The logic of science is the logic of business and of life.
—John Stuart Mill
In an earlier era, when many people were involved in surveying land, it made sense to require that almost every student entering a top college know something of trigonometry. Today, a basic grounding in probability, statistics and decision analysis makes far more sense.
—Lawrence Summers, former president of Harvard University
The word “cosine” never ever comes up.
—Roz Chast, Secrets of Adulthood
You paid twelve dollars for a ticket to a movie that, you realize after a half an hour of watching it, is quite uninteresting and tedious. Should you stay at the theater or leave?
You own two stocks, one of which has done quite well over the past few years and the other of which has actually lost a little since you bought it. You need some money and have to sell one of the stocks. Do you sell the successful stock in order to avoid locking in your losses on the unsuccessful stock, or do you sell the unsuccessful stock in hopes that the successful one will continue to make more money?
You must choose between two candidates for a job. Candidate A has more experience and stronger recommendations than candidate B, but in the interview candidate B seems brighter and more energetic than candidate A. Which do you hire?
You are a human relations officer for a company. Several women have written you to complain that their job applications were turned down in favor of men with poorer job qualifications. How could you go about finding whether there is really discrimination on the basis of gender?
Time magazine recently reported that parents should not try to control their children’s food intake because parents who do that have children who are likely to be overweight. Do you see anything dubious about that claim?
People who have a drink or two of alcohol once a day have fewer cardiovascular problems than people who don’t. Assuming you drink less than that, should you increase your alcohol intake? Should you decrease it if you drink more than that?
Problems like those above don’t appear on IQ tests, but there are smarter and less smart ways of solving them. By the time you’ve finished this book, you’ll have a cognitive tool kit that will allow you to think about such problems—and infinitely more besides—much differently than you would now. The tools are one hundred or so concepts, principles, and rules of inference developed by scientists in many fields—especially psychology and economics—and by statisticians, logicians, and philosophers. Sometimes commonsense approaches to problems produce errors in judgment and unfortunate actions. The concepts in this book will show you how to think and act more effectively. The ideas provide a supplement to common sense—rules and principles you can learn to apply automatically and effortlessly to countless problems that crop up in everyday life.
This book addresses some of the most fundamental questions about how to reason and make valid inferences. What counts as an explanation (for everything from why our friend acts in such an annoying way to why a product launch failed)? How can we tell the difference between events that are causally related and events that are merely associated with each other in time or place? What kinds of knowledge can be considered certain and what kinds only conjectural? What are the characteristics of a good theory—in science and in everyday life? How can we tell the difference between theories that can be falsified and those that can’t? If we have a theory about what kinds of business or professional practices are effective, how can we test that theory in a convincing way?
The media bombard us with alleged scientific findings, many of which are simply wrong. How can we evaluate conflicting scientific claims we encounter in the media? When should we trust the experts—assuming we can find them—and when should we be dubious?
And most important, how can we increase the likelihood that the choices we make will best serve our purposes and improve the lives of ourselves and others?
Can Reasoning Really Be Taught?
But can people actually be taught to think more effectively? Not just to know more things, such as the capital of Uzbekistan or the procedure for extracting square roots, but actually to reason more correctly and solve personal and professional problems more satisfactorily.
The answer to this question is far from obvious, though for twenty-six hundred years many philosophers and educators were confident that reasoning could be taught. Plato said, “Even the dull, if they have had arithmetical training,… always become much quicker than they would otherwise have been … We must endeavor to persuade those who are to be the principal men of our state to go and learn arithmetic.” Later, Roman philosophers added studying grammar and exercising the memory to the practices that would improve reasoning. The medieval scholastics emphasized logic, particularly syllogisms (e.g., All men are mortal. Socrates is a man, therefore Socrates is mortal). The humanists of the Renaissance added Latin and Greek, possibly because they thought that using those languages contributed to the success of these ancient civilizations.
The faith in drilling mathematical, logical, and linguistic rules was strong enough that by the nineteenth century some people believed that pure exercise of the brain on difficult rule systems—any difficult rule system—was enough to make people smarter. A nineteenth-century educator was able to maintain, “My claim for Latin, as an Englishman and a teacher, is simply that it would be impossible to devise for English boys a better teaching instrument. The acquisition of a language is educationally of no importance; what is important is the process of acquiring it. The one great merit of Latin as a teaching instrument is its tremendous difficulty.”
There never was a shred of evidence for any of these educational views—from those of Plato to those of the fusty old Latin teacher. So psychologists in the early twentieth century set out to produce some scientific evidence about reasoning and how to improve it.
The early returns were not good for what had come to be called “formal discipline”—training in how to think as opposed to what to know. At the turn of the century, Edward Thorndike maintained that no amount of brain exercise or drilling in abstract rules of thought would serve to make people smarter and pronounced the “learning Latin” theory of education to be defunct. He claimed that his experiments showed that “transfer of training” from one cognitive task to another occurred only if the problems were extremely similar in their concrete features. But the tasks that Thorndike studied didn’t really qualify as ones involving reasoning: for example, he found that practicing cancellation of letters in a sentence produced no increase in speed of canceling parts of speech in a paragraph. This is scarcely what you would think of as reasoning.
Herbert Simon and Allen Newell, the great midcentury computer scientists, also claimed that people couldn’t learn abstract rules for reasoning and provided somewhat better evidence. But their argument was based on very limited observations. Learning how to solve the Towers of Hanoi problem (transferring a stack of disks from one pole to another without ever placing a bigger disk on a smaller one, a game you may have played as a child) didn’t produce improvement on the Missionaries and Cannibals problem, which requires a plan for getting missionaries across a river without ever allowing the missionaries on the boat to be outnumbered by the cannibals. The two problems have the same formal structure, but there was no transfer of training on how to solve one problem to ability to solve the other. This result was interesting, but scarcely enough to convince us that training on a given problem could never generalize to solving a problem with a similar structure.
Jean Piaget, the great Swiss cognitive psychologist who studied children’s learning, was an exception to the mid-twentieth-century consensus against abstract rules for reasoning. He believed that people did indeed possess such rules, including logical rules and “schemas” for understanding concepts such as probability. But he believed such rules couldn’t be taught; rather, they could only be induced as the child encounters more and more problems that can be solved using a particular rule that she discovers for herself. Moreover, the set of abstract rules for understanding the world is complete by adolescence, and every cognitively normal person ends up with the exact same set of rules.
Piaget got it right about the existence of abstract concepts and rule systems that people could apply in everyday life but got everything else wrong. Such rule systems can be taught as well as induced—we keep on learning them well beyond adolescence—and people differ dramatically in the particular set of abstract rules for reasoning that they use.
The early twentieth-century psychologists opposed to the concept of formal discipline were right about one very important matter: getting smarter is not a matter of sheer exercise of the brain. The mind is like a muscle in some ways but not in others. Lifting pretty much anything will make you stronger. But thinking about just anything in any old way is not likely to make you smarter. Learning Latin almost certainly produces little gain in reasoning ability. The nature of the concepts and rules you’re trying to learn is everything when it comes to building the muscles of the mind. Some are useless for building brain muscles and some are priceless.
Ideas That Travel
The idea for this book came from my fascination with the fact that scientists’ ideas in one field can be extremely valuable for other fields. A favorite buzzword in academia is “interdisciplinary.” I’m pretty sure that some people who use the word might not be able to tell you why interdisciplinary research is a good idea. But it is, and here’s why.
Science is often described as a “seamless web.” What’s meant by that is that the facts, methods, theories, and rules of inference discovered in one field can be helpful for other fields. And philosophy and logic can affect reasoning in literally every field of science.
Field theory in physics gave rise to field theory in psychology. Particle physicists use statistics developed for psychologists. Scientists studying agricultural practice invented statistical tools that are crucial for behavioral scientists. Theories developed by psychologists to describe how rats learn to run mazes guided computer scientists in their effort to teach machines how to learn.
Darwin’s theory of natural selection owes a great deal to eighteenth-century Scottish philosophers’ theories about social systems, in particular Adam Smith’s theory that societal wealth is created by rational actors pursuing their own selfish interests.1
Economists are now making major contributions to the understanding of human intelligence and self-control. Economists’ views about how people make choices were transformed by cognitive psychologists, and economists’ scientific tools were greatly expanded by adopting the experimental techniques used by social psychologists.
Modern sociologists owe a great deal to eighteenth- and nineteenth-century philosophers who theorized about the nature of society. Cognitive psychologists and social psychologists are broadening the range of questions raised by philosophers and have begun to propose answers to some long-standing philosophical conundrums. Philosophical questions about ethics and theory of knowledge guide the research of psychologists and economists. Neuroscience research and concepts are transforming psychology, economics, and even philosophy.
A few examples from my own research will show how extensive the borrowing can be from one field of science to another.
I was trained as a social psychologist, but most of my early research dealt with feeding behavior and obesity. When I began the work, the lay assumption, as well as the scientific and medical view, was that people who are overweight get that way by eating too much. But eventually it became clear that most overweight people were actually hungry. Psychologists studying obesity borrowed from biology the homeostatic concept of a “set point.” The body attempts to maintain a set point for temperature, for example. The obese have a set point for the ratio of fat to other tissue that differs from that of normal-weight people. But social norms drive them toward being thin, with the result that they’re chronically hungry.2
The next problem I studied was how people understand the causes of the behavior of other people and themselves. Field theory in physics prompted research showing that situational and contextual factors are often more important in producing behavior than personal dispositions such as traits, abilities, and preferences. This conceptualization made it easy to see that our causal explanations for behavior—our own, other people’s, and even that of objects—tend to slight situational factors while overemphasizing dispositional factors.
In studying causal attributions it became clear to me that much of the time we have very limited insight into the causes of our own behavior; and we have no direct access at all to our thought processes. This work on self-awareness owes a great deal to Michael Polanyi, a chemist turned philosopher of science.3 He argued that much of our knowledge, even about matters we deal with in our field of expertise—perhaps especially about such matters—is “tacit” and difficult or impossible to articulate. Work by me and others on the vagaries of introspection called into question all research that depends on self-reports about mental processes and the causes of one’s own behavior. Measurement techniques in psychology and throughout the behavioral and social sciences have changed as a result of this work. The research has also convinced some students of the law that self-reports about motives and goals can be highly unreliable—not for reasons of self-enhancement or self-protection, but because so much of mental life is inaccessible.
The errors discovered in self-reports led me to a concern with the accuracy of our inferences in everyday life in general. Following the cognitive psychologists Amos Tversky and Daniel Kahneman, I compared people’s reasoning to scientific, statistical, and logical standards and found large classes of judgments to be systematically mistaken. Inferences frequently violate principles of statistics, economics, logic, and basic scientific methodology. Work by psychologists on these questions has influenced philosophers, economists, and policy makers.
Finally, I’ve done research showing that East Asians and Westerners sometimes make inferences about the world in fundamentally different ways. This research was guided by the ideas of philosophers, historians, and anthropologists. I became convinced that Eastern habits of thought, which have been called dialectical, provide powerful tools for thinking that can benefit Westerners as much as they have helped Easterners for thousands of years.4
Scientific and Philosophical Thinking Can Be Taught in Ways That Affect Reasoning in Everyday Life
My research on reasoning has had big effects on my reasoning in everyday life. I am constantly discovering that many of the concepts that travel across scientific fields are also affecting my approach to professional and personal problems. At the same time, I am constantly being made aware of my failures to use the kinds of reasoning tools I study and teach.
Naturally I began to wonder whether other people’s thinking about everyday life events are affected by training in concepts learned in school. Initially I was quite dubious that a course or two dealing with one or another approach to reasoning could have the kind of impact on people that long exposure to the concepts had on me. The twentieth-century skepticism about the possibility of teaching reasoning continued to influence my thinking.
I could not have been more mistaken. It turns out that the courses people take in college really do affect inferences about the world—often very markedly. Rules of logic, statistical principles such as the law of large numbers and regression to the mean, principles of scientific methodology such as how to establish control groups when making assertions about cause and effect, classical economic principles, and decision theory concepts all influence the way people think about problems that crop up in everyday life.5 They affect how people reason about athletic events, what procedures they think are best for going about the process of hiring someone, and even their approach to such minor questions as whether they should finish a meal that isn’t very tasty.
Since some university courses greatly improve people’s reasoning about everyday life events, I decided to see whether I could teach such concepts in the laboratory.6 My coworkers and I developed techniques for teaching inferential rules that are helpful for reasoning about common personal and professional problems. As it turned out, people readily learned from these brief sessions. Teaching about the statistical concept of the law of large numbers affected their reasoning about how much evidence is needed to reach accurate beliefs about some object or person. Teaching about the economic principle of avoiding opportunity costs affected how they reasoned about time usage. Most impressively, we sometimes questioned subjects weeks later, in contexts where they didn’t know they were being studied, such as telephone polls allegedly being conducted by survey researchers. We were delighted to find that people often retained substantial ability to apply the concepts to ordinary problems outside the laboratory context in which the concepts had been taught.
Most important, we discovered how to greatly extend the reach of inferential rules to problems of everyday life. We can have complete command over good principles for reasoning in a particular field and yet be unable to apply them to the full panoply of problems that we encounter in everyday life. But these inferential principles can be made more accessible and usable. The key is learning how to frame events in such a way that the relevance of the principles to the solutions of particular problems is made clear, and learning how to code events in such a way that the principles can actually be applied to the events. We don’t normally think of forming impressions of an individual’s personality as a statistical process consisting of sampling a population of events, but they are exactly that. And framing them in that way makes us both more cautious about some kinds of personality ascriptions and better able to predict the individual’s behavior in the future.
There were several criteria that guided me in selecting particular concepts to write about.
1. The concept had to be important—for science and for life. There are scores of syllogisms that have been around since the Middle Ages, but only a few have even the remotest relevance to everyday life, and it’s those that are in the book. There are hundreds of types of fallacious reasoning that have been identified, but only a relative few are mistakes that intelligent people actually make with any frequency. It’s those few that I deal with.
2. The concept had to be teachable—in my opinion, at least. I know for a fact that many of the concepts are teachable in such a way that they can be used in scientific and professional pursuits and in everyday life. This is true of many concepts that university courses teach, and I have successfully taught many of those as well as many others in brief laboratory sessions. The remainder of the concepts are similar enough to the ones I know to be teachable that I include them in the book.
3. Most of the concepts form the core of systems of thought. For example, all of the concepts taught in the crucial first-semester statistics course are presented in this book. These concepts are essential for reasoning about a huge variety of problems ranging from what retirement plan to choose to whether you have enough evidence to decide whether a given job candidate would make a good employee. Taking a course in statistics is not going to help you much in solving those problems, though. Statistics is usually taught in such a way that people can see only that it applies to data of particular, rather limited types. What’s needed is what’s provided in this book—namely the ability to code events and objects in such a way that rough-and-ready versions of statistical principles can be applied to them. The book also presents the most important concepts of microeconomics and decision theory, the basic principles of the scientific method as they apply to solving everyday problems, the basic concepts of formal logic, the much less familiar principles of dialectical reasoning, and some of the most important concepts developed by philosophers who study how scientists as well as ordinary folks think (or should think).
4. The concepts in the book can be triangulated to understand a given problem from many perspectives. For example, a particularly serious error in everyday life is gross overgeneralization from a small number of observations of a person, object, or event. This error is based on at least four mistakes that compound one another: one psychological, one statistical, one epistemological (epistemology concerns theory of knowledge), and one metaphysical (metaphysics concerns beliefs about the fundamental nature of the world). Once each of these kinds of concepts is well understood, they can all be brought to bear on a given problem, supplementing and enhancing one another.
Every concept in this book is relevant to the way you live your life and conduct your business. We fail to make a friend because we made hasty judgments based on insufficient evidence. We hire people who are not the most capable because we trusted firsthand information too much and more extensive and superior information from other sources too little. We lose money because we don’t realize the applicability of statistical concepts such as standard deviation and regression and the relevance of psychological concepts such as the endowment effect, which causes us to want to keep things for no better reason than that we have them, and economic concepts such as sunk costs, which cause us to send good money after bad. We eat foods and take medicines and consume vitamins and other supplements that aren’t good for us because we’re not sufficiently skilled in evaluating alleged scientific findings about health practices. Society tolerates government and business practices that make our lives worse because they were developed without following effective evaluation procedures and remain untested long after they were introduced—sometimes for decades and at costs in the billions of dollars.
A Sampling of the Things to Come
The first section of the book deals with thinking about the world and ourselves—how we do it, how we flub it, how to fix it, and how we can make far better use than we do of the dark matter of the mind, namely the unconscious.
The second section is about choices—how classical economists think choices are made and how they think they ought to be made, and why modern behavioral economics provides both descriptions of actual choice behavior and prescriptions for it that are better and more useful in some ways than those of classical economics. The section provides suggestions for how to structure your life in order to avoid a wide range of choice pitfalls.
The third section is about how to make categorizations of the world more accurately, how to detect relationships among events, and just as important, how to avoid seeing relationships when they aren’t there. Here, we’ll examine how to detect errors in reasoning we encounter in the media, at the office, and in bull sessions.
The fourth section is about causality: how to distinguish between cases where one event causes another and cases where events occur close together in time or place but aren’t causally related; how to identify the circumstances in which experiments—and only experiments—can make us confident that events are related causally; and how we can learn to be happier and more effective by conducting experiments on ourselves.
The fifth section is about two very different types of reasoning. One of these, logic, is abstract and formal and has always been central to Western thought. The other, dialectical reasoning, consists of principles for deciding about the truth and practical utility of propositions about the world. This approach to reasoning has always been central to Eastern thought. Versions of the approach have been around in Western thought since the time of Socrates. But only recently have thinkers tried to describe dialectical thought in a systematic way or relate it to the tradition of formal logic.
The sixth section is about what constitutes a good theory about some aspect of the world. How can we be sure that what we believe is actually true? Why is it that simpler explanations are normally more useful than more complicated ones? How can we avoid coming up with slipshod and overly facile theories? How can theories be verified, and why should we be skeptical of any assertion that can’t, at least in principle, be falsified?
The sections of the book support one another. Understanding what we can and can’t observe about our mental life tells us when to rely on intuition when solving a problem and when to turn to explicit rules about categorization, choice, or assessment of causal explanations. Learning about how to maximize the outcomes of choices depends on what’s been learned about the unconscious and how to make it an equal partner with the conscious mind when choosing actions or predicting what will make us happy. Learning about statistical principles tips us off about when we need to reach for our rules for assessing causality. Knowledge of how to assess causality encourages us to trust experiments far more than simple observation of events and shows how important (and how easy) it can be to conduct experiments to tell us what business practices and personal behaviors are most likely to benefit us. Learning about logic and dialectical reasoning provides suggestions for different ways to come up with theories about a given aspect of the world, which in turn can suggest what kinds of methods will be necessary to test those theories.
You won’t have a higher IQ when you finish this book, but you’ll be smarter.