we obtain new evidence regarding its likelihood of being true or false. By way of gaining a direct feeling for the fact that your beliefs about the world do indeed vary in strength, you may wish to do the exercise in Table 2. 3.5

CONSERVATIVISM

One could probablyfindevidence to support the notion that many of us find general statements attractive. Somehow, we seem to prefer to be able to say,

28

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BELIEFS

"All A are B" than to be able to say, "Many A are B" or even, "Most A are B." It is important to recognize, however, that the statement "AIM are B" is a much more extreme statement than the other two. In general, the most extreme statement is less likely to be true than are the less extreme statements; it is also much more easily proven to be untrue when in fact it is untrue. Those are points worth bearing in mind when forming beliefs based on generalization. Having noted that all the members of class A that I have observed have property B, I am tempted to infer that all members of class A, including those that I have not observed, have property B. Before making such an inference, however, I might do well to bear in mind that a much safer inference to make is that many, or perhaps most, members of class A have property B, and that the conclusion that some members of class A have property B involves no risk of error at all. Whether I opt for a more or less conservative statement should depend on how important it is that it be correct or, more precisely, on how I feel about the various ways in which I could be wrong. Think

about

it

• Consider the advantages and disadvantages of stating something too conservatively or not conservatively enough; in other words, the advantages and disadvantages of understanding and overstating. • Consider the following assertion : General statements are risky because they tend to be easy to prove wrong when they are wrong and very difficult to prove true when they are true. 3.6

SUSPENDED JUDGMENT

In keeping with our preference for saying, "All A are B," decisiveness is often applauded as a commendable personality trait, and indecisiveness is viewed as a sign of weakness or lack of character. There may be something to that view. It is certainly true that life often demands that we make decisions, even when we lack the information necessary to give us high confidence that the decisions we make are correct. The ability to act decisively when decisiveness is called for should not be confused, however, with the habit of jumping to conclusions prematurely. While we are sometimes forced to make decisions on the basis of incomplete information, it is also true that we often have the option of suspending judgment on an issue until more complete information can be obtained. It is not always true that the failure to take a strong stand on an issue is evidence

3.7

THE R E A S O N A B L E USE OF INCOMPLETE INFORMATION

29

of weakness. If we have insufficient information on which to base a stand, we might do well in refusing to take one. The ability to suspend judgment is a skill that requires cultivation. We seem to like to have explanations, so much so as to invent them readily when they are not otherwise forthcoming. Similarly, we seem to feel compelled to take sides on an issue even when we may be ill-prepared (in terms of the information in our possession) to do so. Unfortunately, we often are not very critical with respect to the explanations that we are willing to accept or the positions we are willing to adopt. Think

about

it

• Consider the following proposition: One should always be prepared to take some side of any issue. Do you find this a reasonable proposition? • Consider the idea that when we encounter a claim and cannot decide whether or not to believe it, we have the option of "suspending judgment"—that is, of taking the position of neither believing nor disbelieving it. 3.7

THE REASONABLE USE OF INCOMPLETE INFORMATION

Given that we are sometimes forced by circumstances to make decisions, or to come to conclusions, on the basis of less than complete information, how can we act reasonably in such cases? Several formal techniques have been developed in response to that concern. These techniques are designed to help us achieve certain specific goals. One such goal might be to quantify our degree of knowledge or uncertainty about the particular situation. Another might be to help us make a decision in such a way as to limit the potentially undesirable effects from that decision or to try to maximize the desirable effects. We will not cover such techniques in this book. Descriptions of them can be found in books on decision making (in particular, decision making under uncertainty) and on probability theory. However, two points about dealing with incomplete information are worth noting here. First, when faced with the prospect of making a decision or drawing a conclusion on the basis of inadequate information, it is always reasonable to consider whether additional information can be obtained. While additional useful information is not always available, we sometimes deal with information that is unnecessarily incomplete; that is, we could obtain more information if we made the effort to get it. One important aspect of being an effective reasoner is skill in seeking and finding information. That means knowing where to look to find answers to specific

30

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BELIEFS

types of factual questions. It means being familiar with encyclopedias, almanacs, atlases, dictionaries, and other standard information sources; and it means knowing how to use information "pointers," such as tables of contents, indices, reference lists, and catalogs. The second point about dealing with incomplete information is this: When we are forced by circumstances to come to a conclusion or to make a decision on the basis of inadequate information, we do well to bear in mind that inadequacy. This means we should recognize the tentativeness of the conclusion that is drawn or the riskiness of the decision that is made. It also means that we should stand ready to modify the conclusion or reverse the decision (if that is possible) if further information indicates that a change is warranted. Think about it

• When we are faced with the need to make decisions, and we do not have as much information as we would like, sometimes we may realize that more information could be obtained, albeit at some cost in terms of time and effort. Consider the notion that whether we should try to obtain the additional information under such circumstances depends on the worth of the information relative to the cost of obtaining it. How we determine the worth of information is an interesting topic. For present purposes, it is perhaps enough to note that the value of the information that might influence a given decision depends in part on how important it is that the decision be made correctly, or, in other words, on what the cost would be of making the wrong decision. • Researchers have noted that once people have made a decision or taken a stand on an issue, especially if they have done so publicly, they are likely to become less objective in their use of information relevant to that decision. Before we have made a decision, we seem to be able to assess relevant information in a less biased fashion than after we have made a decision. Afterward, we are inclined to attach more weight to the information that supports the decision we have made than to information that tends to show it to be wrong. Consider what we can do when forced to make a decision on the basis of incomplete information to maintain an open mind with respect to the issue and to be able to evaluate subsequently acquired information objectively. 3.8

RELEVANCE

An aspect of reasoning we take very much for granted is that of judging relevance. If you were to say, "I believe that medical science willfinda cure for most types of cancer within 25 years," and I replied, "But Napoleon was

3.9

THE MYTH OF OBJECTIVITY

31

really defeated by the Russian winter," you would think me odd. If you wished to give me the benefit of the doubt and not write me off as completely irrational, you would suspect either that I had misunderstood your comment or that I was trying to make a point in a metaphorical or indirect way. Napoleon's encounter with the Russian winter simply seems to have nothing to do with your belief that cancer may be conquered in the near future. We all make judgments of relevance. Indeed, we do so with such frequency and so naturally that we are hardly aware of what we are doing. We do not really know, however, how relevance is judged. What determines whether a particular fact will be considered relevant to some belief, or, more precisely, what determines how relevant it will be considered to be is not clear. Sometimes relevance or its absence is easy to determine, but not always. That is to say, in some cases we would expect to get general agreement as to whether or not a particular fact is relevant to a particular belief. There are exceptions, however. It is not uncommon for an item of information introduced in a court proceeding to be stricken from the record on the grounds that it is irrelevant to the issue under consideration. Presumably, the individual who introduced the item as evidence believed it to be relevant, whereas the judge did not. Similarly, most of us have undoubtedly had the experience during a dispute of disagreeing with someone as to whether or not some particular point was relevant to the focus of the dispute. Think

about

it

• Consider the question of what makes a fact relevant to a decision or belief. • Think about the notion that the weight that should be attached to any given consideration in a decision problem depends in large part on the degree of relevance of that consideration to the problem. 3.9

THE M Y T H OF OBJECTIVITY

Much homage is paid to the idea that one should approach problems objectively and with an open mind. Probably few people would challenge that idea. Clearly it is a noble one. However, there is very little evidence that the philosophy has many practicing adherents. People find it exceedingly difficult to approach problems objectively, except perhaps problems in which they have little interest. That observation is particularly germane to the subject of beliefs. There can be little doubt that beliefs are strongly influenced by personal preferences and desires. Thus, information that might be considered mildly supportive of a belief toward which one is indifferent may be taken as

32

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BELIEFS

compellingly supportive of that same belief by one who has a strong vested interest in it. Moreover, the amount of contrary evidence that is required in order to change an established belief is probably greater the more that belief reflects one's own preferences. Of course, we should try to be as objective as possible, but while doing so we should recognize the very great likelihood that in spite of the best of intentions our reasoning is likely to be influenced by our own desires and biases. In other words, it is prudent to work on the assumption that objectivity is probably the exception to the rule, and it is prudent to be on our guard, especially for the possibility that our own reasoning is less than completely free of bias. Think

about

it

• Write down several issues about which you would find it relatively easy to be objective; then list several issues about which you would find it relatively difficult to be objective. • Think of reasons why it may sometimes be difficult to be completely objective about beliefs that are important to you personally. 3.10

C O N S E Q U E N C E S OF F A L S E BELIEFS

Some false beliefs are inconsequential, and some are not. The fact that some false beliefs are inconsequential means they may not be corrected as the result of a natural process; the person who is convinced that walking under ladders is bad luck will probably not suffer greatly as a consequence of behaving as though this were true. Most of us probably indulge ourselves in similar harmless superstitions, even though we may not recognize them as such. On the other hand, some false beliefs, such as the belief that one can fly byflappingone's arms, would get us into difficulty and should be avoided at all costs. The problem is that false beliefs are, by definition, not recognized as false by those who hold them, and whether or not they are consequential may be discovered, in some cases, only at considerable expense. There are times when we must choose among alternative beliefs or viewpoints on some basis other than objective evidence regarding their truth or falsity. It may be, for example, that two competing points of view are equally plausible in terms of the available evidence. What does a reasonable person do in such a case? One approach is to resort to some variant of Pascal's wager. The French philosopher Blaire Pascal pointed out that when there are more ways than one to be wrong, some ways may be preferred to others. It may make sense to apply that line of reasoning when we find ourselves with what appear to be

3.11

SUMMARY

33

equally likely hypotheses only one of which can be correct. Here, consideration might best be given to the consequences of the ways in which we can make the wrong choice. If some possible ways of erring are strongly preferred over others, we may be able to narrow the set of alternatives on that basis. Suppose, for example, that someone has just invented a new kind of flying machine. The inventor claims that the machine is perfectly safe and can be flown by anyone on the very first try. Imagine that the inventor has the machine on the top of a very high cliff and has just asked you to try it out by getting in it and having it pushed over the edge. Your problem is to decide whether you believe the assertion that the machine is safe and can be flown by anyone on the veryfirsttry. There are two ways in which you can make an error. One is to believe that the assertion is false when it is really true, and the other is to believe that it is true when it is really false. It seems reasonable in such a situation to consider the consequences of both possibilities. If you believe the assertion to be true when it is really false, and you act on that belief, you will have a very serious problem. You will get in the machine, have someone push you off the cliff, and discover that the machine does not fly. Alternatively, if you believe the assertion to be false when it is really true, the consequences are benign by contrast. In this case your refusal to get in the machine would cost you only the opportunity of flying it. Assuming you would consider the successful flying of such a machine to be a pleasurable experience, either way of being wrong is undesirable; however, foregoing a pleasurable experience may strike you as a somewhat more tolerable decision outcome than ending up in a heap at the bottom of the cliff. 3.11

A P P R E C I A T I N G O P P O S I N G BELIEFS

If we want to be able to reason effectively, a skill well worth cultivating is that of being able to see things from a point of view different from our own. It is an exceedingly difficult thing to do. It is one thing to be able to state someone else's position; it is quite another thing to be able to appreciate it and to state it in nonpejorative terms. In the nature of things, if we believe X, and if y is antithetical to X, we are unlikely to believe Y. Not believing Y, it is difficult—perhaps impossible—to see y from the vantage point of someone who does believe it. However, the fact that it is difficult makes the skill all the more important to develop. The possibility that it is impossible should make us aware that even having tried to see an issue from another person's point of view, we may have failed to do so; but that is not a good reason for not trying. Lack of interest in how other people view things and failure to try to understand other points of view are

34

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BELIEFS

undoubtedly at the root of countless unnecessary misunderstandings and disputes. Think about it

• Consider the notion that probably one of the greatest single contributors to misunderstandings and disagreements is the inability or unwillingness to see things from another person's point of view. 3.12

SUMMARY

In the introduction to this chapter, the point was made that beliefs are the "stuff of reasoning, that they are what reasoning produces and the basis on which reasoning is done. The ultimate goal of all reasoning is to yield beliefs that are consistent with reality. It is important to recognize that when we have done the best we can to realize that goal, our beliefs are still beliefs. We have no way of assuring their accuracy in any absolute sense. In this chapter, we have considered several ideas pertaining to what beliefs are and how they are formed and modified. However, we have barely scratched the surface of that enormously important topic. Forming and modifying beliefs are lifelong activities. Careful reasoners will be conscious of that fact, and will work hard to assure that their own beliefs are as well reasoned and asfirmlybased on evidence as possible.

4

Assertions

An assertion is a statement that asserts (states positively) something to be true. It is a claim about reality. Here are some examples of assertions: The earth makes one complete revolution on its axis every 24 hours. My soup is cold. Some vegetables are green. There will be an above-average amount of rain next year. Dogs are larger than cats. Assertions are important to reasoning because they are the vehicles through which we express and share our beliefs. That is not to say that one cannot have beliefs that have never been verbalized. It is quite possible that many of us have beliefs that we have never put into words, that affect our behavior nonetheless. However, in order to talk about beliefs, to share them, and to expose them to evaluation, we must make them explicit, and we do so by way of assertions. Assertions are also important to reasoning because they are the building blocks of arguments, and a major aspect of reasoning involves the generation and evaluation of arguments. In arguments, assertions play two roles. On the one hand, they represent the information that is taken as given or known, the input to a reasoning process; on the other hand, they represent the outcome of the reasoning process, or the conclusions that are drawn. Arguments will be discussed in Chapter 5.

35

36

4.

ASSERTIONS

4.1

UNDERSTANDING ASSERTIONS

The first objective we should have with respect to any assertion is to understand it clearly. Some assertions are relatively easy to understand; others can be quite difficult. Some are perhaps beyond understanding. An assertion can be difficult to understand for any of several reasons. It may be poorly expressed; that is, it may be ungrammatical, or the individual who produced it may not have chosen quite the right words to convey the intended meaning. It may be ambiguous, which is to say that it may have more than one possible interpretation. It may be intentionally obscure or unclear, if, for example, the person who produced it wished to speak in riddles or to convey a meaning to some people, but not to others. It may deal with a topic about which we have little knowledge. Sometimes it helps to understand exactly what an assertion means if we represent the relationships mentioned in it with a picture or diagram. Diagrams can be especially helpful when we wish to see whether the relationships mentioned in two or more assertions are consistent and how they fit together. Whenever we use diagrams to represent relationships it is important to bear in mind that there usually is no single correct way to make the diagrams. Usually, any given relationship can be represented in a variety of ways. You should choose the way you find most helpful. We will return to the topic of diagrams in Section 4.5. Think

about

it

• For one day, keep a list of the claims (assertions) that you encounter from all sources (radio, TV, newspapers, books, magazines, friends). • Make a list of reasons why we might fail to understand an assertion. 4.2

T Y P E S OF A S S E R T I O N S

It is important to sound reasoning to distinguish between several types of assertions. In particular, we should be careful to distinguish between assumptions, hypotheses, and statements the truth of which is believed to be supported by evidence. For short, we will refer to the last type as statements of fact, but we should bear in mind that a fact is simply a belief for which there is enough evidence to justify a high degree of confidence. We should also distinguish between premises and conclusions, because those concepts distinguish different roles that assertions play in arguments. An assumption is an assertion that we either believe to be true in spite of being unable to produce compelling evidence of its truth, or are willing to

4.3

QUANTIFIERS

37

accept as true for purposes of debate or discussion. A hypothesis is an assertion that we do not know to be true but that we believe to be testable or at least to have testable implications. In calling something a hypothesis, we make it clear to ourselves and others that we recognize that there is a good chance that the hypothesized claim may be false. A statement of fact is an assertion, evidence for the truth of which we believe to be highly convincing. Failure to distinguish clearly among these types of assertions can often lead to misunderstandings or disputes. The distinction between premises and conclusions is independent of the distinction between assumptions, hypotheses, and statements of fact. A premise is any assertion that is used to support a conclusion. A conclusion is an assertion that is derived from a set of premises. Although we have not yet considered what an argument is, we will anticipate a bit to make the point that a logical argument always contains one or more premises and one or more conclusions. Simple logical arguments typically contain two premises and a single conclusion; however, more complex arguments may contain several premises and more than one conclusion. In such cases, it is usually possible to decompose the complex argument into two or more simple ones, each having only a single conclusion. Premises cannot be distinguished from conclusions except in the context of specific arguments, because premises and conclusions are both assertions and an assertion that functions as a premise in one context may function as a conclusion in another. Any of the first three types of assertions mentioned—assumptions, hypotheses, statements of fact—may serve as premises in arguments. Each of them also may serve as a conclusion. The credibility of a conclusion can be no greater than the least credible of the premises from which it is drawn, so a conclusion cannot be considered a statement of fact unless all of the premises are statements of fact. It is essential to bear that point in mind when evaluating arguments. If the conclusion follows from two premises one of which is considered to be a fact and the other an assumption, the conclusion should not be considered a statement of fact. Think about it

• Look up the definition of hypothesis in the dictionary. Think about how a hypothesis differs from a statement of fact, and why it is important to recognize this distinction. 4.3

QUANTIFIERS

Many of the assertions that we will be discussing can be expressed as statements in forms such as the following:

38

4.

ASSERTIONS

All No Some

are are

are

. .

.

The blanks in those statements could be filled in with any of a large number of words. Of course, whether or not a particular statement is true after the blanks have beenfilledin depends on what words are inserted in the blanks. For example, if we were tofillin thefirstblank of thefirststatement with dogs and the second with animals we would get a statement that is true. However, if we were to fill in the first blank with sheep and the second with insects, we would get a statement that is false. The words all, no, and some are referred to as quantifiers. They are used to make it clear whether or not an assertion is meant to refer to every member of some class. Assertions that contain the quantifiers all or no are sometimes referred to as universal assertions, because whatever is being asserted is being asserted about every member of a class. That may be more apparent in the case of all, but it is also true in the case of no. The assertion "No dogs have wings," for example, is an assertion about every dog, namely that it is true of every dog that it does not have wings. Assertions that begin with some are referred to as particular assertions because what is being asserted is being claimed to be true for only some of the members of a class. In everyday speech, some usually conveys the notion of several, or at least more than one. In logic, however, some is more commonly used to mean literally "one or more," or in other words, "at least one." While ally no, and some are the most common quantifiers, for each of them, there are several other words that are more or less synonymous. Every and each are both often synonymous with all. None or not any may be used in place of no. Many words might be considered logically equivalent to some, for example, a few, many, several, and seven. Sometimes the omission of quantifiers from assertions causes no problem, because what is intended is apparent. For example, if we were to encounter the assertion "Turtles have shells," we would probably interpret that to mean that all turtles have shells. Similarly, if we were to see the assertion "Horses do notfly,"we would probably be willing to interpret that to mean that no horsesfly.On the other hand, most of us probably would not be willing to rephrase "Good things come in small packages" either as "All good things come in small packages" or as "All small packages contain good things." Our willingness to interpret the first two assertions as universal assertions, but not the last, illustrates that our interpretation of language in general and our understanding of assertions in particular are very much dependent on our knowledge of the world. We are willing to interpret the assertion "Horses do not fly" as meaning that no horses fly, because we

4.4

FORM VERSUS MEANING

39

believe that interpretation to be true. We are unwilling to interpret the assertion "Good things come in small packages" as a universal assertion, because we are aware that there are exceptions to that rule. While sometimes the absence of explicit quantifiers in assertions causes us little difficulty because we are able to supply the appropriate quantifiers ourselves, that is not always true. Sometimes it is not possible to determine how inclusive an assertion was intended to be. Consider, for example, the assertion "Dogs are larger than cats." What are we to take that assertion to mean? All dogs are larger than all cats? Some dogs are larger than all cats? Some dogs are larger than some cats? Most dogs are larger than most cats? Average-size dogs are larger than average-size cats? An important thing to note about the ambiguity of the assertion is that we cannot decide whether we believe the assertion to be true or false without first deciding which of the several possible interpretations to put on it. That illustrates a fundamental principle regarding reasoning and, more particularly, the problem of assessing assertions and deciding what to believe: before we can decide whether to believe an assertion, we must be sure we have a clear understanding of what the assertion means. Think

about

it

• Make a list of assertions, without quantifiers, that you consider to be true in some sense but ambiguous. Then add the quantifiers that are necessary to make the assertions unambiguous. 4.4

FORM VERSUS MEANING

It is convenient, for some purposes, to focus on the form of an assertion rather than on its meaning. To help us do that, it is customary to use such statements as: All A are B. No A are B. Some A are B. When we do that, we are using A and B (or other letters) as placeholders for words. That is, we are using a sentence such as All A are B to represent all sentences that have that particular form, irrespective of what words are substituted for A and B.

40

4.

ASSERTIONS

Expressing assertions in this abbreviated way can be a great convenience, because it lets us consider relationships that hold for whole classes of assertions independently of their meanings. Most importantly, however, using abstract symbols (e.g., A, B), rather than meaningful words, helps us focus on the forms of assertions (and of arguments) without being distracted by their meanings. That is especially helpful for maintaining the distinction in our thinking between logical validity and empirical truth. Whenever we evaluate an argument, it is important to keep that distinction in mind: we may want to reject an argument either because it is invalid or because one or more of its premises is untrue, but the basis for the rejection should be clear. We know from the results of many studies, however, that the distinction often is not maintained, and that faulty reasoning may occur as a result. Thus, for example, we are more likely to consider an argument to be valid if we believe the conclusion to be true than if we believe it to be false, even though we know that in evaluating an argument with respect to its validity, we should not be influenced by the truth or falsity of its component assertions. (Regarding the distinction between validity and truth, see Section 5.8.) By using assertions that have no content (e.g., All A are B), we essentially sidestep the problem. 4.5

USING REPRESENTATIONS

Sometimes it helps us to understand assertions better if we represent them with simple diagrams. One way to represent the relationships described in some assertions is with Euler diagrams or Venn diagrams. With such diagrams, we can use circles to represent classes or categories of things and show the way one class relates to another through the way the circles in the diagram relate to each other. For example, consider the assertion "All dogs are animals." That assertion says something about the relationship between two classes of things—dogs and animals. In particular, it says that anything that is a member of thefirstclass, dogs, is also a member of the second class, animals. One way to represent that relationship with a simple diagram is to use one circle to represent the class dogs and another to represent the class animals, and then to show what the assertion says about the relationship between those two classes by the way the circles are positioned. When we draw a circle and label it dogs,

41 we are pretending that all dogs are in that circle and everything that is not a dog is outside the circle. Another way to say that is that the area inside the circle represents dogs and the area outside the circle represents non-dogs. Now, if we want to represent the fact that all dogs are animals, which is to say that everything that is a member of the class dogs is also a member of the class animals, we might draw the following diagram: 4.5

USING REPRESENTATIONS

That is we draw a diagram showing a circle representing the class dogs contained within a circle representing the class animals. If we were to indicate the part of the diagram that represents dogs by shading it, the diagram would look like this:

If we were to shade the part that represents animals, the diagram would look like this:

42 4. ASSERTIONS It is important to note that the part representing animals also includes the part that represents dogs. The shaded area in the following diagram represents animals other than dogs.

Now, the part of the diagram that represents things other than animals is all the area outside the large circle. The part that represents nondogs is all the area outside the little circle, including, of course, the area that is in the big circle but outside the little one. Inasmuch as it would be difficult indeed to shade all the area outside either the big or the little circle, the convention is often followed of enclosing the circles in a rectangle that is used to represent the "universe of discourse," which means, in a word, everything. So with this convention, we could represent nonanimals with this diagram

and nondogs with the following one:

4.5

USING REPRESENTATIONS

43

So far we have used diagrams to represent only the relationship of inclusion, which is the relationship expressed by assertions of the form All A are B. They may also be used to represent relationships of exclusion No A are B and relationships of overlap Some A are B. Thus we could represent the relationship No dogs are cats with the following diagram:

which makes it clear that anything that is in the one class cannot be in the other. The relationship Some dogs are pets could be represented thus:

In this case, one circle represents dogs

44

4.

ASSERTIONS

the other represents pets

and the area common to both circles, the overlap, represents things that are both dogs and pets, which is to say, pet dogs.

We should note that there are two ways to diagram the relationship expressed by the assertion "Some A are Which diagram is appropriate in a particular case depends on whether B is included in A. If we know only that some A are B and know no more about the relationship between the classes, the safest diagram to use to represent the relationship is the one on the left in Figure 1. We must bear in mind, however, the possibility that the area that represents B but not A may have no members. When that is the case, then the left-hand diagram is equivalent, in a sense, to the diagram showing B as included in A1. 1Inasmuch as the assertion "Some A are B" does not logically imply the existence of A's that are not B's, it is consistent both with a diagram showing A within B and with one showing the complete overlap (equivalence) of A and B. That is, when it is true that all A are B, or when it is true that A and B are the same set, it is also true that some A are B. However, the two situations shown in Figure 1 represent the more common uses of the word some.

4.5

USING REPRESENTATIONS

45

Figure 1

Figure 1 illustrates an important point about the correspondence between verbal assertions and pictorial representations of relationships. The pictorial representations typically are less ambiguous than the verbal ones. Thus, the assertion "Some A are tells us only that there are some A's that are B's, whereas the pictures in Figure 1 show different relationships between A and B for which that assertion would be true. In using diagrams to help understand assertions and the implications of sets of assertions, that fact must be borne in mind. Diagrams can be helpful in many cases, but their usefulness is often limited by the fact that a given assertion may be consistent with several diagrams. In logic, various names are used to represent various classes, subclasses, and combinations of classes represented by the overlap diagram. The two classes in combination are referred to as the union, sum, disjunction, or inclusive or of the individual classes (Figure 2A). The subclass common to both classes is referred to as the intersection, product, conjunction, or and of the two classes (Figure 2B). The combination of the two classes exclusive of the subclass they have in common is referred to as the exclusive disjunction or exclusive or (Figure 2C). In this case, it is the combination of things that are dogs but not pets and those that are pets but not dogs. The examples we have considered so far all involve two classes; however, such diagrams can also be used to represent relationships among several classes. Figure 3, for example, represents the relationships among the classes dogs, pets, cats, amoebas, people, Europeans, Spanish speakers, living creatures, gemstones, and rubies. Before we leave the subject of representational diagrams, it is important to note that the diagrammatic scheme considered here is only one among many that can serve the same purpose. Which of the various possibilities

46

4.

ASSERTIONS

Figure 2A.

Figure 2B.

Figure 2C.

would be most suitable in any particular instance may depend on the details of what is to be represented and on the preferences of the user. The main point is that often an attempt to produce a diagram of the relationships expressed by an assertion or a set of assertions can be a useful way of helping to clarify what those assertions do and do not mean.

4.6

WHETHER DIFFERENT ASSERTIONS MEAN THE S A M E THING

47

Figure 3

4.6

O N DECIDING W H E T H E R DIFFERENT A S S E R T I O N S M E A N THE S A M E THING

Before deciding whether to believe an assertion, we should be sure that we understand what it means. Consider the following assertion: Any number in a Fibonacci sequence can be inferred from the preceding two numbers. We cannot know whether or not to believe that assertion if we do not know what a Fibonacci sequence is. Similarly, we cannot decide whether to believe Some pachyderms are ungulates unless we know what pachyderms and ungulates are. Although it is necessary to understand what an assertion means in order to decide whether or not to believe it, it is not always necessary to know what each of two assertions means in order to know whether or not they mean the same thing. That may seem like a strange claim. The reason the claim is true is because the judgment as to whether two assertions mean the same thing sometimes can be made on the basis of the forms of the assertions independently of their meanings. That is an important point, because certain

48

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types of common reasoning errors can be attributed to a failure to understand when different forms mean the same thing and when they mean different things. The point can be illustrated by contrasting positive and negative universal assertions; that is, assertions of the form All A are B and No A are B. There is some evidence to suggest that people often behave as though the assertions All A are B and All B are A mean the same thing. The error is sufficiently common to have a name, and it is called the premise conversion error. In fact the two assertions do not mean the same thing; it is possible for one of them to be false while the other is true. In contrast, the assertions No A are B and No B are A do mean the same thing, because it is not possible for one of them to be false if the other is true. Each of these assertions implies the other. The preceding examples are rather simple and straightforward, although, as noted earlier, we do not always recognize that in interchanging the A and B terms in an assertion of the form "All A are B" we change the meaning of the assertion. There are other instances, however, in which the judgment of whether two assertions mean the same thing is somewhat less apparent. Consider, for example, the assertions Some A are B and Not all A are B. As the terms some and not all are used in everyday conversation, those assertions might be considered equivalent. However, when the terms are given a more precise interpretation, as they are in logic, it is apparent that the assertions do not mean the same thing. In thefirstcase, we are asserting that there are some A's that are also B's (which is an assertion that can be

49 made on the basis of an awareness of one or more A's that are ZTs); but we are not asserting that there exist A's that are not B's (which would require an awareness of one or more things that are A' s but not B's). In contrast, the assertion "NotallA'sare B's" does require an awareness of one or more A's that are not B's, but it does not require an awareness of any A's that are B's. Thus, it could be that one of the assertions is false while the other is true, or, as is more apparent in this case, we could have enough information to know that one of the assertions is true or false without knowing whether the other was true or false. If, for example, you were to hear someone say "some of my dogs are brown", you might well interpret that to mean that some but not all of the speaker's dogs were brown. You probably would be correct, because in everyday speech that is the way the term some is used. If all of the dogs were brown, you would have expected the speaker to say that, rather than to say that some of them were. From a more strictly logical point of view, however, some and not all mean quite different things. The distinction between some and not all may be sharpened by reference to Figure 4. Each of the two following assertions is true about the shapes in the figure: Some of the squares are black. Not all of the squares are black. To see that those assertions do not mean the same thing, imagine that only the top half of the figure is visible. If that were the case, we could say, Some of the squares are black but we could not say with confidence, Not all of the squares are black. It is often helpful in interpreting assertions beginning with some to think of some as meaning "at least one," which, as we have already noted, is really what it does mean when used in the context of a logical argument. Thinking of it that way also helps us to understand the relationship between assertions beginning with some and those beginning with all. Since those terms are used in everyday language, we might consider the assertions All A are B, and Some A are B to be inconsistent. In fact, however, they are not. If we think of some as meaning "at least one," we see that the second assertion is not only consistent with the first, but is implied by it. 4.6

WHETHER DIFFERENT ASSERTIONS MEAN THE S A M E THING

50

4.

ASSERTIONS

Figure 4

Think

about

it

• Think of instances in which you would be willing to make an assertion of the form "Some A are B" but unwilling to make a comparable assertion "Not all A are B" Conversely, think of instances in which you would be willing to assert "Not all A are B?," but would not be willing to assert "Some A areB?." 4.7

REWRITING A S S E R T I O N S

We have been considering assertions of the forms "All A are B" and "No A are B;" such assertions play an important role in reasoning. However, not

51 all assertions that begin with all or with no have the word are in them. We might say, for example: All fish swim. No frogs can fly. Some students wear uniforms. We have learned that we can make diagrams of assertions of the form "All A are B" or "No A are B" that help us understand them. We can also ask questions about the reversibility of the key words in such assertions. We know that when the A and B terms are reversed in assertions of the form "All A are the resulting assertions are different from the original ones. We know too that when the A and B words are reversed in assertions of the form "No A are B,'' the resulting assertions are equivalent to the original ones. Unfortunately, it is not clear how to apply what we have learned about assertions of the form "All A are B" or "No A are B" to other assertions beginning with all or no that do not contain the verb are. However, if we could rewrite such assertions—without changing their meanings, of course—so that they assumed one of these more familiar forms, then we could treat them just like the assertions we have been considering. In fact, rephrasing assertions such as the examples given above so that they assume a desired form is usually a relatively easy thing to do. Thus, All fish swim may be rephrased as All fish are creatures that swim or as All fish are swimmers. Now we have an assertion in the form All A are B, in which A represents fish and B represents creatures that swim. That assertion can be diagrammed as 4.7

REWRITING ASSERTIONS

52

4.

ASSERTIONS

Similarly, No frogs can fly can be rephrased as No frogs are creatures that can fly and Some students wear uniforms can be restated as Some students are people who wear uniforms. Rephrasing assertions in this way can help us avoid drawing incorrect conclusions about what assertions mean. It was noted earlier, for example, that the two assertions "No A are B" and "No B are A" are equivalent in meaning. That is not to say, however, that the subject and object in every assertion beginning with no can be reversed. For example, No canaries eat cats and

No cats eat canaries do not mean the same thing. However, No canaries are creatures that eat cats and No creatures that eat cats are canaries do mean the same thing. Here is a tricky example of an assertion that would have to be rewritten before it could be diagrammed: No mice are larger than elephants. At first glance it looks like an assertion of the form "No A are where A represents mice, and B, elephants. Now, we have learned that "No A are B" and "No B are A" are equivalent, but clearly No mice are larger than elephants and No elephants are larger than mice do not mean the same thing. The first of those statements is true and the second is false. What went wrong?

4.8

ASSERTIONS ABOUT CAUSE AND EFFECT

53

In fact, No mice are larger than elephants is not in the form "No A are B." It is in the form No A are larger than B, which is quite different. We can rewrite the assertion so that it does have the desired form, however, as No mice are creatures that are larger than elephants, where A represents mice, and B represents creatures that are larger than elephants. Now, we see that the A and B terms can be interchanged and the meaning of the assertion is not changed, because No mice are creatures that are larger than elephants and No creatures that are larger than elephants are mice do mean the same thing. 4.8

A S S E R T I O N S A B O U T C A U S E A N D EFFECT

One of the things we do every day that involves reasoning is to ascribe causes to events. The process relates to reasoning in a variety of ways. Indeed, causes are often referred to as "reasons." Sometimes we might say, for example, that the reason for X was Y, when we might as well have said that the cause of A" was Y. Causes are like premises in some ways, and the effects of those causes are like conclusions. Just as conclusions follow from premises, effects follow from causes. The most straightforward form that a cause-effect assertion can take is the following: "A is the cause ofB?."Or perhaps "B is the effect of A" Most cause-effect assertions are not phrased in such a straightforward way, however, and sometimes we must study an assertion carefully in order to determine whether, in fact, it is a claim of cause and effect. Moreover, the term cause is used in a variety of ways. A common distinction in that regard is the distinction between a necessary cause and a sufficient cause. A cause may be either necessary or sufficient, or both necessary and sufficient. A necessary cause is one without which the effect cannot occur. We would say that the presence of oxygen is a necessary cause of most of the forms of life that are found on earth, because in the absence of oxygen those forms of life could not exist. Note, however, that the presence of oxygen by itself is not enough to guarantee the existence of those life-forms. Water is

54 4. ASSERTIONS also required, as is a temperature that is neither too high nor too low, and so on. Thus, we would say that whereas oxygen is a necessary cause of most of earth's life-forms, it is not a sufficient cause of them. In contrast, being without gas is a sufficient cause for not operating an automobile. It is not a necessary cause, however. That is, there are other reasons why someone might not be able to operate an automobile; aflattire is one example, a broken steering wheel is another. Each by itself is a sufficient cause of putting an automobile out of service, but no one of them is a necessary cause. Causes that are both necessary and sufficient are very difficult to identify. In order for a cause to be both necessary and sufficient, it must be the one and only cause of the effect and it must invariably cause that effect. For example, being born in Florida is a necessary and sufficient cause of being a native Floridian. However, that is not really very interesting. It seems like playing with words, because by definition, a native Floridian is someone who is born in Florida. That seems to be the case for most of the necessary and sufficient causes we can think of. They are necessary and sufficient only because the effects are defined in terms of those causes. Think

about

it

• Does the distinction between necessary cause and sufficient cause appear to you to be a useful one? • Consider what kinds of reasoning problems might result from failure to make this distinction. 4.9

INDIRECT A S S E R T I O N S

All of us use language in indirect and nonliteral ways. When, for example, you ask someone, "Do you know what time it is?" you probably do not intend that person to interpret the question literally and answer yes or no. You expect the person to understand that you wish to know the time and are indirectly asking what it is. Sometimes we actually mean to convey precisely the opposite of what we say; for example, we sarcastically say, "That's wonderful," when it is clear that we really mean "That's awful." The preceding examples of nonliteral use of language are straightforward and easily understood. We also frequently use language to convey meanings indirectly in much more subtle ways, as for example when we damn by faint praise, or when we make points by implication or innuendo that we are not willing to make explicitly. Effective reasoning requires that we be attuned to

4.10

DEALING WITH THE IMPRECISION OF LANGUAGE

55

such indirect meanings and be able to distinguish between what is literally said and the meaning that is intended. A particularly devious way of asserting something indirectly is by means of "loaded" questions. Often, such questions involve hidden assumptions, and in answering the questions, we may unknowingly acknowledge the validity of those assumptions. A classical example of a question of this sort is one that begins, "Do you still..." Suppose you are asked, "Do you still dislike Bill?" Whether you answer that question yes or no, you implicitly acknowledge the validity of the assumption that you did dislike Bill in the past. Consider the hidden assumption in each of the following questions: Why did you go to Patrick's house after leaving the restaurant? Where do you keep your revolver? Who is the first person you told about our plans? Folk wisdom tells us that if we want really to understand what someone is saying, we must be able "to read (or to listen as the case may be) between the lines." It is good advice, because much of the information that we convey when talking or writing is conveyed not explicitly but by implication or innuendo. Think

about

it

• Write down several examples of indirect assertions that you have heard or read, or possibly produced. 4.10

D E A L I N G WITH THE IMPRECISION OF L A N G U A G E

In Section 4.3, we noted that assertions that lack explicit quantifiers are sometimes ambiguous, and cannot be judged to be true or false in the absence of an assumption about what the assertion was intended to mean. In fact, questions of intention or interpretation arise even with carefully worded assertions that do have appropriate quantifiers. That is because language, as it is typically used, is extremely imprecise, and even words whose meanings we think are clear can often be interpreted in more than one way. Consider the assertion "All birds lay eggs." There is a sense in which that assertion is false and another in which it is true. It is not true that every single bird lays eggs: Male birds do not lay eggs; baby birds do not lay eggs; dead birds do not lay eggs; it is not even true that every living adult female bird lays eggs. It is true, however, that for every known species of bird the method of reproduction involves laying eggs. It is also true that, normally, adult female birds lay eggs. Those that do not are exceptions to the rule.

56

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Thus, in order to decide whether even such a straightforward sentence as "All birds lay eggs" should be considered true or false, we must know what it is intended to mean, and, in particular, whether the word birds is intended to mean individual birds or species of birds. Failure to recognize that even relatively simple sentences can be interpreted in different ways is often responsible for controversies and disputes. A way to avoid such controversies is to try to agree on how language is being used in any particular case. Thus, if one were to ask, "Do you agree that all birds lay eggs?" it would be reasonable to reply, "What do you mean by 'all birds'?" Often the context in which an assertion is encountered or the situation in which it is made provides the information necessary to resolve any ambiguities that may exist in the wording. If, for example, we encountered the assertion "All birds lay eggs" in the context of a discussion about what distinguishes one life-form from another,we would probably assume that it was intended to mean that all species of birds lay eggs, not that every bird that has ever lived has laid at least one egg. Context is not an infallible guide to meaning, however, and two people encountering the same assertion in the same context may sometimes interpret it differently. There are two rules of thumb that can help considerably to minimize the difficulties arising from the ambiguities of language: 1. If the person who has made an ambiguous assertion is present, ask for a clarification. 2. If asking for a clarification is not possible, be explicit about what you will assume the assertion to mean. Thus, if you are pressed to say whether or not you believe a given assertion to be true, it is quite appropriate to answer, "If the assertion means X, yes, but if it means Y, no." Care in the use of language is an immensely important aspect of effective reasoning. This applies both to the production of language and to language interpretation. We should be as precise as possible in our choice of words in expressing assertions; similarly, when trying to understand assertions that others have produced, our first objective should be to resolve any ambiguities that exist, or if not to resolve them, at least to recognize them for what they are. It is difficult to stress this concern for careful attention to language enough; careless language usage is bound to impede effective reasoning and often leads to unnecessary misunderstandings and disputes. Think about it

• Try to think of several assertions that, like "All birds lay eggs," may seem perfectly clear at first, but may prove to be somewhat ambiguous when considered further. • List all the interpretations you can think of that could possibly be put on the assertion "Women live longer than men."

4.11

4.11

IMPLICATION AND CONTRADICTION

57

IMPLICATION A N D CONTRADICTION

Assertions can relate to each other in a variety of ways. They may be similar or dissimilar in form; they may address the same or different subjects; when they address the same subject, they may make similar or dissimilar points; and so on. Two relationships that are of special significance to reasoning are implication and contradiction. One assertion is said to imply another if it is the case that the latter must be true if the former is true. One assertion is said to contradict another if it is the case that one must be false if the other is true. Although we are treating implication and contradiction as different relationships, we can think of contradiction as a type of implication. To say that A contradicts B is to say that the truth of A implies the falsity of B. Contradiction is a symmetrical, or bidirectional, relationship: if A contradicts B, B contradicts A. Thus, we may say that if two assertions are contradictory, they cannot both be true; one of them must be false. Implication, however, is not necessarily a symmetrical relationship: just because A implies B, it need not be the case that B implies A. It sometimes is the case that A implies B, and B implies A, but that is a special type of implication, and in logic it has a special name. One-way implication is referred to as a conditional relationship and is sometimes represented as or

A —> B

B if A, which means A implies B, or B is true if A is true. Bidirectional implication is referred to as a biconditional relationship and is sometimes represented as or

A B

5 iff A, which means A and B imply each other, or B is true if and only if(iff) A is true. It should be apparent that B iff A and A iff B are equivalent. The ability to recognize the relationships of implication and contradiction can be very important to effective reasoning. Or, to state the case negatively, an inability to recognize those relationships can lead to faulty reasoning. Conversely, believing that a relationship of implication, or contradiction, exists when it does not can also lead to reasoning difficulties. A particularly problematic confusion that people make illustrates this point. That is to treat a statement of the form

58

4.

ASSERTIONS

If A then B (or equivalently, B if A) as though it meant the same thing as If B then A (or equivalently, A HB). The assertion If he has the measles, he will have a rash Is not the same as the assertion If he has a rash, he must have the measles. We will return to this point in Section 5.6. We have already noted a closely related confusion that is so common that psychologists have given it a name. It is called the premise conversion error. A premise conversion error occurs when a person treats an assertion of the form All A are B as if it meant the same as All B are A. These two assertions are not equivalent; neither implies the other, and failure to recognize that fact can be the source of much difficulty in reasoning. The preceding examples do not exhaust the issue of recognizing the relationship of implication between assertions, but they are particularly important examples because they seem to be poorly understood so frequently. We have noted two ways in which two assertions may be related. One may imply the other, or they may be mutually contradictory. A third relationship worth mentioning is consistency. To say that two assertions are consistent with each other is to say that knowledge of the truth or falsity of one does not provide information regarding the truth or falsity of the other. In particular, if two assertions are consistent, they are not contradictory: both may be true. The assertions All mammals are warm blooded and Some mammals hibernate are consistent, because neither of them rules out the possibility that the other may be true. They are no more than consistent, however, because neither of them implies the truth of the other. The assertions

4.12

and

EVALUATING ASSERTIONS

59

All mammals are warm blooded

Some birds swim are also consistent and for the same reasons. The latter example illustrates the fact that it is not necessary that assertions be closely related in order to be logically consistent. Indeed, the most likely relationship between assertions that are completely irrelevant to each other is that of logical consistency. Of course, when one assertion implies another, the two are obviously consistent, but the notion of consistency is more inclusive than that of implication: assertions need not be related by implication in order to be consistent. 4.12

EVALUATING ASSERTIONS

As has already been pointed out, one of the main challenges to reasoning in everyday life is that of evaluating the plausibility of assertions. We are urged to vote the Democratic slate in a presidential election on the grounds that if the Republicans are elected, there will be an economic depression. We are implored to vote Republican on the grounds that the Democrats will continue deficit spending until the country goes bankrupt. Our problem is not so much to decide whether we prefer an economic depression to national bankruptcy, but to decide how much credence to give to either claim. Often it is not possible to decide whether an assertion is true or false. That can be so for any of several reasons. First, we may be unable to decide the truth or falsity of an assertion simply because we lack the knowledge necessary to make the decision. If, for example, I were to encounter the assertion that Angola has rich deposits of iron and copper, I would be at a loss to judge its truth or falsity because I know nothing about Angola's mineral deposits. A second reason for being unable to judge the truth or falsity of an assertion is that the meaning of the assertion may not be clear. There are various types of lack of clarity. An assertion may be ambiguous, for example, and may be interpreted in more than one way. In such cases, it is possible for there to be one interpretation that would be considered true and another that would be considered false. Sometimes we encounter an assertion that is so unclear that we are unable to interpret it in any meaningful way. This is not a question of ambiguity but simply of not having any clear idea of what the author of the assertion had in mind. Obviously, it is not possible to judge the truth or falsity of an assertion unless we can attach some meaning to it.

60

4.

ASSERTIONS

Third, there are some assertions the truth or falsity of which is logically impossible to determine. Consider, for example, the assertion "This assertion is untrue." In trying to judge its truth or falsity, wefindourselves in a dilemma. If we decide the assertion is true, then it is obviously false because it claims to be false; but if the assertion is false, it is true because it is what it claims to be, namely, false. There is no way out of this pit. Assertions of this kind are considered logical paradoxes and neither true nor false. The significance of such assertions and the question of whether they should be considered meaningless are interesting topics for logicians to discuss, but will not concern us here. Even when problems such as these do not arise, it is often difficult to say, in a yes-no fashion, whether or not we believe a particular assertion to be true or false. With respect to the perceived truth or falsity of assertions, things often are not cases of either-or. As we have already noted, in the matter of belief, we recognize differences of degree. To be sure, we have very little doubt of the truth of some things and very little doubt of the falsity of others. However, there are many things that we believe or disbelieve with less than complete certainty. There are two critical questions we might ask here about plausibility. What determines how plausible we willfindan assertion to be? What should determine plausibility? Inasmuch as the factors that should determine plausibility are probably included among those that do, it is convenient to consider the second question first. The plausibility of an assertion must depend in some manner on what we know or believe both about the subject of the assertion and about its source. A necessary condition of plausibility is consistency with what we know or believe to be true. The assertion that lightning never strikes the same place twice will be plausible to me only if I am unaware of any examples of it having struck twice in the same place. Consistency is a necessary but not sufficient condition of plausibility, because lack of it is adequate grounds for dismissing the assertion as implausible; however, consistency is only weak evidence in its behalf. How much support we derive from known facts that are considered to be consistent with an assertion depends on how relevant those facts are to the assertion. A sufficient but not necessary condition for plausibility is that the assertion be deducible or at least strongly suggested by other things that are believed to be true. Thus, if A and B are believed to be true, and C is not only consistent with A and B but follows from them or is strongly suggested by them, then we should find C to be highly plausible. We sometimes encounter the advice to "consider the source" in determining the plausibility of an assertion. It seems like good advice. If the source is believed to be trustworthy and knowledgeable with respect to the subject of the assertion, we should be more willing to believe the assertion

4.13

CONSISTENCY, CORROBORATION, AND PROOF

61

than if the source is either untrustworthy or unknowledgeable. However, we should note two qualifications. First, it is not the case that a normally trustworthy source cannot lie or make mistakes, or that a normally untrustworthy source cannot tell the truth; so what we believe about the habitual truth-telling characteristic of a source is a useful but imperfect indicator. Second, whereas the importance of trustworthiness is obvious and is probably taken into account by most people (few of us would be willing to attach much credence to information obtained from a source that we know from experience to be unreliable), we tend to be less demanding with respect to knowledgeability. In particular, we seem to be unduly willing to accept as authoritative, information in domain B from individuals who are known to be experts in domain A. Such willingness is exploited quite effectively by promoters and advertisers who engage people who are known for their expertise or accomplishments in one area (e.g., sports or theater) to endorse positions or products that bear little if any relationship to the demonstrated competence of the endorsers. On the question of how people do judge plausibility, there is considerable evidence that several factors may play a role in addition to those that should. One such factor (the importance of which has been recognized for a long time) is personal preference: most of us are likely to give more credence to something we would like to believe than we would give to something we would prefer not to believe. Another, closely associated, factor is our like or dislike of a source: we are probably more willing to believe something that is claimed by someone we like than something that is claimed by someone we dislike. It should be apparent that neither factor should affect credibility, but both of them undoubtedly do. There are numerous other factors that probably help determine the plausibility of assertions, although they should not. We will examine them later, in Chapter 7, in the context of a discussion of some common reasoning fallacies. Think

about

it

• Make a list of factors that might help determine whether one would be willing to accept an assertion as true. 4.13

CONSISTENCY, CORROBORATION, AND PROOF

Part of what it means to be rational or reasonable is to be willing to give proper weight to evidence for or against an assertion. Proper weight is a key concept. We want to give just the right amount of weight to evidence,

62 4. ASSERTIONS neither more nor less. Therefore, it is helpful to distinguish between the concepts of consistency, corroboration, and proof. Consistency is the weakest form of positive evidence among the three notions. As we have already noted, to say that A is consistent with B is to say only that it is possible to believe B given the knowledge A. For example, the knowledge that dinosaurs have been extinct upon the earth for about 65 million years is consistent with the hypothesis that UFOs are really visits from extraterrestrial beings. The first bit of knowledge does not appear to be very closely related to the hypothesis, but it certainly is not inconsistent with it. Let us see how consistency with other known facts might increase the plausibility of an assertion. Suppose you have heard a claim that a particular individual has performed a certain heroic act. Suppose that the reported act was something that you would not expect many people to be willing to perform, and, further, that you were not convinced of the reliability of the person making the report. Then you discover from a highly reliable source that the same individual who was reported to have performed the heroic act had, in fact, done something equally heroic in the past. The new bit of information tells you something about the character of the individual, and inasmuch as that is consistent with the report of more recent heroism, you might now find that report more plausible than before. To say that a hypothesis has been corroborated is to make a somewhat stronger statement than to say that something is consistent with it. When we test a prediction of a hypothesis and discover that the prediction holds, we say that we have corroborated the hypothesis. But in corroborating a hypothesis, we have not demonstrated its truth beyond doubt. The degree to which a hypothesis may be said to be corroborated by experimental evidence depends on such factors as how many different predictions derived from the hypothesis have proven to hold true and how much of an effort has been made to derive predictions that would prove to be untrue. How much our confidence in the truth of a hypothesis is increased as a consequence of the fact that it is capable of making an accurate prediction should depend on the nature of the prediction. More specifically, it should depend on the uniqueness and surprise value of the prediction. If the prediction were "Do X, and the sun will rise tomorrow," the rising of the sun tomorrow probably would not increase our confidence in the hypothesis very much. If, however, the predicted result of doing A" is a very strange and unexpected event (especially if the result is one that no other hypothesis would predict), and if when A" is done, the predicted result is observed, our confidence in the hypothesis may be increased appreciably. The most impressive theories make the most precise and surprising predictions. They are said to have predictive power. The accepted way of testing a hypothesis that is stated in the form of a general rule is to attempt very hard tofindexceptions to the rule. If we make

4.13

CONSISTENCY, CORROBORATION, AND PROOF

63

an honest attempt tofindexceptions and fail to do so, our confidence in the hypothesis is thereby increased. Given the hypothesis that all members of class A have property B, looking for further examples of members of class A that have property B is not as convincing a test of the hypothesis as looking hard for members of class A that do not have property B, and failing in the attempt. (See comments on the falsifiability principle in the next section.) Proof is another matter altogether. Mathematics and most systems of logic are axiomatic systems: They begin with certain axioms and rules of inference (or operations) by which theorems can be deduced. An axiom is an assertion, or proposition, that is considered self-evident or is true by definition. A proof in mathematics or logic is a demonstration (using the accepted rules of inference) that what is to be proved follows deductively from axioms or from other propositions that have already been proved. It is important to recognize that the theorems (proven propositions) of mathematics and logic are contained implicitly in the axioms; that is, those theorems contain no information that was not already contained, albeit only implicitly, in the axioms from which they were deduced. In science, proof has a different connotation. Indeed, there is a peculiar asymmetry about the notion of proof in that context. A goal of science is the development of theories with which to explain various aspects of the world. Those theories, if they are to be sufficiently general to be of interest, must be expressed in terms of general principles, principles that are true for all cases to which they apply. However, it is in the nature of any general principle that is descriptive of real-world phenomena that there is no way to demonstrate with complete certainty that it is true; in other words, there is no way to prove it beyond any possible doubt. It is relatively easy, though—and here is the asymmetry—to prove a general principle to be false if indeed it is false. One counterexample is enough to do the trick. The claim that all objects in the universe obey the law of gravity is a very powerful claim and has a great deal of corroboration, but it has not been proved. To prove it true would require checking every last object to make sure there were no exceptions to the rule; to prove it false would require the finding of only one such exception. In the case of gravity, we consider it unlikely that an exception will be found, which illustrates the fact that for practical purposes extensive corroboration is about as good as proof, but it is not quite the same. The history of science is replete with examples of principles that were thought at one time to be general, but had to be discarded in favor of a revision when an exception was found. In short, scientific theories can never be said to have been proved to be true, although many have indeed been proved to be false. The best we can say of a theory about real-world phenomena is that it has stood up well to testing, that in spite of concerted efforts by competent investigators, it has not (yet) been shown to be false. We can also say that a theory is powerful, that it makes many specific predictions that can be shown to be true, and that

64

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ASSERTIONS

it can serve as a useful practical tool for helping to understand and perhaps control many real-world phenomena. To be able to say such things, although it falls short of claiming truth, is to be able to say a lot indeed. What implications do the distinctions between consistency, corroboration, and proof have for reasoning in everyday situations? First, a minimum requirement for the plausibility of an assertion is that it be consistent with whatever else a person believes to be true. That is an important principle and one to which an effective reasoner will subscribe. Internal consistency is a fundamental requirement of any scientific theory that is to be taken seriously. It also should be an objective of any individual with respect to the various beliefs that he holds. A person should not knowingly entertain selfcontradictory views. Admittedly, the criterion of internal consistency is an exceedingly difficult one to be sure we have attained. All of us have a great deal of information in our heads. We know or believe much more than we can recall on demand. To be sure that everything that we believe is consistent with everything else we believe is perhaps too much to expect of mere mortals. It is not too much to expect, however, that when we discover that two things we believe are inconsistent with each other, we modify one or both of those beliefs. Second, the degree of credence we give to an assertion should be commensurate with the degree to which the assertion is corroborated by evidence. That may vary from very little (which would justify little confidence in the assertion's truth), to a great deal (which might justify acting as though the assertion were certainly true). Third, the fact that a general principle intended to be descriptive of some aspect of the world can never have been proved true should give us the modesty to recognize the fallibility of even our strongest beliefs and the honesty to acknowledge, especially to ourselves, that they could be wrong. Think

about

it

• Suppose that one could believe only assertions that had been proved beyond doubt to be true. What effect would this have on one's view of the world and one's behavior? • In our legal system a person is assumed to be innocent until proven guilty. What does proven mean in this context? 4.14

THE PRINCIPLE OF FALSIFIABILITY

In science, some beliefs are called hypotheses. As we have noted, the most interesting and powerful scientific hypotheses are not known with certainty to be true. Scientists may have a high degree of confidence in the truth of

4.14

THE PRINCIPLE OF FALSIFIABILITY

65

some of those hypotheses, but that is different from being certain beyond any doubt. The reason that the most interesting and powerful scientific hypotheses are not known to be true is that they typically are expressed as "universal" laws. A universal law is a law that pertains to every instance of some class of things or events. As we have also noted, it usually is logically impossible to prove such a law to be true, because in order to do so, we would have to examine every instance to which it applies, and that usually cannot be done. Scientists have found an interesting way out of the predicament of not being able to prove hypotheses that are expressed as universal laws—a way that is fundamental to science. What they have done is to require that any hypothesis that is to be respectable from a scientific point of view must be "falsifiable" in principle. The principle of falsifiability says that for a hypothesis to be taken seriously, there must be a way to show it to be false if in fact it is false. This is really a very interesting approach to the problem of developing believable theories about the world. Of course, we would like to develop theories that are provable; but given that that cannot be done, the next best thing is to develop theories that are falsifiable, theories that can be shown to be false, if they are false. Suppose that a scientist were to come up with a hypothesis about some aspect of the world. Suppose further that the hypothesis was a very interesting one, but there was no way to tell that it was false if in fact it was false. This means that whenever an experiment was done it would not matter how the experiment came out. No result that could be obtained would shed any light on the truth or falsity of the hypothesis. Clearly such a hypothesis would not be of very much use. Not only must a hypothesis be falsifiable in principle in order to be scientifically respectable, it must have survived sincere efforts to show it to be false. In general, when we are trying to test a hypothesis, and we want to make the hypothesis as believable as possible, the strategy we should use is to try very hard to disprove it. If a hypothesis has not been disproved in spite of concerted efforts to disprove it, we can have more confidence in it than in a hypothesis that has not been disproved because no one has tried to disprove it. Although the falsifiability principle was developed by scientists, the same principle applies to everyday thinking. Assertions that cannot be tested and, more specifically, assertions that cannot be shown to be false if in fact they are false are not very useful. T h i n k a b o u t it

• Try to think of an explanation of some natural phenomenon that is not falsifiable; that is, try to think of an explanation that cannot be shown to be false if it is false.

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4.15

COUNTEREXAMPLES

The concept of a counterexample is an important tool in evaluating assertions, because it is necessary to find only one counterexample to a general rule to prove that that general rule is wrong. Recall that all that is required to disprove a universal assertion—an assertion that begins with all or no—is one exception to the assertion's claim. For example, my knowledge that whales are mammals is enough to let me know beyond doubt that the assertion that no mammals live in the ocean is untrue. Such an exception is called a counterexample. Thus, whenever we encounter a universal assertion and wonder whether or not to believe it, thefirstthing we should do is attempt to think of a counterexample. If we succeed, we can conclude that the assertion is false. Suppose we try as hard as we can to think of a counterexample for a universal assertion, and fail. Does that mean we can then conclude that the assertion must be true? No. The inability to think of a counterexample does not constitute conclusive evidence that none exists. However, the fact that we are unable to think of a counterexample should increase our confidence that the assertion is true. If we feel fairly sure that we could think of a counterexample if it existed, our inability to think of one may increase our confidence in the assertion quite a bit; and if we know that other people also have tried hard to think of a counterexample and have failed to do so, then our confidence in the truth of the assertion might be increased even more. Counterexamples play an important role in helping us assess the plausibility of universal assertions. What about particular assertions! Consider the assertion "Some people speak German." What would constitute a counterexample for it? Would it be "Some people do not speak German"? Certainly it is true that some people do not speak German, but does that mean that the original assertion is wrong? No. Counterexamples do not disprove particular assertions: the assertion "Some people speak German" and the one "Some people do not speak German" both can be true at the same time. Neither contradicts the other. Think

about

it

• The tendency to think of people in terms of stereotypes is responsible for many misunderstandings and ill feelings among people. How might counterexamples be used to address this problem? 4.16

SUMMARY

Assertions are the elements from which arguments, both logical and plausible are made. They vary in both form and content, so it is possible to have as-

67 sertions in the same form that mean quite different things and to have assertions in different forms that mean the same thing. Assertions can differ considerably in their clarity of meaning. The ability to recognize different assertion forms can be useful in making clear what an assertion implies as distinct from what it says explicitly. Sometimes representing the meaning of an assertion pictorially can also help make clear what that meaning, explicit or implicit, is. Assertions bear relationships to other assertions such as implication and contradiction. A basic challenge to effective reasoning is that of evaluating the plausibility of assertions. This involves the application of evidence, judgments of consistency and corroboration, testing in accordance with the principle of falsifiability, and consideration of counterexamples. 4.16

SUMMARY

5

Arguments

5.1

W H A T IS A N A R G U M E N T ?

As it is used in everyday speech, the term argument often refers to a verbal disagreement. In that sense, an argument is something that contentious people enjoy but that agreeable people attempt to avoid. In the context of deductive logic, however, an argument is a sequence of assertions, some of which are premises and one of which is called the conclusion. If the reasoning is logically valid, the conclusion follows from the premises. If the reasoning is not logically valid the conclusion does not follow from the premises. Here, the term argument will be given a somewhat broader connotation than its strictly deductive one. It will be used to connote any set of assertions that is intended to support some conclusion or influence a person's beliefs. We all have probably had some exposure to courtroom proceedings—on television, if nowhere else. We know that at a trial one lawyer tries to convince the members of the jury that the accused person is guilty of the crime for which he or she is being tried, and the other lawyer tries to convince them that the accused is innocent. We say that each of the lawyers makes an argument, one for the prosecution and the other for the defense. It is the jury's job to decide which of the arguments is the most convincing. What the jury has to do in a court case is not very different from what we all have to do in our everyday lives. We continually have to evaluate arguments and decide whether or not to accept them. Also, we often produce arguments of our own when we want to convince somebody that something is true or when we want to persuade someone to do something. 68

5.1

WHAT IS A N ARGUMENT?

69

As we have seen, an argument can be defined in several ways. Here are two definitions that we will find useful: An argument is an effort to convince someone to believe or do something. An argument is a set of assertions, one of which is a conclusion or key assertion, and the rest of which are intended to support that conclusion or key assertion. There are a number of things we should notice about an argument:

• • • • • • • • • •

It is something that someone has made. Some arguments are made well; some are made poorly. Probably most arguments can be improved. Arguments have a purpose. Usually that purpose is to convince someone that something is true or to convince someone to behave in a certain way. An argument can be strong (convincing) or weak (unconvincing). Some arguments are more persuasive than others. An argument has parts. Those parts are of two types: a conclusion or key assertion, and premises or supporting assertions. Because an argument has parts, it can be taken apart. We can look at the individual components, at the individual assertions, and at the individual words that make up those assertions. In fact, we have to do exactly that when we try to evaluate arguments. If arguments can be taken apart, they can also be put together. That is, we can think of them not only as things that we can analyze, but also as things that we can construct or build. Arguments can be changed. If we have an argument that we think is not a very good one, we might be able to improve it by changing it in specific ways. Arguments can be more or less complete. Sometimes when we look at an argument carefully, we may discover that certain parts are missing. When that is the case, the missing parts should be filled in before the argument is evaluated. Arguments can be simple, or they can be complex. A complex argument usually involves several assertions in support of one or more conclusions. Sometimes a complex argument may contain assertions that serve both as conclusions and as premises; that is, an assertion may be a conclusion that is drawn from what precedes it, and also be a premise with respect to what follows it. Fortunately, a complex argument usually can be broken down into several simpler arguments. Arguments can be evaluated. It is extremely important to understand not only that arguments can be evaluated, but also how to evaluate arguments. If we did not know how to evaluate arguments, we would

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often be unable to decide whether to accept or to reject the conclusions they are intended to support. 5.2

INDUCTIVE V E R S U S DEDUCTIVE I N F E R E N C E

One may think of an argument as a process for which premises or supporting assertions are inputs, and conclusions or key assertions are outputs. The way one gets from the inputs to the outputs is by making inferences. It is customary to distinguish two types of inference: inductive and deductive. Both are essential in science and in everyday life. The scientific method may be viewed as a repetitious process in which induction and deduction occur in an alternating fashion. Based on observations of natural phenomena or on the results of controlled experiments, one induces hypotheses in terms of which to explain the phenomena one has observed. From those hypotheses, one deduces what would happen under specified conditions. One then makes observations under those conditions; that is, one performs experiments. On the basis of the results from the experiments, one inductively modifies the hypotheses, deduces new predictions, makes further observations, and so on. What one hopes to accomplish by means of this process is the development of a theory of ever increasing scope, precision, and predictive power. Inductive reasoning, as the term typically is used, involves generalization; which is to say, reasoning from parts to wholes, from a few to all, from the particular to the general. For example, having observed that certain members of class A have property B, and not having observed any exceptions to the rule, one might be inclined to infer (inductively) that all members of class A have property B. Indeed, we all make such inferences regularly and quite naturally, although we may not recognize that we are doing so. Most people do not have to be stung many times in order to know that it is a generally good policy to be careful in the vicinity of hornets. We quickly impute to all hornets the same capacity and willingness to be unpleasant that we observe in a few cases. In making such an inference, we are going beyond the data at hand, and drawing a conclusion that we cannot prove, but the benefit of doing so is, in this case at least, obvious. We would pay a dear price if we were willing to impute nastiness only to those individual hornets who had demonstrated it beyond doubt. Of course, inductive reasoning can lead to false conclusions, and often does; for example, we conclude that all redheads have violent tempers because we know a few hot-tempered individuals who happen to have red hair. However, in spite of the fact that induction does not lead to conclusions whose truth is demonstrable beyond doubt, the ability to generalize, to go

71 beyond the data at our disposal, to impute properties to classes of things on the basis of nonexhaustive observations of members of those classes is an extremely important one. If we did not have it, our conceptual world would be a hopeless jumble of unconnected particulars. Such order and structure that our thinking has are due to the invariants that we discover in, or impose upon, the sensory data that we receive from our environment, and the general principles that we induce from those invariants concerning the way things work. When we reason inductively, we are, in effect, displaying an underlying confidence in the lawfulness and noncapriciousness of the world. If we frequently observe that B follows A, we are likely to assume that we have detected a regularity in nature and that B is likely to continue to follow A. The alternative assumption would be that the apparent regularity is coincidental, and that would be a difficult assumption for us to make. Our experience with the world in general leads us to believe that the regularities we encounter are not happenstance, but a reflection of the lawfulness and underlying structure of the world. A major purpose of the area of mathematics called statistics is to facilitate the process of making effective inductive inferences. The rules of statistical inference tell us precisely what we can infer about the quantitative properties of populations on the basis of observations of the quantitative properties of samples drawn from those populations. The procedures are highly formalized and are based on well- established mathematical theory. Like inductive reasoning, deductive reasoning plays a pervasive role in our daily lives. Moreover, we learn very early to reason deductively. A child who has acquired enough wordly wisdom to know that all licorice tastes good does not require a course in logic to make the deduction that if the thing in his hand is a piece of licorice, it will taste good. He knows that it will taste good, because it follows from the fact that it is a piece of licorice and the fact that all licorice tastes good. (Of course, the knowledge that all licorice tastes good may itself be based on an inductive inference that the child has made on the basis of the fact that the licorice sampling he has done has never produced a counter-indicative case.) Deductive reasoning, like inductive reasoning, can go astray and produce incorrect conclusions. When it does so—which is often—it is because of one of two problems: either one of the premises from which the conclusion was drawn is false or the rules of deductive inference were violated. If we infer that J.D. is a rascal from the assumption that all used-car salesmen are rascals and the fact that J.D. is a used-car salesman, the inference is valid (because the logic is sound), but the conclusion is not necessarily true. If the assumption happens to be false, then the conclusion could be (but is not necessarily) false. On the other hand, when a man concludes that he worries too much from the assumption that if people worry too much they get ulcers and the fact that he has ulcers, he is making 5.2

INDUCTIVE VERSUS DEDUCTIVE INFERENCE

72 5. ARGUMENTS an invalid inference. The logical fallacy is a particularly common one. It is known as the fallacy of affirming the consequent (See Section 5.6). The conclusion may be true, but it is invalid—arrived at by an illogical inference—nevertheless. Think

about

it

• Consider the various ways in which deductive inferences can go wrong. • Consider the various ways in which inductive inferences can go wrong. • Think of several examples of how you use both deductive and inductive reasoning in your daily life. 5.3 T Y P E S OF A R G U M E N T S

Arguments can be classified in various ways. We can distinguish, for example, between direct arguments and indirect arguments, or between formal arguments and informal arguments, or between complete arguments and incomplete, or elliptical, arguments. A distinction that will be useful for our purposes is the distinction between logical and plausible arguments. Logical versus Plausible A r g u m e n t s

The distinction between logical and plausible arguments is very similar to the distinction between deductive and inductive inference, but is somewhat more general. A logical argument, as the term is used here, is one that makes use of deductive inference. It is one in which one of the assertions (the conclusion) is implied by, or may be deduced from, the others (the premises). A plausible argument, in contrast, is one in which a key assertion is made more believable by the other assertions composing the argument. The distinction hinges on the concept of implication. To say that the conclusion of a logical argument is implied by, or may be deduced from, the argument's premises is to say that if the premises are true (and the form of the argument is logically valid), then the conclusion must be true. (Regarding the distinction between validity and truth, see Section 5.8.) Note that this is not to say that if the premises are false or if the argument has an invalid form the conclusion must be false. In the case of a plausible argument, the relationship between the supporting assertions and the key assertion is not one of implication. Moreover, the concept of validity does not apply, at least not in the same way, in this case. The most that can be claimed for a plausible argument is that it is more or less forceful or convincing. To say that a plausible argument is forceful or convincing is to say that its supporting assertions make the key assertion more plausible or easier to believe.

5.3 TYPES OF ARGUMENTS

73

An argument that uses inductive reasoning is a plausible argument, but as the term plausible argument is being used here, it is intended to be sufficiently broad to include types of reasoning other than that of arguing from particulars to the general case. It is intended, indeed, to include any form of argument thatfitsthe model of a set of assertions, one of which is key and the others of which are provided for the purpose of increasing its plausibility. The following are examples of arguments that fit that model: Natural resources such as coal, oil, and gas are limited. Even if we use them efficiently and try hard not to waste them, someday our supply of them will run out. Therefore, we should be working now to develop alternative sources of energy. John has been accused of stealing the money that was missing from his friend Harry's desk, but he is not guilty. He had no need of the money. If he had needed money, he would not have stolen it from his friend. If he had taken it, he would have been clever enough about it so that he would not have been suspected. And anyway, he is really an honest person. Some way of motivating people to make more use of public transportation must be devised, because if the number of private automobiles in the city increases, the traffic jams will make the streets impassable. By going to college one increases one's chances of getting an interesting and well-paying job. Perhaps even more important, one broaden's one's horizons and becomes aware of many interesting aspects of the world. Therefore, anyone who can do so should go to college. Note that in none of the preceding cases can we identify a conclusion that is logically implied by, or deducible from, the other assertions that constitute the argument. In all cases, however, it is possible to identify a key assertion, and other assertions the purpose of which seems to be to make the key assertion easier to believe. In contrast, in the case of logical arguments, conclusions follow from, or are implied by, the premises: which is to say, if the premises are known to be true and the form of the argument is valid, we can be certain the conclusion is also true. Here are some examples of arguments of this type. All people born in the United States are U.S. citizens. Dorothy was born in the United States. Therefore, she is a U.S. citizen. If there is not much rain in June and July, the vegetable crop in this area is poor. There was not much rain this June and July. Therefore, there will be a poor crop. No one without a ticket will be admitted to the concert. I cannot get a ticket, so I will not be able to attend.

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In each case, thefinalassertion follows directly from the preceding ones, and its truth is guaranteed by theirs. A difference between logical and plausible arguments that has some practical significance is the fact that there are unambiguous objective criteria against which logical arguments can be evaluated, but there are no such criteria for plausible arguments. A logical argument can be determined to be valid or invalid by the application of objective criteria; but all that can be said of a plausible argument is that it is more or less convincing; and convincingness is a somewhat subjective matter— what is convincing to one person may be quite unconvincing to another. Consider, for example the following two arguments: Every country should maintain an army. If a country does not do so, it can be easily subdued by an aggressive enemy. An army can be used for purposes other than war, such as helping during times of disaster (with hurricanes, floods, and earthquakes). An army provides jobs for young people and thereby helps to keep unemployment down. Also military service represents an opportunity for some young people to receive technical or vocational training they might not otherwise get. Not every country should maintain an army. The maintenance of armies increases the probability that there will be wars. An army is costly to maintain and represents a burden on a country's economy. For some young people, military service would be a disruption of their education or careers. A decision not to maintain an army might be viewed by neighboring countries as compelling evidence of peace seeking, and a country that attacked another that maintained no army would be censured by the rest of the world. It seems safe to assume that not everyone will have the same reaction to those arguments. Some people will find the first more compelling, and some the second. Argument by Analogy There is perhaps no form of reasoning that is more widely used, more helpful when used appropriately, or more subject to misuse than argument by analogy. It is a particular type of plausible argument. Basically, an analogy is a likeness. To say that A is analogous to B in certain respects is to say that A is similar to B in those respects. Understanding a difficult relationship or principle can often be facilitated by reference to an analogous but simpler or more familiar relationship. Analogies also can be useful as sources of hypotheses. If X and Y are known to be alike with respect to properties A, B, and C, one may be prompted to

5.4

RECOGNIZING ARGUMENTS

75

hypothesize that they are also alike with respect to property D. But similarity with respect to properties A, B, and C is not, by itself, compelling evidence of similarity with respect to property D. Ignoring that fact is the basis of one of the most common ways in which analogies are misused—in an attempt to prove points. (See Section 7.19.) Think

about

it

• Make a list of familiar analogies. • Invent some analogies and make clear for each its limitations. Consider how the analogs differ as well as how they are similar to each other. 5.4

RECOGNIZING A R G U M E N T S

Sometimes arguments are easy to recognize, and sometimes they are not. Sometimes people intentionally disguise an argument because they prefer to appear not to be making one, even though they are; and sometimes people make arguments that are very indirect. Such arguments can be difficult to recognize and understand. They may be effective, however, in spite of that fact. We will return to the topic of disguised and indirect arguments later. For now, we will consider only arguments that are relatively clear and direct. There are certain words that are very helpful in recognizing arguments because they serve as clues that the speaker or writer is making an inference or wishes the listener or reader to do so. These words include: therefore, for, because, thus, so, consequently, since, inasmuch as, and a few others. When one comes across one of these words or terms, one should pay very careful attention because it may be a signal that an argument is being put forth. These words are not perfect clues to when an argument is being made, because sometimes they are used in ways other than as part of an argument; and sometimes arguments are made without the use of any of these words. Nevertheless, whenever we see one of these words, especially when it is the first word of a clause (when it follows a semicolon, a comma, or a period), the chances are quite good that an argument is being made. In trying to decide whether or not a particular passage is an argument, it may also help to ask ourselves the following question: Does it try to convince me to believe or do something by giving one or more reasons why I should? If the answer to this question is yes, that is also a good indication that the passage is probably an argument.

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Again, however, we should note, that this indication also is not perfect; and this is because it is not always clear what constitutes a reason for one to believe or do a particular thing. Most of us would probably consider the following passage to be an argument: All of us should take a greater interest in conservation, because if we do not, some day we mayfindthat the world's supply of certain critical resources has been exhausted. The person who made this argument is trying to convince us that we should take a greater interest in conservation and gives a rather compelling reason why we should do so. Now consider the following passage: Jupiter is the largest planet in the solar system. Its diameter is about 89,000 miles, and it weighs about two trillion trillion tons. Is that an argument or not? Probably most of us would say that it is not, because it simply states a set of facts about the planet Jupiter. On the other hand, suppose we were to claim that the second statement provides reasons why we should believe thefirst,and that therefore, it is an argument. Is that really wrong? It depends. To a person who knows very little about the solar system, the information that Jupiter has a diameter of 89,000 miles and weighs two trillion trillion tons is probably not very useful; and, in particular, it does not help very much in deciding whether thefirstassertion should be accepted as true. In the absence of knowledge about the diameters and weights of other planets, there is no way to tell whether the diameter and weight of Jupiter are relatively large or small. If we insist that the passage is an argument, we must at least admit that it is not a very effective one. Now, consider the following passage: John is the largest boy in our school. He is 6 feet 10 inches tall, and he weighs 278 pounds. Probably most of us would not see that as an argument either. However, if someone were to insist that it is an argument, we probably would have less difficulty viewing it as one than we did in the case of the passage about Jupiter. That is because we know enough about the sizes of people to know that a 6-foot 10-inch, 278-pound boy is a large boy indeed, and that a boy of that size would have a very good chance of being the largest boy in his school. Thus, while some arguments are easy to recognize, others are not. Moreover, what constitutes an argument may depend on such factors as the intent of the speaker (writer) and the knowledge of the listener (reader); so

5.5

ANALYZING ARGUMENTS

77

what constitutes an argument for one listener (reader) may not for another. Such considerations complicate the problem of recognizing arguments, but they also make it a more interesting problem. Think

about

it

• List as many words as you can that might indicate that an argument is being made. 5.5

ANALYZING ARGUMENTS

One of the things we want to be able to do with arguments is to analyze them. That means being able to break them down into their components, or take them apart. Before being able to do that, however, we need to have a clear idea of what the parts are. We have already noted that an argument is made up of assertions. We have also noted that one of those assertions is the conclusion or key assertion and that the purpose of the other assertions is to support that conclusion or key assertion. In the case of logical arguments, those other assertions are called premises. An important aspect of analyzing an argument is being able to distinguish between its conclusion and its premises, or between its key assertion and its supporting assertions. When we have broken an argument down into the individual assertions that comprise it, and have identified one of those assertions as the conclusion or key assertion and the others as premises or supporting assertions, we have gone a long way in analyzing the argument—in taking it apart. When we read or hear an argument, we must decide whether to accept it, and, in particular, whether to accept the conclusion or key assertion that the argument is intended to support. Before making that decision, we want to be sure we understand the argument. In some cases, that may be very difficult because arguments may be phrased in a complex way or they may be incomplete. In analyzing an argument, there are two things we want to accomplish: 1. to make all the assertions that comprise it explicit (including those that are not stated), and 2. to show how those assertions relate to each other. In other words, we need to make the argument's structure clear. It may be necessary to restate the argument in order to accomplish those goals and in doing that, we must be very careful not to change the meaning of the argument in any way. We should be sure that after an argument has been restated it still expresses exactly what the person who originally constructed it intended.

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In the simplest of logical arguments, there are a small number of premises (often two) from which a conclusion is drawn. Such arguments are relatively easy to understand and evaluate. More often, the arguments we encounter are likely to involve chains of inferences. In such cases, a given assertion may function as a premise with respect to one conclusion, and also as a conclusion that follows from other premises. In analyzing an argument, we should list individually all of the assertions that make it up. That is an important step because the assertions often are buried among a lot of verbal "noise" that contributes nothing to the argument. By listing the assertions individually, we can strip away the obscuring irrelevancies and get down to the essentials. A good way to start the process is to identify the conclusion or key assertion. Usually when a logical argument is expressed in a formal way, the conclusion is the last assertion. However, the arguments that we encounter in everyday life usually are not expressed formally, and the conclusion need not be the last assertion. Often, in fact, it is not; sometimes it is the first assertion. Consider the following hypothetical logical argument against a proposed new law to increase the speed limit on major U.S. highways from 55 to 65 miles per hour: The proposed law to increase the speed limit should be defeated, because if the law is enacted it will mean a significant increase in the death toll on U.S. highways. Any proposal that would result in more deaths on our highways, which already claim more than 50,000 lives per year, should be vigorously opposed. Here the conclusion is stated first, and the supporting premises follow. Rephrased in more conventional, or textbook, form, the argument becomes: Any (all) proposal(s) that would result in more deaths on the highways should be defeated. The proposed increase in the speed limit would result in more deaths on the highways. Therefore, the proposed increase in the speed limit should be defeated. In trying to identify the conclusion or key assertion of an argument, it is helpful to bear in mind that it is the main point of the argument. It is what the person making the argument wants us to believe and remember. Everything else is said in support of it. Once we have identified the conclusion or key assertion, we should then identify all the supporting assertions. In doing this, it is helpful to bear in mind that the role of these assertions is to provide

79 information from which the conclusion can be deduced or to make the key assertion credible. When we are attempting to analyze a complex logical argument, it can be helpful to outline it, using the major conclusion as an anchor point and classifying the premises in terms of their logical distance from that point. Assertions from which the major conclusion (presumably) follows may be considered first-level assertions and numbered with single integers (e.g., 1, 2, 3). Assertions from which first-level assertions follow may be considered second-level assertions and numbered with two integers, separated by a point (e.g., 1.1, 1.2, 1.3, 2.1). The first integer of each pair identifies the first-level assertion for which the second-level assertion is a premise. Assertions from which second-level assertions follow may be considered third-level assertions and numbered with three integers, separated by points (e.g., 1.1.1, 1.1.2, 2.1.1), thefirsttwo integers identifying the second-level assertion for which the third-level assertion is a premise; and so on. To make the structure of a complex argument explicit, each of the assertions that comprise the argument should be appropriately numbered and written on a separate line. In order to highlight the structure, it is helpful to follow two simple rules: 1. show the level of the assertion by the amount by which it is indented; and 2. write an assertion immediately below (or above) those from which it follows. The procedure for analyzing an argument can be summarized as follows: 7. Identify the conclusion or key assertion. 2. List all of the other assertions that make up the argument. 3. Order the premises (or supporting assertions) and the conclusion (or key assertion) so as to show the structure of the argument. The procedure will work, of course, only if the argument, as originally expressed, is complete. Unfortunately, the arguments we encounter in everyday life typically are not complete, so analyzing them is not as easy as this passage may suggest, and the simple procedure described above will not work until the missing components have been filled in. In attempting to determine the structure of an argument, especially for those with little experience, it can be helpful to write each assertion on a separate slip of paper. You can then experiment with various structures simply by moving the slips of paper around, and as you identify missing premises, you can write them on other slips and insert them at the appropriate places. 5.5

ANALYZING ARGUMENTS

Think about it

• Analyze an argument to ascertain what conclusion or key assertion the arguer intends.

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5.6

F O R M S OF L O G I C A L A R G U M E N T S

Logicians distinguish among many forms of logical arguments. Form in this context refers to an argument's structure and in particular to the forms of the assertions that comprise it. The argument All A are B All B are C Therefore all A are C is different in form from the argument If X then Y Not Y Therefore not X. The various forms in which an argument can be cast may be found in books on introductory logic. Here we will consider briefly two forms that are particularly important both because they are very commonly used and because they are frequently used incorrectly. Modusponens is an argument of the form: If X then Y X Therefore Y where A" and y represent assertions. Xis referred to as the antecedent and Y as the consequent, (^and Fare used here instead of A9 B, and C, because the first letters of the alphabet have been used in the foregoing material to represent classes; whereas X and Y are being used here to represent assertions.) An example of a statement in the form "If X, then 7" would be "If the book is blue, then it belongs to Mary." In that example, the two assertions represented by X and y are respectively "the book is blue" and "it belongs to Mary.") In a modus ponens argument, the conclusion follows from the conditional (if-then) statement and the affirmation of the antecedent. Modus tollens is an argument of the form: If X then Y Not Y Therefore not X.

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FORMS OF LOGICAL ARGUMENTS

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In that case, the conclusion follows from the conditional statement and the denial of the consequent. Both forms of argument are valid; so in each case, if the premises are true, the conclusion must also be true. The modusponens and modus tollens forms are very widely used, not only in formal contexts but in everyday reasoning as well. Understanding them is especially important because two particularly common types of reasoning errors are associated with them. In one erroneous form, the argument is structured as follows: If X then Y Y Therefore X. It is known as affirming the consequent. It is an error because the conclusion does not follow from the premises. The other common erroneous form is structured as follows: If-then Y Not X Therefore not Y. It is known as denying the antecedent. Some examples of valid modus ponens and modus tollens arguments are shown in Tables 3 and 4. Errors of Table 3. Examples of Modus Ponens Arguments

If the experiment was done properly, the color of the liquid should change from green to blue. The experiment was done properly. Therefore the color of the liquid should change from green to blue. If one practices an instrument faithfully, one's performance should improve. I have been practicing faithfully. So my performance should be improving. If one plays with fire, one is likely to get burned. They are playing with fire. They will probably get burned. If the sky is red in the evening, the following day is supposed to be a pleasant one. The sky is red this evening. So tomorrow should be a pleasant day. If one takes good care of an automobile, it should last a long time. I take good care of my automobile. So I expect it to last a long time.

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If he tried hard, he would get good grades. He is not getting good grades. So he must not be trying hard. If she had the measles as a child, she would not have gotten them as an adult. She did get them as an adult. So she must not have had them as a child. If the experiment had been done properly, the color of the water should have changed from green to blue. The color of the water did not change. Therefore, the experiment must not have been done properly. If the dog were a Dalmatian, it would be white with black spots. It is red. So it is not a Dalmatian. If the bicycle had been assembled properly, there should be no parts left over. There are parts left over. Therefore, it must not have been assembled properly.

If

affirming the consequent and denying the antecedent are illustrated in Tables 5 and 6. One way to characterize the erroneous forms is to see them as involving a confusion between one-way and bidirectional implication. (See Section 4.11.) If the first premise of either argument were and only if X then Y, it would be valid to complete the argument either with " Y; therefore X"; or "not X; therefore not Y"; because If and only if X then Y and If and only if Y then X mean the same thing. Think

about

it

• Create some modus ponens and modus tollens arguments, making use of your knowledge of the world. • Make up some invalid logical arguments involving affirming the consequent or denying the antecedent.

Table 5 Examples of Erroneous Arguments Involving Affirmation of the Consequent

If it is Luisa's bicycle, it is a red one. This bicycle is red. So it must be Luisa's. If one is a Columbian, one is very likely to be able to speak Spanish. Leo speaks Spanish. So Leo is probably a Columbian. If the Martins were not at home, the lights in their house would be off. There are no lights on in their house. Therefore they must not be home. If he were the culprit, he would have a good alibi. He has a good alibi. Therefore he must be the culprit. If it is the chicken pox, he should have red spots and a high fever. He has red spots and a high fever. Therefore it must be the chicken pox.

Table 6 Examples of Erroneous Arguments Involving Denial of the Antecedent

If the sky is red in the evening, the weather is likely to be pleasant on the following day. The sky is not red this evening. So the weather will probably be unpleasant tomorrow. If petroleum is used wastefully, eventually the supply of it will be exhausted. We plan not to use petroleum wastefully. Therefore the supply should never run out. If one acts unthinkingly, one will make mistakes. Mary never acts unthinkingly. So she should not make mistakes. If one eats that stuff, one is sure to get sick. I am not going to eat it. So I should not get sick. If one fails to weed one's garden regularly, one will not get a good crop. I weed my garden regularly. Therefore I should get a good crop.

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5.7

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A N A L Y Z I N G I N C O M P L E T E LOGICAL A R G U M E N T S

It is an exception to the rule when we find an argument spelled out in its entirety any place other than in a textbook on logic. Typically, something that is necessary to make the argument complete is left unstated. One of the more difficult aspects of evaluating the reasoning wefindin prose or hear in conversation is to fill in the missing pieces that are necessary to make the arguments whole. The ability to fill in the missing pieces is important, because the force of an argument often depends on the plausibility of something that has been left unstated. Any part of a logical argument may be missing—one or more premises, or the conclusion. The omission of a part of an argument could be due to an oversight; more commonly, however, an omission probably results from the assumption by the person making the argument that there is no need to make the omitted part explicit, because it is obvious. Sometimes, however, a part may be omitted in the hope of avoiding critical scrutiny of it. Whatever the reasons for omitting parts of arguments, it is extremely important to fill in those missing parts when analyzing an argument before attempting to evaluate it. M i s s i n g Premises

Sometimes missing premises are easy to identify. That is especially likely when a premise has been omitted because the person making the argument feels that it is so obvious that stating it would be a waste of words. Consider again, for example, the argument against increasing the speed limit. Suppose it had been expressed with one of its premises missing, as follows: The proposed law to increase the speed limit should be defeated, because if the law is enacted, it will mean a significant increase in the death toll on U.S. highways. The argument is unquestionably incomplete; the missing premise is needed if the desired conclusion is to follow. You might well feel comfortable stating the argument in that way, however, on the assumption that the missing premise (any proposal that would result in more highway deaths should be defeated) is too obvious to require stating. On the other hand, what is missing in an argument can also be hard to specify. Indeed, sometimes so much is missing that it is not possible to tell whether what you have was intended to be an argument at all. In any case, in analyzing an argument (even to the point of deciding whether what you have is an argument) it is important to try to determine what premises are missing and to state them explicitly. When outlining the structure of an argument, it is helpful to distinguish clearly between the premises that were explicit in the

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argument as originally stated and those that had to befilledin. A convenient way of doing this is by enclosing the latter type in parentheses. Making explicit the premises that have been omitted from a logical argument can be an instructive exercise, not only for deciding whether to accept an assertion that someone else has made, but also for obtaining a better understanding of our own beliefs and of the assumptions that are necessary to support them. Awareness of the assumptions that are required to support a belief may, in some cases, cause us to revise that belief. If I realize that the belief that A'is true is justified only if I also believe that Y is true, I may be less willing to believe that X is true. It is not always easy to take an informally expressed argument and recast it into a form that makes the logical structure apparent. There are many factors, in addition to missing premises, that may make an argument's structure difficult to discover. The argument may be logically unsound, it may contain irrelevancies, it may be stated ungrammatically, or what is being asserted may be unclear. The attempt to make the structure of an argument explicit should reveal such problems if they exist. Missing Conclusions

Sometimes what is missing in an argument is not one of the premises, but the conclusion. That may seem strange, inasmuch as the conclusion usually is the most important part of an argument, but there are various reasons why a conclusion might be left unstated. Sometimes the conclusion may be an unpleasant thing to state; so in order to avoid stating it, we just state the premises and leave the listener to draw the conclusion. (For example, if we want to make the point that John Doe is not to be trusted, it may be easier to do so by making the general observation that no one is completely honest than by asserting John Doe's dishonesty directly.) Sometimes we may feel that the conclusion is too obvious to require stating, and for that reason we do not state it. Whatever the reason, we often encounter arguments that fail to make the conclusion explicit. In such cases, it is important not only to be able to recognize that the conclusion is missing, but to determine what the intended conclusion is. An argument with an unstated conclusion can be a very subtle form of argument. Very Incomplete Logical A r g u m e n t s

We have noted that an argument may be incomplete because it lacks a premise or even a conclusion. In fact, it is possible to have an argument that lacks both a premise and a conclusion. Consider the following example. An accident involving a red car and a blue car has just occurred, and the driver of the blue car makes the following observation:

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If the other driver (the driver of the red car) had obeyed the traffic signal, the accident would not have happened. Notice that the driver of the blue car does not claim explicitly that the driver of the red car disobeyed the traffic signal; however, that appears to be the conclusion he expects the listener to draw. Moreover, he does not state the second premise of the argument, namely the fact that an accident did occur. Presumably, he considers that unnecessary inasmuch as its occurrence is known to the listener. The complete argument is: If the driver of the red car had obeyed the traffic signal, the accident would not have occurred. The accident did occur. Therefore, the driver of the red car did not obey the traffic signal. It is, in fact, a modus tollens argument, in which the conclusion follows from the denial of the consequent of a hypothetical syllogism. The example also illustrates another point about arguments. Although the conclusion that follows directly from the premises, as they have been stated, is that the driver of the red car did not obey the traffic signal, the conclusion that the driver of the blue car really wants drawn is that the driver of the red car was responsible for the accident. It may seem that having drawn thefirstconclusion is tantamount to having drawn the second one, but in fact another inferential sequence is necessary: If one fails to obey a traffic signal and becomes involved in an accident as a consequence, one is responsible for the accident. The driver of the red car failed to obey a traffic signal and became involved in an accident as a consequence. Therefore, the driver of the red car is responsible for the accident. Probably few people would feel the necessity for making that argument explicit, because the connection between responsibility for an accident and failure to obey a traffic signal is a rather strong one. The important point is that the example is probably representative of many in real life, in which the conclusion that is explicit in a particular argument may be somewhat different from the one the producer of the argument really wants drawn. Summary As we have noted, many of the logical arguments we encounter in everyday life are incomplete. One reason for that is that people typically do not state what they consider to be obvious. It is a very good idea, however, to try to fill in all the missing pieces of an argument before evaluating it, because what

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may be obvious to one person may not be obvious to another. The only way we can avoid unintentionally accepting as true an unstated assertion that we do not really believe to be true, is to make that assertion explicit. Sometimes when we do fill in the missing pieces of an argument, we discover to our surprise that it contains one or more assertions we do not believe. When that is the case, the entire argument may lose its force. Given that many arguments are incomplete, our procedure for analyzing arguments must be modified to accommodate the fact, if it is to be useful. Specifically, we must add the following step: • Add any unstated assertions that are necessary to make the argument complete. Where should this step appear in the sequence? For convenience, we will make it the third item, and rewrite the procedure as follows: 1. Identify the conclusion or key assertion. 2. List all the other explicit assertions that make up the argument as given. 3. Add any unstated assertions that are necessary to make the argument complete. (Put them in parentheses to distinguish them from assertions that are explicit in the argument as given.) 4. Order the premises (or supporting assertions) and conclusion (or key assertion) so as to show the structure of the argument. Although a rationale can be given for the order in which the steps in this procedure are listed, this order should not be viewed as one that must always be followed. Indeed, sometimes it may not be convenient to begin by identifying the conclusion. This is especially likely to be the case if the conclusion has been left unstated. In general, determining first what the individual who has produced the argument wants us to conclude may help to put the whole argument in perspective. It may also help us to distinguish between those portions of a narrative that are part of that argument and those that are not. But if the conclusion has been left unstated, we will have to examine the premise(s) in order to determine what the intended conclusion is. Another reason why the order of the steps in the procedure should not be taken too seriously is that it may prove to be necessary, especially when analyzing a complicated argument, to return to a given step one or more times. For example, you may believe that you have listed all of the assertions (stated and unstated) that comprise an argument, and then discover (when trying to order the premises so as to show the logical structure of the argument) that something essential is still missing. The important thing is that the objective of an analysis is to make both the

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meaning and the structure of an argument clear, to show explicitly the conclusion and the premises from which that conclusion is drawn. The characterization of that process as a set of steps is intended to be helpful to the beginner. As you gain experience in analyzing arguments, you are likely to evolve your own approach, which is fine, provided it produces the desired results. Think

about

it

• Formulate some logical arguments from which a premise and a conclusion are missing, but which, nevertheless, would make sense to a listener. 5.8

E V A L U A T I N G LOGICAL A R G U M E N T S

One of the major benefits to be derived from reasoning skill is the ability to evaluate arguments. If we cannot evaluate arguments effectively, we are at the mercy of every attempt to mold our beliefs. No less important than the need to evaluate arguments presented to us by others is the ability to criticize the arguments we produce ourselves. Self-deception comes naturally for most of us. We are especially adept at convincing ourselves of that of which we want to be convinced. Being critical of our own reasoning is undoubtedly more difficult than being critical of the reasoning of others. Playing prosecutor, judge, and jury when one is oneself the defendant requires an unusual degree of objectivity and commitment to truth; but the ability to evaluate one's own reasoning aggressively and fairly is the acid test of rationality. The main reason to evaluate an argument is to determine whether or not to accept the conclusion of the argument as true. There are four questions we should ask when evaluating a logical argument: 1. 2. 3. 4.

Is it complete? Is its meaning clear? Is it valid? (Does the conclusion follow from the premises?) Do I believe the premises?

If the answer to each of those questions is yes, then we should accept the conclusion as true. Let's consider the four questions individually, starting with the question of completeness. How do we determine whether an argument is complete? The best thing to do is to put it in standard form, as discussed in preceding sections. By doing that, we make missing premises (or a missing conclusion) more apparent than they otherwise might be. When we find that an argument is incomplete, we may complete it byfillingin whatever is missing;

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EVALUATING LOGICAL ARGUMENTS

89

but when we do so, we have to wonder whether the person who originally constructed the argument would still acknowledge it to be his or her own. Sometimes when we discover what has to be added to make one of our own arguments complete, we may decide that we no longer want to make that argument, because we do not wish to make the assertion or assertions that are required to complete it. The second criterion is clarity. Is the meaning of each of an argument's components (premises and conclusion) clear? It is a more difficult criterion to satisfy than one might think, because language often is rather vague and imprecise, as we have already noted. The third criterion for evaluating a logical argument is the criterion of validity. Is the reasoning valid? Validity is a logical concept; it has to do with the formal structure of arguments. We could spend a lot of time thinking about validity, and anyone who takes a course in formal logic will do so. For now, we will be satisfied with a beginner's understanding of the concept. We should realize that some arguments are valid and some are not. We should also realize that there is a difference between validity and truth. Validity (or invalidity) is a property of arguments; truth (or falsity) is a property of assertions. Validity has to do with whether a conclusion follows from an argument's premises. To be sure, if the premises are true and the logic is valid, then the conclusion of an argument must also be true. However, it is possible to have a valid argument with false premises. That is because the validity of an argument does not depend upon having true premises; an argument is valid if the conclusion follows logically from the premises, whether or not the premises are true. That does not mean, of course, that we are obliged to believe the conclusion of a valid argument. That brings us to the next point. The fourth criterion to use in evaluating arguments is the criterion of plausibility: Do I believe the premises to be true? The reason it is so important is that only if the reasoning is valid and the premises are true can we be sure that the conclusion is true. If any one of the premises, even of a valid argument, is false, then the conclusion too may be false. (It is possible to have a true conclusion follow from false premises, but the point is that if one or more of the premises is false, we cannot be sure that the conclusion is true.) The distinction between logical validity and empirical truth is a fundamental one for effective reasoning. Apropos of this distinction, there are two ways in which we might challenge an argument: 1. with respect to the validity of the logic (if the rules of inference are violated, the conclusion does not follow from the premises); and 2. with respect to the plausibility of the premises (if one or more of the premises is believed to be false, we cannot be confident that the conclusion is true). Assuming an argument is valid, we must assess the plausibility of its premises before deciding whether to believe its conclusion. We must decide,

90 5. ARGUMENTS with respect to each premise, whether or not we believe it, or more generally, the degree of credence to give to it. The premises of an argument can be either true or false, as can the conclusion. Figure 5 represents the four possible combinations of true or false premises and a true or false conclusion in a valid logical argument. As the figure indicates, a true conclusion must follow from true premises, but either true or false conclusions can follow from false premises. Conclusion

True Premises

False

True Necessary (Conclusion must be true if premises are true) Possible (Conclusion may be true even if premises are false)

False Impossible (Conclusion cannot be false if premises are true) Possible (Conclusion may be false if premises are false)

Figure 5. The four combinations of true or false premises and conclusions in a valid logical argument. Entries in the table indicate how the truth or falsity of the conclusion depends upon the truth or falsity of the premises.

The fact that a true conclusion can follow from false premises but a false conclusion cannot follow from true premises is a curious asymmetry. It is another way of saying that truth does not contradict itself. If X and Y are true, and Z follows from A'and Y, then Z must also be true. However, given that one or more of the premises are false, the conclusion need not be false; it could be either true or false. Falsity is not subject to the same consistency constraint as is truth. Think a b o u t it

• In evaluating a logical argument, why is it important to consider both the validity of the argument and the plausibility of the premises? What does one risk if one considers only one of these factors? 5.9 USING DIAGRAMS TO HELP JUDGE THE VALIDITY OF LOGICAL ARGUMENTS

When trying to determine whether a logical argument is valid, it may be helpful to try to represent the argument with a diagram. Here is a procedure that often works well:

91 Step 1: Make a separate diagram for each premise and the conclusion. Step 2: Combine the diagrams for the premises into a single diagram in as many ways as possible. Step 3 : See if all of the resulting diagrams of the premises are consistent with the diagram of the conclusion. 5.9

EVALUATING PLAUSIBLE ARGUMENTS

If any of the diagrams of the premises are inconsistent with the conclusion, the argument is invalid. If it is impossible to produce a diagram of the premises that is inconsistent with the conclusion, then the argument is valid. Of course, one must be careful here: the fact that one cannot think of a way to diagram the premises that is inconsistent with the conclusion does not necessarily mean that such a diagram is impossible to construct. To see how the procedure might be applied, consider the logical argument: All A are B All B are C Therefore, all A are C. Step 1: first premise

second premise

Step 2: both premises

conclusion

5. ARGUMENTS Inasmuch as there is no other way to combine the diagrams for the premises, we ask: Step 3: Are all the diagrams that represent the premises consistent with the diagram of the conclusion?

92

Since the answer is yes, we have some assurance that the argument is valid. Now consider the following argument, which, superficially, looks very similar to the one we just considered. No A are B No B are C Therefore, no A are C first premise

both premises

second premise

conclusion

consistent with? yes

or

no

or

no

5.10

EVALUATING PLAUSIBLE ARGUMENTS

or

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no

In this case, we find that there are several ways to represent the two premises that are not consistent with the representation of the conclusion; therefore we know that the argument is invalid. It is probably obvious from this example that it is not really necessary to produce all of the diagrams in order to show the argument to be invalid. Producing one representation of the premises that is inconsistent with a representation of the conclusion suffices. In order to be sure that an argument is valid, however, one must be sure that all the ways of representing the premises are consistent with all the ways of representing the conclusion. Think a b o u t it

1. Use diagrams to help decide whether each of the following arguments is valid: No A are B. All B are C. Therefore, no A are C. All A are B. No B are C. Therefore, no A are C. No A are B. All C are A. Therefore, no C are B. No A are B. All A are C. Therefore, no B are C. Some A are B. Some B are C. Therefore, some A are C.

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5.10

EVALUATING PLAUSIBLE ARGUMENTS

Plausible arguments are less susceptible to objective evaluation than are logical arguments. The question of validity does not arise in this case because plausible arguments do not have to fit any prescribed forms. A question that does arise, however, as in the case of logical arguments, is that of the truth of the supporting assertions. If the evaluation of an argument considers an assertion that is intended to support the key assertion to be untrue, then that assertion should carry no weight. Assuming that the supporting assertions in a plausible argument are true, the problem then becomes that of judging the degree to which those assertions (individually and as a group) do indeed make the key assertion more plausible. Here, personal judgment must play a prominent role. Information that would be considered compelling evidence of the truth of a key assertion to one individual might not be considered very compelling to another. How we react to the information in the supporting assertions will undoubtedly depend to some degree on what else we know about the topic of the argument. Often when people make plausible arguments, especially about controversial topics, they knowingly or unknowingly include in the argument only assertions that support the key assertion they wish to promote. Not surprisingly, they do not include assertions that would tend to weaken the plausibility of the key assertions. A person who is knowledgeable about the topic of the argument is more likely to be able to think of such countermanding assertions than one who is not, and consequently that person might attach less weight to the supporting assertions in the argument. That observation brings us to another important point regarding the evaluation of plausible arguments. One very effective evaluation strategy is that of constructing counterarguments. For example, if we encountered a plausible argument that all countries should maintain a standing army, one approach to evaluating the argument would be to try to construct an argument that it is not a good thing for all countries to maintain a standing army. Having constructed the counterargument, we could then compare the two arguments and attempt to decide which is the more compelling. There are two points worth making here. First, one of the things that becomes apparent as we use this procedure is that plausible arguments seldom have a clear and irrefutable outcome. It is more likely that arguments that some people willfindcompelling can be made on each side of an issue. Second, in order to use the approach of constructing counterarguments effectively, we must have some knowledge of the topic of the argument; indeed, the more we know about the topic, the more persuasive a

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EVALUATING PLAUSIBLE ARGUMENTS

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counterargument we are likely to be able to construct. In general, the construction and evaluation of plausible arguments is very much a knowledge-dependent process, and it is undoubtedly the case that, other things being equal, an individual who knows more about a topic will be better able to construct arguments and counterarguments about that topic than will one who knows less. Finally, in assessing the various assertions that can be made in support of or against a given assertion, there is one error that probably all of usfindvery easy to make. We are likely to give more weight to assertions we like than to those we dislike. That is, we are likely to accept those assertions that agree with our preconceived ideas and reject those that disagree with them. Thus, it is very difficult for us to evaluate plausible arguments entirely objectively and without bias. T h i n k a b o u t it

The following letter to the editor was written by a smoker in reaction to an editorial supporting an aggressive antismoking campaign aimed at making smoking illegal in public places such as restaurants, theater lobbies, bus stations, and so on. The writer of the editorial had argued that smoking in a public place pollutes the air and forces nonsmokers to inhale smoke against their will and is therefore an infringement of their right to clean air. As a smoker, I am tired of being told that my smoking constitutes a violation of the rights of people who do not smoke. I do not own a car; should I therefore feel that everyone who drives one, and pumps the air full of carbon monoxide by doing so, is violating my right to clean air? I do not like the odor of most perfumes and "fragrances"; should I therefore mount a campaign to ban their use? Ifindthe smell of onions, garlic, and spicy foods especially offensive; should I therefore try to make people who eat such things feel like second class citizens? [Signed] P.G. Consider the following questions: • Does P.G. explicitly deny the claim of the editorial writer that smoking in a public place pollutes the air in that place? • Does P.G. explicitly quarrel with the idea that when someone willfully does something that pollutes the air that other people have to breathe, he or she is infringing on the rights of those people?

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• What is the main point that P.G. makes? • P.G. seems to be suggesting that people should not criticize other people for polluting the air if they are helping to pollute it themselves. What do you think of that suggestion? • Do you think the letter also raises a question as to what it means to pollute the air? In particular, does the reference to "perfumes and 'fragrances'" seem to suggest that different people may have different opinions regarding what constitutes pollution? How does the aphorism "One person's meat is another's poison" relate to this issue? • Suppose that you too object to smoking in public places (even if you don't). How might you answer P.G's letter? 5.11

WEIGHING EVIDENCE V E R S U S BUILDING A CASE

There is a very important distinction that we should make at this point. That is the distinction between weighing evidence impartially and building a case. When we are weighing evidence impartially so as to arrive at a correct conclusion, we pay equal attention to evidence that favors a particular conclusion and evidence that opposes it. However, when we are building a case, we tend to consider only the information that is favorable to the desired conclusion and to ignore or downplay information that is inconsistent with that conclusion. We should be sure to understand this distinction because it is an extremely important one. One of the procedural differences between building a case and weighing evidence is that when we build a case, we begin with the conclusion and then try to defend it. On the other hand, when we weigh evidence, we begin with the evidence, and draw the conclusion only after all the evidence has been considered. It should be clear which of the two activities (building a case or weighing evidence) is more deserving of being called reasoning. Are there times when it is acceptable to build a case? Probably. For example, in a court trial, lawyers are expected to build a case. The lawyer for the prosecution builds a case for the prosecution and the lawyer for the defense builds a case for the defense. The assumption is that when each side has done its best to present the evidence favoring its position, the judge or jury will be able to weigh that evidence impartially to determine the truth with respect to whatever question the trial is intended to resolve. There is a particularly vexing problem relating to the distinction between weighing evidence and building a case that we should be aware of. That is this: we often believe that we are weighing evidence impartially when in fact we are building a case. As we have already noted, it is surprisingly easy for us to fool ourselves into thinking that we are impartial in a particular instance when we really are not. And if we favor one conclusion over another, it is

97 very easy for us to give more weight than we should to the evidence that favors that conclusion and less weight than we should to the evidence that opposes it. Being able to weigh evidence impartially when we strongly prefer to believe one thing rather than another is a very difficult thing to do. 5.12

DISPUTES

Think a b o u t it

• If people in general were consistently more interested in weighing evidence than in building cases, what effect do you think that would have on interpersonal—or international—relations? • Why might it be more difficult to distinguish case building from evidence weighing in one's own behavior than in that of others? 5.12

DISPUTES

The tendency to build cases rather than to weigh evidence, which we all have to some degree, is a major cause of disputes. A dispute, which we want to distinguish from an argument, is a disagreement, often an emotional one. Disputes often arise when each of two people builds a case favoring the opposite conclusion and tries to convince the other person that he or she is wrong. Disputes can be very frustrating. Even highly intelligent people sometimes act childishly when engaged in them. It often seems that the more each person tries to change the other person's mind, or to prove the other person wrong, the more strongly each becomes committed to his own position and the less likely it seems that the dispute can be resolved. It is important to note that there is a great difference between winning a dispute and resolving one. In particular, "winning" a dispute and persuading someone to believe something are not necessarily the same things. Indeed, winning a dispute may be the least likely way of winning an opponent over to your point of view. Disputes are rarely resolved by reason, because the disputing parties typically are not seeking resolution; rather each is seeking to win. Disputes can be resolved, but only if the people engaged in them desire to have them resolved. There are at least four strategies that are sometimes worth trying in the interest of resolving a dispute. • Analyze the arguments. Disputes sometimes are the result of misunderstandings and failures in communication. One step that can be helpful in resolving a dispute is to analyze the argument of each disputant very carefully and make sure that each person understands both his or her own argument and that of the other person. Sometimes making the arguments clear is all that is required to resolve the dispute.

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• Define terms. Understanding an argument involves not only understanding its structure, but also understanding the meaning of each of the individual assertions that it contains. That requires understanding the words that make up those assertions. Often disputes arise, or are unnecessarily prolonged, because the disputants use the same words in different ways. It is helpful, therefore, to try to get agreement on how the key words in the arguments are to be defined. • Get the facts. Sometimes a dispute may involve factual information that is readily available. For example, one person may claim that thus and so is the case, while the other person claims that thus and so is not the case. If the claim in question is a statement of fact, it may be possible to resolve the dispute simply by consulting an appropriate information source (e.g., an almanac, an atlas, an encyclopedia). It is silly to have disputes over questions to which factual answers are easily obtained. • Exchange roles. A good way to increase our understanding of someone else's point of view is to try to argue about an issue from that person's perspective. It is not an easy thing to do, but it can be a very useful strategy if we are willing to invest the effort it requires. Sometimes we are reluctant to try to really understand someone else's point of view because (although we may not admit it to ourselves) we may be afraid that if we really understood it, we might adopt it for our own. 5.13

INDIRECT A N D D E V I O U S A R G U M E N T S

We have been thinking about arguments and about ways to analyze and evaluate them. So far, we have focused on relatively straightforward arguments in which the originators' intentions and, in particular, the conclusions they wished us to draw were fairly clear. However, many of the arguments to which we are exposed from day to day are indirect and sometimes even quite devious. Some of them are are used to persuade us, often without our realizing that we are being persuaded, to believe things or to do things that we otherwise might not believe or do. Examples are abundant in advertising, but that is by no means the only place where they can be found. When we look at advertisements, we should consider not only what each one says explicitly, but what message it is attempting to convey indirectly, and what it is attempting to get us to do. We should not be surprised to discover that the techniques that are used are exceedingly clever and quite effective. Advertising is a very large business, and whether or not a particular product is widely sold may depend on the cleverness of the advertising done to promote it. Consider, for instance, the two examples that follow. We will assume that what each says is precisely true. We should ask ourselves, however, what it is

5.14

CONSTRUCTING ARGUMENTS

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that the advertiser wants us to believe when we read the ad. In particular, we should ask whether it appears that the advertiser wants us to believe something that the ad does not say explicitly, but seems to suggest. Example No. 1. Ninety percent of all the Brand X automobiles (an imported model) sold in the United States during the last 10 years are still on the road. What do you think this ad is intended to make the reader believe? How might it be misleading? It appears that the ad is intended to make us believe that Brand X automobiles last an unusually long time. What it fails to tell us, however, is how sales have been distributed over the last ten years. If sales have been increasing, then many more Brand X automobiles were sold recently than were sold 10 years ago. Suppose that a large majority of all Brand X automobiles sold in the United States during the last 10 years were actually sold during the last 2 years. The claim in the advertisement could be true, but it would not support the conclusion that Brand Xautomobiles last an unusually long time. Example No. 2. Of all the brands of toothpaste tested, none proved to be more effective in preventing tooth decay than Brand X. What do you think this ad is intended to make us believe? What does it fail to tell us? Clearly, it is trying to convince us to buy Brand ^toothpaste because of its demonstrated effectiveness in preventing tooth decay. What it fails to tell us is how many brands were tested and which ones. Nor does it claim that Brand X did better than any of the others tested. It makes the much weaker claim that none of the others did better than Brand X. We might suspect that Brand x did not do better than the others on the assumption that if it had, the advertiser surely would have said so. Think

about

it

• Consider where, besides in advertising, we might expect to find indirect arguments used. • The following claim is printed in bold letters on the wrapper of a popular candy bar: "10 percent more chocolate." 1. What exactly is being claimed? 2. Ten percent more than what? 3. What is the claim intended to make the reader believe? 4. What is it intended to influence the reader to do? 5.14

CONSTRUCTING ARGUMENTS

A common purpose for making an argument is to convince someone of the truth, or at least of the plausibility, of an assertion, namely that assertion that is the conclusion or key assertion of the argument. Thus, in structuring a

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logical argument we attempt to show that the conclusion that is drawn follows logically from a set of true premises; in composing a plausible argument, we attempt to convince, by weight of the supporting assertions, that the key assertion should be believed. In constructing an argument, we may or may not lay out the steps by which we ourselves became convinced of the truth of the argument's conclusion or key assertion. Most likely, we will not do it, because we often arrive at conclusions or beliefs only after long and complex chains of inferences involving many false steps. When presenting an argument for the purpose of convincing someone else of something that we already believe, we want to present the argument in "cleaned up" form, as it were, stripped of the irrelevancies and complicating tangential lines of thought that may have characterized the process by which we originally arrived at the belief. That is, we want to state the premises or supporting assertions of the argument as clearly and unambiguously as possible and in such a way as to show how the conclusion or key assertion follows from, or is supported by, them. However, a caveat is in order here. A distinction has already been made between weighing evidence and building a case. In constructing an argument, we should be clear about what we are attempting to do. If we are building a case, then we may be intentionally selective about the evidence we use in the argument, and may in particular choose to ignore evidence that does not support the conclusion that is being drawn or the claim that is being made. That comment should not be interpreted as approval of this strategy, but simply as a recognition of the fact that it is sometimes adopted. T h i n k a b o u t it

• Choose two or three assertions that you believe to be true, and construct arguments that would help convince someone else of their truth. • A town has to decide whether to spend limited resources on upgrading public transportation or on improving its school system. Think of as many arguments as you can favoring one of those alternatives, and then think of as many as you can favoring the other, assuming that the town cannot do both things at the same time. 5.15

SUMMARY

The term argument has been used here to connote any set of assertions that is intended to support some conclusion or influence a person's beliefs. Arguments involve both deductive and inductive inferences and take many

101 forms. Typically, the arguments we encounter in our daily lives are incomplete in one way or another, and often are not easily recognized as arguments. The ability not only to recognize arguments but to evaluate them critically and objectively is extremely important to effective reasoning. This includes arguments that we ourselves construct, as well as those that we encounter from all sides in our daily lives. This ability is not trivial nor is it easy to acquire. It requires knowledge, effort, and a commitment to truth; which is to say, a deep desire to hold beliefs that insofar as possible correspond to reality. It also requires years of practice in recognizing arguments, analyzing them, and critically evaluating them. 5.15

SUMMARY

6

Stratagems

There are many techniques that can be used to persuade that do not have the force of reason when examined critically. Moreover, all of us are subject to a variety of reasoning errors. Part of the task of being an effective reasoner is to be aware of the many ways in which we can be led to reach unreasoned conclusions and of the types of reasoning errors that we are especially prone to make. It is to those topics that we now turn. Effective debaters know that disputes are often won or lost on the strength of factors other than reason and logic. There are many ways to bring down or frustrate your opponent that have little to do with the merits of your position vis-a-vis the issue in dispute. The 19th-century philosopher Arthur Schopenhauer described numerous stratagems that parties to a controversy can use against an adversary. His list included such ploys as the following: pretending that your opponent in a dispute has made a more general assertion than he has actually made and then attacking that general assertion; intentionally making your opponent angry in the hope of thereby impairing his judgment; claiming that the conclusion you want drawn follows from assertions to which your opponent has agreed, even if it does not; diverting attention from the main point of a dispute if you find that your opponent is getting the better of you. It is essential to effective reasoning that we be aware of such stratagems and their powerful, if devious, influence in determining the course that a dispute will take. To the unwary, they can indeed be overpowering, not to say devastating, on occasion. The purpose of this chapter is to consider various ways in which people's beliefs are influenced other than by means of reasonable arguments. The 102

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THE ART OF INDIRECT PERSUASION

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intent is not to provide skill in the use of alogical or unreasoning stratagems, nor to encourage their use, but rather to acknowledge their existence and to foster the kind of awareness that will, it is hoped, make us less susceptible to their influence. The following chapter deals with the topic of reasoning fallacies. The distinction between a stratagem and a fallacy, as those terms are used here, is not a sharp one; however, neither do the two terms have the same meaning. One basis for the distinction centers on the question of intention. A stratagem, as the word is used here, connotes an approach that is taken for the purpose of persuading someone of the truth of some assertion, of influencing someone to draw a desired conclusion, or of getting the better of an opponent in a dispute. Stratagems may involve fallacious reasoning, and often do, but they need not. The term fallacy, on the other hand, connotes a particular way in which reasoning may go wrong. It does not carry the notion of intent and certainly not of intentional deception. Indeed, when deception is involved, it is as likely as not to be the reasoner who is deceived, being unable to recognize the fallaciousness of his reasoning process. The stratagems discussed here are in no sense a complete list. The intent is simply to mention a sample of the stratagems that most of us will probably recognize because we have come in contact with them in our daily lives. The reader is invited to think of others that could be added to this short list. 6.1

THE A R T OF INDIRECT P E R S U A S I O N

Persuasion is the process by which we convince someone to believe or to do a particular thing. Unhappily, the art of persuasion shares with the art of disputation the fact that the effectiveness with which it is practiced has amazingly little to do with reasoning. One way to persuade is to present explicitly arguments intended to convince others of the reasonableness of adopting a particular belief or of behaving in a desired way. Sometimes that approach works; sometimes it does not. It should not be surprising, of course, if the approach fails when the arguments offered are not very compelling. In any case, people who practice the art of persuasion often find it more effective to persuade by indirect, rather than direct, means. Obvious examples of the indirect approach can be found in advertising. The art of motivating people to buy specific products is afinelydeveloped art indeed. We are told of famous people who buy and love a particular product. We are assured that people who have compared that product with competing products have overwhelmingly chosen it over the competitors. We are given the privilege of witnessing the product in use by Beautiful People, and are led to believe either that our use of the product will make us beautiful too, or

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that if we do not use the product, it is evidence that we are not members of the beautiful class. We are shown the product in the context of some entertainment that we enjoy, with the expectation that the good feelings about the entertainment will transfer to the product. And so it goes. Rational people will attempt to discount such attempts to practice the art of indirect persuasion; however, the methods are very subtle, and it is not clear that the defenses of even the most critically minded people are as effective as we might hope. Think

about

it

• Make a list of the ways that people try to influence the behavior of other people. How, for example, do parents try to influence the behavior of their children? How do teachers try to influence the behavior of students? How do children try to influence the behavior of parents? How do students try to influence the behavior of teachers? How do advertisers try to influence the behavior of consumers? How do politicians try to influence the behavior of voters? How do citizens try to influence the behavior of politicians? • Make a list of the various tricks that advertisers use to attempt to get people to purchase specific products. Characterize the persuasion techniques that are used in a sample of advertisements. • Analyze some advertisements for the purpose of identifying relevant things that are left unsaid. 6.2

MISREPRESENTATIONS

A common stratagem when arguing against a position we wish to discredit is to misrepresent that position. The misrepresentation need not be as flagrant and unsubtle as a direct misstatement of fact. It can take many more subtle guises. For example, it might involve stating a position somewhat more extremely than an advocate for the position would; it might involve stating it in such a way that its weaknesses are apparent and its strengths are not; or it might involve stating it incompletely or neglecting to mention compelling arguments that could be presented in its favor. Sometimes the misrepresentation of a position that we wish to discredit is undoubtedly intentional. However, we should recognize that it may be extremely difficult to do justice to a position that we do not believe, even when we make every effort to do so. For that reason, if we really want to understand a position, and how it is that some people find it credible, we should probably have it explained by someone who not only understands it, but believes it as well.

6.3

Think

about

THE DECEPTIVE USE OF TRUTH

105

it

• Think of ways we might unintentionally misrepresent a position we oppose. • Think of ways in which we might intentionally misrepresent a position that we oppose. 6.3

THE DECEPTIVE U S E OF T R U T H

Everyone knows what it means to lie, and probably most people believe that lying is not a good thing to do. One of the practical problems with lying is that if a person gets a reputation of being untruthful, people will be likely to mistrust anything he says, even when it is the truth. It is important to recognize that it is possible to be deceptive or misleading without actually lying. Probably most people would agree that that is not a good thing to do either. None of us likes to be deceived, and we are likely to be disappointed or angry if we discover that we have been. As a society, we are sufficiently concerned about truthfulness to have laws that require certain standards of conformity to fact in advertising and in the disclosure of ingredients of foodstuffs and medicines. It is well to be mindful, however, that precluding the deceptive use of the truth is probably not possible. There are many ways to deceive with statistics without lying; and statistics aside, it is certainly possible to deliberately promote beliefs that are inconsistent with the facts without ever explicitly telling an untruth. One of the more obvious possibilities is to tell the truth, but only part of it. Given the strictures against false advertising in this country, we would expect advertisers to be quite careful not to make factually false statements when promoting their products. We should not be at all surprised, however, if the information they provide is rather strongly biased: we would expect them to make whatever truthful statements they can that put their products in a favorable light, but we would also expect them to refrain from making equally truthful statements that would make those products unattractive, unless, as in the case of cigarette advertising, they are obliged by law to do so. Advertisers are not alone in using the truth in biased and self-serving ways. Probably all of us do it to some degree. It is exceedingly difficult for us to see things really objectively when our personal preferences, values, and reputations are involved. Thus, it is particularly important to remember that being scrupulously careful to avoid untruths is not in itself sufficient to guarantee complete objectivity and lack of bias in what we say or think.

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6.4

STRATEGEMS

O V E R S T A T E M E N T OF A N O P P O S I N G POSITION

In arguing against a position that we desire to discredit, a common stratagem is to state the position in more extreme terms than would one who holds it, and then attack the position as stated. The unfairness of such a stratagem is apparent. What we are attacking is not a position that anyone holds, but a caricature of such a position. Here are some examples of overstatement: A complains to B (a store owner) thatB'sprices are too high. B replies, "You want me to give my merchandise away." A asks B's opinion about something that A has written. B makes a suggestion regarding how it might be improved. A, who was hoping that B would praise the piece, complains that B is impossible to please. A, a candidate for political office, argues that the government should spend less money on the military and more on education. B, the opponent, accuses A of wanting to destroy the military and leave the country defenseless. Think a b o u t it

• The next time you are listening to a radio talk program in which a controversial topic is being discussed, or viewing a TV program on which people representing opposing views on some issue are appearing, listen carefully for instances of one person overstating the position of another, so as to make it more easily criticized. 6.5

AUTHORITATIVE M A N N E R

The story is told of a public speaker who made a note in the margin of a prepared speech, "Argument weak, be forceful here." It is perhaps an apocryphal story, but it conveys an important point, namely that the persuasiveness of an argument can depend in part on the manner in which it is made. Thus, a speaker who gives an appearance of authority and who seems to be confident of what he is saying may be more credible to the hearer than one who appears less knowledgeable and less sure of the subject. This is undoubtedly true and indeed unfortunate. History is replete with examples of individuals who won the allegiance of masses of people less on the basis of what they said than on the basis of how they said it.

6.7

6.6

LEADING QUESTIONS

107

SLOGANISM

Slogans, maxims, aphorisms, and pithy sayings are powerful tools of persuasion. Typically, they encapsulate some bit of folk wisdom or self-evident truth; therefore, they are difficult to dispute. Moreover, they tend to be both brief and graphic, and hence easy to remember. The danger in such sayings is that they tend to be gross oversimplifications; you canfindone to suit any purpose. Often they are used to justify behavior; however, there is hardly any behavior that could not be justified in this way. In other words, for every maxim that seems to encapsulate some self-evident truth, you can probably find an equally compelling one that encapsulates a contradictory "truth." (See page 5.) 6.7

LEADING Q U E S T I O N S

A stratagem that is commonly used by lawyers in a court of law is to ask questions in such a way as to tease admissions out of a witness that the witness might not willingly make. Consider the following question, which might be asked by a prosecutor of a defendant: "Did anyone else know of your intention to embezzle the funds?" The question involves a presumption that the person being questioned corroborates implicitly simply by virtue of answering, regardless of whether the answer is yes or no. The presumption is that the individual did intend to embezzle the funds. Assuming the presumption is false, the appropriate response to the question is protestation that the question is meaningless because of the falseness of the presupposition on which it is based. Leading questions that are encountered in real life are typically more subtle than the preceding example. Indeed, the fact that they are leading questions may not be at all apparent. That such questions may have considerable effect on the answers given in response to them is well established, however. For example, one psychologist showed that after viewing a film of two automobiles colliding at an intersection, people who were asked how fast the cars were going when they "smashed" into each other often estimated the speeds to be higher than did people who were asked how fast the cars were going when they "hit" each other. Apparently the greater suggestion of violence carried by the word smashed influenced some individuals' memories, or at least reports, of what they had seen. Think

about

it

• Make up some questions calling for a yes or no answer that are phrased in such a way that either answer would appear to corroborate the assumption(s) on which the questions were based.

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6.8

Q U O T I N G O U T OF C O N T E X T

A particularly offensive stratagem that is sometimes used either to provide support for a position that we wish to defend or to discredit a position or person that we oppose, is to quote an individual out of context in such a way that the quote appears to mean something quite different from what was originally intended. The quote may be accurate, but when lifted from the context in which it was made, its original connotation may be drastically changed. That that is possible is a consequence of the fact that the meaning of language is highly dependent upon the particular situation; precisely the same utterance made in two different contexts may convey very different meanings. The practice of quoting out of context is repugnant when it is done with the intention of misrepresenting a person's views. It is a dangerous practice, however, even when we have no intention of misleading. It requires no malice to use a quotation in such a way that the interpretation put on it in its new context is somewhat more favorable to the position being supported than its originator might have intended. To some extent, we hear what we want to hear; and most of us are probably capable of interpreting statements that are mildly supportive of our beliefs as more strongly supportive than they really are. Also, when a speaker or writer has said many things, some of which are supportive of our views and some of which are not, we are probably more likely to remember the former than the latter. In quoting other people, it is important to be sensitive to these possibilities. The responsibility to represent accurately the views of an individual we are quoting is a heavy one; often it is not discharged very effectively. Think

about

it

• Examine an editorial in a local newspaper and find two comments that when taken out of context could be used to support mutually contradictory positions. 6.9

PUT-DOWNS

Disputes are not always (perhaps not even typically) won or lost on the strength of logic or reason. There are many ways to put down an opponent, or to be put down by one, that have nothing to do with the merits of the case. Who has not encountered such quips as the following: How could anyone believe such a thing? You can't be serious. I don't believe you said that.

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AVOIDING THE ISSUE

109

It's as plain as the nose on your face. Everyone knows that. That is the silliest thing I have ever heard. An exhaustive list of the put-downs that are used to win disputes would be a long list indeed. The rational person is not defeated or diverted by such tactics. However, we cannot afford to let down our guard against them; they can be amazingly effective if we fail to recognize them for what they are. Think

about

it

• Generate a list of put-downs that you have encountered in your own experience. 6.10

DILUTION B Y G E N E R A L I Z A T I O N

One of the stratagems that is sometimes used to dilute the significance of an act or character trait of an individual is to impute that same act or trait to a class to which the individual belongs. By making the point that all members of the class are alike in that particular regard, one gives the responsibility or credit, as the case may be, not to the individual, but to the class. Thus, when it is discovered that Johnny cheats, the stigma attached to cheating is presumably diminished by the claim that "all kids cheat." A similar stratagem is used when instead of attributing a characteristic to a class to which an individual belongs, one generalizes the characteristic itself. In that case, the response to the revelation that Johnny cheats might be "No one is perfect. " What is being said in this case is that cheating is a type of imperfection, and inasmuch as imperfections are the common lot of humankind, the fact that a particular individual cheats in no way distinguishes him from his fellows. Whether we accept that line of reasoning depends on whether we are willing to accept the notion that all types of imperfection should be considered equivalent. Note that if we do, we can make precisely the same excuse for murder as we make for cheating, that is, "No one is perfect." Think

about

it

• Think of some specific examples of dilution by generalization. 6.11

AVOIDING THE ISSUE

A common stratagem for dealing with exam questions to which we do not know the answer is to answer a question for which we do know the answer

110 6. STRATEGEMS and try to make the teacher believe that that is the question that was asked. Sometimes the technique works. It is one that some politicians are quite good at using. When asked an embarrassing question at a press conference, for example, the astute politician may simply pretend that a different and preferred question was asked, and then proceed to answer it. This is only one of many devices that are used to avoid focusing on a point. Others may involve introducing irrelevancies or digressive comments into the flow of a dialogue, with the intention of diverting the focus. A common stratagem in disputation when you are losing is to divert the focus of the discussion by drawing your opponent's attention away from the issue that is being debated. You may then hope to get yourself on more solid ground, or at least to disengage from the losing situation. The term red herring (from the practice of dragging a red herring across a trail to throw dogs off the scent) is sometimes used to denote something that calls attention away from the real issue. The use of red herrings for distractive purposes is a well-recognized stratagem in disputation. Of course, straying from the subject need not be intentional. It is quite easy to get off the track even when you have no intention of doing so. Indeed, we might argue that there is a natural tendency for disputes to wander into irrelevancies unless a rather concerted effort is made to keep them focused. Think a b o u t it

• Think of some ways in which one can help to keep a discussion or debate focused on a topic. • Identify and name as many ploys as you can to add to the list of alogical stratagems. 6.12

SUMMARY

The stratagems that are used in efforts to persuade or to win disputes are many and diverse. There can be little doubt that they often work; people are persuaded to believe or do things, and disputes are won, by such means. The particular stratagems that we have considered here are very common. Although they should be easy to recognize when we know what to look for, we often fail to see them for what they are.

7

Some Common Reasoning Fallacies

There are many ways in which we fail to reason effectively or, perhaps more to the point, there are many ways in which we succeed in being unreasonable. Certain reasoning errors, or fallacies, are especially common. Being aware of those particular errors should help us guard against them. That is not to say that by being able to recognize fallacies as such we will be able to avoid them completely, but we should be able to deal with them more effectively. In what follows, several examples of reasoning fallacies are identified and discussed. While the term "fallacies" is commonly used to denote the various approaches to problems that are considered here, it is important to note at the outset that what may be fallacious or inappropriate reasoning in one context may be quite appropriate in another. So we have to be careful in describing fallacies that we do not make the mistake of rejecting a perfectly good reasoning technique simply because it is frequently misapplied. 7.1

PARTIALITY IN THE U S E S OF EVIDENCE

If there is one reasoning flaw that is more pervasive and perhaps more insidious than all the others, it is probably our tendency to be biased in our uses of evidence. This tendency has been mentioned several times already, but it bears repeating. It has been known for a long time that wefindit easy to give favored treatment to favored beliefs. Francis Bacon once observed: "What a man had rather were true, that he more readily believes". Wefindit 111

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easier to draw conclusions we strongly like than those we strongly dislike, and we are quite capable of interpreting evidence in accordance with our preferences. That is, we are inclined to attach a great deal of significance to evidence that seems to support a favored belief, whereas we tend to overlook, discount, or distort evidence that is damaging to such a belief. We are not, in a word, objective in our assessment of evidence when that evidence relates to beliefs that are particularly important to us. It should be clear that such partiality can have very serious consequences. Recognizing the problem can help us understand how disputes between intelligent people can sometimes persist for a very long time, each party to the dispute being fully convinced of the indefensibility of the other party's position and of the complete reasonableness of his own. Note that the fallacy of partiality has nothing to do with knowingly and willfully distorting evidence or otherwise treating it in biased ways. On the contrary, the problem is that even with the best of intentions of being objective and unbiased, we find it exceedingly difficult not to be influenced in our reasoning by our preferences and desires. That observation applies as well to people who are trained in the sciences as to those who are not. It is not a moral issue, but rather a question of human cognitive capabilities and limitations. Denying the problem—especially denying that the problem applies to oneself—simply compounds it. While not really an antidote to this particular problem, recognition that each of us is capable of interpreting evidence in a biased way should at least make us somewhat more critical of conclusions that we ourselves draw. In acknowledging the problem, we at least have some chance of working around it. Think

about

it

• Consider what you might do in order to minimize the problem of using evidence in a biased way. 7.2

BIASED INFORMATION GATHERING

The problem of bias in gathering information is closely related to the problem of partiality in the uses of evidence. There are at least two perspectives from which we can gather information that is relevant to some issue or decision that is to be made. One is to gather it impartially, with the intent of assessing objectively the relative merits of the various positions that can be taken. Another is to attempt to support (build a case for) a particular position or to justify a particular decision alternative. Whether or not we accept the idea that the latter is ever appropriate, at the very least, a

7.3

USED OF IRRELEVANT REASONS

113

requirement of rationality is that we be clear about which objective we are pursuing in a particular instance. Unfortunately, we are adept at deceiving ourselves in this regard. We frequently believe ourselves to be gathering information impartially when in fact we are building a case for some conclusion we wish to draw or trying to support a decision that we have already made. There is evidence that the way we seek information and the information we seek are greatly influenced by our attitudes toward the beliefs we are ostensibly evaluating. Thus, if we are assessing the credibility of a favored hypothesis, we are likely to seek information that will support the hypothesis and to avoid information that would tend to disconfirm it. Conversely, if the hypothesis in question is one we prefer not to believe, we are more likely to seek disconfirming information. 7.3

USES OF IRRELEVANT REASONS

When asked to give reasons for a belief we hold, we usually can do it. However, typically, some of the reasons seem to be much more relevant to the belief and thus provide more substantive support for it than do others. Thus, another type of reasoning fallacy involves supporting a belief with irrelevant evidence or with evidence that is only marginally relevant to that belief. While this is an easy fallacy to define, it is not such an easy one to diagnose. The problem is that relevance is largely a subjective concept and a matter of judgment, and there is no satisfactory objective way of defining it. What appears relevant to one individual may appear irrelevant to another. However, this difficulty makes the tendency none the less fallacious, and while we might disagree on what constitutes relevance in a particular case, we can agree on the general principle that irrelevant facts contribute nothing to the plausibility or implausibility of any particular belief. Conversely, one of the characteristics of an effective reasoner is an ability to marshal facts that are highly relevant to an issue. Interpreted broadly, irrelevant reasons include several of the following fallacies as special cases. Each of them seems sufficiently important in its own right, however, to justify focusing on it as a specific problem. Think

about

it

• Define in your own words the concept of relevance. • Consider the idea that relevance is a matter of degree and that it makes more sense to think of facts as being more or less relevant to an issue than to think of them as being either relevant or irrelevant.

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7.4

A R G U M E N T U M AD HOMINEM

The fact that argumentum ad hominem has a Latin name suggests that the fallacy has been recognized for a very long time and is acknowledged to be exceptionally prevalent. It means arguing "to the man"—that is, instead of to the point of the argument. When, for example, we are judging the merits of a position and instead of considering the pros and cons of that position, we attack the credibility of people who hold it, we are arguing ad hominem. Sometimes we may refuse to acknowledge the weight of counterarguments against a position simply because that position is identified with an individual to whom we feel loyal. A child, for example, might refuse to consider the possibility that some strongly held belief of its parents is wrong. Demagogues and charismatic leaders often have such influence over the thinking of their followers that whatever they assert is likely to be accepted uncritically and to be appropriated even in the face of compelling evidence that those assertions are wrong. Argumentum ad hominem is considered a fallacy because the merits of a position are independent of who holds it: the fact that an assertion is made by a disreputable person is not sufficient grounds for considering it false; and conversely, even saints can be wrong. On the other hand, this example illustrates the point that what may be fallacious in one context may be quite acceptable in another: clearly, not all instances of considering personal credibility are instances of erroneous reasoning. For example, when we have the task of deciding whether or not to believe some claim and we have little objective evidence on which to base the decision, we do well to consider the credibility of the source of that claim. Our legal system recognizes the force of that principle, and lawyers go to some lengths to establish or destroy the credibility of witnesses in court proceedings. It is important to remember, however, that the fact that a position is held by a person whose credibility is low does not necessarily make that position wrong; nor is a position necessarily right because it is held by a person whose credibility is high. 7.5

A P P E A L TO A U T H O R I T Y

Appeal to authority is a type of ad hominem argument: you add to the persuasiveness of some position by pointing out that the position is held by someone who is recognized as an authority on the topic. Again, whether or not this should be considered a fallacy depends upon the particular situation. The fact that an authoritative person holds a particular view does not make that view correct. Authorities can be, and often are, wrong; that is clearly demonstrated by the fact that equally authoritative individuals often disagree on specific issues. Nevertheless, the fact that a highly knowledgea-

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ble individual holds a certain belief with respect to his particular area of knowledge should carry some weight. If nothing else, it demonstrates that that belief is not dependent on ignorance of the area, but, on the contrary, can be held by a person with considerable relevant knowledge. However, again, the important point to remember, is that a belief is not necessarily right because it is held by an expert. 7.6

A P P E A L TO INAPPROPRIATE A U T H O R I T Y

For the testimony of an authority to carry much weight, the authority's expertise must derive from knowledge of the domain to which the testimony pertains. Sometimes people attempt to enhance the credibility of a position by pointing out that that position is held by an individual who is recognized as being an expert in an unrelated area. That seems likely to be a genuine fallacy whenever it is encountered. To be sure, we might be willing to assume that, on the average, people who have distinguished themselves in a particular area are also capable of distinguishing themselves in other areas. However, it seems unreasonable to make the assumption that because a person is qualified to speak with some authority in a particular area, perhaps as a result of years of study of that area, that person is qualified to speak with authority on unrelated topics as well. 7.7

CREDIT OR DISCREDIT BY A S S O C I A T I O N

The notion of guilt by association is a familiar one; the same principle can operate either to increase or decrease one's credibility. Thus, if we want to increase the credibility of an individual, we point out that he is a close friend of highly respected people or belongs to certain well-though-of organizations. Conversely, if we want to discredit an individual, we point out that he has nefarious friends and keeps questionable company. The underlying assumption seems to be that people are likely to resemble the company they keep; it is captured by the familiar proverb "Birds of a feather flock together." The fallacy of credit or discredit by association resembles many others inasmuch as it may contain an element of truth. In particular, it may be true that people have more in common with their friends than with people who are not their friends; and it may even be true that both reputable and disreputable people tend to associate with people like themselves. However, two considerations make such a use of association a fallacy. First, even if we ascribe some truth to the birds-of-a-feather adage, it is intended to be a general observation and not to apply to every individual case. It is certainly not true that no reputable people have disreputable friends, or, conversely,

116 7. SOME COMMON REASONING FACILITIES that no disreputable people have reputable friends. Second, disreputable people are not incapable of speaking the truth, nor are reputable people incapable of promoting falsehoods or making mistakes. The principle of establishing credit or discredit by association is also sometimes used in the association of a particular position with some institution or philosophy. Thus, for example, when we respond to an assertion with something like "That idea is part of the United Nations Charter" or "That is exactly the position that Marx takes in the Communist Manifesto" or "That is what Zen Buddhists believe," we may be attempting to support or discredit the assertion by linking it to a philosophy or institution we suppose the listener holds in either high or low regard. Perhaps the simplest and most direct form of this strategy is attaching labels to positions: such and such an assertion is capitalistic or communistic, dictatorial or democratic, fascist or anarchistic, and so on. The strategy is undoubtedly effective in influencing people's beliefs and attitudes. We seem to be both overly sensitive to labels and particularly disinclined to be caught sharing views with institutions or philosophies that we oppose. In general, we are more likely to agree with a specific assertion if the perceived source of that assertion is one we respect than if it is one we do not. Again, the fallacy has its roots in a plausible assumption. We are probably more likely to be in genuine disagreement with the views of institutions or philosophies we oppose than with the views of those we support. However, it is unlikely that any two people (institutions, philosophies) would totally agree or disagree on every issue. Credit or discredit by association becomes a fallacy when it is applied in a blind and uncritical way. Whether or not a particular view is one that is held by a specific individual, institution, or philosophy that we generally support (or oppose) is very meager evidence as to the tenability of that view. In the absence of any other evidence, it may be slightly better than none, but only slightly; and in the presence of other evidence, it should probably count for little, if anything at all. Think

about

it

• Consider the idea that the fallacy of credit or discredit by association does a disservice to the notion of human individuality and devalues the uniqueness of every human being. 7.8

A P P E A L TO

NUMBERS

A common strategy in advertising is to claim that some product is preferred by more people than its competitors, ("Two out of three people polled preferred BrandX"soda to its nearest competitor"). Sometimes the appeal to numbers is combined with appeal to authority, thus the claim that a

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particular product is preferred by people who are well qualified to judge such things; for example, "More doctors recommend Brand X aspirin for headache than any other brand." The objective of such advertisements, of course, is to influence the listener/reader to join the majority and select Brand X too. The force of appeals to numbers, or to popularity, rests on the assumption that large numbers of people, and in particular the majority, cannot be wrong. In fact, evidence that large numbers of people, including majorities, cannot be wrong is virtually nonexistent. There was a time when nearly all rational people who thought about such matters believed the world wasflat,that the sun and moon were approximately equal in size, that bodies moved only in response to some external force, and so on. In spite of some progress in understanding the world, we, too, undoubtedly believe many things that are false. Scientific progress replaces old explanations about how things work with new ones, but the new explanations themselves will eventually give way to ideas that are newer still. There are also many examples of very large collections of people believing something that even in the light of the knowledge of their day must be considered gullible in the extreme. Indeed, history is replete with examples of large masses of people who have followed demagogues and charlatans on perilous escapades, and there is more than one instance of an entire nation following a demented leader to its destruction. In short, while there may be some comfort in numbers, it does not derive from solid evidence that the majority is never, or even seldom, wrong. Moreover, we needn't look to history to know that we can take little comfort in the fact that a particular belief is held by a large number of people. It seems safe to assume that when countries are engaged in disputes, the majority of people on each side typically believe strongly that their country is in the right and the adversary is in the wrong. Trade unions and management have very different views on the same issues, as do members of different political parties and members of different religious groups. We can hardly argue that such differences arise because all the intelligent or reasonable people, or all the people who really understand the issues, are in one group. It is easy to believe, however, that people on both sides of an issue may be less than completely objective in their treatment of information that relates to the matter in dispute. Probably most of us accept fairly uncritically many of the ideas that pervade our culture. Consider the following ideas, which are examples of the kinds of assumptions that most of us accept uncritically because they are widely held: That an annually increasing gross national product is a good thing for the country.

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That a higher standard of living generally makes for greater happiness. That every person who is capable of doing so should get a college education. That meals should be taken three times daily. The fact that such ideas are widely held does not make them wrong, of course; but neither does it make them right. A careful reasoner will consider the supportive evidence for any idea before accepting it, and the number of people who happen to hold that idea will not count greatly one way or the other. Think

about

it

• Try to think of some examples from history of occasions on which large numbers of people have been wrong. 7.9

A P P E A L TO TRADITION

Sometimes things are done the way they are simply because that is the way they have been done in the past. Similarly, sometimes the best reason we can give for holding a belief is that we have always held it. However, the fact that something has been done a certain way in the past is, by itself, an inadequate reason for continuing to do it in that way; nor is the fact that one has previously believed something a good reason for continuing to believe it. Whether something should be done a particular way depends on whether we can think of better ways to do it (whether it should be done at all depends on present needs and not on the needs of the past), and whether we should hold a particular belief depends on the weight of current evidence as to its truth or falsity. As in the case of other reasoning fallacies, the appeal to tradition is not entirely without justification. It becomes a true fallacy when it is used blindly or to excess. While we can argue that valued ways of doing things should not be lightly discarded, their useful purpose in the past is not a good reason either for retaining them in the face of evidence that they are no longer valid or for refusing to consider such evidence. Think

about

it

• Consider the possibility that unreasonable persistence can be an impediment to new ideas and novel approaches to problems. • What are some of the risks involved in dismissing tradition too cavalierly?

7.10

UNCRITICAL A C C E P T A N C E OF SIMPLE EXPLANATIONS

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UNCRITICAL A C C E P T A N C E OF S I M P L E EXPLANATIONS

We seem to have a need for explanations: when we get ill, we want to know what caused the illness; when a friend behaves in a surprising way, we want to know how to account for the unexpected behavior; when we hear a strange sound in our house, we want to know what is causing it. Reference to this need for explanations in a list of reasoning fallacies may seem strange. What could be wrong with wanting to know why? Indeed, in the absence of that desire, we might not have such things as philosophy, religion, and science. Certainly, without it we would not have accumulated the knowledge we now have about the world. The difficulties arise when we permit ourselves to satisfy the need for explanations in an uncritical way. Science may be born of that need; but so is superstition. It is fallacious reasoning when we accept uncritically the first explanation offered, without making any attempt to evaluate carefully the adequacy of that explanation or to compare it with alternatives. Rationality demands that explanations be consistent with known facts. Science demands not only that explanations be consistent with known facts, but also that they be testable (falsifiable) by objective means. In short, it is a fallacy to indulge the desire for explanations in a nondiscriminating way, to behave, in effect, as though any explanation will do. The tendency to accept explanations too quickly assures the violation of rationality. It is a basis not only of misconceptions that many of us entertain daily, but also of the development of superstitions, pseudosciences, and cults. The desire for explanations is sufficiently strong that when they are not provided, we often invent our own. Moreover, the explanations we typically invent are relatively simple ones. We become ill (we tell ourselves) because the food we ate did not agree with us; our friend's strange behavior was the consequence of a quarrel with his boss. We are overly quick to assign causes to effects, and too seldom do we attempt to test the soundness of such explanations. In many cases, no great harm is done because the consequences of invalid explanations are not significant. Sometimes, though, such untested explanations can represent gross injustices to people or can lead to inappropriate actions with unfortunate consequences. The challenge is not to stifle our desire to know why, but to make ourselves aware of the danger of wanting to know why so badly that we are willing to accept an answer for which the evidence is inadequate. We must learn to seek alternative explanations, to appreciate the difference between a hypothesis and a conclusion, and to form the habit of subjecting hypotheses to fair and powerful tests. Think

about

it

• Think of some criteria that a good explanation should satisfy.

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7.11

HASTY CLOSURE

Hasty closure is closely related to the preceding fallacy, and perhaps includes it as a special case. The idea, which seems worth highlighting by listing it separately, is that our beliefs often are stronger than they should be given the evidence on which they are based. The desire for closure on a reasoning problem seems, for example, to foster a willingness to "jump to" a conclusion before there is sufficient evidence to warrant the conclusion. Hasty closure, like other fallacies, has certain redeeming qualities. The desire to reach closure can motivate us to try to solve problems we might otherwise ignore. What is needed here is both a greater sensitivity to the tentative nature of conclusions drawn early in the reasoning process and a willingness to treat those conclusions as hypotheses and conjectures for further testing. A real danger in arriving too quickly at a conclusion and failing to treat that conclusion as a hypothesis for additional scrutiny is that the conclusion will bias subsequent reasoning about the subject. The creator of Sherlock Holmes recognized that problem and gave the inspector a sensitivity to it as well. When Dr. Watson asks Holmes what he makes of a mysterious note that has just arrived, Holmes replies, "I have no data yet. It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts."1 Think

about

it

• How might a clear understanding of the concepts of assumption, hypothesis and conclusion, and of the differences between them, help avoid the fallacy of hasty closure? • Might a greater willingness to recognize explicitly the tentativeness of conclusions that are formed early in a thought process decrease the probability of this type of error? • Several of the fallacies considered above have the feature that by committing the fallacy one saves oneself some mental effort. Such fallacies represent ways of avoiding thinking deeply about an issue. Which of the fallacies do you think are fairly characterized in this way? 7.12

INAPPROPRIATE PERSISTENCE

Having once arrived at a conclusion, we sometimes are overly reluctant to change our minds in the face of compelling evidence that we should do so. 1 Doyle, A.C. Adventures of Sherlock Holmes—A Scandal in Bohemia. In The illustrated Sherlock Holmes Treasury. New York: Avenel Books, 1976.

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INAPPROPRIATE DICHOTOMIZING

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Without denying that beliefs may sometimes be held in spite of evidence of their inappropriateness, it is only fair to acknowledge that the reluctance of people to give up old beliefs readily may serve a useful purpose. Some beliefs, especially those that are particularly important to an individual, are developed over a period of years; it is easy to imagine that there may be good reasons at the foundation of such a belief, also developed over the years, that the holder is unable to recall at will. Unless the legitimate reasons that we have for retaining a belief (even those that cannot be recalled on demand) contributed to the strength of that belief, we would be continual victims of the last argument we had heard. We would constantly jump from one position to another. Thus, the tendency to retain old beliefs, even in the face of some evidence that they may be wrong, may have a generally stabilizing effect on us as individuals and on our view of the world. Clearly, we should not retain beliefs in the face of truly compelling evidence that they are wrong. However, it may be just as well that we require somewhat more evidence before forsaking an old established belief then we would require to toss out one that was recently formed. Whether reluctance to change our minds should be viewed as serving a useful purpose or as a reasoning fallacy probably hinges on the question of degree. Some reluctance seems justified; however, when that reluctance precludes us from applying new information to a familiar question in a reasonable way, it becomes inappropriate persistence. Think

about

it

• Consider how one might have legitimate reasons for holding a particular belief other than those that one can make explicit on demand. 7.13

INAPPROPRIATE DICHOTOMIZING

Probably most descriptions are oversimplifications. That observation applies to descriptions of visual scenes, of social situations, of moral dilemmas, and just about anything we might wish to describe. Moreover, such simplification is probably necessary. Most things are sufficiently complex that to describe them thoroughly and in great detail would overtax the ability and patience of most of us. The failure to recognize descriptions as simplifications, however, can—and assuredly does—lead to reasoning difficulties. A particularly compelling illustration of that fact is our tendency to oversimplify many problems involving choice by presenting them as dichotomous situations in which there are only two alternatives from which to choose.Often a situation is described as an either-or situation when in fact, there may be many intermediate possibilities.

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Dilemmas are particularly interesting cases of problem situations with only two choices because, in a dilemma, both choices are undesirable. A reasonable approach in dealing with an apparent dilemma, therefore, is to askfirstwhether it is truly a dilemma. Are there really only two alternative possibilities? Think a b o u t it

• Think of some choices that have been presented to you as dichotomous choices and that, on reflection, might not really have been dichotomous. 7.14

DRAWING CONTRARY CONCLUSIONS FROM INCONCLUSIVE ARGUMENTS

When a person argues for a position and does it badly, or fails to support the conclusion he wishes us to draw, we are likely to take that as evidence that the conclusion is untrue. That kind of reasoning involves a form of the error of denying the antecedent: if someone can present a convincing argument, the conclusion must be true; A'has presented an argument that is not convincing, therefore the conclusion must be false. The truth or falsity of a conclusion is not determined by the ability of a particular individual to argue effectively for or against it. If someone presents arguments for the purpose of demonstrating the truth of an assertion, but does so ineffectively, the most that can be concluded is that the truth of the assertion has not been demonstrated. It does not follow that the assertion is false. Of course, if we believe that the individual presenting the arguments is knowledgeable about the topic and is doing his best to demonstrate the assertion to be true yet fails to do so, we may legitimately have doubts as to whether the assertion really is true. An important manifestation of this can be found in judicial proceedings in this country, in which an accused person is presumed innocent until proven guilty. If a prosecutor fails to demonstrate the guilt of the accused, the accused is declared innocent. Note that there is no requirement that innocence be proved. It is the default assumption, and the burden of proof is on the accuser. Although we take this system very much for granted, it is extremely important for the safeguarding of human rights and liberties. If the requirement were to prove innocence beyond doubt, the notion of individual rights would be very different. 7.15

C O N F U S I N G N A M I N G WITH E X P L A I N I N G

Names are often invoked as explanations. Why do the planets remain in their orbits? Because of gravity. Why do people fight with each other?

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CONFUSING TEMPORAL SUCCESSION WITH CAUSATION

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Because of aggression. Why does the cost of living seem to rise continually? Because of inflation. It is very easy to find such examples of "explaining" by naming. What actually constitutes an explanation is a controversial question. One view is that in order to explain a phenomenon, we must describe it at a more fundamental or microscopic level. Accordingly, we would explain psychology in terms of biology, biology in terms of chemistry, chemistry in terms of physics, and so on. The view has its opponents. Whatever we think about the nature of explanation, few people would be willing to accept a definition that included naming. Naming does nothing more than attach a label to the phenomenon to be explained and beg the question, perhaps rephrased. What is gravity? Why are people aggressive? What is the cause of inflation? Think

about

it

• Think of several more examples of "explaining" by naming. 7.16

C O N F U S I N G T E M P O R A L S U C C E S S I O N WITH CAUSATION

A very easy confusion—and one that probably most of us make—is the confusion between cause and temporal succession. If B invariably follows A, it seems natural for us to assume that B is caused by A but the fact that consistent temporal succession is not a reliable indication of a cause-effect relationship is readily demonstrated by counterexamples. Night invariably follows day; however, we would not say that day causes night. If we were to equate cause with invariable temporal succession, then we would say that day causes night; but for the sake of consistency, we would also be obliged, of course, to say that night causes day, inasmuch as the temporal succession applies in this case as well. Inferring from the fact that B follows A that B is caused by A is another of the reasoning fallacies that has been recognized for a sufficiently long time to have been given a Latin name. In this case, the name is post hoc ergo propter hoc, which means "after this, therefore because of this." There is an important asymmetry about temporal succession that has relevance for reasoning about cause-effect relationships. The statements "B is always preceded by A" and "A is always followed by B" are not equivalent statements. While neither of these statements implies a cause-effect relationship between A and B, both are suggestive of such a relationship, because cause-effect relationships lead us to expect these types of sequential dependencies. In particular, if A is a necessary cause of B, we expect it to be the case that B is always preceded by A ; and if A is a sufficient cause of B, we expect tofindthat A is always followed by B. Finally, if A is a necessary and sufficient cause of B, we expect both relationships to hold.

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Think a b o u t it

• Think of reasons why A might always be followed by B, or B might always be preceded by A, other than A being the cause of B. 7.17

C O N F U S I N G S H A R E D CHARACTERISTICS WITH DISTINGUISHING CHARACTERISTICS

Sometimes it is useful to be able to identify the members of a class by their characteristics. The distinction between shared characteristics and distinguishing characteristics is important in this regard. In identifying the characteristics that distinguish members of a class from nonmembers of that class, it is not sufficient to determine what characteristics the class members have in common. Rather, the task is to determine the characteristics that the members of the class have in common with each other, but do not share with nonmembers of the class. Failure to make that distinction can be the basis of inappropriate stereotyping. When we notice, for example, that most Swedes of our acquaintance have blonde hair and blue eyes, we are noticing a characteristic that is (presumably) common to many Swedes. If we then use that characteristic as a basis for classifying people's ethnic origins, and conclude that new acquaintances with blonde hair and blue eyes must be Swedes, we are committing the error of confusing common characteristics with distinguishing characteristics. We have failed to recognize the fact that there are many people with blonde hair and blue eyes who are not Swedes and that therefore the blonde-hair blue-eye characteristic does not reliably distinguish Swedes from people of other nationalities. To take a perhaps more serious example of the same error, suppose several people, all of whom have committed one or more acts of violence, are found to have a similar type of chromosomal abnormality. Now, suppose that all people who have that abnormality are classified as violence prone. Such a step would not be justified. In order to use the chromosomal abnormality as a basis for making that type of classification, it would be necessary to demonstrate not only that people who are prone to violence have the abnormality, but also that people who are not prone to violence do not have it. 7.18

C O N F U S I N G T R U T H WITH VALIDITY

As we have noted several times already, the validity of a logical argument is independent of the truth or falsity of the assertions that comprise it. The following argument is perfectly valid, although the conclusion and both premises are false.

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"PROOF" BY A N A L O G Y

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All spiders are quadrupeds. All quadrupeds are ungulates. Therefore all spiders are ungulates. Validity has to do strictly with the form of a logical argument. If the form obeys the rules of logic, the argument is valid. If it violates those rules, it is invalid. Unfortunately, the evidence is quite compelling that our judgments of the validity or invalidity of an argument are often strongly influenced by our beliefs regarding the truth or falsity of the premises or conclusion. In particular, if we believe the premises and conclusion to be true, we are more likely to consider the argument to be valid than if we believe the premises or conclusion to be false. Of course, in everyday life we may be less interested in whether or not the form of an argument is valid than in whether the conclusion that is drawn is, in fact, true. However, for purposes of effective reasoning, it is important that the distinction between validity and truth be clear. Sometimes in trying to understand another person's point of view, it may be necessary to recognize that he is operating on a different set of assumptions. In such a case, it is useful to ask ourselves, given those assumptions, what we are led to conclude. Thus, we are obliged to focus on logical validity because we want to know what follows from assumptions, even though we may be unwilling to accept those assumptions as true. A confusion between logical validity and empirical truth can contribute to fallacious reasoning in a variety of ways. When we criticize a correctly structured argument as being invalid simply because it contains an untrue premise, our criticism is not correct. We might, of course, question the truth of the premise (and therefore of the conclusion), but that has nothing to do with the argument's validity. Conversely, when we accept an argument as valid simply because its conclusion is considered true, we are also reasoning fallaciously. Note that this type of error may be transparent. Suppose an argument is valid and that its premises and, therefore, its conclusion are true. It is quite possible for us to accept such an argument as valid, but to do so not as a consequence of having verified that the argument's structure is formally correct, but because it has produced a true conclusion. In that case, we have made the right judgment about the validity of the argument, but have done so for the wrong reason. It is an example of fallacious reasoning producing a correct result—and we should note that the same reasoning applied in another situation might well produce an incorrect result. 7.19

" P R O O F " BY A N A L O G Y

Analogies are useful devices for instructional purposes. A common way of misusing them, however, is for the purpose of "proving" a point. For

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example: A computer is like a brain; a brain thinks, therefore, a computer thinks. Every analogy involves a limited likeness between two things. The two analogs are alike in some ways and different in others. When we state that two things are alike with respect to properties A, B, and C, we are doing nothing more than calling attention to the aspects of their similarity. Knowing that two things are alike with respect to A, B, and C provides no basis, however, for concluding that they must also be alike with respect to D. If it is already known that they are alike with respect to D, then it is not necessary to use the analogy to prove that point. If it is not already known, then the analogy does not constitute proof of the likeness. Thus, when we say that because X is analogous to y with respect to properties A, B, and C, it must also have property D because Y has it, we are using the analogy inappropriately. Xmay indeed have property D, but the fact that Y has it is not proof that it does, even though X and Y are known to be analogous in several other ways. Think

about

it

• Try to construct an argument that involves using an analogy to prove an assertion, and then evaluate the argument. • Think of some analogies that you have heard in the context of arguments and note their limitations. 7.20

OVERGENERALIZATION

A common reasoning fallacy that is encountered in everyday life is that of overgeneralization, or what might be called the problem of imputing to a class the characteristics of one or a few of its members. When we conclude, for example, that all used-car dealers are untrustworthy because we have had an unpleasant experience with a used-car dealer, or when on the basis of an acquaintance with a couple of New Englanders, we impute certain traits to New Englanders as a group, we are guilty of overgeneralization. We should note that generalization per se is not evidence of deficient thinking. Indeed, the ability to generalize is an extremely important one; without it, we would be severely handicapped intellectually. The issue is one of degree, and the danger is that of generalizing on the basis of too meager a sample, or of carrying a generalization to the extreme of failing to recognize the possibility of exceptions to the rule. Think

about

it

• Imagine that you overheard the following conversation: A: I would not trust Tom. B: Why not? A: Because he is a Blankian.

7.21

B: A: B: A:

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What does that have to do with anything? Blankians are not trustworthy. Why do you say that? Because I know several of them and every one I know is dishonest.

What do you think of A's reasoning? • Think of examples of overgeneralization that you have encountered in your personal experience. 7.21

STEREOTYPING

We think in terms of conceptual categories. If we did not, thinking would be very much less efficient than it is. Indeed, it is questionable whether we could think in any meaningful sense at all without the use of categories. Try to imagine what it would be like to get along without the concept chair. Each of those things that we now refer to as a chair we would have to treat as a unique entity, rather than as a member of a class. We would have to refer to each individual chair in terms of its own set of characteristics. Thus, we might refer to the thing to the left of the door in the foyer that has four wooden legs, a wooden back, an upholstered seat, and so on. Note that in that description, however, although the concept chair is not being used, other conceptual categories (e.g., thing, leg, back, seat) are. It is clearly impossible to communicate without making use of conceptual categories. Perhaps it is impossible to think without doing so as well. Stereotyping is an example of categorizing being carried to an extreme. We stereotype an individual when we label the individual as a member of some class and then impute to that individual all the properties of that class. It is easy to find examples of such stereotyping. The case of young male automobile drivers will illustrate the point. In the United States, male automobile drivers under 25 years of age are involved in more accidents per driven mile than are drivers over 25 years of age. On the average, therefore, they are a greater insurance risk than older drivers, and this fact is reflected in automobile insurance rates. It is not true, however, that all young male drivers are more accident prone than all older drivers, and when we impute to any young male driver the quality of accident proneness simply by virtue of the fact that he is young, we are stereotyping. Think a b o u t it

• The list of reasoning fallacies that has been considered in this chapter is far from exhaustive. Think of other types of reasoning fallacies that you have encountered in your own experience.

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SUMMARY

We have considered a number of ways in which reasoning can go astray. They are not the only ways, and the careful observer will find it easy to extend the list. It is unlikely that any of us will altogether avoid problems such as those we have considered, but being aware of them should make us more effective monitors of our own reasoning processes. Developing a critical attitude toward our own reasoning is an important aspect of improving our reasoning ability; effective reasoners are their own most severe critics.

8

Conclusion

Thefirstrequirement for reasoning well is desiring to do so. Reasoning can be hard work. It is much easier to "play hunches" and to "follow one's intuitions" than to think through the consequences of various actions we might be considering. It is easier to assume that people who disagree with us on controversial issues are wrong, than to attempt to see things from their points of view. It takes less energy to guess at the answer to a complicated inferential problem than to work out the implications of the information in hand. Not only can reasoning be difficult, intentionally improving our reasoning ability can be a demanding task as well. The assumption is made here that we can improve our reasoning ability if we are willing to make the effort to do so. That means learning about reasoning and, in particular, about ways in which people commonly reason fallaciously or suboptimally. it means critically monitoring our own reasoning and becoming sensitized to our own specific strengths and weaknesses. It means learning how to use the various tools and procedures that have been invented for the purpose of facilitating reasoning. There is no simple prescription that will guarantee rationality. The presentation here of some "rules" for reasoning should not be taken as inconsistent with that claim. These rules are offered as suggestions only. They are not, even taken collectively, a blueprint for effective reasoning in general; some of them could, however, prove to be useful advice on particular issues. 129

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CONCLUSION

8.1

SOME RULES

Use Language Carefully

Be sure you understand the terms in any argument that you are attempting to evaluate. When involved in a dispute, check to be sure that you and your opponent(s) are giving the same meanings to the words that you use. That is not as straightforward as it sounds, because all of us use many words every day that we wouldfindit difficult to define very precisely. That is not to say that we use the words improperly—although undoubtedly we sometimes do—but simply to acknowledge that many words, as used in everyday speech, do not have very precise meanings in the minds of their users. It becomes doubly important, therefore, to be careful in the use of words when evaluating arguments, and it is never inappropriate to ask what someone means by a specified word in a particular context. Cultivate the Skill of Seeing Things From Other People's Points of V i e w

The ability to see something from another person's viewpoint is not easy, but it is an extraordinarily useful skill to have. Bear in mind that it is likely to be most difficult precisely when it is most important to do so, namely, when the other person's viewpoint differs most drastically from your own. Beware of Drawing Hasty Conclusions

It is remarkably easy to overlook facts relevant to the drawing of a conclusion. One danger in reaching a conclusion prematurely is that of considering the matter "closed" and of consequently closing your mind to additional relevant facts. Do not be afraid to suspend judgment on an issue until you have sufficient information to make a rational decision. In view of the evidence that information-seeking behavior becomes more selective and biased after a public commitment has been made to a given position, be particularly careful to avoid making a commitment until you have sufficient information to justify doing so. When forced by circumstances to take a position on less than adequate information, recognize the tentativeness of the position and be ready to change it, should further information indicate the reasonableness of doing so. Be S u s p i c i o u s of S l o g a n s in the Form of S w e e p i n g Generalizations

Slogans or maxims are powerful because they express ideas in graphic and memorable terms. They can be dangerous, however, inasmuch as they

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SOME RULES

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usually have a limited domain of applicability. That fact is often ignored in their use. Slogans are intended to express some commonsense or widely acknowledged truth in a terse way. The "truth" that is expressed typically appears to be an intuitively compelling bit of folk wisdom. The limited applicability of such truths is illustrated by the fact that, for most familiar slogans, you can find another one equally familiar and equally compelling and with precisely the opposite meaning. Be Particularly S u s p i c i o u s of Beliefs Y o u Want to Hold

Recognize that most of us are willing to hold a favored belief on the strength of evidence that we would consider inconclusive, or possibly even irrelevant, if the belief were one that we preferred not to hold. Remind yourself that objectivity is very difficult to maintain when you have a vested interest in a particular conclusion or position, and ask yourself whether you are really being objective in your evaluation of arguments, especially those that you yourself construct. Be W i l l i n g to Reevaluate Old Beliefs

It is especially important to be willing to reconsider the plausibility of old beliefs in the light of new information. Remember that no plausible arguments are ever really complete. New information often provides a good and adequate reason for reassessing old conclusions and positions. Sometimes, even when there is no new information available, réévaluation is appropriate because sometimes when we think deeply about a belief, we may discover that we had insufficient justification for holding it in the first place. Learn to Use T o o l s That Can Facilitate Reasoning

Useful tools for reasoning include diagrams, truth tables, symbolic logic, decision trees, and so on. None of them will guarantee effective reasoning, but they can be very helpful nevertheless. As is true of most tools, learning to use reasoning tools well requires considerable practice. It is not enough to know about them. It is important to get the feel of them, and one does this only by using them often. Develop the Skill of Using Counterexamples and Co u n te ra rg u m ents

Before accepting a generalization, try hard to think of a counterexample that disproves it. Before accepting a plausible argument, try to construct a plausible counterargument. Remember that the inability to think of a

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counterexample or to construct a counterargument does not prove the original generalization or the key assertion of the plausible argument to be true. If you are knowledgeable about the subject, however, and are unable to produce a counterexample or counterargument, your confidence in the generalization or the plausible argument should be increased. R e c o g n i z e That There is N o S u b s t i t u t e for K n o w l e d g e

If you want to reason effectively about some subject, you must know something about that subject, and, in general, the more you know about it, the more effectively you can reason about it. The first rule of effective reasoning is to get your facts straight, so learn what you can about the subject at hand. That is not to say that there is nothing more to reasoning than knowing a lot, but other things being equal, people who know a lot will be in a much better position to reason effectively than those who do not. R e c o g n i z e a n d A c c e p t Y o u r O w n Fallibility

There are perhaps no more serious impediments to effective reasoning than an unwillingness to admit that you are wrong and an inability to change your views on an issue in the light of evidence that those views should be changed. You must be able to maintain a sense of proportion, to see the humor in your own reasoning fallibilities, and to learn from your mistakes. It is no disgrace to be wrong sometimes and it is a sign of intellectual maturity to be able to admit it gracefully. 8.2

SUMMARY

The ability to reason well is immensely important. It is an ability that can be improved, but only through serious effort. It is not a matter of simply following a set of rules, although suggestions like the preceding have value and can be helpful to some degree. Learning to reason well is a life-long process. It requires a deep commitment to truth, a willingness to examine evidence impartially wherever it may lead, a recognition that one's reasoning skills are always subject to improvement, and an abiding desire to improve them.

Appendix A Answer Key

Table 1. 1. O 2. O 3. B 4. O 5. B

6. 7. 8. 9. 10.

O B O B B

Answers to Table 2 Questions 1. The sun is larger than the moon. True. The sun's diameter (864,000 miles) is about four hundred times as great as the moon's, and it weighs approximately 27 million times as much. In general, the farther away from us an object is, the smaller it looks. The distance between the earth and the sun is just sufficiently greater than the distance between the earth and the moon to make the sun and the moon appear to be equal in size when viewed from the earth. 2. The population of Spain is larger than the population of Italy. False. As of 1982, the population of Spain, which was about 38 million, was only about two-thirds as great as the population of Italy, which was about 57 million. Spain, with an area of about 195,000 square miles, is larger in size, however, than Italy, with its area of about 116,000 square miles. 3. Bananas are a good source of protein. False. Bananas are not a good source of protein. A medium-sized banana, which would weigh about 150 grams, contains only about one gram of protein. By contrast, 150 133

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7.

8. 9. 10. 11.

12. 13. 14.

APPENDIX A

grams of peanuts contain about 39 grams of protein. Bananas are a good source of potassium, which is one of several minerals the body needs in small quantities. Caracas is the capital of Venezuela. True. Caracas is not only the capital of Venezuela, but also its largest city, with an estimated population of over 3 million people. Turtles lay eggs. True. Turtles do lay eggs, usually burying them in sand. Unlike birds, however, mother turtles do not guard their nests, nor do they feed their young. They abandon the eggs as soon as they have buried them. The Suez Canal is in Asia. False. The Suez Canal is in Africa; more specifically, in Egypt. The canal, which is about a hundred miles long, connects the Mediterranean Sea with the Red Sea. Work on the canal was begun in 1859 and finished about 10 years later. The canal has been a major gateway facilitating trade between Europe, Africa, and Asia. Many cities are located near rivers. True. A primary problem of any large city is that of obtaining enough water for its inhabitants and its industry. Many of the world's greatest cities have been built along the banks of major rivers, for example: London, on the Thames; Paris, on the Seine; Bonn, on the Rhine; Rome, on the Tiber; Belgrade, on the Danube; São Paulo (Brazil) on the Tiete; Moscow, on the Volga; Cairo, on the Nile; New Delhi, on the Ganges. If the following statement is true, "this man" is me: Brothers and sisters have I none, but this man's father is my father's son. False. "This man" is my son. All species of birds can fly. False. Most birds can fly, but some cannot —for example, ostriches, emus, kiwis, and penguins. Peru is larger in land area than Brazil. False. Peru is less than one-sixth the size of Brazil; whereas Peru has about 496,000 square miles, Brazil has about 3,286,000 square miles. The longest river in the world is the Amazon. False. The Nile River in Egypt, which measures 4,145 miles, is the longest in the world. It is only slightly longer than the Amazon, however, which is about 4,000 miles long. The Mississippi River, which is the longest in North America, measures 3,710 miles. The earth is the fourth closest planet to the sun in the solar system. False. The earth is the third closest planet to the sun. Mars is the fourth closest. The largest bird with an ability to fly is the albatross. True. An albatross can attain a wing span of 11 to 12 feet and a weight of about 30 pounds. Wombats are marsupials. True. A marsupial is a type of mammal whose offspring are very tiny and not well developed at birth. A new-

ANSWER KEY

15. 16.

17. 18.

19.

20.

21.

22.

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born marsupial is so delicate that it must be carried in its mother's protective pouch for several months following birth. Other examples of the marsupial order are kangaroos and opossums. Infants have more bones than adults. True. A newborn baby has 300 bones; whereas an adult has 206. As a child grows, some of its bones fuse so that two or three become one. Mt. Everest in Asia is the tallest mountain in the world. True. The highest point on Mt. Everest is just over 29,000 feet, or about five and a half miles, above sea level. Mt. Everest is part of the Himalayan Mountain Range and is located on the border between Tibet and Nepal. Although many people have tried to climb to its top, very few have succeeded. The first person to do so was Sir Edmund Hillary, who accomplished the feat in 1953. Water boils at a higher temperature on a mountaintop than at sea level. False. The lower the air pressure, the lower the temperature at which water will boil. Since air pressure decreases as altitude increases, the temperature at which water will boil decreases as you go higher. There is more nitrogen than oxygen in the earth's atmosphere. True. The two major components of the earth's atmosphere are nitrogen, which makes up approximately 78 percent of the atmosphere, and oxygen, which makes up approximately 21 percent of it. No other component makes up as much as 1 percent. The scientist who is remembered as having first described the law of gravitation is Sir Isaac Newton. True. One of the greatest scientists of all time, Newton, an Englishman, lived during the 17th century. He is remembered for discovering the laws of motion and the law of gravitation, and for inventing the calculus. The liver is the largest gland in the body. True. The liver is not only the largest gland in the body, it is the largest organ, and it has the greatest number of functions. Moreover, the liver is absolutely essential to life; you cannot survive without one. The liver is remarkably able to function even when damaged, however, and is often capable of repairing itself and regaining its full capacity after injury. Viruses are larger than bacteria. False. Viruses are much smaller than bacteria. In fact, they are the smallest known form of life. Bacteria themselves are very, very small—several million of them would fit on a human thumbnail—but a virus is so much smaller than a bacterium that if the bacterium were as large as a person, the virus would be only about as large as that person's thumb. Viruses infect bacteria, just as both viruses and bacteria can infect larger forms of life, including human beings. Chess is one of the oldest games known. True. Chess is indeed one of the oldest games in the world. No one really knows when and by whom

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APPENDIX A

it was invented, but one hypothesis is that it originated in India. It has been a very popular game all over the world for many centuries. 23. The printing press was invented by a man named Switzer. False. Type for printing was probably invented in China; however, invention of the printing press as we know it is credited to Johann Gutenberg, who is believed to have produced the first book (traditionally said to be the Mazarin Bible) printed from movable type in Europe, by 1456. Before the development of the printing press, few people knew how to read, and there was little point in learning, inasmuch as reading material, which had to be produced by hand, was not readily accessible. 24. Franklin Pierce was the 21st President of the United States. False. Pierce was the 14th President of the United States, in office from 1853 to 1857. The 21st President was Chester Alan Arthur, who served from 1881 to 1885. 25. The flag of Sweden is yellow and blue. True. It is a yellow cross on a blue field.