Another key element of metacognitive judgments is the time of elicitation. Judgments can be prospective (i.e., occurring before performing a task), or retrospective (i.e., occurring after task completion). For example, a student may reflect on their current knowledge to predict their success on an upcoming test (prospective judgment) and, judge afterwards how well they did, trying to estimate their grade (retrospective judgment). Few behavioral studies have pitted prospective against retrospective judgments for the same task. Siedlecka, Paulewicz and Wierzchon (2016) compared prospective and retrospective ´ confidence judgments. Participants rated whether presented words were the solution to anagram tasks. Participants also rated their certainty, either before or after seeing the suggested solution. The authors found that post-decision confidence ratings were more accurate than ratings made prospectively. Resolution and calibration were also found to be higher

in retrospective than in prospective judgments by Fleming, Massoni, Gajdos, and Vergnaud (2016), using a perceptual decision task. Retrospective confidence ratings were provided on every trial, whereas prospective judgments were only provided prior to every fifth trial. The authors found dissociable influences on prospective and retrospective judgments. Whereas retrospective judgments were strongly influenced by current-trial fluency, and accuracy and confidence in the immediately preceding decision, prospective judgments were influenced by previous confidence over a longer time frame. Furthermore, individual overconfidence was stable across prospective and retrospective judgments, suggesting that overconfidence represents a stable personality trait (Ais, Zylberberg, Barttfeld, & Sigman, 2016; Jackson & Kleitman, 2014).

As many reasoning and problem-solving tasks go on over an extended period of time, the assessment of performance and success probability must be updated repeatedly (Ackerman, 2014). Intermediate confidence is an internal estimate of the adequacy of possible responses considered before arriving at a final solution (see Ackerman & Thompson, 2017). To study this process, Ackerman (2014) asked participants to rate their intermediate confidence every few seconds until they provided a solution, after which they rated their final confidence. The first intermediate judgment turned out to be a good predictor of the amount of time participants spent solving the problems. Confidence tended to increase over time. However, whereas at the beginning, participants tended to provide answers when confidence was high, over time they became more willing to provide answers at a lower level of confidence. Final low-confidence responses could be as low as 20%, even when there was an option to give up, by answering "I don't know".

The study of confidence judgments has been extended in the last few decades to collective decision making. In numerous perceptual as well as cognitive decisions, interacting individuals can make more accurate decisions by discussing one's own perceptual experiences with others and integrating different opinions, achieving a reliable collective benefit even in the absence of objective feedback (Bahrami et al., 2010). That is, the accuracy achieved by sharing

and combining subjective information via social interaction can exceed the accuracy of each individual opinion, even that of the best individual in the group. This phenomenon is known as the "two-heads-betterthan-one" effect (Koriat, 2012) or "wisdom of the crowd" (Surowiecki, 2004). Koriat (2012) presented participants with two-alternative forced inference tasks and showed that members of a dyad can take advantage of the wisdom of the group by using a simple heuristic: choosing the response expressed with the highest level of confidence. These findings have relevant implications for collective and democratic decisions and actions.

## 6.2.4 Neuroscience of Metacognition

In recent years, the study of metacognition was enriched by growing evidence from neuroscience concerning the underlying neurocognitive architecture. Specific neural substrates (especially in frontolateral, frontomedial, and parietal regions; see Figure 6.3) are involved in metacognition (e.g., Fleming, Huijgen, & Dolan, 2012; Fleming, Ryu, Golfinos, & Blackmon, 2014; Fleming, Weil, Nagy, Dolan, & Rees, 2010). However, the neural bases of human metacognition remain controversial. Metacognition operates on a variety of first-order processes, ranging from memory to perception, problem solving, etc. The diversity of the tasks to be monitored and controlled complicates the study of its neural signature, as it can be difficult to differentiate between the neural activations attributable to the metacognitive monitoring and control processes and the neural signature of the first-order cognitive/emotional processes (Metcalfe & Schwartz, 2016).

Existing attempts to isolate the metacognitive monitoring and control processes from first-order processes, testify to the uniqueness of metacognitive processes. Initial evidence was obtained from neuropsychological cases. For instance, Shimamura and Squire (1986) suggested that frontal lobe (behind forehead) impairments in patients with Korsakoff's syndrome—a chronic memory disorder characterized by severe anterograde amnesia—can impact metacognitive judgments independently of cognitive performance per se. A common finding suggests that neural signals involved in error monitoring originate in the posterior medial frontal cortex (pMFC; Dehaene, Posner, & Tucker, 1994).

Since the introduction of these seminal studies, further research into such domains as memory, perception, and decision making, has identified neural correlates of metacognitive judgments and further dissociated cognitive from metacognitive processes. Fleming et al. (2010) had participants performing a perceptual decision-making task and providing ratings of confidence after each decision. The authors found considerable variation between participants in metacognitive accuracy. Using MRI, this variation in confidence accuracy was found to be correlated with grey matter volume in the right rostrolateral areas of the prefrontal cortex (PFC). Furthermore, greater accuracy in metacognitive judgments was associated with increased white-matter microstructure connected with this area of the PFC. These results point to neural bases of metacognition that differ from those supporting primary perception. Similarly, in a study by Do Lam and colleagues (2012), participants who had first learned the pairwise associations between faces and names were then presented again with each face and asked to provide judgments of learning (JOLs) regarding the chance of recalling the associated name. A neurological dissociation was found between the processes of memory retrieval, which were located in the hippocampal region (i.e., medial temporal lobes), and those underlying JOLs, which were located in the medial PFC, orbitofrontal cortex (OFC) and anterior cingulate cortex (ACC).

Anatomical, functional, and neuropsychological studies have confirmed the consistent involvement of a frontoparietal network in metacognition (Vaccaro & Fleming, 2018). Activations were located in the posterior medial PFC, ventromedial PFC and bilateral anterior PFC/ dorsolateral PFC. Other researchers observed activations in the bilateral insula and dorsal precuneus (Vaccaro & Fleming, 2018). These results suggest that the parietal cortex, particularly precuneus, and insula represent key nodes supporting metacognition, together with the PFC.

Existing research supports the existence of neural dissociations between prospective and retrospective metacognitive judgments (Chua, Schacter, & Sperling, 2009; Fleming & Dolan, 2012). For example, in a study on patients with lateral frontal lesions,

Pannu, Kaszniak, and Rapcsak (2005) found impaired retrospective confidence judgments, but preserved judgments of future task performance. Conversely, Schnyer and colleagues (2004) found an association between damage to the right ventromedial PFC and a decrease in accuracy for metacognitive judgments about future recall (feeling of knowing), but not for accuracy of retrospective confidence judgments. Further evidence comes from functional MRI studies, which have shown that prospective metacog-

nition activates medial aspects of the PFC, while retrospective metacognitive accuracy is correlated with lateral PFC activity (Fleming & Dolan, 2012). When separating metamemory judgments by temporal focus in their meta-analysis, Vaccaro and Fleming (2018) found that retrospective judgments were associated with activity in the bilateral parahippocampal cortex and left inferior frontal gyrus, whereas prospective judgments activated the posterior medial PFC, left dorsolateral PFC, and right insula.

Figure 6.3: Gross neuroanatomy. a) Relative position and direction of brain structures. b) The four brain lobes from a lateral view. c) and d) Approximate locations of the broadest subdivisions of the PFC and other areas linked to metacognition. Illustrations adapted from Patrick J. Lynch, medical illustrator, C. Carl Jaffe, MD, cardiologist, under the Creative Commons Attribution 2.5 License, 2006 (CC-BY-2.5). Retrieved from https://commons.wikimedia.org/wiki/File:Brain\_human\_lateral\_view.svg and https://commons.wikimedia.org/wiki/File:Brain\_human\_sagittal\_section.svg. *Abbreviations*: dmPFC, dorsomedial prefrontal cortex; vmPFC, ventromedial prefrontal cortex; ACC, anterior cingulate cortex; dlPFC, dorsolateral prefrontal cortex; rlPFC, rostrolateral prefrontal; vlPFC, ventrolateral prefrontal cortex; OFC, orbitofrontal cortex.

Nevertheless, neuroimaging evidence directly comparing between different judgement types is scarce. In one of the few studies directly comparing neural activation related to prospective feeling of knowing and retrospective confidence judgment, Chua and colleagues (2009) found an association between prospective judgements and activation in medial parietal and medial temporal lobe, whereas retrospective judgements were associated with inferior prefrontal activity. However, common activations associated with both prospective and retrospective judgments were also observed in regions of medial and lateral PFC, and mid-posterior areas of cingulate cortex. These results suggest that neural activations related to different judgment type may differ in degree rather than in kind (Vaccaro & Fleming, 2018).

Another relevant question tackled in neuroscience is whether metacognition relies on a common, domain-general resource or on domain-specific components that are particular to the respective first-order tasks. Recent neuroimaging studies yielded pertinent evidence for both domain-general and domain-specific neural markers (see Rouault, McWilliams, Allen, & Fleming, 2018, for a review). A frontoparietal network contributes to metacognitive judgments across a range of different domains. Still, neuroimaging evidence for direct comparisons is scarce. In a recent meta-analysis, Vaccaro and Fleming (2018) observed common regions in separate investigations of memory and decision-making tasks, which included: insula, lateral PFC, and posterior medial PFC. As suggested by Morales et al. (2018), this result may indicate that judgments in both memory and decision making are driven by common inputs. The meta-analysis also pointed to further regions that are activated by specific tasks. More precisely, meta-memory engaged left dorsolateral PFC and clusters in bilateral parahippocampal cortex, whereas right anterior dorsolateral PFC was involved in decision making (Vaccaro & Fleming, 2018).

In summary, the neural underpinnings of even the most straightforward metacognitive judgments are complicated. Although metacognition can be dissociated from task performance, most studies have revealed activations in multiple brain areas, and differences have emerged between prospective

and retrospective judgments. Convergent evidence indicates that the function of the rostral and dorsal areas of the lateral PFC is important for the accuracy of retrospective judgments of performance. In contrast, prospective judgments of performance seem to depend on medial PFC. Recent studies have resulted in a rather nuanced picture, suggesting the co-existence in the brain of both domain-specific and domain-general signals.

# 6.3 Metacognitive Perspectives on Applied Rationality

The research reviewed so far has proven to be fruitful and thought-provoking, suggesting metacognitive explanations of adaptive behavior. We have seen that metacognitive deficits can lead to irrationality and inefficiency. In particular, we have reviewed memorable evidence on the illusion of knowledge, which consists of the gross overestimation of one's chance of success, typically brought about by deceptive feelings of fluency or flow (Fiedler, 2013). Overconfidence, in particular, can be a major source of bias and a dangerous obstacle in decision making under risk and under uncertainty (Glaser & Weber, 2007; Kruger & Dunning, 1999).

The metacognitive perspective is of particular importance for applied research on rational thinking, adaptive regulation, medical diagnosis and treatment, democratic decision making, lie detection, debunking of fake news, argumentation, trust, (im)moral action, and procedural justice in courtrooms, selection committees, or executive decisions. Checking and optimizing the quality of higher-order cognitive operations—the very domain of metacognition—is crucial for rational and responsible behavior. We illustrate this point in the remainder of this section.

# 6.3.1 Legal Judgments and Decisions

A classical domain of metacognitive research in legal psychology is eyewitness identification performance. Because everybody expects eyewitnesses to identify the perpetrator in a lineup and because the persons in the presented lineup are much more

vivid than the original persons in a past episode, the enhanced readiness to make a positive recognition decision produces many correct identifications (when the identified suspect is indeed the perpetrator) but also many incorrect identifications (when the identified suspect is not the perpetrator).

As illustrated in Figure 6.4, a liberal identification criterion (rather left position of C) produces, say, 90% correct identifications but roughly 40% incorrect identifications. A high false-alarm rate can be conceived as a case of overconfidence; C is apparently too weak a criterion to discriminate guilty and innocent persons, yielding an intolerably high rate of wrong convictions. Consistent with this account, a majority of exoneration cases after the introduction of DNA proofs turned out to be innocent victims of incorrect eyewitness identification.

The distinction between prospective and retrospective confidence judgments is also relevant to eyewitness testimony (Nguyen, Abed, & Pezdek, 2018). Witnesses are often asked to rate shortly after witnessing a crime their ability to recognize the perpetrator in the future (prospective confidence). Subsequently, when asked to identify someone from a lineup, eyewitnesses are asked how confident they are that they identified the correct person as the perpetrator (retrospective confidence). Nguyen, Abed, and Pezdek (2018) found that postdictive confidence was a better indicator of identification accuracy than predictive confidence, both for faces of the same race as the witness and for cross-race faces. Consistent with the lab findings reviewed above, this suggests that eyewitness confidence should be collected at the time of identification rather than earlier on the crime scene.

# 6.3.2 Metacognitive Myopia as a Major Impediment of Rationality

Fewer optimistic insights were obtained in other areas of metacognition research. Rational judgments and decisions about economic, political, legal, and health-related issues rely heavily on the critical assessment of both the logical correctness of mental operations and the validity of the underlying evidence. A conspicuous deficit in this sorely needed function of critical assessment has been termed

metacognitive myopia (Fiedler, 2000, 2008, 2012). As the term "myopia" (short-sightedness) suggests, experimentally demonstrated violations of rational norms typically do not reflect insufficient attention or insensitivity to the stimulus data. On the contrary, people are quite sensitive to the data given; they are in a way too sensitive, taking the data for granted and failing to discriminate between valid and invalid information. For example, when judging the success of different stocks on the stock-market, participants were quite sensitive to the frequency with which various stocks were reported in TV programs among the daily winners. However, they failed to take into account that the daily winning outcomes of some stocks had been reported in more than one TV program (Unkelbach, Fiedler, & Freytag, 2007). Although they fully understand that two TV programs on the same day provide the same stock-market news, participants do not exhibit much success in taking the redundancy into account. Even when they are explicitly reminded of the redundancy and instructed not to be misled by such repetitions, they cannot avoid their misleading influence. This failure to overcome a known pitfall is a metacognitive flaw.

Analogous findings were observed across many experimental tasks. Fully irrelevant numerical anchors influence quantitative judgments (Wilson, Houston, Etling, & Brekke, 1996). Samples that dramatically over-represent the base-rate of rare events (e.g., samples in which the prevalence of HIV is 50% rather than 0.1% as in reality) are used to estimate associated risks (Fiedler, Hütter, Schott, & Kutzner, 2018). Correctly denied questions referring to objects or behaviors not included in a film nevertheless increased the probability that the non-existing objects were later recalled erroneously (Fiedler, Armbruster, Nickel, Walther, & Asbeck, 1996). In a perseverance paradigm, explicit debriefing about an experimental lie did not erase the implications and psychological consequences of the lie (Ross, Lepper, & Hubbard, 1975). Common to all these findings is that participants, who fully understand that invalid stimulus information should be discarded, are nevertheless influenced by that invalid information.

The conspicuous naivety with which information is used and retained uncritically, regardless of its

Figure 6.4: Signal detection analysis of eyewitness-identification performance: the solid (dashed) curve represents the distribution of memory strength when the suspect in a lineup is (is not) the real perpetrator. Discriminability is the average horizontal difference d' between curves. An identification decision is made when memory strength exceeds the criterion C. The areas right of C under the solid (dashed) curve are the probabilities of correct (incorrect) identification.

invalidity, is reminiscent of Hannah Arendt's (1963) admonition that compliance and uncritical conformity are the origin of severe harm and violations of legal norms of humanity. But although the superego residing in the metacognition's pre-frontal brain area is ethically obliged to engage in critical test and reconfirmation, its role in higher-order cognition is often impoverished. Meta-analyses of modern research on debunking (Chan, Jones, Hall Jamieson, & Albarracín, 2017), for instance, testify to the inability of scientific or political debriefing to erase fake news or obvious myths. Thus, even when the public are fully debriefed that Iraq did not possess any atomic bombs when the US invaded, that the evidence on global warming is uncontestable, or that polygraph lie detection is not supported by reliable studies, people change their erroneous beliefs only slightly and continue to hold the discredited wrong beliefs to a considerable extent.

When it comes to integrating different individual opinions in group decision making or advice taking, a typical uncritical strategy is equal weighting of opinions, in spite of better knowledge or even explicit feedback about clearly unequal competence of different advice givers (Fiedler et al., 2018; Mahmoodi et al., 2015). Recent research by Powell, Yu, DeWolf, and Holyoak (2017) showed that the

attractiveness of products offered by Amazon may depend on quantity (number of available reviews) more than on quality (mean rating provided by previous customers). Confusion of quantity and quality was also observed by Fiedler, Kareev, Avrahami, Beier, Kutzner, and Hütter (2016), who found that increases (decreases) between samples of two symbols in the proportion of one critical symbol were readily detected only when absolute sample size increased (decreased) well.

In causal reasoning, metacognitive myopia is evident in a tendency to exclusively focus on effect strength and to disregard the strength of the causal input that was necessary to induce the observed effect strength. For example, the impact of a drug on athletic performance is judged to be higher if the same dose of the drug causes a performance increase of 10 scale points rather than 1 point. However, whether 254 mg or only 34 mg of the drug were necessary to induce the same observed performance change is given little weight (Hansen, Rim, & Fiedler, 2013).

Why do irrational consequences of metacognitive myopia extend from objectively difficult to such trivially easy task settings? Why do people continue to be influenced by invalid information which is obviously wrong (like an irrelevant numerical anchor) and which they explicitly classify as invalid?

A tentative answer might lie in a kind of metacognitive learned-helplessness effect (Maier & Seligman, 1976). Homo sapiens may have learned that many real-life tasks do not provide us with sufficient information for a normatively sound monitoring and control process. Thus, a Bayesian algorithm required to correct for biases in an information sample is often unknown or does not exist at all. This experience may then be over-generalized to easy situations in which monitoring and control would be simple and

straightforward. In any case, metacognitive myopia seems to constitute a major impediment in the way of rational behavior.

# Acknowledgment

The work underlying the present article was supported by a grant provided by the Deutsche Forschungsgemeinschaft to the first author (FI 294/26-1).

#### Summary

#### Review Questions

### Hot Topic

#### More on eyewitness memory

Signal-detection analysis has been extremely helpful in clarifying the metacognitive origin of the serious errors in eyewitness identifications. Even though witness' memory cannot be influenced in retrospect—that is, the discriminability d' of correct and incorrect memories is typically invariant—it has been shown that the rate of false identifications can be markedly reduced by simply inducing a more conservative response strategy, that is, a higher criterion C. A glance at Figure 6.4 will easily confirm that a rightward shift of C (up to the intersection point of both curves) will reduce the number of incorrect identifications (area right of C under the dashed curve) more than the number of correct identifications (are under the solid curve), thus increasing the overall rate of correct decisions. Such clever metacognition research has

Klaus Fiedler

led to a commonly noted improvement of legal practices (Wells et al., 2000).

Now after two or three decades of improved lineup procedures, a recent state-of-the art review by Wixted and Wells (2017) has arrived at the optimistic conclusion that ". . . our understanding of how to properly conduct a lineup has evolved considerably". Under pristine testing conditions (e.g., fair lineups uncontaminated with administrator influence; immediate confidence statement), eyewitness ". . . (a) confidence and accuracy are strongly related and (b) high-confidence suspect identifications are remarkably accurate." [p. 10].

#### Computerized learning environments

Computerized environments are replacing paper-based environments for training, learning, and assessment. However, a puzzling finding is screen inferiority—a disadvantage in learning from computer screens even when the task draws on capabilities considered well-suited for modern technologies like computers or e-books (see Gu, Wu, & Xu, 2015, for a review).

A recently arising metacognitive explanation proposes that computerized environments provide a contextual cue that induces shallower processing than paper environments (e.g., Daniel & Woody, 2013; Morineau, Blanche, Tobin, & Guéguen, 2005). Metacognitive research on reading comprehension has found that JOL reliability is poor (see Dunlosky & Lipko, 2007, for a review).

Rakefet Ackerman Notably, studies provide growing evidence that associates computerized learning with inferior metacognitive processes, particularly with consistent overconfidence and less effective effort regulation (for a review, see Sidi et al., 2017).

Chiara Scarampi

Self-regulated learning needs guidance. Metacognitive scaffolding can support preparatory phases of orientation and planning, monitoring of progress while learning, and retroactive activities such as reflection (Roll, Holmes, Day, & Bonn, 2012). Given that learning and JOL reliability can be improved through self-questioning, appropriate test expectancy, analyzing the task, and delayed summaries (Wiley, Thiede, & Griffin, 2016), it is interesting that screen inferiority could be ameliorated by guiding participants to increase mental effort expenditure. This was achieved by asking participants to proofread, edit, and write keywords summarizing texts' contents (Eden & Eshet-Alkalai, 2013; Lauterman & Ackerman, 2014). Apparently, then, in-depth text processing is the default on paper, whereas on screen an external trigger is required to enhance metacognitive processes leading to enhanced performance (Sidi et al., 2017).

#### References

# References

test. *Metacognition and Learning*, *9*(1), 25–49. doi:10.1007/s11409-013-9110-y

dictions. *Psychological Bulletin*, *95*(1), 109–133. doi:10.1037/0033-29<IP_ADDRESS>

ments: Evidence from patients with lesions to frontal cortex. *Neuropsychologia*, *42*(7), 957–966. doi:10.1016/j.neuropsychologia.2003.11.020

actual solvability, and length on intuitive problem assessments of anagrams. *Cognition*, *146*, 439–452.doi: doi:10.1016/j.cognition.2015.10.019

fects of stimulus size on judgments of learning. *Journal of Memory and Language*, *92*, 293–304. doi:10.1016/j.jml.2016.07.003

# Glossary

# Chapter 7

# Deductive Reasoning

JONATHAN ST. B. T. EVANS

University of Plymouth

A deduction is a conclusion that follows from things we believe or assume. Frequently, we combine some fact or observation with a rule or rules that we already believe.  You immediately infer that Sue is Mary's daughter, although that is not the fact that was presented to you. This means that you must carry around rules such as

If x is the mother of y and y is female, then y is the daughter of x

Of course, I am not saying that you are conscious of this rule or of applying it to make this deduction but it must be there in some form in your brain, together with some mechanism for applying it to facts and observations. In this case, the inference occurs rapidly and effortlessly but this is not always the case with deductive reasoning. Take the case of claiming allowances when completing an income tax return. In this case there may be many rules and their wording may be complex and opaque to those who are not expert in tax law. If your financial affairs are complex, even establishing the relevant facts may be headache. This is why people often pay expert tax advisers to do the reasoning for them.

Deduction has a clear and obvious benefit for human beings. Our memories are limited and our brains can only store so many beliefs about the world. However, if we also hold a number of general rules, then these can be applied to draw out implications as and when they are required. Deduction

is also involved in hypothetical thinking, when we ask 'What if?' questions. An example is science in which theories must be tested against empirical evidence. Scientific theories take the form of rules, often formalised with mathematics. When experimental studies are run, we set up some conditions and then predict the outcome. The prediction is a deduction, which is used to test the theory. For example, climate change scientists have been predicting for the past twenty years or more that warming temperatures would disrupt the jet stream and lead to more extreme weather events. These predictions were calculated from their mathematical models, which is a form of deductive reasoning. Both abnormal jet stream flows and extreme weather events have been observed in recent years with increasing frequency, lending credibility to these models.

For deduction to be useful, it needs to be accurate. This has been recognised in the discipline of philosophy for centuries. Philosophers devised systems of *logic*, whose purpose is to ensure accurate deduction. A logically valid argument is one whose conclusion necessarily follows from its premises. Put simply, this means that in a logical argument the conclusion must be true if the premises are true. If the motherdaughter rule given earlier is true (which it is by convention) and your observation that Sue is female is also correct, then she *must* be Mary's daughter.

Logic provides rules for reasoning. Here are a couple of examples

Modus Ponens Given if x then y, and the assumption of x, y is a valid conclusion

Disjunction elimination Given x or y and not-x, y is a valid conclusion

Modus Ponens is very useful, because it means we can state hypothetical beliefs, which only apply when some condition is met. Some of the conditional sentences we use in everyday life are necessarily true, for example, 'if a number is even and greater than two, it cannot be prime', but most are not. For example, we may advise someone 'if you catch the 8.00 am train then you will get to work on time'. If this is generally true, then it is good advice, but of course the train might break down. The real world rarely allows inferences to be certain, but we nevertheless use conditional statements a great deal because of the natural power of Modus Ponens. A disjunctive statement is an either-or. For example, someone might say 'I will either catch the 8.00 am train or take the bus at 8.10'. If you later learn that they did not catch the train you can deduce that they took the bus instead. Once again, in the real world, the inference will not be certain. The individual may have called in sick and not gone to work at all. But our deduction is valid, given the assumptions on which is based.

There is a tradition in philosophy that logic is the basis for rational thought (Henle, 1962; Wason & Johnson-Laird, 1972). This view held a powerful influence on psychology during the second half of the twentieth century and was responsible for a major method of studying human reasoning, which I will call the deduction paradigm (Evans, 2002). Huge numbers of experiments were run with this paradigm and I will try to summarise their main findings in this chapter. While many important things were learnt about the nature of human thinking and reasoning, a lot of psychologists eventually lost faith in the importance of logic for rational thinking. In recent years, this has a led many to revise their methods and adopt what is called the new paradigm psychology of reasoning. I will explain the new paradigm and some of the findings it has led to at the end of this chapter. For now, I will focus on the deduction paradigm and the theories and findings that are associated with it.

The deduction paradigm tests whether people *untrained in logic* can make valid inferences. The idea behind this is that if logic is the basis for rationality in everyday thinking then everyone should comply with it, not just those who have taken logic classes. So the first condition in this method is to exclude participants with formal training. The next is to present them with some premises, or assumptions, from which a logical deduction can be made. Often a conclusion is also given and people are asked whether it follows or not. Two other instructions are usually given: (1) assume that the premises given are true and (2) only make or endorse a conclusion which necessarily follows from them. Given these instructions, only the form of the argument should matter, not the content. For example, people should always agree that Modus Ponens and disjunction elimination are valid arguments, no matter what we substitute for x and y in the rules given above. By this means, the paradigm assesses whether or not people are logical in their deductive reasoning.

# 7.1 The Deduction Paradigm: The Main Methods and Findings

A small number of experiments on deductive reasoning were published early in the twentieth century (Wilkins, 1928; Woodworth & Sells, 1935), which immediately demonstrated what was to come from the intensive study that occurred from the 1960s onwards. That is to say, people were observed to make frequent logical errors, to show systematic biases, and to be influenced by their beliefs about the content of the premises and conclusions. All of these findings have been replicated many times since using three major methods, or sub-paradigms. These are syllogistic reasoning, conditional inference, and the Wason selection task. In this section I will discuss each in turn, explaining the methods and typical findings.

#### 7.1.1 Syllogistic Reasoning

A syllogism involves two premises and three terms, which I will call A, B and C. This is the most ancient system of logic, devised by Aristotle. You may

have come across the famous syllogism 'All men are mortal, Socrates is a man, therefore Socrates is mortal.' Classical syllogisms have statements in four *moods*, shown in Table 7.1 (a). These statements can be used for either the first premise, the second premise, or the conclusion in any combination. Let us consider them in turn.

Figure 7.1 shows diagrammatically several different models for the relation between two categories, A and B. When we examine the different statements in Table 7.1 (a) we see that most of them are ambiguous and can be represented by at least two different models. For example, All A are B would be true for a model of identity – All men have Y chromosomes – or where B includes A – All boys are male. No A are B is unambiguous; it can only refer to a model of exclusion. Some A are B is highly ambiguous – it is true in all models except exclusion. Finally, Some A are not B is true for exclusion but also for a model in which A includes B – Some males are not boys. This gives us a clue to the complexity of syllogistic reasoning, as we have to take account of all possible ways that the categories could be related. Moreover, when we combine two premises, we have to consider the ways in which all three categories A,

Table 7.1: The structure of classical syllogisms.

#### (a) Mood of premises

#### (b) Figure of syllogism

*Note*: The letters A, E, I and O are classically used as abbreviations for the four moods of the premises.

B, and C could be related. For the argument to be valid, its conclusion has to be true in all models of this three-way relationship that the premises allow.

A fallacy is an argument whose conclusion need not be true, given the premises. A basic finding with syllogistic reasoning is that participants endorse many fallacies. This has been reported by many authors and confirmed in the one study (to my knowledge) that presented every possible combination of premises and conclusions for evaluation (Evans, Handley, Harper, & Johnson-Laird, 1999). But these mistakes are not random – there are systematic biases in syllogistic reasoning. Consider the following syllogism:

All A are B

#### All B are C

#### Therefore, All C are A

This is a fallacy: the conclusion does not necessarily follow. Yet in the study of Evans et al. (1999), 77% of participants (university students) said that the conclusion necessarily followed from

the premises. This is really odd when you consider the set relationships involved (see Figure 7.2). Surely, the most likely situation that describes the premises is the model to the left, showing that A is a subset of B and B a subset of C. For example

All Alsatians are dogs; all dogs are mammals

But in that the case, the conclusions endorsed would be 'All mammals are Alsatians,' which is obviously false. The conclusion All C are A would only be true in the second model, where A, B, and C are all identical, a most unusual state of affairs. This is a finding which you only get with abstract materials, where letters are used to represent categories. But why does it occur? It is consistent with a very old claim called the *atmosphere effect*: participants are inclined to accept conclusions whose mood matches that of the premises. In the same study, only 47% of participants said the following syllogism was valid

All A are B

All B are C

Therefore, Some C are A

This is stranger still because Some C are A has to be true whenever All C are A. Not only that, but

Evans Deductive Reasoning

the conclusion is actually *valid* in this case. You can verify that by examining the models of the premises shown in Figure 7.2. Of course, the mood of the conclusion does not match that of the premises here, so it does conform with the atmosphere effect. In fact, atmosphere is consistent with many but not all responses observed in syllogistic reasoning tasks (Evans, Newstead, & Byrne, 1993). Another known biasing factor is the figure of the syllogism, which is the order in which terms are arranged (Table 7.1b). This also affects people's perception of validity.

There are a number of high-profile theories of syllogistic reasoning based on different principles and giving broadly accurate explanations of the data (for reviews, see Evans et al., 1993; Manktelow, 1999). When realistic content is introduced, however, other factors come into play, especially belief bias. Consider the following syllogism:

No addictive things are inexpensive

Some cigarettes are inexpensive

Therefore, some addictive things are not cigarettes 71%

A major study which established the influence of beliefs was that of Evans, Barston, and Pollard (1983). Over three experiments, they found that

Figure 7.1: Models of relations between two categories, A and B.

Figure 7.2: Models of relations between three categories, A and B and C consistent with the premises All A are B, All B are C.

71% of participants agreed that this syllogism was valid, that is, that the conclusion must be true if the premises are true. Now consider this syllogism presented in the same study:

No millionaires are hard workers

Some rich people are hard workers

Therefore, some millionaires are not rich people 10%

In this case, only 10% thought the syllogism was valid. But if you look carefully you can see that both syllogisms have the same logical form. The syllogism is actually *invalid*. The key difference between these two is that the first realistic version has a conclusion which is believable (we know that there are other addictive drugs) but the second has a conclusion which is unbelievable – millionaires are rich by definition. When valid arguments were used, people also more often thought they were valid if they believed the conclusion (89%) than if they did not (56%), so there is a belief bias for valid arguments as well, although not as a strong. These findings have been replicated many times since (for a review see Klauer, Musch, & Naumer, 2000).

#### 7.1.2 Conditional Inference

Conditional statements, also known just as conditionals, have the form, if p then q. We use many such statements in real life for all kinds of purposes. Here are some examples:

*Causal*: If you heat water sufficiently, it will boil.

*Prediction*: If you vote Republican, you will get your taxes cut.

*Tip*: If you study hard, you will pass the examination.

*Warning*: If you miss the 8.00 am train, you will be late for work.

*Promise*: If you wash my car, I will give you ten dollars.

*Threat*: If you stay out late again, you will be grounded.

*Counterfactual*: If you had putted well, you would have won the match.

Philosophers have long studied conditional statements, considering them of particular importance for human reasoning, writing many books on the subject (an excellent review of philosophical work

Table 7.2: The four main conditional inferences.

is given by Edgington, 1995). A great deal of work in the psychology of reasoning has also focussed on conditional statements (for a recent review see Nickerson, 2015). I wrote an entire book on 'if' myself, collaborating with a philosopher to cover the perspectives of both traditions—philosophy and psychology (Evans & Over, 2004). The reason they are so important is that they are central to a unique human facility which I call *hypothetical thinking* (Evans, 2007). That is the ability to imagine how things might be in the future or how they might have been different in the past.

Standard logic provides an account of how we should reason with conditionals. Some of this standard account is disputed by both philosophers and psychologists, but all are agreed about the four inferences shown in Table 7.2. We have already encountered Modus Ponens (MP) as an example of a valid deductive argument. Imagine a situation where cards have a letter written on one side and a number on the other. Then we can express a conditional hypothesis such as

#### If the letter is B, then the number is 3

For conditional inference, we need to assume that the conditional is true. This is the *major premise* of the deductive argument. The *minor premise* is an assertion that either the first or second part of the conditional is true or false, leading to the four

arguments illustrated in Table 7.2. For example, if we suppose that the first part is true – the letter is B – then it follows by MP (Modus Ponens) that the number is 3. The other valid argument that can be made is Modus Tollens (MT). Suppose that the number on the card is not a 3. Then it follows logically that the letter is not a B. Why? Because the conditional is true, so if there had been a B on the card, then there would also have to have been a 3. This argument is equally valid, if less immediately obvious. What all psychological studies of such abstract inferences show is that the MP inference is made nearly 100% of the time, while the MT inference is only endorsed about 60% of the time in the same experiments (see Figure 7.3).

The other two arguments shown in Table 7.2 are fallacies. That is, the conclusions given do not *necessarily* follow. If we assume that the number is 3, it does not necessarily follow that the letter is a B (Affirmation of the Consequent, AC), because the conditional does not say that only B cards can have 3s. Similarly, if we know that the letter is not B, we cannot say that the number is not a 3 (Denial of the Antecedent, DA). And yet we see that university students endorse both of these fallacies about 40% of the time (see Figure 7.2). A likely reason for this is that people are making inferences that are *pragmatically* rather than logically implied. For example, the Denial of the Antecedent fallacy

Figure 7.3: Percentage frequencies of endorsement of the four conditional inferences with abstract materials (weighted average of 11 studies reported by Evans et al. 1983, Table 2.4, total N = 457). Key: MP – Modus Ponens, DA – Denial of the antecedent, AC – Affirmation of the consequent, MT – Modus Tollens.

is endorsed much more often for conditional statements that express causal relationships or are used to make threats or promises (Newstead, Ellis, Evans, & Dennis, 1997). Consider the promise: if you wash my car, I will give you ten dollars. Most people will say that if you suppose the car is not washed then the ten dollars will not be paid (DA). Although not logically implied this makes every sense in terms of the pragmatics of everyday conversation. The speaker wants the car washed and is providing an incentive: it would make no sense to pay someone who did not wash the car. A tip is weaker than a promise pragmatically because the speaker suggests an action will produce a desired outcome but has no actual control over it. An example might be 'if you wash Dad's car, he will give you ten dollars.' The frequency of endorsing even Modus Ponens drops significantly when a tip is substituted for a promise as do *all the other* conditional inferences.

There are many experiments published on how beliefs influence conditional inferences, far too many to discuss here (for reviews, see Evans et al., 1993; Evans & Over, 2004; Nickerson, 2015). All of them show that belief affects conditional reasoning in very significant ways when logically equivalent

inferences are presented with different problem content.

# 7.1.3 The Wason Selection Task

Peter Wason was a British psychologist who is regarded as the father of the modern psychology of reasoning. Most of his influential work was published between about 1960 and 1980, including a book which helped to identify the psychology of reasoning as a research field (Wason & Johnson-Laird, 1972). Of lasting importance has been the invention of several novel tasks for studying reasoning, the most influential of which has been the four-card selection task. Strictly speaking, the selection task does not meet all the definitions of the deduction paradigm as I have given them, as it involves hypothesis testing as well as reasoning. However, the task is focussed on the logic of conditional statements and has been extensively studied by the same research community that has studied conditional inferences and other more conventional reasoning tasks. It has also been used to address broadly the same set of theoretical issues

A typical standard abstract form of the problem is presented in Figure 7.4. The generally accepted cor-

Figure 7.4: The standard abstract Wason selection task.

rect answer is to choose the A and 7 cards, although few participants make these selections. Most people choose either the A card alone, or the A and the 3. Wason pointed out that the conditional statement can only be falsified if there is a card which has an A on one side and does not have a 3 on the other. Clearly, the A card must be turned over because it must have a 3 on the back, and if it does not, disproves the claim. Similarly, the 7 card – which is not a 3 – could have an A on the back, which would also disprove the statement. Turning the 3 is unnecessary, as it cannot disprove the rule. It need not have an A on other side.

Why do people choose A and often 3 and ignore the 7? Wason originally suggested that they had a verification or confirmation bias. They were trying to prove the rule true rather than false, and hence looking to find a confirming combination of A and 3. In support of this account, if you ask people to give written justifications for their choices, they typically say that they were looking for 3 when turning the A and vice versa because this would make the rule true (Wason & Evans, 1975). However, in an early research paper of my own, I showed that this account cannot be right. The trick is to include a negative in the second part of the conditional as in the example shown in Figure 7.5. When the rule says, as in the

example, that if there is G on one side of the card, then there cannot be a 4 on the other side of the card, most people choose the G and 4 cards. But these choices do not verify the rule, they correctly falsify it. The combination that falsifies this statement is, of course, G and 4. Once again, participants say that they are turning the G to find a 4 and vice versa (Wason & Evans, 1975) but now in order to make it *false*. It is as though the negative has helped them to understand the logic or the problem.

The effect here is called *matching bias*. People tend to choose the cards which match those named in the conditional, whether or not negations are present. But these negations affect the logic of the task, so it is a puzzling finding. Matching bias is another example of a cognitive bias, like the atmosphere effect, which operates with abstract materials. With the other methods, I showed that the introduction of realistic materials makes a big difference to responding. The same is true of the selection task. It was thought initially that simply using realistic materials made the problem a lot easier with higher rates of correct selections (Wason & Johnson-Laird, 1972). This was known as the *thematic facilitation effect*. However, it was later shown that the versions that make the task really easy include a subtle change to the logic. An example, known as the 'drinking age

Figure 7.5: The abstract Wason selection task with an added negation.

rule,' is shown in Figure 7.6. People are first of all given a short context. In this case, they are asked to imagine that they are police officers enforcing rules. Then the rule is given which requires beer drinkers to be over 18 years of age. Now most people will check the beer drinkers and those *under 18* of years of age. This is correct as only underage drinkers can violate the rule. Experiments which give the drinking age rule find much higher rates of correct answers than with the standard abstract version.

As later authors pointed out, problems like the drinking age rule change the task from one of indicative logic (concerned with truth and falsity) to one of deontic logic, concerned with obeying rules and regulations. A number of different theoretical accounts have been offered to explain why the deontic version is so much easier. One idea is that we acquire and apply *pragmatic reasoning schemas*: rules which apply in certain contexts and can be instantiated with the content of a particular problem (Cheng & Holyoak, 1985). So people might solve the drinking age rule because they have a permission schema such as 'if an action A is to be taken, then condition C must be filled', which could be instantiated as A = drinking beer and C = 18 years or age or older. The schema tells them violations of this rule occur when the action is taken without the precondition being

filled. Other proposals included the use of innate evolved rules for social exchange (Cosmides, 1989), interpreting the problems as a decision-making task in order to maximise perceived benefits (Manktelow & Over, 1991) and the role of pragmatic relevance for different forms of conditional statement (Sperber, Cara, & Girotto, 1995).

# 7.2 Theoretical Issues in the Psychology of Deduction

Having described the main methods and typical findings in the study of deduction, I now turn to some broader theoretical issue and arguments that have arisen.

# 7.2.1 How We Reason: Rules or Models?

Despite the frequency of errors and biases, people do show some level of deductive competency on reasoning tasks, especially those of higher cognitive ability (Stanovich, 2011). For example, people endorse far more inferences that are valid than invalid on both syllogistic and conditional inference tasks. Some psychologist have focussed on the competence rather than the errors and asked questions

Figure 7.6: The Deontic selection task: Drinking age rule.

about the mechanisms by which people draw deductions. One approach is often described as mental logic but should more accurately be described as mental rule theory (Braine & O'Brien, 1998; Rips, 1994). Traditional logics are usually presented as rules, but other techniques for generating valid deductive inferences are available. The term 'mental logic' was devised to distinguish the logic inside people's heads from that in the philosopher's textbooks. The idea is that ordinary people reason by built-in logical rules. However, the psychological authors were mindful from the start of certain psychological findings. For example, in proposing a mental logic account of conditional inference, psychologists were well aware that people find Modus Ponens a lot easier than Modus Tollens. In standard logic, these would both be primitive rules of equal standing, but that cannot be the case in a mental logic.

Mental logicians have tried to address this problem by proposing only Modus Ponens is a simple rule allowing direct inference. Modus Tollens can be drawn but by an indirect reasoning procedure called *reductio* reasoning. In this kind of reasoning, one makes a supposition p and tries to show that this leads to contradiction, q and not-q. Since a contradiction cannot exist in logic, the supposition must

be false, hence not-p follows. Consider our earlier examples of a conditional which applies to cards with a letter on one side and a number on the other

If the letter is B, then the number is 3

If people are told there is a B, then they can immediately apply their built-in rule for Modus Ponens and conclude that there is a 3. When told there is not a 3, however, they do not have a rule for Modus Tollens that can be applied in the same way. Instead, they have to reason as follows:

'If I imagine there is a B on the card, then there must be a 3. But I have been told there is not a 3 which is a contradiction. So I must have been wrong to suppose that there was a B on the card. Hence, I can conclude that there is not a B.'

This indirect reasoning is harder to execute and more prone to errors, explaining the lower acceptance rate of Modus Tollens. Hence a fully specified mental logic account consists of a set of direct rules of inference together with indirect reasoning procedures and can be implemented as a working computer program (Rips, 1994).

For many years now, rule-based mental logics have had a major rival, which is mental model theory, championed by Phil Johnson-Laird (1983, 2006; Johnson-Laird & Byrne, 1991) and followed

and supported by many other psychologists. This theory also proposes that people are deductively competent in principle, but fallible in practice, but does not rely on the application of mental rules. The core of the theory is the idea that people reason about possibilities, which are states of the world that might be true or false. These possibilities are represented by mental models. When the premises of an argument are presented, people are supposed to construct mental models to represent all possibilities and then reason as follows:

Consider the inference of disjunction elimination, discussed earlier. Given the major premise Either the letter is B or the number is 3, people construct the following models as possibilities:

B

3

B 3

Each line here represents a separate mental model. So this reads as: one possibility is that there is a B, the second that there is a 3 and the third that there is both a B and a 3.

Now given the minor premise, the number is not 3, the last two models are eliminated leaving only the possibility of B. Hence, people will conclude B as a correct deduction but without having any rule of disjunction elimination for the inference. The model theory of conditionals (Johnson-Laird & Byrne, 2002) is more complex and controversial (Evans, Over, & Handley, 2005). Consider the statement

If there is a B, then there is a 3

The full set of possibilities for this statement, according to the published theory, is the following:

Given these possibilities, the minor premise B eliminates all but the first model, so the conclusion 3 follows (Modus Ponens). The minor premise not-3, eliminates all the last model, so that not-B follows (Modus Tollens). However, like the mental-logic theorists, Johnson-Laird and Byrne were well aware of the relative difficulty of Modus Tollens. So they actually proposed that people initially represent the conditional statement as follows:

[B] 3

. . .

The first model means that in all cases of B (meaning of []), there is a 3. The ellipsis '. . . ' means there are other possibilities. So if B is presented, people can immediately do Modus Ponens and conclude 3. However, if not-3 is presented, then they have to 'flesh out' the models to the fully explicit set given above in order to make Modus Tollens.  The theory has been applied to many other types of reasoning, including with syllogisms.

I think it fair to say that both mental rule and mental model theory are firmly rooted in the traditional deduction paradigm, as they both put an account of logical competence foremost and deal with effects of beliefs and pragmatics as add-ons. Whether belief rather than logic should be the focus of psychological accounts of reasoning is precisely the issue for researchers in the new paradigm, to which I return later. We next consider dual-process theory which is not directly concerned with how logical reasoning occurs, but rather with the idea that such reasoning competes with other kinds of cognitive processes of a more intuitive nature.

# 7.2.2 Dual-process Theories of Reasoning

In 1982, I published my first book which was a review of the psychology of deductive reasoning. Even at that time, with many of the key studies in the field yet to be conducted, it was clear that logical errors were frequent, and there was much evidence of systematic biases and belief-based reasoning. I was struck by what seemed to be two factors influencing many different reasoning tasks. People's choices were indeed influenced by the logic of the problems, just as had been originally expected, but also by non-logical factors that were completely irrelevant to the task such as atmosphere or matching bias. But two-factor theory is descriptive and provides no real explanation of the cognitive processes that underlie our observations.

An important theoretical leap is from dual sources to dual processes. What if the two factors reflect quite different mental processes? I mentioned earlier that Wason and Evans (1975) observed that when matching bias cued a correct choice on the selection task, people appeared to understand the logic of the problem and the importance of falsification. But in the standard version, they talked as though they could prove the rule true. In this early paper, we suggested a distinction between unconscious Type 1 processes responsible for the matching selections and conscious Type 2 reasoning, which simply served to rationalise or justify the unconsciously cued cards. The radical suggestion was that actual choices were determined by one kind of process but the verbal justifications by something entirely different. The next important step, in work also described earlier, was the belief-bias study of Evans et al. (1983). What we observed there was that syllogistic reasoning was influenced heavily by both the logic of the syllogism and the believability of conclusion. We showed that the two factors were in conflict and that individuals would sometimes go with logic and other times with belief.

The linkage with the Wason and Evans work was not made immediately but in retrospect the view developed was that Type 2, explicit (slow, reflective) reasoning processes were responsible for the preference for valid over invalid conclusions. However, these competed with Type 1 (fast, intuitive) processes, which favoured believable over unbelievable conclusions. So on tasks other than the selection task, at least, Type 2 reasoning could solve problems and not just rationalise intuitions. (Later research showed that Type 2 processes have a role in the selection task choices as well.) As different dual-process accounts were developed over the next quarter of a century, there was a particular emphasis on the idea that Type 2 reasoning was responsible for logically correct answers and Type 1 processing for non-logical effects, such as matching and belief bias (see Evans, 2007; Stanovich, 1999; see also Chapter 10, "Decision Making", for application of dual-process theory to decision making).

A large individual-differences programme conducted by Keith Stanovich and Richard West, who showed that on a wide variety of reasoning and decision-making tasks, cognitive ability or IQ (see Chapter 14, "Intelligence") was strongly correlated with the ability to give the correct answer. The theoretical idea here is that people with higher IQs also have higher working memory capacity and are therefore more able to manipulate mental representations of premises and conclusions in order to reason logically. In fact, the engagement of working memory is now considered a defining feature of Type 2 processing (Evans & Stanovich, 2013). Other methodologies were developed that supported this view. For example, if people are given a very short time to respond, they are less likely to give the logical answer and were more likely to show a bias, such as matching or belief. Similar results occur if a working-memory load has to be carried while reasoning (for reviews see Evans, 2007; Evans & Stanovich, 2013). However, Stanovich and West also showed that general intelligence was not the only individual difference factor in human reasoning. In particular, people vary in rational thinking disposition which measures the inclination to accept an intuitive answer or to check it out by high effort reasoning.

Some dual-process theorists have suggested that there are ruled-based (Type 2) and associative (Type 1) processes that operate in parallel (Sloman, 1996) but more popular among deductive-reasoning researchers is the idea that fast intuitive (Type 1) answers come to mind immediately and are subject to checking and possible revision by slower, reflective (Type 2) processes that follow (Evans & Stanovich, 2013; Kahneman, 2011). This leads to the important question of why it is that some intuitive answers are more carefully checked than others. A hot topic in the field right now is whether people's initial answers are accompanied by feelings of rightness, which help them decide whether to accept the intuitive answer or whether to check it out with careful reasoning (Hot Topic, see also Chapter 6, "Metacognition").

# 7.3 The New Paradigm Psychology of Reasoning

The deduction paradigm was developed about 50 years ago to assess the then-prevalent view that logic was the basis of rational reasoning. As evidence of logical errors, cognitive biases, and belief-based reasoning accumulated, this presented a clear problem both for psychologists and for philosophers who became aware of the findings of research on deduction as well as other kinds of human reasoning with similar findings. The problem was that, by the original assumptions, people were turning out to be irrational. Peter Wason, for example, was quite clearly of the view that people were illogical and therefore irrational (see Evans, 2002). In a famous paper, the philosopher Jonathan Cohen argued that people were in fact inherently rational and that psychological experiments could never prove otherwise (Cohen, 1981). He suggested that the experiments were unrepresentative or being misinterpreted. He also pointed out that standard logic, for example, is not the only kind that logicians have offered. There could be alternative normative accounts of how to be rational. A normative theory is one of how people *ought* to reason. Subsequently, a number of psychologists engaged with the issue of what counts as rational reasoning (e.g. Evans & Over, 1996; Stanovich, 1999).

A major issue is whether traditional logic provides the correct standard for human reasoning. One major research programme, that of Mike Oaksford and Nick Chater, has disputed this from the start (Oaksford & Chater, 2001, 2007). Their first important contribution was an alternative normative account of the Wason selection task, arguing that the typical answer can be seen as rational from a decision-making perspective (Oaksford & Chater, 1994). Like Cohen, they took the view that human behaviour must be rationally adapted to the environment and if a standard normative account does not explain it, then we should look for another. They have presented various theories of reasoning tasks based on probability theory and decision theory. Naturally this approach is controversial and has been branded Panglossian by some authors (Stanovich, 1999). Pangloss was a fictional philosopher in a novel by Voltaire who as prone to say 'all is for the best in the best of all possible worlds'!

The essence of the new paradigm is that people naturally reason from their beliefs about the world and that this should not be treated as an error or cognitive bias. Strong deductive reasoning instructions are artificial: they require people to ignore what they believe for the sake of the experiment. Other methods have been explored. For example, people can be asked what inference follows from some information and allowed to express degrees of belief in their conclusions. A key feature of the new paradigm is the proposal of the *suppositional conditional*, also known as the probability conditional (Evans & Over, 2004; Oaksford & Chater, 2001). The conditional statement of standard logic is equivalent to a disjunction. For example,

If the letter is B, then the number is 3

is true except when we have a B and not a 3. Hence it is equivalent in meaning to

Either the letter is not a B or the number is a 3

This is what logicians term the *material conditional*. However, many philosophers have rejected the material conditional as an account of the ordinary conditional of everyday language (Edgington, 1995). This is because it leads to unacceptable inferences. The material conditional, if p then q, is true whenever p is false or q is true. So the following statements must be true

If President Trump is French, then Paris is the capital of the USA

#### If 2+2 = 5, then 3 is a prime number

It is clear that no normal person would endorse these statements.

If the ordinary conditional is not material, then what is it? The philosopher Ramsey famously argued that belief in the ordinary conditional if p then q, is in effect the probability that q will be true if p is (Ramsey, 1931/1990). He also suggested that we do this by adding p to our current stock of beliefs and arguing about q on that basis. This is known as the Ramsey test and we suggested that conditional statements are suppositional – they depend on the supposition of p (Evans & Over, 2004). Let us consider some examples

If teachers' pay is raised, then recruitment will increase

Many people will agree with this statement or assign a high probability to it. They do this by supposing first that teacher's pay is in fact raised and then using other beliefs to calculate the likelihood that they will prove easier to recruit. They may be aware that recruitment has been difficult in recent years and that one factor is almost certainly that salary levels have fallen behind those of workers in other professions. So, they believe that financial incentive will help address the issue. In doing this, they ignore any beliefs they have about what will happen if pay is *not* increased, which they regard as irrelevant. The Ramsey test is also related to findings with Modus Ponens mentioned earlier. When people believe a conditional statement to be true, they also believe that q is probable when p is assumed and so will readily infer q from p. Consider, however, this statement

If the global economy grows then there will be less poverty and starvation in the world

The Ramsey test will not produce a high level of confidence in this conditional for many people. They may believe, for example, that the growth in the global economy increases wealth for rich individuals and rich countries but is not likely to be distributed to the third world. where most of the poverty and starvation is concentrated. If their belief in the conditional is low, they will also be reluctant to draw inferences from it, even the apparently obvious Modus Ponens. There is now much evidence that, with real-life conditionals like these, people do indeed assign very similar belief levels to if p then q as they do to the probability of q given p (e.g. Over, Hadjichristidis, Evans, Handley, & Sloman, 2007). People act as though the conditional only applies on the supposition that p is true, in people's minds, and is otherwise irrelevant. This is not consistent at all with the material conditional of standard logic.

The essence of the new paradigm is to view beliefbased reasoning as natural and rational, rather than to consider it necessarily a source of bias. The new paradigm is, however, not yet as clearly defined as the old. A lot of authors are pursing alternative normative theories of reasoning to standard logic or seeking explanations in terms of Bayesian decision theory – a system which takes account of subjective beliefs. Others have argued that the new paradigm should concern itself less with normative theory and more with describing what people actually do when they reason. One thing that all agree upon is that the traditional standard logic is neither a good account of how we actually reason, nor of how we ought to reason.

#### Summary

#### Review Questions

Hot Topic: Feelings of rightness in reasoning and implications for dualprocess theory

Jonathan Evans

The standard dual-process approach assumes that an intuitive answer to reasoning (and decision making) problems comes to mind quickly and rapidly due to Type 1 processing. It is then subject to checking by Type 2 processes, which may rationalise the intuitive answer or substitute more complex reasoning to provide a different answer. An important question is why we sometimes rely on the initial intuition with minimal reasoning and other times engage Type 2 processes. Some known factors are the processing style of the individual and time available for thinking. However, an additional factor has been proposed by Valerie Thompson and her colleagues – metacognitive feelings. The initial intuition comes with a *feeling of rightness (FOR)*, which could determine whether we accept it or expend effort on reasoning (Thompson,

Prowse Turner, & Pennycook, 2011). Thompson has claimed in several papers that FOR is the key factor in determining whether extensive Type 2 processing occurs.

Thompson invented a methodology called the two-response task (Thompson et al., 2011). Participants are given a reasoning or decision task and asked to generate an initial answer as quickly as possible without reflecting on it. They then rate the degree to which they are confident that the answer is correct – the FOR. Following this, they are then asked to think again about the problem, taking as long as they like. After this, they again give a response to the problem which may or may not be the same as first answer. Using a range of different tasks, the following pattern was established: when FOR is high, the initial answer tends to be given quickly, rethinking time tends to be short and second response usually matches the first. In other words, when we are intuitively convinced of our original answer, we expend little effort in trying to check or correct it. Conversely, when FOR is low, we are more likely to take time rethinking the problem and to change our original answer.

There are some unresolved difficulties with this account. First, none of the studies on this report a relation between FOR and actual accuracy. We are no more likely to be confident of a correct answer than a biased one and we are just as likely to change a right answer to a wrong one after reflection as the other way around. So if FOR has evolved to help us make good decisions, using our cognitive resources effectively, why is it not helping us identify errors? In fact, the opposite seems to be true. Matching bias and belief bias, for example, have been shown to be supported by false feelings of rightness. Matching cards and believable conclusions *feel* right, even when they are wrong. Another difficulty is that there is no direct evidence for a casual connection between FOR and Type 2 reasoning as Thompson and colleagues claim. Everything is in fact correlational. All we really know is that answers with high FOR are also made more quickly, thought about less and changed less often.

There are also some recent empirical findings which raise difficulties for the dual-process story here. On relatively simple tasks, when a correct choice is put in conflict with a bias, there is evidence that this conflict is detected very rapidly by the brain, indicating that some kind of 'logical intuition' (De Neys, 2014) is available to conflict with the bias. Recently, using the two-response task with syllogistic reasoning, Bago and De Neys (2017) showed that most people who are correct at time 2 were also correct at time 1. There was little evidence for people correcting intuitive responses by a period of reflection, as might be expected with Type 2 intervention. However, it is possible that studies of this kind provide a misleading impression, as the tasks are relatively simple. Hence, it could be that 'logical intuitions' arise from Type 1 rather than Type 2 processing as these solutions do not require the engagement of working memory on the tasks used (Evans, 2018). As is the nature of hot topics, there is as yet no clear resolutions to the questions I have raised, and research continues.

#### References

Thompson, V. A., Prowse Turner, J. A., & Pennycook, G. (2011). Intuition, reason, and metacognition. *Cognitive Psychology*, *63*(3), 107–140. doi:10.1016/j.cogpsych.2011.06.001

### References

ference. *Psychological Review*, *109*(4), 646–678. doi:10.1037//0033-295x.109.4.646

#### Evans Glossary

# Glossary

# Chapter 8

# Inductive Reasoning

#### JANET E. DAVIDSON

Lewis & Clark College

Inductive reasoning involves inferring likely conclusions from observations or other forms of evidence. For example, if your car starts making loud clunking noises, you might conclude that it probably has a serious and expensive problem. Without reasoning in this manner, the world would be a more primitive and confusing place. It would be impossible to develop scientific theories, forecast the weather, persuasively argue legal cases, learn from mistakes, make predictions about how a best friend will behave around strangers, use previous experiences to help transition to a new job, or think critically before making important decisions. Furthermore, people would probably be less creative (Goswami, 2011; Vartanian, Martindale, & Kwiatkowski, 2003). It even takes inductive reasoning to predict how life would be different without it. In short, this form of reasoning expands and deepens world knowledge, helps social interactions, and allows us to adapt to new environments (Heit, 2000; Rhodes, Brickman, & Gelman, 2008).

As implied above, induction is viewed as the most common form of reasoning that people use in their daily lives (Hayes & Heit, 2017). It can occur so automatically that we are often unaware of quickly using examples, observations, and other existing knowledge to draw conclusions or make predictions about the future. It might seem odd that we frequently rely on inductive reasoning, given that the conclusions from it are never guaranteed to be correct. The data on which they are based is always po-

tentially incomplete or perhaps even flawed, which means the conclusions at their very best can only have a high probability of being right. There is always the chance that they will need to be modified or even rescinded in the future after new evidence is acquired.

Although induction never provides definitive answers, we habitually use it for two primary reasons related to being human. One, we categorize, infer causality, and reason by analogy in an attempt to explain and manage almost everything that happens around us (Feeney & Heit, 2007). For example, people who live near different kinds of dogs might use size, breed, and amount of barking to infer which ones will be friendly and which ones to avoid. Second, we reduce our uneasiness about an uncertain future by using past experiences to predict upcoming events or outcomes (Murphy & Ross, 2007). For example, if you take a new course from a professor who taught two of your other courses, you might reasonably assume that the same study skills that worked well for you in the other two courses will work well in this one.

Why is it important to learn about inductive reasoning? Knowledge about this topic provides us with insight into how humans use limited data to make rational inferences and how, across our lifespans, we generalize from the known to the unknown (Hayes & Heit, 2017). On a personal basis, it helps us learn how to construct strong persuasive arguments that could convince others to adopt our point

of view (Jones, 2013). Additionally, induction is a major component of other fundamental cognitive activities, such as decision-making, categorization, and similarity judgments (Heit, 2007). In other words, we cannot comprehend the full-range of how humans think and behave if we do not understand when and how inductive reasoning is performed.

Given that inductive reasoning is a central part of being human, it has been examined through a wide variety of approaches. If you are a philosopher like David Hume (1739), you might conclude that inductions are a questionable habit of the mind because using past experiences to predict an unknown future is not logically justifiable. In other words, it is not rational to assume that life twenty years from now will closely resemble the world today. Furthermore, according to Goodman's new riddle of induction, if there is more than one possible future, it is not clear how best to distinguish which one to select (Goodman, 1983). Goodman's answer to his own riddle is that we make projections that are entrenched or well established simply because they are familiar and may have worked in the past. However, there are several psychological approaches to inductive reasoning that are data-driven and examine induction through a wide range of problems, methodologies, models, and developmental perspectives. This rich collection of research has increased our knowledge about the cognitive processes used to reach probabilistic conclusions and how these processes and their regularities relate to other forms of thinking and problem solving (Heit, 2007).

This chapter is divided into five sections. The first compares induction with deduction, the other commonly used type of reasoning. It then examines the attributes that help create strong inductive arguments, followed by descriptions of some different forms of induction. The fourth section reviews how inductive reasoning develops in children. Finally, the chapter's main points are summarized.

# 8.1 Comparing Inductive Reasoning with Deductive Reasoning

In the past, inductive reasoning has primarily been understood by contrasting it with deduction (Heit, 2007; see Chapter 7 for an in-depth review of deductive reasoning). Inductive reasoning is sometimes described as "bottom-up" logic because specific observations are often used to draw general conclusions or principles that explain the evidence (Johnson-Laird, 2000). For example, after observing that students who show up on time for my classes tend to perform better than ones who arrive late, I might induce that effective time management is a crucial component of academic success. In contrast, deductive reasoning is sometimes defined as the opposite because it often uses "top-down" logic to reason from general principles to derive specific conclusions (Johnson-Laird, 2000). For example, given the premises that every first-year student at my small college must live on campus and Brenda is a first-year student, I deduce that she lives on campus, which means I know how to track her down.

Table 8.1: Key differences between inductive and deductive reasoning.

However, it is important to note that recently the distinction between bottom-up and top-down processing is viewed by some researchers as too simplistic because it does not apply to all cases of induction and deduction (Feeny & Heit, 2007). For example, inductive reasoning sometimes results in specific conclusions. Consider the following problem: "It rained in Seattle yesterday. It rained in Seattle today. Will it rain in Seattle tomorrow?" This scenario requires the solver to determine a probabilistic conclusion that is specific rather than general. Furthermore, there are problems that some people solve inductively and others solve deductively, which means that problem type cannot be used to determine which form of reasoning is being used. Consider, for example, the task of buying a new car. One individual might observe which models are commonly or rarely found in car repair shops before inducing which type of car seems to need the least amount of mechanical work. Another individual might use the premises that "All cars made in Japan are good cars and Toyotas are made in Japan" to deduce that a Toyota is a good car that would be worth buying. Evidence that some problems can be solved either inductively or deductively has resulted in the process view of reasoning (Heit, 2007). Instead of the traditional procedure of using type of problem to determine the form of reasoning being applied, the focus is on the mental processes that each individual employs.

What are the current key differences between inductive and deductive reasoning? Unlike induction, deduction can be independent of external knowledge of the world or it may even contradict such knowledge (Goswami, 2011). The conclusion is completely derivable from the premises and additional information is not required. Consider, for example, the following problem: "All dogs fly. Fido is a dog. Does Fido fly?" The correct answer that Fido flies is unsound and counterfactual but logically valid because the premises, despite being false, require the conclusion to be logically true. If the problem had been "No dogs fly. Fido is a dog. Does Fido fly?" the correct answer that Fido does not fly is sound because it is logically valid and the premises, in reality, are true. In contrast, inductive arguments are dependent on world knowledge rather than on formal rules of logic and they are viewed on

a continuum of weak to strong, rather than on the dichotomy of logically valid or invalid (Foresman, Fosl, & Watson, 2017). Extremely weak arguments have such little support that conclusions drawn from them are quite unlikely to be true. Ones that are quite strong are based on relevant, substantial, and compelling evidence. However, even if the premises or arguments are accurate and convincing, we cannot know that new information will be not be found that will overturn our earlier conclusions. In other words, inductive conclusions can be thought of as educated guesses based on our current knowledge. Deductively valid conclusions are not guesses; they are guaranteed to be logically true. Furthermore, inductive reasoning tends to happen more quickly, intuitively, and automatically than deductive reasoning, which often requires more conscious, analytical processing (Heit & Rotello, 2010). Some research has also found more activation in the brain's left prefrontal cortex during inductive reasoning than during deductive reasoning (Hayes, Heit, & Swendsen, 2010). Table 8.1 summarizes key differences between these two forms of reasoning.

There are several similarities between induction and deduction that deserve recognition. For example, both involve evidence, logic, working memory, and are central to critical thinking (Foresman et al., 2017; Süß, Oberauer, Wittmann, Wilhelm, Schulze, 2002). Both are used in the scientific method. As John Steinbeck (1954) describes,

Everyone knows about Newton's apple. Charles Darwin and his *Origin of Species* flashed complete in one second, and he spent the rest of his life backing it up; and the theory of relativity occurred to Einstein in the time it takes to clap your hands. This is the greatest mystery of the human mind–the inductive leap. Everything falls into place, irrelevancies relate, dissonance becomes harmony, and nonsense wears a crown of meaning. (p. 20)

Although Steinbeck undoubtedly over-estimated the frequency of true inductive leaps, inductive reasoning is used to form hypotheses and theories that advance scientific knowledge. However, this is not nearly enough; scientists then need to use deductive

reasoning to test their hypotheses and theories on specific situations in order to verify their accuracy. In addition, both forms of reasoning are continuous across our lifespans and are susceptible to similar heuristics and biases (Goswami, 2011).

# 8.2 Inductive Reasoning at Its Best

As noted earlier, we can never be 100% certain that our inductive conclusions are right. However, by keeping the following attributes in mind, we can reduce errors and biases, which increases the likelihood that our inductive arguments are strong and the conclusions are warranted, justifiable, and have a high probability of being true.

# 8.2.1 A Sizeable Sample

A large number of observations typically increases the strength of inductive arguments, which makes the conclusions more likely to be accurate (Nisbett, Krantz, Jepson, & Kundra, 1983). Consider the following two examples:

*Observations*: Every morning for the past 8 months, George drank a large glass of milk and thirty minutes later his stomach consistently started hurting.

*Conclusion*: George has lactose intolerance.

*Observation*: Natalie ate a peanut and then had trouble breathing.

*Conclusion*: Natalie has a peanut allergy.

The first example has a stronger argument than the second because it is based on approximately 250 observations or pieces of evidence rather than only one. Although there are exceptions (Osherson, Smith, Wilkie, Lopez, & Shafir, 1990), a large sample size helps maximize information, reduces distortions in the evidence, and makes the conclusions more likely to be correct (McDonald, Samuels, & Rispoli, 1996; Nisbett et al., 1983).

The importance of a large sample is highly relevant to both scientific research and inductive reasoning in our daily lives. Given that there are individual differences in human behavior, psychological research, in particular, needs to have a large number of participants and numerous experimental trials or survey questions in order for the data to be robust and trustworthy. Non-scientists have also been found to pay attention to number of observations, especially when making inductions about highly variable attributes. For example, Nisbett and his colleagues (1983) asked college students to estimate the percentage of obese male members of the Barratos tribe if they observed one obese tribesman, three obese tribesmen, or twenty of them. Results showed that participants were least likely to make strong inferences based on only one tribe member; conclusions were strongest for the highest number of observations. This finding is known as premise monotonicity, which means that a higher number of inclusive premises results in a stronger inductive argument than a smaller number (Osherson et al., 1990). However, as will be explained in the section on representativeness, individuals do not always take sample size into account as much as they should.

# 8.2.2 Diverse Evidence

Although the milk example presented earlier involves numerous observations, the conclusion that George has lactose intolerance would have a higher probability of being true if it were based on a wide range of evidence, such as George getting stomach aches after consuming other lactose-based foods, George's health history, and observations conducted at different times of the day and night. In other words, inductive arguments are stronger if they present a range of converging evidence taken from different sources (Heit, 2000). For this reason, scientific experiments are often conducted in various ways using different types of participants in order to test a single hypothesis. For example, inductive reasoning has been studied using objects, cartoon pictures, complex verbal arguments, computational models, and participants of different ages from various backgrounds (Heit, 2007).

Given that it would be time consuming and often impossible to collect every possible observation, people often use shortcuts or heuristics to reach inductive conclusions (see Chapter 10,"Decision Making", for more information about heuristics.). In many cases these heuristics can result in quick and highly probable conclusions. Unfortunately, sometimes they can cause errors. One of these heuristics or "rules of thumb" is the availability heuristic, which can undermine our diversity of evidence. We tend to use information that easily comes to mind, without also considering a significant number of cases that take longer to retrieve from memory. For example, when Amos Tversky and Daniel Kahneman (1973) asked people to predict whether there are more words in the English language beginning with the letter R or more words with R as the third letter, 69% of their participants erroneously predicted that more words begin with R. In other words, it is easier to generate words like "rutabaga", "rat", and "ridiculous" than it is to think of instances like "bard", "certify", and "dare." According to Tversky and Kahneman, "to assess availability it is not necessary to perform the actual operations of retrieval or construction. It suffices to assess the ease with which these operations can be performed" (p. 208). However, other researchers believe information must be retrieved from memory because it is used to guide and evaluate inductive inferences (Shafto, Coley, & Vitkin, 2007).

Moreover, the availability heuristic applies when people easily retrieve information from memory that indicates there is a relationship between events, categories, or attributes. They then base their inductive conclusions on this perceived correlation, which can often be quite useful. For example, if you remember that your professor has granted requests for paper extensions when he or she is in a good mood, you might take this information into account when you want permission to turn your paper in late. However, the availability heuristic can sometimes result in an illusory correlation, which means that people believe a relationship exists when, in reality, it does not (Hamilton & Lickel, 2000). For example, prejudicial conclusions are sometimes drawn when individuals have information readily available in memory that leads them to believe there is a correlation between

negative personality traits and a particular group of people. In short, making predictions based only on easily retrievable evidence can result in wrongly assuming correlations exist, which lowers the strength of our arguments and reduces the likelihood that our inductive conclusions are correct.

Having a range of evidence, if it is chosen correctly, can also help prevent confirmation bias. We have a tendency selectively to seek data that supports our hypotheses, while overlooking information that would invalidate them. Suppose someone gave you the numbers 2, 4, and 6 that conform to a rule and asked you to discover the rule by generating sets of three numbers you think would fit. What do you think the rule is and which three numbers would you select to test your hypothesis? When Peter Wason (1960) gave this task to adults, his nonobvious rule was "three numbers in increasing order of magnitude" but most participants assumed the rule was "increasing intervals of two". Box 8.1 shows his instructions and examples of different ways of responding. Thirty-one percent of the participants practiced what Wason refers to as enumerative induction; they did not try to disconfirm their hypothesis by testing odd numbers or descending ones. As a result, they never discovered the correct rule. In science and in everyday life, it is essential to practice eliminative induction by seeking both confirming and disconfirming evidence before drawing conclusions.

The availability of different types of knowledge to inform our inductive reasoning is dynamic; it can change based on context and effects of prior experience (Shafto et al., 2007). More specifically, the information in the premises of an inductive problem can have an immediate consequence for which knowledge we retrieve from memory in order to make our generalizations. If we are told that dogs have a recently discovered illness, we might infer that cats will get it too because we remember they often live in the same households. However, if we discover that dogs have a recently discovered gene, we would be more likely to conclude that wolves also carry it because we remember that the two species are genetically closely related. In contrast, prior experience has long-term consequences for knowledge availability. For example, novices in a domain

are more likely to retrieve taxonomic or categorical information than are domain experts, who tend to rely more on causal, thematic, and ecological relationships. Interestingly, if put under time pressure, experts often fall back on using taxonomic similarity to draw their conclusions (Shafto, Coley, & Baldwin, 2007).

# Textbox 8.1: Examples of Enumerative and Eliminative Induction on the 2-4-6 task

#### Instructions

You will be given three numbers which conform to a simple rule that I have in mind. This rule is concerned with a relation between any three numbers and not with their absolute magnitude. . . . Your aim is to discover this rule by writing down sets of three numbers, together with reasons for your choice of them. After you have written down each set, I shall tell you whether your numbers conform to the rule or not. . . . There is no time limit but you should try to discover this rule by citing the minimum sets of numbers. Remember that your aim is not simply to find numbers which conform to the rule, but to discover the rule itself. When you feel highly confident that you have discovered it, *and not before*, you are to write it down and tell me what it is (Wason, 1960, p. 131).

### 8.2.3 Representative Observations

To achieve strong inductive arguments, it is not enough to have several observations that include diverse evidence. The observations must also fully

represent the entire population or category of interest. For example, suppose you wanted to predict whether the citizens of California believe the legal drinking age should be lowered from age 21 to 18. Polling undergraduates at several universities in California would probably tell you more about college students than it would about the beliefs of people in the entire state. To draw potentially accurate conclusions about drinking attitudes in California, it would be important to obtain opinions from a representative cross-section of the people who live there. Similarly, results from scientific studies can only be safely generalized to the population represented in the sample of participants. Experiments conducted on mice, college students, males, or individuals from a specific culture are often replicated using members of other populations so that the conclusions can encompass other species or all humans.

In solving inductive reasoning problems, individuals often use the representativeness heuristic. When trying to estimate the probability of an event, this short cut involves finding a comparable case or prototype and assuming that the two events have similar probabilities. Consider a problem developed by Tversky and Kahneman (1974): "Steve is very shy and withdrawn, invariably helpful, but with little interest in people, or in the world of reality" (p. 1124). Is Steve more likely to be a farmer, librarian, salesman, airline pilot, or physician? Using the representativeness heuristic, people are likely to respond that Steve has the highest probability of being a librarian because he best fits how they view a typical librarian. However, this conclusion can be inaccurate if important base rate information is not taken into account.

In addition, people do not always take small sample sizes into account to assess representativeness. One demonstration of this is another study conducted by Tversky and Kahneman (1974). Ninetyfive participants were asked the following question:

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60 percent of the

babies born were boys. Which hospital do you think recorded more such days? (p. 1125)

The answer options were (1) the larger hospital, (2) the smaller hospital, or (3) about the same (within 5 percent of each other) for the two hospitals. Over half of the participants predicted the recordings would be about the same, presumably because they assumed that both hospitals would be equally representative of male and female birth rates in the general population. However, the correct answer is the smaller hospital because about 15 babies born each day will show more fluctuation in the number of males and females born than will the bigger sample size at the larger hospital, which is more likely to reflect the statistic found in the general population.

# 8.3 Different Forms of Inductive Reasoning

Given that induction is central to our daily lives as we engage in a variety of activities, it is not surprising that there are different ways we use it. Four of these will be covered in this section.

# 8.3.1 Category-based Induction

Category-based induction has probably been studied more than any other form of inductive reasoning (Heit, 2007). In this type of reasoning, if people are told that one or more members of a category have a certain property, they then determine whether other members of the category are likely to have the same property. For example, if you observe that chimpanzees groom each other, you would probably infer that gorillas have the same behavior. Would you also conclude that groundhogs groom each other?

#### <IP_ADDRESS> Premise Typicality

In a classic study conducted by Lance Rips (1975), participants were told that a particular species on an isolated island had a new contagious disease and then asked to estimate the likelihood that other kinds of animals on the island would contract the disease. Results indicated that species' typicality had a large influence on individuals' inductive judgments, even

when similarity was held constant. In other words, if one species (e.g., a robin) is highly representative of an inferred superordinate category (e.g., birds), individuals were more likely to generalize to other members (e.g., sparrows) than if the same information was given about an atypical member (e.g., canary). It is more convincing to project the robins' disease onto sparrows than it is to generalize the disease from canaries to sparrows.

There is also premise-conclusion asymmetry, which means a single-premise argument is viewed as stronger if the more typical member of an inferred superordinate category is used in the premise rather than in the conclusion. For example, it is more convincing to project a property of lions onto bats than the other way around because lions are viewed as a better prototype of mammals than are bats (Smith, Shafer, & Osherson, 1993).

#### <IP_ADDRESS> Category Similarity

Two categories are highly similar if they have several features in common and few distinctive ones they do not share. Perceived similarity between the premise category and the conclusion category strengthens inductive arguments and increases the likelihood that a novel property of one category will be generalized to another category (Hayes & Heit, 2017). For example, individuals are more likely to generalize a property from lions to wolves than from hippopotamuses to giraffes.

The similarity-coverage model (Osherson et al., 1990) posits that individuals automatically compute similarity and make inductive generalizations when (a) there is a great deal of overlap between the features of the premise and conclusion categories and (b) there is substantial similarity between premise features and the inferred superordinate category (e.g., mammals) that is inclusive of the premises and conclusion. This model is predictive of the premise-conclusion similarity effect found in many studies of category-based induction (Hayes & Heit, 2017). It can also account for the premise typicality results mentioned earlier. Typical premises have higher mean similarity to the inferred superordinate category than do atypical ones, which means that typicality provides better coverage.

### <IP_ADDRESS> Premise Diversity

After typicality and premise-conclusion similarity, probably the next most important attribute to consider is diversity of the actual premises. Other things being equal, arguments are stronger and conclusions are more probable if dissimilar subordinate categories are used as evidence (Smith et al., 1993). For example, if given the information that mice and lions share the same property, it is more likely that we will predict that elephants and other mammals also have the property than if we are told that cougars and lions share the property. Similarly, as mentioned earlier, premise monotonicity increases the amount of evidence and typically strengthens inductive arguments (Osherson et al., 1990). For example, information that mice, lions, bears, dog, and horses share a property is stronger evidence than knowing only about mice and lions.

The similarity-coverage model (Osherson et al., 1990) mentioned above accounts for this diversity effect; less similar subordinate categories tend to provide more coverage of the inferred superordinate category (e.g., mammals) than do subordinate categories that are quite similar. In the same way, premise monotonicity provides more coverage of the inferred superordinate category and makes a property more likely to be generalized.

Premise typicality, category similarity, premise diversity, and premise monotonicity involve taxonomic relationships between premises and conclusions. As noted earlier, novices in a domain are more likely than experts to be influenced by these taxonomic relations (Hayes & Heit, 2017). Experts tend to rely instead on thematic, causal, and ecological relations for their generalizations of properties related to their domain of expertise. For example, when tree experts were asked to infer which of two novel diseases would be most likely to affect all trees, they focused on causal-ecological factors related to how tree diseases work and "local coverage", which involves extending the property to other members of the same folk family. In other words, they were not very influenced by typicality and diversity of the premises (Proffitt, Coley, & Medin, 2000).

# 8.3.2 Causal Induction

Predicting what causes certain events and outcomes is an important part of being human. This form of reasoning is commonly used in both science and in our daily lives to advance knowledge and give us a sense of control. For example, predicting that not going to class or turning in the work will result in a failing grade can motivate students to attend and finish assignments. However, poorly executed causal reasoning can result in superstitions, such as believing that breaking a mirror causes seven years of bad luck.

Causal relations are so important to us that they typically outweigh other information. Even for nonexperts, for example, the presence of a causal relation can over-ride taxonomic ones, such as premise typicality, category similarity, premise diversity, and premise monotonicity. In a demonstration of causality's strong influence (Rehder, 2006), participants were given a novel category (e.g., Kehoe ants) and told characteristic features of its members (e.g., their blood has high amounts of iron sulfate). Participants were then told about a novel property possessed by one of the category members (e.g., it has a venom that gives it a stinging bite) and asked to estimate the proportion of all category members that also possessed this new property. In some conditions, participants were told that the new property was caused by a characteristic feature they had previously learned (e.g., the stinging bite is caused by the high amounts of iron sulfate in its blood). When causal explanations were present, the standard effect of typicality was almost completely eliminated. Additional experiments demonstrated that causal explanations also

drastically reduced the effects of premise typicality, diversity, and similarity.

John Stuart Mill (1843) was one of the first to propose a theory of causality and it includes five methods (or canons) of causal analysis that focus on the observation of patterns. Four of the five involve inductive reasoning and each of these is paraphrased and briefly described below. The first three help people practice Wason's (1960) notion of eliminative induction; ruling out some possible causes helps narrow the hypotheses for what actually is the cause.

Table 8.2: Method of agreement indicating fish as the source of illness.

Table 8.3: Method of disagreement indicating pie as the source of iIllness.

likely to be the cause of the other or a third unknown variable might be causing the variation in both. Suppose you did not eat berry pie at the buffet, your mom had half a piece, your brother had a whole one, and your dad ate five pieces.  A highly probable conclusion to infer from this evidence is that suffering from the effect (i.e., food poisoning) is proportional to the cause (i.e., the amount of pie consumed).

Mill's methods provide useful tools for finding potential reasons for effects but they are limited to what we choose to focus on. Potential causes will not be observed and found unless we already have relevant hypotheses about what the causes are likely to be. For example, in discovering the source of food poisoning, factors other than a buffet dinner might be involved.

Miriam Schustack and Robert Sternberg (1981) examined what sources of information people actually use when making causal inferences about un-

Table 8.4: Joint Method of agreement and disagreement indicating salad as the source of illness.

certain and complicated situations. For example, participants were given information about various cosmetic companies, including the facts that (a) a company did or did not have a major product under suspicion as a carcinogen and (b) the company's stock had or had not drastically dropped. Participants were then asked to infer the probability that some other cosmetic company would have its stock values drop drastically if it had a major product under suspicion as a carcinogen. Overall results indicated that people confirm a causal relationship in one of two ways. One, which is related to Mill's method of agreement, is based on evidence of the joint presence of the hypothesized cause (e.g., suspicion of a carcinogen) and effect (e.g., declining stock values). The other, which is related to Mill's method of disagreement, is based on evidence of the joint absence of the hypothesized cause and effect. Overall results also indicated that people disconfirm causality in one of two ways. The first focuses on the presence of the hypothesized cause but the absence of the outcome and the other is based on the absence of the cause, yet the outcome still occurs. These overall findings are supported by Rehder's (2006) result that an effect is viewed as more prevalent if the cause is also prevalent.

#### 8.3.3 Analogical Reasoning

Even though many people hate answering analogy problems on standardized tests, this form of induction allows us to use familiar knowledge to understand something we do not know. For example, learning the structure of an atom might be easier if it is compared to already acquired knowledge about the solar system. The sun and its orbiting planets can help us comprehend the atom's nucleus and the electrons that move about it. Analogical reasoning can also cause us to consider familiar material in new ways. When Kevin Dunbar and his colleagues (Dunbar, 1995; Dunbar & Blanchette, 2001) videotaped immunologists and molecular biologists during their lab meetings, they discovered that the scientists frequently used analogies 3 to 15 times in any given meeting as an important source of knowledge and conceptual change. For example, when discussing the flagellar pocket, a postdoctoral

fellow said, "Things get in, but things. . . It's like the Hotel California - you can check in but you can never check out" (Dunbar, 1995, p. 383).

As implied above, analogical reasoning typically works by comparing two domains of knowledge in order to infer a quality they have in common. The first domain is often the more familiar of the two and it serves as the base or source. It provides a model for understanding and drawing inferences about the target, which is often the more novel or abstract domain (Gentner & Smith, 2012).

Robert Sternberg (1977) used simple picture, verbal, and geometric analogies to determine the components of analogical reasoning (Figure 8.1 shows examples similar to the ones he used). Consider the following verbal problem, which involves choosing the best option for the end of the analogy.

A lawyer is to a trial as a surgeon is to:

(a) a stethoscope, (b) medical school, (c) an operation, (d) patients.

The successful analogy solver encodes the first two terms of the base (i.e., lawyer and trial), which includes forming an appropriate mental representation of them in memory. Next one or more relations between these two items are inferred (e.g., lawyers present their cases during a trial). The term 'surgeon' is then encoded and an overall relation is mapped between a lawyer and a doctor (e.g., they are both practicing professionals). This is followed by applying the relation in the base to the target. Finally, a response is prepared and given (i.e., operation is the correct answer because surgeons perform their procedures during an operation and lawyers perform theirs during a trial.)

Using mathematical modeling, Sternberg (1977) analyzed the amounts of time participants spent on the components of analogical reasoning mentioned above: encoding, inference, mapping, application of the relation, and preparation-response. Interestingly, he found that participants spent quite a bit more time on encoding and preparation-response than inference, mapping, and application. Furthermore, for all three types of analogies (picture, verbal, and geometric), the preparation-response component was the one most highly correlated with standardized tests of reasoning.

Figure 8.1: Examples of different types of analogies.

In later work, Sternberg identified higher-order components (metacomponents) that are used successfully to plan, evaluate, and monitor strategies and solutions for analogies and other problems. For example, some individuals do not form a connection between the first and second halves of an analogy because they do not select the lower-level component of mapping (Sternberg & Rivkin, 1979). Other individuals might not select the best strategy for combining lower-level components and they end up using an inefficient search strategy for inferring relations between the first two terms in an analogy (Sternberg & Keatron, 1982). Not surprisingly, Sternberg's work on analogical reasoning plays an influential role in his triarchic theory of intelligence (1988) and his theory of successful intelligence (1997).

As Sternberg's work indicates, the elements in an analogy need to be linked by a relation they have in common. In other words, relational (or struc-

tural) similarity is a basic constraint of this form of reasoning (Goswami, 2011). Surface similarity is not required; objects in each domain do not need to resemble each other physically or have the same behaviors. For example, computers and humans do not look or act alike but they are relationally similar in terms of information processing. However, surface similarities can facilitate the mapping of relations and improve performance (Gentner, 1989; Holyoak & Koh, 1987).

Interestingly, analogical reasoning is not always done consciously and deliberately. For example, Blanchette and Dunbar (2002) had participants read descriptions of a target topic (e.g., legalization of marijuana) and then read shorter information about a potential analogical base (e.g., prohibition). Afterwards, when participants were given a recognition test, they erroneously believed that their analogical inferences were concrete facts actually presented in the target description. In other words, they unconsciously inserted their inferences into their mental representations of the target domain.

# 8.3.4 Insight

Sudden insight into the solution of a seemingly impenetrable problem is another form of inductive reasoning (Goswani, 2011) or what Steinbeck (1954) referred to as the inductive leap. The Gestalt psychologists paved the way for later research on this creative and productive way of thinking, which occurs when an individual goes beyond old associations and suddenly views information in a new way (see Chapter 9, "Problem Solving", for more information about Gestalt theory and insight). A novel solution and a subjective feeling of "aha", or suddenly knowing something new without consciously processing how one arrived at it, often accompany this new perception of the situation (Topolinski & Reber, 2010). In contrast, an analytic process involves consciously and systematically evaluating the problem, using strategic thinking and deduction.

In support of this view of insight, Janet Metcalfe (1986a, 1986b; Metcalfe & Weibe, 1987) and Davidson (1995) found that incremental increases in feelings of confidence (or warmth) that one is nearing a solution negatively predict correct solution of insight problems but positively predict correct solution of deductive reasoning problems. In other words, individuals who felt they were gradually getting closer to solving insight problems tended to arrive at incorrect solutions; others who thought they were far from solving the insight problems and then suddenly realized the answers tended to be accurate. Metcalfe concludes that insight is a subjectively catastrophic process, not an incremental one.

An important source of insight involves cognitive restructuring of a problem's components, which can occur multiple times as an individual moves from general to specific mental representations of a problem (Mayer, 1995). Unlike routine or welldefined problems, ill-defined or non-routine ones are more likely to require individuals to search through a space of alternative approaches (Newell, & Simon, 1972) because the givens, goals, and obstacles are not clear. However, it should be emphasized that insight is process rather than problem oriented. One

individual may solve a problem by having an inductive leap; another person may solve the same problem incrementally and consciously, especially if it is familiar (Davidson, 1995; Webb, Little, & Cropper, 2016).

The Gestalt psychologists believed that people's inability to restructure a problem's components and produce an insightful solution is often due to their fixation on past experience and associations. For example, in what is now seen as a classic insight problem, Karl Duncker (1945) gave individuals three small cardboard boxes, candles, matches, and thumbtacks. The participants' task was to mount a candle vertically on a screen so that it could be used as a reading light. The solution is to light a candle, melt wax onto the top of a box, stick the candle into the wax, and tack the box to the screen. Participants who were given boxes filled with tacks, matches, and candles had much more difficulty solving the problem than did those who received the same supplies outside of the boxes. According to Duncker, seeing a box serve the typical function of a container made it difficult for many individuals also to view the box as a structural support. This phenomenon became known as functional fixedness.

Similar types of mental blocks can interfere with insightful problem solving. In particular, even when we realize that we are approaching a problem incorrectly, we often cannot break our fixation on this approach in order to change our strategies or search for new evidence. Fortunately, taking a break when we reach an impasse often allows us to stop this fixation and see material in a new way when we return to it (Davidson, 2003).

# 8.4 How Does Inductive Reasoning Develop?

Young children have limited knowledge about the world and they have a lot to learn in a relatively short amount of time in order to adapt well to their environments. Inductive reasoning allows them to acquire new information and fill in gaps in their knowledge. Not surprisingly, research shows this form of reasoning appears early in development. For example, infants between 9-16 months of age make

inductive inferences based on perceptual similarities of objects, expecting new ones to wail when squeezed if they physically resemble a previously squeezed one that wailed (Baldwin, Markman, & Melartin, 1993). Although inductive reasoning is relatively continuous across the human lifespan, it becomes more complex as children's cognitive skills, experience, and knowledge base expand and they become better able to evaluate and apply evidence to draw likely conclusions (Goswami, 2011; Hayes, 2007).

# 8.4.1 How Children Use Inductive Evidence

#### <IP_ADDRESS> Sample size

Do children, like adults, take sample size into account when making inductive generalizations? Evidence indicates that they do if the tasks are made simple enough. Grant Gutheil and Susan Gelman (1997) asked 8-10 year old children to make inductions based on small and large samples of observable features. For example, children were shown a picture of one butterfly and told that it has blue eyes. They were also shown a picture of five butterflies and told that all of these butterflies have gray eyes. The experimenter then looked at a picture but did not show it to the children and asked whether they thought the butterfly in the picture has blue eyes or gray eyes. The children were significantly more likely to generalize traits, such as eye color, from the large sample than from the small one.

Similarly, it has been found that children younger than age 6 take number of observations into account for their inductive generalizations if the task involves only one sample of evidence (Jacobs & Narloch, 2001; Lawson & Fisher, 2011). If they need to compare a larger sample with a smaller one, the cognitive demands are too great for them to do this well (Gutheil & Gelman, 1997; Lopez, Gelman, Gutheil, & Smith, 1992).

#### <IP_ADDRESS> Diversity

As discussed earlier, adults are more likely to make inductive generalizations from different types of

converging evidence than from only one type. The results for children under age 10 have been more mixed, with some studies finding no evidence of diversity effects (Carey, 1985; Gutheil & Gelman, 1997; Lopez et al., 1992) and others finding that young children often over-generalize from diverse data (Carey, 1985; Lawson & Fisher, 2011). However, if the tasks have low cognitive demands and no hidden properties, young children seem capable of taking diversity into account. For example, when shown pictures of three very different types of dolls played with by Jane and three quite similar dolls played with by Danielle and then shown a picture of another kind of doll, 73% of participants ages 5 and 6 inferred that Jane rather than Danielle would want to play with the new type of doll (Heit & Hahn, 2001). However, it was also found that children were less likely to use diverse evidence when making inferences about remote categories or hidden properties of objects.

Interestingly, Margorie Rhodes and Peter Liebenson (2015) found that children ages 5-8 appropriately used diverse evidence more than non-diverse information when making inductions about novel categories but not when making them about familiar natural kinds (e.g., birds). In other words, category knowledge interfered with their diversity-based reasoning. In contrast, children ages 9 and 10 generalized more broadly from diverse samples than nondiverse ones when reasoning about both novel categories and natural kinds. These results indicate both developmental continuity and change in diversitybased inductions. At least by age 5, children have the cognitive mechanisms for incorporating different types of information into their generalizations, as shown by their use of diverse evidence when reasoning about novel categories. However, there is developmental change for the situations in which children access these mechanisms.

#### <IP_ADDRESS> Typicality

Several studies have found that young children are similar to adults in making inductive inferences based on premise typicality or how well an item represents a familiar category. For example, Gelman and Coley (1990) showed 2-year-old children a picture of a typical bird (e.g., robin), told them it was a bird, and asked them about one of its properties (e.g., "Does it live in a nest?"). The children were then shown atypical (e.g., dodo) and typical (e.g., bluebird) category members without the category name (e.g., bird) being repeated and asked if each one lives in a nest. The results were that children projected the property (e.g., living in a nest) to typical category members (e.g., bluebird) 76% of the time and to atypical members (e.g., dodo) only 42% of the time. Similar behavior was found for 3- and 4-year old children (Gelman and Markman, 1986). In addition, as with adults, premise-conclusion similarity also increased inductive inferences.

# 8.5 Development of Forms of Induction

As implied by the previous section, young children can usually perform category-based inductive reasoning, causal reasoning, and analogical reasoning if the tasks are simple and the children have the requisite knowledge about the properties, categories, and causal or functional relations that are used in the tasks (Goswami, 2011; Hayes, 2007). As Goswami notes about the development of analogical reasoning, "in the absence of the requisite knowledge, it is difficult to reason by induction" (p. 405).

Research indicates that by the time children are around age 5, they most likely use the same broad relations and cues that adults use for their inductive inferences (Hayes, 2007). The developmental changes that do occur are mostly quantitative and gradual, with some types of information, such as causal relations, being applied more frequently and across more domains. As they develop, children's knowledge base increases, their inhibition and memory retrieval processes become more efficient, and their relational working memory capacity improves (Perret, 2015). These cognitive changes allow children to perform more complex category-based inferences, causal inductions, and analogical reasoning.

In addition, some research indicates that children age 6 or older are more likely to have insights than those who are younger. For example, Tim German and Margaret Anne Defeyter (2000) gave children aged 5-7 an analogous task to Duncker's candle problem described earlier in this chapter. Their results showed that 6- and 7-year-olds in the experimental condition were significantly slower to think of the solution, which involved emptying and turning over a wooden box and using it as a support, than the same-age control group that received an empty box. Interestingly, the 5-year-olds in the experimental condition were significantly faster to think of the solution than their older cohorts. Furthermore, they were equally as fast as their same-age peers in the control condition. German and Defeyter conclude that around age 6, children develop a more narrow criterion for an object's function than they had earlier in life. Seeing the box used as a container placed that function in their initial representation of the problem. As with the adult participants in Duncker's experiment (1945), these children had to overcome functional fixedness and restructure their initial representation of the problem before they could insightfully solve it. In contrast, the 5 year-olds' fluid conception of the box's function required no restructuring or insight.

To conclude, both children and adults habitually use different forms of inductive reasoning to help make sense of their worlds and to predict future events. Throughout the human lifespan, this form of reasoning is influenced by similar attributes and constraints. These characteristics include number of observations, knowledge base, inhibitory processes, working memory capacity, memory retrieval processes, and the cognitive ability to detect relational similarity (Goswami, 2011; Perret, 2015). As individuals gain experience and expertise in multiple domains, their inductive reasoning becomes increasingly sophisticated for a wider-range of problems.

#### Summary

#### Review Questions

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Janet E. Davidson

My research on insight began in 1982 when Robert Sternberg and I developed a three-process theory of insight. According to this theory, the cognitive processes of selective encoding, selective combination, and selective comparison are used to restructure one's mental representation of the givens, the relations among the givens, and the goals found in a problem in order to find a novel solution.

Selective encoding occurs when an individual suddenly finds one or more important elements in a problem situation that previously had been nonobvious. Selective encoding elicits insight by abruptly restructuring one's mental representation so that information that

was originally viewed as being irrelevant is now seen as relevant for problem solution and vice versa.

Selective combination occurs when an individual discovers a previously nonobvious framework for the relevant elements of a problem situation. In many problems, even when the relevant features are known, it is often difficult to know that these features should be combined and then to find a procedure to combine them appropriately. Selective comparison occurs when one suddenly discovers a nonobvious connection between new information and prior knowledge. Analogies, for example, can often be useful for solving new problems.

To be referred to as insightful, the relevant selections must not occur to people immediately upon presentation of a problem. After individuals reach an impasse, they must spontaneously search for and select previously overlooked relevant elements, methods for combining the elements, or connections between prior knowledge and the problem situation. Also, successful search for this relevant information must result in a seemingly abrupt change in the problem solver's mental representation of the problem.