Unit 2 - Minda - The Psychology of Thinking Reasoning, Decision-Making and Problem-Solving.pdf

Indexer: Silvia Benvenuto Marketing manager: Camille Richmond Cover design: Wendy Scott Typeset by: Cenveo Publisher Services © John Paul Minda 2021 This edition first published 2021 First edition published 2015. Reprinted 2017, and 2019 Apart from any fair dealing for the purposes of research or pr...

Indexer: Silvia Benvenuto Marketing manager: Camille Richmond Cover design: Wendy Scott Typeset by: Cenveo Publisher Services © John Paul Minda 2021 This edition first published 2021 First edition published 2015. Reprinted 2017, and 2019 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Library of Congress Control Number: 2020933224 British Library Cataloguing in Publication data A catalogue record for this book is available from the British Library ISBN 978-1-5297-0207-1 ISBN 978-1-5297-0206-4 (pbk) Printed in the UK At SAGE we take sustainability seriously. Most of our products are printed in the UK using FSC papers and boards. When we print overseas we ensure sustainable papers are used as measured by the PREPS grading system. We undertake an annual audit to monitor our sustainability. 7 Deductive Reasoning When my kids were younger (they were 10 and 13 when I wrote the first edition of this book) they occasionally left something at school, such as a jacket, a book, or even a phone. Later, when they were home, one of them might say “I can't find my jacket”. The conversation that usually proceeded was one of retracing steps and trying to remember where the object was last seen. I might offer a suggestion, such as “Well, if it's not in your backpack then it must be at school”. By saying that, I'm essentially inviting a logical deduction. We start with the fact that it must be at one location or another and then look to verify the conclusion. My kids might not realize it, but they are working through a basic deduction problem. And sometimes this deductive process results in finding the missing item. Objectives On completing this chapter you should be able to achieve the following: Understand the difference between inductive logic and deductive logic. Be able to describe what a syllogism is and what the parts of a syllogism are. Be able to differentiate between valid and non-valid forms of deductive logic. Be able to diagram logical arguments and determine validity using circle diagrams. Understand conditional reasoning and categorical reasoning. Deduction and Induction The previous chapter discussed inductive reasoning. Induction involves making predictive inferences from observations. Induction moves from specific to general (based on evidence) and drawing conclusions that are likely to be true. In induction, the outcomes are probabilistic. For that reason, many of the examples in the literature were framed as statements of confidence in a prediction or a generalization. Induction can also be described as going beyond the given evidence to discover something new via thinking. With deductive logic, on the other hand, we are attempting to explain how people make specific conclusions and to determine if that conclusion is valid. Deduction often starts with a general statement (“My jacket is either in my backpack or at school”), and then proceeds to more specific statements (“It's not in my backpack”). Rather than going beyond the given evidence to discover something new via thinking, deduction often involves verifying that which is already known. The two kinds of reasoning are related in terms of how we use them in everyday thinking. Although the psychology of induction and deduction differ, we tend to use them together and it can be difficult to tell if you are using inductive reasoning or deductive reasoning. For example, if I buy a coffee from McDonald's, take a sip, and discover that it is very hot, I conclude that McDonald's coffee is very hot. That is a generalization, and I can infer that other McDonald's will serve hot coffee. Categorical induction might even allow me to project the property of “hot” to coffee purchased at other, similar restaurants. In both cases, I am relying on inductive reasoning and past experience to make some conclusions about the future. Suppose, then, that I form a general premise about McDonald's coffee. This premise can be stated as: Premise: McDonald's coffee is hot. A premise is a statement of facts about something. In this case, it's a statement of fact about McDonald's coffee. A premise like this can be used to make precise conclusions. For example, combined with additional premises and a conclusion, we can create an entire categorical syllogism. Premise: All McDonald's coffee is hot. Premise: This coffee is from McDonald's. Conclusion: Therefore, this coffee is hot. In a deductive statement, it is assumed that the premises are true. Given these two premises, the deduction is considered to be valid if the conclusion follows on directly from the premises. A valid argument is one where the conclusion is the only possible conclusion given the premises. In other words, there can be no other possible conclusion from these premises. If these true premises allow for alternative conclusions, then the deduction is not valid. It's also important to consider the soundness of the argument. A sound argument is one that is valid (the only conclusion that can be drawn from the premises) and one for which the premises are known to be true. It is possible to have valid arguments that are not sound. In the case above, the argument is only sound if we know that “All McDonald's coffee is hot”. If there is evidence to contrary, the argument can still be valid, but it is not a sound deduction, and so we may not trust the conclusions In the following sections, I consider some examples that show how deduction is used in a simple, everyday context. I then consider more complex examples and show how people often fail to consider the parameters of logical reasoning. Finally, the chapter discusses classical reasoning and conditional reasoning in greater detail, and how these are occasionally challenging for people in reasoning tasks. The Structure of a Logical Task The previous example with McDonald's coffee shows that deduction can be used to arrive at a conclusion about a member of a category (McDonald's coffee). People can also rely on deduction to make predictions about options and outcomes. For example, imagine that you are planning to go shopping at the shopping centre with a friend. She texts you to say she will meet you by the Starbucks coffee store or by the shoe store. You have two options that cannot both be true, but one that must be true. This can be stated more formally as: Premise: Your friend is waiting at Starbucks or by the shoe store. Premise: Your friend is not at Starbucks. Conclusion: Therefore, your friend is by the shoe store. This deductive argument has several components. As with the examples in the preceding chapter on induction and also with the McDonald's coffee examples, the statement has one or more premises and a conclusion. The premise gives basic factual information that we can reason from and reason about. In a deductive task, we assume that the premises are true. That is a crucial aspect of deductive logic, because, in many ways, the challenge of deductive logic is evaluating the validity structure of the task (we will discuss some problems with this idea later in the chapter). Each premise can contain facts and operators. Facts are just what you would expect them to be: facts are things that can be true or things that can be false, descriptions, statements about properties, and predicates. The operators are crucial to the deduction task, and they are part of what make this different from inductive reasoning. In the example above, the operator “OR” adds meaning to the understanding of the task. This is what allows us to think conditionally about the two alternatives. She is either here OR there. One must be true, but both of these cannot be simultaneously true. If you are given information that one of these is false, then you can conclude that the other must be true. Other common operators are AND, NOT, IF, ALL, SOME, NONE, etc. Each of these defines the nature of the deduction and can modify the complexity of the argument. The deductive task also has a conclusion, which is usually marked off with expressions like THEREFORE, THEN, etc. In most deductive logic tasks, subjects are usually asked to assume that the premises are true and then determine whether or not the conclusion logically follows. A valid conclusion is one in which the given conclusion is the only possible conclusion given the truth of the premises. An invalid conclusion in one where the same set of premises can give rise to more than one possible opposing conclusion. Deduction can seem counterintuitive Although we are constantly making inferences, drawing conclusions, and making predictions about things, deductive logic can often seem counterintuitive. One of the reasons for this is that we may agree with a stated conclusion even if it is not logically valid. Alternatively, we may reject conclusions that are valid. This is an effect known as belief bias, in which we have a bias to assume that deductions we believe, or are more believable, are valid and that those that do not seem believable are less likely to be valid. This is a bias, because validity is determined by the structure of a logical task, and not its believability. And in other cases, we may agree with a valid conclusion, but for idiosyncratic reasons. Consider an example that comes from a paper by Mary Henle (1962). This was one of the earliest attempts to understand the psychology of deductive logic and thinking. People in Henle's research were presented syllogisms that appeared in the form of a basic narrative and were then asked about their conclusions. Here's an example of a valid deduction. I'll explain later why this is valid and how to verify that: Syllogism: A group of women were discussing their household problems. Mrs Shivers broke the ice by saying: “I'm so glad we're talking about these problems. It's so important to talk about things that are in our minds. We spend so much of our time in the kitchen that of course household problems are in our minds. So it is important to talk about them”. This is a fairly straightforward, if somewhat dated-sounding syllogism. Henle asked her subjects to verify if the conclusion (i.e., that it is important to talk about household problems) was valid. She also asked her subjects to explain why or how they arrived at that conclusion. In other words, she asked them to engage in a logical deduction task. She found that many of her research subjects failed to reason logically. That is, they failed to distinguish between a conclusion that was logically valid and one that was factually correct or one that they agreed with. These two things are not the same, as we have seen earlier in our discussion of belief bias. Henle referred to this as the failure to accept the logical task. That is, people seemed to place a heavy premium on the content of the anecdote and thus did not reason logically. For example, one person in her study suggested this was not a valid conclusion, and said: “The conclusion does not follow (i.e. it is not valid). The women must talk about household problems because it is important to talk about their problems not because the problem is in their minds”. In this case, the person was incorrect to suggest that the conclusion was not valid, and the subject also provided a reason that was based on their own understanding of why we should talk about problems. This is a failure to accept a logical task. Other subjects suggested correctly that this was a valid conclusion, but they gave reasons which suggested that even though they correctly identified it as valid, they were still failing reason logically. For example, another person said: “Yes. It could be very important to the individual doing the talking and possibly to some of those listening, because it is important for people to get a load off their chest. But not for any other reason unless in the process one of the others learned something new of value”. This subject suggested the conclusion was valid, but again provided an answer that was idiosyncratic and rooted in personal belief. Although the conclusion was correct, this is still a failure to reason logically. One way in which we can evaluate the validity of this statement is to simplify it somewhat, and then replace some of the facts with variables. Using variables can help because it allows us to examine the structure of the argument separately from the semantics. Henle's syllogism can be simplified as follows: Premise 1: It is important to talk about the things that are on our mind. Premise 2: Household problems are on our mind. Conclusion: It is important to talk about household problems. We can replace the facts with variables as follows: the phrase “It is important to talk about the things that are on our mind” can be rewritten as “It is important to do A”. The second premise tells us something else is equivalent to the first fact and we can say B is equal to A. Premise 1: It is important to do A. Premise 2: B is equal to A. Conclusion: It is important to do B. This shows how and why the logical deduction is valid, and it is a fairly straightforward task as a substitution. Henle's point was that people often misunderstand what it means to be logical. They end up paying attention to the semantics and the content, which is important for understanding people, and tend to ignore or miss the underlying logical structure even when explicitly asked to do so. Henle noted other, related problems with deductive thought. For example, subjects often restated specific premises as being universal (Henle, 1962). Consider this syllogism: Syllogism: Mrs. Cooke had studied home economics in college. “Youth is a time of rapid growth and great demands on energy”, she said. “Many youngsters don't get enough vitamins in their daily diet. And since some vitamin deficiencies are dangerous to health, it follows that the health of many of our youngsters is being endangered by inadequate diet”. Subjects were asked to indicate if they thought that it was a valid conclusion to say that the “health of many youngsters is being endangered by inadequate diet”. Many subjects extended the first premise to be universal by ignoring the word “many” and restating it as “Youngsters do not get enough vitamins”. In doing so, they endorsed the wrong conclusion. In short, Henle (1962) noted that people seem not to accept logical tasks as being deducto-logical. They misstate premises, omit premises, and generally fall prey to the kinds of cognitive biases that Kahneman and Tversky would later describe with respect to judgement, inductive reasoning, and decision-making (Kahneman & Tversky, 1973; Tversky & Kahneman, 1973, 1974). It is important to note that these results do not indicate that subjects were unable to reason logically, but only that they did not treat this as a logical task, even when directed to. Henle (1962) suggested that the problem was that people focused on the semantics and the content rather than on the form of the argument itself. And later work confirmed many of these biases and shortcomings. Johnson-Laird suggests that naïve reasoners with no training in formal thought may make many cognitive errors in reasoning and yet still manage to achieve their goals and make good decisions (Johnson-Laird, 1999). He refers to this as a fundamental paradox of rationality. This is a paradox because rationality should be a necessary condition for correct decision-making and a hallmark of formal, mature thinking, and yet in many ways it does not seem to be necessary at all. Deductive logic is challenging for most people. The fact that we fail can be attributed to both the complexity and abstractness of the tasks (JohnsonLaird, 1999) as well as the general effectiveness of many cognitive heuristics (Anderson, 1990; Gigerenzer et al., 2011; Sloman, 1996). It may be that for many basic decisions and conclusions, logical deduction is not needed, and that the additional resources needed to reason correctly may be suboptimal. 7.1 Theory in the Real World When I lecture about the psychology of deduction, I have occasionally referred to a movie from 1985 called Labyrinth (and despite being from the 1980s, I am surprised how many students have seen it). It is principally a children's movie, but several parts are interesting for adults as well. I will summarize the plot briefly. At the beginning of the movie a young girl, Sarah, expresses some frustration about having to take care of her baby brother. It is a fantasy movie. At some point she wishes that a goblin king will take the baby away. Of course, her wish comes true and the goblin king (played by the late and terrific David Bowie) steals the infant and hides him in a castle. Sarah can retrieve the baby only if she makes it through a labyrinth. Early in the movie, she is faced with a single passage that ends with two doors. One of the doors is red and one of the doors is blue, and each of these doors has a guard who relates the rules of the “game” she must play in order to figure out which door to open. The game is a version of a classical logical problem known as the “Knights and Knaves” problem. The guards tell her that “one of the doors leads to the castle and the other leads to certain death”. They also tell her that “one of them always lies and the other always tells the truth”. Sarah has to figure out which door to open. In other words, we can state the problems as follows: Premise: Either the red door leads to the castle or the blue door leads to the castle. Premise: Either the red guard tells the truth or the blue guard tells the truth. If you haven't seen this movie before, you may want to take a moment to find this clip on YouTube: it is easily available (search for “Sarah's Certain Death Riddle”). And whether or not you have seen the clip, try to solve the problem. There is a correct answer, and I will give the solution at the end of the chapter. Categorical Reasoning Categorical reasoning occurs when we make conclusions on the basis of category membership. This is also referred to as classical reasoning, because we are reasoning about a class of things. In the previous chapter on inductive reasoning, we also emphasized the importance of categories. In that case, the emphasis was on the similarity between the premise and the conclusion. Stronger similarity results in stronger inductions. With respect to deduction, the emphasis is on the actual category membership rather than similarity. An often-repeated classical syllogism is the following: Major premise: All men are mortal. Minor premise: Socrates is a man. Conclusion: Therefore, Socrates is mortal. In the classical syllogism, the standard format is a major premise, which refers to a statement about the category. In this case, we are suggesting that the category “men” is predicated by the category “mortal”. In other words, there is an overlap between the category of men in the category of mortal. In the minor premise, the statement offers specific information. In this syllogism, the major premise tells us about the relationship between the two so that we can transfer the properties of one category to the other. Since all men are mortal and we know that Socrates is a member of the men category, we can conclude that he is also a member of the mortal category, because of the relationship between the two categories stated in the major premise. Notice that there is little role for similarity or featural overlap in these statements. It does not matter how similar (or not) Socrates is to the category of men. All that matters for the argument is that we know he is a man. There are many different varieties of formal classical syllogisms. For our purposes, we can focus on four basic versions. Universal affirmative The universal affirmative is a statement in which the relationship between the two categories is universal for all members, as stated. For example, if we say that “all cats are animals”, we are using the universal affirmative form. Substituting with variables, we have “All As are Bs”, as shown in Figure 7.1. One aspect of this universal affirmative form is that it is not reflexive, and thus has two possible forms. The first, shown on the left, suggests all members of category A are contained within a larger category B. This suggests a hierarchical relationship such that B is the larger category and A is a subcategory. In this case, it is true to say that all A are B, but the reverse is not true. It is not true to say that all B are A. On the right is the other form of “All A are B”. In this case, there is a reflexive relationship and everything in category A is the same as members in category B. Figure 7.1 Two possible circle diagrams that illustrate the universal affirmative. Particular affirmative If we say “some cats are friendly”, we are using an expression known as a particular affirmative. We mean that some members of the cat category are also members of the category of friendly things. The particular affirmative suggests that some members of one category can also be members of another category. As shown in Figure 7.2, there are four possible versions of this statement. Considering the abstract version “Some B are A”, the diagram on the top left shows a large category B and a small subordinate category A. In this universe, the statement “Some B are A” is true, because all of the members of category A are also members of the category B, but there are many other members of the category B which are not also members of category A. At the top right, the diagram shows two partially overlapping categories. In this universe, the statement “Some B are A” is also true, because whatever is contained in the overlap between the A category and the B category confirms this premise. Figure 7.2 Four possible circle diagrams that illustrate the particular affirmative. The two diagrams on the bottom are more difficult conceptually. When we hear that “Some B are A”, it is important to realize that the word “some” can mean at least one, and possibly all. The reason is that as long as one member of category B is also a member of category A, the statement is true. Even if all the Bs are also members of category A, the statement “Some B are A” is still true. Or think about it this way, if it turned out that all cats were friendly, and I said to you “some cats are friendly”, I would not be telling a lie. This would be a true statement. “Some” does not preclude “all”. In the bottom left, the diagram shows a case in which all members of category B are equivalent to the members of category A. Although this is an example of a universal affirmative, it can also be an example of a particular affirmative. The statement “Some B are A” is still true. Admittedly, it is an incomplete statement but in a universe in which all members of category A are equivalent to all members of category B, it does not render the statement “Some B are A” to be untrue. This is also the case for the figure on the bottom right. Here we see that category A is the superordinate category, and that all members of category B are subordinate. In this case, we can still say “Some B are A”, and that is a true statement within this arrangement of categories. What this means is that the particular affirmative is a more difficult statement to evaluate. It gives reliable information about the status of at least one and possibly all members of category B. It tells you very little about the status of category A and it tells you very little about the entire relationship between categories A and B. When evaluating a series of statements for which one of them is a particular affirmative, considerable care must be taken to avoid an invalid conclusion. Universal negative If we say that “no cats are dogs”, we are using a statement referred to as a universal negative. The universal negative expresses a relationship between two concepts for which there is absolutely no overlap. In contrast to the universal affirmative and the particular affirmative, the universal negative has only one representation. It is also reflexive. The statement does not tell us much about other relationships with respect to category A and category B, except to point out that these two categories do not overlap at all (see Figure 7.3). Figure 7.3 The only possible circle diagram that illustrates the universal negative. Particular negative If I say that “some cats are not friendly”, I'm using the particular negative. In this case, I want to get across the point that some members of one category are not members of another category. As with many of the other examples, there are several ways for this statement to be true. In Figure 7.4, we see three different ways in which the statement “Some A are not B” can be true. On the top left is shown the case where the superordinate category A contains a subordinate category B. This allows for the statement to be true, because there are many members of category A which are not contained within the subordinate category B. On the top right, we see the example with a partially overlapping category A and category B. In this example, the statement is still true because there are many members of category A which do not overlap with category B. At the bottom of the figure, a diagram shows a case where the two categories do not overlap at all. Although this diagram also represents a universal negative relationship, the statement “Some A are not B” is still technically true in this case. If it were the case that there were no friendly cats anywhere (impossible!) and I said “some cats are not friendly”, my statement would be still true in this no-friendly-cat universe. Figure 7.4 Three possible circle diagrams that illustrate the particular negative. Context errors in categorical reasoning Reasoning about categories and concepts is a fairly common behaviour, but because of the occasional ambiguity and complexity of these classical relationships people often make errors. In addition, many of the errors we make are a result of conflating personal beliefs and knowledge with the notion of logical validity. One way to avoid making these errors is to use the simple circle diagrams like those shown in Figures 7.1–7.4 to determine whether or not a conclusion is valid. If there is more than one configuration that allows the premises to be true but that lead to different conclusions, then it is not a valid deduction. Consider the following syllogism: Premise: All doctors are professional people. Premise: Some professional people are rich. Conclusion: Therefore, some doctors are rich. The first premise tells us something about the relationship between doctors (let's assume these are medical doctors) and the category of professional people. It tells us that everyone who is a doctor is also a member of this category. It leaves open the possibility that the two categories are entirely overlapping, or that there is a larger category of professional people which also includes teachers, engineers, lawyers, etc. The second premise tells us something about some of the professional people. It tells us some of them (meaning at least one and possibly all) are rich. Both premises express a fact, and in both cases the fact conforms to our beliefs. We know the doctors are professional, and we also know at least some of the people in the category of professional people could be rich. The conclusion we are asked to accept is that some doctors are also rich. The problem with this deduction is that it conforms to our beliefs and those beliefs can interfere with our ability to reason logically. We might know a rich doctor or have friends or family who are rich doctors. That is not an unreasonable thing to believe because although not all doctors are rich, certainly we are all aware that some of them can be. We know this to be true from personal experience, but that knowledge does not guarantee a valid deduction. A conclusion is valid only if it is the only one we can draw from the stated premises. This is an example of a cognitive bias known as the belief bias in which people find it easier to evaluate believable statements as being valid and non-believable statements as being invalid. In this case, the conclusion is not valid, but it is believable. Figure 7.5 shows two of several possible arrangements of the categories. Each of these arrangements allow the premises to be true. But each arrangement also shows how opposing conclusions can be reached from those same premises. On the left, it shows one possible arrangement of the categories such that the premises are true and the conclusion is true. It shows doctors as a subcategory of professional people, and it shows a category of rich people that overlaps with professional people and includes the doctors. And so in this universe, the first premise is true because all of the doctors are professional people. The category of rich people overlaps partially with the category of professional people, allowing the second premise to be true. Finally, because the category of rich people overlaps with the category of professional people and includes the doctors, it allows for the conclusion to be true as well. This state of affairs conforms to our understanding of doctors as generally being financially well-off. Figure 7.5 This is an example of an invalid categorical statement and the belief bias effect. Both sets of circles allow for the premises to be true and yet they support contradictory conclusions. The problem is that this is only one of many possible arrangements of the classes that allows for the premises to be true. On the right is an alternative arrangement. In this case, the category of doctors is still completely subsumed within the category of professional people, thus allowing for the first premise to be true. This also shows that the category of rich people partially overlaps with the category of professional people, thus allowing for the second premise to be true. However, the overlap between the rich people and the professional people excludes all of the doctors. In this arrangement, both premises are still true, but the conclusion (“Therefore, some doctors are rich”) is not. In this arrangement, no doctors are rich. The existence of both of these arrangements, each of which allow for the premises to be true but make different predictions with respect to the conclusion, indicates that this is not a valid syllogism. Of course, one might protest the conclusion of invalidity because it is not true that no doctors are rich. You surely know one or two rich doctors or at least have heard of one or two rich doctors. In doing so, you would be showing a belief bias. That is one of the things that is challenging about deductive logic. This is not a valid argument and yet the conclusion can still be true. In logical deduction, it is often difficult to separate truth from validity. A related problem can also occur for valid deductions. It is possible to have a valid argument that is unsound. An unsound but valid deduction is one for which the conclusion directly follows from the premises but is still unacceptable. This can arise when one of the premises is false. Consider the following example (Evans, 2005): Premise: All frogs are mammals. Premise: No cats are mammals. Conclusion: Therefore, no cats are frogs. In this case, the form is valid and the conclusion is both true and validly drawn. And yet, because the premises are false, the deduction is not sound. Consider another example with a valid structure but a false conclusion rather than a true conclusion, as in the preceding example: Premise: All students are lazy. Premise: No lazy people pass examinations. Conclusion: Therefore, no students pass examinations. In this case, although one could imagine the second premise being true, the first premise is not true. However, the structure of the task is still valid. And so it does follow from these two premises that no students pass examinations. This is demonstrably false, and so this argument is considered to be valid but not sound. A sound argument is a valid argument that is based on true premises. An argument that is sound guarantees a true valid conclusion. All of these examples suggest a clear limitation for deductive reasoning within the scope of human thinking abilities. Johnson-Laird (1999) suggests the main limitation of deduction is that it really does not allow one to learn new information because logical arguments depend on assumptions or suppositions. He suggests deduction may enable you to arrive at conclusions that were drawn about evidence that is present, but it may not add new information in the way induction can. Deduction allows a person to test the strength of their conclusions and beliefs. Induction allows a person to acquire new information by thinking. Conditional Reasoning In the previous section, I considered reasoning about classes of things, but people also reason about conditionality and causality. These kinds of deductions are usually framed within the context of if/then statements. For example, “If you study for an exam, then you will do well”. This statement reflects a relationship between a behaviour (studying) and an outcome (doing well). It reflects only one direction; there may be other things that affect your doing well. And as with categorical reasoning, there are several forms of conditional reasoning. The combination of these forms allows for a variety of valid and not valid statements to be expressed and evaluated. Before describing the different versions of conditional reasoning, consider the components of a conditional reasoning statement: Premise: If A, then B. Premise: A is true. Conclusion: Therefore, B is true. In the first premise, “A” is referred to as the antecedent. It is the thing or fact that occurs first. “B” is referred to as the consequent. The consequent is the thing that happens as a consequence of A being true. Although this might seem causal, it need not be. That is, we do not need to assume that A causes B, only that if A is true, B is true also. The second premise gives information about the antecedent within the premise. In this example, it gives information about the antecedent being true. Modus Ponens: affirming the antecedent A common conditional argument is one in which a relationship is expressed between an antecedent and a consequent and then one is given information that the antecedent is true. Consider the example below: Premise: If the cat is hungry, then she eats her food. Premise: The cat is hungry. Conclusion: Therefore, she eats her food. In this case, we are informed that if the cat is hungry (the antecedent), then she eats her food (the consequent). The second premise indicates that she is hungry and thus affirms the antecedent. Thus, it can be concluded that she will eat her food. If you accept these premises, you know that if the cat is hungry then she eats. This is a straightforward relationship that is often referred to as modus ponens, which in Latin means “the mode of affirming that which is true”. This deduction is valid. It is easy for most of us to understand because it is consistent with our bias to look for confirmatory evidence, and it is also easy to evaluate because it expresses things in the direction of cause and effect. Although conditional reasoning does not need to be causal, we still tend to think in terms of causal relationships. This chapter will discuss confirmation bias later. Modus Tollens: denying the consequent In the previous example, the statement affirmed the antecedent to allow for a valid deduction. However, imagine the same initial premise and now the second premise denies the consequent: Premise: If the cat is hungry, then she eats her food. Premise: She does not eat her food. Conclusion: Therefore, the cat is not hungry. In this example, the consequent is that she will eat her food. If that consequent is denied by saying “She does not eat her food”, then you can deduce the antecedent did not happen. The first premise tells you the relationship between the antecedent and the consequent. If the antecedent occurs, then the consequent must happen. If the consequent did not happen, then it is valid to deduce the antecedent did not happen either. This relationship is more difficult for most people to grasp. It runs counter to the bias to look for confirmatory evidence, even though it is still valid. This form is also known by a Latin name, modus tollens, which means “the mode of denying”. Denying the antecedent When you affirm the antecedent or deny a consequent, you are carrying out a logically valid form of conditional reasoning. Both of these actions allow for a unique conclusion to be drawn from the premises. However, other premises produce invalid conclusions. For example, the statements below show an example of denying the antecedent: Premise: If the cat is hungry, then she eats her food. Premise: The cat is not hungry. Conclusion: Therefore, she does not eat her food. In this example, the first premise is the same as the previous cases, but the second premise denies the antecedent by telling us that the cat is not hungry. With this information, you may be tempted to assume that the consequent will not happen either. After all, you are told that if she is hungry, she eats. You then find out she is not hungry, so it is natural to assume that she will not eat as a result. You cannot conclude this, however. The reason is that the first premise only gives us information about what happens with a true antecedent and a consequent. It does not tell you information about when the antecedent is not true. In other words, it does not rule out the possibility that the cat could eat her food for other reasons. She can eat even if she is not hungry. The cat could eat all the time, 24/7 regardless of hunger and the first premise is still true. And so, finding out that she is not hungry does not allow you to conclude that she will not eat. You can suspect this. You can possibly infer that it might happen. But you cannot arrive at that conclusion exclusively. Affirming the consequent The final example is one where you receive information that the consequent is true. Just like the preceding example, this one might seem intuitive but is not logically valid. An example is below: Premise: If the cat is hungry, then she eats her food. Premise: The cat eats her food. Conclusion: Therefore, the cat is hungry. The first premise is the same as the preceding examples and expresses the relationship between the hungry cat and the cat eating her food. The second premise affirms the consequent, that is, you are told that she does in fact eat her food. You may be tempted to infer backwards that the cat must have been hungry. But just like the preceding example, the first premise tells you a directional relationship between the hungry cat and eating, but does not tell you anything at all about other possible antecedents for the cat eating her food. As a result, knowing that she eats her food (affirming the consequent) does not allow for an exclusive conclusion that the cat's hunger (the antecedent) was true. This is also an invalid deduction. Card Selection Tasks Some of the most well-known reasoning tasks in the psychological literature are the various card selection tasks. These tasks assess people's ability to evaluate evidence and arrive at deductions. Unlike the categorical and conditional examples given above, in which we might be asked to say whether or not a given conclusion is valid, the card selection tasks ask a subject to arrive at the deduction and make a choice on the basis of that deduction. In these tasks, subjects are typically given one or more rules to evaluate. The rules refer to the relationship of symbols, letters, numbers, or facts that are presented on two-sided cards. In order to determine whether or not the rule is valid, subjects indicate which cards should be investigated. In this respect, the card selection tasks might have some degree of ecological validity with respect to how deduction is used in everyday thinking. The card task tries to answer the following question: If you are given a series of facts, how do you go about verifying whether or not those facts are true? Confirmation bias Because these tasks have been so well studied, they have also helped to uncover several biases in human reasoning. The first and most extensive is what I have referred to as the confirmation bias. This bias shows up not only in card selection tasks but also in other kinds of thinking behaviour. A confirmation bias reflects the tendency in humans to search for evidence that confirms our beliefs. This bias is pervasive and ubiquitous (Nickerson, 1998). Earlier in this chapter, I discussed an invalid categorical syllogism concerning some doctors being rich. If you believed that doctors were rich, you might show a confirmation bias if you only searched for evidence of rich doctors. The confirmation bias would also show up if you tended to downplay or discount information that was inconsistent with your belief, or would disconfirm your belief. In other words, even if you did meet a doctor who was not rich, you might downplay that evidence as an anomaly, or someone who just wasn't rich yet. We often see evidence of confirmation bias in popular media. In the 1990s, dietary advice strongly suggested the best way to eat healthily and reduce weight was to reduce the amount of fat in the food you ate. There was a heavy emphasis on “low-fat” foods. At the same time, there was a heavy emphasis on eating high carbohydrate foods. Plain pasta was good, butter and oil were bad. Although we know now that this advice was not very sound, it had a long-lasting effect on personal health. One of the possible reasons is that when people were avoiding fat, they were avoiding higher calorie and richer foods. This may have given the impression that it was the fat that was causing dietary problems when in fact it may have been a simple issue of overall consumption. People notice many positive factors when switching to a restricted diet of any kind, such as vegan diets, ketogenic diets, or so-called “paleo” diets. If you switch to a diet like this, and you notice some weight loss, you tend to attribute the weight loss to the specifics of the diet rather than the general tendency to be more selective. This is a confirmation bias. You believe that eating a high protein diet will result in weight loss, and you may miss the alternative explanation that a restricted diet of any kind can also result in weight loss. The low-fat diet craze of the 1990s was even more difficult because of the strong but incorrect belief of the equivalency between dietary fat and body fat. It is possible that the surface-level correspondence between these two kinds of fats encouraged people to see a confirmatory match where one was not present. Wason card selection task The confirmation bias has often been studied with a card selection task. The most well-known example of a card selection task is the one developed by Wason in the 1960s (Evans, 2005; Wason, 1960, 1966; Wason & Evans, 1975). The most elemental version is shown in Figure 7.6. Subjects are shown four cards laid out on a table. Each card can have a number or a letter on each side. Subjects are then given a rule to evaluate and are told to indicate the minimum number of cards to turn over in order to verify whether or not this rule is true. For example, considering the cards shown in Figure 7.6, the rule might be: Premise: If a card has a vowel on one side then it has an even number on the other side. Figure 7.6 This is the standard version of the card selection task. Looking at these cards, which ones would you turn over in order to evaluate this rule? Most people would agree that the first card to turn over would be the one with the A on it. If you turn this card over and there is no even number, then the rule is false. This is straightforward because it is an example of affirming the antecedent. The antecedent in this case is “If a card has a vowel on one side”, so you can see if that is true with the A card. You turn it over to see if the rule is being followed. In the original studies, Wason also found that people almost always suggested turning over the “4” card in addition to the A card. By turning over the “4” card, subjects were looking to see if there was a vowel on the other side. But this is an example of a confirmation bias where you look for evidence to confirm the statement. This is also an example of affirming the consequent, which is known to be an invalid form of conditional reasoning. The rule does not specify the entire range of possibilities with respect to even number cards. The even number can occur on the other side of a vowel card, as suggested by the rule, but the rule does not exclude the possibility of an even number occurring on the back of other cards. In fact, the rule would be true even if even numbers occurred on the back of all cards. If every single card shown in this array had an even number on the other side, the rule would be true. Wason argued that the correct solution to this problem is to turn over the “A” card, and also the “7” card. The “7” card looks to disconfirm the rule. This is an example of denying the consequent. If the “7” card has a vowel on the other side, then the rule is false. Wason and others have argued that this confirmation bias can also be described as a matching bias (Wason, 1966; Wason & Evans, 1975). In other words, subjects tend to match their behaviour to the stated hypothesis. How does this matching behaviour come about? One possibility is limitations in attention and working memory capacity. Given the statements, it may simply be a less demanding task to pick two cards that conform most closely to the hypothesis that was stated. Choosing to turn over a card that tests for denying the consequent requires the consideration of a premise that is not explicitly stated. In order to arrive at this implicitly stated premise, the subject must have sufficient working memory resources to hold the stated premise in mind along with the unstated premise. This is not impossible, but it may not be straightforward. As a result, people tend to choose confirmatory evidence. In some ways, the pervasiveness of confirmation bias may be related to the notion of entrenchment. It is culturally and linguistically entrenched to think in terms of describing something that is. So when a person confirms a hypothesis, they look for evidence that something is true. The resulting search space is smaller and constrained, and there is a direct correspondence between the hypothesis and the evidence. When searching for disconfirmatory evidence, the search space is much larger because people will be searching for something that “is not”. Goodman and others have argued that “what something is not” is not a projectable predicate (Goodman, 1983). Deontic selection tasks The standard confirmation bias shown in the Wason card selection task does not always play out. Alternative versions of the card selection task can be arranged that are formally equivalent on the surface but ask the subject to adopt a different perspective. In many cases, a permission schema is easier for subjects to consider. That is, when thinking about categories, it makes sense to think about what something is but not so much to think about what it is not. An animal can be described as a member of the DOG category, but it is not very informative to describe the same animal as not being a member of the FORK category, or the BEVERAGE category. The list of categories for which the animal is not a member is essentially infinite. So, with respect to category membership and reasoning, it is understandable that humans display a confirmation bias. Confirmatory evidence is manageable whereas disconfirmatory evidence is potentially unmanageable. But when thinking about permission, it is common to think about what you can do and what you cannot do. In fact, this is essentially how we think about permission. Technically, permission is something you are permitted or allowed to do, but we often conceive permission to be freedom from restriction. Speed limits tell us how fast we are permitted to travel, but we tend to consider the ramifications of exceeding the speed limit. The green light at a traffic intersection permits you to drive, but the bigger deal is what happens when the red light comes on and you have to stop. Figure 7.7 This is the deontic version of the card selection task that invokes a permission schema. Wason's card selection task can be reconstructed as one requiring permission. This is referred to as a deontic selection task (Griggs & Cox, 1983). Figure 7.7 shows an example. In this case, the cards have ages and beverages on either side. Just as in the standard version, subjects are given a rule to evaluate and asked to indicate the minimum number of cards they need to turn over in order to evaluate this rule. In this case the rule might be: Premise: If a person is drinking alcohol, they must be over 19. I am using 19 here because that's the legal drinking age in Ontario where I live. Different countries have different minimum drinking ages, so just replace that with the age where you live when you consider this example. Subjects rarely fail this task. It is straightforward to realize that you need to check the age of the beer drinker, and you need to check with the 17-yearold who is drinking. Even if you have never been in a scenario where you need to ensure that an establishment or club is following the law, most people know what it means to have permission to legally consume alcohol. Very few subjects show a confirmation bias here. The explanation is that this task appeals to the permission schema. The permission schema limits the number of hypotheses that need to be considered. It is important to note that this task succeeds in eliciting logical behaviour not because it makes it more concrete or realistic, but rather because the permission schema reduces the number of options and makes it easier to consider what violates the rule. Other research has shown the same effects even with fairly abstract material (Cheng & Holyoak, 1985). Context effects The deontic selection task shows that perspective and context can affect reasoning behaviour as well. For example, in the task shown in Figure 7.7, if you are trying to enforce drinking laws, you check the beer drinker and the 17-year-old. But if you are trying to make sure people who can drink legally are in fact consuming the alcohol (suppose you want to really increase sales), you can imagine checking the 21-year-old to make sure they are actually drinking beer. After all, in that scenario, you may want them to drink beer. Figure 7.8 A modified version of the selection task that can show the effects of local schema and context. Several studies have looked at the effect of context more systematically. Figure 7.8 shows an example of four cards that have facts about how much a person has spent in the store and whether or not they took a free gift. Subjects are told to evaluate the following rule: Premise: If a customer spends more than $100 they may take a free gift. In addition to just being shown the cards and given the premise, subjects are then given one of two perspectives. If subjects are given the perspective of a store detective looking for customers who might be cheating the free gift policy, they tend to choose cards 2 and 3. In this case, you work for the store and you want to make sure the person who has the free gift spent enough to deserve it, and you also want to make sure the person who did not spend enough to take a free gift did not in fact take one. You don't care about the person who did not take the gift, even if they spent enough, because you are looking out for cheaters. Other subjects are told to assume the perspective of a consumer or customer advocate. In this case, you want to make sure the store is keeping its promise. These subjects turned over cards 1 and 4. In this case, you are on the side of the customer. You want to make sure the person who spent $120 was indeed offered a free gift. And you want to make sure the person who did not take the free gift was not offered one because he or she did not spend enough. You are less concerned about the person who received the free gift. Summary Deductive reasoning is fairly straightforward to describe in many ways. Deductive tasks generally follow a strict logical form. There are clear cases for deductions that are valid and not valid. And there is a fairly straightforward definition for sound and unsound deductions. And yet, most people have difficulty with deductive reasoning. Deductive reasoning seems to be outside the ability of many people. And as discussed in this chapter, many people reason, make decisions, and solve problems in ways that define a logical deduction and yet still succeed in allowing people to accomplish goals. This raises important questions about the role of deductive logic within the psychology of thinking. Several of the upcoming chapters will discuss the psychology of decisionmaking, probability estimation, and problem-solving. Many of the cognitive biases that undermine deductive reasoning will also undermine sound decision-making. But, as with deductive reasoning, the evidence suggests that many people still make adaptive and smart decisions despite these biases. Questions to Think About Why do people struggle with deduction and with evaluating deductive arguments? People often display a belief bias when reasoning about classes and categories. Why does the belief bias occur and why might we often reason from belief without seeing any negative or ill effects? Confirmation bias is pervasive, but we rarely notice our tendency to reason this way. What are some possible downsides to confirmation bias? Are the downsides sufficient to warrant using strategies to avoid confirmation bias? Appendix: Solution to the Two Doors Problem In Box 7.1, I presented a logical problem based on a movie. If you watched the movie, Sarah solves the riddle. She says to the guard of the red door “Would he tell me that this door leads to the castle?” In other words, she asks RED “Would he (BLUE) tell me that this door (RED) leads to the castle?” RED says “yes”. From this, she is able to determine BLUE is the right door and RED is the wrong door. If you watched the movie clip on YouTube, you will see that she chooses the BLUE door. When she opens the door, she falls into a trapdoor and the clip ends. But it's early in the movie: it was still the right door. She solved the riddle. She is able to arrive at this conclusion without knowing who is lying and who is telling the truth. Her reasoning is as follows: If RED is telling the truth, then BLUE is a liar. If BLUE would say RED leads to the castle, it would be a lie. Therefore, RED does not lead to the castle. BLUE = castle, RED = death If RED is telling the lie, then BLUE is telling the truth. It is a lie that BLUE would say that RED leads to the castle. Therefore, BLUE would say that BLUE leads to the castle. Therefore BLUE = castle, RED = death